YES 200.074 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 Ordering a  ->  FiniteMap Ordering a  ->  FiniteMap Ordering a) :: FiniteMap Ordering a  ->  FiniteMap Ordering a  ->  FiniteMap Ordering a)

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

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

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

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

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

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

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

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

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

  sIZE_RATIO :: Int
sIZE_RATIO = 5

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

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

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

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


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

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

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

  
addToFM0 old new = new

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

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

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

  emptyFM :: FiniteMap b a
emptyFM = EmptyFM

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

  findMin :: FiniteMap 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  ->  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 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  ->  d  ->  c)  ->  FiniteMap a b  ->  FiniteMap a d  ->  FiniteMap a 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 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 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



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 Ordering a  ->  FiniteMap Ordering a  ->  FiniteMap Ordering a) :: FiniteMap Ordering a  ->  FiniteMap Ordering a  ->  FiniteMap Ordering a)

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

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

  
addToFM0 old new = new

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

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

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

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

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

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

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

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

  sIZE_RATIO :: Int
sIZE_RATIO = 5

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

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


module Maybe where
  import qualified FiniteMap
import qualified Prelude
  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 Ordering a  ->  FiniteMap Ordering a  ->  FiniteMap Ordering a) :: FiniteMap Ordering a  ->  FiniteMap Ordering a  ->  FiniteMap Ordering 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 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 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 a b
emptyFM = EmptyFM

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

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

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

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

  foldFM :: (c  ->  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_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 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 => (a  ->  c  ->  b)  ->  FiniteMap d a  ->  FiniteMap d c  ->  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 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 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 :: 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



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 Ordering a  ->  FiniteMap Ordering a  ->  FiniteMap Ordering a) :: FiniteMap Ordering a  ->  FiniteMap Ordering a  ->  FiniteMap Ordering a)

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

  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 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 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 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 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 b => FiniteMap b a  ->  FiniteMap b a  ->  FiniteMap b a
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 b => (d  ->  c  ->  a)  ->  FiniteMap b d  ->  FiniteMap b c  ->  FiniteMap b a
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 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 b => b  ->  a  ->  FiniteMap b a  ->  FiniteMap b a  ->  FiniteMap b a
mkVBalBranch key elt EmptyFM fm_r = addToFM fm_r key elt
mkVBalBranch key elt fm_l EmptyFM = addToFM fm_l key elt
mkVBalBranch key elt (Branch 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 a => FiniteMap a b  ->  a  ->  FiniteMap a b
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 a => FiniteMap a b  ->  a  ->  FiniteMap a b
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

splitGT0 key elt vw fm_l fm_r split_key True = fm_r

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)

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)

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)

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_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_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_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

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)

splitLT0 key elt vvz fm_l fm_r split_key True = fm_l

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

compare0 x y True = GT

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

compare3 x y = compare2 x y (x == y)

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

is transformed to
gcd' x 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 Ordering a  ->  FiniteMap Ordering a  ->  FiniteMap Ordering a) :: FiniteMap Ordering a  ->  FiniteMap Ordering a  ->  FiniteMap Ordering 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 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 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 a b
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  ->  b  ->  c  ->  c)  ->  c  ->  FiniteMap a b  ->  c
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 = 
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 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) = 
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 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 => (d  ->  c  ->  b)  ->  FiniteMap a d  ->  FiniteMap a c  ->  FiniteMap a b
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 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 b => FiniteMap b a  ->  b  ->  FiniteMap b a
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_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_C2Maybe_elt1 yzw yzx = lookupFM 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_C2Lts yzw yzx = splitLT yzw yzx

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

intersectFM_C2Vv1 yzw yzx = intersectFM_C2Maybe_elt1 yzw yzx

intersectFM_C2Elt10 yzw yzx (Just elt1) = elt1

intersectFM_C2Gts yzw yzx = splitGT 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
glueBal2GlueBal0 yzy yzz fm1 fm2 True = mkBalBranch (glueBal2Mid_key1 yzy yzz) (glueBal2Mid_elt1 yzy yzz) (deleteMax fm1) fm2

glueBal2Mid_elt10 yzy yzz (zx,mid_elt1) = mid_elt1

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_key10 yzy yzz (mid_key1,zz) = mid_key1

glueBal2Mid_key20 yzy yzz (mid_key2,vuu) = mid_key2

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

glueBal2Vv3 yzy yzz = findMin yzy

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

glueBal2Mid_elt20 yzy yzz (zy,mid_elt2) = mid_elt2

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

glueBal2Vv2 yzy yzz = findMax yzz

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

The bindings of the following Let/Where expression
mkBalBranch5 key elt fm_L fm_R (size_l + size_r < 2)
where 
double_L fm_l (Branch key_r elt_r 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
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)

mkBalBranch6Size_r zuu zuv zuw zux = sizeFM zuu

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)

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)

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

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

mkBalBranch6Size_l zuu zuv zuw zux = sizeFM zuv

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)

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 zuw zux fm_l fm_rl) fm_rr

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

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 zuw zux fm_l fm_rll) (mkBranch 7 key_r elt_r fm_rlr fm_rr)

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)

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

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

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

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_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 zuw zux fm_lr fm_r)

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 zuw zux fm_lrr fm_r)

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

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 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
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

mkBranchBalance_ok zww zwx zwy = True

mkBranchLeft_size zww zwx zwy = sizeFM zww

mkBranchRight_size zww zwx zwy = sizeFM zwx

mkBranchUnbox zww zwx zwy x = x

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

mkBranchRight_ok zww zwx zwy = mkBranchRight_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

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

are unpacked to the following functions on top level
mkBranchResult zwz zxu zxv zxw = Branch zwz zxu (mkBranchUnbox zxv zxw zwz (1 + mkBranchLeft_size zxv zxw zwz + mkBranchRight_size zxv zxw zwz)) zxv zxw

The bindings of the following Let/Where expression
mkVBalBranch2 key elt 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_r 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

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

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)

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 
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 zzv = fst (findMin zzv)

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 zzw = fst (findMax zzw)

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

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

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

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

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

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

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

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

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



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

mainModule FiniteMap
  ((intersectFM :: FiniteMap Ordering a  ->  FiniteMap Ordering a  ->  FiniteMap Ordering a) :: FiniteMap Ordering a  ->  FiniteMap Ordering a  ->  FiniteMap Ordering a)

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

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

  
addToFM0 old new = new

  addToFM_C :: Ord b => (a  ->  a  ->  a)  ->  FiniteMap b a  ->  b  ->  a  ->  FiniteMap b a
addToFM_C combiner EmptyFM key elt = 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 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 a b
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  ->  b  ->  c  ->  c)  ->  c  ->  FiniteMap a b  ->  c
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 wy wz xu xv xw vy vz wu wv ww vy vz wu wv ww wy wz xu xv xw (sIZE_RATIO * glueVBal3Size_l wy wz xu xv xw vy vz wu wv ww < glueVBal3Size_r wy wz xu xv xw vy vz wu wv ww)

  
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 zvx zvy zvz zwu zwv)

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

  
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 => (d  ->  b  ->  c)  ->  FiniteMap a d  ->  FiniteMap a b  ->  FiniteMap a c
intersectFM_C combiner fm1 EmptyFM = intersectFM_C4 combiner fm1 EmptyFM
intersectFM_C combiner EmptyFM fm2 = intersectFM_C3 combiner EmptyFM fm2
intersectFM_C combiner fm1 (Branch split_key elt2 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 fm_R fm_L key elt key elt fm_L fm_R (mkBalBranch6Size_l fm_R fm_L key elt + mkBalBranch6Size_r fm_R fm_L key elt < 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 zuw zux 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 zuw zux 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 zuw zux 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 zuw zux fm_lr fm_r)

  
mkBalBranch6Size_l zuu zuv zuw zux = sizeFM zuv

  
mkBalBranch6Size_r zuu zuv zuw zux = sizeFM zuu

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

  
mkBranchBalance_ok zww zwx zwy = True

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

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

  
mkBranchLeft_ok0Biggest_left_key zzw = fst (findMax zzw)

  
mkBranchLeft_size zww zwx zwy = sizeFM zww

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

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

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

  
mkBranchRight_ok0Smallest_right_key zzv = fst (findMin zzv)

  
mkBranchRight_size zww zwx zwy = sizeFM zwx

  mkBranchUnbox :: Ord a =>  ->  (FiniteMap a b) ( ->  (FiniteMap a b) ( ->  a (Int  ->  Int)))
mkBranchUnbox zww zwx zwy x = x

  mkVBalBranch :: Ord a => a  ->  b  ->  FiniteMap a b  ->  FiniteMap a b  ->  FiniteMap a b
mkVBalBranch key elt EmptyFM fm_r = mkVBalBranch5 key elt EmptyFM fm_r
mkVBalBranch key elt fm_l EmptyFM = mkVBalBranch4 key elt fm_l EmptyFM
mkVBalBranch key elt (Branch 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 vyz vzu vzv vzw vzx vxz vyu vyv vyw vyx key elt vxz vyu vyv vyw vyx vyz vzu vzv vzw vzx (sIZE_RATIO * mkVBalBranch3Size_l vyz vzu vzv vzw vzx vxz vyu vyv vyw vyx < mkVBalBranch3Size_r vyz vzu vzv vzw vzx vxz vyu vyv vyw vyx)

  
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 zyw zyx zyy zyz zzu)

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

  
mkVBalBranch4 key elt fm_l EmptyFM = addToFM fm_l key elt
mkVBalBranch4 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 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 :: 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



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 Ordering a  ->  FiniteMap Ordering a  ->  FiniteMap Ordering 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 = 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 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  ->  b  ->  c  ->  c)  ->  c  ->  FiniteMap a b  ->  c
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 wy wz xu xv xw vy vz wu wv ww vy vz wu wv ww wy wz xu xv xw (sIZE_RATIO * glueVBal3Size_l wy wz xu xv xw vy vz wu wv ww < glueVBal3Size_r wy wz xu xv xw vy vz wu wv ww)

  
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 zvx zvy zvz zwu zwv)

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

  
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 b => (a  ->  d  ->  c)  ->  FiniteMap b a  ->  FiniteMap b d  ->  FiniteMap b c
intersectFM_C combiner fm1 EmptyFM = intersectFM_C4 combiner fm1 EmptyFM
intersectFM_C combiner EmptyFM fm2 = intersectFM_C3 combiner EmptyFM fm2
intersectFM_C combiner fm1 (Branch split_key elt2 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 fm_R fm_L key elt key elt fm_L fm_R (mkBalBranch6Size_l fm_R fm_L key elt + mkBalBranch6Size_r fm_R fm_L key elt < 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))))))) zuw zux 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))))))))))))) zuw zux 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))))) zuw zux 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)))))))))) zuw zux fm_lr fm_r)

  
mkBalBranch6Size_l zuu zuv zuw zux = sizeFM zuv

  
mkBalBranch6Size_r zuu zuv zuw zux = sizeFM zuu

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

  
mkBranchBalance_ok zww zwx zwy = True

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

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

  
mkBranchLeft_ok0Biggest_left_key zzw = fst (findMax zzw)

  
mkBranchLeft_size zww zwx zwy = sizeFM zww

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

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

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

  
mkBranchRight_ok0Smallest_right_key zzv = fst (findMin zzv)

  
mkBranchRight_size zww zwx zwy = sizeFM zwx

  mkBranchUnbox :: Ord a =>  ->  (FiniteMap a b) ( ->  (FiniteMap a b) ( ->  a (Int  ->  Int)))
mkBranchUnbox zww zwx zwy x = x

  mkVBalBranch :: Ord b => b  ->  a  ->  FiniteMap b a  ->  FiniteMap b a  ->  FiniteMap b a
mkVBalBranch key elt EmptyFM fm_r = mkVBalBranch5 key elt EmptyFM fm_r
mkVBalBranch key elt fm_l EmptyFM = mkVBalBranch4 key elt fm_l EmptyFM
mkVBalBranch key elt (Branch 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 vyz vzu vzv vzw vzx vxz vyu vyv vyw vyx key elt vxz vyu vyv vyw vyx vyz vzu vzv vzw vzx (sIZE_RATIO * mkVBalBranch3Size_l vyz vzu vzv vzw vzx vxz vyu vyv vyw vyx < mkVBalBranch3Size_r vyz vzu vzv vzw vzx vxz vyu vyv vyw vyx)

  
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 zyw zyx zyy zyz zzu)

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

  
mkVBalBranch4 key elt fm_l EmptyFM = addToFM fm_l key elt
mkVBalBranch4 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 b a  ->  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 :: b  ->  a  ->  FiniteMap b a
unitFM key elt = Branch key elt (Pos (Succ Zero)) emptyFM emptyFM


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



Haskell To QDPs


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

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

new_glueBal2Mid_elt10(zzz2191, zzz2192, zzz2193, zzz2194, zzz2195, zzz2196, zzz2197, zzz2198, zzz2199, zzz2200, zzz2201, zzz2202, zzz2203, zzz2204, Branch(zzz22050, zzz22051, zzz22052, zzz22053, zzz22054), h, ba) → new_glueBal2Mid_elt10(zzz2191, zzz2192, zzz2193, zzz2194, zzz2195, zzz2196, zzz2197, zzz2198, zzz2199, zzz2200, zzz22050, zzz22051, zzz22052, zzz22053, zzz22054, h, ba)

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

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



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

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

new_glueBal2Mid_key10(zzz2175, zzz2176, zzz2177, zzz2178, zzz2179, zzz2180, zzz2181, zzz2182, zzz2183, zzz2184, zzz2185, zzz2186, zzz2187, zzz2188, Branch(zzz21890, zzz21891, zzz21892, zzz21893, zzz21894), h, ba) → new_glueBal2Mid_key10(zzz2175, zzz2176, zzz2177, zzz2178, zzz2179, zzz2180, zzz2181, zzz2182, zzz2183, zzz2184, zzz21890, zzz21891, zzz21892, zzz21893, zzz21894, h, ba)

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

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



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

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

new_glueBal2Mid_elt20(zzz2159, zzz2160, zzz2161, zzz2162, zzz2163, zzz2164, zzz2165, zzz2166, zzz2167, zzz2168, zzz2169, zzz2170, zzz2171, Branch(zzz21720, zzz21721, zzz21722, zzz21723, zzz21724), zzz2173, h, ba) → new_glueBal2Mid_elt20(zzz2159, zzz2160, zzz2161, zzz2162, zzz2163, zzz2164, zzz2165, zzz2166, zzz2167, zzz2168, zzz21720, zzz21721, zzz21722, zzz21723, zzz21724, h, ba)

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

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



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

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

new_glueBal2Mid_key20(zzz2143, zzz2144, zzz2145, zzz2146, zzz2147, zzz2148, zzz2149, zzz2150, zzz2151, zzz2152, zzz2153, zzz2154, zzz2155, Branch(zzz21560, zzz21561, zzz21562, zzz21563, zzz21564), zzz2157, h, ba) → new_glueBal2Mid_key20(zzz2143, zzz2144, zzz2145, zzz2146, zzz2147, zzz2148, zzz2149, zzz2150, zzz2151, zzz2152, zzz21560, zzz21561, zzz21562, zzz21563, zzz21564, h, ba)

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

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



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

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

new_primPlusNat(Succ(zzz62000)) → new_primPlusNat(zzz62000)

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

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



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

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

new_primMinusNat(Succ(zzz100100), Succ(zzz542000)) → new_primMinusNat(zzz100100, zzz542000)

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

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



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

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

new_primPlusNat0(Succ(zzz900), Succ(zzz9100)) → new_primPlusNat0(zzz900, zzz9100)

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

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



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

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

new_mkBalBranch6MkBalBranch11(zzz2934, zzz21270, zzz21271, zzz21272, zzz21273, zzz21274, zzz2930, zzz2931, Succ(zzz2262000), Succ(zzz227000), h, ba) → new_mkBalBranch6MkBalBranch11(zzz2934, zzz21270, zzz21271, zzz21272, zzz21273, zzz21274, zzz2930, zzz2931, zzz2262000, zzz227000, 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
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP

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

new_mkBalBranch6MkBalBranch3(zzz2934, zzz2127, zzz2930, zzz2931, Succ(zzz2244000), Succ(zzz224800), h, ba) → new_mkBalBranch6MkBalBranch3(zzz2934, zzz2127, zzz2930, zzz2931, zzz2244000, zzz224800, 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
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP

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

new_mkBalBranch6MkBalBranch01(zzz29340, zzz29341, zzz29342, zzz29343, zzz29344, zzz2127, zzz2930, zzz2931, Succ(zzz2246000), Succ(zzz226000), h, ba) → new_mkBalBranch6MkBalBranch01(zzz29340, zzz29341, zzz29342, zzz29343, zzz29344, zzz2127, zzz2930, zzz2931, zzz2246000, zzz226000, 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
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP

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

new_mkBalBranch6MkBalBranch4(zzz2934, zzz2127, zzz2930, zzz2931, Succ(zzz2221000), Succ(zzz223600), h, ba) → new_mkBalBranch6MkBalBranch4(zzz2934, zzz2127, zzz2930, zzz2931, zzz2221000, zzz223600, 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
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP

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

new_deleteMax(zzz350, zzz351, zzz352, zzz353, Branch(zzz3540, zzz3541, zzz3542, zzz3543, zzz3544), h, ba) → new_deleteMax(zzz3540, zzz3541, zzz3542, zzz3543, zzz3544, 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
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP

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

new_deleteMin(zzz2930, zzz2931, zzz2932, Branch(zzz29330, zzz29331, zzz29332, zzz29333, zzz29334), zzz2934, h, ba) → new_deleteMin(zzz29330, zzz29331, zzz29332, zzz29333, zzz29334, 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
                                    ↳ 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_glueBal2GlueBal1(zzz2930, zzz2931, zzz2932, zzz2933, zzz2934, zzz350, zzz351, zzz352, zzz353, zzz354, Succ(zzz2115000), Succ(zzz2114000), h, ba) → new_glueBal2GlueBal1(zzz2930, zzz2931, zzz2932, zzz2933, zzz2934, zzz350, zzz351, zzz352, zzz353, zzz354, zzz2115000, zzz2114000, 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
                                  ↳ QDP
                                    ↳ DependencyGraphProof
                                  ↳ 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_glueVBal3GlueVBal22(zzz2930, zzz2931, zzz2932, zzz2933, zzz2934, zzz350, zzz351, zzz352, zzz353, zzz354, Zero, Neg(Zero), h, ba) → new_glueVBal3GlueVBal26(zzz2930, zzz2931, zzz2932, zzz2933, zzz2934, zzz350, zzz351, zzz352, zzz353, zzz354, h, ba)
new_glueVBal3GlueVBal27(zzz2930, zzz2931, zzz2932, zzz2933, zzz2934, zzz350, zzz351, zzz352, zzz353, zzz354, Zero, zzz20800, h, ba) → new_glueVBal3GlueVBal25(zzz2930, zzz2931, zzz2932, zzz2933, zzz2934, zzz350, zzz351, zzz352, zzz353, zzz354, h, ba)
new_glueVBal3GlueVBal22(zzz2930, zzz2931, zzz2932, zzz2933, zzz2934, zzz350, zzz351, zzz352, zzz353, zzz354, Succ(zzz20800), Neg(Zero), h, ba) → new_glueVBal3GlueVBal25(zzz2930, zzz2931, zzz2932, zzz2933, zzz2934, zzz350, zzz351, zzz352, zzz353, zzz354, h, ba)
new_glueVBal3GlueVBal26(zzz2930, zzz2931, zzz2932, zzz2933, zzz2934, zzz350, zzz351, zzz352, zzz353, zzz354, h, ba) → new_glueVBal3GlueVBal28(zzz2930, zzz2931, zzz2932, zzz2933, zzz2934, zzz350, zzz351, zzz352, zzz353, zzz354, h, ba)
new_glueVBal3GlueVBal15(zzz2930, zzz2931, zzz2932, zzz2933, zzz2934, zzz350, zzz351, zzz352, zzz353, zzz354, Succ(zzz209600), zzz21030, h, ba) → new_glueVBal3GlueVBal1(zzz2930, zzz2931, zzz2932, zzz2933, zzz2934, zzz350, zzz351, zzz352, zzz353, zzz354, zzz209600, zzz21030, h, ba)
new_glueVBal3GlueVBal12(zzz2930, zzz2931, zzz2932, zzz2933, zzz2934, zzz350, zzz351, zzz352, zzz353, zzz354, Neg(zzz21000), zzz2096, h, ba) → new_glueVBal3GlueVBal14(zzz2930, zzz2931, zzz2932, zzz2933, zzz2934, zzz350, zzz351, zzz352, zzz353, zzz354, new_primMulNat(zzz21000), zzz2096, h, ba)
new_glueVBal3GlueVBal29(zzz2930, zzz2931, zzz2932, zzz2933, zzz2934, zzz350, zzz351, zzz352, zzz353, zzz354, Zero, Succ(Zero), h, ba) → new_glueVBal3GlueVBal26(zzz2930, zzz2931, zzz2932, zzz2933, zzz2934, zzz350, zzz351, zzz352, zzz353, zzz354, h, ba)
new_glueVBal3GlueVBal22(zzz2930, zzz2931, zzz2932, zzz2933, zzz2934, zzz350, zzz351, zzz352, zzz353, zzz354, Zero, Neg(Succ(zzz204800)), h, ba) → new_glueVBal3GlueVBal29(zzz2930, zzz2931, zzz2932, zzz2933, zzz2934, zzz350, zzz351, zzz352, zzz353, zzz354, zzz204800, Zero, h, ba)
new_glueVBal3GlueVBal14(zzz2930, zzz2931, zzz2932, zzz2933, zzz2934, zzz350, zzz351, zzz352, zzz353, zzz354, Zero, Neg(Succ(zzz209600)), h, ba) → new_glueVBal3GlueVBal16(zzz2930, zzz2931, zzz2932, zzz2933, zzz2934, zzz350, zzz351, zzz352, zzz353, zzz354, zzz209600, Zero, h, ba)
new_glueVBal3GlueVBal21(zzz2930, zzz2931, zzz2932, zzz2933, zzz2934, zzz350, zzz351, zzz352, zzz353, zzz354, Succ(zzz20780), Neg(zzz20480), h, ba) → new_glueVBal3GlueVBal11(zzz2930, zzz2931, zzz2932, zzz2933, zzz2934, zzz350, zzz351, zzz352, zzz353, zzz354, new_glueVBal3Size_l(zzz2930, zzz2931, zzz2932, zzz2933, zzz2934, zzz350, zzz351, zzz352, zzz353, zzz354, h, ba), h, ba)
new_glueVBal3GlueVBal15(zzz2930, zzz2931, zzz2932, zzz2933, zzz2934, zzz350, zzz351, zzz352, zzz353, zzz354, Zero, zzz21030, h, ba) → new_glueVBal3GlueVBal10(zzz2930, zzz2931, zzz2932, zzz2933, zzz2934, zzz350, zzz351, zzz352, zzz353, zzz354, h, ba)
new_glueVBal3GlueVBal24(zzz2930, zzz2931, zzz2932, zzz2933, zzz2934, zzz350, zzz351, zzz352, zzz353, zzz354, h, ba) → new_glueVBal3GlueVBal11(zzz2930, zzz2931, zzz2932, zzz2933, zzz2934, zzz350, zzz351, zzz352, zzz353, zzz354, new_glueVBal3Size_l(zzz2930, zzz2931, zzz2932, zzz2933, zzz2934, zzz350, zzz351, zzz352, zzz353, zzz354, h, ba), h, ba)
new_glueVBal3GlueVBal22(zzz2930, zzz2931, zzz2932, zzz2933, zzz2934, zzz350, zzz351, zzz352, zzz353, zzz354, Zero, Pos(Zero), h, ba) → new_glueVBal3GlueVBal26(zzz2930, zzz2931, zzz2932, zzz2933, zzz2934, zzz350, zzz351, zzz352, zzz353, zzz354, h, ba)
new_glueVBal3GlueVBal16(zzz2930, zzz2931, zzz2932, zzz2933, zzz2934, zzz350, zzz351, zzz352, zzz353, zzz354, Succ(zzz210200), Succ(Succ(zzz2096000)), h, ba) → new_glueVBal3GlueVBal1(zzz2930, zzz2931, zzz2932, zzz2933, zzz2934, zzz350, zzz351, zzz352, zzz353, zzz354, zzz210200, zzz2096000, h, ba)
new_glueVBal3GlueVBal10(zzz2930, zzz2931, zzz2932, zzz2933, zzz2934, zzz350, zzz351, zzz352, zzz353, Branch(zzz3540, zzz3541, zzz3542, zzz3543, zzz3544), h, ba) → new_glueVBal3(zzz3540, zzz3541, zzz3542, zzz3543, zzz3544, zzz2930, zzz2931, zzz2932, zzz2933, zzz2934, h, ba)
new_glueVBal3GlueVBal1(zzz2930, zzz2931, zzz2932, zzz2933, zzz2934, zzz350, zzz351, zzz352, zzz353, zzz354, Succ(zzz210200), Succ(zzz2096000), h, ba) → new_glueVBal3GlueVBal1(zzz2930, zzz2931, zzz2932, zzz2933, zzz2934, zzz350, zzz351, zzz352, zzz353, zzz354, zzz210200, zzz2096000, h, ba)
new_glueVBal3GlueVBal21(zzz2930, zzz2931, zzz2932, zzz2933, zzz2934, zzz350, zzz351, zzz352, zzz353, zzz354, Zero, Pos(Succ(zzz204800)), h, ba) → new_glueVBal3GlueVBal27(zzz2930, zzz2931, zzz2932, zzz2933, zzz2934, zzz350, zzz351, zzz352, zzz353, zzz354, Zero, zzz204800, h, ba)
new_glueVBal3GlueVBal21(zzz2930, zzz2931, zzz2932, zzz2933, zzz2934, zzz350, zzz351, zzz352, zzz353, zzz354, Zero, Neg(Zero), h, ba) → new_glueVBal3GlueVBal26(zzz2930, zzz2931, zzz2932, zzz2933, zzz2934, zzz350, zzz351, zzz352, zzz353, zzz354, h, ba)
new_glueVBal3GlueVBal14(zzz2930, zzz2931, zzz2932, zzz2933, zzz2934, zzz350, zzz351, zzz352, zzz353, zzz354, Succ(zzz21030), Neg(Succ(zzz209600)), h, ba) → new_glueVBal3GlueVBal1(zzz2930, zzz2931, zzz2932, zzz2933, zzz2934, zzz350, zzz351, zzz352, zzz353, zzz354, zzz209600, zzz21030, h, ba)
new_glueVBal3GlueVBal25(zzz2930, zzz2931, zzz2932, Branch(zzz29330, zzz29331, zzz29332, zzz29333, zzz29334), zzz2934, zzz350, zzz351, zzz352, zzz353, zzz354, h, ba) → new_glueVBal3GlueVBal2(zzz29330, zzz29331, zzz29332, zzz29333, zzz29334, zzz350, zzz351, zzz352, zzz353, zzz354, new_glueVBal3Size_r(zzz29330, zzz29331, zzz29332, zzz29333, zzz29334, zzz350, zzz351, zzz352, zzz353, zzz354, h, ba), h, ba)
new_glueVBal3GlueVBal29(zzz2930, zzz2931, zzz2932, zzz2933, zzz2934, zzz350, zzz351, zzz352, zzz353, zzz354, Succ(zzz207800), Succ(Succ(zzz2048000)), h, ba) → new_glueVBal3GlueVBal23(zzz2930, zzz2931, zzz2932, zzz2933, zzz2934, zzz350, zzz351, zzz352, zzz353, zzz354, zzz207800, zzz2048000, h, ba)
new_glueVBal3GlueVBal14(zzz2930, zzz2931, zzz2932, zzz2933, zzz2934, zzz350, zzz351, zzz352, zzz353, zzz354, Zero, Pos(Succ(zzz209600)), h, ba) → new_glueVBal3GlueVBal10(zzz2930, zzz2931, zzz2932, zzz2933, zzz2934, zzz350, zzz351, zzz352, zzz353, zzz354, h, ba)
new_glueVBal3GlueVBal29(zzz2930, zzz2931, zzz2932, zzz2933, zzz2934, zzz350, zzz351, zzz352, zzz353, zzz354, Succ(zzz207800), Succ(Zero), h, ba) → new_glueVBal3GlueVBal24(zzz2930, zzz2931, zzz2932, zzz2933, zzz2934, zzz350, zzz351, zzz352, zzz353, zzz354, h, ba)
new_glueVBal3GlueVBal20(zzz2930, zzz2931, zzz2932, zzz2933, zzz2934, zzz350, zzz351, zzz352, zzz353, zzz354, Pos(zzz20630), zzz2048, h, ba) → new_glueVBal3GlueVBal21(zzz2930, zzz2931, zzz2932, zzz2933, zzz2934, zzz350, zzz351, zzz352, zzz353, zzz354, new_primMulNat(zzz20630), zzz2048, h, ba)
new_glueVBal3GlueVBal14(zzz2930, zzz2931, zzz2932, zzz2933, zzz2934, zzz350, zzz351, zzz352, zzz353, Branch(zzz3540, zzz3541, zzz3542, zzz3543, zzz3544), Succ(zzz21030), Pos(zzz20960), h, ba) → new_glueVBal3(zzz3540, zzz3541, zzz3542, zzz3543, zzz3544, zzz2930, zzz2931, zzz2932, zzz2933, zzz2934, h, ba)
new_glueVBal3GlueVBal27(zzz2930, zzz2931, zzz2932, zzz2933, zzz2934, zzz350, zzz351, zzz352, zzz353, zzz354, Succ(zzz204800), zzz20800, h, ba) → new_glueVBal3GlueVBal23(zzz2930, zzz2931, zzz2932, zzz2933, zzz2934, zzz350, zzz351, zzz352, zzz353, zzz354, zzz204800, zzz20800, h, ba)
new_glueVBal3GlueVBal29(zzz2930, zzz2931, zzz2932, zzz2933, zzz2934, zzz350, zzz351, zzz352, zzz353, zzz354, Zero, Succ(Succ(zzz2048000)), h, ba) → new_glueVBal3GlueVBal25(zzz2930, zzz2931, zzz2932, zzz2933, zzz2934, zzz350, zzz351, zzz352, zzz353, zzz354, h, ba)
new_glueVBal3GlueVBal16(zzz2930, zzz2931, zzz2932, zzz2933, zzz2934, zzz350, zzz351, zzz352, zzz353, zzz354, Zero, Succ(Succ(zzz2096000)), h, ba) → new_glueVBal3GlueVBal10(zzz2930, zzz2931, zzz2932, zzz2933, zzz2934, zzz350, zzz351, zzz352, zzz353, zzz354, h, ba)
new_glueVBal3GlueVBal13(zzz2930, zzz2931, zzz2932, zzz2933, zzz2934, zzz350, zzz351, zzz352, zzz353, zzz354, Succ(Zero), Pos(Succ(Succ(zzz2096000))), h, ba) → new_glueVBal3GlueVBal10(zzz2930, zzz2931, zzz2932, zzz2933, zzz2934, zzz350, zzz351, zzz352, zzz353, zzz354, h, ba)
new_glueVBal3GlueVBal21(zzz2930, zzz2931, zzz2932, zzz2933, zzz2934, zzz350, zzz351, zzz352, zzz353, zzz354, Succ(Zero), Pos(Succ(Succ(zzz2048000))), h, ba) → new_glueVBal3GlueVBal25(zzz2930, zzz2931, zzz2932, zzz2933, zzz2934, zzz350, zzz351, zzz352, zzz353, zzz354, h, ba)
new_glueVBal3GlueVBal21(zzz2930, zzz2931, zzz2932, zzz2933, zzz2934, zzz350, zzz351, zzz352, zzz353, zzz354, Succ(Succ(zzz207800)), Pos(Succ(Succ(zzz2048000))), h, ba) → new_glueVBal3GlueVBal23(zzz2930, zzz2931, zzz2932, zzz2933, zzz2934, zzz350, zzz351, zzz352, zzz353, zzz354, zzz207800, zzz2048000, h, ba)
new_glueVBal3GlueVBal21(zzz2930, zzz2931, zzz2932, zzz2933, zzz2934, zzz350, zzz351, zzz352, zzz353, zzz354, Succ(Succ(zzz207800)), Pos(Succ(Zero)), h, ba) → new_glueVBal3GlueVBal24(zzz2930, zzz2931, zzz2932, zzz2933, zzz2934, zzz350, zzz351, zzz352, zzz353, zzz354, h, ba)
new_glueVBal3GlueVBal23(zzz2930, zzz2931, zzz2932, zzz2933, zzz2934, zzz350, zzz351, zzz352, zzz353, zzz354, Succ(zzz207800), Succ(zzz2048000), h, ba) → new_glueVBal3GlueVBal23(zzz2930, zzz2931, zzz2932, zzz2933, zzz2934, zzz350, zzz351, zzz352, zzz353, zzz354, zzz207800, zzz2048000, h, ba)
new_glueVBal3GlueVBal11(zzz2930, zzz2931, zzz2932, zzz2933, zzz2934, zzz350, zzz351, zzz352, zzz353, zzz354, zzz2096, h, ba) → new_glueVBal3GlueVBal12(zzz2930, zzz2931, zzz2932, zzz2933, zzz2934, zzz350, zzz351, zzz352, zzz353, zzz354, new_glueVBal3Size_r(zzz2930, zzz2931, zzz2932, zzz2933, zzz2934, zzz350, zzz351, zzz352, zzz353, zzz354, h, ba), zzz2096, h, ba)
new_glueVBal3GlueVBal23(zzz2930, zzz2931, zzz2932, zzz2933, zzz2934, zzz350, zzz351, zzz352, zzz353, zzz354, Zero, Succ(zzz2048000), h, ba) → new_glueVBal3GlueVBal25(zzz2930, zzz2931, zzz2932, zzz2933, zzz2934, zzz350, zzz351, zzz352, zzz353, zzz354, h, ba)
new_glueVBal3GlueVBal2(zzz2930, zzz2931, zzz2932, zzz2933, zzz2934, zzz350, zzz351, zzz352, zzz353, zzz354, zzz2048, h, ba) → new_glueVBal3GlueVBal20(zzz2930, zzz2931, zzz2932, zzz2933, zzz2934, zzz350, zzz351, zzz352, zzz353, zzz354, new_glueVBal3Size_l(zzz2930, zzz2931, zzz2932, zzz2933, zzz2934, zzz350, zzz351, zzz352, zzz353, zzz354, h, ba), zzz2048, h, ba)
new_glueVBal3GlueVBal1(zzz2930, zzz2931, zzz2932, zzz2933, zzz2934, zzz350, zzz351, zzz352, zzz353, zzz354, Zero, Succ(zzz2096000), h, ba) → new_glueVBal3GlueVBal10(zzz2930, zzz2931, zzz2932, zzz2933, zzz2934, zzz350, zzz351, zzz352, zzz353, zzz354, h, ba)
new_glueVBal3GlueVBal21(zzz2930, zzz2931, zzz2932, zzz2933, zzz2934, zzz350, zzz351, zzz352, zzz353, zzz354, Zero, Pos(Zero), h, ba) → new_glueVBal3GlueVBal28(zzz2930, zzz2931, zzz2932, zzz2933, zzz2934, zzz350, zzz351, zzz352, zzz353, zzz354, h, ba)
new_glueVBal3GlueVBal22(zzz2930, zzz2931, zzz2932, zzz2933, zzz2934, zzz350, zzz351, zzz352, zzz353, zzz354, Zero, Pos(Succ(zzz204800)), h, ba) → new_glueVBal3GlueVBal25(zzz2930, zzz2931, zzz2932, zzz2933, zzz2934, zzz350, zzz351, zzz352, zzz353, zzz354, h, ba)
new_glueVBal3GlueVBal21(zzz2930, zzz2931, zzz2932, zzz2933, zzz2934, zzz350, zzz351, zzz352, zzz353, zzz354, Succ(Zero), Pos(Succ(Zero)), h, ba) → new_glueVBal3GlueVBal26(zzz2930, zzz2931, zzz2932, zzz2933, zzz2934, zzz350, zzz351, zzz352, zzz353, zzz354, h, ba)
new_glueVBal3(zzz350, zzz351, zzz352, zzz353, zzz354, zzz29330, zzz29331, zzz29332, zzz29333, zzz29334, h, ba) → new_glueVBal3GlueVBal2(zzz29330, zzz29331, zzz29332, zzz29333, zzz29334, zzz350, zzz351, zzz352, zzz353, zzz354, new_glueVBal3Size_r(zzz29330, zzz29331, zzz29332, zzz29333, zzz29334, zzz350, zzz351, zzz352, zzz353, zzz354, h, ba), h, ba)
new_glueVBal3GlueVBal21(zzz2930, zzz2931, zzz2932, zzz2933, zzz2934, zzz350, zzz351, zzz352, zzz353, zzz354, Succ(zzz20780), Pos(Zero), h, ba) → new_glueVBal3GlueVBal24(zzz2930, zzz2931, zzz2932, zzz2933, zzz2934, zzz350, zzz351, zzz352, zzz353, zzz354, h, ba)
new_glueVBal3GlueVBal14(zzz2930, zzz2931, zzz2932, zzz2933, zzz2934, zzz350, zzz351, zzz352, zzz353, zzz354, Succ(zzz21030), Neg(Zero), h, ba) → new_glueVBal3GlueVBal10(zzz2930, zzz2931, zzz2932, zzz2933, zzz2934, zzz350, zzz351, zzz352, zzz353, zzz354, h, ba)
new_glueVBal3GlueVBal23(zzz2930, zzz2931, zzz2932, zzz2933, zzz2934, zzz350, zzz351, zzz352, zzz353, zzz354, Succ(zzz207800), Zero, h, ba) → new_glueVBal3GlueVBal24(zzz2930, zzz2931, zzz2932, zzz2933, zzz2934, zzz350, zzz351, zzz352, zzz353, zzz354, h, ba)
new_glueVBal3GlueVBal12(zzz2930, zzz2931, zzz2932, zzz2933, zzz2934, zzz350, zzz351, zzz352, zzz353, zzz354, Pos(zzz21000), zzz2096, h, ba) → new_glueVBal3GlueVBal13(zzz2930, zzz2931, zzz2932, zzz2933, zzz2934, zzz350, zzz351, zzz352, zzz353, zzz354, new_primMulNat(zzz21000), zzz2096, h, ba)
new_glueVBal3GlueVBal13(zzz2930, zzz2931, zzz2932, zzz2933, zzz2934, zzz350, zzz351, zzz352, zzz353, zzz354, Succ(Succ(zzz210200)), Pos(Succ(Succ(zzz2096000))), h, ba) → new_glueVBal3GlueVBal1(zzz2930, zzz2931, zzz2932, zzz2933, zzz2934, zzz350, zzz351, zzz352, zzz353, zzz354, zzz210200, zzz2096000, h, ba)
new_glueVBal3GlueVBal22(zzz2930, zzz2931, zzz2932, Branch(zzz29330, zzz29331, zzz29332, zzz29333, zzz29334), zzz2934, zzz350, zzz351, zzz352, zzz353, zzz354, Succ(zzz20800), Pos(zzz20480), h, ba) → new_glueVBal3GlueVBal2(zzz29330, zzz29331, zzz29332, zzz29333, zzz29334, zzz350, zzz351, zzz352, zzz353, zzz354, new_glueVBal3Size_r(zzz29330, zzz29331, zzz29332, zzz29333, zzz29334, zzz350, zzz351, zzz352, zzz353, zzz354, h, ba), h, ba)
new_glueVBal3GlueVBal28(zzz2930, zzz2931, zzz2932, zzz2933, zzz2934, zzz350, zzz351, zzz352, zzz353, zzz354, h, ba) → new_glueVBal3GlueVBal11(zzz2930, zzz2931, zzz2932, zzz2933, zzz2934, zzz350, zzz351, zzz352, zzz353, zzz354, new_glueVBal3Size_l(zzz2930, zzz2931, zzz2932, zzz2933, zzz2934, zzz350, zzz351, zzz352, zzz353, zzz354, h, ba), h, ba)
new_glueVBal3GlueVBal20(zzz2930, zzz2931, zzz2932, zzz2933, zzz2934, zzz350, zzz351, zzz352, zzz353, zzz354, Neg(zzz20630), zzz2048, h, ba) → new_glueVBal3GlueVBal22(zzz2930, zzz2931, zzz2932, zzz2933, zzz2934, zzz350, zzz351, zzz352, zzz353, zzz354, new_primMulNat(zzz20630), zzz2048, h, ba)
new_glueVBal3GlueVBal21(zzz2930, zzz2931, zzz2932, zzz2933, zzz2934, zzz350, zzz351, zzz352, zzz353, zzz354, Zero, Neg(Succ(zzz204800)), h, ba) → new_glueVBal3GlueVBal24(zzz2930, zzz2931, zzz2932, zzz2933, zzz2934, zzz350, zzz351, zzz352, zzz353, zzz354, h, ba)
new_glueVBal3GlueVBal22(zzz2930, zzz2931, zzz2932, zzz2933, zzz2934, zzz350, zzz351, zzz352, zzz353, zzz354, Succ(zzz20800), Neg(Succ(zzz204800)), h, ba) → new_glueVBal3GlueVBal23(zzz2930, zzz2931, zzz2932, zzz2933, zzz2934, zzz350, zzz351, zzz352, zzz353, zzz354, zzz204800, zzz20800, h, ba)
new_glueVBal3GlueVBal29(zzz2930, zzz2931, zzz2932, zzz2933, zzz2934, zzz350, zzz351, zzz352, zzz353, zzz354, zzz20780, Zero, h, ba) → new_glueVBal3GlueVBal24(zzz2930, zzz2931, zzz2932, zzz2933, zzz2934, zzz350, zzz351, zzz352, zzz353, zzz354, h, ba)
new_glueVBal3GlueVBal13(zzz2930, zzz2931, zzz2932, zzz2933, zzz2934, zzz350, zzz351, zzz352, zzz353, zzz354, Zero, Pos(Succ(zzz209600)), h, ba) → new_glueVBal3GlueVBal15(zzz2930, zzz2931, zzz2932, zzz2933, zzz2934, zzz350, zzz351, zzz352, zzz353, zzz354, Zero, zzz209600, h, ba)
new_glueVBal3GlueVBal23(zzz2930, zzz2931, zzz2932, zzz2933, zzz2934, zzz350, zzz351, zzz352, zzz353, zzz354, Zero, Zero, h, ba) → new_glueVBal3GlueVBal26(zzz2930, zzz2931, zzz2932, zzz2933, zzz2934, zzz350, zzz351, zzz352, zzz353, zzz354, h, ba)

The TRS R consists of the following rules:

new_primPlusNat1(Zero) → Zero
new_primPlusNat3(zzz90, Zero) → Succ(zzz90)
new_primMulNat(Zero) → Zero
new_glueVBal3Size_r(zzz2930, zzz2931, zzz2932, zzz2933, zzz2934, zzz350, zzz351, zzz352, zzz353, zzz354, h, ba) → new_sizeFM(Branch(zzz2930, zzz2931, zzz2932, zzz2933, zzz2934), h, ba)
new_glueVBal3Size_l(zzz2930, zzz2931, zzz2932, zzz2933, zzz2934, zzz350, zzz351, zzz352, zzz353, zzz354, h, ba) → new_sizeFM(Branch(zzz350, zzz351, zzz352, zzz353, zzz354), h, ba)
new_primPlusNat2(Zero, Zero) → Zero
new_primPlusNat2(Zero, Succ(zzz9100)) → Succ(zzz9100)
new_primPlusNat2(Succ(zzz900), Zero) → Succ(zzz900)
new_primPlusNat2(Succ(zzz900), Succ(zzz9100)) → Succ(Succ(new_primPlusNat2(zzz900, zzz9100)))
new_primMulNat0(zzz6200) → new_primPlusNat3(Succ(new_primPlusNat3(new_primPlusNat1(zzz6200), zzz6200)), Succ(zzz6200))
new_primPlusNat3(zzz90, Succ(zzz910)) → Succ(Succ(new_primPlusNat2(zzz90, zzz910)))
new_sizeFM(EmptyFM, bb, bc) → Pos(Zero)
new_primMulNat(Succ(zzz206300)) → new_primPlusNat2(new_primMulNat0(zzz206300), Succ(zzz206300))
new_sizeFM(Branch(zzz13040, zzz13041, zzz13042, zzz13043, zzz13044), bb, bc) → zzz13042
new_primPlusNat1(Succ(zzz62000)) → Succ(Succ(new_primPlusNat1(zzz62000)))

The set Q consists of the following terms:

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

We have to consider all minimal (P,Q,R)-chains.
The approximation of the Dependency Graph [15,17,22] contains 1 SCC with 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
                                  ↳ QDP
                                    ↳ DependencyGraphProof
                                      ↳ QDP
                                        ↳ UsableRulesProof
                                  ↳ 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_glueVBal3GlueVBal22(zzz2930, zzz2931, zzz2932, zzz2933, zzz2934, zzz350, zzz351, zzz352, zzz353, zzz354, Zero, Neg(Zero), h, ba) → new_glueVBal3GlueVBal26(zzz2930, zzz2931, zzz2932, zzz2933, zzz2934, zzz350, zzz351, zzz352, zzz353, zzz354, h, ba)
new_glueVBal3GlueVBal21(zzz2930, zzz2931, zzz2932, zzz2933, zzz2934, zzz350, zzz351, zzz352, zzz353, zzz354, Succ(Zero), Pos(Succ(Succ(zzz2048000))), h, ba) → new_glueVBal3GlueVBal25(zzz2930, zzz2931, zzz2932, zzz2933, zzz2934, zzz350, zzz351, zzz352, zzz353, zzz354, h, ba)
new_glueVBal3GlueVBal27(zzz2930, zzz2931, zzz2932, zzz2933, zzz2934, zzz350, zzz351, zzz352, zzz353, zzz354, Zero, zzz20800, h, ba) → new_glueVBal3GlueVBal25(zzz2930, zzz2931, zzz2932, zzz2933, zzz2934, zzz350, zzz351, zzz352, zzz353, zzz354, h, ba)
new_glueVBal3GlueVBal21(zzz2930, zzz2931, zzz2932, zzz2933, zzz2934, zzz350, zzz351, zzz352, zzz353, zzz354, Succ(Succ(zzz207800)), Pos(Succ(Succ(zzz2048000))), h, ba) → new_glueVBal3GlueVBal23(zzz2930, zzz2931, zzz2932, zzz2933, zzz2934, zzz350, zzz351, zzz352, zzz353, zzz354, zzz207800, zzz2048000, h, ba)
new_glueVBal3GlueVBal21(zzz2930, zzz2931, zzz2932, zzz2933, zzz2934, zzz350, zzz351, zzz352, zzz353, zzz354, Succ(Succ(zzz207800)), Pos(Succ(Zero)), h, ba) → new_glueVBal3GlueVBal24(zzz2930, zzz2931, zzz2932, zzz2933, zzz2934, zzz350, zzz351, zzz352, zzz353, zzz354, h, ba)
new_glueVBal3GlueVBal11(zzz2930, zzz2931, zzz2932, zzz2933, zzz2934, zzz350, zzz351, zzz352, zzz353, zzz354, zzz2096, h, ba) → new_glueVBal3GlueVBal12(zzz2930, zzz2931, zzz2932, zzz2933, zzz2934, zzz350, zzz351, zzz352, zzz353, zzz354, new_glueVBal3Size_r(zzz2930, zzz2931, zzz2932, zzz2933, zzz2934, zzz350, zzz351, zzz352, zzz353, zzz354, h, ba), zzz2096, h, ba)
new_glueVBal3GlueVBal23(zzz2930, zzz2931, zzz2932, zzz2933, zzz2934, zzz350, zzz351, zzz352, zzz353, zzz354, Succ(zzz207800), Succ(zzz2048000), h, ba) → new_glueVBal3GlueVBal23(zzz2930, zzz2931, zzz2932, zzz2933, zzz2934, zzz350, zzz351, zzz352, zzz353, zzz354, zzz207800, zzz2048000, h, ba)
new_glueVBal3GlueVBal22(zzz2930, zzz2931, zzz2932, zzz2933, zzz2934, zzz350, zzz351, zzz352, zzz353, zzz354, Succ(zzz20800), Neg(Zero), h, ba) → new_glueVBal3GlueVBal25(zzz2930, zzz2931, zzz2932, zzz2933, zzz2934, zzz350, zzz351, zzz352, zzz353, zzz354, h, ba)
new_glueVBal3GlueVBal23(zzz2930, zzz2931, zzz2932, zzz2933, zzz2934, zzz350, zzz351, zzz352, zzz353, zzz354, Zero, Succ(zzz2048000), h, ba) → new_glueVBal3GlueVBal25(zzz2930, zzz2931, zzz2932, zzz2933, zzz2934, zzz350, zzz351, zzz352, zzz353, zzz354, h, ba)
new_glueVBal3GlueVBal26(zzz2930, zzz2931, zzz2932, zzz2933, zzz2934, zzz350, zzz351, zzz352, zzz353, zzz354, h, ba) → new_glueVBal3GlueVBal28(zzz2930, zzz2931, zzz2932, zzz2933, zzz2934, zzz350, zzz351, zzz352, zzz353, zzz354, h, ba)
new_glueVBal3GlueVBal2(zzz2930, zzz2931, zzz2932, zzz2933, zzz2934, zzz350, zzz351, zzz352, zzz353, zzz354, zzz2048, h, ba) → new_glueVBal3GlueVBal20(zzz2930, zzz2931, zzz2932, zzz2933, zzz2934, zzz350, zzz351, zzz352, zzz353, zzz354, new_glueVBal3Size_l(zzz2930, zzz2931, zzz2932, zzz2933, zzz2934, zzz350, zzz351, zzz352, zzz353, zzz354, h, ba), zzz2048, h, ba)
new_glueVBal3GlueVBal1(zzz2930, zzz2931, zzz2932, zzz2933, zzz2934, zzz350, zzz351, zzz352, zzz353, zzz354, Zero, Succ(zzz2096000), h, ba) → new_glueVBal3GlueVBal10(zzz2930, zzz2931, zzz2932, zzz2933, zzz2934, zzz350, zzz351, zzz352, zzz353, zzz354, h, ba)
new_glueVBal3GlueVBal12(zzz2930, zzz2931, zzz2932, zzz2933, zzz2934, zzz350, zzz351, zzz352, zzz353, zzz354, Neg(zzz21000), zzz2096, h, ba) → new_glueVBal3GlueVBal14(zzz2930, zzz2931, zzz2932, zzz2933, zzz2934, zzz350, zzz351, zzz352, zzz353, zzz354, new_primMulNat(zzz21000), zzz2096, h, ba)
new_glueVBal3GlueVBal21(zzz2930, zzz2931, zzz2932, zzz2933, zzz2934, zzz350, zzz351, zzz352, zzz353, zzz354, Zero, Pos(Zero), h, ba) → new_glueVBal3GlueVBal28(zzz2930, zzz2931, zzz2932, zzz2933, zzz2934, zzz350, zzz351, zzz352, zzz353, zzz354, h, ba)
new_glueVBal3GlueVBal22(zzz2930, zzz2931, zzz2932, zzz2933, zzz2934, zzz350, zzz351, zzz352, zzz353, zzz354, Zero, Pos(Succ(zzz204800)), h, ba) → new_glueVBal3GlueVBal25(zzz2930, zzz2931, zzz2932, zzz2933, zzz2934, zzz350, zzz351, zzz352, zzz353, zzz354, h, ba)
new_glueVBal3GlueVBal22(zzz2930, zzz2931, zzz2932, zzz2933, zzz2934, zzz350, zzz351, zzz352, zzz353, zzz354, Zero, Neg(Succ(zzz204800)), h, ba) → new_glueVBal3GlueVBal29(zzz2930, zzz2931, zzz2932, zzz2933, zzz2934, zzz350, zzz351, zzz352, zzz353, zzz354, zzz204800, Zero, h, ba)
new_glueVBal3GlueVBal15(zzz2930, zzz2931, zzz2932, zzz2933, zzz2934, zzz350, zzz351, zzz352, zzz353, zzz354, Zero, zzz21030, h, ba) → new_glueVBal3GlueVBal10(zzz2930, zzz2931, zzz2932, zzz2933, zzz2934, zzz350, zzz351, zzz352, zzz353, zzz354, h, ba)
new_glueVBal3GlueVBal21(zzz2930, zzz2931, zzz2932, zzz2933, zzz2934, zzz350, zzz351, zzz352, zzz353, zzz354, Succ(Zero), Pos(Succ(Zero)), h, ba) → new_glueVBal3GlueVBal26(zzz2930, zzz2931, zzz2932, zzz2933, zzz2934, zzz350, zzz351, zzz352, zzz353, zzz354, h, ba)
new_glueVBal3GlueVBal21(zzz2930, zzz2931, zzz2932, zzz2933, zzz2934, zzz350, zzz351, zzz352, zzz353, zzz354, Succ(zzz20780), Neg(zzz20480), h, ba) → new_glueVBal3GlueVBal11(zzz2930, zzz2931, zzz2932, zzz2933, zzz2934, zzz350, zzz351, zzz352, zzz353, zzz354, new_glueVBal3Size_l(zzz2930, zzz2931, zzz2932, zzz2933, zzz2934, zzz350, zzz351, zzz352, zzz353, zzz354, h, ba), h, ba)
new_glueVBal3(zzz350, zzz351, zzz352, zzz353, zzz354, zzz29330, zzz29331, zzz29332, zzz29333, zzz29334, h, ba) → new_glueVBal3GlueVBal2(zzz29330, zzz29331, zzz29332, zzz29333, zzz29334, zzz350, zzz351, zzz352, zzz353, zzz354, new_glueVBal3Size_r(zzz29330, zzz29331, zzz29332, zzz29333, zzz29334, zzz350, zzz351, zzz352, zzz353, zzz354, h, ba), h, ba)
new_glueVBal3GlueVBal24(zzz2930, zzz2931, zzz2932, zzz2933, zzz2934, zzz350, zzz351, zzz352, zzz353, zzz354, h, ba) → new_glueVBal3GlueVBal11(zzz2930, zzz2931, zzz2932, zzz2933, zzz2934, zzz350, zzz351, zzz352, zzz353, zzz354, new_glueVBal3Size_l(zzz2930, zzz2931, zzz2932, zzz2933, zzz2934, zzz350, zzz351, zzz352, zzz353, zzz354, h, ba), h, ba)
new_glueVBal3GlueVBal22(zzz2930, zzz2931, zzz2932, zzz2933, zzz2934, zzz350, zzz351, zzz352, zzz353, zzz354, Zero, Pos(Zero), h, ba) → new_glueVBal3GlueVBal26(zzz2930, zzz2931, zzz2932, zzz2933, zzz2934, zzz350, zzz351, zzz352, zzz353, zzz354, h, ba)
new_glueVBal3GlueVBal10(zzz2930, zzz2931, zzz2932, zzz2933, zzz2934, zzz350, zzz351, zzz352, zzz353, Branch(zzz3540, zzz3541, zzz3542, zzz3543, zzz3544), h, ba) → new_glueVBal3(zzz3540, zzz3541, zzz3542, zzz3543, zzz3544, zzz2930, zzz2931, zzz2932, zzz2933, zzz2934, h, ba)
new_glueVBal3GlueVBal1(zzz2930, zzz2931, zzz2932, zzz2933, zzz2934, zzz350, zzz351, zzz352, zzz353, zzz354, Succ(zzz210200), Succ(zzz2096000), h, ba) → new_glueVBal3GlueVBal1(zzz2930, zzz2931, zzz2932, zzz2933, zzz2934, zzz350, zzz351, zzz352, zzz353, zzz354, zzz210200, zzz2096000, h, ba)
new_glueVBal3GlueVBal21(zzz2930, zzz2931, zzz2932, zzz2933, zzz2934, zzz350, zzz351, zzz352, zzz353, zzz354, Zero, Neg(Zero), h, ba) → new_glueVBal3GlueVBal26(zzz2930, zzz2931, zzz2932, zzz2933, zzz2934, zzz350, zzz351, zzz352, zzz353, zzz354, h, ba)
new_glueVBal3GlueVBal21(zzz2930, zzz2931, zzz2932, zzz2933, zzz2934, zzz350, zzz351, zzz352, zzz353, zzz354, Zero, Pos(Succ(zzz204800)), h, ba) → new_glueVBal3GlueVBal27(zzz2930, zzz2931, zzz2932, zzz2933, zzz2934, zzz350, zzz351, zzz352, zzz353, zzz354, Zero, zzz204800, h, ba)
new_glueVBal3GlueVBal14(zzz2930, zzz2931, zzz2932, zzz2933, zzz2934, zzz350, zzz351, zzz352, zzz353, zzz354, Succ(zzz21030), Neg(Succ(zzz209600)), h, ba) → new_glueVBal3GlueVBal1(zzz2930, zzz2931, zzz2932, zzz2933, zzz2934, zzz350, zzz351, zzz352, zzz353, zzz354, zzz209600, zzz21030, h, ba)
new_glueVBal3GlueVBal14(zzz2930, zzz2931, zzz2932, zzz2933, zzz2934, zzz350, zzz351, zzz352, zzz353, zzz354, Succ(zzz21030), Neg(Zero), h, ba) → new_glueVBal3GlueVBal10(zzz2930, zzz2931, zzz2932, zzz2933, zzz2934, zzz350, zzz351, zzz352, zzz353, zzz354, h, ba)
new_glueVBal3GlueVBal21(zzz2930, zzz2931, zzz2932, zzz2933, zzz2934, zzz350, zzz351, zzz352, zzz353, zzz354, Succ(zzz20780), Pos(Zero), h, ba) → new_glueVBal3GlueVBal24(zzz2930, zzz2931, zzz2932, zzz2933, zzz2934, zzz350, zzz351, zzz352, zzz353, zzz354, h, ba)
new_glueVBal3GlueVBal25(zzz2930, zzz2931, zzz2932, Branch(zzz29330, zzz29331, zzz29332, zzz29333, zzz29334), zzz2934, zzz350, zzz351, zzz352, zzz353, zzz354, h, ba) → new_glueVBal3GlueVBal2(zzz29330, zzz29331, zzz29332, zzz29333, zzz29334, zzz350, zzz351, zzz352, zzz353, zzz354, new_glueVBal3Size_r(zzz29330, zzz29331, zzz29332, zzz29333, zzz29334, zzz350, zzz351, zzz352, zzz353, zzz354, h, ba), h, ba)
new_glueVBal3GlueVBal14(zzz2930, zzz2931, zzz2932, zzz2933, zzz2934, zzz350, zzz351, zzz352, zzz353, zzz354, Zero, Pos(Succ(zzz209600)), h, ba) → new_glueVBal3GlueVBal10(zzz2930, zzz2931, zzz2932, zzz2933, zzz2934, zzz350, zzz351, zzz352, zzz353, zzz354, h, ba)
new_glueVBal3GlueVBal23(zzz2930, zzz2931, zzz2932, zzz2933, zzz2934, zzz350, zzz351, zzz352, zzz353, zzz354, Succ(zzz207800), Zero, h, ba) → new_glueVBal3GlueVBal24(zzz2930, zzz2931, zzz2932, zzz2933, zzz2934, zzz350, zzz351, zzz352, zzz353, zzz354, h, ba)
new_glueVBal3GlueVBal20(zzz2930, zzz2931, zzz2932, zzz2933, zzz2934, zzz350, zzz351, zzz352, zzz353, zzz354, Pos(zzz20630), zzz2048, h, ba) → new_glueVBal3GlueVBal21(zzz2930, zzz2931, zzz2932, zzz2933, zzz2934, zzz350, zzz351, zzz352, zzz353, zzz354, new_primMulNat(zzz20630), zzz2048, h, ba)
new_glueVBal3GlueVBal13(zzz2930, zzz2931, zzz2932, zzz2933, zzz2934, zzz350, zzz351, zzz352, zzz353, zzz354, Succ(Succ(zzz210200)), Pos(Succ(Succ(zzz2096000))), h, ba) → new_glueVBal3GlueVBal1(zzz2930, zzz2931, zzz2932, zzz2933, zzz2934, zzz350, zzz351, zzz352, zzz353, zzz354, zzz210200, zzz2096000, h, ba)
new_glueVBal3GlueVBal12(zzz2930, zzz2931, zzz2932, zzz2933, zzz2934, zzz350, zzz351, zzz352, zzz353, zzz354, Pos(zzz21000), zzz2096, h, ba) → new_glueVBal3GlueVBal13(zzz2930, zzz2931, zzz2932, zzz2933, zzz2934, zzz350, zzz351, zzz352, zzz353, zzz354, new_primMulNat(zzz21000), zzz2096, h, ba)
new_glueVBal3GlueVBal14(zzz2930, zzz2931, zzz2932, zzz2933, zzz2934, zzz350, zzz351, zzz352, zzz353, Branch(zzz3540, zzz3541, zzz3542, zzz3543, zzz3544), Succ(zzz21030), Pos(zzz20960), h, ba) → new_glueVBal3(zzz3540, zzz3541, zzz3542, zzz3543, zzz3544, zzz2930, zzz2931, zzz2932, zzz2933, zzz2934, h, ba)
new_glueVBal3GlueVBal22(zzz2930, zzz2931, zzz2932, Branch(zzz29330, zzz29331, zzz29332, zzz29333, zzz29334), zzz2934, zzz350, zzz351, zzz352, zzz353, zzz354, Succ(zzz20800), Pos(zzz20480), h, ba) → new_glueVBal3GlueVBal2(zzz29330, zzz29331, zzz29332, zzz29333, zzz29334, zzz350, zzz351, zzz352, zzz353, zzz354, new_glueVBal3Size_r(zzz29330, zzz29331, zzz29332, zzz29333, zzz29334, zzz350, zzz351, zzz352, zzz353, zzz354, h, ba), h, ba)
new_glueVBal3GlueVBal28(zzz2930, zzz2931, zzz2932, zzz2933, zzz2934, zzz350, zzz351, zzz352, zzz353, zzz354, h, ba) → new_glueVBal3GlueVBal11(zzz2930, zzz2931, zzz2932, zzz2933, zzz2934, zzz350, zzz351, zzz352, zzz353, zzz354, new_glueVBal3Size_l(zzz2930, zzz2931, zzz2932, zzz2933, zzz2934, zzz350, zzz351, zzz352, zzz353, zzz354, h, ba), h, ba)
new_glueVBal3GlueVBal20(zzz2930, zzz2931, zzz2932, zzz2933, zzz2934, zzz350, zzz351, zzz352, zzz353, zzz354, Neg(zzz20630), zzz2048, h, ba) → new_glueVBal3GlueVBal22(zzz2930, zzz2931, zzz2932, zzz2933, zzz2934, zzz350, zzz351, zzz352, zzz353, zzz354, new_primMulNat(zzz20630), zzz2048, h, ba)
new_glueVBal3GlueVBal21(zzz2930, zzz2931, zzz2932, zzz2933, zzz2934, zzz350, zzz351, zzz352, zzz353, zzz354, Zero, Neg(Succ(zzz204800)), h, ba) → new_glueVBal3GlueVBal24(zzz2930, zzz2931, zzz2932, zzz2933, zzz2934, zzz350, zzz351, zzz352, zzz353, zzz354, h, ba)
new_glueVBal3GlueVBal22(zzz2930, zzz2931, zzz2932, zzz2933, zzz2934, zzz350, zzz351, zzz352, zzz353, zzz354, Succ(zzz20800), Neg(Succ(zzz204800)), h, ba) → new_glueVBal3GlueVBal23(zzz2930, zzz2931, zzz2932, zzz2933, zzz2934, zzz350, zzz351, zzz352, zzz353, zzz354, zzz204800, zzz20800, h, ba)
new_glueVBal3GlueVBal13(zzz2930, zzz2931, zzz2932, zzz2933, zzz2934, zzz350, zzz351, zzz352, zzz353, zzz354, Succ(Zero), Pos(Succ(Succ(zzz2096000))), h, ba) → new_glueVBal3GlueVBal10(zzz2930, zzz2931, zzz2932, zzz2933, zzz2934, zzz350, zzz351, zzz352, zzz353, zzz354, h, ba)
new_glueVBal3GlueVBal29(zzz2930, zzz2931, zzz2932, zzz2933, zzz2934, zzz350, zzz351, zzz352, zzz353, zzz354, zzz20780, Zero, h, ba) → new_glueVBal3GlueVBal24(zzz2930, zzz2931, zzz2932, zzz2933, zzz2934, zzz350, zzz351, zzz352, zzz353, zzz354, h, ba)
new_glueVBal3GlueVBal13(zzz2930, zzz2931, zzz2932, zzz2933, zzz2934, zzz350, zzz351, zzz352, zzz353, zzz354, Zero, Pos(Succ(zzz209600)), h, ba) → new_glueVBal3GlueVBal15(zzz2930, zzz2931, zzz2932, zzz2933, zzz2934, zzz350, zzz351, zzz352, zzz353, zzz354, Zero, zzz209600, h, ba)
new_glueVBal3GlueVBal23(zzz2930, zzz2931, zzz2932, zzz2933, zzz2934, zzz350, zzz351, zzz352, zzz353, zzz354, Zero, Zero, h, ba) → new_glueVBal3GlueVBal26(zzz2930, zzz2931, zzz2932, zzz2933, zzz2934, zzz350, zzz351, zzz352, zzz353, zzz354, h, ba)

The TRS R consists of the following rules:

new_primPlusNat1(Zero) → Zero
new_primPlusNat3(zzz90, Zero) → Succ(zzz90)
new_primMulNat(Zero) → Zero
new_glueVBal3Size_r(zzz2930, zzz2931, zzz2932, zzz2933, zzz2934, zzz350, zzz351, zzz352, zzz353, zzz354, h, ba) → new_sizeFM(Branch(zzz2930, zzz2931, zzz2932, zzz2933, zzz2934), h, ba)
new_glueVBal3Size_l(zzz2930, zzz2931, zzz2932, zzz2933, zzz2934, zzz350, zzz351, zzz352, zzz353, zzz354, h, ba) → new_sizeFM(Branch(zzz350, zzz351, zzz352, zzz353, zzz354), h, ba)
new_primPlusNat2(Zero, Zero) → Zero
new_primPlusNat2(Zero, Succ(zzz9100)) → Succ(zzz9100)
new_primPlusNat2(Succ(zzz900), Zero) → Succ(zzz900)
new_primPlusNat2(Succ(zzz900), Succ(zzz9100)) → Succ(Succ(new_primPlusNat2(zzz900, zzz9100)))
new_primMulNat0(zzz6200) → new_primPlusNat3(Succ(new_primPlusNat3(new_primPlusNat1(zzz6200), zzz6200)), Succ(zzz6200))
new_primPlusNat3(zzz90, Succ(zzz910)) → Succ(Succ(new_primPlusNat2(zzz90, zzz910)))
new_sizeFM(EmptyFM, bb, bc) → Pos(Zero)
new_primMulNat(Succ(zzz206300)) → new_primPlusNat2(new_primMulNat0(zzz206300), Succ(zzz206300))
new_sizeFM(Branch(zzz13040, zzz13041, zzz13042, zzz13043, zzz13044), bb, bc) → zzz13042
new_primPlusNat1(Succ(zzz62000)) → Succ(Succ(new_primPlusNat1(zzz62000)))

The set Q consists of the following terms:

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

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

↳ HASKELL
  ↳ LR
    ↳ HASKELL
      ↳ CR
        ↳ HASKELL
          ↳ IFR
            ↳ HASKELL
              ↳ BR
                ↳ HASKELL
                  ↳ COR
                    ↳ HASKELL
                      ↳ LetRed
                        ↳ HASKELL
                          ↳ NumRed
                            ↳ HASKELL
                              ↳ Narrow
                                ↳ AND
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                    ↳ DependencyGraphProof
                                      ↳ QDP
                                        ↳ UsableRulesProof
                                          ↳ 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_glueVBal3GlueVBal22(zzz2930, zzz2931, zzz2932, zzz2933, zzz2934, zzz350, zzz351, zzz352, zzz353, zzz354, Zero, Neg(Zero), h, ba) → new_glueVBal3GlueVBal26(zzz2930, zzz2931, zzz2932, zzz2933, zzz2934, zzz350, zzz351, zzz352, zzz353, zzz354, h, ba)
new_glueVBal3GlueVBal21(zzz2930, zzz2931, zzz2932, zzz2933, zzz2934, zzz350, zzz351, zzz352, zzz353, zzz354, Succ(Zero), Pos(Succ(Succ(zzz2048000))), h, ba) → new_glueVBal3GlueVBal25(zzz2930, zzz2931, zzz2932, zzz2933, zzz2934, zzz350, zzz351, zzz352, zzz353, zzz354, h, ba)
new_glueVBal3GlueVBal27(zzz2930, zzz2931, zzz2932, zzz2933, zzz2934, zzz350, zzz351, zzz352, zzz353, zzz354, Zero, zzz20800, h, ba) → new_glueVBal3GlueVBal25(zzz2930, zzz2931, zzz2932, zzz2933, zzz2934, zzz350, zzz351, zzz352, zzz353, zzz354, h, ba)
new_glueVBal3GlueVBal21(zzz2930, zzz2931, zzz2932, zzz2933, zzz2934, zzz350, zzz351, zzz352, zzz353, zzz354, Succ(Succ(zzz207800)), Pos(Succ(Succ(zzz2048000))), h, ba) → new_glueVBal3GlueVBal23(zzz2930, zzz2931, zzz2932, zzz2933, zzz2934, zzz350, zzz351, zzz352, zzz353, zzz354, zzz207800, zzz2048000, h, ba)
new_glueVBal3GlueVBal21(zzz2930, zzz2931, zzz2932, zzz2933, zzz2934, zzz350, zzz351, zzz352, zzz353, zzz354, Succ(Succ(zzz207800)), Pos(Succ(Zero)), h, ba) → new_glueVBal3GlueVBal24(zzz2930, zzz2931, zzz2932, zzz2933, zzz2934, zzz350, zzz351, zzz352, zzz353, zzz354, h, ba)
new_glueVBal3GlueVBal11(zzz2930, zzz2931, zzz2932, zzz2933, zzz2934, zzz350, zzz351, zzz352, zzz353, zzz354, zzz2096, h, ba) → new_glueVBal3GlueVBal12(zzz2930, zzz2931, zzz2932, zzz2933, zzz2934, zzz350, zzz351, zzz352, zzz353, zzz354, new_glueVBal3Size_r(zzz2930, zzz2931, zzz2932, zzz2933, zzz2934, zzz350, zzz351, zzz352, zzz353, zzz354, h, ba), zzz2096, h, ba)
new_glueVBal3GlueVBal23(zzz2930, zzz2931, zzz2932, zzz2933, zzz2934, zzz350, zzz351, zzz352, zzz353, zzz354, Succ(zzz207800), Succ(zzz2048000), h, ba) → new_glueVBal3GlueVBal23(zzz2930, zzz2931, zzz2932, zzz2933, zzz2934, zzz350, zzz351, zzz352, zzz353, zzz354, zzz207800, zzz2048000, h, ba)
new_glueVBal3GlueVBal22(zzz2930, zzz2931, zzz2932, zzz2933, zzz2934, zzz350, zzz351, zzz352, zzz353, zzz354, Succ(zzz20800), Neg(Zero), h, ba) → new_glueVBal3GlueVBal25(zzz2930, zzz2931, zzz2932, zzz2933, zzz2934, zzz350, zzz351, zzz352, zzz353, zzz354, h, ba)
new_glueVBal3GlueVBal23(zzz2930, zzz2931, zzz2932, zzz2933, zzz2934, zzz350, zzz351, zzz352, zzz353, zzz354, Zero, Succ(zzz2048000), h, ba) → new_glueVBal3GlueVBal25(zzz2930, zzz2931, zzz2932, zzz2933, zzz2934, zzz350, zzz351, zzz352, zzz353, zzz354, h, ba)
new_glueVBal3GlueVBal26(zzz2930, zzz2931, zzz2932, zzz2933, zzz2934, zzz350, zzz351, zzz352, zzz353, zzz354, h, ba) → new_glueVBal3GlueVBal28(zzz2930, zzz2931, zzz2932, zzz2933, zzz2934, zzz350, zzz351, zzz352, zzz353, zzz354, h, ba)
new_glueVBal3GlueVBal2(zzz2930, zzz2931, zzz2932, zzz2933, zzz2934, zzz350, zzz351, zzz352, zzz353, zzz354, zzz2048, h, ba) → new_glueVBal3GlueVBal20(zzz2930, zzz2931, zzz2932, zzz2933, zzz2934, zzz350, zzz351, zzz352, zzz353, zzz354, new_glueVBal3Size_l(zzz2930, zzz2931, zzz2932, zzz2933, zzz2934, zzz350, zzz351, zzz352, zzz353, zzz354, h, ba), zzz2048, h, ba)
new_glueVBal3GlueVBal1(zzz2930, zzz2931, zzz2932, zzz2933, zzz2934, zzz350, zzz351, zzz352, zzz353, zzz354, Zero, Succ(zzz2096000), h, ba) → new_glueVBal3GlueVBal10(zzz2930, zzz2931, zzz2932, zzz2933, zzz2934, zzz350, zzz351, zzz352, zzz353, zzz354, h, ba)
new_glueVBal3GlueVBal12(zzz2930, zzz2931, zzz2932, zzz2933, zzz2934, zzz350, zzz351, zzz352, zzz353, zzz354, Neg(zzz21000), zzz2096, h, ba) → new_glueVBal3GlueVBal14(zzz2930, zzz2931, zzz2932, zzz2933, zzz2934, zzz350, zzz351, zzz352, zzz353, zzz354, new_primMulNat(zzz21000), zzz2096, h, ba)
new_glueVBal3GlueVBal21(zzz2930, zzz2931, zzz2932, zzz2933, zzz2934, zzz350, zzz351, zzz352, zzz353, zzz354, Zero, Pos(Zero), h, ba) → new_glueVBal3GlueVBal28(zzz2930, zzz2931, zzz2932, zzz2933, zzz2934, zzz350, zzz351, zzz352, zzz353, zzz354, h, ba)
new_glueVBal3GlueVBal22(zzz2930, zzz2931, zzz2932, zzz2933, zzz2934, zzz350, zzz351, zzz352, zzz353, zzz354, Zero, Pos(Succ(zzz204800)), h, ba) → new_glueVBal3GlueVBal25(zzz2930, zzz2931, zzz2932, zzz2933, zzz2934, zzz350, zzz351, zzz352, zzz353, zzz354, h, ba)
new_glueVBal3GlueVBal22(zzz2930, zzz2931, zzz2932, zzz2933, zzz2934, zzz350, zzz351, zzz352, zzz353, zzz354, Zero, Neg(Succ(zzz204800)), h, ba) → new_glueVBal3GlueVBal29(zzz2930, zzz2931, zzz2932, zzz2933, zzz2934, zzz350, zzz351, zzz352, zzz353, zzz354, zzz204800, Zero, h, ba)
new_glueVBal3GlueVBal15(zzz2930, zzz2931, zzz2932, zzz2933, zzz2934, zzz350, zzz351, zzz352, zzz353, zzz354, Zero, zzz21030, h, ba) → new_glueVBal3GlueVBal10(zzz2930, zzz2931, zzz2932, zzz2933, zzz2934, zzz350, zzz351, zzz352, zzz353, zzz354, h, ba)
new_glueVBal3GlueVBal21(zzz2930, zzz2931, zzz2932, zzz2933, zzz2934, zzz350, zzz351, zzz352, zzz353, zzz354, Succ(Zero), Pos(Succ(Zero)), h, ba) → new_glueVBal3GlueVBal26(zzz2930, zzz2931, zzz2932, zzz2933, zzz2934, zzz350, zzz351, zzz352, zzz353, zzz354, h, ba)
new_glueVBal3GlueVBal21(zzz2930, zzz2931, zzz2932, zzz2933, zzz2934, zzz350, zzz351, zzz352, zzz353, zzz354, Succ(zzz20780), Neg(zzz20480), h, ba) → new_glueVBal3GlueVBal11(zzz2930, zzz2931, zzz2932, zzz2933, zzz2934, zzz350, zzz351, zzz352, zzz353, zzz354, new_glueVBal3Size_l(zzz2930, zzz2931, zzz2932, zzz2933, zzz2934, zzz350, zzz351, zzz352, zzz353, zzz354, h, ba), h, ba)
new_glueVBal3(zzz350, zzz351, zzz352, zzz353, zzz354, zzz29330, zzz29331, zzz29332, zzz29333, zzz29334, h, ba) → new_glueVBal3GlueVBal2(zzz29330, zzz29331, zzz29332, zzz29333, zzz29334, zzz350, zzz351, zzz352, zzz353, zzz354, new_glueVBal3Size_r(zzz29330, zzz29331, zzz29332, zzz29333, zzz29334, zzz350, zzz351, zzz352, zzz353, zzz354, h, ba), h, ba)
new_glueVBal3GlueVBal24(zzz2930, zzz2931, zzz2932, zzz2933, zzz2934, zzz350, zzz351, zzz352, zzz353, zzz354, h, ba) → new_glueVBal3GlueVBal11(zzz2930, zzz2931, zzz2932, zzz2933, zzz2934, zzz350, zzz351, zzz352, zzz353, zzz354, new_glueVBal3Size_l(zzz2930, zzz2931, zzz2932, zzz2933, zzz2934, zzz350, zzz351, zzz352, zzz353, zzz354, h, ba), h, ba)
new_glueVBal3GlueVBal22(zzz2930, zzz2931, zzz2932, zzz2933, zzz2934, zzz350, zzz351, zzz352, zzz353, zzz354, Zero, Pos(Zero), h, ba) → new_glueVBal3GlueVBal26(zzz2930, zzz2931, zzz2932, zzz2933, zzz2934, zzz350, zzz351, zzz352, zzz353, zzz354, h, ba)
new_glueVBal3GlueVBal10(zzz2930, zzz2931, zzz2932, zzz2933, zzz2934, zzz350, zzz351, zzz352, zzz353, Branch(zzz3540, zzz3541, zzz3542, zzz3543, zzz3544), h, ba) → new_glueVBal3(zzz3540, zzz3541, zzz3542, zzz3543, zzz3544, zzz2930, zzz2931, zzz2932, zzz2933, zzz2934, h, ba)
new_glueVBal3GlueVBal1(zzz2930, zzz2931, zzz2932, zzz2933, zzz2934, zzz350, zzz351, zzz352, zzz353, zzz354, Succ(zzz210200), Succ(zzz2096000), h, ba) → new_glueVBal3GlueVBal1(zzz2930, zzz2931, zzz2932, zzz2933, zzz2934, zzz350, zzz351, zzz352, zzz353, zzz354, zzz210200, zzz2096000, h, ba)
new_glueVBal3GlueVBal21(zzz2930, zzz2931, zzz2932, zzz2933, zzz2934, zzz350, zzz351, zzz352, zzz353, zzz354, Zero, Neg(Zero), h, ba) → new_glueVBal3GlueVBal26(zzz2930, zzz2931, zzz2932, zzz2933, zzz2934, zzz350, zzz351, zzz352, zzz353, zzz354, h, ba)
new_glueVBal3GlueVBal21(zzz2930, zzz2931, zzz2932, zzz2933, zzz2934, zzz350, zzz351, zzz352, zzz353, zzz354, Zero, Pos(Succ(zzz204800)), h, ba) → new_glueVBal3GlueVBal27(zzz2930, zzz2931, zzz2932, zzz2933, zzz2934, zzz350, zzz351, zzz352, zzz353, zzz354, Zero, zzz204800, h, ba)
new_glueVBal3GlueVBal14(zzz2930, zzz2931, zzz2932, zzz2933, zzz2934, zzz350, zzz351, zzz352, zzz353, zzz354, Succ(zzz21030), Neg(Succ(zzz209600)), h, ba) → new_glueVBal3GlueVBal1(zzz2930, zzz2931, zzz2932, zzz2933, zzz2934, zzz350, zzz351, zzz352, zzz353, zzz354, zzz209600, zzz21030, h, ba)
new_glueVBal3GlueVBal14(zzz2930, zzz2931, zzz2932, zzz2933, zzz2934, zzz350, zzz351, zzz352, zzz353, zzz354, Succ(zzz21030), Neg(Zero), h, ba) → new_glueVBal3GlueVBal10(zzz2930, zzz2931, zzz2932, zzz2933, zzz2934, zzz350, zzz351, zzz352, zzz353, zzz354, h, ba)
new_glueVBal3GlueVBal21(zzz2930, zzz2931, zzz2932, zzz2933, zzz2934, zzz350, zzz351, zzz352, zzz353, zzz354, Succ(zzz20780), Pos(Zero), h, ba) → new_glueVBal3GlueVBal24(zzz2930, zzz2931, zzz2932, zzz2933, zzz2934, zzz350, zzz351, zzz352, zzz353, zzz354, h, ba)
new_glueVBal3GlueVBal25(zzz2930, zzz2931, zzz2932, Branch(zzz29330, zzz29331, zzz29332, zzz29333, zzz29334), zzz2934, zzz350, zzz351, zzz352, zzz353, zzz354, h, ba) → new_glueVBal3GlueVBal2(zzz29330, zzz29331, zzz29332, zzz29333, zzz29334, zzz350, zzz351, zzz352, zzz353, zzz354, new_glueVBal3Size_r(zzz29330, zzz29331, zzz29332, zzz29333, zzz29334, zzz350, zzz351, zzz352, zzz353, zzz354, h, ba), h, ba)
new_glueVBal3GlueVBal14(zzz2930, zzz2931, zzz2932, zzz2933, zzz2934, zzz350, zzz351, zzz352, zzz353, zzz354, Zero, Pos(Succ(zzz209600)), h, ba) → new_glueVBal3GlueVBal10(zzz2930, zzz2931, zzz2932, zzz2933, zzz2934, zzz350, zzz351, zzz352, zzz353, zzz354, h, ba)
new_glueVBal3GlueVBal23(zzz2930, zzz2931, zzz2932, zzz2933, zzz2934, zzz350, zzz351, zzz352, zzz353, zzz354, Succ(zzz207800), Zero, h, ba) → new_glueVBal3GlueVBal24(zzz2930, zzz2931, zzz2932, zzz2933, zzz2934, zzz350, zzz351, zzz352, zzz353, zzz354, h, ba)
new_glueVBal3GlueVBal20(zzz2930, zzz2931, zzz2932, zzz2933, zzz2934, zzz350, zzz351, zzz352, zzz353, zzz354, Pos(zzz20630), zzz2048, h, ba) → new_glueVBal3GlueVBal21(zzz2930, zzz2931, zzz2932, zzz2933, zzz2934, zzz350, zzz351, zzz352, zzz353, zzz354, new_primMulNat(zzz20630), zzz2048, h, ba)
new_glueVBal3GlueVBal13(zzz2930, zzz2931, zzz2932, zzz2933, zzz2934, zzz350, zzz351, zzz352, zzz353, zzz354, Succ(Succ(zzz210200)), Pos(Succ(Succ(zzz2096000))), h, ba) → new_glueVBal3GlueVBal1(zzz2930, zzz2931, zzz2932, zzz2933, zzz2934, zzz350, zzz351, zzz352, zzz353, zzz354, zzz210200, zzz2096000, h, ba)
new_glueVBal3GlueVBal12(zzz2930, zzz2931, zzz2932, zzz2933, zzz2934, zzz350, zzz351, zzz352, zzz353, zzz354, Pos(zzz21000), zzz2096, h, ba) → new_glueVBal3GlueVBal13(zzz2930, zzz2931, zzz2932, zzz2933, zzz2934, zzz350, zzz351, zzz352, zzz353, zzz354, new_primMulNat(zzz21000), zzz2096, h, ba)
new_glueVBal3GlueVBal14(zzz2930, zzz2931, zzz2932, zzz2933, zzz2934, zzz350, zzz351, zzz352, zzz353, Branch(zzz3540, zzz3541, zzz3542, zzz3543, zzz3544), Succ(zzz21030), Pos(zzz20960), h, ba) → new_glueVBal3(zzz3540, zzz3541, zzz3542, zzz3543, zzz3544, zzz2930, zzz2931, zzz2932, zzz2933, zzz2934, h, ba)
new_glueVBal3GlueVBal22(zzz2930, zzz2931, zzz2932, Branch(zzz29330, zzz29331, zzz29332, zzz29333, zzz29334), zzz2934, zzz350, zzz351, zzz352, zzz353, zzz354, Succ(zzz20800), Pos(zzz20480), h, ba) → new_glueVBal3GlueVBal2(zzz29330, zzz29331, zzz29332, zzz29333, zzz29334, zzz350, zzz351, zzz352, zzz353, zzz354, new_glueVBal3Size_r(zzz29330, zzz29331, zzz29332, zzz29333, zzz29334, zzz350, zzz351, zzz352, zzz353, zzz354, h, ba), h, ba)
new_glueVBal3GlueVBal28(zzz2930, zzz2931, zzz2932, zzz2933, zzz2934, zzz350, zzz351, zzz352, zzz353, zzz354, h, ba) → new_glueVBal3GlueVBal11(zzz2930, zzz2931, zzz2932, zzz2933, zzz2934, zzz350, zzz351, zzz352, zzz353, zzz354, new_glueVBal3Size_l(zzz2930, zzz2931, zzz2932, zzz2933, zzz2934, zzz350, zzz351, zzz352, zzz353, zzz354, h, ba), h, ba)
new_glueVBal3GlueVBal20(zzz2930, zzz2931, zzz2932, zzz2933, zzz2934, zzz350, zzz351, zzz352, zzz353, zzz354, Neg(zzz20630), zzz2048, h, ba) → new_glueVBal3GlueVBal22(zzz2930, zzz2931, zzz2932, zzz2933, zzz2934, zzz350, zzz351, zzz352, zzz353, zzz354, new_primMulNat(zzz20630), zzz2048, h, ba)
new_glueVBal3GlueVBal21(zzz2930, zzz2931, zzz2932, zzz2933, zzz2934, zzz350, zzz351, zzz352, zzz353, zzz354, Zero, Neg(Succ(zzz204800)), h, ba) → new_glueVBal3GlueVBal24(zzz2930, zzz2931, zzz2932, zzz2933, zzz2934, zzz350, zzz351, zzz352, zzz353, zzz354, h, ba)
new_glueVBal3GlueVBal22(zzz2930, zzz2931, zzz2932, zzz2933, zzz2934, zzz350, zzz351, zzz352, zzz353, zzz354, Succ(zzz20800), Neg(Succ(zzz204800)), h, ba) → new_glueVBal3GlueVBal23(zzz2930, zzz2931, zzz2932, zzz2933, zzz2934, zzz350, zzz351, zzz352, zzz353, zzz354, zzz204800, zzz20800, h, ba)
new_glueVBal3GlueVBal13(zzz2930, zzz2931, zzz2932, zzz2933, zzz2934, zzz350, zzz351, zzz352, zzz353, zzz354, Succ(Zero), Pos(Succ(Succ(zzz2096000))), h, ba) → new_glueVBal3GlueVBal10(zzz2930, zzz2931, zzz2932, zzz2933, zzz2934, zzz350, zzz351, zzz352, zzz353, zzz354, h, ba)
new_glueVBal3GlueVBal29(zzz2930, zzz2931, zzz2932, zzz2933, zzz2934, zzz350, zzz351, zzz352, zzz353, zzz354, zzz20780, Zero, h, ba) → new_glueVBal3GlueVBal24(zzz2930, zzz2931, zzz2932, zzz2933, zzz2934, zzz350, zzz351, zzz352, zzz353, zzz354, h, ba)
new_glueVBal3GlueVBal13(zzz2930, zzz2931, zzz2932, zzz2933, zzz2934, zzz350, zzz351, zzz352, zzz353, zzz354, Zero, Pos(Succ(zzz209600)), h, ba) → new_glueVBal3GlueVBal15(zzz2930, zzz2931, zzz2932, zzz2933, zzz2934, zzz350, zzz351, zzz352, zzz353, zzz354, Zero, zzz209600, h, ba)
new_glueVBal3GlueVBal23(zzz2930, zzz2931, zzz2932, zzz2933, zzz2934, zzz350, zzz351, zzz352, zzz353, zzz354, Zero, Zero, h, ba) → new_glueVBal3GlueVBal26(zzz2930, zzz2931, zzz2932, zzz2933, zzz2934, zzz350, zzz351, zzz352, zzz353, zzz354, h, ba)

The TRS R consists of the following rules:

new_glueVBal3Size_l(zzz2930, zzz2931, zzz2932, zzz2933, zzz2934, zzz350, zzz351, zzz352, zzz353, zzz354, h, ba) → new_sizeFM(Branch(zzz350, zzz351, zzz352, zzz353, zzz354), h, ba)
new_sizeFM(Branch(zzz13040, zzz13041, zzz13042, zzz13043, zzz13044), bb, bc) → zzz13042
new_primMulNat(Zero) → Zero
new_primMulNat(Succ(zzz206300)) → new_primPlusNat2(new_primMulNat0(zzz206300), Succ(zzz206300))
new_primMulNat0(zzz6200) → new_primPlusNat3(Succ(new_primPlusNat3(new_primPlusNat1(zzz6200), zzz6200)), Succ(zzz6200))
new_primPlusNat2(Zero, Succ(zzz9100)) → Succ(zzz9100)
new_primPlusNat2(Succ(zzz900), Succ(zzz9100)) → Succ(Succ(new_primPlusNat2(zzz900, zzz9100)))
new_primPlusNat2(Zero, Zero) → Zero
new_primPlusNat2(Succ(zzz900), Zero) → Succ(zzz900)
new_primPlusNat1(Zero) → Zero
new_primPlusNat1(Succ(zzz62000)) → Succ(Succ(new_primPlusNat1(zzz62000)))
new_primPlusNat3(zzz90, Zero) → Succ(zzz90)
new_primPlusNat3(zzz90, Succ(zzz910)) → Succ(Succ(new_primPlusNat2(zzz90, zzz910)))
new_glueVBal3Size_r(zzz2930, zzz2931, zzz2932, zzz2933, zzz2934, zzz350, zzz351, zzz352, zzz353, zzz354, h, ba) → new_sizeFM(Branch(zzz2930, zzz2931, zzz2932, zzz2933, zzz2934), h, ba)

The set Q consists of the following terms:

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

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

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



↳ HASKELL
  ↳ LR
    ↳ HASKELL
      ↳ CR
        ↳ HASKELL
          ↳ IFR
            ↳ HASKELL
              ↳ BR
                ↳ HASKELL
                  ↳ COR
                    ↳ HASKELL
                      ↳ LetRed
                        ↳ HASKELL
                          ↳ NumRed
                            ↳ HASKELL
                              ↳ Narrow
                                ↳ AND
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                    ↳ 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_splitGT(Branch(LT, zzz21291, zzz21292, zzz21293, zzz21294), h) → new_splitGT(zzz21294, h)
new_splitGT(Branch(EQ, zzz21291, zzz21292, zzz21293, zzz21294), h) → new_splitGT(zzz21294, 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
                                    ↳ QDPSizeChangeProof
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP

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

new_addToFM_C(Branch(LT, zzz341, zzz342, zzz343, zzz344), zzz31, h) → new_addToFM_C(zzz344, zzz31, h)
new_addToFM_C(Branch(EQ, zzz341, zzz342, zzz343, zzz344), zzz31, h) → new_addToFM_C(zzz344, zzz31, 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
                                    ↳ DependencyGraphProof
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP

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

new_mkVBalBranch3MkVBalBranch11(zzz2033, zzz2034, zzz2035, zzz2036, zzz2037, zzz2038, zzz2039, zzz2040, zzz2041, zzz2042, zzz2043, Zero, Succ(zzz20450), bb) → new_mkVBalBranch(zzz2043, zzz2042, Branch(zzz2033, zzz2034, Pos(Succ(zzz2035)), zzz2036, zzz2037), bb)
new_mkVBalBranch3MkVBalBranch26(zzz1133, zzz1134, zzz1135, zzz1136, zzz1137, zzz1138, zzz1139, zzz1140, zzz1141, zzz1142, Succ(zzz11430), Succ(zzz11440), be) → new_mkVBalBranch3MkVBalBranch26(zzz1133, zzz1134, zzz1135, zzz1136, zzz1137, zzz1138, zzz1139, zzz1140, zzz1141, zzz1142, zzz11430, zzz11440, be)
new_mkVBalBranch3MkVBalBranch24(zzz340, zzz341, Neg(Succ(Succ(Succ(zzz3420000)))), zzz343, zzz344, zzz520, zzz521, Zero, zzz523, zzz524, zzz31, Succ(Zero), h) → new_mkVBalBranch3MkVBalBranch26(zzz340, zzz341, Succ(Succ(zzz3420000)), zzz343, zzz344, zzz520, zzz521, zzz523, zzz524, zzz31, Succ(zzz3420000), Zero, h)
new_mkVBalBranch3MkVBalBranch15(zzz537, zzz538, zzz539, zzz540, zzz541, zzz542, zzz543, zzz544, zzz545, zzz546, zzz547, Zero, bc) → new_mkVBalBranch3MkVBalBranch16(zzz537, zzz538, zzz539, zzz540, zzz541, zzz542, zzz543, Succ(zzz544), zzz545, zzz546, zzz547, Succ(Succ(zzz544)), Zero, bc)
new_mkVBalBranch3MkVBalBranch24(zzz340, zzz341, Neg(Succ(Zero)), zzz343, zzz344, zzz520, zzz521, Zero, zzz523, zzz524, zzz31, Zero, h) → new_mkVBalBranch3MkVBalBranch29(zzz340, zzz341, Zero, zzz343, zzz344, zzz520, zzz521, zzz523, zzz524, zzz31, h)
new_mkVBalBranch3MkVBalBranch20(zzz929, zzz930, zzz931, zzz932, zzz933, zzz934, zzz935, zzz936, zzz937, zzz938, zzz939, Zero, Succ(zzz9410), ba) → new_mkVBalBranch(zzz939, Branch(zzz934, zzz935, Pos(Succ(zzz936)), zzz937, zzz938), zzz932, ba)
new_mkVBalBranch3MkVBalBranch17(zzz340, zzz341, zzz34200, zzz343, zzz344, zzz520, zzz521, zzz52200, zzz523, zzz524, zzz31, h) → new_mkVBalBranch(zzz31, zzz524, Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), h)
new_mkVBalBranch3MkVBalBranch26(zzz1133, zzz1134, zzz1135, zzz1136, zzz1137, zzz1138, zzz1139, zzz1140, zzz1141, zzz1142, Zero, Zero, be) → new_mkVBalBranch3MkVBalBranch29(zzz1133, zzz1134, zzz1135, zzz1136, zzz1137, zzz1138, zzz1139, zzz1140, zzz1141, zzz1142, be)
new_mkVBalBranch3MkVBalBranch20(zzz929, zzz930, zzz931, zzz932, zzz933, zzz934, zzz935, zzz936, zzz937, zzz938, zzz939, Zero, Zero, ba) → new_mkVBalBranch3MkVBalBranch23(zzz929, zzz930, zzz931, zzz932, zzz933, zzz934, zzz935, zzz936, zzz937, zzz938, zzz939, ba)
new_mkVBalBranch(zzz31, Branch(zzz520, zzz521, Pos(Zero), zzz523, zzz524), Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), h) → new_mkVBalBranch3MkVBalBranch12(zzz340, zzz341, zzz34200, zzz343, zzz344, zzz520, zzz521, zzz523, zzz524, zzz31, new_primMulNat1(zzz34200), h)
new_mkVBalBranch3MkVBalBranch24(zzz340, zzz341, Neg(Succ(Succ(Zero))), zzz343, zzz344, zzz520, zzz521, Succ(zzz522000), zzz523, zzz524, zzz31, Succ(Zero), h) → new_mkVBalBranch3MkVBalBranch25(zzz340, zzz341, Succ(Zero), zzz343, zzz344, zzz520, zzz521, zzz522000, zzz523, zzz524, zzz31, Zero, Succ(zzz522000), h)
new_mkVBalBranch3MkVBalBranch20(zzz929, zzz930, zzz931, zzz932, zzz933, zzz934, zzz935, zzz936, zzz937, zzz938, zzz939, Succ(zzz9400), Succ(zzz9410), ba) → new_mkVBalBranch3MkVBalBranch20(zzz929, zzz930, zzz931, zzz932, zzz933, zzz934, zzz935, zzz936, zzz937, zzz938, zzz939, zzz9400, zzz9410, ba)
new_mkVBalBranch3MkVBalBranch24(zzz340, zzz341, Neg(Succ(Succ(Succ(zzz3420000)))), zzz343, zzz344, zzz520, zzz521, Succ(zzz522000), zzz523, zzz524, zzz31, Succ(Zero), h) → new_mkVBalBranch3MkVBalBranch25(zzz340, zzz341, Succ(Succ(zzz3420000)), zzz343, zzz344, zzz520, zzz521, zzz522000, zzz523, zzz524, zzz31, Succ(zzz3420000), Succ(zzz522000), h)
new_mkVBalBranch3MkVBalBranch24(zzz340, zzz341, Neg(Succ(Succ(zzz342000))), zzz343, zzz344, zzz520, zzz521, Succ(zzz522000), zzz523, zzz524, zzz31, Zero, h) → new_mkVBalBranch3MkVBalBranch25(zzz340, zzz341, Succ(zzz342000), zzz343, zzz344, zzz520, zzz521, zzz522000, zzz523, zzz524, zzz31, zzz342000, zzz522000, h)
new_mkVBalBranch3MkVBalBranch26(zzz1133, zzz1134, zzz1135, zzz1136, zzz1137, zzz1138, zzz1139, zzz1140, zzz1141, zzz1142, Succ(zzz11430), Zero, be) → new_mkVBalBranch3MkVBalBranch212(zzz1133, zzz1134, zzz1135, zzz1136, zzz1137, zzz1138, zzz1139, zzz1140, zzz1141, zzz1142, be)
new_mkVBalBranch3MkVBalBranch214(zzz340, zzz341, zzz342000, zzz343, zzz344, zzz520, zzz521, zzz523, zzz524, zzz31, h) → new_mkVBalBranch3MkVBalBranch14(zzz340, zzz341, Succ(zzz342000), zzz343, zzz344, zzz520, zzz521, zzz523, zzz524, zzz31, new_primMulNat1(Succ(zzz342000)), h)
new_mkVBalBranch3MkVBalBranch11(zzz2033, zzz2034, zzz2035, zzz2036, zzz2037, zzz2038, zzz2039, zzz2040, zzz2041, zzz2042, zzz2043, Succ(zzz20440), Succ(zzz20450), bb) → new_mkVBalBranch3MkVBalBranch11(zzz2033, zzz2034, zzz2035, zzz2036, zzz2037, zzz2038, zzz2039, zzz2040, zzz2041, zzz2042, zzz2043, zzz20440, zzz20450, bb)
new_mkVBalBranch3MkVBalBranch25(zzz537, zzz538, zzz539, zzz540, zzz541, zzz542, zzz543, zzz544, zzz545, zzz546, zzz547, Succ(zzz5480), Succ(zzz5490), bc) → new_mkVBalBranch3MkVBalBranch25(zzz537, zzz538, zzz539, zzz540, zzz541, zzz542, zzz543, zzz544, zzz545, zzz546, zzz547, zzz5480, zzz5490, bc)
new_mkVBalBranch3MkVBalBranch2(zzz340, zzz341, Neg(zzz3420), zzz343, zzz344, zzz520, zzz521, zzz52200, zzz523, zzz524, zzz31, Zero, h) → new_mkVBalBranch3MkVBalBranch22(zzz340, zzz341, zzz3420, zzz343, zzz344, zzz520, zzz521, zzz52200, zzz523, zzz524, zzz31, h)
new_mkVBalBranch3MkVBalBranch24(zzz340, zzz341, Neg(Succ(Zero)), zzz343, zzz344, zzz520, zzz521, Succ(zzz522000), zzz523, zzz524, zzz31, Zero, h) → new_mkVBalBranch3MkVBalBranch28(zzz340, zzz341, zzz343, zzz344, zzz520, zzz521, Succ(zzz522000), zzz523, zzz524, zzz31, h)
new_mkVBalBranch3MkVBalBranch24(zzz340, zzz341, Neg(Succ(Succ(zzz342000))), zzz343, zzz344, zzz520, zzz521, Zero, zzz523, zzz524, zzz31, Zero, h) → new_mkVBalBranch3MkVBalBranch14(zzz340, zzz341, Succ(zzz342000), zzz343, zzz344, zzz520, zzz521, zzz523, zzz524, zzz31, new_primMulNat1(Succ(zzz342000)), h)
new_mkVBalBranch3MkVBalBranch210(zzz340, zzz341, zzz343, zzz344, zzz520, zzz521, zzz52200, zzz523, zzz524, zzz31, h) → new_mkVBalBranch(zzz31, Branch(zzz520, zzz521, Neg(Succ(zzz52200)), zzz523, zzz524), zzz343, h)
new_mkVBalBranch3MkVBalBranch26(zzz1133, zzz1134, zzz1135, zzz1136, zzz1137, zzz1138, zzz1139, zzz1140, zzz1141, zzz1142, Zero, Succ(zzz11440), be) → new_mkVBalBranch(zzz1142, Branch(zzz1138, zzz1139, Neg(Succ(Zero)), zzz1140, zzz1141), zzz1136, be)
new_mkVBalBranch3MkVBalBranch24(zzz340, zzz341, Neg(Succ(Succ(Zero))), zzz343, zzz344, zzz520, zzz521, Zero, zzz523, zzz524, zzz31, Succ(Zero), h) → new_mkVBalBranch3MkVBalBranch26(zzz340, zzz341, Succ(Zero), zzz343, zzz344, zzz520, zzz521, zzz523, zzz524, zzz31, Zero, Zero, h)
new_mkVBalBranch(zzz31, Branch(zzz520, zzz521, Pos(Zero), zzz523, zzz524), Branch(zzz340, zzz341, Pos(Succ(zzz34200)), zzz343, zzz344), h) → new_mkVBalBranch(zzz31, Branch(zzz520, zzz521, Pos(Zero), zzz523, zzz524), zzz343, h)
new_mkVBalBranch3MkVBalBranch29(zzz818, zzz819, zzz820, zzz821, zzz822, zzz823, zzz824, zzz825, zzz826, zzz827, bf) → new_mkVBalBranch3MkVBalBranch14(zzz818, zzz819, zzz820, zzz821, zzz822, zzz823, zzz824, zzz825, zzz826, zzz827, new_primMulNat1(zzz820), bf)
new_mkVBalBranch3MkVBalBranch2(zzz340, zzz341, Pos(Zero), zzz343, zzz344, zzz520, zzz521, zzz52200, zzz523, zzz524, zzz31, Succ(zzz680), h) → new_mkVBalBranch(zzz31, zzz524, Branch(zzz340, zzz341, Pos(Zero), zzz343, zzz344), h)
new_mkVBalBranch3MkVBalBranch21(zzz340, zzz341, zzz343, zzz344, zzz520, zzz521, zzz52200, zzz523, zzz524, zzz31, h) → new_mkVBalBranch(zzz31, zzz524, Branch(zzz340, zzz341, Pos(Zero), zzz343, zzz344), h)
new_mkVBalBranch(zzz31, Branch(zzz520, zzz521, Neg(Succ(zzz52200)), zzz523, zzz524), Branch(zzz340, zzz341, zzz342, zzz343, zzz344), h) → new_mkVBalBranch3MkVBalBranch24(zzz340, zzz341, zzz342, zzz343, zzz344, zzz520, zzz521, zzz52200, zzz523, zzz524, zzz31, new_primMulNat0(zzz52200), h)
new_mkVBalBranch3MkVBalBranch24(zzz340, zzz341, Pos(zzz3420), zzz343, zzz344, zzz520, zzz521, zzz52200, zzz523, zzz524, zzz31, Zero, h) → new_mkVBalBranch3MkVBalBranch27(zzz340, zzz341, zzz3420, zzz343, zzz344, zzz520, zzz521, zzz52200, zzz523, zzz524, zzz31, h)
new_mkVBalBranch3MkVBalBranch23(zzz929, zzz930, zzz931, zzz932, zzz933, zzz934, zzz935, zzz936, zzz937, zzz938, zzz939, ba) → new_mkVBalBranch3MkVBalBranch10(zzz929, zzz930, zzz931, zzz932, zzz933, zzz934, zzz935, zzz936, zzz937, zzz938, zzz939, new_primMulNat1(zzz931), ba)
new_mkVBalBranch3MkVBalBranch212(zzz818, zzz819, zzz820, zzz821, zzz822, zzz823, zzz824, zzz825, zzz826, zzz827, bf) → new_mkVBalBranch3MkVBalBranch14(zzz818, zzz819, zzz820, zzz821, zzz822, zzz823, zzz824, zzz825, zzz826, zzz827, new_primMulNat1(zzz820), bf)
new_mkVBalBranch3MkVBalBranch211(zzz537, zzz538, zzz539, zzz540, zzz541, zzz542, zzz543, zzz544, zzz545, zzz546, zzz547, bc) → new_mkVBalBranch3MkVBalBranch15(zzz537, zzz538, zzz539, zzz540, zzz541, zzz542, zzz543, zzz544, zzz545, zzz546, zzz547, new_primMulNat1(zzz539), bc)
new_mkVBalBranch3MkVBalBranch24(zzz340, zzz341, Neg(Succ(Succ(Succ(zzz3420000)))), zzz343, zzz344, zzz520, zzz521, Zero, zzz523, zzz524, zzz31, Succ(Succ(zzz6900)), h) → new_mkVBalBranch3MkVBalBranch26(zzz340, zzz341, Succ(Succ(zzz3420000)), zzz343, zzz344, zzz520, zzz521, zzz523, zzz524, zzz31, Succ(zzz3420000), Succ(zzz6900), h)
new_mkVBalBranch3MkVBalBranch15(zzz537, zzz538, zzz539, zzz540, zzz541, zzz542, zzz543, zzz544, zzz545, zzz546, zzz547, Succ(zzz6990), bc) → new_mkVBalBranch3MkVBalBranch16(zzz537, zzz538, zzz539, zzz540, zzz541, zzz542, zzz543, Succ(zzz544), zzz545, zzz546, zzz547, Succ(Succ(zzz544)), Succ(zzz6990), bc)
new_mkVBalBranch3MkVBalBranch27(zzz340, zzz341, zzz3420, zzz343, zzz344, zzz520, zzz521, zzz52200, zzz523, zzz524, zzz31, h) → new_mkVBalBranch(zzz31, Branch(zzz520, zzz521, Neg(Succ(zzz52200)), zzz523, zzz524), zzz343, h)
new_mkVBalBranch3MkVBalBranch24(zzz340, zzz341, Pos(zzz3420), zzz343, zzz344, zzz520, zzz521, zzz52200, zzz523, zzz524, zzz31, Succ(zzz690), h) → new_mkVBalBranch(zzz31, Branch(zzz520, zzz521, Neg(Succ(zzz52200)), zzz523, zzz524), zzz343, h)
new_mkVBalBranch3MkVBalBranch12(zzz340, zzz341, zzz34200, zzz343, zzz344, zzz520, zzz521, zzz523, zzz524, zzz31, Succ(zzz1250), h) → new_mkVBalBranch(zzz31, zzz524, Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), h)
new_mkVBalBranch3MkVBalBranch213(zzz340, zzz341, zzz342000, zzz343, zzz344, zzz520, zzz521, zzz523, zzz524, zzz31, h) → new_mkVBalBranch3MkVBalBranch14(zzz340, zzz341, Succ(zzz342000), zzz343, zzz344, zzz520, zzz521, zzz523, zzz524, zzz31, new_primMulNat1(Succ(zzz342000)), h)
new_mkVBalBranch3MkVBalBranch28(zzz340, zzz341, zzz343, zzz344, zzz520, zzz521, zzz52200, zzz523, zzz524, zzz31, h) → new_mkVBalBranch(zzz31, Branch(zzz520, zzz521, Neg(Succ(zzz52200)), zzz523, zzz524), zzz343, h)
new_mkVBalBranch3MkVBalBranch25(zzz537, zzz538, zzz539, zzz540, zzz541, zzz542, zzz543, zzz544, zzz545, zzz546, zzz547, Succ(zzz5480), Zero, bc) → new_mkVBalBranch3MkVBalBranch15(zzz537, zzz538, zzz539, zzz540, zzz541, zzz542, zzz543, zzz544, zzz545, zzz546, zzz547, new_primMulNat1(zzz539), bc)
new_mkVBalBranch3MkVBalBranch24(zzz340, zzz341, Neg(Succ(Succ(Zero))), zzz343, zzz344, zzz520, zzz521, Zero, zzz523, zzz524, zzz31, Succ(Succ(zzz6900)), h) → new_mkVBalBranch3MkVBalBranch26(zzz340, zzz341, Succ(Zero), zzz343, zzz344, zzz520, zzz521, zzz523, zzz524, zzz31, Zero, Succ(zzz6900), h)
new_mkVBalBranch3MkVBalBranch1(zzz340, zzz341, zzz34200, zzz343, zzz344, zzz520, zzz521, zzz52200, zzz523, zzz524, zzz31, Succ(zzz1430), h) → new_mkVBalBranch(zzz31, zzz524, Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), h)
new_mkVBalBranch3MkVBalBranch22(zzz340, zzz341, Zero, zzz343, zzz344, zzz520, zzz521, zzz52200, zzz523, zzz524, zzz31, h) → new_mkVBalBranch(zzz31, zzz524, Branch(zzz340, zzz341, Neg(Zero), zzz343, zzz344), h)
new_mkVBalBranch3MkVBalBranch22(zzz340, zzz341, Succ(zzz34200), zzz343, zzz344, zzz520, zzz521, zzz52200, zzz523, zzz524, zzz31, h) → new_mkVBalBranch3MkVBalBranch1(zzz340, zzz341, zzz34200, zzz343, zzz344, zzz520, zzz521, zzz52200, zzz523, zzz524, zzz31, new_primPlusNat2(new_primMulNat0(zzz34200), Succ(zzz34200)), h)
new_mkVBalBranch3MkVBalBranch24(zzz340, zzz341, Neg(Succ(Zero)), zzz343, zzz344, zzz520, zzz521, zzz52200, zzz523, zzz524, zzz31, Succ(zzz690), h) → new_mkVBalBranch(zzz31, Branch(zzz520, zzz521, Neg(Succ(zzz52200)), zzz523, zzz524), zzz343, h)
new_mkVBalBranch3MkVBalBranch13(zzz340, zzz341, zzz34200, zzz343, zzz344, zzz520, zzz521, zzz523, zzz524, zzz31, Succ(zzz1290), h) → new_mkVBalBranch(zzz31, zzz524, Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), h)
new_mkVBalBranch3MkVBalBranch2(zzz340, zzz341, Pos(Succ(zzz34200)), zzz343, zzz344, zzz520, zzz521, zzz52200, zzz523, zzz524, zzz31, Succ(zzz680), h) → new_mkVBalBranch3MkVBalBranch20(zzz340, zzz341, zzz34200, zzz343, zzz344, zzz520, zzz521, zzz52200, zzz523, zzz524, zzz31, Succ(new_primPlusNat2(zzz680, zzz52200)), zzz34200, h)
new_mkVBalBranch3MkVBalBranch24(zzz340, zzz341, Neg(Zero), zzz343, zzz344, zzz520, zzz521, zzz52200, zzz523, zzz524, zzz31, Succ(zzz690), h) → new_mkVBalBranch(zzz31, Branch(zzz520, zzz521, Neg(Succ(zzz52200)), zzz523, zzz524), zzz343, h)
new_mkVBalBranch(zzz31, Branch(zzz520, zzz521, Neg(Zero), zzz523, zzz524), Branch(zzz340, zzz341, Pos(Succ(zzz34200)), zzz343, zzz344), h) → new_mkVBalBranch(zzz31, Branch(zzz520, zzz521, Neg(Zero), zzz523, zzz524), zzz343, h)
new_mkVBalBranch3MkVBalBranch1(zzz340, zzz341, zzz34200, zzz343, zzz344, zzz520, zzz521, zzz52200, zzz523, zzz524, zzz31, Zero, h) → new_mkVBalBranch3MkVBalBranch17(zzz340, zzz341, zzz34200, zzz343, zzz344, zzz520, zzz521, zzz52200, zzz523, zzz524, zzz31, h)
new_mkVBalBranch3MkVBalBranch16(zzz1702, zzz1703, zzz1704, zzz1705, zzz1706, zzz1707, zzz1708, zzz1709, zzz1710, zzz1711, zzz1712, Succ(zzz17130), Succ(zzz17140), bd) → new_mkVBalBranch3MkVBalBranch16(zzz1702, zzz1703, zzz1704, zzz1705, zzz1706, zzz1707, zzz1708, zzz1709, zzz1710, zzz1711, zzz1712, zzz17130, zzz17140, bd)
new_mkVBalBranch3MkVBalBranch25(zzz537, zzz538, zzz539, zzz540, zzz541, zzz542, zzz543, zzz544, zzz545, zzz546, zzz547, Zero, Succ(zzz5490), bc) → new_mkVBalBranch(zzz547, Branch(zzz542, zzz543, Neg(Succ(Succ(zzz544))), zzz545, zzz546), zzz540, bc)
new_mkVBalBranch3MkVBalBranch10(zzz929, zzz930, zzz931, zzz932, zzz933, zzz934, zzz935, zzz936, zzz937, zzz938, zzz939, Succ(zzz10020), ba) → new_mkVBalBranch3MkVBalBranch11(zzz929, zzz930, zzz931, zzz932, zzz933, zzz934, zzz935, zzz936, zzz937, zzz938, zzz939, Succ(zzz10020), Succ(zzz936), ba)
new_mkVBalBranch3MkVBalBranch2(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344, zzz520, zzz521, zzz52200, zzz523, zzz524, zzz31, Succ(zzz680), h) → new_mkVBalBranch3MkVBalBranch1(zzz340, zzz341, zzz34200, zzz343, zzz344, zzz520, zzz521, zzz52200, zzz523, zzz524, zzz31, new_primPlusNat2(new_primMulNat0(zzz34200), Succ(zzz34200)), h)
new_mkVBalBranch3MkVBalBranch14(zzz818, zzz819, zzz820, zzz821, zzz822, zzz823, zzz824, zzz825, zzz826, zzz827, Succ(zzz8960), bf) → new_mkVBalBranch3MkVBalBranch16(zzz818, zzz819, zzz820, zzz821, zzz822, zzz823, zzz824, Zero, zzz825, zzz826, zzz827, Succ(Zero), Succ(zzz8960), bf)
new_mkVBalBranch3MkVBalBranch24(zzz340, zzz341, Neg(Succ(Succ(Succ(zzz3420000)))), zzz343, zzz344, zzz520, zzz521, Succ(zzz522000), zzz523, zzz524, zzz31, Succ(Succ(zzz6900)), h) → new_mkVBalBranch3MkVBalBranch25(zzz340, zzz341, Succ(Succ(zzz3420000)), zzz343, zzz344, zzz520, zzz521, zzz522000, zzz523, zzz524, zzz31, Succ(zzz3420000), Succ(Succ(new_primPlusNat2(zzz6900, zzz522000))), h)
new_mkVBalBranch3MkVBalBranch2(zzz340, zzz341, Pos(Succ(zzz34200)), zzz343, zzz344, zzz520, zzz521, zzz52200, zzz523, zzz524, zzz31, Zero, h) → new_mkVBalBranch3MkVBalBranch20(zzz340, zzz341, zzz34200, zzz343, zzz344, zzz520, zzz521, zzz52200, zzz523, zzz524, zzz31, zzz52200, zzz34200, h)
new_mkVBalBranch3MkVBalBranch14(zzz818, zzz819, zzz820, zzz821, zzz822, zzz823, zzz824, zzz825, zzz826, zzz827, Zero, bf) → new_mkVBalBranch3MkVBalBranch16(zzz818, zzz819, zzz820, zzz821, zzz822, zzz823, zzz824, Zero, zzz825, zzz826, zzz827, Succ(Zero), Zero, bf)
new_mkVBalBranch3MkVBalBranch24(zzz340, zzz341, Neg(Zero), zzz343, zzz344, zzz520, zzz521, zzz52200, zzz523, zzz524, zzz31, Zero, h) → new_mkVBalBranch3MkVBalBranch210(zzz340, zzz341, zzz343, zzz344, zzz520, zzz521, zzz52200, zzz523, zzz524, zzz31, h)
new_mkVBalBranch3MkVBalBranch24(zzz340, zzz341, Neg(Succ(Succ(Zero))), zzz343, zzz344, zzz520, zzz521, Succ(zzz522000), zzz523, zzz524, zzz31, Succ(Succ(zzz6900)), h) → new_mkVBalBranch3MkVBalBranch25(zzz340, zzz341, Succ(Zero), zzz343, zzz344, zzz520, zzz521, zzz522000, zzz523, zzz524, zzz31, Zero, Succ(Succ(new_primPlusNat2(zzz6900, zzz522000))), h)
new_mkVBalBranch3MkVBalBranch20(zzz929, zzz930, zzz931, zzz932, zzz933, zzz934, zzz935, zzz936, zzz937, zzz938, zzz939, Succ(zzz9400), Zero, ba) → new_mkVBalBranch3MkVBalBranch10(zzz929, zzz930, zzz931, zzz932, zzz933, zzz934, zzz935, zzz936, zzz937, zzz938, zzz939, new_primMulNat1(zzz931), ba)
new_mkVBalBranch3MkVBalBranch2(zzz340, zzz341, Neg(Zero), zzz343, zzz344, zzz520, zzz521, zzz52200, zzz523, zzz524, zzz31, Succ(zzz680), h) → new_mkVBalBranch(zzz31, zzz524, Branch(zzz340, zzz341, Neg(Zero), zzz343, zzz344), h)
new_mkVBalBranch(zzz31, Branch(zzz520, zzz521, Pos(Succ(zzz52200)), zzz523, zzz524), Branch(zzz340, zzz341, zzz342, zzz343, zzz344), h) → new_mkVBalBranch3MkVBalBranch2(zzz340, zzz341, zzz342, zzz343, zzz344, zzz520, zzz521, zzz52200, zzz523, zzz524, zzz31, new_primMulNat0(zzz52200), h)
new_mkVBalBranch(zzz31, Branch(zzz520, zzz521, Neg(Zero), zzz523, zzz524), Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), h) → new_mkVBalBranch3MkVBalBranch13(zzz340, zzz341, zzz34200, zzz343, zzz344, zzz520, zzz521, zzz523, zzz524, zzz31, new_primMulNat1(zzz34200), h)
new_mkVBalBranch3MkVBalBranch16(zzz1702, zzz1703, zzz1704, zzz1705, zzz1706, zzz1707, zzz1708, zzz1709, zzz1710, zzz1711, zzz1712, Zero, Succ(zzz17140), bd) → new_mkVBalBranch(zzz1712, zzz1711, Branch(zzz1702, zzz1703, Neg(Succ(zzz1704)), zzz1705, zzz1706), bd)
new_mkVBalBranch3MkVBalBranch10(zzz929, zzz930, zzz931, zzz932, zzz933, zzz934, zzz935, zzz936, zzz937, zzz938, zzz939, Zero, ba) → new_mkVBalBranch3MkVBalBranch11(zzz929, zzz930, zzz931, zzz932, zzz933, zzz934, zzz935, zzz936, zzz937, zzz938, zzz939, Zero, Succ(zzz936), ba)
new_mkVBalBranch3MkVBalBranch25(zzz537, zzz538, zzz539, zzz540, zzz541, zzz542, zzz543, zzz544, zzz545, zzz546, zzz547, Zero, Zero, bc) → new_mkVBalBranch3MkVBalBranch211(zzz537, zzz538, zzz539, zzz540, zzz541, zzz542, zzz543, zzz544, zzz545, zzz546, zzz547, bc)
new_mkVBalBranch3MkVBalBranch2(zzz340, zzz341, Pos(Zero), zzz343, zzz344, zzz520, zzz521, zzz52200, zzz523, zzz524, zzz31, Zero, h) → new_mkVBalBranch3MkVBalBranch21(zzz340, zzz341, zzz343, zzz344, zzz520, zzz521, zzz52200, zzz523, zzz524, zzz31, h)

The TRS R consists of the following rules:

new_primPlusNat1(Zero) → Zero
new_primMulNat0(zzz6200) → new_primPlusNat3(Succ(new_primPlusNat3(new_primPlusNat1(zzz6200), zzz6200)), Succ(zzz6200))
new_primPlusNat2(Succ(zzz900), Succ(zzz9100)) → Succ(Succ(new_primPlusNat2(zzz900, zzz9100)))
new_primPlusNat3(zzz90, Succ(zzz910)) → Succ(Succ(new_primPlusNat2(zzz90, zzz910)))
new_primPlusNat3(zzz90, Zero) → Succ(zzz90)
new_primMulNat1(zzz34200) → new_primPlusNat2(new_primMulNat0(zzz34200), Succ(zzz34200))
new_primPlusNat2(Zero, Zero) → Zero
new_primPlusNat1(Succ(zzz62000)) → Succ(Succ(new_primPlusNat1(zzz62000)))
new_primPlusNat2(Succ(zzz900), Zero) → Succ(zzz900)
new_primPlusNat2(Zero, Succ(zzz9100)) → Succ(zzz9100)

The set Q consists of the following terms:

new_primPlusNat2(Zero, Succ(x0))
new_primMulNat1(x0)
new_primMulNat0(x0)
new_primPlusNat3(x0, Succ(x1))
new_primPlusNat2(Succ(x0), Succ(x1))
new_primPlusNat3(x0, Zero)
new_primPlusNat1(Zero)
new_primPlusNat2(Zero, Zero)
new_primPlusNat1(Succ(x0))
new_primPlusNat2(Succ(x0), Zero)

We have to consider all minimal (P,Q,R)-chains.
The approximation of the Dependency Graph [15,17,22] contains 1 SCC with 4 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
                                    ↳ DependencyGraphProof
                                      ↳ QDP
                                        ↳ Rewriting
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP

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

new_mkVBalBranch3MkVBalBranch11(zzz2033, zzz2034, zzz2035, zzz2036, zzz2037, zzz2038, zzz2039, zzz2040, zzz2041, zzz2042, zzz2043, Zero, Succ(zzz20450), bb) → new_mkVBalBranch(zzz2043, zzz2042, Branch(zzz2033, zzz2034, Pos(Succ(zzz2035)), zzz2036, zzz2037), bb)
new_mkVBalBranch3MkVBalBranch26(zzz1133, zzz1134, zzz1135, zzz1136, zzz1137, zzz1138, zzz1139, zzz1140, zzz1141, zzz1142, Succ(zzz11430), Succ(zzz11440), be) → new_mkVBalBranch3MkVBalBranch26(zzz1133, zzz1134, zzz1135, zzz1136, zzz1137, zzz1138, zzz1139, zzz1140, zzz1141, zzz1142, zzz11430, zzz11440, be)
new_mkVBalBranch3MkVBalBranch24(zzz340, zzz341, Neg(Succ(Succ(Succ(zzz3420000)))), zzz343, zzz344, zzz520, zzz521, Zero, zzz523, zzz524, zzz31, Succ(Zero), h) → new_mkVBalBranch3MkVBalBranch26(zzz340, zzz341, Succ(Succ(zzz3420000)), zzz343, zzz344, zzz520, zzz521, zzz523, zzz524, zzz31, Succ(zzz3420000), Zero, h)
new_mkVBalBranch3MkVBalBranch24(zzz340, zzz341, Neg(Succ(Zero)), zzz343, zzz344, zzz520, zzz521, Zero, zzz523, zzz524, zzz31, Zero, h) → new_mkVBalBranch3MkVBalBranch29(zzz340, zzz341, Zero, zzz343, zzz344, zzz520, zzz521, zzz523, zzz524, zzz31, h)
new_mkVBalBranch3MkVBalBranch20(zzz929, zzz930, zzz931, zzz932, zzz933, zzz934, zzz935, zzz936, zzz937, zzz938, zzz939, Zero, Succ(zzz9410), ba) → new_mkVBalBranch(zzz939, Branch(zzz934, zzz935, Pos(Succ(zzz936)), zzz937, zzz938), zzz932, ba)
new_mkVBalBranch3MkVBalBranch17(zzz340, zzz341, zzz34200, zzz343, zzz344, zzz520, zzz521, zzz52200, zzz523, zzz524, zzz31, h) → new_mkVBalBranch(zzz31, zzz524, Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), h)
new_mkVBalBranch3MkVBalBranch26(zzz1133, zzz1134, zzz1135, zzz1136, zzz1137, zzz1138, zzz1139, zzz1140, zzz1141, zzz1142, Zero, Zero, be) → new_mkVBalBranch3MkVBalBranch29(zzz1133, zzz1134, zzz1135, zzz1136, zzz1137, zzz1138, zzz1139, zzz1140, zzz1141, zzz1142, be)
new_mkVBalBranch3MkVBalBranch20(zzz929, zzz930, zzz931, zzz932, zzz933, zzz934, zzz935, zzz936, zzz937, zzz938, zzz939, Zero, Zero, ba) → new_mkVBalBranch3MkVBalBranch23(zzz929, zzz930, zzz931, zzz932, zzz933, zzz934, zzz935, zzz936, zzz937, zzz938, zzz939, ba)
new_mkVBalBranch(zzz31, Branch(zzz520, zzz521, Pos(Zero), zzz523, zzz524), Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), h) → new_mkVBalBranch3MkVBalBranch12(zzz340, zzz341, zzz34200, zzz343, zzz344, zzz520, zzz521, zzz523, zzz524, zzz31, new_primMulNat1(zzz34200), h)
new_mkVBalBranch3MkVBalBranch24(zzz340, zzz341, Neg(Succ(Succ(Zero))), zzz343, zzz344, zzz520, zzz521, Succ(zzz522000), zzz523, zzz524, zzz31, Succ(Zero), h) → new_mkVBalBranch3MkVBalBranch25(zzz340, zzz341, Succ(Zero), zzz343, zzz344, zzz520, zzz521, zzz522000, zzz523, zzz524, zzz31, Zero, Succ(zzz522000), h)
new_mkVBalBranch3MkVBalBranch20(zzz929, zzz930, zzz931, zzz932, zzz933, zzz934, zzz935, zzz936, zzz937, zzz938, zzz939, Succ(zzz9400), Succ(zzz9410), ba) → new_mkVBalBranch3MkVBalBranch20(zzz929, zzz930, zzz931, zzz932, zzz933, zzz934, zzz935, zzz936, zzz937, zzz938, zzz939, zzz9400, zzz9410, ba)
new_mkVBalBranch3MkVBalBranch24(zzz340, zzz341, Neg(Succ(Succ(Succ(zzz3420000)))), zzz343, zzz344, zzz520, zzz521, Succ(zzz522000), zzz523, zzz524, zzz31, Succ(Zero), h) → new_mkVBalBranch3MkVBalBranch25(zzz340, zzz341, Succ(Succ(zzz3420000)), zzz343, zzz344, zzz520, zzz521, zzz522000, zzz523, zzz524, zzz31, Succ(zzz3420000), Succ(zzz522000), h)
new_mkVBalBranch3MkVBalBranch26(zzz1133, zzz1134, zzz1135, zzz1136, zzz1137, zzz1138, zzz1139, zzz1140, zzz1141, zzz1142, Succ(zzz11430), Zero, be) → new_mkVBalBranch3MkVBalBranch212(zzz1133, zzz1134, zzz1135, zzz1136, zzz1137, zzz1138, zzz1139, zzz1140, zzz1141, zzz1142, be)
new_mkVBalBranch3MkVBalBranch24(zzz340, zzz341, Neg(Succ(Succ(zzz342000))), zzz343, zzz344, zzz520, zzz521, Succ(zzz522000), zzz523, zzz524, zzz31, Zero, h) → new_mkVBalBranch3MkVBalBranch25(zzz340, zzz341, Succ(zzz342000), zzz343, zzz344, zzz520, zzz521, zzz522000, zzz523, zzz524, zzz31, zzz342000, zzz522000, h)
new_mkVBalBranch3MkVBalBranch11(zzz2033, zzz2034, zzz2035, zzz2036, zzz2037, zzz2038, zzz2039, zzz2040, zzz2041, zzz2042, zzz2043, Succ(zzz20440), Succ(zzz20450), bb) → new_mkVBalBranch3MkVBalBranch11(zzz2033, zzz2034, zzz2035, zzz2036, zzz2037, zzz2038, zzz2039, zzz2040, zzz2041, zzz2042, zzz2043, zzz20440, zzz20450, bb)
new_mkVBalBranch3MkVBalBranch2(zzz340, zzz341, Neg(zzz3420), zzz343, zzz344, zzz520, zzz521, zzz52200, zzz523, zzz524, zzz31, Zero, h) → new_mkVBalBranch3MkVBalBranch22(zzz340, zzz341, zzz3420, zzz343, zzz344, zzz520, zzz521, zzz52200, zzz523, zzz524, zzz31, h)
new_mkVBalBranch3MkVBalBranch25(zzz537, zzz538, zzz539, zzz540, zzz541, zzz542, zzz543, zzz544, zzz545, zzz546, zzz547, Succ(zzz5480), Succ(zzz5490), bc) → new_mkVBalBranch3MkVBalBranch25(zzz537, zzz538, zzz539, zzz540, zzz541, zzz542, zzz543, zzz544, zzz545, zzz546, zzz547, zzz5480, zzz5490, bc)
new_mkVBalBranch3MkVBalBranch24(zzz340, zzz341, Neg(Succ(Zero)), zzz343, zzz344, zzz520, zzz521, Succ(zzz522000), zzz523, zzz524, zzz31, Zero, h) → new_mkVBalBranch3MkVBalBranch28(zzz340, zzz341, zzz343, zzz344, zzz520, zzz521, Succ(zzz522000), zzz523, zzz524, zzz31, h)
new_mkVBalBranch3MkVBalBranch210(zzz340, zzz341, zzz343, zzz344, zzz520, zzz521, zzz52200, zzz523, zzz524, zzz31, h) → new_mkVBalBranch(zzz31, Branch(zzz520, zzz521, Neg(Succ(zzz52200)), zzz523, zzz524), zzz343, h)
new_mkVBalBranch3MkVBalBranch24(zzz340, zzz341, Neg(Succ(Succ(zzz342000))), zzz343, zzz344, zzz520, zzz521, Zero, zzz523, zzz524, zzz31, Zero, h) → new_mkVBalBranch3MkVBalBranch14(zzz340, zzz341, Succ(zzz342000), zzz343, zzz344, zzz520, zzz521, zzz523, zzz524, zzz31, new_primMulNat1(Succ(zzz342000)), h)
new_mkVBalBranch3MkVBalBranch26(zzz1133, zzz1134, zzz1135, zzz1136, zzz1137, zzz1138, zzz1139, zzz1140, zzz1141, zzz1142, Zero, Succ(zzz11440), be) → new_mkVBalBranch(zzz1142, Branch(zzz1138, zzz1139, Neg(Succ(Zero)), zzz1140, zzz1141), zzz1136, be)
new_mkVBalBranch3MkVBalBranch24(zzz340, zzz341, Neg(Succ(Succ(Zero))), zzz343, zzz344, zzz520, zzz521, Zero, zzz523, zzz524, zzz31, Succ(Zero), h) → new_mkVBalBranch3MkVBalBranch26(zzz340, zzz341, Succ(Zero), zzz343, zzz344, zzz520, zzz521, zzz523, zzz524, zzz31, Zero, Zero, h)
new_mkVBalBranch(zzz31, Branch(zzz520, zzz521, Pos(Zero), zzz523, zzz524), Branch(zzz340, zzz341, Pos(Succ(zzz34200)), zzz343, zzz344), h) → new_mkVBalBranch(zzz31, Branch(zzz520, zzz521, Pos(Zero), zzz523, zzz524), zzz343, h)
new_mkVBalBranch3MkVBalBranch29(zzz818, zzz819, zzz820, zzz821, zzz822, zzz823, zzz824, zzz825, zzz826, zzz827, bf) → new_mkVBalBranch3MkVBalBranch14(zzz818, zzz819, zzz820, zzz821, zzz822, zzz823, zzz824, zzz825, zzz826, zzz827, new_primMulNat1(zzz820), bf)
new_mkVBalBranch3MkVBalBranch2(zzz340, zzz341, Pos(Zero), zzz343, zzz344, zzz520, zzz521, zzz52200, zzz523, zzz524, zzz31, Succ(zzz680), h) → new_mkVBalBranch(zzz31, zzz524, Branch(zzz340, zzz341, Pos(Zero), zzz343, zzz344), h)
new_mkVBalBranch(zzz31, Branch(zzz520, zzz521, Neg(Succ(zzz52200)), zzz523, zzz524), Branch(zzz340, zzz341, zzz342, zzz343, zzz344), h) → new_mkVBalBranch3MkVBalBranch24(zzz340, zzz341, zzz342, zzz343, zzz344, zzz520, zzz521, zzz52200, zzz523, zzz524, zzz31, new_primMulNat0(zzz52200), h)
new_mkVBalBranch3MkVBalBranch21(zzz340, zzz341, zzz343, zzz344, zzz520, zzz521, zzz52200, zzz523, zzz524, zzz31, h) → new_mkVBalBranch(zzz31, zzz524, Branch(zzz340, zzz341, Pos(Zero), zzz343, zzz344), h)
new_mkVBalBranch3MkVBalBranch24(zzz340, zzz341, Pos(zzz3420), zzz343, zzz344, zzz520, zzz521, zzz52200, zzz523, zzz524, zzz31, Zero, h) → new_mkVBalBranch3MkVBalBranch27(zzz340, zzz341, zzz3420, zzz343, zzz344, zzz520, zzz521, zzz52200, zzz523, zzz524, zzz31, h)
new_mkVBalBranch3MkVBalBranch23(zzz929, zzz930, zzz931, zzz932, zzz933, zzz934, zzz935, zzz936, zzz937, zzz938, zzz939, ba) → new_mkVBalBranch3MkVBalBranch10(zzz929, zzz930, zzz931, zzz932, zzz933, zzz934, zzz935, zzz936, zzz937, zzz938, zzz939, new_primMulNat1(zzz931), ba)
new_mkVBalBranch3MkVBalBranch212(zzz818, zzz819, zzz820, zzz821, zzz822, zzz823, zzz824, zzz825, zzz826, zzz827, bf) → new_mkVBalBranch3MkVBalBranch14(zzz818, zzz819, zzz820, zzz821, zzz822, zzz823, zzz824, zzz825, zzz826, zzz827, new_primMulNat1(zzz820), bf)
new_mkVBalBranch3MkVBalBranch211(zzz537, zzz538, zzz539, zzz540, zzz541, zzz542, zzz543, zzz544, zzz545, zzz546, zzz547, bc) → new_mkVBalBranch3MkVBalBranch15(zzz537, zzz538, zzz539, zzz540, zzz541, zzz542, zzz543, zzz544, zzz545, zzz546, zzz547, new_primMulNat1(zzz539), bc)
new_mkVBalBranch3MkVBalBranch24(zzz340, zzz341, Neg(Succ(Succ(Succ(zzz3420000)))), zzz343, zzz344, zzz520, zzz521, Zero, zzz523, zzz524, zzz31, Succ(Succ(zzz6900)), h) → new_mkVBalBranch3MkVBalBranch26(zzz340, zzz341, Succ(Succ(zzz3420000)), zzz343, zzz344, zzz520, zzz521, zzz523, zzz524, zzz31, Succ(zzz3420000), Succ(zzz6900), h)
new_mkVBalBranch3MkVBalBranch15(zzz537, zzz538, zzz539, zzz540, zzz541, zzz542, zzz543, zzz544, zzz545, zzz546, zzz547, Succ(zzz6990), bc) → new_mkVBalBranch3MkVBalBranch16(zzz537, zzz538, zzz539, zzz540, zzz541, zzz542, zzz543, Succ(zzz544), zzz545, zzz546, zzz547, Succ(Succ(zzz544)), Succ(zzz6990), bc)
new_mkVBalBranch3MkVBalBranch27(zzz340, zzz341, zzz3420, zzz343, zzz344, zzz520, zzz521, zzz52200, zzz523, zzz524, zzz31, h) → new_mkVBalBranch(zzz31, Branch(zzz520, zzz521, Neg(Succ(zzz52200)), zzz523, zzz524), zzz343, h)
new_mkVBalBranch3MkVBalBranch24(zzz340, zzz341, Pos(zzz3420), zzz343, zzz344, zzz520, zzz521, zzz52200, zzz523, zzz524, zzz31, Succ(zzz690), h) → new_mkVBalBranch(zzz31, Branch(zzz520, zzz521, Neg(Succ(zzz52200)), zzz523, zzz524), zzz343, h)
new_mkVBalBranch3MkVBalBranch12(zzz340, zzz341, zzz34200, zzz343, zzz344, zzz520, zzz521, zzz523, zzz524, zzz31, Succ(zzz1250), h) → new_mkVBalBranch(zzz31, zzz524, Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), h)
new_mkVBalBranch3MkVBalBranch25(zzz537, zzz538, zzz539, zzz540, zzz541, zzz542, zzz543, zzz544, zzz545, zzz546, zzz547, Succ(zzz5480), Zero, bc) → new_mkVBalBranch3MkVBalBranch15(zzz537, zzz538, zzz539, zzz540, zzz541, zzz542, zzz543, zzz544, zzz545, zzz546, zzz547, new_primMulNat1(zzz539), bc)
new_mkVBalBranch3MkVBalBranch28(zzz340, zzz341, zzz343, zzz344, zzz520, zzz521, zzz52200, zzz523, zzz524, zzz31, h) → new_mkVBalBranch(zzz31, Branch(zzz520, zzz521, Neg(Succ(zzz52200)), zzz523, zzz524), zzz343, h)
new_mkVBalBranch3MkVBalBranch24(zzz340, zzz341, Neg(Succ(Succ(Zero))), zzz343, zzz344, zzz520, zzz521, Zero, zzz523, zzz524, zzz31, Succ(Succ(zzz6900)), h) → new_mkVBalBranch3MkVBalBranch26(zzz340, zzz341, Succ(Zero), zzz343, zzz344, zzz520, zzz521, zzz523, zzz524, zzz31, Zero, Succ(zzz6900), h)
new_mkVBalBranch3MkVBalBranch1(zzz340, zzz341, zzz34200, zzz343, zzz344, zzz520, zzz521, zzz52200, zzz523, zzz524, zzz31, Succ(zzz1430), h) → new_mkVBalBranch(zzz31, zzz524, Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), h)
new_mkVBalBranch3MkVBalBranch22(zzz340, zzz341, Zero, zzz343, zzz344, zzz520, zzz521, zzz52200, zzz523, zzz524, zzz31, h) → new_mkVBalBranch(zzz31, zzz524, Branch(zzz340, zzz341, Neg(Zero), zzz343, zzz344), h)
new_mkVBalBranch3MkVBalBranch24(zzz340, zzz341, Neg(Succ(Zero)), zzz343, zzz344, zzz520, zzz521, zzz52200, zzz523, zzz524, zzz31, Succ(zzz690), h) → new_mkVBalBranch(zzz31, Branch(zzz520, zzz521, Neg(Succ(zzz52200)), zzz523, zzz524), zzz343, h)
new_mkVBalBranch3MkVBalBranch22(zzz340, zzz341, Succ(zzz34200), zzz343, zzz344, zzz520, zzz521, zzz52200, zzz523, zzz524, zzz31, h) → new_mkVBalBranch3MkVBalBranch1(zzz340, zzz341, zzz34200, zzz343, zzz344, zzz520, zzz521, zzz52200, zzz523, zzz524, zzz31, new_primPlusNat2(new_primMulNat0(zzz34200), Succ(zzz34200)), h)
new_mkVBalBranch3MkVBalBranch13(zzz340, zzz341, zzz34200, zzz343, zzz344, zzz520, zzz521, zzz523, zzz524, zzz31, Succ(zzz1290), h) → new_mkVBalBranch(zzz31, zzz524, Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), h)
new_mkVBalBranch3MkVBalBranch2(zzz340, zzz341, Pos(Succ(zzz34200)), zzz343, zzz344, zzz520, zzz521, zzz52200, zzz523, zzz524, zzz31, Succ(zzz680), h) → new_mkVBalBranch3MkVBalBranch20(zzz340, zzz341, zzz34200, zzz343, zzz344, zzz520, zzz521, zzz52200, zzz523, zzz524, zzz31, Succ(new_primPlusNat2(zzz680, zzz52200)), zzz34200, h)
new_mkVBalBranch3MkVBalBranch24(zzz340, zzz341, Neg(Zero), zzz343, zzz344, zzz520, zzz521, zzz52200, zzz523, zzz524, zzz31, Succ(zzz690), h) → new_mkVBalBranch(zzz31, Branch(zzz520, zzz521, Neg(Succ(zzz52200)), zzz523, zzz524), zzz343, h)
new_mkVBalBranch(zzz31, Branch(zzz520, zzz521, Neg(Zero), zzz523, zzz524), Branch(zzz340, zzz341, Pos(Succ(zzz34200)), zzz343, zzz344), h) → new_mkVBalBranch(zzz31, Branch(zzz520, zzz521, Neg(Zero), zzz523, zzz524), zzz343, h)
new_mkVBalBranch3MkVBalBranch1(zzz340, zzz341, zzz34200, zzz343, zzz344, zzz520, zzz521, zzz52200, zzz523, zzz524, zzz31, Zero, h) → new_mkVBalBranch3MkVBalBranch17(zzz340, zzz341, zzz34200, zzz343, zzz344, zzz520, zzz521, zzz52200, zzz523, zzz524, zzz31, h)
new_mkVBalBranch3MkVBalBranch16(zzz1702, zzz1703, zzz1704, zzz1705, zzz1706, zzz1707, zzz1708, zzz1709, zzz1710, zzz1711, zzz1712, Succ(zzz17130), Succ(zzz17140), bd) → new_mkVBalBranch3MkVBalBranch16(zzz1702, zzz1703, zzz1704, zzz1705, zzz1706, zzz1707, zzz1708, zzz1709, zzz1710, zzz1711, zzz1712, zzz17130, zzz17140, bd)
new_mkVBalBranch3MkVBalBranch25(zzz537, zzz538, zzz539, zzz540, zzz541, zzz542, zzz543, zzz544, zzz545, zzz546, zzz547, Zero, Succ(zzz5490), bc) → new_mkVBalBranch(zzz547, Branch(zzz542, zzz543, Neg(Succ(Succ(zzz544))), zzz545, zzz546), zzz540, bc)
new_mkVBalBranch3MkVBalBranch10(zzz929, zzz930, zzz931, zzz932, zzz933, zzz934, zzz935, zzz936, zzz937, zzz938, zzz939, Succ(zzz10020), ba) → new_mkVBalBranch3MkVBalBranch11(zzz929, zzz930, zzz931, zzz932, zzz933, zzz934, zzz935, zzz936, zzz937, zzz938, zzz939, Succ(zzz10020), Succ(zzz936), ba)
new_mkVBalBranch3MkVBalBranch14(zzz818, zzz819, zzz820, zzz821, zzz822, zzz823, zzz824, zzz825, zzz826, zzz827, Succ(zzz8960), bf) → new_mkVBalBranch3MkVBalBranch16(zzz818, zzz819, zzz820, zzz821, zzz822, zzz823, zzz824, Zero, zzz825, zzz826, zzz827, Succ(Zero), Succ(zzz8960), bf)
new_mkVBalBranch3MkVBalBranch2(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344, zzz520, zzz521, zzz52200, zzz523, zzz524, zzz31, Succ(zzz680), h) → new_mkVBalBranch3MkVBalBranch1(zzz340, zzz341, zzz34200, zzz343, zzz344, zzz520, zzz521, zzz52200, zzz523, zzz524, zzz31, new_primPlusNat2(new_primMulNat0(zzz34200), Succ(zzz34200)), h)
new_mkVBalBranch3MkVBalBranch24(zzz340, zzz341, Neg(Succ(Succ(Succ(zzz3420000)))), zzz343, zzz344, zzz520, zzz521, Succ(zzz522000), zzz523, zzz524, zzz31, Succ(Succ(zzz6900)), h) → new_mkVBalBranch3MkVBalBranch25(zzz340, zzz341, Succ(Succ(zzz3420000)), zzz343, zzz344, zzz520, zzz521, zzz522000, zzz523, zzz524, zzz31, Succ(zzz3420000), Succ(Succ(new_primPlusNat2(zzz6900, zzz522000))), h)
new_mkVBalBranch3MkVBalBranch2(zzz340, zzz341, Pos(Succ(zzz34200)), zzz343, zzz344, zzz520, zzz521, zzz52200, zzz523, zzz524, zzz31, Zero, h) → new_mkVBalBranch3MkVBalBranch20(zzz340, zzz341, zzz34200, zzz343, zzz344, zzz520, zzz521, zzz52200, zzz523, zzz524, zzz31, zzz52200, zzz34200, h)
new_mkVBalBranch3MkVBalBranch24(zzz340, zzz341, Neg(Zero), zzz343, zzz344, zzz520, zzz521, zzz52200, zzz523, zzz524, zzz31, Zero, h) → new_mkVBalBranch3MkVBalBranch210(zzz340, zzz341, zzz343, zzz344, zzz520, zzz521, zzz52200, zzz523, zzz524, zzz31, h)
new_mkVBalBranch3MkVBalBranch24(zzz340, zzz341, Neg(Succ(Succ(Zero))), zzz343, zzz344, zzz520, zzz521, Succ(zzz522000), zzz523, zzz524, zzz31, Succ(Succ(zzz6900)), h) → new_mkVBalBranch3MkVBalBranch25(zzz340, zzz341, Succ(Zero), zzz343, zzz344, zzz520, zzz521, zzz522000, zzz523, zzz524, zzz31, Zero, Succ(Succ(new_primPlusNat2(zzz6900, zzz522000))), h)
new_mkVBalBranch3MkVBalBranch20(zzz929, zzz930, zzz931, zzz932, zzz933, zzz934, zzz935, zzz936, zzz937, zzz938, zzz939, Succ(zzz9400), Zero, ba) → new_mkVBalBranch3MkVBalBranch10(zzz929, zzz930, zzz931, zzz932, zzz933, zzz934, zzz935, zzz936, zzz937, zzz938, zzz939, new_primMulNat1(zzz931), ba)
new_mkVBalBranch(zzz31, Branch(zzz520, zzz521, Pos(Succ(zzz52200)), zzz523, zzz524), Branch(zzz340, zzz341, zzz342, zzz343, zzz344), h) → new_mkVBalBranch3MkVBalBranch2(zzz340, zzz341, zzz342, zzz343, zzz344, zzz520, zzz521, zzz52200, zzz523, zzz524, zzz31, new_primMulNat0(zzz52200), h)
new_mkVBalBranch3MkVBalBranch2(zzz340, zzz341, Neg(Zero), zzz343, zzz344, zzz520, zzz521, zzz52200, zzz523, zzz524, zzz31, Succ(zzz680), h) → new_mkVBalBranch(zzz31, zzz524, Branch(zzz340, zzz341, Neg(Zero), zzz343, zzz344), h)
new_mkVBalBranch(zzz31, Branch(zzz520, zzz521, Neg(Zero), zzz523, zzz524), Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), h) → new_mkVBalBranch3MkVBalBranch13(zzz340, zzz341, zzz34200, zzz343, zzz344, zzz520, zzz521, zzz523, zzz524, zzz31, new_primMulNat1(zzz34200), h)
new_mkVBalBranch3MkVBalBranch16(zzz1702, zzz1703, zzz1704, zzz1705, zzz1706, zzz1707, zzz1708, zzz1709, zzz1710, zzz1711, zzz1712, Zero, Succ(zzz17140), bd) → new_mkVBalBranch(zzz1712, zzz1711, Branch(zzz1702, zzz1703, Neg(Succ(zzz1704)), zzz1705, zzz1706), bd)
new_mkVBalBranch3MkVBalBranch10(zzz929, zzz930, zzz931, zzz932, zzz933, zzz934, zzz935, zzz936, zzz937, zzz938, zzz939, Zero, ba) → new_mkVBalBranch3MkVBalBranch11(zzz929, zzz930, zzz931, zzz932, zzz933, zzz934, zzz935, zzz936, zzz937, zzz938, zzz939, Zero, Succ(zzz936), ba)
new_mkVBalBranch3MkVBalBranch2(zzz340, zzz341, Pos(Zero), zzz343, zzz344, zzz520, zzz521, zzz52200, zzz523, zzz524, zzz31, Zero, h) → new_mkVBalBranch3MkVBalBranch21(zzz340, zzz341, zzz343, zzz344, zzz520, zzz521, zzz52200, zzz523, zzz524, zzz31, h)
new_mkVBalBranch3MkVBalBranch25(zzz537, zzz538, zzz539, zzz540, zzz541, zzz542, zzz543, zzz544, zzz545, zzz546, zzz547, Zero, Zero, bc) → new_mkVBalBranch3MkVBalBranch211(zzz537, zzz538, zzz539, zzz540, zzz541, zzz542, zzz543, zzz544, zzz545, zzz546, zzz547, bc)

The TRS R consists of the following rules:

new_primPlusNat1(Zero) → Zero
new_primMulNat0(zzz6200) → new_primPlusNat3(Succ(new_primPlusNat3(new_primPlusNat1(zzz6200), zzz6200)), Succ(zzz6200))
new_primPlusNat2(Succ(zzz900), Succ(zzz9100)) → Succ(Succ(new_primPlusNat2(zzz900, zzz9100)))
new_primPlusNat3(zzz90, Succ(zzz910)) → Succ(Succ(new_primPlusNat2(zzz90, zzz910)))
new_primPlusNat3(zzz90, Zero) → Succ(zzz90)
new_primMulNat1(zzz34200) → new_primPlusNat2(new_primMulNat0(zzz34200), Succ(zzz34200))
new_primPlusNat2(Zero, Zero) → Zero
new_primPlusNat1(Succ(zzz62000)) → Succ(Succ(new_primPlusNat1(zzz62000)))
new_primPlusNat2(Succ(zzz900), Zero) → Succ(zzz900)
new_primPlusNat2(Zero, Succ(zzz9100)) → Succ(zzz9100)

The set Q consists of the following terms:

new_primPlusNat2(Zero, Succ(x0))
new_primMulNat1(x0)
new_primMulNat0(x0)
new_primPlusNat3(x0, Succ(x1))
new_primPlusNat2(Succ(x0), Succ(x1))
new_primPlusNat3(x0, Zero)
new_primPlusNat1(Zero)
new_primPlusNat2(Zero, Zero)
new_primPlusNat1(Succ(x0))
new_primPlusNat2(Succ(x0), Zero)

We have to consider all minimal (P,Q,R)-chains.
By rewriting [15] the rule new_mkVBalBranch(zzz31, Branch(zzz520, zzz521, Pos(Zero), zzz523, zzz524), Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), h) → new_mkVBalBranch3MkVBalBranch12(zzz340, zzz341, zzz34200, zzz343, zzz344, zzz520, zzz521, zzz523, zzz524, zzz31, new_primMulNat1(zzz34200), h) at position [10] we obtained the following new rules:

new_mkVBalBranch(zzz31, Branch(zzz520, zzz521, Pos(Zero), zzz523, zzz524), Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), h) → new_mkVBalBranch3MkVBalBranch12(zzz340, zzz341, zzz34200, zzz343, zzz344, zzz520, zzz521, zzz523, zzz524, zzz31, new_primPlusNat2(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
                                    ↳ DependencyGraphProof
                                      ↳ QDP
                                        ↳ Rewriting
                                          ↳ QDP
                                            ↳ Rewriting
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP

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

new_mkVBalBranch3MkVBalBranch11(zzz2033, zzz2034, zzz2035, zzz2036, zzz2037, zzz2038, zzz2039, zzz2040, zzz2041, zzz2042, zzz2043, Zero, Succ(zzz20450), bb) → new_mkVBalBranch(zzz2043, zzz2042, Branch(zzz2033, zzz2034, Pos(Succ(zzz2035)), zzz2036, zzz2037), bb)
new_mkVBalBranch3MkVBalBranch26(zzz1133, zzz1134, zzz1135, zzz1136, zzz1137, zzz1138, zzz1139, zzz1140, zzz1141, zzz1142, Succ(zzz11430), Succ(zzz11440), be) → new_mkVBalBranch3MkVBalBranch26(zzz1133, zzz1134, zzz1135, zzz1136, zzz1137, zzz1138, zzz1139, zzz1140, zzz1141, zzz1142, zzz11430, zzz11440, be)
new_mkVBalBranch3MkVBalBranch24(zzz340, zzz341, Neg(Succ(Succ(Succ(zzz3420000)))), zzz343, zzz344, zzz520, zzz521, Zero, zzz523, zzz524, zzz31, Succ(Zero), h) → new_mkVBalBranch3MkVBalBranch26(zzz340, zzz341, Succ(Succ(zzz3420000)), zzz343, zzz344, zzz520, zzz521, zzz523, zzz524, zzz31, Succ(zzz3420000), Zero, h)
new_mkVBalBranch3MkVBalBranch24(zzz340, zzz341, Neg(Succ(Zero)), zzz343, zzz344, zzz520, zzz521, Zero, zzz523, zzz524, zzz31, Zero, h) → new_mkVBalBranch3MkVBalBranch29(zzz340, zzz341, Zero, zzz343, zzz344, zzz520, zzz521, zzz523, zzz524, zzz31, h)
new_mkVBalBranch3MkVBalBranch20(zzz929, zzz930, zzz931, zzz932, zzz933, zzz934, zzz935, zzz936, zzz937, zzz938, zzz939, Zero, Succ(zzz9410), ba) → new_mkVBalBranch(zzz939, Branch(zzz934, zzz935, Pos(Succ(zzz936)), zzz937, zzz938), zzz932, ba)
new_mkVBalBranch3MkVBalBranch17(zzz340, zzz341, zzz34200, zzz343, zzz344, zzz520, zzz521, zzz52200, zzz523, zzz524, zzz31, h) → new_mkVBalBranch(zzz31, zzz524, Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), h)
new_mkVBalBranch3MkVBalBranch26(zzz1133, zzz1134, zzz1135, zzz1136, zzz1137, zzz1138, zzz1139, zzz1140, zzz1141, zzz1142, Zero, Zero, be) → new_mkVBalBranch3MkVBalBranch29(zzz1133, zzz1134, zzz1135, zzz1136, zzz1137, zzz1138, zzz1139, zzz1140, zzz1141, zzz1142, be)
new_mkVBalBranch3MkVBalBranch20(zzz929, zzz930, zzz931, zzz932, zzz933, zzz934, zzz935, zzz936, zzz937, zzz938, zzz939, Zero, Zero, ba) → new_mkVBalBranch3MkVBalBranch23(zzz929, zzz930, zzz931, zzz932, zzz933, zzz934, zzz935, zzz936, zzz937, zzz938, zzz939, ba)
new_mkVBalBranch3MkVBalBranch24(zzz340, zzz341, Neg(Succ(Succ(Zero))), zzz343, zzz344, zzz520, zzz521, Succ(zzz522000), zzz523, zzz524, zzz31, Succ(Zero), h) → new_mkVBalBranch3MkVBalBranch25(zzz340, zzz341, Succ(Zero), zzz343, zzz344, zzz520, zzz521, zzz522000, zzz523, zzz524, zzz31, Zero, Succ(zzz522000), h)
new_mkVBalBranch3MkVBalBranch24(zzz340, zzz341, Neg(Succ(Succ(Succ(zzz3420000)))), zzz343, zzz344, zzz520, zzz521, Succ(zzz522000), zzz523, zzz524, zzz31, Succ(Zero), h) → new_mkVBalBranch3MkVBalBranch25(zzz340, zzz341, Succ(Succ(zzz3420000)), zzz343, zzz344, zzz520, zzz521, zzz522000, zzz523, zzz524, zzz31, Succ(zzz3420000), Succ(zzz522000), h)
new_mkVBalBranch3MkVBalBranch20(zzz929, zzz930, zzz931, zzz932, zzz933, zzz934, zzz935, zzz936, zzz937, zzz938, zzz939, Succ(zzz9400), Succ(zzz9410), ba) → new_mkVBalBranch3MkVBalBranch20(zzz929, zzz930, zzz931, zzz932, zzz933, zzz934, zzz935, zzz936, zzz937, zzz938, zzz939, zzz9400, zzz9410, ba)
new_mkVBalBranch3MkVBalBranch24(zzz340, zzz341, Neg(Succ(Succ(zzz342000))), zzz343, zzz344, zzz520, zzz521, Succ(zzz522000), zzz523, zzz524, zzz31, Zero, h) → new_mkVBalBranch3MkVBalBranch25(zzz340, zzz341, Succ(zzz342000), zzz343, zzz344, zzz520, zzz521, zzz522000, zzz523, zzz524, zzz31, zzz342000, zzz522000, h)
new_mkVBalBranch3MkVBalBranch26(zzz1133, zzz1134, zzz1135, zzz1136, zzz1137, zzz1138, zzz1139, zzz1140, zzz1141, zzz1142, Succ(zzz11430), Zero, be) → new_mkVBalBranch3MkVBalBranch212(zzz1133, zzz1134, zzz1135, zzz1136, zzz1137, zzz1138, zzz1139, zzz1140, zzz1141, zzz1142, be)
new_mkVBalBranch3MkVBalBranch11(zzz2033, zzz2034, zzz2035, zzz2036, zzz2037, zzz2038, zzz2039, zzz2040, zzz2041, zzz2042, zzz2043, Succ(zzz20440), Succ(zzz20450), bb) → new_mkVBalBranch3MkVBalBranch11(zzz2033, zzz2034, zzz2035, zzz2036, zzz2037, zzz2038, zzz2039, zzz2040, zzz2041, zzz2042, zzz2043, zzz20440, zzz20450, bb)
new_mkVBalBranch3MkVBalBranch25(zzz537, zzz538, zzz539, zzz540, zzz541, zzz542, zzz543, zzz544, zzz545, zzz546, zzz547, Succ(zzz5480), Succ(zzz5490), bc) → new_mkVBalBranch3MkVBalBranch25(zzz537, zzz538, zzz539, zzz540, zzz541, zzz542, zzz543, zzz544, zzz545, zzz546, zzz547, zzz5480, zzz5490, bc)
new_mkVBalBranch3MkVBalBranch2(zzz340, zzz341, Neg(zzz3420), zzz343, zzz344, zzz520, zzz521, zzz52200, zzz523, zzz524, zzz31, Zero, h) → new_mkVBalBranch3MkVBalBranch22(zzz340, zzz341, zzz3420, zzz343, zzz344, zzz520, zzz521, zzz52200, zzz523, zzz524, zzz31, h)
new_mkVBalBranch3MkVBalBranch24(zzz340, zzz341, Neg(Succ(Zero)), zzz343, zzz344, zzz520, zzz521, Succ(zzz522000), zzz523, zzz524, zzz31, Zero, h) → new_mkVBalBranch3MkVBalBranch28(zzz340, zzz341, zzz343, zzz344, zzz520, zzz521, Succ(zzz522000), zzz523, zzz524, zzz31, h)
new_mkVBalBranch3MkVBalBranch24(zzz340, zzz341, Neg(Succ(Succ(zzz342000))), zzz343, zzz344, zzz520, zzz521, Zero, zzz523, zzz524, zzz31, Zero, h) → new_mkVBalBranch3MkVBalBranch14(zzz340, zzz341, Succ(zzz342000), zzz343, zzz344, zzz520, zzz521, zzz523, zzz524, zzz31, new_primMulNat1(Succ(zzz342000)), h)
new_mkVBalBranch3MkVBalBranch210(zzz340, zzz341, zzz343, zzz344, zzz520, zzz521, zzz52200, zzz523, zzz524, zzz31, h) → new_mkVBalBranch(zzz31, Branch(zzz520, zzz521, Neg(Succ(zzz52200)), zzz523, zzz524), zzz343, h)
new_mkVBalBranch3MkVBalBranch26(zzz1133, zzz1134, zzz1135, zzz1136, zzz1137, zzz1138, zzz1139, zzz1140, zzz1141, zzz1142, Zero, Succ(zzz11440), be) → new_mkVBalBranch(zzz1142, Branch(zzz1138, zzz1139, Neg(Succ(Zero)), zzz1140, zzz1141), zzz1136, be)
new_mkVBalBranch3MkVBalBranch24(zzz340, zzz341, Neg(Succ(Succ(Zero))), zzz343, zzz344, zzz520, zzz521, Zero, zzz523, zzz524, zzz31, Succ(Zero), h) → new_mkVBalBranch3MkVBalBranch26(zzz340, zzz341, Succ(Zero), zzz343, zzz344, zzz520, zzz521, zzz523, zzz524, zzz31, Zero, Zero, h)
new_mkVBalBranch(zzz31, Branch(zzz520, zzz521, Pos(Zero), zzz523, zzz524), Branch(zzz340, zzz341, Pos(Succ(zzz34200)), zzz343, zzz344), h) → new_mkVBalBranch(zzz31, Branch(zzz520, zzz521, Pos(Zero), zzz523, zzz524), zzz343, h)
new_mkVBalBranch3MkVBalBranch29(zzz818, zzz819, zzz820, zzz821, zzz822, zzz823, zzz824, zzz825, zzz826, zzz827, bf) → new_mkVBalBranch3MkVBalBranch14(zzz818, zzz819, zzz820, zzz821, zzz822, zzz823, zzz824, zzz825, zzz826, zzz827, new_primMulNat1(zzz820), bf)
new_mkVBalBranch3MkVBalBranch2(zzz340, zzz341, Pos(Zero), zzz343, zzz344, zzz520, zzz521, zzz52200, zzz523, zzz524, zzz31, Succ(zzz680), h) → new_mkVBalBranch(zzz31, zzz524, Branch(zzz340, zzz341, Pos(Zero), zzz343, zzz344), h)
new_mkVBalBranch3MkVBalBranch21(zzz340, zzz341, zzz343, zzz344, zzz520, zzz521, zzz52200, zzz523, zzz524, zzz31, h) → new_mkVBalBranch(zzz31, zzz524, Branch(zzz340, zzz341, Pos(Zero), zzz343, zzz344), h)
new_mkVBalBranch(zzz31, Branch(zzz520, zzz521, Neg(Succ(zzz52200)), zzz523, zzz524), Branch(zzz340, zzz341, zzz342, zzz343, zzz344), h) → new_mkVBalBranch3MkVBalBranch24(zzz340, zzz341, zzz342, zzz343, zzz344, zzz520, zzz521, zzz52200, zzz523, zzz524, zzz31, new_primMulNat0(zzz52200), h)
new_mkVBalBranch3MkVBalBranch24(zzz340, zzz341, Pos(zzz3420), zzz343, zzz344, zzz520, zzz521, zzz52200, zzz523, zzz524, zzz31, Zero, h) → new_mkVBalBranch3MkVBalBranch27(zzz340, zzz341, zzz3420, zzz343, zzz344, zzz520, zzz521, zzz52200, zzz523, zzz524, zzz31, h)
new_mkVBalBranch3MkVBalBranch23(zzz929, zzz930, zzz931, zzz932, zzz933, zzz934, zzz935, zzz936, zzz937, zzz938, zzz939, ba) → new_mkVBalBranch3MkVBalBranch10(zzz929, zzz930, zzz931, zzz932, zzz933, zzz934, zzz935, zzz936, zzz937, zzz938, zzz939, new_primMulNat1(zzz931), ba)
new_mkVBalBranch3MkVBalBranch211(zzz537, zzz538, zzz539, zzz540, zzz541, zzz542, zzz543, zzz544, zzz545, zzz546, zzz547, bc) → new_mkVBalBranch3MkVBalBranch15(zzz537, zzz538, zzz539, zzz540, zzz541, zzz542, zzz543, zzz544, zzz545, zzz546, zzz547, new_primMulNat1(zzz539), bc)
new_mkVBalBranch3MkVBalBranch212(zzz818, zzz819, zzz820, zzz821, zzz822, zzz823, zzz824, zzz825, zzz826, zzz827, bf) → new_mkVBalBranch3MkVBalBranch14(zzz818, zzz819, zzz820, zzz821, zzz822, zzz823, zzz824, zzz825, zzz826, zzz827, new_primMulNat1(zzz820), bf)
new_mkVBalBranch3MkVBalBranch15(zzz537, zzz538, zzz539, zzz540, zzz541, zzz542, zzz543, zzz544, zzz545, zzz546, zzz547, Succ(zzz6990), bc) → new_mkVBalBranch3MkVBalBranch16(zzz537, zzz538, zzz539, zzz540, zzz541, zzz542, zzz543, Succ(zzz544), zzz545, zzz546, zzz547, Succ(Succ(zzz544)), Succ(zzz6990), bc)
new_mkVBalBranch3MkVBalBranch24(zzz340, zzz341, Neg(Succ(Succ(Succ(zzz3420000)))), zzz343, zzz344, zzz520, zzz521, Zero, zzz523, zzz524, zzz31, Succ(Succ(zzz6900)), h) → new_mkVBalBranch3MkVBalBranch26(zzz340, zzz341, Succ(Succ(zzz3420000)), zzz343, zzz344, zzz520, zzz521, zzz523, zzz524, zzz31, Succ(zzz3420000), Succ(zzz6900), h)
new_mkVBalBranch3MkVBalBranch27(zzz340, zzz341, zzz3420, zzz343, zzz344, zzz520, zzz521, zzz52200, zzz523, zzz524, zzz31, h) → new_mkVBalBranch(zzz31, Branch(zzz520, zzz521, Neg(Succ(zzz52200)), zzz523, zzz524), zzz343, h)
new_mkVBalBranch3MkVBalBranch24(zzz340, zzz341, Pos(zzz3420), zzz343, zzz344, zzz520, zzz521, zzz52200, zzz523, zzz524, zzz31, Succ(zzz690), h) → new_mkVBalBranch(zzz31, Branch(zzz520, zzz521, Neg(Succ(zzz52200)), zzz523, zzz524), zzz343, h)
new_mkVBalBranch3MkVBalBranch12(zzz340, zzz341, zzz34200, zzz343, zzz344, zzz520, zzz521, zzz523, zzz524, zzz31, Succ(zzz1250), h) → new_mkVBalBranch(zzz31, zzz524, Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), h)
new_mkVBalBranch3MkVBalBranch28(zzz340, zzz341, zzz343, zzz344, zzz520, zzz521, zzz52200, zzz523, zzz524, zzz31, h) → new_mkVBalBranch(zzz31, Branch(zzz520, zzz521, Neg(Succ(zzz52200)), zzz523, zzz524), zzz343, h)
new_mkVBalBranch3MkVBalBranch25(zzz537, zzz538, zzz539, zzz540, zzz541, zzz542, zzz543, zzz544, zzz545, zzz546, zzz547, Succ(zzz5480), Zero, bc) → new_mkVBalBranch3MkVBalBranch15(zzz537, zzz538, zzz539, zzz540, zzz541, zzz542, zzz543, zzz544, zzz545, zzz546, zzz547, new_primMulNat1(zzz539), bc)
new_mkVBalBranch3MkVBalBranch24(zzz340, zzz341, Neg(Succ(Succ(Zero))), zzz343, zzz344, zzz520, zzz521, Zero, zzz523, zzz524, zzz31, Succ(Succ(zzz6900)), h) → new_mkVBalBranch3MkVBalBranch26(zzz340, zzz341, Succ(Zero), zzz343, zzz344, zzz520, zzz521, zzz523, zzz524, zzz31, Zero, Succ(zzz6900), h)
new_mkVBalBranch(zzz31, Branch(zzz520, zzz521, Pos(Zero), zzz523, zzz524), Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), h) → new_mkVBalBranch3MkVBalBranch12(zzz340, zzz341, zzz34200, zzz343, zzz344, zzz520, zzz521, zzz523, zzz524, zzz31, new_primPlusNat2(new_primMulNat0(zzz34200), Succ(zzz34200)), h)
new_mkVBalBranch3MkVBalBranch22(zzz340, zzz341, Zero, zzz343, zzz344, zzz520, zzz521, zzz52200, zzz523, zzz524, zzz31, h) → new_mkVBalBranch(zzz31, zzz524, Branch(zzz340, zzz341, Neg(Zero), zzz343, zzz344), h)
new_mkVBalBranch3MkVBalBranch1(zzz340, zzz341, zzz34200, zzz343, zzz344, zzz520, zzz521, zzz52200, zzz523, zzz524, zzz31, Succ(zzz1430), h) → new_mkVBalBranch(zzz31, zzz524, Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), h)
new_mkVBalBranch3MkVBalBranch22(zzz340, zzz341, Succ(zzz34200), zzz343, zzz344, zzz520, zzz521, zzz52200, zzz523, zzz524, zzz31, h) → new_mkVBalBranch3MkVBalBranch1(zzz340, zzz341, zzz34200, zzz343, zzz344, zzz520, zzz521, zzz52200, zzz523, zzz524, zzz31, new_primPlusNat2(new_primMulNat0(zzz34200), Succ(zzz34200)), h)
new_mkVBalBranch3MkVBalBranch24(zzz340, zzz341, Neg(Succ(Zero)), zzz343, zzz344, zzz520, zzz521, zzz52200, zzz523, zzz524, zzz31, Succ(zzz690), h) → new_mkVBalBranch(zzz31, Branch(zzz520, zzz521, Neg(Succ(zzz52200)), zzz523, zzz524), zzz343, h)
new_mkVBalBranch3MkVBalBranch13(zzz340, zzz341, zzz34200, zzz343, zzz344, zzz520, zzz521, zzz523, zzz524, zzz31, Succ(zzz1290), h) → new_mkVBalBranch(zzz31, zzz524, Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), h)
new_mkVBalBranch3MkVBalBranch2(zzz340, zzz341, Pos(Succ(zzz34200)), zzz343, zzz344, zzz520, zzz521, zzz52200, zzz523, zzz524, zzz31, Succ(zzz680), h) → new_mkVBalBranch3MkVBalBranch20(zzz340, zzz341, zzz34200, zzz343, zzz344, zzz520, zzz521, zzz52200, zzz523, zzz524, zzz31, Succ(new_primPlusNat2(zzz680, zzz52200)), zzz34200, h)
new_mkVBalBranch(zzz31, Branch(zzz520, zzz521, Neg(Zero), zzz523, zzz524), Branch(zzz340, zzz341, Pos(Succ(zzz34200)), zzz343, zzz344), h) → new_mkVBalBranch(zzz31, Branch(zzz520, zzz521, Neg(Zero), zzz523, zzz524), zzz343, h)
new_mkVBalBranch3MkVBalBranch24(zzz340, zzz341, Neg(Zero), zzz343, zzz344, zzz520, zzz521, zzz52200, zzz523, zzz524, zzz31, Succ(zzz690), h) → new_mkVBalBranch(zzz31, Branch(zzz520, zzz521, Neg(Succ(zzz52200)), zzz523, zzz524), zzz343, h)
new_mkVBalBranch3MkVBalBranch1(zzz340, zzz341, zzz34200, zzz343, zzz344, zzz520, zzz521, zzz52200, zzz523, zzz524, zzz31, Zero, h) → new_mkVBalBranch3MkVBalBranch17(zzz340, zzz341, zzz34200, zzz343, zzz344, zzz520, zzz521, zzz52200, zzz523, zzz524, zzz31, h)
new_mkVBalBranch3MkVBalBranch16(zzz1702, zzz1703, zzz1704, zzz1705, zzz1706, zzz1707, zzz1708, zzz1709, zzz1710, zzz1711, zzz1712, Succ(zzz17130), Succ(zzz17140), bd) → new_mkVBalBranch3MkVBalBranch16(zzz1702, zzz1703, zzz1704, zzz1705, zzz1706, zzz1707, zzz1708, zzz1709, zzz1710, zzz1711, zzz1712, zzz17130, zzz17140, bd)
new_mkVBalBranch3MkVBalBranch25(zzz537, zzz538, zzz539, zzz540, zzz541, zzz542, zzz543, zzz544, zzz545, zzz546, zzz547, Zero, Succ(zzz5490), bc) → new_mkVBalBranch(zzz547, Branch(zzz542, zzz543, Neg(Succ(Succ(zzz544))), zzz545, zzz546), zzz540, bc)
new_mkVBalBranch3MkVBalBranch10(zzz929, zzz930, zzz931, zzz932, zzz933, zzz934, zzz935, zzz936, zzz937, zzz938, zzz939, Succ(zzz10020), ba) → new_mkVBalBranch3MkVBalBranch11(zzz929, zzz930, zzz931, zzz932, zzz933, zzz934, zzz935, zzz936, zzz937, zzz938, zzz939, Succ(zzz10020), Succ(zzz936), ba)
new_mkVBalBranch3MkVBalBranch2(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344, zzz520, zzz521, zzz52200, zzz523, zzz524, zzz31, Succ(zzz680), h) → new_mkVBalBranch3MkVBalBranch1(zzz340, zzz341, zzz34200, zzz343, zzz344, zzz520, zzz521, zzz52200, zzz523, zzz524, zzz31, new_primPlusNat2(new_primMulNat0(zzz34200), Succ(zzz34200)), h)
new_mkVBalBranch3MkVBalBranch14(zzz818, zzz819, zzz820, zzz821, zzz822, zzz823, zzz824, zzz825, zzz826, zzz827, Succ(zzz8960), bf) → new_mkVBalBranch3MkVBalBranch16(zzz818, zzz819, zzz820, zzz821, zzz822, zzz823, zzz824, Zero, zzz825, zzz826, zzz827, Succ(Zero), Succ(zzz8960), bf)
new_mkVBalBranch3MkVBalBranch24(zzz340, zzz341, Neg(Succ(Succ(Succ(zzz3420000)))), zzz343, zzz344, zzz520, zzz521, Succ(zzz522000), zzz523, zzz524, zzz31, Succ(Succ(zzz6900)), h) → new_mkVBalBranch3MkVBalBranch25(zzz340, zzz341, Succ(Succ(zzz3420000)), zzz343, zzz344, zzz520, zzz521, zzz522000, zzz523, zzz524, zzz31, Succ(zzz3420000), Succ(Succ(new_primPlusNat2(zzz6900, zzz522000))), h)
new_mkVBalBranch3MkVBalBranch2(zzz340, zzz341, Pos(Succ(zzz34200)), zzz343, zzz344, zzz520, zzz521, zzz52200, zzz523, zzz524, zzz31, Zero, h) → new_mkVBalBranch3MkVBalBranch20(zzz340, zzz341, zzz34200, zzz343, zzz344, zzz520, zzz521, zzz52200, zzz523, zzz524, zzz31, zzz52200, zzz34200, h)
new_mkVBalBranch3MkVBalBranch24(zzz340, zzz341, Neg(Zero), zzz343, zzz344, zzz520, zzz521, zzz52200, zzz523, zzz524, zzz31, Zero, h) → new_mkVBalBranch3MkVBalBranch210(zzz340, zzz341, zzz343, zzz344, zzz520, zzz521, zzz52200, zzz523, zzz524, zzz31, h)
new_mkVBalBranch3MkVBalBranch24(zzz340, zzz341, Neg(Succ(Succ(Zero))), zzz343, zzz344, zzz520, zzz521, Succ(zzz522000), zzz523, zzz524, zzz31, Succ(Succ(zzz6900)), h) → new_mkVBalBranch3MkVBalBranch25(zzz340, zzz341, Succ(Zero), zzz343, zzz344, zzz520, zzz521, zzz522000, zzz523, zzz524, zzz31, Zero, Succ(Succ(new_primPlusNat2(zzz6900, zzz522000))), h)
new_mkVBalBranch3MkVBalBranch20(zzz929, zzz930, zzz931, zzz932, zzz933, zzz934, zzz935, zzz936, zzz937, zzz938, zzz939, Succ(zzz9400), Zero, ba) → new_mkVBalBranch3MkVBalBranch10(zzz929, zzz930, zzz931, zzz932, zzz933, zzz934, zzz935, zzz936, zzz937, zzz938, zzz939, new_primMulNat1(zzz931), ba)
new_mkVBalBranch3MkVBalBranch2(zzz340, zzz341, Neg(Zero), zzz343, zzz344, zzz520, zzz521, zzz52200, zzz523, zzz524, zzz31, Succ(zzz680), h) → new_mkVBalBranch(zzz31, zzz524, Branch(zzz340, zzz341, Neg(Zero), zzz343, zzz344), h)
new_mkVBalBranch(zzz31, Branch(zzz520, zzz521, Pos(Succ(zzz52200)), zzz523, zzz524), Branch(zzz340, zzz341, zzz342, zzz343, zzz344), h) → new_mkVBalBranch3MkVBalBranch2(zzz340, zzz341, zzz342, zzz343, zzz344, zzz520, zzz521, zzz52200, zzz523, zzz524, zzz31, new_primMulNat0(zzz52200), h)
new_mkVBalBranch3MkVBalBranch16(zzz1702, zzz1703, zzz1704, zzz1705, zzz1706, zzz1707, zzz1708, zzz1709, zzz1710, zzz1711, zzz1712, Zero, Succ(zzz17140), bd) → new_mkVBalBranch(zzz1712, zzz1711, Branch(zzz1702, zzz1703, Neg(Succ(zzz1704)), zzz1705, zzz1706), bd)
new_mkVBalBranch(zzz31, Branch(zzz520, zzz521, Neg(Zero), zzz523, zzz524), Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), h) → new_mkVBalBranch3MkVBalBranch13(zzz340, zzz341, zzz34200, zzz343, zzz344, zzz520, zzz521, zzz523, zzz524, zzz31, new_primMulNat1(zzz34200), h)
new_mkVBalBranch3MkVBalBranch10(zzz929, zzz930, zzz931, zzz932, zzz933, zzz934, zzz935, zzz936, zzz937, zzz938, zzz939, Zero, ba) → new_mkVBalBranch3MkVBalBranch11(zzz929, zzz930, zzz931, zzz932, zzz933, zzz934, zzz935, zzz936, zzz937, zzz938, zzz939, Zero, Succ(zzz936), ba)
new_mkVBalBranch3MkVBalBranch25(zzz537, zzz538, zzz539, zzz540, zzz541, zzz542, zzz543, zzz544, zzz545, zzz546, zzz547, Zero, Zero, bc) → new_mkVBalBranch3MkVBalBranch211(zzz537, zzz538, zzz539, zzz540, zzz541, zzz542, zzz543, zzz544, zzz545, zzz546, zzz547, bc)
new_mkVBalBranch3MkVBalBranch2(zzz340, zzz341, Pos(Zero), zzz343, zzz344, zzz520, zzz521, zzz52200, zzz523, zzz524, zzz31, Zero, h) → new_mkVBalBranch3MkVBalBranch21(zzz340, zzz341, zzz343, zzz344, zzz520, zzz521, zzz52200, zzz523, zzz524, zzz31, h)

The TRS R consists of the following rules:

new_primPlusNat1(Zero) → Zero
new_primMulNat0(zzz6200) → new_primPlusNat3(Succ(new_primPlusNat3(new_primPlusNat1(zzz6200), zzz6200)), Succ(zzz6200))
new_primPlusNat2(Succ(zzz900), Succ(zzz9100)) → Succ(Succ(new_primPlusNat2(zzz900, zzz9100)))
new_primPlusNat3(zzz90, Succ(zzz910)) → Succ(Succ(new_primPlusNat2(zzz90, zzz910)))
new_primPlusNat3(zzz90, Zero) → Succ(zzz90)
new_primMulNat1(zzz34200) → new_primPlusNat2(new_primMulNat0(zzz34200), Succ(zzz34200))
new_primPlusNat2(Zero, Zero) → Zero
new_primPlusNat1(Succ(zzz62000)) → Succ(Succ(new_primPlusNat1(zzz62000)))
new_primPlusNat2(Succ(zzz900), Zero) → Succ(zzz900)
new_primPlusNat2(Zero, Succ(zzz9100)) → Succ(zzz9100)

The set Q consists of the following terms:

new_primPlusNat2(Zero, Succ(x0))
new_primMulNat1(x0)
new_primMulNat0(x0)
new_primPlusNat3(x0, Succ(x1))
new_primPlusNat2(Succ(x0), Succ(x1))
new_primPlusNat3(x0, Zero)
new_primPlusNat1(Zero)
new_primPlusNat2(Zero, Zero)
new_primPlusNat1(Succ(x0))
new_primPlusNat2(Succ(x0), Zero)

We have to consider all minimal (P,Q,R)-chains.
By rewriting [15] the rule new_mkVBalBranch(zzz31, Branch(zzz520, zzz521, Neg(Succ(zzz52200)), zzz523, zzz524), Branch(zzz340, zzz341, zzz342, zzz343, zzz344), h) → new_mkVBalBranch3MkVBalBranch24(zzz340, zzz341, zzz342, zzz343, zzz344, zzz520, zzz521, zzz52200, zzz523, zzz524, zzz31, new_primMulNat0(zzz52200), h) at position [11] we obtained the following new rules:

new_mkVBalBranch(zzz31, Branch(zzz520, zzz521, Neg(Succ(zzz52200)), zzz523, zzz524), Branch(zzz340, zzz341, zzz342, zzz343, zzz344), h) → new_mkVBalBranch3MkVBalBranch24(zzz340, zzz341, zzz342, zzz343, zzz344, zzz520, zzz521, zzz52200, zzz523, zzz524, zzz31, new_primPlusNat3(Succ(new_primPlusNat3(new_primPlusNat1(zzz52200), zzz52200)), Succ(zzz52200)), 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
                                    ↳ DependencyGraphProof
                                      ↳ QDP
                                        ↳ Rewriting
                                          ↳ QDP
                                            ↳ Rewriting
                                              ↳ QDP
                                                ↳ Rewriting
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP

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

new_mkVBalBranch3MkVBalBranch11(zzz2033, zzz2034, zzz2035, zzz2036, zzz2037, zzz2038, zzz2039, zzz2040, zzz2041, zzz2042, zzz2043, Zero, Succ(zzz20450), bb) → new_mkVBalBranch(zzz2043, zzz2042, Branch(zzz2033, zzz2034, Pos(Succ(zzz2035)), zzz2036, zzz2037), bb)
new_mkVBalBranch3MkVBalBranch26(zzz1133, zzz1134, zzz1135, zzz1136, zzz1137, zzz1138, zzz1139, zzz1140, zzz1141, zzz1142, Succ(zzz11430), Succ(zzz11440), be) → new_mkVBalBranch3MkVBalBranch26(zzz1133, zzz1134, zzz1135, zzz1136, zzz1137, zzz1138, zzz1139, zzz1140, zzz1141, zzz1142, zzz11430, zzz11440, be)
new_mkVBalBranch3MkVBalBranch24(zzz340, zzz341, Neg(Succ(Succ(Succ(zzz3420000)))), zzz343, zzz344, zzz520, zzz521, Zero, zzz523, zzz524, zzz31, Succ(Zero), h) → new_mkVBalBranch3MkVBalBranch26(zzz340, zzz341, Succ(Succ(zzz3420000)), zzz343, zzz344, zzz520, zzz521, zzz523, zzz524, zzz31, Succ(zzz3420000), Zero, h)
new_mkVBalBranch3MkVBalBranch24(zzz340, zzz341, Neg(Succ(Zero)), zzz343, zzz344, zzz520, zzz521, Zero, zzz523, zzz524, zzz31, Zero, h) → new_mkVBalBranch3MkVBalBranch29(zzz340, zzz341, Zero, zzz343, zzz344, zzz520, zzz521, zzz523, zzz524, zzz31, h)
new_mkVBalBranch3MkVBalBranch20(zzz929, zzz930, zzz931, zzz932, zzz933, zzz934, zzz935, zzz936, zzz937, zzz938, zzz939, Zero, Succ(zzz9410), ba) → new_mkVBalBranch(zzz939, Branch(zzz934, zzz935, Pos(Succ(zzz936)), zzz937, zzz938), zzz932, ba)
new_mkVBalBranch3MkVBalBranch17(zzz340, zzz341, zzz34200, zzz343, zzz344, zzz520, zzz521, zzz52200, zzz523, zzz524, zzz31, h) → new_mkVBalBranch(zzz31, zzz524, Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), h)
new_mkVBalBranch3MkVBalBranch26(zzz1133, zzz1134, zzz1135, zzz1136, zzz1137, zzz1138, zzz1139, zzz1140, zzz1141, zzz1142, Zero, Zero, be) → new_mkVBalBranch3MkVBalBranch29(zzz1133, zzz1134, zzz1135, zzz1136, zzz1137, zzz1138, zzz1139, zzz1140, zzz1141, zzz1142, be)
new_mkVBalBranch3MkVBalBranch20(zzz929, zzz930, zzz931, zzz932, zzz933, zzz934, zzz935, zzz936, zzz937, zzz938, zzz939, Zero, Zero, ba) → new_mkVBalBranch3MkVBalBranch23(zzz929, zzz930, zzz931, zzz932, zzz933, zzz934, zzz935, zzz936, zzz937, zzz938, zzz939, ba)
new_mkVBalBranch3MkVBalBranch24(zzz340, zzz341, Neg(Succ(Succ(Zero))), zzz343, zzz344, zzz520, zzz521, Succ(zzz522000), zzz523, zzz524, zzz31, Succ(Zero), h) → new_mkVBalBranch3MkVBalBranch25(zzz340, zzz341, Succ(Zero), zzz343, zzz344, zzz520, zzz521, zzz522000, zzz523, zzz524, zzz31, Zero, Succ(zzz522000), h)
new_mkVBalBranch3MkVBalBranch20(zzz929, zzz930, zzz931, zzz932, zzz933, zzz934, zzz935, zzz936, zzz937, zzz938, zzz939, Succ(zzz9400), Succ(zzz9410), ba) → new_mkVBalBranch3MkVBalBranch20(zzz929, zzz930, zzz931, zzz932, zzz933, zzz934, zzz935, zzz936, zzz937, zzz938, zzz939, zzz9400, zzz9410, ba)
new_mkVBalBranch3MkVBalBranch24(zzz340, zzz341, Neg(Succ(Succ(Succ(zzz3420000)))), zzz343, zzz344, zzz520, zzz521, Succ(zzz522000), zzz523, zzz524, zzz31, Succ(Zero), h) → new_mkVBalBranch3MkVBalBranch25(zzz340, zzz341, Succ(Succ(zzz3420000)), zzz343, zzz344, zzz520, zzz521, zzz522000, zzz523, zzz524, zzz31, Succ(zzz3420000), Succ(zzz522000), h)
new_mkVBalBranch3MkVBalBranch26(zzz1133, zzz1134, zzz1135, zzz1136, zzz1137, zzz1138, zzz1139, zzz1140, zzz1141, zzz1142, Succ(zzz11430), Zero, be) → new_mkVBalBranch3MkVBalBranch212(zzz1133, zzz1134, zzz1135, zzz1136, zzz1137, zzz1138, zzz1139, zzz1140, zzz1141, zzz1142, be)
new_mkVBalBranch3MkVBalBranch24(zzz340, zzz341, Neg(Succ(Succ(zzz342000))), zzz343, zzz344, zzz520, zzz521, Succ(zzz522000), zzz523, zzz524, zzz31, Zero, h) → new_mkVBalBranch3MkVBalBranch25(zzz340, zzz341, Succ(zzz342000), zzz343, zzz344, zzz520, zzz521, zzz522000, zzz523, zzz524, zzz31, zzz342000, zzz522000, h)
new_mkVBalBranch3MkVBalBranch11(zzz2033, zzz2034, zzz2035, zzz2036, zzz2037, zzz2038, zzz2039, zzz2040, zzz2041, zzz2042, zzz2043, Succ(zzz20440), Succ(zzz20450), bb) → new_mkVBalBranch3MkVBalBranch11(zzz2033, zzz2034, zzz2035, zzz2036, zzz2037, zzz2038, zzz2039, zzz2040, zzz2041, zzz2042, zzz2043, zzz20440, zzz20450, bb)
new_mkVBalBranch3MkVBalBranch2(zzz340, zzz341, Neg(zzz3420), zzz343, zzz344, zzz520, zzz521, zzz52200, zzz523, zzz524, zzz31, Zero, h) → new_mkVBalBranch3MkVBalBranch22(zzz340, zzz341, zzz3420, zzz343, zzz344, zzz520, zzz521, zzz52200, zzz523, zzz524, zzz31, h)
new_mkVBalBranch3MkVBalBranch25(zzz537, zzz538, zzz539, zzz540, zzz541, zzz542, zzz543, zzz544, zzz545, zzz546, zzz547, Succ(zzz5480), Succ(zzz5490), bc) → new_mkVBalBranch3MkVBalBranch25(zzz537, zzz538, zzz539, zzz540, zzz541, zzz542, zzz543, zzz544, zzz545, zzz546, zzz547, zzz5480, zzz5490, bc)
new_mkVBalBranch(zzz31, Branch(zzz520, zzz521, Neg(Succ(zzz52200)), zzz523, zzz524), Branch(zzz340, zzz341, zzz342, zzz343, zzz344), h) → new_mkVBalBranch3MkVBalBranch24(zzz340, zzz341, zzz342, zzz343, zzz344, zzz520, zzz521, zzz52200, zzz523, zzz524, zzz31, new_primPlusNat3(Succ(new_primPlusNat3(new_primPlusNat1(zzz52200), zzz52200)), Succ(zzz52200)), h)
new_mkVBalBranch3MkVBalBranch24(zzz340, zzz341, Neg(Succ(Zero)), zzz343, zzz344, zzz520, zzz521, Succ(zzz522000), zzz523, zzz524, zzz31, Zero, h) → new_mkVBalBranch3MkVBalBranch28(zzz340, zzz341, zzz343, zzz344, zzz520, zzz521, Succ(zzz522000), zzz523, zzz524, zzz31, h)
new_mkVBalBranch3MkVBalBranch210(zzz340, zzz341, zzz343, zzz344, zzz520, zzz521, zzz52200, zzz523, zzz524, zzz31, h) → new_mkVBalBranch(zzz31, Branch(zzz520, zzz521, Neg(Succ(zzz52200)), zzz523, zzz524), zzz343, h)
new_mkVBalBranch3MkVBalBranch24(zzz340, zzz341, Neg(Succ(Succ(zzz342000))), zzz343, zzz344, zzz520, zzz521, Zero, zzz523, zzz524, zzz31, Zero, h) → new_mkVBalBranch3MkVBalBranch14(zzz340, zzz341, Succ(zzz342000), zzz343, zzz344, zzz520, zzz521, zzz523, zzz524, zzz31, new_primMulNat1(Succ(zzz342000)), h)
new_mkVBalBranch3MkVBalBranch26(zzz1133, zzz1134, zzz1135, zzz1136, zzz1137, zzz1138, zzz1139, zzz1140, zzz1141, zzz1142, Zero, Succ(zzz11440), be) → new_mkVBalBranch(zzz1142, Branch(zzz1138, zzz1139, Neg(Succ(Zero)), zzz1140, zzz1141), zzz1136, be)
new_mkVBalBranch3MkVBalBranch24(zzz340, zzz341, Neg(Succ(Succ(Zero))), zzz343, zzz344, zzz520, zzz521, Zero, zzz523, zzz524, zzz31, Succ(Zero), h) → new_mkVBalBranch3MkVBalBranch26(zzz340, zzz341, Succ(Zero), zzz343, zzz344, zzz520, zzz521, zzz523, zzz524, zzz31, Zero, Zero, h)
new_mkVBalBranch(zzz31, Branch(zzz520, zzz521, Pos(Zero), zzz523, zzz524), Branch(zzz340, zzz341, Pos(Succ(zzz34200)), zzz343, zzz344), h) → new_mkVBalBranch(zzz31, Branch(zzz520, zzz521, Pos(Zero), zzz523, zzz524), zzz343, h)
new_mkVBalBranch3MkVBalBranch29(zzz818, zzz819, zzz820, zzz821, zzz822, zzz823, zzz824, zzz825, zzz826, zzz827, bf) → new_mkVBalBranch3MkVBalBranch14(zzz818, zzz819, zzz820, zzz821, zzz822, zzz823, zzz824, zzz825, zzz826, zzz827, new_primMulNat1(zzz820), bf)
new_mkVBalBranch3MkVBalBranch2(zzz340, zzz341, Pos(Zero), zzz343, zzz344, zzz520, zzz521, zzz52200, zzz523, zzz524, zzz31, Succ(zzz680), h) → new_mkVBalBranch(zzz31, zzz524, Branch(zzz340, zzz341, Pos(Zero), zzz343, zzz344), h)
new_mkVBalBranch3MkVBalBranch21(zzz340, zzz341, zzz343, zzz344, zzz520, zzz521, zzz52200, zzz523, zzz524, zzz31, h) → new_mkVBalBranch(zzz31, zzz524, Branch(zzz340, zzz341, Pos(Zero), zzz343, zzz344), h)
new_mkVBalBranch3MkVBalBranch24(zzz340, zzz341, Pos(zzz3420), zzz343, zzz344, zzz520, zzz521, zzz52200, zzz523, zzz524, zzz31, Zero, h) → new_mkVBalBranch3MkVBalBranch27(zzz340, zzz341, zzz3420, zzz343, zzz344, zzz520, zzz521, zzz52200, zzz523, zzz524, zzz31, h)
new_mkVBalBranch3MkVBalBranch23(zzz929, zzz930, zzz931, zzz932, zzz933, zzz934, zzz935, zzz936, zzz937, zzz938, zzz939, ba) → new_mkVBalBranch3MkVBalBranch10(zzz929, zzz930, zzz931, zzz932, zzz933, zzz934, zzz935, zzz936, zzz937, zzz938, zzz939, new_primMulNat1(zzz931), ba)
new_mkVBalBranch3MkVBalBranch212(zzz818, zzz819, zzz820, zzz821, zzz822, zzz823, zzz824, zzz825, zzz826, zzz827, bf) → new_mkVBalBranch3MkVBalBranch14(zzz818, zzz819, zzz820, zzz821, zzz822, zzz823, zzz824, zzz825, zzz826, zzz827, new_primMulNat1(zzz820), bf)
new_mkVBalBranch3MkVBalBranch211(zzz537, zzz538, zzz539, zzz540, zzz541, zzz542, zzz543, zzz544, zzz545, zzz546, zzz547, bc) → new_mkVBalBranch3MkVBalBranch15(zzz537, zzz538, zzz539, zzz540, zzz541, zzz542, zzz543, zzz544, zzz545, zzz546, zzz547, new_primMulNat1(zzz539), bc)
new_mkVBalBranch3MkVBalBranch24(zzz340, zzz341, Neg(Succ(Succ(Succ(zzz3420000)))), zzz343, zzz344, zzz520, zzz521, Zero, zzz523, zzz524, zzz31, Succ(Succ(zzz6900)), h) → new_mkVBalBranch3MkVBalBranch26(zzz340, zzz341, Succ(Succ(zzz3420000)), zzz343, zzz344, zzz520, zzz521, zzz523, zzz524, zzz31, Succ(zzz3420000), Succ(zzz6900), h)
new_mkVBalBranch3MkVBalBranch15(zzz537, zzz538, zzz539, zzz540, zzz541, zzz542, zzz543, zzz544, zzz545, zzz546, zzz547, Succ(zzz6990), bc) → new_mkVBalBranch3MkVBalBranch16(zzz537, zzz538, zzz539, zzz540, zzz541, zzz542, zzz543, Succ(zzz544), zzz545, zzz546, zzz547, Succ(Succ(zzz544)), Succ(zzz6990), bc)
new_mkVBalBranch3MkVBalBranch27(zzz340, zzz341, zzz3420, zzz343, zzz344, zzz520, zzz521, zzz52200, zzz523, zzz524, zzz31, h) → new_mkVBalBranch(zzz31, Branch(zzz520, zzz521, Neg(Succ(zzz52200)), zzz523, zzz524), zzz343, h)
new_mkVBalBranch3MkVBalBranch24(zzz340, zzz341, Pos(zzz3420), zzz343, zzz344, zzz520, zzz521, zzz52200, zzz523, zzz524, zzz31, Succ(zzz690), h) → new_mkVBalBranch(zzz31, Branch(zzz520, zzz521, Neg(Succ(zzz52200)), zzz523, zzz524), zzz343, h)
new_mkVBalBranch3MkVBalBranch12(zzz340, zzz341, zzz34200, zzz343, zzz344, zzz520, zzz521, zzz523, zzz524, zzz31, Succ(zzz1250), h) → new_mkVBalBranch(zzz31, zzz524, Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), h)
new_mkVBalBranch3MkVBalBranch25(zzz537, zzz538, zzz539, zzz540, zzz541, zzz542, zzz543, zzz544, zzz545, zzz546, zzz547, Succ(zzz5480), Zero, bc) → new_mkVBalBranch3MkVBalBranch15(zzz537, zzz538, zzz539, zzz540, zzz541, zzz542, zzz543, zzz544, zzz545, zzz546, zzz547, new_primMulNat1(zzz539), bc)
new_mkVBalBranch3MkVBalBranch28(zzz340, zzz341, zzz343, zzz344, zzz520, zzz521, zzz52200, zzz523, zzz524, zzz31, h) → new_mkVBalBranch(zzz31, Branch(zzz520, zzz521, Neg(Succ(zzz52200)), zzz523, zzz524), zzz343, h)
new_mkVBalBranch3MkVBalBranch24(zzz340, zzz341, Neg(Succ(Succ(Zero))), zzz343, zzz344, zzz520, zzz521, Zero, zzz523, zzz524, zzz31, Succ(Succ(zzz6900)), h) → new_mkVBalBranch3MkVBalBranch26(zzz340, zzz341, Succ(Zero), zzz343, zzz344, zzz520, zzz521, zzz523, zzz524, zzz31, Zero, Succ(zzz6900), h)
new_mkVBalBranch3MkVBalBranch1(zzz340, zzz341, zzz34200, zzz343, zzz344, zzz520, zzz521, zzz52200, zzz523, zzz524, zzz31, Succ(zzz1430), h) → new_mkVBalBranch(zzz31, zzz524, Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), h)
new_mkVBalBranch3MkVBalBranch22(zzz340, zzz341, Zero, zzz343, zzz344, zzz520, zzz521, zzz52200, zzz523, zzz524, zzz31, h) → new_mkVBalBranch(zzz31, zzz524, Branch(zzz340, zzz341, Neg(Zero), zzz343, zzz344), h)
new_mkVBalBranch(zzz31, Branch(zzz520, zzz521, Pos(Zero), zzz523, zzz524), Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), h) → new_mkVBalBranch3MkVBalBranch12(zzz340, zzz341, zzz34200, zzz343, zzz344, zzz520, zzz521, zzz523, zzz524, zzz31, new_primPlusNat2(new_primMulNat0(zzz34200), Succ(zzz34200)), h)
new_mkVBalBranch3MkVBalBranch24(zzz340, zzz341, Neg(Succ(Zero)), zzz343, zzz344, zzz520, zzz521, zzz52200, zzz523, zzz524, zzz31, Succ(zzz690), h) → new_mkVBalBranch(zzz31, Branch(zzz520, zzz521, Neg(Succ(zzz52200)), zzz523, zzz524), zzz343, h)
new_mkVBalBranch3MkVBalBranch22(zzz340, zzz341, Succ(zzz34200), zzz343, zzz344, zzz520, zzz521, zzz52200, zzz523, zzz524, zzz31, h) → new_mkVBalBranch3MkVBalBranch1(zzz340, zzz341, zzz34200, zzz343, zzz344, zzz520, zzz521, zzz52200, zzz523, zzz524, zzz31, new_primPlusNat2(new_primMulNat0(zzz34200), Succ(zzz34200)), h)
new_mkVBalBranch3MkVBalBranch13(zzz340, zzz341, zzz34200, zzz343, zzz344, zzz520, zzz521, zzz523, zzz524, zzz31, Succ(zzz1290), h) → new_mkVBalBranch(zzz31, zzz524, Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), h)
new_mkVBalBranch3MkVBalBranch2(zzz340, zzz341, Pos(Succ(zzz34200)), zzz343, zzz344, zzz520, zzz521, zzz52200, zzz523, zzz524, zzz31, Succ(zzz680), h) → new_mkVBalBranch3MkVBalBranch20(zzz340, zzz341, zzz34200, zzz343, zzz344, zzz520, zzz521, zzz52200, zzz523, zzz524, zzz31, Succ(new_primPlusNat2(zzz680, zzz52200)), zzz34200, h)
new_mkVBalBranch3MkVBalBranch24(zzz340, zzz341, Neg(Zero), zzz343, zzz344, zzz520, zzz521, zzz52200, zzz523, zzz524, zzz31, Succ(zzz690), h) → new_mkVBalBranch(zzz31, Branch(zzz520, zzz521, Neg(Succ(zzz52200)), zzz523, zzz524), zzz343, h)
new_mkVBalBranch(zzz31, Branch(zzz520, zzz521, Neg(Zero), zzz523, zzz524), Branch(zzz340, zzz341, Pos(Succ(zzz34200)), zzz343, zzz344), h) → new_mkVBalBranch(zzz31, Branch(zzz520, zzz521, Neg(Zero), zzz523, zzz524), zzz343, h)
new_mkVBalBranch3MkVBalBranch1(zzz340, zzz341, zzz34200, zzz343, zzz344, zzz520, zzz521, zzz52200, zzz523, zzz524, zzz31, Zero, h) → new_mkVBalBranch3MkVBalBranch17(zzz340, zzz341, zzz34200, zzz343, zzz344, zzz520, zzz521, zzz52200, zzz523, zzz524, zzz31, h)
new_mkVBalBranch3MkVBalBranch16(zzz1702, zzz1703, zzz1704, zzz1705, zzz1706, zzz1707, zzz1708, zzz1709, zzz1710, zzz1711, zzz1712, Succ(zzz17130), Succ(zzz17140), bd) → new_mkVBalBranch3MkVBalBranch16(zzz1702, zzz1703, zzz1704, zzz1705, zzz1706, zzz1707, zzz1708, zzz1709, zzz1710, zzz1711, zzz1712, zzz17130, zzz17140, bd)
new_mkVBalBranch3MkVBalBranch25(zzz537, zzz538, zzz539, zzz540, zzz541, zzz542, zzz543, zzz544, zzz545, zzz546, zzz547, Zero, Succ(zzz5490), bc) → new_mkVBalBranch(zzz547, Branch(zzz542, zzz543, Neg(Succ(Succ(zzz544))), zzz545, zzz546), zzz540, bc)
new_mkVBalBranch3MkVBalBranch10(zzz929, zzz930, zzz931, zzz932, zzz933, zzz934, zzz935, zzz936, zzz937, zzz938, zzz939, Succ(zzz10020), ba) → new_mkVBalBranch3MkVBalBranch11(zzz929, zzz930, zzz931, zzz932, zzz933, zzz934, zzz935, zzz936, zzz937, zzz938, zzz939, Succ(zzz10020), Succ(zzz936), ba)
new_mkVBalBranch3MkVBalBranch14(zzz818, zzz819, zzz820, zzz821, zzz822, zzz823, zzz824, zzz825, zzz826, zzz827, Succ(zzz8960), bf) → new_mkVBalBranch3MkVBalBranch16(zzz818, zzz819, zzz820, zzz821, zzz822, zzz823, zzz824, Zero, zzz825, zzz826, zzz827, Succ(Zero), Succ(zzz8960), bf)
new_mkVBalBranch3MkVBalBranch2(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344, zzz520, zzz521, zzz52200, zzz523, zzz524, zzz31, Succ(zzz680), h) → new_mkVBalBranch3MkVBalBranch1(zzz340, zzz341, zzz34200, zzz343, zzz344, zzz520, zzz521, zzz52200, zzz523, zzz524, zzz31, new_primPlusNat2(new_primMulNat0(zzz34200), Succ(zzz34200)), h)
new_mkVBalBranch3MkVBalBranch24(zzz340, zzz341, Neg(Succ(Succ(Succ(zzz3420000)))), zzz343, zzz344, zzz520, zzz521, Succ(zzz522000), zzz523, zzz524, zzz31, Succ(Succ(zzz6900)), h) → new_mkVBalBranch3MkVBalBranch25(zzz340, zzz341, Succ(Succ(zzz3420000)), zzz343, zzz344, zzz520, zzz521, zzz522000, zzz523, zzz524, zzz31, Succ(zzz3420000), Succ(Succ(new_primPlusNat2(zzz6900, zzz522000))), h)
new_mkVBalBranch3MkVBalBranch2(zzz340, zzz341, Pos(Succ(zzz34200)), zzz343, zzz344, zzz520, zzz521, zzz52200, zzz523, zzz524, zzz31, Zero, h) → new_mkVBalBranch3MkVBalBranch20(zzz340, zzz341, zzz34200, zzz343, zzz344, zzz520, zzz521, zzz52200, zzz523, zzz524, zzz31, zzz52200, zzz34200, h)
new_mkVBalBranch3MkVBalBranch24(zzz340, zzz341, Neg(Zero), zzz343, zzz344, zzz520, zzz521, zzz52200, zzz523, zzz524, zzz31, Zero, h) → new_mkVBalBranch3MkVBalBranch210(zzz340, zzz341, zzz343, zzz344, zzz520, zzz521, zzz52200, zzz523, zzz524, zzz31, h)
new_mkVBalBranch3MkVBalBranch24(zzz340, zzz341, Neg(Succ(Succ(Zero))), zzz343, zzz344, zzz520, zzz521, Succ(zzz522000), zzz523, zzz524, zzz31, Succ(Succ(zzz6900)), h) → new_mkVBalBranch3MkVBalBranch25(zzz340, zzz341, Succ(Zero), zzz343, zzz344, zzz520, zzz521, zzz522000, zzz523, zzz524, zzz31, Zero, Succ(Succ(new_primPlusNat2(zzz6900, zzz522000))), h)
new_mkVBalBranch3MkVBalBranch20(zzz929, zzz930, zzz931, zzz932, zzz933, zzz934, zzz935, zzz936, zzz937, zzz938, zzz939, Succ(zzz9400), Zero, ba) → new_mkVBalBranch3MkVBalBranch10(zzz929, zzz930, zzz931, zzz932, zzz933, zzz934, zzz935, zzz936, zzz937, zzz938, zzz939, new_primMulNat1(zzz931), ba)
new_mkVBalBranch(zzz31, Branch(zzz520, zzz521, Pos(Succ(zzz52200)), zzz523, zzz524), Branch(zzz340, zzz341, zzz342, zzz343, zzz344), h) → new_mkVBalBranch3MkVBalBranch2(zzz340, zzz341, zzz342, zzz343, zzz344, zzz520, zzz521, zzz52200, zzz523, zzz524, zzz31, new_primMulNat0(zzz52200), h)
new_mkVBalBranch3MkVBalBranch2(zzz340, zzz341, Neg(Zero), zzz343, zzz344, zzz520, zzz521, zzz52200, zzz523, zzz524, zzz31, Succ(zzz680), h) → new_mkVBalBranch(zzz31, zzz524, Branch(zzz340, zzz341, Neg(Zero), zzz343, zzz344), h)
new_mkVBalBranch(zzz31, Branch(zzz520, zzz521, Neg(Zero), zzz523, zzz524), Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), h) → new_mkVBalBranch3MkVBalBranch13(zzz340, zzz341, zzz34200, zzz343, zzz344, zzz520, zzz521, zzz523, zzz524, zzz31, new_primMulNat1(zzz34200), h)
new_mkVBalBranch3MkVBalBranch16(zzz1702, zzz1703, zzz1704, zzz1705, zzz1706, zzz1707, zzz1708, zzz1709, zzz1710, zzz1711, zzz1712, Zero, Succ(zzz17140), bd) → new_mkVBalBranch(zzz1712, zzz1711, Branch(zzz1702, zzz1703, Neg(Succ(zzz1704)), zzz1705, zzz1706), bd)
new_mkVBalBranch3MkVBalBranch10(zzz929, zzz930, zzz931, zzz932, zzz933, zzz934, zzz935, zzz936, zzz937, zzz938, zzz939, Zero, ba) → new_mkVBalBranch3MkVBalBranch11(zzz929, zzz930, zzz931, zzz932, zzz933, zzz934, zzz935, zzz936, zzz937, zzz938, zzz939, Zero, Succ(zzz936), ba)
new_mkVBalBranch3MkVBalBranch2(zzz340, zzz341, Pos(Zero), zzz343, zzz344, zzz520, zzz521, zzz52200, zzz523, zzz524, zzz31, Zero, h) → new_mkVBalBranch3MkVBalBranch21(zzz340, zzz341, zzz343, zzz344, zzz520, zzz521, zzz52200, zzz523, zzz524, zzz31, h)
new_mkVBalBranch3MkVBalBranch25(zzz537, zzz538, zzz539, zzz540, zzz541, zzz542, zzz543, zzz544, zzz545, zzz546, zzz547, Zero, Zero, bc) → new_mkVBalBranch3MkVBalBranch211(zzz537, zzz538, zzz539, zzz540, zzz541, zzz542, zzz543, zzz544, zzz545, zzz546, zzz547, bc)

The TRS R consists of the following rules:

new_primPlusNat1(Zero) → Zero
new_primMulNat0(zzz6200) → new_primPlusNat3(Succ(new_primPlusNat3(new_primPlusNat1(zzz6200), zzz6200)), Succ(zzz6200))
new_primPlusNat2(Succ(zzz900), Succ(zzz9100)) → Succ(Succ(new_primPlusNat2(zzz900, zzz9100)))
new_primPlusNat3(zzz90, Succ(zzz910)) → Succ(Succ(new_primPlusNat2(zzz90, zzz910)))
new_primPlusNat3(zzz90, Zero) → Succ(zzz90)
new_primMulNat1(zzz34200) → new_primPlusNat2(new_primMulNat0(zzz34200), Succ(zzz34200))
new_primPlusNat2(Zero, Zero) → Zero
new_primPlusNat1(Succ(zzz62000)) → Succ(Succ(new_primPlusNat1(zzz62000)))
new_primPlusNat2(Succ(zzz900), Zero) → Succ(zzz900)
new_primPlusNat2(Zero, Succ(zzz9100)) → Succ(zzz9100)

The set Q consists of the following terms:

new_primPlusNat2(Zero, Succ(x0))
new_primMulNat1(x0)
new_primMulNat0(x0)
new_primPlusNat3(x0, Succ(x1))
new_primPlusNat2(Succ(x0), Succ(x1))
new_primPlusNat3(x0, Zero)
new_primPlusNat1(Zero)
new_primPlusNat2(Zero, Zero)
new_primPlusNat1(Succ(x0))
new_primPlusNat2(Succ(x0), Zero)

We have to consider all minimal (P,Q,R)-chains.
By rewriting [15] the rule new_mkVBalBranch3MkVBalBranch212(zzz818, zzz819, zzz820, zzz821, zzz822, zzz823, zzz824, zzz825, zzz826, zzz827, bf) → new_mkVBalBranch3MkVBalBranch14(zzz818, zzz819, zzz820, zzz821, zzz822, zzz823, zzz824, zzz825, zzz826, zzz827, new_primMulNat1(zzz820), bf) at position [10] we obtained the following new rules:

new_mkVBalBranch3MkVBalBranch212(zzz818, zzz819, zzz820, zzz821, zzz822, zzz823, zzz824, zzz825, zzz826, zzz827, bf) → new_mkVBalBranch3MkVBalBranch14(zzz818, zzz819, zzz820, zzz821, zzz822, zzz823, zzz824, zzz825, zzz826, zzz827, new_primPlusNat2(new_primMulNat0(zzz820), Succ(zzz820)), bf)



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

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

new_mkVBalBranch3MkVBalBranch11(zzz2033, zzz2034, zzz2035, zzz2036, zzz2037, zzz2038, zzz2039, zzz2040, zzz2041, zzz2042, zzz2043, Zero, Succ(zzz20450), bb) → new_mkVBalBranch(zzz2043, zzz2042, Branch(zzz2033, zzz2034, Pos(Succ(zzz2035)), zzz2036, zzz2037), bb)
new_mkVBalBranch3MkVBalBranch26(zzz1133, zzz1134, zzz1135, zzz1136, zzz1137, zzz1138, zzz1139, zzz1140, zzz1141, zzz1142, Succ(zzz11430), Succ(zzz11440), be) → new_mkVBalBranch3MkVBalBranch26(zzz1133, zzz1134, zzz1135, zzz1136, zzz1137, zzz1138, zzz1139, zzz1140, zzz1141, zzz1142, zzz11430, zzz11440, be)
new_mkVBalBranch3MkVBalBranch24(zzz340, zzz341, Neg(Succ(Succ(Succ(zzz3420000)))), zzz343, zzz344, zzz520, zzz521, Zero, zzz523, zzz524, zzz31, Succ(Zero), h) → new_mkVBalBranch3MkVBalBranch26(zzz340, zzz341, Succ(Succ(zzz3420000)), zzz343, zzz344, zzz520, zzz521, zzz523, zzz524, zzz31, Succ(zzz3420000), Zero, h)
new_mkVBalBranch3MkVBalBranch24(zzz340, zzz341, Neg(Succ(Zero)), zzz343, zzz344, zzz520, zzz521, Zero, zzz523, zzz524, zzz31, Zero, h) → new_mkVBalBranch3MkVBalBranch29(zzz340, zzz341, Zero, zzz343, zzz344, zzz520, zzz521, zzz523, zzz524, zzz31, h)
new_mkVBalBranch3MkVBalBranch20(zzz929, zzz930, zzz931, zzz932, zzz933, zzz934, zzz935, zzz936, zzz937, zzz938, zzz939, Zero, Succ(zzz9410), ba) → new_mkVBalBranch(zzz939, Branch(zzz934, zzz935, Pos(Succ(zzz936)), zzz937, zzz938), zzz932, ba)
new_mkVBalBranch3MkVBalBranch17(zzz340, zzz341, zzz34200, zzz343, zzz344, zzz520, zzz521, zzz52200, zzz523, zzz524, zzz31, h) → new_mkVBalBranch(zzz31, zzz524, Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), h)
new_mkVBalBranch3MkVBalBranch26(zzz1133, zzz1134, zzz1135, zzz1136, zzz1137, zzz1138, zzz1139, zzz1140, zzz1141, zzz1142, Zero, Zero, be) → new_mkVBalBranch3MkVBalBranch29(zzz1133, zzz1134, zzz1135, zzz1136, zzz1137, zzz1138, zzz1139, zzz1140, zzz1141, zzz1142, be)
new_mkVBalBranch3MkVBalBranch20(zzz929, zzz930, zzz931, zzz932, zzz933, zzz934, zzz935, zzz936, zzz937, zzz938, zzz939, Zero, Zero, ba) → new_mkVBalBranch3MkVBalBranch23(zzz929, zzz930, zzz931, zzz932, zzz933, zzz934, zzz935, zzz936, zzz937, zzz938, zzz939, ba)
new_mkVBalBranch3MkVBalBranch24(zzz340, zzz341, Neg(Succ(Succ(Zero))), zzz343, zzz344, zzz520, zzz521, Succ(zzz522000), zzz523, zzz524, zzz31, Succ(Zero), h) → new_mkVBalBranch3MkVBalBranch25(zzz340, zzz341, Succ(Zero), zzz343, zzz344, zzz520, zzz521, zzz522000, zzz523, zzz524, zzz31, Zero, Succ(zzz522000), h)
new_mkVBalBranch3MkVBalBranch24(zzz340, zzz341, Neg(Succ(Succ(Succ(zzz3420000)))), zzz343, zzz344, zzz520, zzz521, Succ(zzz522000), zzz523, zzz524, zzz31, Succ(Zero), h) → new_mkVBalBranch3MkVBalBranch25(zzz340, zzz341, Succ(Succ(zzz3420000)), zzz343, zzz344, zzz520, zzz521, zzz522000, zzz523, zzz524, zzz31, Succ(zzz3420000), Succ(zzz522000), h)
new_mkVBalBranch3MkVBalBranch20(zzz929, zzz930, zzz931, zzz932, zzz933, zzz934, zzz935, zzz936, zzz937, zzz938, zzz939, Succ(zzz9400), Succ(zzz9410), ba) → new_mkVBalBranch3MkVBalBranch20(zzz929, zzz930, zzz931, zzz932, zzz933, zzz934, zzz935, zzz936, zzz937, zzz938, zzz939, zzz9400, zzz9410, ba)
new_mkVBalBranch3MkVBalBranch24(zzz340, zzz341, Neg(Succ(Succ(zzz342000))), zzz343, zzz344, zzz520, zzz521, Succ(zzz522000), zzz523, zzz524, zzz31, Zero, h) → new_mkVBalBranch3MkVBalBranch25(zzz340, zzz341, Succ(zzz342000), zzz343, zzz344, zzz520, zzz521, zzz522000, zzz523, zzz524, zzz31, zzz342000, zzz522000, h)
new_mkVBalBranch3MkVBalBranch26(zzz1133, zzz1134, zzz1135, zzz1136, zzz1137, zzz1138, zzz1139, zzz1140, zzz1141, zzz1142, Succ(zzz11430), Zero, be) → new_mkVBalBranch3MkVBalBranch212(zzz1133, zzz1134, zzz1135, zzz1136, zzz1137, zzz1138, zzz1139, zzz1140, zzz1141, zzz1142, be)
new_mkVBalBranch3MkVBalBranch11(zzz2033, zzz2034, zzz2035, zzz2036, zzz2037, zzz2038, zzz2039, zzz2040, zzz2041, zzz2042, zzz2043, Succ(zzz20440), Succ(zzz20450), bb) → new_mkVBalBranch3MkVBalBranch11(zzz2033, zzz2034, zzz2035, zzz2036, zzz2037, zzz2038, zzz2039, zzz2040, zzz2041, zzz2042, zzz2043, zzz20440, zzz20450, bb)
new_mkVBalBranch3MkVBalBranch25(zzz537, zzz538, zzz539, zzz540, zzz541, zzz542, zzz543, zzz544, zzz545, zzz546, zzz547, Succ(zzz5480), Succ(zzz5490), bc) → new_mkVBalBranch3MkVBalBranch25(zzz537, zzz538, zzz539, zzz540, zzz541, zzz542, zzz543, zzz544, zzz545, zzz546, zzz547, zzz5480, zzz5490, bc)
new_mkVBalBranch3MkVBalBranch2(zzz340, zzz341, Neg(zzz3420), zzz343, zzz344, zzz520, zzz521, zzz52200, zzz523, zzz524, zzz31, Zero, h) → new_mkVBalBranch3MkVBalBranch22(zzz340, zzz341, zzz3420, zzz343, zzz344, zzz520, zzz521, zzz52200, zzz523, zzz524, zzz31, h)
new_mkVBalBranch(zzz31, Branch(zzz520, zzz521, Neg(Succ(zzz52200)), zzz523, zzz524), Branch(zzz340, zzz341, zzz342, zzz343, zzz344), h) → new_mkVBalBranch3MkVBalBranch24(zzz340, zzz341, zzz342, zzz343, zzz344, zzz520, zzz521, zzz52200, zzz523, zzz524, zzz31, new_primPlusNat3(Succ(new_primPlusNat3(new_primPlusNat1(zzz52200), zzz52200)), Succ(zzz52200)), h)
new_mkVBalBranch3MkVBalBranch24(zzz340, zzz341, Neg(Succ(Zero)), zzz343, zzz344, zzz520, zzz521, Succ(zzz522000), zzz523, zzz524, zzz31, Zero, h) → new_mkVBalBranch3MkVBalBranch28(zzz340, zzz341, zzz343, zzz344, zzz520, zzz521, Succ(zzz522000), zzz523, zzz524, zzz31, h)
new_mkVBalBranch3MkVBalBranch24(zzz340, zzz341, Neg(Succ(Succ(zzz342000))), zzz343, zzz344, zzz520, zzz521, Zero, zzz523, zzz524, zzz31, Zero, h) → new_mkVBalBranch3MkVBalBranch14(zzz340, zzz341, Succ(zzz342000), zzz343, zzz344, zzz520, zzz521, zzz523, zzz524, zzz31, new_primMulNat1(Succ(zzz342000)), h)
new_mkVBalBranch3MkVBalBranch210(zzz340, zzz341, zzz343, zzz344, zzz520, zzz521, zzz52200, zzz523, zzz524, zzz31, h) → new_mkVBalBranch(zzz31, Branch(zzz520, zzz521, Neg(Succ(zzz52200)), zzz523, zzz524), zzz343, h)
new_mkVBalBranch3MkVBalBranch26(zzz1133, zzz1134, zzz1135, zzz1136, zzz1137, zzz1138, zzz1139, zzz1140, zzz1141, zzz1142, Zero, Succ(zzz11440), be) → new_mkVBalBranch(zzz1142, Branch(zzz1138, zzz1139, Neg(Succ(Zero)), zzz1140, zzz1141), zzz1136, be)
new_mkVBalBranch3MkVBalBranch24(zzz340, zzz341, Neg(Succ(Succ(Zero))), zzz343, zzz344, zzz520, zzz521, Zero, zzz523, zzz524, zzz31, Succ(Zero), h) → new_mkVBalBranch3MkVBalBranch26(zzz340, zzz341, Succ(Zero), zzz343, zzz344, zzz520, zzz521, zzz523, zzz524, zzz31, Zero, Zero, h)
new_mkVBalBranch(zzz31, Branch(zzz520, zzz521, Pos(Zero), zzz523, zzz524), Branch(zzz340, zzz341, Pos(Succ(zzz34200)), zzz343, zzz344), h) → new_mkVBalBranch(zzz31, Branch(zzz520, zzz521, Pos(Zero), zzz523, zzz524), zzz343, h)
new_mkVBalBranch3MkVBalBranch29(zzz818, zzz819, zzz820, zzz821, zzz822, zzz823, zzz824, zzz825, zzz826, zzz827, bf) → new_mkVBalBranch3MkVBalBranch14(zzz818, zzz819, zzz820, zzz821, zzz822, zzz823, zzz824, zzz825, zzz826, zzz827, new_primMulNat1(zzz820), bf)
new_mkVBalBranch3MkVBalBranch2(zzz340, zzz341, Pos(Zero), zzz343, zzz344, zzz520, zzz521, zzz52200, zzz523, zzz524, zzz31, Succ(zzz680), h) → new_mkVBalBranch(zzz31, zzz524, Branch(zzz340, zzz341, Pos(Zero), zzz343, zzz344), h)
new_mkVBalBranch3MkVBalBranch21(zzz340, zzz341, zzz343, zzz344, zzz520, zzz521, zzz52200, zzz523, zzz524, zzz31, h) → new_mkVBalBranch(zzz31, zzz524, Branch(zzz340, zzz341, Pos(Zero), zzz343, zzz344), h)
new_mkVBalBranch3MkVBalBranch24(zzz340, zzz341, Pos(zzz3420), zzz343, zzz344, zzz520, zzz521, zzz52200, zzz523, zzz524, zzz31, Zero, h) → new_mkVBalBranch3MkVBalBranch27(zzz340, zzz341, zzz3420, zzz343, zzz344, zzz520, zzz521, zzz52200, zzz523, zzz524, zzz31, h)
new_mkVBalBranch3MkVBalBranch23(zzz929, zzz930, zzz931, zzz932, zzz933, zzz934, zzz935, zzz936, zzz937, zzz938, zzz939, ba) → new_mkVBalBranch3MkVBalBranch10(zzz929, zzz930, zzz931, zzz932, zzz933, zzz934, zzz935, zzz936, zzz937, zzz938, zzz939, new_primMulNat1(zzz931), ba)
new_mkVBalBranch3MkVBalBranch211(zzz537, zzz538, zzz539, zzz540, zzz541, zzz542, zzz543, zzz544, zzz545, zzz546, zzz547, bc) → new_mkVBalBranch3MkVBalBranch15(zzz537, zzz538, zzz539, zzz540, zzz541, zzz542, zzz543, zzz544, zzz545, zzz546, zzz547, new_primMulNat1(zzz539), bc)
new_mkVBalBranch3MkVBalBranch15(zzz537, zzz538, zzz539, zzz540, zzz541, zzz542, zzz543, zzz544, zzz545, zzz546, zzz547, Succ(zzz6990), bc) → new_mkVBalBranch3MkVBalBranch16(zzz537, zzz538, zzz539, zzz540, zzz541, zzz542, zzz543, Succ(zzz544), zzz545, zzz546, zzz547, Succ(Succ(zzz544)), Succ(zzz6990), bc)
new_mkVBalBranch3MkVBalBranch24(zzz340, zzz341, Neg(Succ(Succ(Succ(zzz3420000)))), zzz343, zzz344, zzz520, zzz521, Zero, zzz523, zzz524, zzz31, Succ(Succ(zzz6900)), h) → new_mkVBalBranch3MkVBalBranch26(zzz340, zzz341, Succ(Succ(zzz3420000)), zzz343, zzz344, zzz520, zzz521, zzz523, zzz524, zzz31, Succ(zzz3420000), Succ(zzz6900), h)
new_mkVBalBranch3MkVBalBranch27(zzz340, zzz341, zzz3420, zzz343, zzz344, zzz520, zzz521, zzz52200, zzz523, zzz524, zzz31, h) → new_mkVBalBranch(zzz31, Branch(zzz520, zzz521, Neg(Succ(zzz52200)), zzz523, zzz524), zzz343, h)
new_mkVBalBranch3MkVBalBranch24(zzz340, zzz341, Pos(zzz3420), zzz343, zzz344, zzz520, zzz521, zzz52200, zzz523, zzz524, zzz31, Succ(zzz690), h) → new_mkVBalBranch(zzz31, Branch(zzz520, zzz521, Neg(Succ(zzz52200)), zzz523, zzz524), zzz343, h)
new_mkVBalBranch3MkVBalBranch12(zzz340, zzz341, zzz34200, zzz343, zzz344, zzz520, zzz521, zzz523, zzz524, zzz31, Succ(zzz1250), h) → new_mkVBalBranch(zzz31, zzz524, Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), h)
new_mkVBalBranch3MkVBalBranch28(zzz340, zzz341, zzz343, zzz344, zzz520, zzz521, zzz52200, zzz523, zzz524, zzz31, h) → new_mkVBalBranch(zzz31, Branch(zzz520, zzz521, Neg(Succ(zzz52200)), zzz523, zzz524), zzz343, h)
new_mkVBalBranch3MkVBalBranch25(zzz537, zzz538, zzz539, zzz540, zzz541, zzz542, zzz543, zzz544, zzz545, zzz546, zzz547, Succ(zzz5480), Zero, bc) → new_mkVBalBranch3MkVBalBranch15(zzz537, zzz538, zzz539, zzz540, zzz541, zzz542, zzz543, zzz544, zzz545, zzz546, zzz547, new_primMulNat1(zzz539), bc)
new_mkVBalBranch3MkVBalBranch24(zzz340, zzz341, Neg(Succ(Succ(Zero))), zzz343, zzz344, zzz520, zzz521, Zero, zzz523, zzz524, zzz31, Succ(Succ(zzz6900)), h) → new_mkVBalBranch3MkVBalBranch26(zzz340, zzz341, Succ(Zero), zzz343, zzz344, zzz520, zzz521, zzz523, zzz524, zzz31, Zero, Succ(zzz6900), h)
new_mkVBalBranch(zzz31, Branch(zzz520, zzz521, Pos(Zero), zzz523, zzz524), Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), h) → new_mkVBalBranch3MkVBalBranch12(zzz340, zzz341, zzz34200, zzz343, zzz344, zzz520, zzz521, zzz523, zzz524, zzz31, new_primPlusNat2(new_primMulNat0(zzz34200), Succ(zzz34200)), h)
new_mkVBalBranch3MkVBalBranch22(zzz340, zzz341, Zero, zzz343, zzz344, zzz520, zzz521, zzz52200, zzz523, zzz524, zzz31, h) → new_mkVBalBranch(zzz31, zzz524, Branch(zzz340, zzz341, Neg(Zero), zzz343, zzz344), h)
new_mkVBalBranch3MkVBalBranch1(zzz340, zzz341, zzz34200, zzz343, zzz344, zzz520, zzz521, zzz52200, zzz523, zzz524, zzz31, Succ(zzz1430), h) → new_mkVBalBranch(zzz31, zzz524, Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), h)
new_mkVBalBranch3MkVBalBranch22(zzz340, zzz341, Succ(zzz34200), zzz343, zzz344, zzz520, zzz521, zzz52200, zzz523, zzz524, zzz31, h) → new_mkVBalBranch3MkVBalBranch1(zzz340, zzz341, zzz34200, zzz343, zzz344, zzz520, zzz521, zzz52200, zzz523, zzz524, zzz31, new_primPlusNat2(new_primMulNat0(zzz34200), Succ(zzz34200)), h)
new_mkVBalBranch3MkVBalBranch24(zzz340, zzz341, Neg(Succ(Zero)), zzz343, zzz344, zzz520, zzz521, zzz52200, zzz523, zzz524, zzz31, Succ(zzz690), h) → new_mkVBalBranch(zzz31, Branch(zzz520, zzz521, Neg(Succ(zzz52200)), zzz523, zzz524), zzz343, h)
new_mkVBalBranch3MkVBalBranch13(zzz340, zzz341, zzz34200, zzz343, zzz344, zzz520, zzz521, zzz523, zzz524, zzz31, Succ(zzz1290), h) → new_mkVBalBranch(zzz31, zzz524, Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), h)
new_mkVBalBranch3MkVBalBranch2(zzz340, zzz341, Pos(Succ(zzz34200)), zzz343, zzz344, zzz520, zzz521, zzz52200, zzz523, zzz524, zzz31, Succ(zzz680), h) → new_mkVBalBranch3MkVBalBranch20(zzz340, zzz341, zzz34200, zzz343, zzz344, zzz520, zzz521, zzz52200, zzz523, zzz524, zzz31, Succ(new_primPlusNat2(zzz680, zzz52200)), zzz34200, h)
new_mkVBalBranch(zzz31, Branch(zzz520, zzz521, Neg(Zero), zzz523, zzz524), Branch(zzz340, zzz341, Pos(Succ(zzz34200)), zzz343, zzz344), h) → new_mkVBalBranch(zzz31, Branch(zzz520, zzz521, Neg(Zero), zzz523, zzz524), zzz343, h)
new_mkVBalBranch3MkVBalBranch24(zzz340, zzz341, Neg(Zero), zzz343, zzz344, zzz520, zzz521, zzz52200, zzz523, zzz524, zzz31, Succ(zzz690), h) → new_mkVBalBranch(zzz31, Branch(zzz520, zzz521, Neg(Succ(zzz52200)), zzz523, zzz524), zzz343, h)
new_mkVBalBranch3MkVBalBranch1(zzz340, zzz341, zzz34200, zzz343, zzz344, zzz520, zzz521, zzz52200, zzz523, zzz524, zzz31, Zero, h) → new_mkVBalBranch3MkVBalBranch17(zzz340, zzz341, zzz34200, zzz343, zzz344, zzz520, zzz521, zzz52200, zzz523, zzz524, zzz31, h)
new_mkVBalBranch3MkVBalBranch16(zzz1702, zzz1703, zzz1704, zzz1705, zzz1706, zzz1707, zzz1708, zzz1709, zzz1710, zzz1711, zzz1712, Succ(zzz17130), Succ(zzz17140), bd) → new_mkVBalBranch3MkVBalBranch16(zzz1702, zzz1703, zzz1704, zzz1705, zzz1706, zzz1707, zzz1708, zzz1709, zzz1710, zzz1711, zzz1712, zzz17130, zzz17140, bd)
new_mkVBalBranch3MkVBalBranch25(zzz537, zzz538, zzz539, zzz540, zzz541, zzz542, zzz543, zzz544, zzz545, zzz546, zzz547, Zero, Succ(zzz5490), bc) → new_mkVBalBranch(zzz547, Branch(zzz542, zzz543, Neg(Succ(Succ(zzz544))), zzz545, zzz546), zzz540, bc)
new_mkVBalBranch3MkVBalBranch212(zzz818, zzz819, zzz820, zzz821, zzz822, zzz823, zzz824, zzz825, zzz826, zzz827, bf) → new_mkVBalBranch3MkVBalBranch14(zzz818, zzz819, zzz820, zzz821, zzz822, zzz823, zzz824, zzz825, zzz826, zzz827, new_primPlusNat2(new_primMulNat0(zzz820), Succ(zzz820)), bf)
new_mkVBalBranch3MkVBalBranch10(zzz929, zzz930, zzz931, zzz932, zzz933, zzz934, zzz935, zzz936, zzz937, zzz938, zzz939, Succ(zzz10020), ba) → new_mkVBalBranch3MkVBalBranch11(zzz929, zzz930, zzz931, zzz932, zzz933, zzz934, zzz935, zzz936, zzz937, zzz938, zzz939, Succ(zzz10020), Succ(zzz936), ba)
new_mkVBalBranch3MkVBalBranch2(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344, zzz520, zzz521, zzz52200, zzz523, zzz524, zzz31, Succ(zzz680), h) → new_mkVBalBranch3MkVBalBranch1(zzz340, zzz341, zzz34200, zzz343, zzz344, zzz520, zzz521, zzz52200, zzz523, zzz524, zzz31, new_primPlusNat2(new_primMulNat0(zzz34200), Succ(zzz34200)), h)
new_mkVBalBranch3MkVBalBranch14(zzz818, zzz819, zzz820, zzz821, zzz822, zzz823, zzz824, zzz825, zzz826, zzz827, Succ(zzz8960), bf) → new_mkVBalBranch3MkVBalBranch16(zzz818, zzz819, zzz820, zzz821, zzz822, zzz823, zzz824, Zero, zzz825, zzz826, zzz827, Succ(Zero), Succ(zzz8960), bf)
new_mkVBalBranch3MkVBalBranch24(zzz340, zzz341, Neg(Succ(Succ(Succ(zzz3420000)))), zzz343, zzz344, zzz520, zzz521, Succ(zzz522000), zzz523, zzz524, zzz31, Succ(Succ(zzz6900)), h) → new_mkVBalBranch3MkVBalBranch25(zzz340, zzz341, Succ(Succ(zzz3420000)), zzz343, zzz344, zzz520, zzz521, zzz522000, zzz523, zzz524, zzz31, Succ(zzz3420000), Succ(Succ(new_primPlusNat2(zzz6900, zzz522000))), h)
new_mkVBalBranch3MkVBalBranch2(zzz340, zzz341, Pos(Succ(zzz34200)), zzz343, zzz344, zzz520, zzz521, zzz52200, zzz523, zzz524, zzz31, Zero, h) → new_mkVBalBranch3MkVBalBranch20(zzz340, zzz341, zzz34200, zzz343, zzz344, zzz520, zzz521, zzz52200, zzz523, zzz524, zzz31, zzz52200, zzz34200, h)
new_mkVBalBranch3MkVBalBranch24(zzz340, zzz341, Neg(Zero), zzz343, zzz344, zzz520, zzz521, zzz52200, zzz523, zzz524, zzz31, Zero, h) → new_mkVBalBranch3MkVBalBranch210(zzz340, zzz341, zzz343, zzz344, zzz520, zzz521, zzz52200, zzz523, zzz524, zzz31, h)
new_mkVBalBranch3MkVBalBranch24(zzz340, zzz341, Neg(Succ(Succ(Zero))), zzz343, zzz344, zzz520, zzz521, Succ(zzz522000), zzz523, zzz524, zzz31, Succ(Succ(zzz6900)), h) → new_mkVBalBranch3MkVBalBranch25(zzz340, zzz341, Succ(Zero), zzz343, zzz344, zzz520, zzz521, zzz522000, zzz523, zzz524, zzz31, Zero, Succ(Succ(new_primPlusNat2(zzz6900, zzz522000))), h)
new_mkVBalBranch3MkVBalBranch20(zzz929, zzz930, zzz931, zzz932, zzz933, zzz934, zzz935, zzz936, zzz937, zzz938, zzz939, Succ(zzz9400), Zero, ba) → new_mkVBalBranch3MkVBalBranch10(zzz929, zzz930, zzz931, zzz932, zzz933, zzz934, zzz935, zzz936, zzz937, zzz938, zzz939, new_primMulNat1(zzz931), ba)
new_mkVBalBranch3MkVBalBranch2(zzz340, zzz341, Neg(Zero), zzz343, zzz344, zzz520, zzz521, zzz52200, zzz523, zzz524, zzz31, Succ(zzz680), h) → new_mkVBalBranch(zzz31, zzz524, Branch(zzz340, zzz341, Neg(Zero), zzz343, zzz344), h)
new_mkVBalBranch(zzz31, Branch(zzz520, zzz521, Pos(Succ(zzz52200)), zzz523, zzz524), Branch(zzz340, zzz341, zzz342, zzz343, zzz344), h) → new_mkVBalBranch3MkVBalBranch2(zzz340, zzz341, zzz342, zzz343, zzz344, zzz520, zzz521, zzz52200, zzz523, zzz524, zzz31, new_primMulNat0(zzz52200), h)
new_mkVBalBranch3MkVBalBranch16(zzz1702, zzz1703, zzz1704, zzz1705, zzz1706, zzz1707, zzz1708, zzz1709, zzz1710, zzz1711, zzz1712, Zero, Succ(zzz17140), bd) → new_mkVBalBranch(zzz1712, zzz1711, Branch(zzz1702, zzz1703, Neg(Succ(zzz1704)), zzz1705, zzz1706), bd)
new_mkVBalBranch(zzz31, Branch(zzz520, zzz521, Neg(Zero), zzz523, zzz524), Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), h) → new_mkVBalBranch3MkVBalBranch13(zzz340, zzz341, zzz34200, zzz343, zzz344, zzz520, zzz521, zzz523, zzz524, zzz31, new_primMulNat1(zzz34200), h)
new_mkVBalBranch3MkVBalBranch10(zzz929, zzz930, zzz931, zzz932, zzz933, zzz934, zzz935, zzz936, zzz937, zzz938, zzz939, Zero, ba) → new_mkVBalBranch3MkVBalBranch11(zzz929, zzz930, zzz931, zzz932, zzz933, zzz934, zzz935, zzz936, zzz937, zzz938, zzz939, Zero, Succ(zzz936), ba)
new_mkVBalBranch3MkVBalBranch25(zzz537, zzz538, zzz539, zzz540, zzz541, zzz542, zzz543, zzz544, zzz545, zzz546, zzz547, Zero, Zero, bc) → new_mkVBalBranch3MkVBalBranch211(zzz537, zzz538, zzz539, zzz540, zzz541, zzz542, zzz543, zzz544, zzz545, zzz546, zzz547, bc)
new_mkVBalBranch3MkVBalBranch2(zzz340, zzz341, Pos(Zero), zzz343, zzz344, zzz520, zzz521, zzz52200, zzz523, zzz524, zzz31, Zero, h) → new_mkVBalBranch3MkVBalBranch21(zzz340, zzz341, zzz343, zzz344, zzz520, zzz521, zzz52200, zzz523, zzz524, zzz31, h)

The TRS R consists of the following rules:

new_primPlusNat1(Zero) → Zero
new_primMulNat0(zzz6200) → new_primPlusNat3(Succ(new_primPlusNat3(new_primPlusNat1(zzz6200), zzz6200)), Succ(zzz6200))
new_primPlusNat2(Succ(zzz900), Succ(zzz9100)) → Succ(Succ(new_primPlusNat2(zzz900, zzz9100)))
new_primPlusNat3(zzz90, Succ(zzz910)) → Succ(Succ(new_primPlusNat2(zzz90, zzz910)))
new_primPlusNat3(zzz90, Zero) → Succ(zzz90)
new_primMulNat1(zzz34200) → new_primPlusNat2(new_primMulNat0(zzz34200), Succ(zzz34200))
new_primPlusNat2(Zero, Zero) → Zero
new_primPlusNat1(Succ(zzz62000)) → Succ(Succ(new_primPlusNat1(zzz62000)))
new_primPlusNat2(Succ(zzz900), Zero) → Succ(zzz900)
new_primPlusNat2(Zero, Succ(zzz9100)) → Succ(zzz9100)

The set Q consists of the following terms:

new_primPlusNat2(Zero, Succ(x0))
new_primMulNat1(x0)
new_primMulNat0(x0)
new_primPlusNat3(x0, Succ(x1))
new_primPlusNat2(Succ(x0), Succ(x1))
new_primPlusNat3(x0, Zero)
new_primPlusNat1(Zero)
new_primPlusNat2(Zero, Zero)
new_primPlusNat1(Succ(x0))
new_primPlusNat2(Succ(x0), Zero)

We have to consider all minimal (P,Q,R)-chains.
By rewriting [15] the rule new_mkVBalBranch(zzz31, Branch(zzz520, zzz521, Pos(Succ(zzz52200)), zzz523, zzz524), Branch(zzz340, zzz341, zzz342, zzz343, zzz344), h) → new_mkVBalBranch3MkVBalBranch2(zzz340, zzz341, zzz342, zzz343, zzz344, zzz520, zzz521, zzz52200, zzz523, zzz524, zzz31, new_primMulNat0(zzz52200), h) at position [11] we obtained the following new rules:

new_mkVBalBranch(zzz31, Branch(zzz520, zzz521, Pos(Succ(zzz52200)), zzz523, zzz524), Branch(zzz340, zzz341, zzz342, zzz343, zzz344), h) → new_mkVBalBranch3MkVBalBranch2(zzz340, zzz341, zzz342, zzz343, zzz344, zzz520, zzz521, zzz52200, zzz523, zzz524, zzz31, new_primPlusNat3(Succ(new_primPlusNat3(new_primPlusNat1(zzz52200), zzz52200)), Succ(zzz52200)), 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
                                    ↳ DependencyGraphProof
                                      ↳ QDP
                                        ↳ Rewriting
                                          ↳ QDP
                                            ↳ Rewriting
                                              ↳ QDP
                                                ↳ Rewriting
                                                  ↳ QDP
                                                    ↳ Rewriting
                                                      ↳ QDP
                                                        ↳ Rewriting
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP

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

new_mkVBalBranch3MkVBalBranch11(zzz2033, zzz2034, zzz2035, zzz2036, zzz2037, zzz2038, zzz2039, zzz2040, zzz2041, zzz2042, zzz2043, Zero, Succ(zzz20450), bb) → new_mkVBalBranch(zzz2043, zzz2042, Branch(zzz2033, zzz2034, Pos(Succ(zzz2035)), zzz2036, zzz2037), bb)
new_mkVBalBranch3MkVBalBranch26(zzz1133, zzz1134, zzz1135, zzz1136, zzz1137, zzz1138, zzz1139, zzz1140, zzz1141, zzz1142, Succ(zzz11430), Succ(zzz11440), be) → new_mkVBalBranch3MkVBalBranch26(zzz1133, zzz1134, zzz1135, zzz1136, zzz1137, zzz1138, zzz1139, zzz1140, zzz1141, zzz1142, zzz11430, zzz11440, be)
new_mkVBalBranch3MkVBalBranch24(zzz340, zzz341, Neg(Succ(Succ(Succ(zzz3420000)))), zzz343, zzz344, zzz520, zzz521, Zero, zzz523, zzz524, zzz31, Succ(Zero), h) → new_mkVBalBranch3MkVBalBranch26(zzz340, zzz341, Succ(Succ(zzz3420000)), zzz343, zzz344, zzz520, zzz521, zzz523, zzz524, zzz31, Succ(zzz3420000), Zero, h)
new_mkVBalBranch3MkVBalBranch24(zzz340, zzz341, Neg(Succ(Zero)), zzz343, zzz344, zzz520, zzz521, Zero, zzz523, zzz524, zzz31, Zero, h) → new_mkVBalBranch3MkVBalBranch29(zzz340, zzz341, Zero, zzz343, zzz344, zzz520, zzz521, zzz523, zzz524, zzz31, h)
new_mkVBalBranch3MkVBalBranch20(zzz929, zzz930, zzz931, zzz932, zzz933, zzz934, zzz935, zzz936, zzz937, zzz938, zzz939, Zero, Succ(zzz9410), ba) → new_mkVBalBranch(zzz939, Branch(zzz934, zzz935, Pos(Succ(zzz936)), zzz937, zzz938), zzz932, ba)
new_mkVBalBranch3MkVBalBranch17(zzz340, zzz341, zzz34200, zzz343, zzz344, zzz520, zzz521, zzz52200, zzz523, zzz524, zzz31, h) → new_mkVBalBranch(zzz31, zzz524, Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), h)
new_mkVBalBranch3MkVBalBranch26(zzz1133, zzz1134, zzz1135, zzz1136, zzz1137, zzz1138, zzz1139, zzz1140, zzz1141, zzz1142, Zero, Zero, be) → new_mkVBalBranch3MkVBalBranch29(zzz1133, zzz1134, zzz1135, zzz1136, zzz1137, zzz1138, zzz1139, zzz1140, zzz1141, zzz1142, be)
new_mkVBalBranch3MkVBalBranch20(zzz929, zzz930, zzz931, zzz932, zzz933, zzz934, zzz935, zzz936, zzz937, zzz938, zzz939, Zero, Zero, ba) → new_mkVBalBranch3MkVBalBranch23(zzz929, zzz930, zzz931, zzz932, zzz933, zzz934, zzz935, zzz936, zzz937, zzz938, zzz939, ba)
new_mkVBalBranch3MkVBalBranch24(zzz340, zzz341, Neg(Succ(Succ(Zero))), zzz343, zzz344, zzz520, zzz521, Succ(zzz522000), zzz523, zzz524, zzz31, Succ(Zero), h) → new_mkVBalBranch3MkVBalBranch25(zzz340, zzz341, Succ(Zero), zzz343, zzz344, zzz520, zzz521, zzz522000, zzz523, zzz524, zzz31, Zero, Succ(zzz522000), h)
new_mkVBalBranch3MkVBalBranch20(zzz929, zzz930, zzz931, zzz932, zzz933, zzz934, zzz935, zzz936, zzz937, zzz938, zzz939, Succ(zzz9400), Succ(zzz9410), ba) → new_mkVBalBranch3MkVBalBranch20(zzz929, zzz930, zzz931, zzz932, zzz933, zzz934, zzz935, zzz936, zzz937, zzz938, zzz939, zzz9400, zzz9410, ba)
new_mkVBalBranch3MkVBalBranch24(zzz340, zzz341, Neg(Succ(Succ(Succ(zzz3420000)))), zzz343, zzz344, zzz520, zzz521, Succ(zzz522000), zzz523, zzz524, zzz31, Succ(Zero), h) → new_mkVBalBranch3MkVBalBranch25(zzz340, zzz341, Succ(Succ(zzz3420000)), zzz343, zzz344, zzz520, zzz521, zzz522000, zzz523, zzz524, zzz31, Succ(zzz3420000), Succ(zzz522000), h)
new_mkVBalBranch3MkVBalBranch26(zzz1133, zzz1134, zzz1135, zzz1136, zzz1137, zzz1138, zzz1139, zzz1140, zzz1141, zzz1142, Succ(zzz11430), Zero, be) → new_mkVBalBranch3MkVBalBranch212(zzz1133, zzz1134, zzz1135, zzz1136, zzz1137, zzz1138, zzz1139, zzz1140, zzz1141, zzz1142, be)
new_mkVBalBranch3MkVBalBranch24(zzz340, zzz341, Neg(Succ(Succ(zzz342000))), zzz343, zzz344, zzz520, zzz521, Succ(zzz522000), zzz523, zzz524, zzz31, Zero, h) → new_mkVBalBranch3MkVBalBranch25(zzz340, zzz341, Succ(zzz342000), zzz343, zzz344, zzz520, zzz521, zzz522000, zzz523, zzz524, zzz31, zzz342000, zzz522000, h)
new_mkVBalBranch(zzz31, Branch(zzz520, zzz521, Pos(Succ(zzz52200)), zzz523, zzz524), Branch(zzz340, zzz341, zzz342, zzz343, zzz344), h) → new_mkVBalBranch3MkVBalBranch2(zzz340, zzz341, zzz342, zzz343, zzz344, zzz520, zzz521, zzz52200, zzz523, zzz524, zzz31, new_primPlusNat3(Succ(new_primPlusNat3(new_primPlusNat1(zzz52200), zzz52200)), Succ(zzz52200)), h)
new_mkVBalBranch3MkVBalBranch11(zzz2033, zzz2034, zzz2035, zzz2036, zzz2037, zzz2038, zzz2039, zzz2040, zzz2041, zzz2042, zzz2043, Succ(zzz20440), Succ(zzz20450), bb) → new_mkVBalBranch3MkVBalBranch11(zzz2033, zzz2034, zzz2035, zzz2036, zzz2037, zzz2038, zzz2039, zzz2040, zzz2041, zzz2042, zzz2043, zzz20440, zzz20450, bb)
new_mkVBalBranch3MkVBalBranch2(zzz340, zzz341, Neg(zzz3420), zzz343, zzz344, zzz520, zzz521, zzz52200, zzz523, zzz524, zzz31, Zero, h) → new_mkVBalBranch3MkVBalBranch22(zzz340, zzz341, zzz3420, zzz343, zzz344, zzz520, zzz521, zzz52200, zzz523, zzz524, zzz31, h)
new_mkVBalBranch3MkVBalBranch25(zzz537, zzz538, zzz539, zzz540, zzz541, zzz542, zzz543, zzz544, zzz545, zzz546, zzz547, Succ(zzz5480), Succ(zzz5490), bc) → new_mkVBalBranch3MkVBalBranch25(zzz537, zzz538, zzz539, zzz540, zzz541, zzz542, zzz543, zzz544, zzz545, zzz546, zzz547, zzz5480, zzz5490, bc)
new_mkVBalBranch(zzz31, Branch(zzz520, zzz521, Neg(Succ(zzz52200)), zzz523, zzz524), Branch(zzz340, zzz341, zzz342, zzz343, zzz344), h) → new_mkVBalBranch3MkVBalBranch24(zzz340, zzz341, zzz342, zzz343, zzz344, zzz520, zzz521, zzz52200, zzz523, zzz524, zzz31, new_primPlusNat3(Succ(new_primPlusNat3(new_primPlusNat1(zzz52200), zzz52200)), Succ(zzz52200)), h)
new_mkVBalBranch3MkVBalBranch24(zzz340, zzz341, Neg(Succ(Zero)), zzz343, zzz344, zzz520, zzz521, Succ(zzz522000), zzz523, zzz524, zzz31, Zero, h) → new_mkVBalBranch3MkVBalBranch28(zzz340, zzz341, zzz343, zzz344, zzz520, zzz521, Succ(zzz522000), zzz523, zzz524, zzz31, h)
new_mkVBalBranch3MkVBalBranch210(zzz340, zzz341, zzz343, zzz344, zzz520, zzz521, zzz52200, zzz523, zzz524, zzz31, h) → new_mkVBalBranch(zzz31, Branch(zzz520, zzz521, Neg(Succ(zzz52200)), zzz523, zzz524), zzz343, h)
new_mkVBalBranch3MkVBalBranch24(zzz340, zzz341, Neg(Succ(Succ(zzz342000))), zzz343, zzz344, zzz520, zzz521, Zero, zzz523, zzz524, zzz31, Zero, h) → new_mkVBalBranch3MkVBalBranch14(zzz340, zzz341, Succ(zzz342000), zzz343, zzz344, zzz520, zzz521, zzz523, zzz524, zzz31, new_primMulNat1(Succ(zzz342000)), h)
new_mkVBalBranch3MkVBalBranch26(zzz1133, zzz1134, zzz1135, zzz1136, zzz1137, zzz1138, zzz1139, zzz1140, zzz1141, zzz1142, Zero, Succ(zzz11440), be) → new_mkVBalBranch(zzz1142, Branch(zzz1138, zzz1139, Neg(Succ(Zero)), zzz1140, zzz1141), zzz1136, be)
new_mkVBalBranch3MkVBalBranch24(zzz340, zzz341, Neg(Succ(Succ(Zero))), zzz343, zzz344, zzz520, zzz521, Zero, zzz523, zzz524, zzz31, Succ(Zero), h) → new_mkVBalBranch3MkVBalBranch26(zzz340, zzz341, Succ(Zero), zzz343, zzz344, zzz520, zzz521, zzz523, zzz524, zzz31, Zero, Zero, h)
new_mkVBalBranch(zzz31, Branch(zzz520, zzz521, Pos(Zero), zzz523, zzz524), Branch(zzz340, zzz341, Pos(Succ(zzz34200)), zzz343, zzz344), h) → new_mkVBalBranch(zzz31, Branch(zzz520, zzz521, Pos(Zero), zzz523, zzz524), zzz343, h)
new_mkVBalBranch3MkVBalBranch29(zzz818, zzz819, zzz820, zzz821, zzz822, zzz823, zzz824, zzz825, zzz826, zzz827, bf) → new_mkVBalBranch3MkVBalBranch14(zzz818, zzz819, zzz820, zzz821, zzz822, zzz823, zzz824, zzz825, zzz826, zzz827, new_primMulNat1(zzz820), bf)
new_mkVBalBranch3MkVBalBranch2(zzz340, zzz341, Pos(Zero), zzz343, zzz344, zzz520, zzz521, zzz52200, zzz523, zzz524, zzz31, Succ(zzz680), h) → new_mkVBalBranch(zzz31, zzz524, Branch(zzz340, zzz341, Pos(Zero), zzz343, zzz344), h)
new_mkVBalBranch3MkVBalBranch21(zzz340, zzz341, zzz343, zzz344, zzz520, zzz521, zzz52200, zzz523, zzz524, zzz31, h) → new_mkVBalBranch(zzz31, zzz524, Branch(zzz340, zzz341, Pos(Zero), zzz343, zzz344), h)
new_mkVBalBranch3MkVBalBranch24(zzz340, zzz341, Pos(zzz3420), zzz343, zzz344, zzz520, zzz521, zzz52200, zzz523, zzz524, zzz31, Zero, h) → new_mkVBalBranch3MkVBalBranch27(zzz340, zzz341, zzz3420, zzz343, zzz344, zzz520, zzz521, zzz52200, zzz523, zzz524, zzz31, h)
new_mkVBalBranch3MkVBalBranch23(zzz929, zzz930, zzz931, zzz932, zzz933, zzz934, zzz935, zzz936, zzz937, zzz938, zzz939, ba) → new_mkVBalBranch3MkVBalBranch10(zzz929, zzz930, zzz931, zzz932, zzz933, zzz934, zzz935, zzz936, zzz937, zzz938, zzz939, new_primMulNat1(zzz931), ba)
new_mkVBalBranch3MkVBalBranch211(zzz537, zzz538, zzz539, zzz540, zzz541, zzz542, zzz543, zzz544, zzz545, zzz546, zzz547, bc) → new_mkVBalBranch3MkVBalBranch15(zzz537, zzz538, zzz539, zzz540, zzz541, zzz542, zzz543, zzz544, zzz545, zzz546, zzz547, new_primMulNat1(zzz539), bc)
new_mkVBalBranch3MkVBalBranch24(zzz340, zzz341, Neg(Succ(Succ(Succ(zzz3420000)))), zzz343, zzz344, zzz520, zzz521, Zero, zzz523, zzz524, zzz31, Succ(Succ(zzz6900)), h) → new_mkVBalBranch3MkVBalBranch26(zzz340, zzz341, Succ(Succ(zzz3420000)), zzz343, zzz344, zzz520, zzz521, zzz523, zzz524, zzz31, Succ(zzz3420000), Succ(zzz6900), h)
new_mkVBalBranch3MkVBalBranch15(zzz537, zzz538, zzz539, zzz540, zzz541, zzz542, zzz543, zzz544, zzz545, zzz546, zzz547, Succ(zzz6990), bc) → new_mkVBalBranch3MkVBalBranch16(zzz537, zzz538, zzz539, zzz540, zzz541, zzz542, zzz543, Succ(zzz544), zzz545, zzz546, zzz547, Succ(Succ(zzz544)), Succ(zzz6990), bc)
new_mkVBalBranch3MkVBalBranch27(zzz340, zzz341, zzz3420, zzz343, zzz344, zzz520, zzz521, zzz52200, zzz523, zzz524, zzz31, h) → new_mkVBalBranch(zzz31, Branch(zzz520, zzz521, Neg(Succ(zzz52200)), zzz523, zzz524), zzz343, h)
new_mkVBalBranch3MkVBalBranch24(zzz340, zzz341, Pos(zzz3420), zzz343, zzz344, zzz520, zzz521, zzz52200, zzz523, zzz524, zzz31, Succ(zzz690), h) → new_mkVBalBranch(zzz31, Branch(zzz520, zzz521, Neg(Succ(zzz52200)), zzz523, zzz524), zzz343, h)
new_mkVBalBranch3MkVBalBranch12(zzz340, zzz341, zzz34200, zzz343, zzz344, zzz520, zzz521, zzz523, zzz524, zzz31, Succ(zzz1250), h) → new_mkVBalBranch(zzz31, zzz524, Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), h)
new_mkVBalBranch3MkVBalBranch25(zzz537, zzz538, zzz539, zzz540, zzz541, zzz542, zzz543, zzz544, zzz545, zzz546, zzz547, Succ(zzz5480), Zero, bc) → new_mkVBalBranch3MkVBalBranch15(zzz537, zzz538, zzz539, zzz540, zzz541, zzz542, zzz543, zzz544, zzz545, zzz546, zzz547, new_primMulNat1(zzz539), bc)
new_mkVBalBranch3MkVBalBranch28(zzz340, zzz341, zzz343, zzz344, zzz520, zzz521, zzz52200, zzz523, zzz524, zzz31, h) → new_mkVBalBranch(zzz31, Branch(zzz520, zzz521, Neg(Succ(zzz52200)), zzz523, zzz524), zzz343, h)
new_mkVBalBranch3MkVBalBranch24(zzz340, zzz341, Neg(Succ(Succ(Zero))), zzz343, zzz344, zzz520, zzz521, Zero, zzz523, zzz524, zzz31, Succ(Succ(zzz6900)), h) → new_mkVBalBranch3MkVBalBranch26(zzz340, zzz341, Succ(Zero), zzz343, zzz344, zzz520, zzz521, zzz523, zzz524, zzz31, Zero, Succ(zzz6900), h)
new_mkVBalBranch3MkVBalBranch1(zzz340, zzz341, zzz34200, zzz343, zzz344, zzz520, zzz521, zzz52200, zzz523, zzz524, zzz31, Succ(zzz1430), h) → new_mkVBalBranch(zzz31, zzz524, Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), h)
new_mkVBalBranch3MkVBalBranch22(zzz340, zzz341, Zero, zzz343, zzz344, zzz520, zzz521, zzz52200, zzz523, zzz524, zzz31, h) → new_mkVBalBranch(zzz31, zzz524, Branch(zzz340, zzz341, Neg(Zero), zzz343, zzz344), h)
new_mkVBalBranch(zzz31, Branch(zzz520, zzz521, Pos(Zero), zzz523, zzz524), Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), h) → new_mkVBalBranch3MkVBalBranch12(zzz340, zzz341, zzz34200, zzz343, zzz344, zzz520, zzz521, zzz523, zzz524, zzz31, new_primPlusNat2(new_primMulNat0(zzz34200), Succ(zzz34200)), h)
new_mkVBalBranch3MkVBalBranch24(zzz340, zzz341, Neg(Succ(Zero)), zzz343, zzz344, zzz520, zzz521, zzz52200, zzz523, zzz524, zzz31, Succ(zzz690), h) → new_mkVBalBranch(zzz31, Branch(zzz520, zzz521, Neg(Succ(zzz52200)), zzz523, zzz524), zzz343, h)
new_mkVBalBranch3MkVBalBranch22(zzz340, zzz341, Succ(zzz34200), zzz343, zzz344, zzz520, zzz521, zzz52200, zzz523, zzz524, zzz31, h) → new_mkVBalBranch3MkVBalBranch1(zzz340, zzz341, zzz34200, zzz343, zzz344, zzz520, zzz521, zzz52200, zzz523, zzz524, zzz31, new_primPlusNat2(new_primMulNat0(zzz34200), Succ(zzz34200)), h)
new_mkVBalBranch3MkVBalBranch13(zzz340, zzz341, zzz34200, zzz343, zzz344, zzz520, zzz521, zzz523, zzz524, zzz31, Succ(zzz1290), h) → new_mkVBalBranch(zzz31, zzz524, Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), h)
new_mkVBalBranch3MkVBalBranch2(zzz340, zzz341, Pos(Succ(zzz34200)), zzz343, zzz344, zzz520, zzz521, zzz52200, zzz523, zzz524, zzz31, Succ(zzz680), h) → new_mkVBalBranch3MkVBalBranch20(zzz340, zzz341, zzz34200, zzz343, zzz344, zzz520, zzz521, zzz52200, zzz523, zzz524, zzz31, Succ(new_primPlusNat2(zzz680, zzz52200)), zzz34200, h)
new_mkVBalBranch3MkVBalBranch24(zzz340, zzz341, Neg(Zero), zzz343, zzz344, zzz520, zzz521, zzz52200, zzz523, zzz524, zzz31, Succ(zzz690), h) → new_mkVBalBranch(zzz31, Branch(zzz520, zzz521, Neg(Succ(zzz52200)), zzz523, zzz524), zzz343, h)
new_mkVBalBranch(zzz31, Branch(zzz520, zzz521, Neg(Zero), zzz523, zzz524), Branch(zzz340, zzz341, Pos(Succ(zzz34200)), zzz343, zzz344), h) → new_mkVBalBranch(zzz31, Branch(zzz520, zzz521, Neg(Zero), zzz523, zzz524), zzz343, h)
new_mkVBalBranch3MkVBalBranch1(zzz340, zzz341, zzz34200, zzz343, zzz344, zzz520, zzz521, zzz52200, zzz523, zzz524, zzz31, Zero, h) → new_mkVBalBranch3MkVBalBranch17(zzz340, zzz341, zzz34200, zzz343, zzz344, zzz520, zzz521, zzz52200, zzz523, zzz524, zzz31, h)
new_mkVBalBranch3MkVBalBranch16(zzz1702, zzz1703, zzz1704, zzz1705, zzz1706, zzz1707, zzz1708, zzz1709, zzz1710, zzz1711, zzz1712, Succ(zzz17130), Succ(zzz17140), bd) → new_mkVBalBranch3MkVBalBranch16(zzz1702, zzz1703, zzz1704, zzz1705, zzz1706, zzz1707, zzz1708, zzz1709, zzz1710, zzz1711, zzz1712, zzz17130, zzz17140, bd)
new_mkVBalBranch3MkVBalBranch25(zzz537, zzz538, zzz539, zzz540, zzz541, zzz542, zzz543, zzz544, zzz545, zzz546, zzz547, Zero, Succ(zzz5490), bc) → new_mkVBalBranch(zzz547, Branch(zzz542, zzz543, Neg(Succ(Succ(zzz544))), zzz545, zzz546), zzz540, bc)
new_mkVBalBranch3MkVBalBranch10(zzz929, zzz930, zzz931, zzz932, zzz933, zzz934, zzz935, zzz936, zzz937, zzz938, zzz939, Succ(zzz10020), ba) → new_mkVBalBranch3MkVBalBranch11(zzz929, zzz930, zzz931, zzz932, zzz933, zzz934, zzz935, zzz936, zzz937, zzz938, zzz939, Succ(zzz10020), Succ(zzz936), ba)
new_mkVBalBranch3MkVBalBranch212(zzz818, zzz819, zzz820, zzz821, zzz822, zzz823, zzz824, zzz825, zzz826, zzz827, bf) → new_mkVBalBranch3MkVBalBranch14(zzz818, zzz819, zzz820, zzz821, zzz822, zzz823, zzz824, zzz825, zzz826, zzz827, new_primPlusNat2(new_primMulNat0(zzz820), Succ(zzz820)), bf)
new_mkVBalBranch3MkVBalBranch14(zzz818, zzz819, zzz820, zzz821, zzz822, zzz823, zzz824, zzz825, zzz826, zzz827, Succ(zzz8960), bf) → new_mkVBalBranch3MkVBalBranch16(zzz818, zzz819, zzz820, zzz821, zzz822, zzz823, zzz824, Zero, zzz825, zzz826, zzz827, Succ(Zero), Succ(zzz8960), bf)
new_mkVBalBranch3MkVBalBranch2(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344, zzz520, zzz521, zzz52200, zzz523, zzz524, zzz31, Succ(zzz680), h) → new_mkVBalBranch3MkVBalBranch1(zzz340, zzz341, zzz34200, zzz343, zzz344, zzz520, zzz521, zzz52200, zzz523, zzz524, zzz31, new_primPlusNat2(new_primMulNat0(zzz34200), Succ(zzz34200)), h)
new_mkVBalBranch3MkVBalBranch24(zzz340, zzz341, Neg(Succ(Succ(Succ(zzz3420000)))), zzz343, zzz344, zzz520, zzz521, Succ(zzz522000), zzz523, zzz524, zzz31, Succ(Succ(zzz6900)), h) → new_mkVBalBranch3MkVBalBranch25(zzz340, zzz341, Succ(Succ(zzz3420000)), zzz343, zzz344, zzz520, zzz521, zzz522000, zzz523, zzz524, zzz31, Succ(zzz3420000), Succ(Succ(new_primPlusNat2(zzz6900, zzz522000))), h)
new_mkVBalBranch3MkVBalBranch2(zzz340, zzz341, Pos(Succ(zzz34200)), zzz343, zzz344, zzz520, zzz521, zzz52200, zzz523, zzz524, zzz31, Zero, h) → new_mkVBalBranch3MkVBalBranch20(zzz340, zzz341, zzz34200, zzz343, zzz344, zzz520, zzz521, zzz52200, zzz523, zzz524, zzz31, zzz52200, zzz34200, h)
new_mkVBalBranch3MkVBalBranch24(zzz340, zzz341, Neg(Zero), zzz343, zzz344, zzz520, zzz521, zzz52200, zzz523, zzz524, zzz31, Zero, h) → new_mkVBalBranch3MkVBalBranch210(zzz340, zzz341, zzz343, zzz344, zzz520, zzz521, zzz52200, zzz523, zzz524, zzz31, h)
new_mkVBalBranch3MkVBalBranch24(zzz340, zzz341, Neg(Succ(Succ(Zero))), zzz343, zzz344, zzz520, zzz521, Succ(zzz522000), zzz523, zzz524, zzz31, Succ(Succ(zzz6900)), h) → new_mkVBalBranch3MkVBalBranch25(zzz340, zzz341, Succ(Zero), zzz343, zzz344, zzz520, zzz521, zzz522000, zzz523, zzz524, zzz31, Zero, Succ(Succ(new_primPlusNat2(zzz6900, zzz522000))), h)
new_mkVBalBranch3MkVBalBranch20(zzz929, zzz930, zzz931, zzz932, zzz933, zzz934, zzz935, zzz936, zzz937, zzz938, zzz939, Succ(zzz9400), Zero, ba) → new_mkVBalBranch3MkVBalBranch10(zzz929, zzz930, zzz931, zzz932, zzz933, zzz934, zzz935, zzz936, zzz937, zzz938, zzz939, new_primMulNat1(zzz931), ba)
new_mkVBalBranch3MkVBalBranch2(zzz340, zzz341, Neg(Zero), zzz343, zzz344, zzz520, zzz521, zzz52200, zzz523, zzz524, zzz31, Succ(zzz680), h) → new_mkVBalBranch(zzz31, zzz524, Branch(zzz340, zzz341, Neg(Zero), zzz343, zzz344), h)
new_mkVBalBranch(zzz31, Branch(zzz520, zzz521, Neg(Zero), zzz523, zzz524), Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), h) → new_mkVBalBranch3MkVBalBranch13(zzz340, zzz341, zzz34200, zzz343, zzz344, zzz520, zzz521, zzz523, zzz524, zzz31, new_primMulNat1(zzz34200), h)
new_mkVBalBranch3MkVBalBranch16(zzz1702, zzz1703, zzz1704, zzz1705, zzz1706, zzz1707, zzz1708, zzz1709, zzz1710, zzz1711, zzz1712, Zero, Succ(zzz17140), bd) → new_mkVBalBranch(zzz1712, zzz1711, Branch(zzz1702, zzz1703, Neg(Succ(zzz1704)), zzz1705, zzz1706), bd)
new_mkVBalBranch3MkVBalBranch10(zzz929, zzz930, zzz931, zzz932, zzz933, zzz934, zzz935, zzz936, zzz937, zzz938, zzz939, Zero, ba) → new_mkVBalBranch3MkVBalBranch11(zzz929, zzz930, zzz931, zzz932, zzz933, zzz934, zzz935, zzz936, zzz937, zzz938, zzz939, Zero, Succ(zzz936), ba)
new_mkVBalBranch3MkVBalBranch2(zzz340, zzz341, Pos(Zero), zzz343, zzz344, zzz520, zzz521, zzz52200, zzz523, zzz524, zzz31, Zero, h) → new_mkVBalBranch3MkVBalBranch21(zzz340, zzz341, zzz343, zzz344, zzz520, zzz521, zzz52200, zzz523, zzz524, zzz31, h)
new_mkVBalBranch3MkVBalBranch25(zzz537, zzz538, zzz539, zzz540, zzz541, zzz542, zzz543, zzz544, zzz545, zzz546, zzz547, Zero, Zero, bc) → new_mkVBalBranch3MkVBalBranch211(zzz537, zzz538, zzz539, zzz540, zzz541, zzz542, zzz543, zzz544, zzz545, zzz546, zzz547, bc)

The TRS R consists of the following rules:

new_primPlusNat1(Zero) → Zero
new_primMulNat0(zzz6200) → new_primPlusNat3(Succ(new_primPlusNat3(new_primPlusNat1(zzz6200), zzz6200)), Succ(zzz6200))
new_primPlusNat2(Succ(zzz900), Succ(zzz9100)) → Succ(Succ(new_primPlusNat2(zzz900, zzz9100)))
new_primPlusNat3(zzz90, Succ(zzz910)) → Succ(Succ(new_primPlusNat2(zzz90, zzz910)))
new_primPlusNat3(zzz90, Zero) → Succ(zzz90)
new_primMulNat1(zzz34200) → new_primPlusNat2(new_primMulNat0(zzz34200), Succ(zzz34200))
new_primPlusNat2(Zero, Zero) → Zero
new_primPlusNat1(Succ(zzz62000)) → Succ(Succ(new_primPlusNat1(zzz62000)))
new_primPlusNat2(Succ(zzz900), Zero) → Succ(zzz900)
new_primPlusNat2(Zero, Succ(zzz9100)) → Succ(zzz9100)

The set Q consists of the following terms:

new_primPlusNat2(Zero, Succ(x0))
new_primMulNat1(x0)
new_primMulNat0(x0)
new_primPlusNat3(x0, Succ(x1))
new_primPlusNat2(Succ(x0), Succ(x1))
new_primPlusNat3(x0, Zero)
new_primPlusNat1(Zero)
new_primPlusNat2(Zero, Zero)
new_primPlusNat1(Succ(x0))
new_primPlusNat2(Succ(x0), Zero)

We have to consider all minimal (P,Q,R)-chains.
By rewriting [15] the rule new_mkVBalBranch3MkVBalBranch22(zzz340, zzz341, Succ(zzz34200), zzz343, zzz344, zzz520, zzz521, zzz52200, zzz523, zzz524, zzz31, h) → new_mkVBalBranch3MkVBalBranch1(zzz340, zzz341, zzz34200, zzz343, zzz344, zzz520, zzz521, zzz52200, zzz523, zzz524, zzz31, new_primPlusNat2(new_primMulNat0(zzz34200), Succ(zzz34200)), h) at position [11,0] we obtained the following new rules:

new_mkVBalBranch3MkVBalBranch22(zzz340, zzz341, Succ(zzz34200), zzz343, zzz344, zzz520, zzz521, zzz52200, zzz523, zzz524, zzz31, h) → new_mkVBalBranch3MkVBalBranch1(zzz340, zzz341, zzz34200, zzz343, zzz344, zzz520, zzz521, zzz52200, zzz523, zzz524, zzz31, new_primPlusNat2(new_primPlusNat3(Succ(new_primPlusNat3(new_primPlusNat1(zzz34200), zzz34200)), Succ(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
                                    ↳ DependencyGraphProof
                                      ↳ QDP
                                        ↳ Rewriting
                                          ↳ QDP
                                            ↳ Rewriting
                                              ↳ QDP
                                                ↳ Rewriting
                                                  ↳ QDP
                                                    ↳ Rewriting
                                                      ↳ QDP
                                                        ↳ Rewriting
                                                          ↳ QDP
                                                            ↳ Rewriting
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP

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

new_mkVBalBranch3MkVBalBranch11(zzz2033, zzz2034, zzz2035, zzz2036, zzz2037, zzz2038, zzz2039, zzz2040, zzz2041, zzz2042, zzz2043, Zero, Succ(zzz20450), bb) → new_mkVBalBranch(zzz2043, zzz2042, Branch(zzz2033, zzz2034, Pos(Succ(zzz2035)), zzz2036, zzz2037), bb)
new_mkVBalBranch3MkVBalBranch26(zzz1133, zzz1134, zzz1135, zzz1136, zzz1137, zzz1138, zzz1139, zzz1140, zzz1141, zzz1142, Succ(zzz11430), Succ(zzz11440), be) → new_mkVBalBranch3MkVBalBranch26(zzz1133, zzz1134, zzz1135, zzz1136, zzz1137, zzz1138, zzz1139, zzz1140, zzz1141, zzz1142, zzz11430, zzz11440, be)
new_mkVBalBranch3MkVBalBranch24(zzz340, zzz341, Neg(Succ(Succ(Succ(zzz3420000)))), zzz343, zzz344, zzz520, zzz521, Zero, zzz523, zzz524, zzz31, Succ(Zero), h) → new_mkVBalBranch3MkVBalBranch26(zzz340, zzz341, Succ(Succ(zzz3420000)), zzz343, zzz344, zzz520, zzz521, zzz523, zzz524, zzz31, Succ(zzz3420000), Zero, h)
new_mkVBalBranch3MkVBalBranch24(zzz340, zzz341, Neg(Succ(Zero)), zzz343, zzz344, zzz520, zzz521, Zero, zzz523, zzz524, zzz31, Zero, h) → new_mkVBalBranch3MkVBalBranch29(zzz340, zzz341, Zero, zzz343, zzz344, zzz520, zzz521, zzz523, zzz524, zzz31, h)
new_mkVBalBranch3MkVBalBranch20(zzz929, zzz930, zzz931, zzz932, zzz933, zzz934, zzz935, zzz936, zzz937, zzz938, zzz939, Zero, Succ(zzz9410), ba) → new_mkVBalBranch(zzz939, Branch(zzz934, zzz935, Pos(Succ(zzz936)), zzz937, zzz938), zzz932, ba)
new_mkVBalBranch3MkVBalBranch17(zzz340, zzz341, zzz34200, zzz343, zzz344, zzz520, zzz521, zzz52200, zzz523, zzz524, zzz31, h) → new_mkVBalBranch(zzz31, zzz524, Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), h)
new_mkVBalBranch3MkVBalBranch26(zzz1133, zzz1134, zzz1135, zzz1136, zzz1137, zzz1138, zzz1139, zzz1140, zzz1141, zzz1142, Zero, Zero, be) → new_mkVBalBranch3MkVBalBranch29(zzz1133, zzz1134, zzz1135, zzz1136, zzz1137, zzz1138, zzz1139, zzz1140, zzz1141, zzz1142, be)
new_mkVBalBranch3MkVBalBranch20(zzz929, zzz930, zzz931, zzz932, zzz933, zzz934, zzz935, zzz936, zzz937, zzz938, zzz939, Zero, Zero, ba) → new_mkVBalBranch3MkVBalBranch23(zzz929, zzz930, zzz931, zzz932, zzz933, zzz934, zzz935, zzz936, zzz937, zzz938, zzz939, ba)
new_mkVBalBranch3MkVBalBranch24(zzz340, zzz341, Neg(Succ(Succ(Zero))), zzz343, zzz344, zzz520, zzz521, Succ(zzz522000), zzz523, zzz524, zzz31, Succ(Zero), h) → new_mkVBalBranch3MkVBalBranch25(zzz340, zzz341, Succ(Zero), zzz343, zzz344, zzz520, zzz521, zzz522000, zzz523, zzz524, zzz31, Zero, Succ(zzz522000), h)
new_mkVBalBranch3MkVBalBranch24(zzz340, zzz341, Neg(Succ(Succ(Succ(zzz3420000)))), zzz343, zzz344, zzz520, zzz521, Succ(zzz522000), zzz523, zzz524, zzz31, Succ(Zero), h) → new_mkVBalBranch3MkVBalBranch25(zzz340, zzz341, Succ(Succ(zzz3420000)), zzz343, zzz344, zzz520, zzz521, zzz522000, zzz523, zzz524, zzz31, Succ(zzz3420000), Succ(zzz522000), h)
new_mkVBalBranch3MkVBalBranch20(zzz929, zzz930, zzz931, zzz932, zzz933, zzz934, zzz935, zzz936, zzz937, zzz938, zzz939, Succ(zzz9400), Succ(zzz9410), ba) → new_mkVBalBranch3MkVBalBranch20(zzz929, zzz930, zzz931, zzz932, zzz933, zzz934, zzz935, zzz936, zzz937, zzz938, zzz939, zzz9400, zzz9410, ba)
new_mkVBalBranch3MkVBalBranch24(zzz340, zzz341, Neg(Succ(Succ(zzz342000))), zzz343, zzz344, zzz520, zzz521, Succ(zzz522000), zzz523, zzz524, zzz31, Zero, h) → new_mkVBalBranch3MkVBalBranch25(zzz340, zzz341, Succ(zzz342000), zzz343, zzz344, zzz520, zzz521, zzz522000, zzz523, zzz524, zzz31, zzz342000, zzz522000, h)
new_mkVBalBranch3MkVBalBranch26(zzz1133, zzz1134, zzz1135, zzz1136, zzz1137, zzz1138, zzz1139, zzz1140, zzz1141, zzz1142, Succ(zzz11430), Zero, be) → new_mkVBalBranch3MkVBalBranch212(zzz1133, zzz1134, zzz1135, zzz1136, zzz1137, zzz1138, zzz1139, zzz1140, zzz1141, zzz1142, be)
new_mkVBalBranch(zzz31, Branch(zzz520, zzz521, Pos(Succ(zzz52200)), zzz523, zzz524), Branch(zzz340, zzz341, zzz342, zzz343, zzz344), h) → new_mkVBalBranch3MkVBalBranch2(zzz340, zzz341, zzz342, zzz343, zzz344, zzz520, zzz521, zzz52200, zzz523, zzz524, zzz31, new_primPlusNat3(Succ(new_primPlusNat3(new_primPlusNat1(zzz52200), zzz52200)), Succ(zzz52200)), h)
new_mkVBalBranch3MkVBalBranch11(zzz2033, zzz2034, zzz2035, zzz2036, zzz2037, zzz2038, zzz2039, zzz2040, zzz2041, zzz2042, zzz2043, Succ(zzz20440), Succ(zzz20450), bb) → new_mkVBalBranch3MkVBalBranch11(zzz2033, zzz2034, zzz2035, zzz2036, zzz2037, zzz2038, zzz2039, zzz2040, zzz2041, zzz2042, zzz2043, zzz20440, zzz20450, bb)
new_mkVBalBranch3MkVBalBranch25(zzz537, zzz538, zzz539, zzz540, zzz541, zzz542, zzz543, zzz544, zzz545, zzz546, zzz547, Succ(zzz5480), Succ(zzz5490), bc) → new_mkVBalBranch3MkVBalBranch25(zzz537, zzz538, zzz539, zzz540, zzz541, zzz542, zzz543, zzz544, zzz545, zzz546, zzz547, zzz5480, zzz5490, bc)
new_mkVBalBranch3MkVBalBranch2(zzz340, zzz341, Neg(zzz3420), zzz343, zzz344, zzz520, zzz521, zzz52200, zzz523, zzz524, zzz31, Zero, h) → new_mkVBalBranch3MkVBalBranch22(zzz340, zzz341, zzz3420, zzz343, zzz344, zzz520, zzz521, zzz52200, zzz523, zzz524, zzz31, h)
new_mkVBalBranch(zzz31, Branch(zzz520, zzz521, Neg(Succ(zzz52200)), zzz523, zzz524), Branch(zzz340, zzz341, zzz342, zzz343, zzz344), h) → new_mkVBalBranch3MkVBalBranch24(zzz340, zzz341, zzz342, zzz343, zzz344, zzz520, zzz521, zzz52200, zzz523, zzz524, zzz31, new_primPlusNat3(Succ(new_primPlusNat3(new_primPlusNat1(zzz52200), zzz52200)), Succ(zzz52200)), h)
new_mkVBalBranch3MkVBalBranch24(zzz340, zzz341, Neg(Succ(Zero)), zzz343, zzz344, zzz520, zzz521, Succ(zzz522000), zzz523, zzz524, zzz31, Zero, h) → new_mkVBalBranch3MkVBalBranch28(zzz340, zzz341, zzz343, zzz344, zzz520, zzz521, Succ(zzz522000), zzz523, zzz524, zzz31, h)
new_mkVBalBranch3MkVBalBranch24(zzz340, zzz341, Neg(Succ(Succ(zzz342000))), zzz343, zzz344, zzz520, zzz521, Zero, zzz523, zzz524, zzz31, Zero, h) → new_mkVBalBranch3MkVBalBranch14(zzz340, zzz341, Succ(zzz342000), zzz343, zzz344, zzz520, zzz521, zzz523, zzz524, zzz31, new_primMulNat1(Succ(zzz342000)), h)
new_mkVBalBranch3MkVBalBranch210(zzz340, zzz341, zzz343, zzz344, zzz520, zzz521, zzz52200, zzz523, zzz524, zzz31, h) → new_mkVBalBranch(zzz31, Branch(zzz520, zzz521, Neg(Succ(zzz52200)), zzz523, zzz524), zzz343, h)
new_mkVBalBranch3MkVBalBranch26(zzz1133, zzz1134, zzz1135, zzz1136, zzz1137, zzz1138, zzz1139, zzz1140, zzz1141, zzz1142, Zero, Succ(zzz11440), be) → new_mkVBalBranch(zzz1142, Branch(zzz1138, zzz1139, Neg(Succ(Zero)), zzz1140, zzz1141), zzz1136, be)
new_mkVBalBranch3MkVBalBranch24(zzz340, zzz341, Neg(Succ(Succ(Zero))), zzz343, zzz344, zzz520, zzz521, Zero, zzz523, zzz524, zzz31, Succ(Zero), h) → new_mkVBalBranch3MkVBalBranch26(zzz340, zzz341, Succ(Zero), zzz343, zzz344, zzz520, zzz521, zzz523, zzz524, zzz31, Zero, Zero, h)
new_mkVBalBranch(zzz31, Branch(zzz520, zzz521, Pos(Zero), zzz523, zzz524), Branch(zzz340, zzz341, Pos(Succ(zzz34200)), zzz343, zzz344), h) → new_mkVBalBranch(zzz31, Branch(zzz520, zzz521, Pos(Zero), zzz523, zzz524), zzz343, h)
new_mkVBalBranch3MkVBalBranch29(zzz818, zzz819, zzz820, zzz821, zzz822, zzz823, zzz824, zzz825, zzz826, zzz827, bf) → new_mkVBalBranch3MkVBalBranch14(zzz818, zzz819, zzz820, zzz821, zzz822, zzz823, zzz824, zzz825, zzz826, zzz827, new_primMulNat1(zzz820), bf)
new_mkVBalBranch3MkVBalBranch2(zzz340, zzz341, Pos(Zero), zzz343, zzz344, zzz520, zzz521, zzz52200, zzz523, zzz524, zzz31, Succ(zzz680), h) → new_mkVBalBranch(zzz31, zzz524, Branch(zzz340, zzz341, Pos(Zero), zzz343, zzz344), h)
new_mkVBalBranch3MkVBalBranch21(zzz340, zzz341, zzz343, zzz344, zzz520, zzz521, zzz52200, zzz523, zzz524, zzz31, h) → new_mkVBalBranch(zzz31, zzz524, Branch(zzz340, zzz341, Pos(Zero), zzz343, zzz344), h)
new_mkVBalBranch3MkVBalBranch24(zzz340, zzz341, Pos(zzz3420), zzz343, zzz344, zzz520, zzz521, zzz52200, zzz523, zzz524, zzz31, Zero, h) → new_mkVBalBranch3MkVBalBranch27(zzz340, zzz341, zzz3420, zzz343, zzz344, zzz520, zzz521, zzz52200, zzz523, zzz524, zzz31, h)
new_mkVBalBranch3MkVBalBranch23(zzz929, zzz930, zzz931, zzz932, zzz933, zzz934, zzz935, zzz936, zzz937, zzz938, zzz939, ba) → new_mkVBalBranch3MkVBalBranch10(zzz929, zzz930, zzz931, zzz932, zzz933, zzz934, zzz935, zzz936, zzz937, zzz938, zzz939, new_primMulNat1(zzz931), ba)
new_mkVBalBranch3MkVBalBranch211(zzz537, zzz538, zzz539, zzz540, zzz541, zzz542, zzz543, zzz544, zzz545, zzz546, zzz547, bc) → new_mkVBalBranch3MkVBalBranch15(zzz537, zzz538, zzz539, zzz540, zzz541, zzz542, zzz543, zzz544, zzz545, zzz546, zzz547, new_primMulNat1(zzz539), bc)
new_mkVBalBranch3MkVBalBranch15(zzz537, zzz538, zzz539, zzz540, zzz541, zzz542, zzz543, zzz544, zzz545, zzz546, zzz547, Succ(zzz6990), bc) → new_mkVBalBranch3MkVBalBranch16(zzz537, zzz538, zzz539, zzz540, zzz541, zzz542, zzz543, Succ(zzz544), zzz545, zzz546, zzz547, Succ(Succ(zzz544)), Succ(zzz6990), bc)
new_mkVBalBranch3MkVBalBranch24(zzz340, zzz341, Neg(Succ(Succ(Succ(zzz3420000)))), zzz343, zzz344, zzz520, zzz521, Zero, zzz523, zzz524, zzz31, Succ(Succ(zzz6900)), h) → new_mkVBalBranch3MkVBalBranch26(zzz340, zzz341, Succ(Succ(zzz3420000)), zzz343, zzz344, zzz520, zzz521, zzz523, zzz524, zzz31, Succ(zzz3420000), Succ(zzz6900), h)
new_mkVBalBranch3MkVBalBranch27(zzz340, zzz341, zzz3420, zzz343, zzz344, zzz520, zzz521, zzz52200, zzz523, zzz524, zzz31, h) → new_mkVBalBranch(zzz31, Branch(zzz520, zzz521, Neg(Succ(zzz52200)), zzz523, zzz524), zzz343, h)
new_mkVBalBranch3MkVBalBranch24(zzz340, zzz341, Pos(zzz3420), zzz343, zzz344, zzz520, zzz521, zzz52200, zzz523, zzz524, zzz31, Succ(zzz690), h) → new_mkVBalBranch(zzz31, Branch(zzz520, zzz521, Neg(Succ(zzz52200)), zzz523, zzz524), zzz343, h)
new_mkVBalBranch3MkVBalBranch12(zzz340, zzz341, zzz34200, zzz343, zzz344, zzz520, zzz521, zzz523, zzz524, zzz31, Succ(zzz1250), h) → new_mkVBalBranch(zzz31, zzz524, Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), h)
new_mkVBalBranch3MkVBalBranch28(zzz340, zzz341, zzz343, zzz344, zzz520, zzz521, zzz52200, zzz523, zzz524, zzz31, h) → new_mkVBalBranch(zzz31, Branch(zzz520, zzz521, Neg(Succ(zzz52200)), zzz523, zzz524), zzz343, h)
new_mkVBalBranch3MkVBalBranch25(zzz537, zzz538, zzz539, zzz540, zzz541, zzz542, zzz543, zzz544, zzz545, zzz546, zzz547, Succ(zzz5480), Zero, bc) → new_mkVBalBranch3MkVBalBranch15(zzz537, zzz538, zzz539, zzz540, zzz541, zzz542, zzz543, zzz544, zzz545, zzz546, zzz547, new_primMulNat1(zzz539), bc)
new_mkVBalBranch3MkVBalBranch24(zzz340, zzz341, Neg(Succ(Succ(Zero))), zzz343, zzz344, zzz520, zzz521, Zero, zzz523, zzz524, zzz31, Succ(Succ(zzz6900)), h) → new_mkVBalBranch3MkVBalBranch26(zzz340, zzz341, Succ(Zero), zzz343, zzz344, zzz520, zzz521, zzz523, zzz524, zzz31, Zero, Succ(zzz6900), h)
new_mkVBalBranch(zzz31, Branch(zzz520, zzz521, Pos(Zero), zzz523, zzz524), Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), h) → new_mkVBalBranch3MkVBalBranch12(zzz340, zzz341, zzz34200, zzz343, zzz344, zzz520, zzz521, zzz523, zzz524, zzz31, new_primPlusNat2(new_primMulNat0(zzz34200), Succ(zzz34200)), h)
new_mkVBalBranch3MkVBalBranch22(zzz340, zzz341, Zero, zzz343, zzz344, zzz520, zzz521, zzz52200, zzz523, zzz524, zzz31, h) → new_mkVBalBranch(zzz31, zzz524, Branch(zzz340, zzz341, Neg(Zero), zzz343, zzz344), h)
new_mkVBalBranch3MkVBalBranch1(zzz340, zzz341, zzz34200, zzz343, zzz344, zzz520, zzz521, zzz52200, zzz523, zzz524, zzz31, Succ(zzz1430), h) → new_mkVBalBranch(zzz31, zzz524, Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), h)
new_mkVBalBranch3MkVBalBranch24(zzz340, zzz341, Neg(Succ(Zero)), zzz343, zzz344, zzz520, zzz521, zzz52200, zzz523, zzz524, zzz31, Succ(zzz690), h) → new_mkVBalBranch(zzz31, Branch(zzz520, zzz521, Neg(Succ(zzz52200)), zzz523, zzz524), zzz343, h)
new_mkVBalBranch3MkVBalBranch13(zzz340, zzz341, zzz34200, zzz343, zzz344, zzz520, zzz521, zzz523, zzz524, zzz31, Succ(zzz1290), h) → new_mkVBalBranch(zzz31, zzz524, Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), h)
new_mkVBalBranch3MkVBalBranch2(zzz340, zzz341, Pos(Succ(zzz34200)), zzz343, zzz344, zzz520, zzz521, zzz52200, zzz523, zzz524, zzz31, Succ(zzz680), h) → new_mkVBalBranch3MkVBalBranch20(zzz340, zzz341, zzz34200, zzz343, zzz344, zzz520, zzz521, zzz52200, zzz523, zzz524, zzz31, Succ(new_primPlusNat2(zzz680, zzz52200)), zzz34200, h)
new_mkVBalBranch(zzz31, Branch(zzz520, zzz521, Neg(Zero), zzz523, zzz524), Branch(zzz340, zzz341, Pos(Succ(zzz34200)), zzz343, zzz344), h) → new_mkVBalBranch(zzz31, Branch(zzz520, zzz521, Neg(Zero), zzz523, zzz524), zzz343, h)
new_mkVBalBranch3MkVBalBranch24(zzz340, zzz341, Neg(Zero), zzz343, zzz344, zzz520, zzz521, zzz52200, zzz523, zzz524, zzz31, Succ(zzz690), h) → new_mkVBalBranch(zzz31, Branch(zzz520, zzz521, Neg(Succ(zzz52200)), zzz523, zzz524), zzz343, h)
new_mkVBalBranch3MkVBalBranch1(zzz340, zzz341, zzz34200, zzz343, zzz344, zzz520, zzz521, zzz52200, zzz523, zzz524, zzz31, Zero, h) → new_mkVBalBranch3MkVBalBranch17(zzz340, zzz341, zzz34200, zzz343, zzz344, zzz520, zzz521, zzz52200, zzz523, zzz524, zzz31, h)
new_mkVBalBranch3MkVBalBranch16(zzz1702, zzz1703, zzz1704, zzz1705, zzz1706, zzz1707, zzz1708, zzz1709, zzz1710, zzz1711, zzz1712, Succ(zzz17130), Succ(zzz17140), bd) → new_mkVBalBranch3MkVBalBranch16(zzz1702, zzz1703, zzz1704, zzz1705, zzz1706, zzz1707, zzz1708, zzz1709, zzz1710, zzz1711, zzz1712, zzz17130, zzz17140, bd)
new_mkVBalBranch3MkVBalBranch25(zzz537, zzz538, zzz539, zzz540, zzz541, zzz542, zzz543, zzz544, zzz545, zzz546, zzz547, Zero, Succ(zzz5490), bc) → new_mkVBalBranch(zzz547, Branch(zzz542, zzz543, Neg(Succ(Succ(zzz544))), zzz545, zzz546), zzz540, bc)
new_mkVBalBranch3MkVBalBranch212(zzz818, zzz819, zzz820, zzz821, zzz822, zzz823, zzz824, zzz825, zzz826, zzz827, bf) → new_mkVBalBranch3MkVBalBranch14(zzz818, zzz819, zzz820, zzz821, zzz822, zzz823, zzz824, zzz825, zzz826, zzz827, new_primPlusNat2(new_primMulNat0(zzz820), Succ(zzz820)), bf)
new_mkVBalBranch3MkVBalBranch10(zzz929, zzz930, zzz931, zzz932, zzz933, zzz934, zzz935, zzz936, zzz937, zzz938, zzz939, Succ(zzz10020), ba) → new_mkVBalBranch3MkVBalBranch11(zzz929, zzz930, zzz931, zzz932, zzz933, zzz934, zzz935, zzz936, zzz937, zzz938, zzz939, Succ(zzz10020), Succ(zzz936), ba)
new_mkVBalBranch3MkVBalBranch2(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344, zzz520, zzz521, zzz52200, zzz523, zzz524, zzz31, Succ(zzz680), h) → new_mkVBalBranch3MkVBalBranch1(zzz340, zzz341, zzz34200, zzz343, zzz344, zzz520, zzz521, zzz52200, zzz523, zzz524, zzz31, new_primPlusNat2(new_primMulNat0(zzz34200), Succ(zzz34200)), h)
new_mkVBalBranch3MkVBalBranch14(zzz818, zzz819, zzz820, zzz821, zzz822, zzz823, zzz824, zzz825, zzz826, zzz827, Succ(zzz8960), bf) → new_mkVBalBranch3MkVBalBranch16(zzz818, zzz819, zzz820, zzz821, zzz822, zzz823, zzz824, Zero, zzz825, zzz826, zzz827, Succ(Zero), Succ(zzz8960), bf)
new_mkVBalBranch3MkVBalBranch24(zzz340, zzz341, Neg(Succ(Succ(Succ(zzz3420000)))), zzz343, zzz344, zzz520, zzz521, Succ(zzz522000), zzz523, zzz524, zzz31, Succ(Succ(zzz6900)), h) → new_mkVBalBranch3MkVBalBranch25(zzz340, zzz341, Succ(Succ(zzz3420000)), zzz343, zzz344, zzz520, zzz521, zzz522000, zzz523, zzz524, zzz31, Succ(zzz3420000), Succ(Succ(new_primPlusNat2(zzz6900, zzz522000))), h)
new_mkVBalBranch3MkVBalBranch2(zzz340, zzz341, Pos(Succ(zzz34200)), zzz343, zzz344, zzz520, zzz521, zzz52200, zzz523, zzz524, zzz31, Zero, h) → new_mkVBalBranch3MkVBalBranch20(zzz340, zzz341, zzz34200, zzz343, zzz344, zzz520, zzz521, zzz52200, zzz523, zzz524, zzz31, zzz52200, zzz34200, h)
new_mkVBalBranch3MkVBalBranch24(zzz340, zzz341, Neg(Zero), zzz343, zzz344, zzz520, zzz521, zzz52200, zzz523, zzz524, zzz31, Zero, h) → new_mkVBalBranch3MkVBalBranch210(zzz340, zzz341, zzz343, zzz344, zzz520, zzz521, zzz52200, zzz523, zzz524, zzz31, h)
new_mkVBalBranch3MkVBalBranch24(zzz340, zzz341, Neg(Succ(Succ(Zero))), zzz343, zzz344, zzz520, zzz521, Succ(zzz522000), zzz523, zzz524, zzz31, Succ(Succ(zzz6900)), h) → new_mkVBalBranch3MkVBalBranch25(zzz340, zzz341, Succ(Zero), zzz343, zzz344, zzz520, zzz521, zzz522000, zzz523, zzz524, zzz31, Zero, Succ(Succ(new_primPlusNat2(zzz6900, zzz522000))), h)
new_mkVBalBranch3MkVBalBranch20(zzz929, zzz930, zzz931, zzz932, zzz933, zzz934, zzz935, zzz936, zzz937, zzz938, zzz939, Succ(zzz9400), Zero, ba) → new_mkVBalBranch3MkVBalBranch10(zzz929, zzz930, zzz931, zzz932, zzz933, zzz934, zzz935, zzz936, zzz937, zzz938, zzz939, new_primMulNat1(zzz931), ba)
new_mkVBalBranch3MkVBalBranch2(zzz340, zzz341, Neg(Zero), zzz343, zzz344, zzz520, zzz521, zzz52200, zzz523, zzz524, zzz31, Succ(zzz680), h) → new_mkVBalBranch(zzz31, zzz524, Branch(zzz340, zzz341, Neg(Zero), zzz343, zzz344), h)
new_mkVBalBranch3MkVBalBranch16(zzz1702, zzz1703, zzz1704, zzz1705, zzz1706, zzz1707, zzz1708, zzz1709, zzz1710, zzz1711, zzz1712, Zero, Succ(zzz17140), bd) → new_mkVBalBranch(zzz1712, zzz1711, Branch(zzz1702, zzz1703, Neg(Succ(zzz1704)), zzz1705, zzz1706), bd)
new_mkVBalBranch(zzz31, Branch(zzz520, zzz521, Neg(Zero), zzz523, zzz524), Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), h) → new_mkVBalBranch3MkVBalBranch13(zzz340, zzz341, zzz34200, zzz343, zzz344, zzz520, zzz521, zzz523, zzz524, zzz31, new_primMulNat1(zzz34200), h)
new_mkVBalBranch3MkVBalBranch10(zzz929, zzz930, zzz931, zzz932, zzz933, zzz934, zzz935, zzz936, zzz937, zzz938, zzz939, Zero, ba) → new_mkVBalBranch3MkVBalBranch11(zzz929, zzz930, zzz931, zzz932, zzz933, zzz934, zzz935, zzz936, zzz937, zzz938, zzz939, Zero, Succ(zzz936), ba)
new_mkVBalBranch3MkVBalBranch22(zzz340, zzz341, Succ(zzz34200), zzz343, zzz344, zzz520, zzz521, zzz52200, zzz523, zzz524, zzz31, h) → new_mkVBalBranch3MkVBalBranch1(zzz340, zzz341, zzz34200, zzz343, zzz344, zzz520, zzz521, zzz52200, zzz523, zzz524, zzz31, new_primPlusNat2(new_primPlusNat3(Succ(new_primPlusNat3(new_primPlusNat1(zzz34200), zzz34200)), Succ(zzz34200)), Succ(zzz34200)), h)
new_mkVBalBranch3MkVBalBranch25(zzz537, zzz538, zzz539, zzz540, zzz541, zzz542, zzz543, zzz544, zzz545, zzz546, zzz547, Zero, Zero, bc) → new_mkVBalBranch3MkVBalBranch211(zzz537, zzz538, zzz539, zzz540, zzz541, zzz542, zzz543, zzz544, zzz545, zzz546, zzz547, bc)
new_mkVBalBranch3MkVBalBranch2(zzz340, zzz341, Pos(Zero), zzz343, zzz344, zzz520, zzz521, zzz52200, zzz523, zzz524, zzz31, Zero, h) → new_mkVBalBranch3MkVBalBranch21(zzz340, zzz341, zzz343, zzz344, zzz520, zzz521, zzz52200, zzz523, zzz524, zzz31, h)

The TRS R consists of the following rules:

new_primPlusNat1(Zero) → Zero
new_primMulNat0(zzz6200) → new_primPlusNat3(Succ(new_primPlusNat3(new_primPlusNat1(zzz6200), zzz6200)), Succ(zzz6200))
new_primPlusNat2(Succ(zzz900), Succ(zzz9100)) → Succ(Succ(new_primPlusNat2(zzz900, zzz9100)))
new_primPlusNat3(zzz90, Succ(zzz910)) → Succ(Succ(new_primPlusNat2(zzz90, zzz910)))
new_primPlusNat3(zzz90, Zero) → Succ(zzz90)
new_primMulNat1(zzz34200) → new_primPlusNat2(new_primMulNat0(zzz34200), Succ(zzz34200))
new_primPlusNat2(Zero, Zero) → Zero
new_primPlusNat1(Succ(zzz62000)) → Succ(Succ(new_primPlusNat1(zzz62000)))
new_primPlusNat2(Succ(zzz900), Zero) → Succ(zzz900)
new_primPlusNat2(Zero, Succ(zzz9100)) → Succ(zzz9100)

The set Q consists of the following terms:

new_primPlusNat2(Zero, Succ(x0))
new_primMulNat1(x0)
new_primMulNat0(x0)
new_primPlusNat3(x0, Succ(x1))
new_primPlusNat2(Succ(x0), Succ(x1))
new_primPlusNat3(x0, Zero)
new_primPlusNat1(Zero)
new_primPlusNat2(Zero, Zero)
new_primPlusNat1(Succ(x0))
new_primPlusNat2(Succ(x0), Zero)

We have to consider all minimal (P,Q,R)-chains.
By rewriting [15] the rule new_mkVBalBranch(zzz31, Branch(zzz520, zzz521, Neg(Zero), zzz523, zzz524), Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), h) → new_mkVBalBranch3MkVBalBranch13(zzz340, zzz341, zzz34200, zzz343, zzz344, zzz520, zzz521, zzz523, zzz524, zzz31, new_primMulNat1(zzz34200), h) at position [10] we obtained the following new rules:

new_mkVBalBranch(zzz31, Branch(zzz520, zzz521, Neg(Zero), zzz523, zzz524), Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), h) → new_mkVBalBranch3MkVBalBranch13(zzz340, zzz341, zzz34200, zzz343, zzz344, zzz520, zzz521, zzz523, zzz524, zzz31, new_primPlusNat2(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
                                    ↳ DependencyGraphProof
                                      ↳ QDP
                                        ↳ Rewriting
                                          ↳ QDP
                                            ↳ Rewriting
                                              ↳ QDP
                                                ↳ Rewriting
                                                  ↳ QDP
                                                    ↳ Rewriting
                                                      ↳ QDP
                                                        ↳ Rewriting
                                                          ↳ QDP
                                                            ↳ Rewriting
                                                              ↳ QDP
                                                                ↳ Rewriting
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP

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

new_mkVBalBranch3MkVBalBranch11(zzz2033, zzz2034, zzz2035, zzz2036, zzz2037, zzz2038, zzz2039, zzz2040, zzz2041, zzz2042, zzz2043, Zero, Succ(zzz20450), bb) → new_mkVBalBranch(zzz2043, zzz2042, Branch(zzz2033, zzz2034, Pos(Succ(zzz2035)), zzz2036, zzz2037), bb)
new_mkVBalBranch3MkVBalBranch26(zzz1133, zzz1134, zzz1135, zzz1136, zzz1137, zzz1138, zzz1139, zzz1140, zzz1141, zzz1142, Succ(zzz11430), Succ(zzz11440), be) → new_mkVBalBranch3MkVBalBranch26(zzz1133, zzz1134, zzz1135, zzz1136, zzz1137, zzz1138, zzz1139, zzz1140, zzz1141, zzz1142, zzz11430, zzz11440, be)
new_mkVBalBranch3MkVBalBranch24(zzz340, zzz341, Neg(Succ(Succ(Succ(zzz3420000)))), zzz343, zzz344, zzz520, zzz521, Zero, zzz523, zzz524, zzz31, Succ(Zero), h) → new_mkVBalBranch3MkVBalBranch26(zzz340, zzz341, Succ(Succ(zzz3420000)), zzz343, zzz344, zzz520, zzz521, zzz523, zzz524, zzz31, Succ(zzz3420000), Zero, h)
new_mkVBalBranch3MkVBalBranch24(zzz340, zzz341, Neg(Succ(Zero)), zzz343, zzz344, zzz520, zzz521, Zero, zzz523, zzz524, zzz31, Zero, h) → new_mkVBalBranch3MkVBalBranch29(zzz340, zzz341, Zero, zzz343, zzz344, zzz520, zzz521, zzz523, zzz524, zzz31, h)
new_mkVBalBranch3MkVBalBranch20(zzz929, zzz930, zzz931, zzz932, zzz933, zzz934, zzz935, zzz936, zzz937, zzz938, zzz939, Zero, Succ(zzz9410), ba) → new_mkVBalBranch(zzz939, Branch(zzz934, zzz935, Pos(Succ(zzz936)), zzz937, zzz938), zzz932, ba)
new_mkVBalBranch3MkVBalBranch17(zzz340, zzz341, zzz34200, zzz343, zzz344, zzz520, zzz521, zzz52200, zzz523, zzz524, zzz31, h) → new_mkVBalBranch(zzz31, zzz524, Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), h)
new_mkVBalBranch3MkVBalBranch26(zzz1133, zzz1134, zzz1135, zzz1136, zzz1137, zzz1138, zzz1139, zzz1140, zzz1141, zzz1142, Zero, Zero, be) → new_mkVBalBranch3MkVBalBranch29(zzz1133, zzz1134, zzz1135, zzz1136, zzz1137, zzz1138, zzz1139, zzz1140, zzz1141, zzz1142, be)
new_mkVBalBranch3MkVBalBranch20(zzz929, zzz930, zzz931, zzz932, zzz933, zzz934, zzz935, zzz936, zzz937, zzz938, zzz939, Zero, Zero, ba) → new_mkVBalBranch3MkVBalBranch23(zzz929, zzz930, zzz931, zzz932, zzz933, zzz934, zzz935, zzz936, zzz937, zzz938, zzz939, ba)
new_mkVBalBranch3MkVBalBranch24(zzz340, zzz341, Neg(Succ(Succ(Zero))), zzz343, zzz344, zzz520, zzz521, Succ(zzz522000), zzz523, zzz524, zzz31, Succ(Zero), h) → new_mkVBalBranch3MkVBalBranch25(zzz340, zzz341, Succ(Zero), zzz343, zzz344, zzz520, zzz521, zzz522000, zzz523, zzz524, zzz31, Zero, Succ(zzz522000), h)
new_mkVBalBranch3MkVBalBranch20(zzz929, zzz930, zzz931, zzz932, zzz933, zzz934, zzz935, zzz936, zzz937, zzz938, zzz939, Succ(zzz9400), Succ(zzz9410), ba) → new_mkVBalBranch3MkVBalBranch20(zzz929, zzz930, zzz931, zzz932, zzz933, zzz934, zzz935, zzz936, zzz937, zzz938, zzz939, zzz9400, zzz9410, ba)
new_mkVBalBranch3MkVBalBranch24(zzz340, zzz341, Neg(Succ(Succ(Succ(zzz3420000)))), zzz343, zzz344, zzz520, zzz521, Succ(zzz522000), zzz523, zzz524, zzz31, Succ(Zero), h) → new_mkVBalBranch3MkVBalBranch25(zzz340, zzz341, Succ(Succ(zzz3420000)), zzz343, zzz344, zzz520, zzz521, zzz522000, zzz523, zzz524, zzz31, Succ(zzz3420000), Succ(zzz522000), h)
new_mkVBalBranch3MkVBalBranch26(zzz1133, zzz1134, zzz1135, zzz1136, zzz1137, zzz1138, zzz1139, zzz1140, zzz1141, zzz1142, Succ(zzz11430), Zero, be) → new_mkVBalBranch3MkVBalBranch212(zzz1133, zzz1134, zzz1135, zzz1136, zzz1137, zzz1138, zzz1139, zzz1140, zzz1141, zzz1142, be)
new_mkVBalBranch3MkVBalBranch24(zzz340, zzz341, Neg(Succ(Succ(zzz342000))), zzz343, zzz344, zzz520, zzz521, Succ(zzz522000), zzz523, zzz524, zzz31, Zero, h) → new_mkVBalBranch3MkVBalBranch25(zzz340, zzz341, Succ(zzz342000), zzz343, zzz344, zzz520, zzz521, zzz522000, zzz523, zzz524, zzz31, zzz342000, zzz522000, h)
new_mkVBalBranch(zzz31, Branch(zzz520, zzz521, Pos(Succ(zzz52200)), zzz523, zzz524), Branch(zzz340, zzz341, zzz342, zzz343, zzz344), h) → new_mkVBalBranch3MkVBalBranch2(zzz340, zzz341, zzz342, zzz343, zzz344, zzz520, zzz521, zzz52200, zzz523, zzz524, zzz31, new_primPlusNat3(Succ(new_primPlusNat3(new_primPlusNat1(zzz52200), zzz52200)), Succ(zzz52200)), h)
new_mkVBalBranch3MkVBalBranch11(zzz2033, zzz2034, zzz2035, zzz2036, zzz2037, zzz2038, zzz2039, zzz2040, zzz2041, zzz2042, zzz2043, Succ(zzz20440), Succ(zzz20450), bb) → new_mkVBalBranch3MkVBalBranch11(zzz2033, zzz2034, zzz2035, zzz2036, zzz2037, zzz2038, zzz2039, zzz2040, zzz2041, zzz2042, zzz2043, zzz20440, zzz20450, bb)
new_mkVBalBranch3MkVBalBranch2(zzz340, zzz341, Neg(zzz3420), zzz343, zzz344, zzz520, zzz521, zzz52200, zzz523, zzz524, zzz31, Zero, h) → new_mkVBalBranch3MkVBalBranch22(zzz340, zzz341, zzz3420, zzz343, zzz344, zzz520, zzz521, zzz52200, zzz523, zzz524, zzz31, h)
new_mkVBalBranch3MkVBalBranch25(zzz537, zzz538, zzz539, zzz540, zzz541, zzz542, zzz543, zzz544, zzz545, zzz546, zzz547, Succ(zzz5480), Succ(zzz5490), bc) → new_mkVBalBranch3MkVBalBranch25(zzz537, zzz538, zzz539, zzz540, zzz541, zzz542, zzz543, zzz544, zzz545, zzz546, zzz547, zzz5480, zzz5490, bc)
new_mkVBalBranch(zzz31, Branch(zzz520, zzz521, Neg(Succ(zzz52200)), zzz523, zzz524), Branch(zzz340, zzz341, zzz342, zzz343, zzz344), h) → new_mkVBalBranch3MkVBalBranch24(zzz340, zzz341, zzz342, zzz343, zzz344, zzz520, zzz521, zzz52200, zzz523, zzz524, zzz31, new_primPlusNat3(Succ(new_primPlusNat3(new_primPlusNat1(zzz52200), zzz52200)), Succ(zzz52200)), h)
new_mkVBalBranch3MkVBalBranch24(zzz340, zzz341, Neg(Succ(Zero)), zzz343, zzz344, zzz520, zzz521, Succ(zzz522000), zzz523, zzz524, zzz31, Zero, h) → new_mkVBalBranch3MkVBalBranch28(zzz340, zzz341, zzz343, zzz344, zzz520, zzz521, Succ(zzz522000), zzz523, zzz524, zzz31, h)
new_mkVBalBranch3MkVBalBranch210(zzz340, zzz341, zzz343, zzz344, zzz520, zzz521, zzz52200, zzz523, zzz524, zzz31, h) → new_mkVBalBranch(zzz31, Branch(zzz520, zzz521, Neg(Succ(zzz52200)), zzz523, zzz524), zzz343, h)
new_mkVBalBranch3MkVBalBranch24(zzz340, zzz341, Neg(Succ(Succ(zzz342000))), zzz343, zzz344, zzz520, zzz521, Zero, zzz523, zzz524, zzz31, Zero, h) → new_mkVBalBranch3MkVBalBranch14(zzz340, zzz341, Succ(zzz342000), zzz343, zzz344, zzz520, zzz521, zzz523, zzz524, zzz31, new_primMulNat1(Succ(zzz342000)), h)
new_mkVBalBranch3MkVBalBranch26(zzz1133, zzz1134, zzz1135, zzz1136, zzz1137, zzz1138, zzz1139, zzz1140, zzz1141, zzz1142, Zero, Succ(zzz11440), be) → new_mkVBalBranch(zzz1142, Branch(zzz1138, zzz1139, Neg(Succ(Zero)), zzz1140, zzz1141), zzz1136, be)
new_mkVBalBranch3MkVBalBranch24(zzz340, zzz341, Neg(Succ(Succ(Zero))), zzz343, zzz344, zzz520, zzz521, Zero, zzz523, zzz524, zzz31, Succ(Zero), h) → new_mkVBalBranch3MkVBalBranch26(zzz340, zzz341, Succ(Zero), zzz343, zzz344, zzz520, zzz521, zzz523, zzz524, zzz31, Zero, Zero, h)
new_mkVBalBranch(zzz31, Branch(zzz520, zzz521, Pos(Zero), zzz523, zzz524), Branch(zzz340, zzz341, Pos(Succ(zzz34200)), zzz343, zzz344), h) → new_mkVBalBranch(zzz31, Branch(zzz520, zzz521, Pos(Zero), zzz523, zzz524), zzz343, h)
new_mkVBalBranch3MkVBalBranch29(zzz818, zzz819, zzz820, zzz821, zzz822, zzz823, zzz824, zzz825, zzz826, zzz827, bf) → new_mkVBalBranch3MkVBalBranch14(zzz818, zzz819, zzz820, zzz821, zzz822, zzz823, zzz824, zzz825, zzz826, zzz827, new_primMulNat1(zzz820), bf)
new_mkVBalBranch3MkVBalBranch2(zzz340, zzz341, Pos(Zero), zzz343, zzz344, zzz520, zzz521, zzz52200, zzz523, zzz524, zzz31, Succ(zzz680), h) → new_mkVBalBranch(zzz31, zzz524, Branch(zzz340, zzz341, Pos(Zero), zzz343, zzz344), h)
new_mkVBalBranch3MkVBalBranch21(zzz340, zzz341, zzz343, zzz344, zzz520, zzz521, zzz52200, zzz523, zzz524, zzz31, h) → new_mkVBalBranch(zzz31, zzz524, Branch(zzz340, zzz341, Pos(Zero), zzz343, zzz344), h)
new_mkVBalBranch3MkVBalBranch24(zzz340, zzz341, Pos(zzz3420), zzz343, zzz344, zzz520, zzz521, zzz52200, zzz523, zzz524, zzz31, Zero, h) → new_mkVBalBranch3MkVBalBranch27(zzz340, zzz341, zzz3420, zzz343, zzz344, zzz520, zzz521, zzz52200, zzz523, zzz524, zzz31, h)
new_mkVBalBranch3MkVBalBranch23(zzz929, zzz930, zzz931, zzz932, zzz933, zzz934, zzz935, zzz936, zzz937, zzz938, zzz939, ba) → new_mkVBalBranch3MkVBalBranch10(zzz929, zzz930, zzz931, zzz932, zzz933, zzz934, zzz935, zzz936, zzz937, zzz938, zzz939, new_primMulNat1(zzz931), ba)
new_mkVBalBranch3MkVBalBranch211(zzz537, zzz538, zzz539, zzz540, zzz541, zzz542, zzz543, zzz544, zzz545, zzz546, zzz547, bc) → new_mkVBalBranch3MkVBalBranch15(zzz537, zzz538, zzz539, zzz540, zzz541, zzz542, zzz543, zzz544, zzz545, zzz546, zzz547, new_primMulNat1(zzz539), bc)
new_mkVBalBranch3MkVBalBranch24(zzz340, zzz341, Neg(Succ(Succ(Succ(zzz3420000)))), zzz343, zzz344, zzz520, zzz521, Zero, zzz523, zzz524, zzz31, Succ(Succ(zzz6900)), h) → new_mkVBalBranch3MkVBalBranch26(zzz340, zzz341, Succ(Succ(zzz3420000)), zzz343, zzz344, zzz520, zzz521, zzz523, zzz524, zzz31, Succ(zzz3420000), Succ(zzz6900), h)
new_mkVBalBranch3MkVBalBranch15(zzz537, zzz538, zzz539, zzz540, zzz541, zzz542, zzz543, zzz544, zzz545, zzz546, zzz547, Succ(zzz6990), bc) → new_mkVBalBranch3MkVBalBranch16(zzz537, zzz538, zzz539, zzz540, zzz541, zzz542, zzz543, Succ(zzz544), zzz545, zzz546, zzz547, Succ(Succ(zzz544)), Succ(zzz6990), bc)
new_mkVBalBranch(zzz31, Branch(zzz520, zzz521, Neg(Zero), zzz523, zzz524), Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), h) → new_mkVBalBranch3MkVBalBranch13(zzz340, zzz341, zzz34200, zzz343, zzz344, zzz520, zzz521, zzz523, zzz524, zzz31, new_primPlusNat2(new_primMulNat0(zzz34200), Succ(zzz34200)), h)
new_mkVBalBranch3MkVBalBranch27(zzz340, zzz341, zzz3420, zzz343, zzz344, zzz520, zzz521, zzz52200, zzz523, zzz524, zzz31, h) → new_mkVBalBranch(zzz31, Branch(zzz520, zzz521, Neg(Succ(zzz52200)), zzz523, zzz524), zzz343, h)
new_mkVBalBranch3MkVBalBranch24(zzz340, zzz341, Pos(zzz3420), zzz343, zzz344, zzz520, zzz521, zzz52200, zzz523, zzz524, zzz31, Succ(zzz690), h) → new_mkVBalBranch(zzz31, Branch(zzz520, zzz521, Neg(Succ(zzz52200)), zzz523, zzz524), zzz343, h)
new_mkVBalBranch3MkVBalBranch12(zzz340, zzz341, zzz34200, zzz343, zzz344, zzz520, zzz521, zzz523, zzz524, zzz31, Succ(zzz1250), h) → new_mkVBalBranch(zzz31, zzz524, Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), h)
new_mkVBalBranch3MkVBalBranch25(zzz537, zzz538, zzz539, zzz540, zzz541, zzz542, zzz543, zzz544, zzz545, zzz546, zzz547, Succ(zzz5480), Zero, bc) → new_mkVBalBranch3MkVBalBranch15(zzz537, zzz538, zzz539, zzz540, zzz541, zzz542, zzz543, zzz544, zzz545, zzz546, zzz547, new_primMulNat1(zzz539), bc)
new_mkVBalBranch3MkVBalBranch28(zzz340, zzz341, zzz343, zzz344, zzz520, zzz521, zzz52200, zzz523, zzz524, zzz31, h) → new_mkVBalBranch(zzz31, Branch(zzz520, zzz521, Neg(Succ(zzz52200)), zzz523, zzz524), zzz343, h)
new_mkVBalBranch3MkVBalBranch24(zzz340, zzz341, Neg(Succ(Succ(Zero))), zzz343, zzz344, zzz520, zzz521, Zero, zzz523, zzz524, zzz31, Succ(Succ(zzz6900)), h) → new_mkVBalBranch3MkVBalBranch26(zzz340, zzz341, Succ(Zero), zzz343, zzz344, zzz520, zzz521, zzz523, zzz524, zzz31, Zero, Succ(zzz6900), h)
new_mkVBalBranch3MkVBalBranch1(zzz340, zzz341, zzz34200, zzz343, zzz344, zzz520, zzz521, zzz52200, zzz523, zzz524, zzz31, Succ(zzz1430), h) → new_mkVBalBranch(zzz31, zzz524, Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), h)
new_mkVBalBranch3MkVBalBranch22(zzz340, zzz341, Zero, zzz343, zzz344, zzz520, zzz521, zzz52200, zzz523, zzz524, zzz31, h) → new_mkVBalBranch(zzz31, zzz524, Branch(zzz340, zzz341, Neg(Zero), zzz343, zzz344), h)
new_mkVBalBranch(zzz31, Branch(zzz520, zzz521, Pos(Zero), zzz523, zzz524), Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), h) → new_mkVBalBranch3MkVBalBranch12(zzz340, zzz341, zzz34200, zzz343, zzz344, zzz520, zzz521, zzz523, zzz524, zzz31, new_primPlusNat2(new_primMulNat0(zzz34200), Succ(zzz34200)), h)
new_mkVBalBranch3MkVBalBranch24(zzz340, zzz341, Neg(Succ(Zero)), zzz343, zzz344, zzz520, zzz521, zzz52200, zzz523, zzz524, zzz31, Succ(zzz690), h) → new_mkVBalBranch(zzz31, Branch(zzz520, zzz521, Neg(Succ(zzz52200)), zzz523, zzz524), zzz343, h)
new_mkVBalBranch3MkVBalBranch13(zzz340, zzz341, zzz34200, zzz343, zzz344, zzz520, zzz521, zzz523, zzz524, zzz31, Succ(zzz1290), h) → new_mkVBalBranch(zzz31, zzz524, Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), h)
new_mkVBalBranch3MkVBalBranch2(zzz340, zzz341, Pos(Succ(zzz34200)), zzz343, zzz344, zzz520, zzz521, zzz52200, zzz523, zzz524, zzz31, Succ(zzz680), h) → new_mkVBalBranch3MkVBalBranch20(zzz340, zzz341, zzz34200, zzz343, zzz344, zzz520, zzz521, zzz52200, zzz523, zzz524, zzz31, Succ(new_primPlusNat2(zzz680, zzz52200)), zzz34200, h)
new_mkVBalBranch3MkVBalBranch24(zzz340, zzz341, Neg(Zero), zzz343, zzz344, zzz520, zzz521, zzz52200, zzz523, zzz524, zzz31, Succ(zzz690), h) → new_mkVBalBranch(zzz31, Branch(zzz520, zzz521, Neg(Succ(zzz52200)), zzz523, zzz524), zzz343, h)
new_mkVBalBranch(zzz31, Branch(zzz520, zzz521, Neg(Zero), zzz523, zzz524), Branch(zzz340, zzz341, Pos(Succ(zzz34200)), zzz343, zzz344), h) → new_mkVBalBranch(zzz31, Branch(zzz520, zzz521, Neg(Zero), zzz523, zzz524), zzz343, h)
new_mkVBalBranch3MkVBalBranch1(zzz340, zzz341, zzz34200, zzz343, zzz344, zzz520, zzz521, zzz52200, zzz523, zzz524, zzz31, Zero, h) → new_mkVBalBranch3MkVBalBranch17(zzz340, zzz341, zzz34200, zzz343, zzz344, zzz520, zzz521, zzz52200, zzz523, zzz524, zzz31, h)
new_mkVBalBranch3MkVBalBranch16(zzz1702, zzz1703, zzz1704, zzz1705, zzz1706, zzz1707, zzz1708, zzz1709, zzz1710, zzz1711, zzz1712, Succ(zzz17130), Succ(zzz17140), bd) → new_mkVBalBranch3MkVBalBranch16(zzz1702, zzz1703, zzz1704, zzz1705, zzz1706, zzz1707, zzz1708, zzz1709, zzz1710, zzz1711, zzz1712, zzz17130, zzz17140, bd)
new_mkVBalBranch3MkVBalBranch25(zzz537, zzz538, zzz539, zzz540, zzz541, zzz542, zzz543, zzz544, zzz545, zzz546, zzz547, Zero, Succ(zzz5490), bc) → new_mkVBalBranch(zzz547, Branch(zzz542, zzz543, Neg(Succ(Succ(zzz544))), zzz545, zzz546), zzz540, bc)
new_mkVBalBranch3MkVBalBranch10(zzz929, zzz930, zzz931, zzz932, zzz933, zzz934, zzz935, zzz936, zzz937, zzz938, zzz939, Succ(zzz10020), ba) → new_mkVBalBranch3MkVBalBranch11(zzz929, zzz930, zzz931, zzz932, zzz933, zzz934, zzz935, zzz936, zzz937, zzz938, zzz939, Succ(zzz10020), Succ(zzz936), ba)
new_mkVBalBranch3MkVBalBranch212(zzz818, zzz819, zzz820, zzz821, zzz822, zzz823, zzz824, zzz825, zzz826, zzz827, bf) → new_mkVBalBranch3MkVBalBranch14(zzz818, zzz819, zzz820, zzz821, zzz822, zzz823, zzz824, zzz825, zzz826, zzz827, new_primPlusNat2(new_primMulNat0(zzz820), Succ(zzz820)), bf)
new_mkVBalBranch3MkVBalBranch14(zzz818, zzz819, zzz820, zzz821, zzz822, zzz823, zzz824, zzz825, zzz826, zzz827, Succ(zzz8960), bf) → new_mkVBalBranch3MkVBalBranch16(zzz818, zzz819, zzz820, zzz821, zzz822, zzz823, zzz824, Zero, zzz825, zzz826, zzz827, Succ(Zero), Succ(zzz8960), bf)
new_mkVBalBranch3MkVBalBranch2(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344, zzz520, zzz521, zzz52200, zzz523, zzz524, zzz31, Succ(zzz680), h) → new_mkVBalBranch3MkVBalBranch1(zzz340, zzz341, zzz34200, zzz343, zzz344, zzz520, zzz521, zzz52200, zzz523, zzz524, zzz31, new_primPlusNat2(new_primMulNat0(zzz34200), Succ(zzz34200)), h)
new_mkVBalBranch3MkVBalBranch24(zzz340, zzz341, Neg(Succ(Succ(Succ(zzz3420000)))), zzz343, zzz344, zzz520, zzz521, Succ(zzz522000), zzz523, zzz524, zzz31, Succ(Succ(zzz6900)), h) → new_mkVBalBranch3MkVBalBranch25(zzz340, zzz341, Succ(Succ(zzz3420000)), zzz343, zzz344, zzz520, zzz521, zzz522000, zzz523, zzz524, zzz31, Succ(zzz3420000), Succ(Succ(new_primPlusNat2(zzz6900, zzz522000))), h)
new_mkVBalBranch3MkVBalBranch2(zzz340, zzz341, Pos(Succ(zzz34200)), zzz343, zzz344, zzz520, zzz521, zzz52200, zzz523, zzz524, zzz31, Zero, h) → new_mkVBalBranch3MkVBalBranch20(zzz340, zzz341, zzz34200, zzz343, zzz344, zzz520, zzz521, zzz52200, zzz523, zzz524, zzz31, zzz52200, zzz34200, h)
new_mkVBalBranch3MkVBalBranch24(zzz340, zzz341, Neg(Zero), zzz343, zzz344, zzz520, zzz521, zzz52200, zzz523, zzz524, zzz31, Zero, h) → new_mkVBalBranch3MkVBalBranch210(zzz340, zzz341, zzz343, zzz344, zzz520, zzz521, zzz52200, zzz523, zzz524, zzz31, h)
new_mkVBalBranch3MkVBalBranch24(zzz340, zzz341, Neg(Succ(Succ(Zero))), zzz343, zzz344, zzz520, zzz521, Succ(zzz522000), zzz523, zzz524, zzz31, Succ(Succ(zzz6900)), h) → new_mkVBalBranch3MkVBalBranch25(zzz340, zzz341, Succ(Zero), zzz343, zzz344, zzz520, zzz521, zzz522000, zzz523, zzz524, zzz31, Zero, Succ(Succ(new_primPlusNat2(zzz6900, zzz522000))), h)
new_mkVBalBranch3MkVBalBranch20(zzz929, zzz930, zzz931, zzz932, zzz933, zzz934, zzz935, zzz936, zzz937, zzz938, zzz939, Succ(zzz9400), Zero, ba) → new_mkVBalBranch3MkVBalBranch10(zzz929, zzz930, zzz931, zzz932, zzz933, zzz934, zzz935, zzz936, zzz937, zzz938, zzz939, new_primMulNat1(zzz931), ba)
new_mkVBalBranch3MkVBalBranch2(zzz340, zzz341, Neg(Zero), zzz343, zzz344, zzz520, zzz521, zzz52200, zzz523, zzz524, zzz31, Succ(zzz680), h) → new_mkVBalBranch(zzz31, zzz524, Branch(zzz340, zzz341, Neg(Zero), zzz343, zzz344), h)
new_mkVBalBranch3MkVBalBranch16(zzz1702, zzz1703, zzz1704, zzz1705, zzz1706, zzz1707, zzz1708, zzz1709, zzz1710, zzz1711, zzz1712, Zero, Succ(zzz17140), bd) → new_mkVBalBranch(zzz1712, zzz1711, Branch(zzz1702, zzz1703, Neg(Succ(zzz1704)), zzz1705, zzz1706), bd)
new_mkVBalBranch3MkVBalBranch10(zzz929, zzz930, zzz931, zzz932, zzz933, zzz934, zzz935, zzz936, zzz937, zzz938, zzz939, Zero, ba) → new_mkVBalBranch3MkVBalBranch11(zzz929, zzz930, zzz931, zzz932, zzz933, zzz934, zzz935, zzz936, zzz937, zzz938, zzz939, Zero, Succ(zzz936), ba)
new_mkVBalBranch3MkVBalBranch2(zzz340, zzz341, Pos(Zero), zzz343, zzz344, zzz520, zzz521, zzz52200, zzz523, zzz524, zzz31, Zero, h) → new_mkVBalBranch3MkVBalBranch21(zzz340, zzz341, zzz343, zzz344, zzz520, zzz521, zzz52200, zzz523, zzz524, zzz31, h)
new_mkVBalBranch3MkVBalBranch25(zzz537, zzz538, zzz539, zzz540, zzz541, zzz542, zzz543, zzz544, zzz545, zzz546, zzz547, Zero, Zero, bc) → new_mkVBalBranch3MkVBalBranch211(zzz537, zzz538, zzz539, zzz540, zzz541, zzz542, zzz543, zzz544, zzz545, zzz546, zzz547, bc)
new_mkVBalBranch3MkVBalBranch22(zzz340, zzz341, Succ(zzz34200), zzz343, zzz344, zzz520, zzz521, zzz52200, zzz523, zzz524, zzz31, h) → new_mkVBalBranch3MkVBalBranch1(zzz340, zzz341, zzz34200, zzz343, zzz344, zzz520, zzz521, zzz52200, zzz523, zzz524, zzz31, new_primPlusNat2(new_primPlusNat3(Succ(new_primPlusNat3(new_primPlusNat1(zzz34200), zzz34200)), Succ(zzz34200)), Succ(zzz34200)), h)

The TRS R consists of the following rules:

new_primPlusNat1(Zero) → Zero
new_primMulNat0(zzz6200) → new_primPlusNat3(Succ(new_primPlusNat3(new_primPlusNat1(zzz6200), zzz6200)), Succ(zzz6200))
new_primPlusNat2(Succ(zzz900), Succ(zzz9100)) → Succ(Succ(new_primPlusNat2(zzz900, zzz9100)))
new_primPlusNat3(zzz90, Succ(zzz910)) → Succ(Succ(new_primPlusNat2(zzz90, zzz910)))
new_primPlusNat3(zzz90, Zero) → Succ(zzz90)
new_primMulNat1(zzz34200) → new_primPlusNat2(new_primMulNat0(zzz34200), Succ(zzz34200))
new_primPlusNat2(Zero, Zero) → Zero
new_primPlusNat1(Succ(zzz62000)) → Succ(Succ(new_primPlusNat1(zzz62000)))
new_primPlusNat2(Succ(zzz900), Zero) → Succ(zzz900)
new_primPlusNat2(Zero, Succ(zzz9100)) → Succ(zzz9100)

The set Q consists of the following terms:

new_primPlusNat2(Zero, Succ(x0))
new_primMulNat1(x0)
new_primMulNat0(x0)
new_primPlusNat3(x0, Succ(x1))
new_primPlusNat2(Succ(x0), Succ(x1))
new_primPlusNat3(x0, Zero)
new_primPlusNat1(Zero)
new_primPlusNat2(Zero, Zero)
new_primPlusNat1(Succ(x0))
new_primPlusNat2(Succ(x0), Zero)

We have to consider all minimal (P,Q,R)-chains.
By rewriting [15] the rule new_mkVBalBranch3MkVBalBranch23(zzz929, zzz930, zzz931, zzz932, zzz933, zzz934, zzz935, zzz936, zzz937, zzz938, zzz939, ba) → new_mkVBalBranch3MkVBalBranch10(zzz929, zzz930, zzz931, zzz932, zzz933, zzz934, zzz935, zzz936, zzz937, zzz938, zzz939, new_primMulNat1(zzz931), ba) at position [11] we obtained the following new rules:

new_mkVBalBranch3MkVBalBranch23(zzz929, zzz930, zzz931, zzz932, zzz933, zzz934, zzz935, zzz936, zzz937, zzz938, zzz939, ba) → new_mkVBalBranch3MkVBalBranch10(zzz929, zzz930, zzz931, zzz932, zzz933, zzz934, zzz935, zzz936, zzz937, zzz938, zzz939, new_primPlusNat2(new_primMulNat0(zzz931), Succ(zzz931)), 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
                                    ↳ DependencyGraphProof
                                      ↳ QDP
                                        ↳ Rewriting
                                          ↳ QDP
                                            ↳ Rewriting
                                              ↳ QDP
                                                ↳ Rewriting
                                                  ↳ QDP
                                                    ↳ Rewriting
                                                      ↳ QDP
                                                        ↳ Rewriting
                                                          ↳ QDP
                                                            ↳ Rewriting
                                                              ↳ QDP
                                                                ↳ Rewriting
                                                                  ↳ QDP
                                                                    ↳ Rewriting
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP

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

new_mkVBalBranch3MkVBalBranch11(zzz2033, zzz2034, zzz2035, zzz2036, zzz2037, zzz2038, zzz2039, zzz2040, zzz2041, zzz2042, zzz2043, Zero, Succ(zzz20450), bb) → new_mkVBalBranch(zzz2043, zzz2042, Branch(zzz2033, zzz2034, Pos(Succ(zzz2035)), zzz2036, zzz2037), bb)
new_mkVBalBranch3MkVBalBranch26(zzz1133, zzz1134, zzz1135, zzz1136, zzz1137, zzz1138, zzz1139, zzz1140, zzz1141, zzz1142, Succ(zzz11430), Succ(zzz11440), be) → new_mkVBalBranch3MkVBalBranch26(zzz1133, zzz1134, zzz1135, zzz1136, zzz1137, zzz1138, zzz1139, zzz1140, zzz1141, zzz1142, zzz11430, zzz11440, be)
new_mkVBalBranch3MkVBalBranch24(zzz340, zzz341, Neg(Succ(Succ(Succ(zzz3420000)))), zzz343, zzz344, zzz520, zzz521, Zero, zzz523, zzz524, zzz31, Succ(Zero), h) → new_mkVBalBranch3MkVBalBranch26(zzz340, zzz341, Succ(Succ(zzz3420000)), zzz343, zzz344, zzz520, zzz521, zzz523, zzz524, zzz31, Succ(zzz3420000), Zero, h)
new_mkVBalBranch3MkVBalBranch24(zzz340, zzz341, Neg(Succ(Zero)), zzz343, zzz344, zzz520, zzz521, Zero, zzz523, zzz524, zzz31, Zero, h) → new_mkVBalBranch3MkVBalBranch29(zzz340, zzz341, Zero, zzz343, zzz344, zzz520, zzz521, zzz523, zzz524, zzz31, h)
new_mkVBalBranch3MkVBalBranch20(zzz929, zzz930, zzz931, zzz932, zzz933, zzz934, zzz935, zzz936, zzz937, zzz938, zzz939, Zero, Succ(zzz9410), ba) → new_mkVBalBranch(zzz939, Branch(zzz934, zzz935, Pos(Succ(zzz936)), zzz937, zzz938), zzz932, ba)
new_mkVBalBranch3MkVBalBranch17(zzz340, zzz341, zzz34200, zzz343, zzz344, zzz520, zzz521, zzz52200, zzz523, zzz524, zzz31, h) → new_mkVBalBranch(zzz31, zzz524, Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), h)
new_mkVBalBranch3MkVBalBranch26(zzz1133, zzz1134, zzz1135, zzz1136, zzz1137, zzz1138, zzz1139, zzz1140, zzz1141, zzz1142, Zero, Zero, be) → new_mkVBalBranch3MkVBalBranch29(zzz1133, zzz1134, zzz1135, zzz1136, zzz1137, zzz1138, zzz1139, zzz1140, zzz1141, zzz1142, be)
new_mkVBalBranch3MkVBalBranch20(zzz929, zzz930, zzz931, zzz932, zzz933, zzz934, zzz935, zzz936, zzz937, zzz938, zzz939, Zero, Zero, ba) → new_mkVBalBranch3MkVBalBranch23(zzz929, zzz930, zzz931, zzz932, zzz933, zzz934, zzz935, zzz936, zzz937, zzz938, zzz939, ba)
new_mkVBalBranch3MkVBalBranch24(zzz340, zzz341, Neg(Succ(Succ(Zero))), zzz343, zzz344, zzz520, zzz521, Succ(zzz522000), zzz523, zzz524, zzz31, Succ(Zero), h) → new_mkVBalBranch3MkVBalBranch25(zzz340, zzz341, Succ(Zero), zzz343, zzz344, zzz520, zzz521, zzz522000, zzz523, zzz524, zzz31, Zero, Succ(zzz522000), h)
new_mkVBalBranch3MkVBalBranch24(zzz340, zzz341, Neg(Succ(Succ(Succ(zzz3420000)))), zzz343, zzz344, zzz520, zzz521, Succ(zzz522000), zzz523, zzz524, zzz31, Succ(Zero), h) → new_mkVBalBranch3MkVBalBranch25(zzz340, zzz341, Succ(Succ(zzz3420000)), zzz343, zzz344, zzz520, zzz521, zzz522000, zzz523, zzz524, zzz31, Succ(zzz3420000), Succ(zzz522000), h)
new_mkVBalBranch3MkVBalBranch20(zzz929, zzz930, zzz931, zzz932, zzz933, zzz934, zzz935, zzz936, zzz937, zzz938, zzz939, Succ(zzz9400), Succ(zzz9410), ba) → new_mkVBalBranch3MkVBalBranch20(zzz929, zzz930, zzz931, zzz932, zzz933, zzz934, zzz935, zzz936, zzz937, zzz938, zzz939, zzz9400, zzz9410, ba)
new_mkVBalBranch3MkVBalBranch24(zzz340, zzz341, Neg(Succ(Succ(zzz342000))), zzz343, zzz344, zzz520, zzz521, Succ(zzz522000), zzz523, zzz524, zzz31, Zero, h) → new_mkVBalBranch3MkVBalBranch25(zzz340, zzz341, Succ(zzz342000), zzz343, zzz344, zzz520, zzz521, zzz522000, zzz523, zzz524, zzz31, zzz342000, zzz522000, h)
new_mkVBalBranch3MkVBalBranch26(zzz1133, zzz1134, zzz1135, zzz1136, zzz1137, zzz1138, zzz1139, zzz1140, zzz1141, zzz1142, Succ(zzz11430), Zero, be) → new_mkVBalBranch3MkVBalBranch212(zzz1133, zzz1134, zzz1135, zzz1136, zzz1137, zzz1138, zzz1139, zzz1140, zzz1141, zzz1142, be)
new_mkVBalBranch(zzz31, Branch(zzz520, zzz521, Pos(Succ(zzz52200)), zzz523, zzz524), Branch(zzz340, zzz341, zzz342, zzz343, zzz344), h) → new_mkVBalBranch3MkVBalBranch2(zzz340, zzz341, zzz342, zzz343, zzz344, zzz520, zzz521, zzz52200, zzz523, zzz524, zzz31, new_primPlusNat3(Succ(new_primPlusNat3(new_primPlusNat1(zzz52200), zzz52200)), Succ(zzz52200)), h)
new_mkVBalBranch3MkVBalBranch11(zzz2033, zzz2034, zzz2035, zzz2036, zzz2037, zzz2038, zzz2039, zzz2040, zzz2041, zzz2042, zzz2043, Succ(zzz20440), Succ(zzz20450), bb) → new_mkVBalBranch3MkVBalBranch11(zzz2033, zzz2034, zzz2035, zzz2036, zzz2037, zzz2038, zzz2039, zzz2040, zzz2041, zzz2042, zzz2043, zzz20440, zzz20450, bb)
new_mkVBalBranch3MkVBalBranch25(zzz537, zzz538, zzz539, zzz540, zzz541, zzz542, zzz543, zzz544, zzz545, zzz546, zzz547, Succ(zzz5480), Succ(zzz5490), bc) → new_mkVBalBranch3MkVBalBranch25(zzz537, zzz538, zzz539, zzz540, zzz541, zzz542, zzz543, zzz544, zzz545, zzz546, zzz547, zzz5480, zzz5490, bc)
new_mkVBalBranch3MkVBalBranch2(zzz340, zzz341, Neg(zzz3420), zzz343, zzz344, zzz520, zzz521, zzz52200, zzz523, zzz524, zzz31, Zero, h) → new_mkVBalBranch3MkVBalBranch22(zzz340, zzz341, zzz3420, zzz343, zzz344, zzz520, zzz521, zzz52200, zzz523, zzz524, zzz31, h)
new_mkVBalBranch(zzz31, Branch(zzz520, zzz521, Neg(Succ(zzz52200)), zzz523, zzz524), Branch(zzz340, zzz341, zzz342, zzz343, zzz344), h) → new_mkVBalBranch3MkVBalBranch24(zzz340, zzz341, zzz342, zzz343, zzz344, zzz520, zzz521, zzz52200, zzz523, zzz524, zzz31, new_primPlusNat3(Succ(new_primPlusNat3(new_primPlusNat1(zzz52200), zzz52200)), Succ(zzz52200)), h)
new_mkVBalBranch3MkVBalBranch24(zzz340, zzz341, Neg(Succ(Zero)), zzz343, zzz344, zzz520, zzz521, Succ(zzz522000), zzz523, zzz524, zzz31, Zero, h) → new_mkVBalBranch3MkVBalBranch28(zzz340, zzz341, zzz343, zzz344, zzz520, zzz521, Succ(zzz522000), zzz523, zzz524, zzz31, h)
new_mkVBalBranch3MkVBalBranch24(zzz340, zzz341, Neg(Succ(Succ(zzz342000))), zzz343, zzz344, zzz520, zzz521, Zero, zzz523, zzz524, zzz31, Zero, h) → new_mkVBalBranch3MkVBalBranch14(zzz340, zzz341, Succ(zzz342000), zzz343, zzz344, zzz520, zzz521, zzz523, zzz524, zzz31, new_primMulNat1(Succ(zzz342000)), h)
new_mkVBalBranch3MkVBalBranch210(zzz340, zzz341, zzz343, zzz344, zzz520, zzz521, zzz52200, zzz523, zzz524, zzz31, h) → new_mkVBalBranch(zzz31, Branch(zzz520, zzz521, Neg(Succ(zzz52200)), zzz523, zzz524), zzz343, h)
new_mkVBalBranch3MkVBalBranch26(zzz1133, zzz1134, zzz1135, zzz1136, zzz1137, zzz1138, zzz1139, zzz1140, zzz1141, zzz1142, Zero, Succ(zzz11440), be) → new_mkVBalBranch(zzz1142, Branch(zzz1138, zzz1139, Neg(Succ(Zero)), zzz1140, zzz1141), zzz1136, be)
new_mkVBalBranch3MkVBalBranch24(zzz340, zzz341, Neg(Succ(Succ(Zero))), zzz343, zzz344, zzz520, zzz521, Zero, zzz523, zzz524, zzz31, Succ(Zero), h) → new_mkVBalBranch3MkVBalBranch26(zzz340, zzz341, Succ(Zero), zzz343, zzz344, zzz520, zzz521, zzz523, zzz524, zzz31, Zero, Zero, h)
new_mkVBalBranch(zzz31, Branch(zzz520, zzz521, Pos(Zero), zzz523, zzz524), Branch(zzz340, zzz341, Pos(Succ(zzz34200)), zzz343, zzz344), h) → new_mkVBalBranch(zzz31, Branch(zzz520, zzz521, Pos(Zero), zzz523, zzz524), zzz343, h)
new_mkVBalBranch3MkVBalBranch29(zzz818, zzz819, zzz820, zzz821, zzz822, zzz823, zzz824, zzz825, zzz826, zzz827, bf) → new_mkVBalBranch3MkVBalBranch14(zzz818, zzz819, zzz820, zzz821, zzz822, zzz823, zzz824, zzz825, zzz826, zzz827, new_primMulNat1(zzz820), bf)
new_mkVBalBranch3MkVBalBranch2(zzz340, zzz341, Pos(Zero), zzz343, zzz344, zzz520, zzz521, zzz52200, zzz523, zzz524, zzz31, Succ(zzz680), h) → new_mkVBalBranch(zzz31, zzz524, Branch(zzz340, zzz341, Pos(Zero), zzz343, zzz344), h)
new_mkVBalBranch3MkVBalBranch21(zzz340, zzz341, zzz343, zzz344, zzz520, zzz521, zzz52200, zzz523, zzz524, zzz31, h) → new_mkVBalBranch(zzz31, zzz524, Branch(zzz340, zzz341, Pos(Zero), zzz343, zzz344), h)
new_mkVBalBranch3MkVBalBranch24(zzz340, zzz341, Pos(zzz3420), zzz343, zzz344, zzz520, zzz521, zzz52200, zzz523, zzz524, zzz31, Zero, h) → new_mkVBalBranch3MkVBalBranch27(zzz340, zzz341, zzz3420, zzz343, zzz344, zzz520, zzz521, zzz52200, zzz523, zzz524, zzz31, h)
new_mkVBalBranch3MkVBalBranch211(zzz537, zzz538, zzz539, zzz540, zzz541, zzz542, zzz543, zzz544, zzz545, zzz546, zzz547, bc) → new_mkVBalBranch3MkVBalBranch15(zzz537, zzz538, zzz539, zzz540, zzz541, zzz542, zzz543, zzz544, zzz545, zzz546, zzz547, new_primMulNat1(zzz539), bc)
new_mkVBalBranch3MkVBalBranch15(zzz537, zzz538, zzz539, zzz540, zzz541, zzz542, zzz543, zzz544, zzz545, zzz546, zzz547, Succ(zzz6990), bc) → new_mkVBalBranch3MkVBalBranch16(zzz537, zzz538, zzz539, zzz540, zzz541, zzz542, zzz543, Succ(zzz544), zzz545, zzz546, zzz547, Succ(Succ(zzz544)), Succ(zzz6990), bc)
new_mkVBalBranch3MkVBalBranch24(zzz340, zzz341, Neg(Succ(Succ(Succ(zzz3420000)))), zzz343, zzz344, zzz520, zzz521, Zero, zzz523, zzz524, zzz31, Succ(Succ(zzz6900)), h) → new_mkVBalBranch3MkVBalBranch26(zzz340, zzz341, Succ(Succ(zzz3420000)), zzz343, zzz344, zzz520, zzz521, zzz523, zzz524, zzz31, Succ(zzz3420000), Succ(zzz6900), h)
new_mkVBalBranch(zzz31, Branch(zzz520, zzz521, Neg(Zero), zzz523, zzz524), Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), h) → new_mkVBalBranch3MkVBalBranch13(zzz340, zzz341, zzz34200, zzz343, zzz344, zzz520, zzz521, zzz523, zzz524, zzz31, new_primPlusNat2(new_primMulNat0(zzz34200), Succ(zzz34200)), h)
new_mkVBalBranch3MkVBalBranch27(zzz340, zzz341, zzz3420, zzz343, zzz344, zzz520, zzz521, zzz52200, zzz523, zzz524, zzz31, h) → new_mkVBalBranch(zzz31, Branch(zzz520, zzz521, Neg(Succ(zzz52200)), zzz523, zzz524), zzz343, h)
new_mkVBalBranch3MkVBalBranch24(zzz340, zzz341, Pos(zzz3420), zzz343, zzz344, zzz520, zzz521, zzz52200, zzz523, zzz524, zzz31, Succ(zzz690), h) → new_mkVBalBranch(zzz31, Branch(zzz520, zzz521, Neg(Succ(zzz52200)), zzz523, zzz524), zzz343, h)
new_mkVBalBranch3MkVBalBranch12(zzz340, zzz341, zzz34200, zzz343, zzz344, zzz520, zzz521, zzz523, zzz524, zzz31, Succ(zzz1250), h) → new_mkVBalBranch(zzz31, zzz524, Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), h)
new_mkVBalBranch3MkVBalBranch28(zzz340, zzz341, zzz343, zzz344, zzz520, zzz521, zzz52200, zzz523, zzz524, zzz31, h) → new_mkVBalBranch(zzz31, Branch(zzz520, zzz521, Neg(Succ(zzz52200)), zzz523, zzz524), zzz343, h)
new_mkVBalBranch3MkVBalBranch25(zzz537, zzz538, zzz539, zzz540, zzz541, zzz542, zzz543, zzz544, zzz545, zzz546, zzz547, Succ(zzz5480), Zero, bc) → new_mkVBalBranch3MkVBalBranch15(zzz537, zzz538, zzz539, zzz540, zzz541, zzz542, zzz543, zzz544, zzz545, zzz546, zzz547, new_primMulNat1(zzz539), bc)
new_mkVBalBranch3MkVBalBranch24(zzz340, zzz341, Neg(Succ(Succ(Zero))), zzz343, zzz344, zzz520, zzz521, Zero, zzz523, zzz524, zzz31, Succ(Succ(zzz6900)), h) → new_mkVBalBranch3MkVBalBranch26(zzz340, zzz341, Succ(Zero), zzz343, zzz344, zzz520, zzz521, zzz523, zzz524, zzz31, Zero, Succ(zzz6900), h)
new_mkVBalBranch(zzz31, Branch(zzz520, zzz521, Pos(Zero), zzz523, zzz524), Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), h) → new_mkVBalBranch3MkVBalBranch12(zzz340, zzz341, zzz34200, zzz343, zzz344, zzz520, zzz521, zzz523, zzz524, zzz31, new_primPlusNat2(new_primMulNat0(zzz34200), Succ(zzz34200)), h)
new_mkVBalBranch3MkVBalBranch22(zzz340, zzz341, Zero, zzz343, zzz344, zzz520, zzz521, zzz52200, zzz523, zzz524, zzz31, h) → new_mkVBalBranch(zzz31, zzz524, Branch(zzz340, zzz341, Neg(Zero), zzz343, zzz344), h)
new_mkVBalBranch3MkVBalBranch1(zzz340, zzz341, zzz34200, zzz343, zzz344, zzz520, zzz521, zzz52200, zzz523, zzz524, zzz31, Succ(zzz1430), h) → new_mkVBalBranch(zzz31, zzz524, Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), h)
new_mkVBalBranch3MkVBalBranch24(zzz340, zzz341, Neg(Succ(Zero)), zzz343, zzz344, zzz520, zzz521, zzz52200, zzz523, zzz524, zzz31, Succ(zzz690), h) → new_mkVBalBranch(zzz31, Branch(zzz520, zzz521, Neg(Succ(zzz52200)), zzz523, zzz524), zzz343, h)
new_mkVBalBranch3MkVBalBranch13(zzz340, zzz341, zzz34200, zzz343, zzz344, zzz520, zzz521, zzz523, zzz524, zzz31, Succ(zzz1290), h) → new_mkVBalBranch(zzz31, zzz524, Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), h)
new_mkVBalBranch3MkVBalBranch2(zzz340, zzz341, Pos(Succ(zzz34200)), zzz343, zzz344, zzz520, zzz521, zzz52200, zzz523, zzz524, zzz31, Succ(zzz680), h) → new_mkVBalBranch3MkVBalBranch20(zzz340, zzz341, zzz34200, zzz343, zzz344, zzz520, zzz521, zzz52200, zzz523, zzz524, zzz31, Succ(new_primPlusNat2(zzz680, zzz52200)), zzz34200, h)
new_mkVBalBranch(zzz31, Branch(zzz520, zzz521, Neg(Zero), zzz523, zzz524), Branch(zzz340, zzz341, Pos(Succ(zzz34200)), zzz343, zzz344), h) → new_mkVBalBranch(zzz31, Branch(zzz520, zzz521, Neg(Zero), zzz523, zzz524), zzz343, h)
new_mkVBalBranch3MkVBalBranch24(zzz340, zzz341, Neg(Zero), zzz343, zzz344, zzz520, zzz521, zzz52200, zzz523, zzz524, zzz31, Succ(zzz690), h) → new_mkVBalBranch(zzz31, Branch(zzz520, zzz521, Neg(Succ(zzz52200)), zzz523, zzz524), zzz343, h)
new_mkVBalBranch3MkVBalBranch1(zzz340, zzz341, zzz34200, zzz343, zzz344, zzz520, zzz521, zzz52200, zzz523, zzz524, zzz31, Zero, h) → new_mkVBalBranch3MkVBalBranch17(zzz340, zzz341, zzz34200, zzz343, zzz344, zzz520, zzz521, zzz52200, zzz523, zzz524, zzz31, h)
new_mkVBalBranch3MkVBalBranch16(zzz1702, zzz1703, zzz1704, zzz1705, zzz1706, zzz1707, zzz1708, zzz1709, zzz1710, zzz1711, zzz1712, Succ(zzz17130), Succ(zzz17140), bd) → new_mkVBalBranch3MkVBalBranch16(zzz1702, zzz1703, zzz1704, zzz1705, zzz1706, zzz1707, zzz1708, zzz1709, zzz1710, zzz1711, zzz1712, zzz17130, zzz17140, bd)
new_mkVBalBranch3MkVBalBranch25(zzz537, zzz538, zzz539, zzz540, zzz541, zzz542, zzz543, zzz544, zzz545, zzz546, zzz547, Zero, Succ(zzz5490), bc) → new_mkVBalBranch(zzz547, Branch(zzz542, zzz543, Neg(Succ(Succ(zzz544))), zzz545, zzz546), zzz540, bc)
new_mkVBalBranch3MkVBalBranch212(zzz818, zzz819, zzz820, zzz821, zzz822, zzz823, zzz824, zzz825, zzz826, zzz827, bf) → new_mkVBalBranch3MkVBalBranch14(zzz818, zzz819, zzz820, zzz821, zzz822, zzz823, zzz824, zzz825, zzz826, zzz827, new_primPlusNat2(new_primMulNat0(zzz820), Succ(zzz820)), bf)
new_mkVBalBranch3MkVBalBranch10(zzz929, zzz930, zzz931, zzz932, zzz933, zzz934, zzz935, zzz936, zzz937, zzz938, zzz939, Succ(zzz10020), ba) → new_mkVBalBranch3MkVBalBranch11(zzz929, zzz930, zzz931, zzz932, zzz933, zzz934, zzz935, zzz936, zzz937, zzz938, zzz939, Succ(zzz10020), Succ(zzz936), ba)
new_mkVBalBranch3MkVBalBranch2(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344, zzz520, zzz521, zzz52200, zzz523, zzz524, zzz31, Succ(zzz680), h) → new_mkVBalBranch3MkVBalBranch1(zzz340, zzz341, zzz34200, zzz343, zzz344, zzz520, zzz521, zzz52200, zzz523, zzz524, zzz31, new_primPlusNat2(new_primMulNat0(zzz34200), Succ(zzz34200)), h)
new_mkVBalBranch3MkVBalBranch14(zzz818, zzz819, zzz820, zzz821, zzz822, zzz823, zzz824, zzz825, zzz826, zzz827, Succ(zzz8960), bf) → new_mkVBalBranch3MkVBalBranch16(zzz818, zzz819, zzz820, zzz821, zzz822, zzz823, zzz824, Zero, zzz825, zzz826, zzz827, Succ(Zero), Succ(zzz8960), bf)
new_mkVBalBranch3MkVBalBranch24(zzz340, zzz341, Neg(Succ(Succ(Succ(zzz3420000)))), zzz343, zzz344, zzz520, zzz521, Succ(zzz522000), zzz523, zzz524, zzz31, Succ(Succ(zzz6900)), h) → new_mkVBalBranch3MkVBalBranch25(zzz340, zzz341, Succ(Succ(zzz3420000)), zzz343, zzz344, zzz520, zzz521, zzz522000, zzz523, zzz524, zzz31, Succ(zzz3420000), Succ(Succ(new_primPlusNat2(zzz6900, zzz522000))), h)
new_mkVBalBranch3MkVBalBranch2(zzz340, zzz341, Pos(Succ(zzz34200)), zzz343, zzz344, zzz520, zzz521, zzz52200, zzz523, zzz524, zzz31, Zero, h) → new_mkVBalBranch3MkVBalBranch20(zzz340, zzz341, zzz34200, zzz343, zzz344, zzz520, zzz521, zzz52200, zzz523, zzz524, zzz31, zzz52200, zzz34200, h)
new_mkVBalBranch3MkVBalBranch24(zzz340, zzz341, Neg(Zero), zzz343, zzz344, zzz520, zzz521, zzz52200, zzz523, zzz524, zzz31, Zero, h) → new_mkVBalBranch3MkVBalBranch210(zzz340, zzz341, zzz343, zzz344, zzz520, zzz521, zzz52200, zzz523, zzz524, zzz31, h)
new_mkVBalBranch3MkVBalBranch24(zzz340, zzz341, Neg(Succ(Succ(Zero))), zzz343, zzz344, zzz520, zzz521, Succ(zzz522000), zzz523, zzz524, zzz31, Succ(Succ(zzz6900)), h) → new_mkVBalBranch3MkVBalBranch25(zzz340, zzz341, Succ(Zero), zzz343, zzz344, zzz520, zzz521, zzz522000, zzz523, zzz524, zzz31, Zero, Succ(Succ(new_primPlusNat2(zzz6900, zzz522000))), h)
new_mkVBalBranch3MkVBalBranch20(zzz929, zzz930, zzz931, zzz932, zzz933, zzz934, zzz935, zzz936, zzz937, zzz938, zzz939, Succ(zzz9400), Zero, ba) → new_mkVBalBranch3MkVBalBranch10(zzz929, zzz930, zzz931, zzz932, zzz933, zzz934, zzz935, zzz936, zzz937, zzz938, zzz939, new_primMulNat1(zzz931), ba)
new_mkVBalBranch3MkVBalBranch23(zzz929, zzz930, zzz931, zzz932, zzz933, zzz934, zzz935, zzz936, zzz937, zzz938, zzz939, ba) → new_mkVBalBranch3MkVBalBranch10(zzz929, zzz930, zzz931, zzz932, zzz933, zzz934, zzz935, zzz936, zzz937, zzz938, zzz939, new_primPlusNat2(new_primMulNat0(zzz931), Succ(zzz931)), ba)
new_mkVBalBranch3MkVBalBranch2(zzz340, zzz341, Neg(Zero), zzz343, zzz344, zzz520, zzz521, zzz52200, zzz523, zzz524, zzz31, Succ(zzz680), h) → new_mkVBalBranch(zzz31, zzz524, Branch(zzz340, zzz341, Neg(Zero), zzz343, zzz344), h)
new_mkVBalBranch3MkVBalBranch16(zzz1702, zzz1703, zzz1704, zzz1705, zzz1706, zzz1707, zzz1708, zzz1709, zzz1710, zzz1711, zzz1712, Zero, Succ(zzz17140), bd) → new_mkVBalBranch(zzz1712, zzz1711, Branch(zzz1702, zzz1703, Neg(Succ(zzz1704)), zzz1705, zzz1706), bd)
new_mkVBalBranch3MkVBalBranch10(zzz929, zzz930, zzz931, zzz932, zzz933, zzz934, zzz935, zzz936, zzz937, zzz938, zzz939, Zero, ba) → new_mkVBalBranch3MkVBalBranch11(zzz929, zzz930, zzz931, zzz932, zzz933, zzz934, zzz935, zzz936, zzz937, zzz938, zzz939, Zero, Succ(zzz936), ba)
new_mkVBalBranch3MkVBalBranch22(zzz340, zzz341, Succ(zzz34200), zzz343, zzz344, zzz520, zzz521, zzz52200, zzz523, zzz524, zzz31, h) → new_mkVBalBranch3MkVBalBranch1(zzz340, zzz341, zzz34200, zzz343, zzz344, zzz520, zzz521, zzz52200, zzz523, zzz524, zzz31, new_primPlusNat2(new_primPlusNat3(Succ(new_primPlusNat3(new_primPlusNat1(zzz34200), zzz34200)), Succ(zzz34200)), Succ(zzz34200)), h)
new_mkVBalBranch3MkVBalBranch25(zzz537, zzz538, zzz539, zzz540, zzz541, zzz542, zzz543, zzz544, zzz545, zzz546, zzz547, Zero, Zero, bc) → new_mkVBalBranch3MkVBalBranch211(zzz537, zzz538, zzz539, zzz540, zzz541, zzz542, zzz543, zzz544, zzz545, zzz546, zzz547, bc)
new_mkVBalBranch3MkVBalBranch2(zzz340, zzz341, Pos(Zero), zzz343, zzz344, zzz520, zzz521, zzz52200, zzz523, zzz524, zzz31, Zero, h) → new_mkVBalBranch3MkVBalBranch21(zzz340, zzz341, zzz343, zzz344, zzz520, zzz521, zzz52200, zzz523, zzz524, zzz31, h)

The TRS R consists of the following rules:

new_primPlusNat1(Zero) → Zero
new_primMulNat0(zzz6200) → new_primPlusNat3(Succ(new_primPlusNat3(new_primPlusNat1(zzz6200), zzz6200)), Succ(zzz6200))
new_primPlusNat2(Succ(zzz900), Succ(zzz9100)) → Succ(Succ(new_primPlusNat2(zzz900, zzz9100)))
new_primPlusNat3(zzz90, Succ(zzz910)) → Succ(Succ(new_primPlusNat2(zzz90, zzz910)))
new_primPlusNat3(zzz90, Zero) → Succ(zzz90)
new_primMulNat1(zzz34200) → new_primPlusNat2(new_primMulNat0(zzz34200), Succ(zzz34200))
new_primPlusNat2(Zero, Zero) → Zero
new_primPlusNat1(Succ(zzz62000)) → Succ(Succ(new_primPlusNat1(zzz62000)))
new_primPlusNat2(Succ(zzz900), Zero) → Succ(zzz900)
new_primPlusNat2(Zero, Succ(zzz9100)) → Succ(zzz9100)

The set Q consists of the following terms:

new_primPlusNat2(Zero, Succ(x0))
new_primMulNat1(x0)
new_primMulNat0(x0)
new_primPlusNat3(x0, Succ(x1))
new_primPlusNat2(Succ(x0), Succ(x1))
new_primPlusNat3(x0, Zero)
new_primPlusNat1(Zero)
new_primPlusNat2(Zero, Zero)
new_primPlusNat1(Succ(x0))
new_primPlusNat2(Succ(x0), Zero)

We have to consider all minimal (P,Q,R)-chains.
By rewriting [15] the rule new_mkVBalBranch3MkVBalBranch20(zzz929, zzz930, zzz931, zzz932, zzz933, zzz934, zzz935, zzz936, zzz937, zzz938, zzz939, Succ(zzz9400), Zero, ba) → new_mkVBalBranch3MkVBalBranch10(zzz929, zzz930, zzz931, zzz932, zzz933, zzz934, zzz935, zzz936, zzz937, zzz938, zzz939, new_primMulNat1(zzz931), ba) at position [11] we obtained the following new rules:

new_mkVBalBranch3MkVBalBranch20(zzz929, zzz930, zzz931, zzz932, zzz933, zzz934, zzz935, zzz936, zzz937, zzz938, zzz939, Succ(zzz9400), Zero, ba) → new_mkVBalBranch3MkVBalBranch10(zzz929, zzz930, zzz931, zzz932, zzz933, zzz934, zzz935, zzz936, zzz937, zzz938, zzz939, new_primPlusNat2(new_primMulNat0(zzz931), Succ(zzz931)), 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
                                    ↳ DependencyGraphProof
                                      ↳ QDP
                                        ↳ Rewriting
                                          ↳ QDP
                                            ↳ Rewriting
                                              ↳ QDP
                                                ↳ Rewriting
                                                  ↳ QDP
                                                    ↳ Rewriting
                                                      ↳ QDP
                                                        ↳ Rewriting
                                                          ↳ QDP
                                                            ↳ Rewriting
                                                              ↳ QDP
                                                                ↳ Rewriting
                                                                  ↳ QDP
                                                                    ↳ Rewriting
                                                                      ↳ QDP
                                                                        ↳ Rewriting
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP

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

new_mkVBalBranch3MkVBalBranch11(zzz2033, zzz2034, zzz2035, zzz2036, zzz2037, zzz2038, zzz2039, zzz2040, zzz2041, zzz2042, zzz2043, Zero, Succ(zzz20450), bb) → new_mkVBalBranch(zzz2043, zzz2042, Branch(zzz2033, zzz2034, Pos(Succ(zzz2035)), zzz2036, zzz2037), bb)
new_mkVBalBranch3MkVBalBranch26(zzz1133, zzz1134, zzz1135, zzz1136, zzz1137, zzz1138, zzz1139, zzz1140, zzz1141, zzz1142, Succ(zzz11430), Succ(zzz11440), be) → new_mkVBalBranch3MkVBalBranch26(zzz1133, zzz1134, zzz1135, zzz1136, zzz1137, zzz1138, zzz1139, zzz1140, zzz1141, zzz1142, zzz11430, zzz11440, be)
new_mkVBalBranch3MkVBalBranch24(zzz340, zzz341, Neg(Succ(Succ(Succ(zzz3420000)))), zzz343, zzz344, zzz520, zzz521, Zero, zzz523, zzz524, zzz31, Succ(Zero), h) → new_mkVBalBranch3MkVBalBranch26(zzz340, zzz341, Succ(Succ(zzz3420000)), zzz343, zzz344, zzz520, zzz521, zzz523, zzz524, zzz31, Succ(zzz3420000), Zero, h)
new_mkVBalBranch3MkVBalBranch24(zzz340, zzz341, Neg(Succ(Zero)), zzz343, zzz344, zzz520, zzz521, Zero, zzz523, zzz524, zzz31, Zero, h) → new_mkVBalBranch3MkVBalBranch29(zzz340, zzz341, Zero, zzz343, zzz344, zzz520, zzz521, zzz523, zzz524, zzz31, h)
new_mkVBalBranch3MkVBalBranch20(zzz929, zzz930, zzz931, zzz932, zzz933, zzz934, zzz935, zzz936, zzz937, zzz938, zzz939, Zero, Succ(zzz9410), ba) → new_mkVBalBranch(zzz939, Branch(zzz934, zzz935, Pos(Succ(zzz936)), zzz937, zzz938), zzz932, ba)
new_mkVBalBranch3MkVBalBranch17(zzz340, zzz341, zzz34200, zzz343, zzz344, zzz520, zzz521, zzz52200, zzz523, zzz524, zzz31, h) → new_mkVBalBranch(zzz31, zzz524, Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), h)
new_mkVBalBranch3MkVBalBranch26(zzz1133, zzz1134, zzz1135, zzz1136, zzz1137, zzz1138, zzz1139, zzz1140, zzz1141, zzz1142, Zero, Zero, be) → new_mkVBalBranch3MkVBalBranch29(zzz1133, zzz1134, zzz1135, zzz1136, zzz1137, zzz1138, zzz1139, zzz1140, zzz1141, zzz1142, be)
new_mkVBalBranch3MkVBalBranch20(zzz929, zzz930, zzz931, zzz932, zzz933, zzz934, zzz935, zzz936, zzz937, zzz938, zzz939, Zero, Zero, ba) → new_mkVBalBranch3MkVBalBranch23(zzz929, zzz930, zzz931, zzz932, zzz933, zzz934, zzz935, zzz936, zzz937, zzz938, zzz939, ba)
new_mkVBalBranch3MkVBalBranch20(zzz929, zzz930, zzz931, zzz932, zzz933, zzz934, zzz935, zzz936, zzz937, zzz938, zzz939, Succ(zzz9400), Zero, ba) → new_mkVBalBranch3MkVBalBranch10(zzz929, zzz930, zzz931, zzz932, zzz933, zzz934, zzz935, zzz936, zzz937, zzz938, zzz939, new_primPlusNat2(new_primMulNat0(zzz931), Succ(zzz931)), ba)
new_mkVBalBranch3MkVBalBranch24(zzz340, zzz341, Neg(Succ(Succ(Zero))), zzz343, zzz344, zzz520, zzz521, Succ(zzz522000), zzz523, zzz524, zzz31, Succ(Zero), h) → new_mkVBalBranch3MkVBalBranch25(zzz340, zzz341, Succ(Zero), zzz343, zzz344, zzz520, zzz521, zzz522000, zzz523, zzz524, zzz31, Zero, Succ(zzz522000), h)
new_mkVBalBranch3MkVBalBranch20(zzz929, zzz930, zzz931, zzz932, zzz933, zzz934, zzz935, zzz936, zzz937, zzz938, zzz939, Succ(zzz9400), Succ(zzz9410), ba) → new_mkVBalBranch3MkVBalBranch20(zzz929, zzz930, zzz931, zzz932, zzz933, zzz934, zzz935, zzz936, zzz937, zzz938, zzz939, zzz9400, zzz9410, ba)
new_mkVBalBranch3MkVBalBranch24(zzz340, zzz341, Neg(Succ(Succ(Succ(zzz3420000)))), zzz343, zzz344, zzz520, zzz521, Succ(zzz522000), zzz523, zzz524, zzz31, Succ(Zero), h) → new_mkVBalBranch3MkVBalBranch25(zzz340, zzz341, Succ(Succ(zzz3420000)), zzz343, zzz344, zzz520, zzz521, zzz522000, zzz523, zzz524, zzz31, Succ(zzz3420000), Succ(zzz522000), h)
new_mkVBalBranch3MkVBalBranch26(zzz1133, zzz1134, zzz1135, zzz1136, zzz1137, zzz1138, zzz1139, zzz1140, zzz1141, zzz1142, Succ(zzz11430), Zero, be) → new_mkVBalBranch3MkVBalBranch212(zzz1133, zzz1134, zzz1135, zzz1136, zzz1137, zzz1138, zzz1139, zzz1140, zzz1141, zzz1142, be)
new_mkVBalBranch3MkVBalBranch24(zzz340, zzz341, Neg(Succ(Succ(zzz342000))), zzz343, zzz344, zzz520, zzz521, Succ(zzz522000), zzz523, zzz524, zzz31, Zero, h) → new_mkVBalBranch3MkVBalBranch25(zzz340, zzz341, Succ(zzz342000), zzz343, zzz344, zzz520, zzz521, zzz522000, zzz523, zzz524, zzz31, zzz342000, zzz522000, h)
new_mkVBalBranch(zzz31, Branch(zzz520, zzz521, Pos(Succ(zzz52200)), zzz523, zzz524), Branch(zzz340, zzz341, zzz342, zzz343, zzz344), h) → new_mkVBalBranch3MkVBalBranch2(zzz340, zzz341, zzz342, zzz343, zzz344, zzz520, zzz521, zzz52200, zzz523, zzz524, zzz31, new_primPlusNat3(Succ(new_primPlusNat3(new_primPlusNat1(zzz52200), zzz52200)), Succ(zzz52200)), h)
new_mkVBalBranch3MkVBalBranch11(zzz2033, zzz2034, zzz2035, zzz2036, zzz2037, zzz2038, zzz2039, zzz2040, zzz2041, zzz2042, zzz2043, Succ(zzz20440), Succ(zzz20450), bb) → new_mkVBalBranch3MkVBalBranch11(zzz2033, zzz2034, zzz2035, zzz2036, zzz2037, zzz2038, zzz2039, zzz2040, zzz2041, zzz2042, zzz2043, zzz20440, zzz20450, bb)
new_mkVBalBranch3MkVBalBranch2(zzz340, zzz341, Neg(zzz3420), zzz343, zzz344, zzz520, zzz521, zzz52200, zzz523, zzz524, zzz31, Zero, h) → new_mkVBalBranch3MkVBalBranch22(zzz340, zzz341, zzz3420, zzz343, zzz344, zzz520, zzz521, zzz52200, zzz523, zzz524, zzz31, h)
new_mkVBalBranch3MkVBalBranch25(zzz537, zzz538, zzz539, zzz540, zzz541, zzz542, zzz543, zzz544, zzz545, zzz546, zzz547, Succ(zzz5480), Succ(zzz5490), bc) → new_mkVBalBranch3MkVBalBranch25(zzz537, zzz538, zzz539, zzz540, zzz541, zzz542, zzz543, zzz544, zzz545, zzz546, zzz547, zzz5480, zzz5490, bc)
new_mkVBalBranch(zzz31, Branch(zzz520, zzz521, Neg(Succ(zzz52200)), zzz523, zzz524), Branch(zzz340, zzz341, zzz342, zzz343, zzz344), h) → new_mkVBalBranch3MkVBalBranch24(zzz340, zzz341, zzz342, zzz343, zzz344, zzz520, zzz521, zzz52200, zzz523, zzz524, zzz31, new_primPlusNat3(Succ(new_primPlusNat3(new_primPlusNat1(zzz52200), zzz52200)), Succ(zzz52200)), h)
new_mkVBalBranch3MkVBalBranch24(zzz340, zzz341, Neg(Succ(Zero)), zzz343, zzz344, zzz520, zzz521, Succ(zzz522000), zzz523, zzz524, zzz31, Zero, h) → new_mkVBalBranch3MkVBalBranch28(zzz340, zzz341, zzz343, zzz344, zzz520, zzz521, Succ(zzz522000), zzz523, zzz524, zzz31, h)
new_mkVBalBranch3MkVBalBranch210(zzz340, zzz341, zzz343, zzz344, zzz520, zzz521, zzz52200, zzz523, zzz524, zzz31, h) → new_mkVBalBranch(zzz31, Branch(zzz520, zzz521, Neg(Succ(zzz52200)), zzz523, zzz524), zzz343, h)
new_mkVBalBranch3MkVBalBranch24(zzz340, zzz341, Neg(Succ(Succ(zzz342000))), zzz343, zzz344, zzz520, zzz521, Zero, zzz523, zzz524, zzz31, Zero, h) → new_mkVBalBranch3MkVBalBranch14(zzz340, zzz341, Succ(zzz342000), zzz343, zzz344, zzz520, zzz521, zzz523, zzz524, zzz31, new_primMulNat1(Succ(zzz342000)), h)
new_mkVBalBranch3MkVBalBranch26(zzz1133, zzz1134, zzz1135, zzz1136, zzz1137, zzz1138, zzz1139, zzz1140, zzz1141, zzz1142, Zero, Succ(zzz11440), be) → new_mkVBalBranch(zzz1142, Branch(zzz1138, zzz1139, Neg(Succ(Zero)), zzz1140, zzz1141), zzz1136, be)
new_mkVBalBranch3MkVBalBranch24(zzz340, zzz341, Neg(Succ(Succ(Zero))), zzz343, zzz344, zzz520, zzz521, Zero, zzz523, zzz524, zzz31, Succ(Zero), h) → new_mkVBalBranch3MkVBalBranch26(zzz340, zzz341, Succ(Zero), zzz343, zzz344, zzz520, zzz521, zzz523, zzz524, zzz31, Zero, Zero, h)
new_mkVBalBranch(zzz31, Branch(zzz520, zzz521, Pos(Zero), zzz523, zzz524), Branch(zzz340, zzz341, Pos(Succ(zzz34200)), zzz343, zzz344), h) → new_mkVBalBranch(zzz31, Branch(zzz520, zzz521, Pos(Zero), zzz523, zzz524), zzz343, h)
new_mkVBalBranch3MkVBalBranch29(zzz818, zzz819, zzz820, zzz821, zzz822, zzz823, zzz824, zzz825, zzz826, zzz827, bf) → new_mkVBalBranch3MkVBalBranch14(zzz818, zzz819, zzz820, zzz821, zzz822, zzz823, zzz824, zzz825, zzz826, zzz827, new_primMulNat1(zzz820), bf)
new_mkVBalBranch3MkVBalBranch2(zzz340, zzz341, Pos(Zero), zzz343, zzz344, zzz520, zzz521, zzz52200, zzz523, zzz524, zzz31, Succ(zzz680), h) → new_mkVBalBranch(zzz31, zzz524, Branch(zzz340, zzz341, Pos(Zero), zzz343, zzz344), h)
new_mkVBalBranch3MkVBalBranch21(zzz340, zzz341, zzz343, zzz344, zzz520, zzz521, zzz52200, zzz523, zzz524, zzz31, h) → new_mkVBalBranch(zzz31, zzz524, Branch(zzz340, zzz341, Pos(Zero), zzz343, zzz344), h)
new_mkVBalBranch3MkVBalBranch24(zzz340, zzz341, Pos(zzz3420), zzz343, zzz344, zzz520, zzz521, zzz52200, zzz523, zzz524, zzz31, Zero, h) → new_mkVBalBranch3MkVBalBranch27(zzz340, zzz341, zzz3420, zzz343, zzz344, zzz520, zzz521, zzz52200, zzz523, zzz524, zzz31, h)
new_mkVBalBranch3MkVBalBranch211(zzz537, zzz538, zzz539, zzz540, zzz541, zzz542, zzz543, zzz544, zzz545, zzz546, zzz547, bc) → new_mkVBalBranch3MkVBalBranch15(zzz537, zzz538, zzz539, zzz540, zzz541, zzz542, zzz543, zzz544, zzz545, zzz546, zzz547, new_primMulNat1(zzz539), bc)
new_mkVBalBranch3MkVBalBranch24(zzz340, zzz341, Neg(Succ(Succ(Succ(zzz3420000)))), zzz343, zzz344, zzz520, zzz521, Zero, zzz523, zzz524, zzz31, Succ(Succ(zzz6900)), h) → new_mkVBalBranch3MkVBalBranch26(zzz340, zzz341, Succ(Succ(zzz3420000)), zzz343, zzz344, zzz520, zzz521, zzz523, zzz524, zzz31, Succ(zzz3420000), Succ(zzz6900), h)
new_mkVBalBranch3MkVBalBranch15(zzz537, zzz538, zzz539, zzz540, zzz541, zzz542, zzz543, zzz544, zzz545, zzz546, zzz547, Succ(zzz6990), bc) → new_mkVBalBranch3MkVBalBranch16(zzz537, zzz538, zzz539, zzz540, zzz541, zzz542, zzz543, Succ(zzz544), zzz545, zzz546, zzz547, Succ(Succ(zzz544)), Succ(zzz6990), bc)
new_mkVBalBranch(zzz31, Branch(zzz520, zzz521, Neg(Zero), zzz523, zzz524), Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), h) → new_mkVBalBranch3MkVBalBranch13(zzz340, zzz341, zzz34200, zzz343, zzz344, zzz520, zzz521, zzz523, zzz524, zzz31, new_primPlusNat2(new_primMulNat0(zzz34200), Succ(zzz34200)), h)
new_mkVBalBranch3MkVBalBranch27(zzz340, zzz341, zzz3420, zzz343, zzz344, zzz520, zzz521, zzz52200, zzz523, zzz524, zzz31, h) → new_mkVBalBranch(zzz31, Branch(zzz520, zzz521, Neg(Succ(zzz52200)), zzz523, zzz524), zzz343, h)
new_mkVBalBranch3MkVBalBranch24(zzz340, zzz341, Pos(zzz3420), zzz343, zzz344, zzz520, zzz521, zzz52200, zzz523, zzz524, zzz31, Succ(zzz690), h) → new_mkVBalBranch(zzz31, Branch(zzz520, zzz521, Neg(Succ(zzz52200)), zzz523, zzz524), zzz343, h)
new_mkVBalBranch3MkVBalBranch12(zzz340, zzz341, zzz34200, zzz343, zzz344, zzz520, zzz521, zzz523, zzz524, zzz31, Succ(zzz1250), h) → new_mkVBalBranch(zzz31, zzz524, Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), h)
new_mkVBalBranch3MkVBalBranch25(zzz537, zzz538, zzz539, zzz540, zzz541, zzz542, zzz543, zzz544, zzz545, zzz546, zzz547, Succ(zzz5480), Zero, bc) → new_mkVBalBranch3MkVBalBranch15(zzz537, zzz538, zzz539, zzz540, zzz541, zzz542, zzz543, zzz544, zzz545, zzz546, zzz547, new_primMulNat1(zzz539), bc)
new_mkVBalBranch3MkVBalBranch28(zzz340, zzz341, zzz343, zzz344, zzz520, zzz521, zzz52200, zzz523, zzz524, zzz31, h) → new_mkVBalBranch(zzz31, Branch(zzz520, zzz521, Neg(Succ(zzz52200)), zzz523, zzz524), zzz343, h)
new_mkVBalBranch3MkVBalBranch24(zzz340, zzz341, Neg(Succ(Succ(Zero))), zzz343, zzz344, zzz520, zzz521, Zero, zzz523, zzz524, zzz31, Succ(Succ(zzz6900)), h) → new_mkVBalBranch3MkVBalBranch26(zzz340, zzz341, Succ(Zero), zzz343, zzz344, zzz520, zzz521, zzz523, zzz524, zzz31, Zero, Succ(zzz6900), h)
new_mkVBalBranch3MkVBalBranch1(zzz340, zzz341, zzz34200, zzz343, zzz344, zzz520, zzz521, zzz52200, zzz523, zzz524, zzz31, Succ(zzz1430), h) → new_mkVBalBranch(zzz31, zzz524, Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), h)
new_mkVBalBranch3MkVBalBranch22(zzz340, zzz341, Zero, zzz343, zzz344, zzz520, zzz521, zzz52200, zzz523, zzz524, zzz31, h) → new_mkVBalBranch(zzz31, zzz524, Branch(zzz340, zzz341, Neg(Zero), zzz343, zzz344), h)
new_mkVBalBranch(zzz31, Branch(zzz520, zzz521, Pos(Zero), zzz523, zzz524), Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), h) → new_mkVBalBranch3MkVBalBranch12(zzz340, zzz341, zzz34200, zzz343, zzz344, zzz520, zzz521, zzz523, zzz524, zzz31, new_primPlusNat2(new_primMulNat0(zzz34200), Succ(zzz34200)), h)
new_mkVBalBranch3MkVBalBranch24(zzz340, zzz341, Neg(Succ(Zero)), zzz343, zzz344, zzz520, zzz521, zzz52200, zzz523, zzz524, zzz31, Succ(zzz690), h) → new_mkVBalBranch(zzz31, Branch(zzz520, zzz521, Neg(Succ(zzz52200)), zzz523, zzz524), zzz343, h)
new_mkVBalBranch3MkVBalBranch13(zzz340, zzz341, zzz34200, zzz343, zzz344, zzz520, zzz521, zzz523, zzz524, zzz31, Succ(zzz1290), h) → new_mkVBalBranch(zzz31, zzz524, Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), h)
new_mkVBalBranch3MkVBalBranch2(zzz340, zzz341, Pos(Succ(zzz34200)), zzz343, zzz344, zzz520, zzz521, zzz52200, zzz523, zzz524, zzz31, Succ(zzz680), h) → new_mkVBalBranch3MkVBalBranch20(zzz340, zzz341, zzz34200, zzz343, zzz344, zzz520, zzz521, zzz52200, zzz523, zzz524, zzz31, Succ(new_primPlusNat2(zzz680, zzz52200)), zzz34200, h)
new_mkVBalBranch3MkVBalBranch24(zzz340, zzz341, Neg(Zero), zzz343, zzz344, zzz520, zzz521, zzz52200, zzz523, zzz524, zzz31, Succ(zzz690), h) → new_mkVBalBranch(zzz31, Branch(zzz520, zzz521, Neg(Succ(zzz52200)), zzz523, zzz524), zzz343, h)
new_mkVBalBranch(zzz31, Branch(zzz520, zzz521, Neg(Zero), zzz523, zzz524), Branch(zzz340, zzz341, Pos(Succ(zzz34200)), zzz343, zzz344), h) → new_mkVBalBranch(zzz31, Branch(zzz520, zzz521, Neg(Zero), zzz523, zzz524), zzz343, h)
new_mkVBalBranch3MkVBalBranch1(zzz340, zzz341, zzz34200, zzz343, zzz344, zzz520, zzz521, zzz52200, zzz523, zzz524, zzz31, Zero, h) → new_mkVBalBranch3MkVBalBranch17(zzz340, zzz341, zzz34200, zzz343, zzz344, zzz520, zzz521, zzz52200, zzz523, zzz524, zzz31, h)
new_mkVBalBranch3MkVBalBranch16(zzz1702, zzz1703, zzz1704, zzz1705, zzz1706, zzz1707, zzz1708, zzz1709, zzz1710, zzz1711, zzz1712, Succ(zzz17130), Succ(zzz17140), bd) → new_mkVBalBranch3MkVBalBranch16(zzz1702, zzz1703, zzz1704, zzz1705, zzz1706, zzz1707, zzz1708, zzz1709, zzz1710, zzz1711, zzz1712, zzz17130, zzz17140, bd)
new_mkVBalBranch3MkVBalBranch25(zzz537, zzz538, zzz539, zzz540, zzz541, zzz542, zzz543, zzz544, zzz545, zzz546, zzz547, Zero, Succ(zzz5490), bc) → new_mkVBalBranch(zzz547, Branch(zzz542, zzz543, Neg(Succ(Succ(zzz544))), zzz545, zzz546), zzz540, bc)
new_mkVBalBranch3MkVBalBranch10(zzz929, zzz930, zzz931, zzz932, zzz933, zzz934, zzz935, zzz936, zzz937, zzz938, zzz939, Succ(zzz10020), ba) → new_mkVBalBranch3MkVBalBranch11(zzz929, zzz930, zzz931, zzz932, zzz933, zzz934, zzz935, zzz936, zzz937, zzz938, zzz939, Succ(zzz10020), Succ(zzz936), ba)
new_mkVBalBranch3MkVBalBranch212(zzz818, zzz819, zzz820, zzz821, zzz822, zzz823, zzz824, zzz825, zzz826, zzz827, bf) → new_mkVBalBranch3MkVBalBranch14(zzz818, zzz819, zzz820, zzz821, zzz822, zzz823, zzz824, zzz825, zzz826, zzz827, new_primPlusNat2(new_primMulNat0(zzz820), Succ(zzz820)), bf)
new_mkVBalBranch3MkVBalBranch14(zzz818, zzz819, zzz820, zzz821, zzz822, zzz823, zzz824, zzz825, zzz826, zzz827, Succ(zzz8960), bf) → new_mkVBalBranch3MkVBalBranch16(zzz818, zzz819, zzz820, zzz821, zzz822, zzz823, zzz824, Zero, zzz825, zzz826, zzz827, Succ(Zero), Succ(zzz8960), bf)
new_mkVBalBranch3MkVBalBranch2(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344, zzz520, zzz521, zzz52200, zzz523, zzz524, zzz31, Succ(zzz680), h) → new_mkVBalBranch3MkVBalBranch1(zzz340, zzz341, zzz34200, zzz343, zzz344, zzz520, zzz521, zzz52200, zzz523, zzz524, zzz31, new_primPlusNat2(new_primMulNat0(zzz34200), Succ(zzz34200)), h)
new_mkVBalBranch3MkVBalBranch24(zzz340, zzz341, Neg(Succ(Succ(Succ(zzz3420000)))), zzz343, zzz344, zzz520, zzz521, Succ(zzz522000), zzz523, zzz524, zzz31, Succ(Succ(zzz6900)), h) → new_mkVBalBranch3MkVBalBranch25(zzz340, zzz341, Succ(Succ(zzz3420000)), zzz343, zzz344, zzz520, zzz521, zzz522000, zzz523, zzz524, zzz31, Succ(zzz3420000), Succ(Succ(new_primPlusNat2(zzz6900, zzz522000))), h)
new_mkVBalBranch3MkVBalBranch2(zzz340, zzz341, Pos(Succ(zzz34200)), zzz343, zzz344, zzz520, zzz521, zzz52200, zzz523, zzz524, zzz31, Zero, h) → new_mkVBalBranch3MkVBalBranch20(zzz340, zzz341, zzz34200, zzz343, zzz344, zzz520, zzz521, zzz52200, zzz523, zzz524, zzz31, zzz52200, zzz34200, h)
new_mkVBalBranch3MkVBalBranch24(zzz340, zzz341, Neg(Zero), zzz343, zzz344, zzz520, zzz521, zzz52200, zzz523, zzz524, zzz31, Zero, h) → new_mkVBalBranch3MkVBalBranch210(zzz340, zzz341, zzz343, zzz344, zzz520, zzz521, zzz52200, zzz523, zzz524, zzz31, h)
new_mkVBalBranch3MkVBalBranch24(zzz340, zzz341, Neg(Succ(Succ(Zero))), zzz343, zzz344, zzz520, zzz521, Succ(zzz522000), zzz523, zzz524, zzz31, Succ(Succ(zzz6900)), h) → new_mkVBalBranch3MkVBalBranch25(zzz340, zzz341, Succ(Zero), zzz343, zzz344, zzz520, zzz521, zzz522000, zzz523, zzz524, zzz31, Zero, Succ(Succ(new_primPlusNat2(zzz6900, zzz522000))), h)
new_mkVBalBranch3MkVBalBranch23(zzz929, zzz930, zzz931, zzz932, zzz933, zzz934, zzz935, zzz936, zzz937, zzz938, zzz939, ba) → new_mkVBalBranch3MkVBalBranch10(zzz929, zzz930, zzz931, zzz932, zzz933, zzz934, zzz935, zzz936, zzz937, zzz938, zzz939, new_primPlusNat2(new_primMulNat0(zzz931), Succ(zzz931)), ba)
new_mkVBalBranch3MkVBalBranch2(zzz340, zzz341, Neg(Zero), zzz343, zzz344, zzz520, zzz521, zzz52200, zzz523, zzz524, zzz31, Succ(zzz680), h) → new_mkVBalBranch(zzz31, zzz524, Branch(zzz340, zzz341, Neg(Zero), zzz343, zzz344), h)
new_mkVBalBranch3MkVBalBranch16(zzz1702, zzz1703, zzz1704, zzz1705, zzz1706, zzz1707, zzz1708, zzz1709, zzz1710, zzz1711, zzz1712, Zero, Succ(zzz17140), bd) → new_mkVBalBranch(zzz1712, zzz1711, Branch(zzz1702, zzz1703, Neg(Succ(zzz1704)), zzz1705, zzz1706), bd)
new_mkVBalBranch3MkVBalBranch10(zzz929, zzz930, zzz931, zzz932, zzz933, zzz934, zzz935, zzz936, zzz937, zzz938, zzz939, Zero, ba) → new_mkVBalBranch3MkVBalBranch11(zzz929, zzz930, zzz931, zzz932, zzz933, zzz934, zzz935, zzz936, zzz937, zzz938, zzz939, Zero, Succ(zzz936), ba)
new_mkVBalBranch3MkVBalBranch2(zzz340, zzz341, Pos(Zero), zzz343, zzz344, zzz520, zzz521, zzz52200, zzz523, zzz524, zzz31, Zero, h) → new_mkVBalBranch3MkVBalBranch21(zzz340, zzz341, zzz343, zzz344, zzz520, zzz521, zzz52200, zzz523, zzz524, zzz31, h)
new_mkVBalBranch3MkVBalBranch25(zzz537, zzz538, zzz539, zzz540, zzz541, zzz542, zzz543, zzz544, zzz545, zzz546, zzz547, Zero, Zero, bc) → new_mkVBalBranch3MkVBalBranch211(zzz537, zzz538, zzz539, zzz540, zzz541, zzz542, zzz543, zzz544, zzz545, zzz546, zzz547, bc)
new_mkVBalBranch3MkVBalBranch22(zzz340, zzz341, Succ(zzz34200), zzz343, zzz344, zzz520, zzz521, zzz52200, zzz523, zzz524, zzz31, h) → new_mkVBalBranch3MkVBalBranch1(zzz340, zzz341, zzz34200, zzz343, zzz344, zzz520, zzz521, zzz52200, zzz523, zzz524, zzz31, new_primPlusNat2(new_primPlusNat3(Succ(new_primPlusNat3(new_primPlusNat1(zzz34200), zzz34200)), Succ(zzz34200)), Succ(zzz34200)), h)

The TRS R consists of the following rules:

new_primPlusNat1(Zero) → Zero
new_primMulNat0(zzz6200) → new_primPlusNat3(Succ(new_primPlusNat3(new_primPlusNat1(zzz6200), zzz6200)), Succ(zzz6200))
new_primPlusNat2(Succ(zzz900), Succ(zzz9100)) → Succ(Succ(new_primPlusNat2(zzz900, zzz9100)))
new_primPlusNat3(zzz90, Succ(zzz910)) → Succ(Succ(new_primPlusNat2(zzz90, zzz910)))
new_primPlusNat3(zzz90, Zero) → Succ(zzz90)
new_primMulNat1(zzz34200) → new_primPlusNat2(new_primMulNat0(zzz34200), Succ(zzz34200))
new_primPlusNat2(Zero, Zero) → Zero
new_primPlusNat1(Succ(zzz62000)) → Succ(Succ(new_primPlusNat1(zzz62000)))
new_primPlusNat2(Succ(zzz900), Zero) → Succ(zzz900)
new_primPlusNat2(Zero, Succ(zzz9100)) → Succ(zzz9100)

The set Q consists of the following terms:

new_primPlusNat2(Zero, Succ(x0))
new_primMulNat1(x0)
new_primMulNat0(x0)
new_primPlusNat3(x0, Succ(x1))
new_primPlusNat2(Succ(x0), Succ(x1))
new_primPlusNat3(x0, Zero)
new_primPlusNat1(Zero)
new_primPlusNat2(Zero, Zero)
new_primPlusNat1(Succ(x0))
new_primPlusNat2(Succ(x0), Zero)

We have to consider all minimal (P,Q,R)-chains.
By rewriting [15] the rule new_mkVBalBranch3MkVBalBranch2(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344, zzz520, zzz521, zzz52200, zzz523, zzz524, zzz31, Succ(zzz680), h) → new_mkVBalBranch3MkVBalBranch1(zzz340, zzz341, zzz34200, zzz343, zzz344, zzz520, zzz521, zzz52200, zzz523, zzz524, zzz31, new_primPlusNat2(new_primMulNat0(zzz34200), Succ(zzz34200)), h) at position [11,0] we obtained the following new rules:

new_mkVBalBranch3MkVBalBranch2(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344, zzz520, zzz521, zzz52200, zzz523, zzz524, zzz31, Succ(zzz680), h) → new_mkVBalBranch3MkVBalBranch1(zzz340, zzz341, zzz34200, zzz343, zzz344, zzz520, zzz521, zzz52200, zzz523, zzz524, zzz31, new_primPlusNat2(new_primPlusNat3(Succ(new_primPlusNat3(new_primPlusNat1(zzz34200), zzz34200)), Succ(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
                                    ↳ DependencyGraphProof
                                      ↳ QDP
                                        ↳ Rewriting
                                          ↳ QDP
                                            ↳ Rewriting
                                              ↳ QDP
                                                ↳ Rewriting
                                                  ↳ QDP
                                                    ↳ Rewriting
                                                      ↳ QDP
                                                        ↳ Rewriting
                                                          ↳ QDP
                                                            ↳ Rewriting
                                                              ↳ QDP
                                                                ↳ Rewriting
                                                                  ↳ QDP
                                                                    ↳ Rewriting
                                                                      ↳ QDP
                                                                        ↳ Rewriting
                                                                          ↳ QDP
                                                                            ↳ Rewriting
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP

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

new_mkVBalBranch3MkVBalBranch11(zzz2033, zzz2034, zzz2035, zzz2036, zzz2037, zzz2038, zzz2039, zzz2040, zzz2041, zzz2042, zzz2043, Zero, Succ(zzz20450), bb) → new_mkVBalBranch(zzz2043, zzz2042, Branch(zzz2033, zzz2034, Pos(Succ(zzz2035)), zzz2036, zzz2037), bb)
new_mkVBalBranch3MkVBalBranch2(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344, zzz520, zzz521, zzz52200, zzz523, zzz524, zzz31, Succ(zzz680), h) → new_mkVBalBranch3MkVBalBranch1(zzz340, zzz341, zzz34200, zzz343, zzz344, zzz520, zzz521, zzz52200, zzz523, zzz524, zzz31, new_primPlusNat2(new_primPlusNat3(Succ(new_primPlusNat3(new_primPlusNat1(zzz34200), zzz34200)), Succ(zzz34200)), Succ(zzz34200)), h)
new_mkVBalBranch3MkVBalBranch26(zzz1133, zzz1134, zzz1135, zzz1136, zzz1137, zzz1138, zzz1139, zzz1140, zzz1141, zzz1142, Succ(zzz11430), Succ(zzz11440), be) → new_mkVBalBranch3MkVBalBranch26(zzz1133, zzz1134, zzz1135, zzz1136, zzz1137, zzz1138, zzz1139, zzz1140, zzz1141, zzz1142, zzz11430, zzz11440, be)
new_mkVBalBranch3MkVBalBranch24(zzz340, zzz341, Neg(Succ(Succ(Succ(zzz3420000)))), zzz343, zzz344, zzz520, zzz521, Zero, zzz523, zzz524, zzz31, Succ(Zero), h) → new_mkVBalBranch3MkVBalBranch26(zzz340, zzz341, Succ(Succ(zzz3420000)), zzz343, zzz344, zzz520, zzz521, zzz523, zzz524, zzz31, Succ(zzz3420000), Zero, h)
new_mkVBalBranch3MkVBalBranch24(zzz340, zzz341, Neg(Succ(Zero)), zzz343, zzz344, zzz520, zzz521, Zero, zzz523, zzz524, zzz31, Zero, h) → new_mkVBalBranch3MkVBalBranch29(zzz340, zzz341, Zero, zzz343, zzz344, zzz520, zzz521, zzz523, zzz524, zzz31, h)
new_mkVBalBranch3MkVBalBranch20(zzz929, zzz930, zzz931, zzz932, zzz933, zzz934, zzz935, zzz936, zzz937, zzz938, zzz939, Zero, Succ(zzz9410), ba) → new_mkVBalBranch(zzz939, Branch(zzz934, zzz935, Pos(Succ(zzz936)), zzz937, zzz938), zzz932, ba)
new_mkVBalBranch3MkVBalBranch17(zzz340, zzz341, zzz34200, zzz343, zzz344, zzz520, zzz521, zzz52200, zzz523, zzz524, zzz31, h) → new_mkVBalBranch(zzz31, zzz524, Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), h)
new_mkVBalBranch3MkVBalBranch26(zzz1133, zzz1134, zzz1135, zzz1136, zzz1137, zzz1138, zzz1139, zzz1140, zzz1141, zzz1142, Zero, Zero, be) → new_mkVBalBranch3MkVBalBranch29(zzz1133, zzz1134, zzz1135, zzz1136, zzz1137, zzz1138, zzz1139, zzz1140, zzz1141, zzz1142, be)
new_mkVBalBranch3MkVBalBranch20(zzz929, zzz930, zzz931, zzz932, zzz933, zzz934, zzz935, zzz936, zzz937, zzz938, zzz939, Zero, Zero, ba) → new_mkVBalBranch3MkVBalBranch23(zzz929, zzz930, zzz931, zzz932, zzz933, zzz934, zzz935, zzz936, zzz937, zzz938, zzz939, ba)
new_mkVBalBranch3MkVBalBranch20(zzz929, zzz930, zzz931, zzz932, zzz933, zzz934, zzz935, zzz936, zzz937, zzz938, zzz939, Succ(zzz9400), Zero, ba) → new_mkVBalBranch3MkVBalBranch10(zzz929, zzz930, zzz931, zzz932, zzz933, zzz934, zzz935, zzz936, zzz937, zzz938, zzz939, new_primPlusNat2(new_primMulNat0(zzz931), Succ(zzz931)), ba)
new_mkVBalBranch3MkVBalBranch24(zzz340, zzz341, Neg(Succ(Succ(Zero))), zzz343, zzz344, zzz520, zzz521, Succ(zzz522000), zzz523, zzz524, zzz31, Succ(Zero), h) → new_mkVBalBranch3MkVBalBranch25(zzz340, zzz341, Succ(Zero), zzz343, zzz344, zzz520, zzz521, zzz522000, zzz523, zzz524, zzz31, Zero, Succ(zzz522000), h)
new_mkVBalBranch3MkVBalBranch24(zzz340, zzz341, Neg(Succ(Succ(Succ(zzz3420000)))), zzz343, zzz344, zzz520, zzz521, Succ(zzz522000), zzz523, zzz524, zzz31, Succ(Zero), h) → new_mkVBalBranch3MkVBalBranch25(zzz340, zzz341, Succ(Succ(zzz3420000)), zzz343, zzz344, zzz520, zzz521, zzz522000, zzz523, zzz524, zzz31, Succ(zzz3420000), Succ(zzz522000), h)
new_mkVBalBranch3MkVBalBranch20(zzz929, zzz930, zzz931, zzz932, zzz933, zzz934, zzz935, zzz936, zzz937, zzz938, zzz939, Succ(zzz9400), Succ(zzz9410), ba) → new_mkVBalBranch3MkVBalBranch20(zzz929, zzz930, zzz931, zzz932, zzz933, zzz934, zzz935, zzz936, zzz937, zzz938, zzz939, zzz9400, zzz9410, ba)
new_mkVBalBranch3MkVBalBranch24(zzz340, zzz341, Neg(Succ(Succ(zzz342000))), zzz343, zzz344, zzz520, zzz521, Succ(zzz522000), zzz523, zzz524, zzz31, Zero, h) → new_mkVBalBranch3MkVBalBranch25(zzz340, zzz341, Succ(zzz342000), zzz343, zzz344, zzz520, zzz521, zzz522000, zzz523, zzz524, zzz31, zzz342000, zzz522000, h)
new_mkVBalBranch3MkVBalBranch26(zzz1133, zzz1134, zzz1135, zzz1136, zzz1137, zzz1138, zzz1139, zzz1140, zzz1141, zzz1142, Succ(zzz11430), Zero, be) → new_mkVBalBranch3MkVBalBranch212(zzz1133, zzz1134, zzz1135, zzz1136, zzz1137, zzz1138, zzz1139, zzz1140, zzz1141, zzz1142, be)
new_mkVBalBranch(zzz31, Branch(zzz520, zzz521, Pos(Succ(zzz52200)), zzz523, zzz524), Branch(zzz340, zzz341, zzz342, zzz343, zzz344), h) → new_mkVBalBranch3MkVBalBranch2(zzz340, zzz341, zzz342, zzz343, zzz344, zzz520, zzz521, zzz52200, zzz523, zzz524, zzz31, new_primPlusNat3(Succ(new_primPlusNat3(new_primPlusNat1(zzz52200), zzz52200)), Succ(zzz52200)), h)
new_mkVBalBranch3MkVBalBranch11(zzz2033, zzz2034, zzz2035, zzz2036, zzz2037, zzz2038, zzz2039, zzz2040, zzz2041, zzz2042, zzz2043, Succ(zzz20440), Succ(zzz20450), bb) → new_mkVBalBranch3MkVBalBranch11(zzz2033, zzz2034, zzz2035, zzz2036, zzz2037, zzz2038, zzz2039, zzz2040, zzz2041, zzz2042, zzz2043, zzz20440, zzz20450, bb)
new_mkVBalBranch3MkVBalBranch25(zzz537, zzz538, zzz539, zzz540, zzz541, zzz542, zzz543, zzz544, zzz545, zzz546, zzz547, Succ(zzz5480), Succ(zzz5490), bc) → new_mkVBalBranch3MkVBalBranch25(zzz537, zzz538, zzz539, zzz540, zzz541, zzz542, zzz543, zzz544, zzz545, zzz546, zzz547, zzz5480, zzz5490, bc)
new_mkVBalBranch3MkVBalBranch2(zzz340, zzz341, Neg(zzz3420), zzz343, zzz344, zzz520, zzz521, zzz52200, zzz523, zzz524, zzz31, Zero, h) → new_mkVBalBranch3MkVBalBranch22(zzz340, zzz341, zzz3420, zzz343, zzz344, zzz520, zzz521, zzz52200, zzz523, zzz524, zzz31, h)
new_mkVBalBranch(zzz31, Branch(zzz520, zzz521, Neg(Succ(zzz52200)), zzz523, zzz524), Branch(zzz340, zzz341, zzz342, zzz343, zzz344), h) → new_mkVBalBranch3MkVBalBranch24(zzz340, zzz341, zzz342, zzz343, zzz344, zzz520, zzz521, zzz52200, zzz523, zzz524, zzz31, new_primPlusNat3(Succ(new_primPlusNat3(new_primPlusNat1(zzz52200), zzz52200)), Succ(zzz52200)), h)
new_mkVBalBranch3MkVBalBranch24(zzz340, zzz341, Neg(Succ(Zero)), zzz343, zzz344, zzz520, zzz521, Succ(zzz522000), zzz523, zzz524, zzz31, Zero, h) → new_mkVBalBranch3MkVBalBranch28(zzz340, zzz341, zzz343, zzz344, zzz520, zzz521, Succ(zzz522000), zzz523, zzz524, zzz31, h)
new_mkVBalBranch3MkVBalBranch24(zzz340, zzz341, Neg(Succ(Succ(zzz342000))), zzz343, zzz344, zzz520, zzz521, Zero, zzz523, zzz524, zzz31, Zero, h) → new_mkVBalBranch3MkVBalBranch14(zzz340, zzz341, Succ(zzz342000), zzz343, zzz344, zzz520, zzz521, zzz523, zzz524, zzz31, new_primMulNat1(Succ(zzz342000)), h)
new_mkVBalBranch3MkVBalBranch210(zzz340, zzz341, zzz343, zzz344, zzz520, zzz521, zzz52200, zzz523, zzz524, zzz31, h) → new_mkVBalBranch(zzz31, Branch(zzz520, zzz521, Neg(Succ(zzz52200)), zzz523, zzz524), zzz343, h)
new_mkVBalBranch3MkVBalBranch26(zzz1133, zzz1134, zzz1135, zzz1136, zzz1137, zzz1138, zzz1139, zzz1140, zzz1141, zzz1142, Zero, Succ(zzz11440), be) → new_mkVBalBranch(zzz1142, Branch(zzz1138, zzz1139, Neg(Succ(Zero)), zzz1140, zzz1141), zzz1136, be)
new_mkVBalBranch3MkVBalBranch24(zzz340, zzz341, Neg(Succ(Succ(Zero))), zzz343, zzz344, zzz520, zzz521, Zero, zzz523, zzz524, zzz31, Succ(Zero), h) → new_mkVBalBranch3MkVBalBranch26(zzz340, zzz341, Succ(Zero), zzz343, zzz344, zzz520, zzz521, zzz523, zzz524, zzz31, Zero, Zero, h)
new_mkVBalBranch(zzz31, Branch(zzz520, zzz521, Pos(Zero), zzz523, zzz524), Branch(zzz340, zzz341, Pos(Succ(zzz34200)), zzz343, zzz344), h) → new_mkVBalBranch(zzz31, Branch(zzz520, zzz521, Pos(Zero), zzz523, zzz524), zzz343, h)
new_mkVBalBranch3MkVBalBranch29(zzz818, zzz819, zzz820, zzz821, zzz822, zzz823, zzz824, zzz825, zzz826, zzz827, bf) → new_mkVBalBranch3MkVBalBranch14(zzz818, zzz819, zzz820, zzz821, zzz822, zzz823, zzz824, zzz825, zzz826, zzz827, new_primMulNat1(zzz820), bf)
new_mkVBalBranch3MkVBalBranch2(zzz340, zzz341, Pos(Zero), zzz343, zzz344, zzz520, zzz521, zzz52200, zzz523, zzz524, zzz31, Succ(zzz680), h) → new_mkVBalBranch(zzz31, zzz524, Branch(zzz340, zzz341, Pos(Zero), zzz343, zzz344), h)
new_mkVBalBranch3MkVBalBranch21(zzz340, zzz341, zzz343, zzz344, zzz520, zzz521, zzz52200, zzz523, zzz524, zzz31, h) → new_mkVBalBranch(zzz31, zzz524, Branch(zzz340, zzz341, Pos(Zero), zzz343, zzz344), h)
new_mkVBalBranch3MkVBalBranch24(zzz340, zzz341, Pos(zzz3420), zzz343, zzz344, zzz520, zzz521, zzz52200, zzz523, zzz524, zzz31, Zero, h) → new_mkVBalBranch3MkVBalBranch27(zzz340, zzz341, zzz3420, zzz343, zzz344, zzz520, zzz521, zzz52200, zzz523, zzz524, zzz31, h)
new_mkVBalBranch3MkVBalBranch211(zzz537, zzz538, zzz539, zzz540, zzz541, zzz542, zzz543, zzz544, zzz545, zzz546, zzz547, bc) → new_mkVBalBranch3MkVBalBranch15(zzz537, zzz538, zzz539, zzz540, zzz541, zzz542, zzz543, zzz544, zzz545, zzz546, zzz547, new_primMulNat1(zzz539), bc)
new_mkVBalBranch3MkVBalBranch15(zzz537, zzz538, zzz539, zzz540, zzz541, zzz542, zzz543, zzz544, zzz545, zzz546, zzz547, Succ(zzz6990), bc) → new_mkVBalBranch3MkVBalBranch16(zzz537, zzz538, zzz539, zzz540, zzz541, zzz542, zzz543, Succ(zzz544), zzz545, zzz546, zzz547, Succ(Succ(zzz544)), Succ(zzz6990), bc)
new_mkVBalBranch3MkVBalBranch24(zzz340, zzz341, Neg(Succ(Succ(Succ(zzz3420000)))), zzz343, zzz344, zzz520, zzz521, Zero, zzz523, zzz524, zzz31, Succ(Succ(zzz6900)), h) → new_mkVBalBranch3MkVBalBranch26(zzz340, zzz341, Succ(Succ(zzz3420000)), zzz343, zzz344, zzz520, zzz521, zzz523, zzz524, zzz31, Succ(zzz3420000), Succ(zzz6900), h)
new_mkVBalBranch(zzz31, Branch(zzz520, zzz521, Neg(Zero), zzz523, zzz524), Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), h) → new_mkVBalBranch3MkVBalBranch13(zzz340, zzz341, zzz34200, zzz343, zzz344, zzz520, zzz521, zzz523, zzz524, zzz31, new_primPlusNat2(new_primMulNat0(zzz34200), Succ(zzz34200)), h)
new_mkVBalBranch3MkVBalBranch27(zzz340, zzz341, zzz3420, zzz343, zzz344, zzz520, zzz521, zzz52200, zzz523, zzz524, zzz31, h) → new_mkVBalBranch(zzz31, Branch(zzz520, zzz521, Neg(Succ(zzz52200)), zzz523, zzz524), zzz343, h)
new_mkVBalBranch3MkVBalBranch24(zzz340, zzz341, Pos(zzz3420), zzz343, zzz344, zzz520, zzz521, zzz52200, zzz523, zzz524, zzz31, Succ(zzz690), h) → new_mkVBalBranch(zzz31, Branch(zzz520, zzz521, Neg(Succ(zzz52200)), zzz523, zzz524), zzz343, h)
new_mkVBalBranch3MkVBalBranch12(zzz340, zzz341, zzz34200, zzz343, zzz344, zzz520, zzz521, zzz523, zzz524, zzz31, Succ(zzz1250), h) → new_mkVBalBranch(zzz31, zzz524, Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), h)
new_mkVBalBranch3MkVBalBranch28(zzz340, zzz341, zzz343, zzz344, zzz520, zzz521, zzz52200, zzz523, zzz524, zzz31, h) → new_mkVBalBranch(zzz31, Branch(zzz520, zzz521, Neg(Succ(zzz52200)), zzz523, zzz524), zzz343, h)
new_mkVBalBranch3MkVBalBranch25(zzz537, zzz538, zzz539, zzz540, zzz541, zzz542, zzz543, zzz544, zzz545, zzz546, zzz547, Succ(zzz5480), Zero, bc) → new_mkVBalBranch3MkVBalBranch15(zzz537, zzz538, zzz539, zzz540, zzz541, zzz542, zzz543, zzz544, zzz545, zzz546, zzz547, new_primMulNat1(zzz539), bc)
new_mkVBalBranch3MkVBalBranch24(zzz340, zzz341, Neg(Succ(Succ(Zero))), zzz343, zzz344, zzz520, zzz521, Zero, zzz523, zzz524, zzz31, Succ(Succ(zzz6900)), h) → new_mkVBalBranch3MkVBalBranch26(zzz340, zzz341, Succ(Zero), zzz343, zzz344, zzz520, zzz521, zzz523, zzz524, zzz31, Zero, Succ(zzz6900), h)
new_mkVBalBranch(zzz31, Branch(zzz520, zzz521, Pos(Zero), zzz523, zzz524), Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), h) → new_mkVBalBranch3MkVBalBranch12(zzz340, zzz341, zzz34200, zzz343, zzz344, zzz520, zzz521, zzz523, zzz524, zzz31, new_primPlusNat2(new_primMulNat0(zzz34200), Succ(zzz34200)), h)
new_mkVBalBranch3MkVBalBranch22(zzz340, zzz341, Zero, zzz343, zzz344, zzz520, zzz521, zzz52200, zzz523, zzz524, zzz31, h) → new_mkVBalBranch(zzz31, zzz524, Branch(zzz340, zzz341, Neg(Zero), zzz343, zzz344), h)
new_mkVBalBranch3MkVBalBranch1(zzz340, zzz341, zzz34200, zzz343, zzz344, zzz520, zzz521, zzz52200, zzz523, zzz524, zzz31, Succ(zzz1430), h) → new_mkVBalBranch(zzz31, zzz524, Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), h)
new_mkVBalBranch3MkVBalBranch24(zzz340, zzz341, Neg(Succ(Zero)), zzz343, zzz344, zzz520, zzz521, zzz52200, zzz523, zzz524, zzz31, Succ(zzz690), h) → new_mkVBalBranch(zzz31, Branch(zzz520, zzz521, Neg(Succ(zzz52200)), zzz523, zzz524), zzz343, h)
new_mkVBalBranch3MkVBalBranch13(zzz340, zzz341, zzz34200, zzz343, zzz344, zzz520, zzz521, zzz523, zzz524, zzz31, Succ(zzz1290), h) → new_mkVBalBranch(zzz31, zzz524, Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), h)
new_mkVBalBranch3MkVBalBranch2(zzz340, zzz341, Pos(Succ(zzz34200)), zzz343, zzz344, zzz520, zzz521, zzz52200, zzz523, zzz524, zzz31, Succ(zzz680), h) → new_mkVBalBranch3MkVBalBranch20(zzz340, zzz341, zzz34200, zzz343, zzz344, zzz520, zzz521, zzz52200, zzz523, zzz524, zzz31, Succ(new_primPlusNat2(zzz680, zzz52200)), zzz34200, h)
new_mkVBalBranch(zzz31, Branch(zzz520, zzz521, Neg(Zero), zzz523, zzz524), Branch(zzz340, zzz341, Pos(Succ(zzz34200)), zzz343, zzz344), h) → new_mkVBalBranch(zzz31, Branch(zzz520, zzz521, Neg(Zero), zzz523, zzz524), zzz343, h)
new_mkVBalBranch3MkVBalBranch24(zzz340, zzz341, Neg(Zero), zzz343, zzz344, zzz520, zzz521, zzz52200, zzz523, zzz524, zzz31, Succ(zzz690), h) → new_mkVBalBranch(zzz31, Branch(zzz520, zzz521, Neg(Succ(zzz52200)), zzz523, zzz524), zzz343, h)
new_mkVBalBranch3MkVBalBranch1(zzz340, zzz341, zzz34200, zzz343, zzz344, zzz520, zzz521, zzz52200, zzz523, zzz524, zzz31, Zero, h) → new_mkVBalBranch3MkVBalBranch17(zzz340, zzz341, zzz34200, zzz343, zzz344, zzz520, zzz521, zzz52200, zzz523, zzz524, zzz31, h)
new_mkVBalBranch3MkVBalBranch16(zzz1702, zzz1703, zzz1704, zzz1705, zzz1706, zzz1707, zzz1708, zzz1709, zzz1710, zzz1711, zzz1712, Succ(zzz17130), Succ(zzz17140), bd) → new_mkVBalBranch3MkVBalBranch16(zzz1702, zzz1703, zzz1704, zzz1705, zzz1706, zzz1707, zzz1708, zzz1709, zzz1710, zzz1711, zzz1712, zzz17130, zzz17140, bd)
new_mkVBalBranch3MkVBalBranch25(zzz537, zzz538, zzz539, zzz540, zzz541, zzz542, zzz543, zzz544, zzz545, zzz546, zzz547, Zero, Succ(zzz5490), bc) → new_mkVBalBranch(zzz547, Branch(zzz542, zzz543, Neg(Succ(Succ(zzz544))), zzz545, zzz546), zzz540, bc)
new_mkVBalBranch3MkVBalBranch212(zzz818, zzz819, zzz820, zzz821, zzz822, zzz823, zzz824, zzz825, zzz826, zzz827, bf) → new_mkVBalBranch3MkVBalBranch14(zzz818, zzz819, zzz820, zzz821, zzz822, zzz823, zzz824, zzz825, zzz826, zzz827, new_primPlusNat2(new_primMulNat0(zzz820), Succ(zzz820)), bf)
new_mkVBalBranch3MkVBalBranch10(zzz929, zzz930, zzz931, zzz932, zzz933, zzz934, zzz935, zzz936, zzz937, zzz938, zzz939, Succ(zzz10020), ba) → new_mkVBalBranch3MkVBalBranch11(zzz929, zzz930, zzz931, zzz932, zzz933, zzz934, zzz935, zzz936, zzz937, zzz938, zzz939, Succ(zzz10020), Succ(zzz936), ba)
new_mkVBalBranch3MkVBalBranch14(zzz818, zzz819, zzz820, zzz821, zzz822, zzz823, zzz824, zzz825, zzz826, zzz827, Succ(zzz8960), bf) → new_mkVBalBranch3MkVBalBranch16(zzz818, zzz819, zzz820, zzz821, zzz822, zzz823, zzz824, Zero, zzz825, zzz826, zzz827, Succ(Zero), Succ(zzz8960), bf)
new_mkVBalBranch3MkVBalBranch24(zzz340, zzz341, Neg(Succ(Succ(Succ(zzz3420000)))), zzz343, zzz344, zzz520, zzz521, Succ(zzz522000), zzz523, zzz524, zzz31, Succ(Succ(zzz6900)), h) → new_mkVBalBranch3MkVBalBranch25(zzz340, zzz341, Succ(Succ(zzz3420000)), zzz343, zzz344, zzz520, zzz521, zzz522000, zzz523, zzz524, zzz31, Succ(zzz3420000), Succ(Succ(new_primPlusNat2(zzz6900, zzz522000))), h)
new_mkVBalBranch3MkVBalBranch2(zzz340, zzz341, Pos(Succ(zzz34200)), zzz343, zzz344, zzz520, zzz521, zzz52200, zzz523, zzz524, zzz31, Zero, h) → new_mkVBalBranch3MkVBalBranch20(zzz340, zzz341, zzz34200, zzz343, zzz344, zzz520, zzz521, zzz52200, zzz523, zzz524, zzz31, zzz52200, zzz34200, h)
new_mkVBalBranch3MkVBalBranch24(zzz340, zzz341, Neg(Zero), zzz343, zzz344, zzz520, zzz521, zzz52200, zzz523, zzz524, zzz31, Zero, h) → new_mkVBalBranch3MkVBalBranch210(zzz340, zzz341, zzz343, zzz344, zzz520, zzz521, zzz52200, zzz523, zzz524, zzz31, h)
new_mkVBalBranch3MkVBalBranch24(zzz340, zzz341, Neg(Succ(Succ(Zero))), zzz343, zzz344, zzz520, zzz521, Succ(zzz522000), zzz523, zzz524, zzz31, Succ(Succ(zzz6900)), h) → new_mkVBalBranch3MkVBalBranch25(zzz340, zzz341, Succ(Zero), zzz343, zzz344, zzz520, zzz521, zzz522000, zzz523, zzz524, zzz31, Zero, Succ(Succ(new_primPlusNat2(zzz6900, zzz522000))), h)
new_mkVBalBranch3MkVBalBranch23(zzz929, zzz930, zzz931, zzz932, zzz933, zzz934, zzz935, zzz936, zzz937, zzz938, zzz939, ba) → new_mkVBalBranch3MkVBalBranch10(zzz929, zzz930, zzz931, zzz932, zzz933, zzz934, zzz935, zzz936, zzz937, zzz938, zzz939, new_primPlusNat2(new_primMulNat0(zzz931), Succ(zzz931)), ba)
new_mkVBalBranch3MkVBalBranch2(zzz340, zzz341, Neg(Zero), zzz343, zzz344, zzz520, zzz521, zzz52200, zzz523, zzz524, zzz31, Succ(zzz680), h) → new_mkVBalBranch(zzz31, zzz524, Branch(zzz340, zzz341, Neg(Zero), zzz343, zzz344), h)
new_mkVBalBranch3MkVBalBranch16(zzz1702, zzz1703, zzz1704, zzz1705, zzz1706, zzz1707, zzz1708, zzz1709, zzz1710, zzz1711, zzz1712, Zero, Succ(zzz17140), bd) → new_mkVBalBranch(zzz1712, zzz1711, Branch(zzz1702, zzz1703, Neg(Succ(zzz1704)), zzz1705, zzz1706), bd)
new_mkVBalBranch3MkVBalBranch10(zzz929, zzz930, zzz931, zzz932, zzz933, zzz934, zzz935, zzz936, zzz937, zzz938, zzz939, Zero, ba) → new_mkVBalBranch3MkVBalBranch11(zzz929, zzz930, zzz931, zzz932, zzz933, zzz934, zzz935, zzz936, zzz937, zzz938, zzz939, Zero, Succ(zzz936), ba)
new_mkVBalBranch3MkVBalBranch22(zzz340, zzz341, Succ(zzz34200), zzz343, zzz344, zzz520, zzz521, zzz52200, zzz523, zzz524, zzz31, h) → new_mkVBalBranch3MkVBalBranch1(zzz340, zzz341, zzz34200, zzz343, zzz344, zzz520, zzz521, zzz52200, zzz523, zzz524, zzz31, new_primPlusNat2(new_primPlusNat3(Succ(new_primPlusNat3(new_primPlusNat1(zzz34200), zzz34200)), Succ(zzz34200)), Succ(zzz34200)), h)
new_mkVBalBranch3MkVBalBranch25(zzz537, zzz538, zzz539, zzz540, zzz541, zzz542, zzz543, zzz544, zzz545, zzz546, zzz547, Zero, Zero, bc) → new_mkVBalBranch3MkVBalBranch211(zzz537, zzz538, zzz539, zzz540, zzz541, zzz542, zzz543, zzz544, zzz545, zzz546, zzz547, bc)
new_mkVBalBranch3MkVBalBranch2(zzz340, zzz341, Pos(Zero), zzz343, zzz344, zzz520, zzz521, zzz52200, zzz523, zzz524, zzz31, Zero, h) → new_mkVBalBranch3MkVBalBranch21(zzz340, zzz341, zzz343, zzz344, zzz520, zzz521, zzz52200, zzz523, zzz524, zzz31, h)

The TRS R consists of the following rules:

new_primPlusNat1(Zero) → Zero
new_primMulNat0(zzz6200) → new_primPlusNat3(Succ(new_primPlusNat3(new_primPlusNat1(zzz6200), zzz6200)), Succ(zzz6200))
new_primPlusNat2(Succ(zzz900), Succ(zzz9100)) → Succ(Succ(new_primPlusNat2(zzz900, zzz9100)))
new_primPlusNat3(zzz90, Succ(zzz910)) → Succ(Succ(new_primPlusNat2(zzz90, zzz910)))
new_primPlusNat3(zzz90, Zero) → Succ(zzz90)
new_primMulNat1(zzz34200) → new_primPlusNat2(new_primMulNat0(zzz34200), Succ(zzz34200))
new_primPlusNat2(Zero, Zero) → Zero
new_primPlusNat1(Succ(zzz62000)) → Succ(Succ(new_primPlusNat1(zzz62000)))
new_primPlusNat2(Succ(zzz900), Zero) → Succ(zzz900)
new_primPlusNat2(Zero, Succ(zzz9100)) → Succ(zzz9100)

The set Q consists of the following terms:

new_primPlusNat2(Zero, Succ(x0))
new_primMulNat1(x0)
new_primMulNat0(x0)
new_primPlusNat3(x0, Succ(x1))
new_primPlusNat2(Succ(x0), Succ(x1))
new_primPlusNat3(x0, Zero)
new_primPlusNat1(Zero)
new_primPlusNat2(Zero, Zero)
new_primPlusNat1(Succ(x0))
new_primPlusNat2(Succ(x0), Zero)

We have to consider all minimal (P,Q,R)-chains.
By rewriting [15] the rule new_mkVBalBranch3MkVBalBranch29(zzz818, zzz819, zzz820, zzz821, zzz822, zzz823, zzz824, zzz825, zzz826, zzz827, bf) → new_mkVBalBranch3MkVBalBranch14(zzz818, zzz819, zzz820, zzz821, zzz822, zzz823, zzz824, zzz825, zzz826, zzz827, new_primMulNat1(zzz820), bf) at position [10] we obtained the following new rules:

new_mkVBalBranch3MkVBalBranch29(zzz818, zzz819, zzz820, zzz821, zzz822, zzz823, zzz824, zzz825, zzz826, zzz827, bf) → new_mkVBalBranch3MkVBalBranch14(zzz818, zzz819, zzz820, zzz821, zzz822, zzz823, zzz824, zzz825, zzz826, zzz827, new_primPlusNat2(new_primMulNat0(zzz820), Succ(zzz820)), bf)



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

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

new_mkVBalBranch3MkVBalBranch11(zzz2033, zzz2034, zzz2035, zzz2036, zzz2037, zzz2038, zzz2039, zzz2040, zzz2041, zzz2042, zzz2043, Zero, Succ(zzz20450), bb) → new_mkVBalBranch(zzz2043, zzz2042, Branch(zzz2033, zzz2034, Pos(Succ(zzz2035)), zzz2036, zzz2037), bb)
new_mkVBalBranch3MkVBalBranch2(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344, zzz520, zzz521, zzz52200, zzz523, zzz524, zzz31, Succ(zzz680), h) → new_mkVBalBranch3MkVBalBranch1(zzz340, zzz341, zzz34200, zzz343, zzz344, zzz520, zzz521, zzz52200, zzz523, zzz524, zzz31, new_primPlusNat2(new_primPlusNat3(Succ(new_primPlusNat3(new_primPlusNat1(zzz34200), zzz34200)), Succ(zzz34200)), Succ(zzz34200)), h)
new_mkVBalBranch3MkVBalBranch26(zzz1133, zzz1134, zzz1135, zzz1136, zzz1137, zzz1138, zzz1139, zzz1140, zzz1141, zzz1142, Succ(zzz11430), Succ(zzz11440), be) → new_mkVBalBranch3MkVBalBranch26(zzz1133, zzz1134, zzz1135, zzz1136, zzz1137, zzz1138, zzz1139, zzz1140, zzz1141, zzz1142, zzz11430, zzz11440, be)
new_mkVBalBranch3MkVBalBranch24(zzz340, zzz341, Neg(Succ(Succ(Succ(zzz3420000)))), zzz343, zzz344, zzz520, zzz521, Zero, zzz523, zzz524, zzz31, Succ(Zero), h) → new_mkVBalBranch3MkVBalBranch26(zzz340, zzz341, Succ(Succ(zzz3420000)), zzz343, zzz344, zzz520, zzz521, zzz523, zzz524, zzz31, Succ(zzz3420000), Zero, h)
new_mkVBalBranch3MkVBalBranch24(zzz340, zzz341, Neg(Succ(Zero)), zzz343, zzz344, zzz520, zzz521, Zero, zzz523, zzz524, zzz31, Zero, h) → new_mkVBalBranch3MkVBalBranch29(zzz340, zzz341, Zero, zzz343, zzz344, zzz520, zzz521, zzz523, zzz524, zzz31, h)
new_mkVBalBranch3MkVBalBranch20(zzz929, zzz930, zzz931, zzz932, zzz933, zzz934, zzz935, zzz936, zzz937, zzz938, zzz939, Zero, Succ(zzz9410), ba) → new_mkVBalBranch(zzz939, Branch(zzz934, zzz935, Pos(Succ(zzz936)), zzz937, zzz938), zzz932, ba)
new_mkVBalBranch3MkVBalBranch17(zzz340, zzz341, zzz34200, zzz343, zzz344, zzz520, zzz521, zzz52200, zzz523, zzz524, zzz31, h) → new_mkVBalBranch(zzz31, zzz524, Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), h)
new_mkVBalBranch3MkVBalBranch26(zzz1133, zzz1134, zzz1135, zzz1136, zzz1137, zzz1138, zzz1139, zzz1140, zzz1141, zzz1142, Zero, Zero, be) → new_mkVBalBranch3MkVBalBranch29(zzz1133, zzz1134, zzz1135, zzz1136, zzz1137, zzz1138, zzz1139, zzz1140, zzz1141, zzz1142, be)
new_mkVBalBranch3MkVBalBranch20(zzz929, zzz930, zzz931, zzz932, zzz933, zzz934, zzz935, zzz936, zzz937, zzz938, zzz939, Zero, Zero, ba) → new_mkVBalBranch3MkVBalBranch23(zzz929, zzz930, zzz931, zzz932, zzz933, zzz934, zzz935, zzz936, zzz937, zzz938, zzz939, ba)
new_mkVBalBranch3MkVBalBranch20(zzz929, zzz930, zzz931, zzz932, zzz933, zzz934, zzz935, zzz936, zzz937, zzz938, zzz939, Succ(zzz9400), Zero, ba) → new_mkVBalBranch3MkVBalBranch10(zzz929, zzz930, zzz931, zzz932, zzz933, zzz934, zzz935, zzz936, zzz937, zzz938, zzz939, new_primPlusNat2(new_primMulNat0(zzz931), Succ(zzz931)), ba)
new_mkVBalBranch3MkVBalBranch24(zzz340, zzz341, Neg(Succ(Succ(Zero))), zzz343, zzz344, zzz520, zzz521, Succ(zzz522000), zzz523, zzz524, zzz31, Succ(Zero), h) → new_mkVBalBranch3MkVBalBranch25(zzz340, zzz341, Succ(Zero), zzz343, zzz344, zzz520, zzz521, zzz522000, zzz523, zzz524, zzz31, Zero, Succ(zzz522000), h)
new_mkVBalBranch3MkVBalBranch20(zzz929, zzz930, zzz931, zzz932, zzz933, zzz934, zzz935, zzz936, zzz937, zzz938, zzz939, Succ(zzz9400), Succ(zzz9410), ba) → new_mkVBalBranch3MkVBalBranch20(zzz929, zzz930, zzz931, zzz932, zzz933, zzz934, zzz935, zzz936, zzz937, zzz938, zzz939, zzz9400, zzz9410, ba)
new_mkVBalBranch3MkVBalBranch24(zzz340, zzz341, Neg(Succ(Succ(Succ(zzz3420000)))), zzz343, zzz344, zzz520, zzz521, Succ(zzz522000), zzz523, zzz524, zzz31, Succ(Zero), h) → new_mkVBalBranch3MkVBalBranch25(zzz340, zzz341, Succ(Succ(zzz3420000)), zzz343, zzz344, zzz520, zzz521, zzz522000, zzz523, zzz524, zzz31, Succ(zzz3420000), Succ(zzz522000), h)
new_mkVBalBranch3MkVBalBranch26(zzz1133, zzz1134, zzz1135, zzz1136, zzz1137, zzz1138, zzz1139, zzz1140, zzz1141, zzz1142, Succ(zzz11430), Zero, be) → new_mkVBalBranch3MkVBalBranch212(zzz1133, zzz1134, zzz1135, zzz1136, zzz1137, zzz1138, zzz1139, zzz1140, zzz1141, zzz1142, be)
new_mkVBalBranch3MkVBalBranch24(zzz340, zzz341, Neg(Succ(Succ(zzz342000))), zzz343, zzz344, zzz520, zzz521, Succ(zzz522000), zzz523, zzz524, zzz31, Zero, h) → new_mkVBalBranch3MkVBalBranch25(zzz340, zzz341, Succ(zzz342000), zzz343, zzz344, zzz520, zzz521, zzz522000, zzz523, zzz524, zzz31, zzz342000, zzz522000, h)
new_mkVBalBranch(zzz31, Branch(zzz520, zzz521, Pos(Succ(zzz52200)), zzz523, zzz524), Branch(zzz340, zzz341, zzz342, zzz343, zzz344), h) → new_mkVBalBranch3MkVBalBranch2(zzz340, zzz341, zzz342, zzz343, zzz344, zzz520, zzz521, zzz52200, zzz523, zzz524, zzz31, new_primPlusNat3(Succ(new_primPlusNat3(new_primPlusNat1(zzz52200), zzz52200)), Succ(zzz52200)), h)
new_mkVBalBranch3MkVBalBranch29(zzz818, zzz819, zzz820, zzz821, zzz822, zzz823, zzz824, zzz825, zzz826, zzz827, bf) → new_mkVBalBranch3MkVBalBranch14(zzz818, zzz819, zzz820, zzz821, zzz822, zzz823, zzz824, zzz825, zzz826, zzz827, new_primPlusNat2(new_primMulNat0(zzz820), Succ(zzz820)), bf)
new_mkVBalBranch3MkVBalBranch11(zzz2033, zzz2034, zzz2035, zzz2036, zzz2037, zzz2038, zzz2039, zzz2040, zzz2041, zzz2042, zzz2043, Succ(zzz20440), Succ(zzz20450), bb) → new_mkVBalBranch3MkVBalBranch11(zzz2033, zzz2034, zzz2035, zzz2036, zzz2037, zzz2038, zzz2039, zzz2040, zzz2041, zzz2042, zzz2043, zzz20440, zzz20450, bb)
new_mkVBalBranch3MkVBalBranch2(zzz340, zzz341, Neg(zzz3420), zzz343, zzz344, zzz520, zzz521, zzz52200, zzz523, zzz524, zzz31, Zero, h) → new_mkVBalBranch3MkVBalBranch22(zzz340, zzz341, zzz3420, zzz343, zzz344, zzz520, zzz521, zzz52200, zzz523, zzz524, zzz31, h)
new_mkVBalBranch3MkVBalBranch25(zzz537, zzz538, zzz539, zzz540, zzz541, zzz542, zzz543, zzz544, zzz545, zzz546, zzz547, Succ(zzz5480), Succ(zzz5490), bc) → new_mkVBalBranch3MkVBalBranch25(zzz537, zzz538, zzz539, zzz540, zzz541, zzz542, zzz543, zzz544, zzz545, zzz546, zzz547, zzz5480, zzz5490, bc)
new_mkVBalBranch(zzz31, Branch(zzz520, zzz521, Neg(Succ(zzz52200)), zzz523, zzz524), Branch(zzz340, zzz341, zzz342, zzz343, zzz344), h) → new_mkVBalBranch3MkVBalBranch24(zzz340, zzz341, zzz342, zzz343, zzz344, zzz520, zzz521, zzz52200, zzz523, zzz524, zzz31, new_primPlusNat3(Succ(new_primPlusNat3(new_primPlusNat1(zzz52200), zzz52200)), Succ(zzz52200)), h)
new_mkVBalBranch3MkVBalBranch24(zzz340, zzz341, Neg(Succ(Zero)), zzz343, zzz344, zzz520, zzz521, Succ(zzz522000), zzz523, zzz524, zzz31, Zero, h) → new_mkVBalBranch3MkVBalBranch28(zzz340, zzz341, zzz343, zzz344, zzz520, zzz521, Succ(zzz522000), zzz523, zzz524, zzz31, h)
new_mkVBalBranch3MkVBalBranch210(zzz340, zzz341, zzz343, zzz344, zzz520, zzz521, zzz52200, zzz523, zzz524, zzz31, h) → new_mkVBalBranch(zzz31, Branch(zzz520, zzz521, Neg(Succ(zzz52200)), zzz523, zzz524), zzz343, h)
new_mkVBalBranch3MkVBalBranch24(zzz340, zzz341, Neg(Succ(Succ(zzz342000))), zzz343, zzz344, zzz520, zzz521, Zero, zzz523, zzz524, zzz31, Zero, h) → new_mkVBalBranch3MkVBalBranch14(zzz340, zzz341, Succ(zzz342000), zzz343, zzz344, zzz520, zzz521, zzz523, zzz524, zzz31, new_primMulNat1(Succ(zzz342000)), h)
new_mkVBalBranch3MkVBalBranch26(zzz1133, zzz1134, zzz1135, zzz1136, zzz1137, zzz1138, zzz1139, zzz1140, zzz1141, zzz1142, Zero, Succ(zzz11440), be) → new_mkVBalBranch(zzz1142, Branch(zzz1138, zzz1139, Neg(Succ(Zero)), zzz1140, zzz1141), zzz1136, be)
new_mkVBalBranch3MkVBalBranch24(zzz340, zzz341, Neg(Succ(Succ(Zero))), zzz343, zzz344, zzz520, zzz521, Zero, zzz523, zzz524, zzz31, Succ(Zero), h) → new_mkVBalBranch3MkVBalBranch26(zzz340, zzz341, Succ(Zero), zzz343, zzz344, zzz520, zzz521, zzz523, zzz524, zzz31, Zero, Zero, h)
new_mkVBalBranch(zzz31, Branch(zzz520, zzz521, Pos(Zero), zzz523, zzz524), Branch(zzz340, zzz341, Pos(Succ(zzz34200)), zzz343, zzz344), h) → new_mkVBalBranch(zzz31, Branch(zzz520, zzz521, Pos(Zero), zzz523, zzz524), zzz343, h)
new_mkVBalBranch3MkVBalBranch2(zzz340, zzz341, Pos(Zero), zzz343, zzz344, zzz520, zzz521, zzz52200, zzz523, zzz524, zzz31, Succ(zzz680), h) → new_mkVBalBranch(zzz31, zzz524, Branch(zzz340, zzz341, Pos(Zero), zzz343, zzz344), h)
new_mkVBalBranch3MkVBalBranch21(zzz340, zzz341, zzz343, zzz344, zzz520, zzz521, zzz52200, zzz523, zzz524, zzz31, h) → new_mkVBalBranch(zzz31, zzz524, Branch(zzz340, zzz341, Pos(Zero), zzz343, zzz344), h)
new_mkVBalBranch3MkVBalBranch24(zzz340, zzz341, Pos(zzz3420), zzz343, zzz344, zzz520, zzz521, zzz52200, zzz523, zzz524, zzz31, Zero, h) → new_mkVBalBranch3MkVBalBranch27(zzz340, zzz341, zzz3420, zzz343, zzz344, zzz520, zzz521, zzz52200, zzz523, zzz524, zzz31, h)
new_mkVBalBranch3MkVBalBranch211(zzz537, zzz538, zzz539, zzz540, zzz541, zzz542, zzz543, zzz544, zzz545, zzz546, zzz547, bc) → new_mkVBalBranch3MkVBalBranch15(zzz537, zzz538, zzz539, zzz540, zzz541, zzz542, zzz543, zzz544, zzz545, zzz546, zzz547, new_primMulNat1(zzz539), bc)
new_mkVBalBranch3MkVBalBranch24(zzz340, zzz341, Neg(Succ(Succ(Succ(zzz3420000)))), zzz343, zzz344, zzz520, zzz521, Zero, zzz523, zzz524, zzz31, Succ(Succ(zzz6900)), h) → new_mkVBalBranch3MkVBalBranch26(zzz340, zzz341, Succ(Succ(zzz3420000)), zzz343, zzz344, zzz520, zzz521, zzz523, zzz524, zzz31, Succ(zzz3420000), Succ(zzz6900), h)
new_mkVBalBranch3MkVBalBranch15(zzz537, zzz538, zzz539, zzz540, zzz541, zzz542, zzz543, zzz544, zzz545, zzz546, zzz547, Succ(zzz6990), bc) → new_mkVBalBranch3MkVBalBranch16(zzz537, zzz538, zzz539, zzz540, zzz541, zzz542, zzz543, Succ(zzz544), zzz545, zzz546, zzz547, Succ(Succ(zzz544)), Succ(zzz6990), bc)
new_mkVBalBranch(zzz31, Branch(zzz520, zzz521, Neg(Zero), zzz523, zzz524), Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), h) → new_mkVBalBranch3MkVBalBranch13(zzz340, zzz341, zzz34200, zzz343, zzz344, zzz520, zzz521, zzz523, zzz524, zzz31, new_primPlusNat2(new_primMulNat0(zzz34200), Succ(zzz34200)), h)
new_mkVBalBranch3MkVBalBranch27(zzz340, zzz341, zzz3420, zzz343, zzz344, zzz520, zzz521, zzz52200, zzz523, zzz524, zzz31, h) → new_mkVBalBranch(zzz31, Branch(zzz520, zzz521, Neg(Succ(zzz52200)), zzz523, zzz524), zzz343, h)
new_mkVBalBranch3MkVBalBranch24(zzz340, zzz341, Pos(zzz3420), zzz343, zzz344, zzz520, zzz521, zzz52200, zzz523, zzz524, zzz31, Succ(zzz690), h) → new_mkVBalBranch(zzz31, Branch(zzz520, zzz521, Neg(Succ(zzz52200)), zzz523, zzz524), zzz343, h)
new_mkVBalBranch3MkVBalBranch12(zzz340, zzz341, zzz34200, zzz343, zzz344, zzz520, zzz521, zzz523, zzz524, zzz31, Succ(zzz1250), h) → new_mkVBalBranch(zzz31, zzz524, Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), h)
new_mkVBalBranch3MkVBalBranch25(zzz537, zzz538, zzz539, zzz540, zzz541, zzz542, zzz543, zzz544, zzz545, zzz546, zzz547, Succ(zzz5480), Zero, bc) → new_mkVBalBranch3MkVBalBranch15(zzz537, zzz538, zzz539, zzz540, zzz541, zzz542, zzz543, zzz544, zzz545, zzz546, zzz547, new_primMulNat1(zzz539), bc)
new_mkVBalBranch3MkVBalBranch28(zzz340, zzz341, zzz343, zzz344, zzz520, zzz521, zzz52200, zzz523, zzz524, zzz31, h) → new_mkVBalBranch(zzz31, Branch(zzz520, zzz521, Neg(Succ(zzz52200)), zzz523, zzz524), zzz343, h)
new_mkVBalBranch3MkVBalBranch24(zzz340, zzz341, Neg(Succ(Succ(Zero))), zzz343, zzz344, zzz520, zzz521, Zero, zzz523, zzz524, zzz31, Succ(Succ(zzz6900)), h) → new_mkVBalBranch3MkVBalBranch26(zzz340, zzz341, Succ(Zero), zzz343, zzz344, zzz520, zzz521, zzz523, zzz524, zzz31, Zero, Succ(zzz6900), h)
new_mkVBalBranch3MkVBalBranch1(zzz340, zzz341, zzz34200, zzz343, zzz344, zzz520, zzz521, zzz52200, zzz523, zzz524, zzz31, Succ(zzz1430), h) → new_mkVBalBranch(zzz31, zzz524, Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), h)
new_mkVBalBranch3MkVBalBranch22(zzz340, zzz341, Zero, zzz343, zzz344, zzz520, zzz521, zzz52200, zzz523, zzz524, zzz31, h) → new_mkVBalBranch(zzz31, zzz524, Branch(zzz340, zzz341, Neg(Zero), zzz343, zzz344), h)
new_mkVBalBranch(zzz31, Branch(zzz520, zzz521, Pos(Zero), zzz523, zzz524), Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), h) → new_mkVBalBranch3MkVBalBranch12(zzz340, zzz341, zzz34200, zzz343, zzz344, zzz520, zzz521, zzz523, zzz524, zzz31, new_primPlusNat2(new_primMulNat0(zzz34200), Succ(zzz34200)), h)
new_mkVBalBranch3MkVBalBranch24(zzz340, zzz341, Neg(Succ(Zero)), zzz343, zzz344, zzz520, zzz521, zzz52200, zzz523, zzz524, zzz31, Succ(zzz690), h) → new_mkVBalBranch(zzz31, Branch(zzz520, zzz521, Neg(Succ(zzz52200)), zzz523, zzz524), zzz343, h)
new_mkVBalBranch3MkVBalBranch13(zzz340, zzz341, zzz34200, zzz343, zzz344, zzz520, zzz521, zzz523, zzz524, zzz31, Succ(zzz1290), h) → new_mkVBalBranch(zzz31, zzz524, Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), h)
new_mkVBalBranch3MkVBalBranch2(zzz340, zzz341, Pos(Succ(zzz34200)), zzz343, zzz344, zzz520, zzz521, zzz52200, zzz523, zzz524, zzz31, Succ(zzz680), h) → new_mkVBalBranch3MkVBalBranch20(zzz340, zzz341, zzz34200, zzz343, zzz344, zzz520, zzz521, zzz52200, zzz523, zzz524, zzz31, Succ(new_primPlusNat2(zzz680, zzz52200)), zzz34200, h)
new_mkVBalBranch3MkVBalBranch24(zzz340, zzz341, Neg(Zero), zzz343, zzz344, zzz520, zzz521, zzz52200, zzz523, zzz524, zzz31, Succ(zzz690), h) → new_mkVBalBranch(zzz31, Branch(zzz520, zzz521, Neg(Succ(zzz52200)), zzz523, zzz524), zzz343, h)
new_mkVBalBranch(zzz31, Branch(zzz520, zzz521, Neg(Zero), zzz523, zzz524), Branch(zzz340, zzz341, Pos(Succ(zzz34200)), zzz343, zzz344), h) → new_mkVBalBranch(zzz31, Branch(zzz520, zzz521, Neg(Zero), zzz523, zzz524), zzz343, h)
new_mkVBalBranch3MkVBalBranch1(zzz340, zzz341, zzz34200, zzz343, zzz344, zzz520, zzz521, zzz52200, zzz523, zzz524, zzz31, Zero, h) → new_mkVBalBranch3MkVBalBranch17(zzz340, zzz341, zzz34200, zzz343, zzz344, zzz520, zzz521, zzz52200, zzz523, zzz524, zzz31, h)
new_mkVBalBranch3MkVBalBranch16(zzz1702, zzz1703, zzz1704, zzz1705, zzz1706, zzz1707, zzz1708, zzz1709, zzz1710, zzz1711, zzz1712, Succ(zzz17130), Succ(zzz17140), bd) → new_mkVBalBranch3MkVBalBranch16(zzz1702, zzz1703, zzz1704, zzz1705, zzz1706, zzz1707, zzz1708, zzz1709, zzz1710, zzz1711, zzz1712, zzz17130, zzz17140, bd)
new_mkVBalBranch3MkVBalBranch25(zzz537, zzz538, zzz539, zzz540, zzz541, zzz542, zzz543, zzz544, zzz545, zzz546, zzz547, Zero, Succ(zzz5490), bc) → new_mkVBalBranch(zzz547, Branch(zzz542, zzz543, Neg(Succ(Succ(zzz544))), zzz545, zzz546), zzz540, bc)
new_mkVBalBranch3MkVBalBranch10(zzz929, zzz930, zzz931, zzz932, zzz933, zzz934, zzz935, zzz936, zzz937, zzz938, zzz939, Succ(zzz10020), ba) → new_mkVBalBranch3MkVBalBranch11(zzz929, zzz930, zzz931, zzz932, zzz933, zzz934, zzz935, zzz936, zzz937, zzz938, zzz939, Succ(zzz10020), Succ(zzz936), ba)
new_mkVBalBranch3MkVBalBranch212(zzz818, zzz819, zzz820, zzz821, zzz822, zzz823, zzz824, zzz825, zzz826, zzz827, bf) → new_mkVBalBranch3MkVBalBranch14(zzz818, zzz819, zzz820, zzz821, zzz822, zzz823, zzz824, zzz825, zzz826, zzz827, new_primPlusNat2(new_primMulNat0(zzz820), Succ(zzz820)), bf)
new_mkVBalBranch3MkVBalBranch14(zzz818, zzz819, zzz820, zzz821, zzz822, zzz823, zzz824, zzz825, zzz826, zzz827, Succ(zzz8960), bf) → new_mkVBalBranch3MkVBalBranch16(zzz818, zzz819, zzz820, zzz821, zzz822, zzz823, zzz824, Zero, zzz825, zzz826, zzz827, Succ(Zero), Succ(zzz8960), bf)
new_mkVBalBranch3MkVBalBranch24(zzz340, zzz341, Neg(Succ(Succ(Succ(zzz3420000)))), zzz343, zzz344, zzz520, zzz521, Succ(zzz522000), zzz523, zzz524, zzz31, Succ(Succ(zzz6900)), h) → new_mkVBalBranch3MkVBalBranch25(zzz340, zzz341, Succ(Succ(zzz3420000)), zzz343, zzz344, zzz520, zzz521, zzz522000, zzz523, zzz524, zzz31, Succ(zzz3420000), Succ(Succ(new_primPlusNat2(zzz6900, zzz522000))), h)
new_mkVBalBranch3MkVBalBranch2(zzz340, zzz341, Pos(Succ(zzz34200)), zzz343, zzz344, zzz520, zzz521, zzz52200, zzz523, zzz524, zzz31, Zero, h) → new_mkVBalBranch3MkVBalBranch20(zzz340, zzz341, zzz34200, zzz343, zzz344, zzz520, zzz521, zzz52200, zzz523, zzz524, zzz31, zzz52200, zzz34200, h)
new_mkVBalBranch3MkVBalBranch24(zzz340, zzz341, Neg(Zero), zzz343, zzz344, zzz520, zzz521, zzz52200, zzz523, zzz524, zzz31, Zero, h) → new_mkVBalBranch3MkVBalBranch210(zzz340, zzz341, zzz343, zzz344, zzz520, zzz521, zzz52200, zzz523, zzz524, zzz31, h)
new_mkVBalBranch3MkVBalBranch24(zzz340, zzz341, Neg(Succ(Succ(Zero))), zzz343, zzz344, zzz520, zzz521, Succ(zzz522000), zzz523, zzz524, zzz31, Succ(Succ(zzz6900)), h) → new_mkVBalBranch3MkVBalBranch25(zzz340, zzz341, Succ(Zero), zzz343, zzz344, zzz520, zzz521, zzz522000, zzz523, zzz524, zzz31, Zero, Succ(Succ(new_primPlusNat2(zzz6900, zzz522000))), h)
new_mkVBalBranch3MkVBalBranch23(zzz929, zzz930, zzz931, zzz932, zzz933, zzz934, zzz935, zzz936, zzz937, zzz938, zzz939, ba) → new_mkVBalBranch3MkVBalBranch10(zzz929, zzz930, zzz931, zzz932, zzz933, zzz934, zzz935, zzz936, zzz937, zzz938, zzz939, new_primPlusNat2(new_primMulNat0(zzz931), Succ(zzz931)), ba)
new_mkVBalBranch3MkVBalBranch2(zzz340, zzz341, Neg(Zero), zzz343, zzz344, zzz520, zzz521, zzz52200, zzz523, zzz524, zzz31, Succ(zzz680), h) → new_mkVBalBranch(zzz31, zzz524, Branch(zzz340, zzz341, Neg(Zero), zzz343, zzz344), h)
new_mkVBalBranch3MkVBalBranch16(zzz1702, zzz1703, zzz1704, zzz1705, zzz1706, zzz1707, zzz1708, zzz1709, zzz1710, zzz1711, zzz1712, Zero, Succ(zzz17140), bd) → new_mkVBalBranch(zzz1712, zzz1711, Branch(zzz1702, zzz1703, Neg(Succ(zzz1704)), zzz1705, zzz1706), bd)
new_mkVBalBranch3MkVBalBranch10(zzz929, zzz930, zzz931, zzz932, zzz933, zzz934, zzz935, zzz936, zzz937, zzz938, zzz939, Zero, ba) → new_mkVBalBranch3MkVBalBranch11(zzz929, zzz930, zzz931, zzz932, zzz933, zzz934, zzz935, zzz936, zzz937, zzz938, zzz939, Zero, Succ(zzz936), ba)
new_mkVBalBranch3MkVBalBranch2(zzz340, zzz341, Pos(Zero), zzz343, zzz344, zzz520, zzz521, zzz52200, zzz523, zzz524, zzz31, Zero, h) → new_mkVBalBranch3MkVBalBranch21(zzz340, zzz341, zzz343, zzz344, zzz520, zzz521, zzz52200, zzz523, zzz524, zzz31, h)
new_mkVBalBranch3MkVBalBranch25(zzz537, zzz538, zzz539, zzz540, zzz541, zzz542, zzz543, zzz544, zzz545, zzz546, zzz547, Zero, Zero, bc) → new_mkVBalBranch3MkVBalBranch211(zzz537, zzz538, zzz539, zzz540, zzz541, zzz542, zzz543, zzz544, zzz545, zzz546, zzz547, bc)
new_mkVBalBranch3MkVBalBranch22(zzz340, zzz341, Succ(zzz34200), zzz343, zzz344, zzz520, zzz521, zzz52200, zzz523, zzz524, zzz31, h) → new_mkVBalBranch3MkVBalBranch1(zzz340, zzz341, zzz34200, zzz343, zzz344, zzz520, zzz521, zzz52200, zzz523, zzz524, zzz31, new_primPlusNat2(new_primPlusNat3(Succ(new_primPlusNat3(new_primPlusNat1(zzz34200), zzz34200)), Succ(zzz34200)), Succ(zzz34200)), h)

The TRS R consists of the following rules:

new_primPlusNat1(Zero) → Zero
new_primMulNat0(zzz6200) → new_primPlusNat3(Succ(new_primPlusNat3(new_primPlusNat1(zzz6200), zzz6200)), Succ(zzz6200))
new_primPlusNat2(Succ(zzz900), Succ(zzz9100)) → Succ(Succ(new_primPlusNat2(zzz900, zzz9100)))
new_primPlusNat3(zzz90, Succ(zzz910)) → Succ(Succ(new_primPlusNat2(zzz90, zzz910)))
new_primPlusNat3(zzz90, Zero) → Succ(zzz90)
new_primMulNat1(zzz34200) → new_primPlusNat2(new_primMulNat0(zzz34200), Succ(zzz34200))
new_primPlusNat2(Zero, Zero) → Zero
new_primPlusNat1(Succ(zzz62000)) → Succ(Succ(new_primPlusNat1(zzz62000)))
new_primPlusNat2(Succ(zzz900), Zero) → Succ(zzz900)
new_primPlusNat2(Zero, Succ(zzz9100)) → Succ(zzz9100)

The set Q consists of the following terms:

new_primPlusNat2(Zero, Succ(x0))
new_primMulNat1(x0)
new_primMulNat0(x0)
new_primPlusNat3(x0, Succ(x1))
new_primPlusNat2(Succ(x0), Succ(x1))
new_primPlusNat3(x0, Zero)
new_primPlusNat1(Zero)
new_primPlusNat2(Zero, Zero)
new_primPlusNat1(Succ(x0))
new_primPlusNat2(Succ(x0), Zero)

We have to consider all minimal (P,Q,R)-chains.
By rewriting [15] the rule new_mkVBalBranch3MkVBalBranch25(zzz537, zzz538, zzz539, zzz540, zzz541, zzz542, zzz543, zzz544, zzz545, zzz546, zzz547, Succ(zzz5480), Zero, bc) → new_mkVBalBranch3MkVBalBranch15(zzz537, zzz538, zzz539, zzz540, zzz541, zzz542, zzz543, zzz544, zzz545, zzz546, zzz547, new_primMulNat1(zzz539), bc) at position [11] we obtained the following new rules:

new_mkVBalBranch3MkVBalBranch25(zzz537, zzz538, zzz539, zzz540, zzz541, zzz542, zzz543, zzz544, zzz545, zzz546, zzz547, Succ(zzz5480), Zero, bc) → new_mkVBalBranch3MkVBalBranch15(zzz537, zzz538, zzz539, zzz540, zzz541, zzz542, zzz543, zzz544, zzz545, zzz546, zzz547, new_primPlusNat2(new_primMulNat0(zzz539), Succ(zzz539)), bc)



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

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

new_mkVBalBranch3MkVBalBranch11(zzz2033, zzz2034, zzz2035, zzz2036, zzz2037, zzz2038, zzz2039, zzz2040, zzz2041, zzz2042, zzz2043, Zero, Succ(zzz20450), bb) → new_mkVBalBranch(zzz2043, zzz2042, Branch(zzz2033, zzz2034, Pos(Succ(zzz2035)), zzz2036, zzz2037), bb)
new_mkVBalBranch3MkVBalBranch2(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344, zzz520, zzz521, zzz52200, zzz523, zzz524, zzz31, Succ(zzz680), h) → new_mkVBalBranch3MkVBalBranch1(zzz340, zzz341, zzz34200, zzz343, zzz344, zzz520, zzz521, zzz52200, zzz523, zzz524, zzz31, new_primPlusNat2(new_primPlusNat3(Succ(new_primPlusNat3(new_primPlusNat1(zzz34200), zzz34200)), Succ(zzz34200)), Succ(zzz34200)), h)
new_mkVBalBranch3MkVBalBranch26(zzz1133, zzz1134, zzz1135, zzz1136, zzz1137, zzz1138, zzz1139, zzz1140, zzz1141, zzz1142, Succ(zzz11430), Succ(zzz11440), be) → new_mkVBalBranch3MkVBalBranch26(zzz1133, zzz1134, zzz1135, zzz1136, zzz1137, zzz1138, zzz1139, zzz1140, zzz1141, zzz1142, zzz11430, zzz11440, be)
new_mkVBalBranch3MkVBalBranch24(zzz340, zzz341, Neg(Succ(Succ(Succ(zzz3420000)))), zzz343, zzz344, zzz520, zzz521, Zero, zzz523, zzz524, zzz31, Succ(Zero), h) → new_mkVBalBranch3MkVBalBranch26(zzz340, zzz341, Succ(Succ(zzz3420000)), zzz343, zzz344, zzz520, zzz521, zzz523, zzz524, zzz31, Succ(zzz3420000), Zero, h)
new_mkVBalBranch3MkVBalBranch25(zzz537, zzz538, zzz539, zzz540, zzz541, zzz542, zzz543, zzz544, zzz545, zzz546, zzz547, Succ(zzz5480), Zero, bc) → new_mkVBalBranch3MkVBalBranch15(zzz537, zzz538, zzz539, zzz540, zzz541, zzz542, zzz543, zzz544, zzz545, zzz546, zzz547, new_primPlusNat2(new_primMulNat0(zzz539), Succ(zzz539)), bc)
new_mkVBalBranch3MkVBalBranch24(zzz340, zzz341, Neg(Succ(Zero)), zzz343, zzz344, zzz520, zzz521, Zero, zzz523, zzz524, zzz31, Zero, h) → new_mkVBalBranch3MkVBalBranch29(zzz340, zzz341, Zero, zzz343, zzz344, zzz520, zzz521, zzz523, zzz524, zzz31, h)
new_mkVBalBranch3MkVBalBranch20(zzz929, zzz930, zzz931, zzz932, zzz933, zzz934, zzz935, zzz936, zzz937, zzz938, zzz939, Zero, Succ(zzz9410), ba) → new_mkVBalBranch(zzz939, Branch(zzz934, zzz935, Pos(Succ(zzz936)), zzz937, zzz938), zzz932, ba)
new_mkVBalBranch3MkVBalBranch17(zzz340, zzz341, zzz34200, zzz343, zzz344, zzz520, zzz521, zzz52200, zzz523, zzz524, zzz31, h) → new_mkVBalBranch(zzz31, zzz524, Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), h)
new_mkVBalBranch3MkVBalBranch26(zzz1133, zzz1134, zzz1135, zzz1136, zzz1137, zzz1138, zzz1139, zzz1140, zzz1141, zzz1142, Zero, Zero, be) → new_mkVBalBranch3MkVBalBranch29(zzz1133, zzz1134, zzz1135, zzz1136, zzz1137, zzz1138, zzz1139, zzz1140, zzz1141, zzz1142, be)
new_mkVBalBranch3MkVBalBranch20(zzz929, zzz930, zzz931, zzz932, zzz933, zzz934, zzz935, zzz936, zzz937, zzz938, zzz939, Zero, Zero, ba) → new_mkVBalBranch3MkVBalBranch23(zzz929, zzz930, zzz931, zzz932, zzz933, zzz934, zzz935, zzz936, zzz937, zzz938, zzz939, ba)
new_mkVBalBranch3MkVBalBranch20(zzz929, zzz930, zzz931, zzz932, zzz933, zzz934, zzz935, zzz936, zzz937, zzz938, zzz939, Succ(zzz9400), Zero, ba) → new_mkVBalBranch3MkVBalBranch10(zzz929, zzz930, zzz931, zzz932, zzz933, zzz934, zzz935, zzz936, zzz937, zzz938, zzz939, new_primPlusNat2(new_primMulNat0(zzz931), Succ(zzz931)), ba)
new_mkVBalBranch3MkVBalBranch24(zzz340, zzz341, Neg(Succ(Succ(Zero))), zzz343, zzz344, zzz520, zzz521, Succ(zzz522000), zzz523, zzz524, zzz31, Succ(Zero), h) → new_mkVBalBranch3MkVBalBranch25(zzz340, zzz341, Succ(Zero), zzz343, zzz344, zzz520, zzz521, zzz522000, zzz523, zzz524, zzz31, Zero, Succ(zzz522000), h)
new_mkVBalBranch3MkVBalBranch24(zzz340, zzz341, Neg(Succ(Succ(Succ(zzz3420000)))), zzz343, zzz344, zzz520, zzz521, Succ(zzz522000), zzz523, zzz524, zzz31, Succ(Zero), h) → new_mkVBalBranch3MkVBalBranch25(zzz340, zzz341, Succ(Succ(zzz3420000)), zzz343, zzz344, zzz520, zzz521, zzz522000, zzz523, zzz524, zzz31, Succ(zzz3420000), Succ(zzz522000), h)
new_mkVBalBranch3MkVBalBranch20(zzz929, zzz930, zzz931, zzz932, zzz933, zzz934, zzz935, zzz936, zzz937, zzz938, zzz939, Succ(zzz9400), Succ(zzz9410), ba) → new_mkVBalBranch3MkVBalBranch20(zzz929, zzz930, zzz931, zzz932, zzz933, zzz934, zzz935, zzz936, zzz937, zzz938, zzz939, zzz9400, zzz9410, ba)
new_mkVBalBranch3MkVBalBranch24(zzz340, zzz341, Neg(Succ(Succ(zzz342000))), zzz343, zzz344, zzz520, zzz521, Succ(zzz522000), zzz523, zzz524, zzz31, Zero, h) → new_mkVBalBranch3MkVBalBranch25(zzz340, zzz341, Succ(zzz342000), zzz343, zzz344, zzz520, zzz521, zzz522000, zzz523, zzz524, zzz31, zzz342000, zzz522000, h)
new_mkVBalBranch3MkVBalBranch26(zzz1133, zzz1134, zzz1135, zzz1136, zzz1137, zzz1138, zzz1139, zzz1140, zzz1141, zzz1142, Succ(zzz11430), Zero, be) → new_mkVBalBranch3MkVBalBranch212(zzz1133, zzz1134, zzz1135, zzz1136, zzz1137, zzz1138, zzz1139, zzz1140, zzz1141, zzz1142, be)
new_mkVBalBranch(zzz31, Branch(zzz520, zzz521, Pos(Succ(zzz52200)), zzz523, zzz524), Branch(zzz340, zzz341, zzz342, zzz343, zzz344), h) → new_mkVBalBranch3MkVBalBranch2(zzz340, zzz341, zzz342, zzz343, zzz344, zzz520, zzz521, zzz52200, zzz523, zzz524, zzz31, new_primPlusNat3(Succ(new_primPlusNat3(new_primPlusNat1(zzz52200), zzz52200)), Succ(zzz52200)), h)
new_mkVBalBranch3MkVBalBranch29(zzz818, zzz819, zzz820, zzz821, zzz822, zzz823, zzz824, zzz825, zzz826, zzz827, bf) → new_mkVBalBranch3MkVBalBranch14(zzz818, zzz819, zzz820, zzz821, zzz822, zzz823, zzz824, zzz825, zzz826, zzz827, new_primPlusNat2(new_primMulNat0(zzz820), Succ(zzz820)), bf)
new_mkVBalBranch3MkVBalBranch11(zzz2033, zzz2034, zzz2035, zzz2036, zzz2037, zzz2038, zzz2039, zzz2040, zzz2041, zzz2042, zzz2043, Succ(zzz20440), Succ(zzz20450), bb) → new_mkVBalBranch3MkVBalBranch11(zzz2033, zzz2034, zzz2035, zzz2036, zzz2037, zzz2038, zzz2039, zzz2040, zzz2041, zzz2042, zzz2043, zzz20440, zzz20450, bb)
new_mkVBalBranch3MkVBalBranch25(zzz537, zzz538, zzz539, zzz540, zzz541, zzz542, zzz543, zzz544, zzz545, zzz546, zzz547, Succ(zzz5480), Succ(zzz5490), bc) → new_mkVBalBranch3MkVBalBranch25(zzz537, zzz538, zzz539, zzz540, zzz541, zzz542, zzz543, zzz544, zzz545, zzz546, zzz547, zzz5480, zzz5490, bc)
new_mkVBalBranch3MkVBalBranch2(zzz340, zzz341, Neg(zzz3420), zzz343, zzz344, zzz520, zzz521, zzz52200, zzz523, zzz524, zzz31, Zero, h) → new_mkVBalBranch3MkVBalBranch22(zzz340, zzz341, zzz3420, zzz343, zzz344, zzz520, zzz521, zzz52200, zzz523, zzz524, zzz31, h)
new_mkVBalBranch(zzz31, Branch(zzz520, zzz521, Neg(Succ(zzz52200)), zzz523, zzz524), Branch(zzz340, zzz341, zzz342, zzz343, zzz344), h) → new_mkVBalBranch3MkVBalBranch24(zzz340, zzz341, zzz342, zzz343, zzz344, zzz520, zzz521, zzz52200, zzz523, zzz524, zzz31, new_primPlusNat3(Succ(new_primPlusNat3(new_primPlusNat1(zzz52200), zzz52200)), Succ(zzz52200)), h)
new_mkVBalBranch3MkVBalBranch24(zzz340, zzz341, Neg(Succ(Zero)), zzz343, zzz344, zzz520, zzz521, Succ(zzz522000), zzz523, zzz524, zzz31, Zero, h) → new_mkVBalBranch3MkVBalBranch28(zzz340, zzz341, zzz343, zzz344, zzz520, zzz521, Succ(zzz522000), zzz523, zzz524, zzz31, h)
new_mkVBalBranch3MkVBalBranch24(zzz340, zzz341, Neg(Succ(Succ(zzz342000))), zzz343, zzz344, zzz520, zzz521, Zero, zzz523, zzz524, zzz31, Zero, h) → new_mkVBalBranch3MkVBalBranch14(zzz340, zzz341, Succ(zzz342000), zzz343, zzz344, zzz520, zzz521, zzz523, zzz524, zzz31, new_primMulNat1(Succ(zzz342000)), h)
new_mkVBalBranch3MkVBalBranch210(zzz340, zzz341, zzz343, zzz344, zzz520, zzz521, zzz52200, zzz523, zzz524, zzz31, h) → new_mkVBalBranch(zzz31, Branch(zzz520, zzz521, Neg(Succ(zzz52200)), zzz523, zzz524), zzz343, h)
new_mkVBalBranch3MkVBalBranch26(zzz1133, zzz1134, zzz1135, zzz1136, zzz1137, zzz1138, zzz1139, zzz1140, zzz1141, zzz1142, Zero, Succ(zzz11440), be) → new_mkVBalBranch(zzz1142, Branch(zzz1138, zzz1139, Neg(Succ(Zero)), zzz1140, zzz1141), zzz1136, be)
new_mkVBalBranch3MkVBalBranch24(zzz340, zzz341, Neg(Succ(Succ(Zero))), zzz343, zzz344, zzz520, zzz521, Zero, zzz523, zzz524, zzz31, Succ(Zero), h) → new_mkVBalBranch3MkVBalBranch26(zzz340, zzz341, Succ(Zero), zzz343, zzz344, zzz520, zzz521, zzz523, zzz524, zzz31, Zero, Zero, h)
new_mkVBalBranch(zzz31, Branch(zzz520, zzz521, Pos(Zero), zzz523, zzz524), Branch(zzz340, zzz341, Pos(Succ(zzz34200)), zzz343, zzz344), h) → new_mkVBalBranch(zzz31, Branch(zzz520, zzz521, Pos(Zero), zzz523, zzz524), zzz343, h)
new_mkVBalBranch3MkVBalBranch2(zzz340, zzz341, Pos(Zero), zzz343, zzz344, zzz520, zzz521, zzz52200, zzz523, zzz524, zzz31, Succ(zzz680), h) → new_mkVBalBranch(zzz31, zzz524, Branch(zzz340, zzz341, Pos(Zero), zzz343, zzz344), h)
new_mkVBalBranch3MkVBalBranch21(zzz340, zzz341, zzz343, zzz344, zzz520, zzz521, zzz52200, zzz523, zzz524, zzz31, h) → new_mkVBalBranch(zzz31, zzz524, Branch(zzz340, zzz341, Pos(Zero), zzz343, zzz344), h)
new_mkVBalBranch3MkVBalBranch24(zzz340, zzz341, Pos(zzz3420), zzz343, zzz344, zzz520, zzz521, zzz52200, zzz523, zzz524, zzz31, Zero, h) → new_mkVBalBranch3MkVBalBranch27(zzz340, zzz341, zzz3420, zzz343, zzz344, zzz520, zzz521, zzz52200, zzz523, zzz524, zzz31, h)
new_mkVBalBranch3MkVBalBranch211(zzz537, zzz538, zzz539, zzz540, zzz541, zzz542, zzz543, zzz544, zzz545, zzz546, zzz547, bc) → new_mkVBalBranch3MkVBalBranch15(zzz537, zzz538, zzz539, zzz540, zzz541, zzz542, zzz543, zzz544, zzz545, zzz546, zzz547, new_primMulNat1(zzz539), bc)
new_mkVBalBranch3MkVBalBranch15(zzz537, zzz538, zzz539, zzz540, zzz541, zzz542, zzz543, zzz544, zzz545, zzz546, zzz547, Succ(zzz6990), bc) → new_mkVBalBranch3MkVBalBranch16(zzz537, zzz538, zzz539, zzz540, zzz541, zzz542, zzz543, Succ(zzz544), zzz545, zzz546, zzz547, Succ(Succ(zzz544)), Succ(zzz6990), bc)
new_mkVBalBranch3MkVBalBranch24(zzz340, zzz341, Neg(Succ(Succ(Succ(zzz3420000)))), zzz343, zzz344, zzz520, zzz521, Zero, zzz523, zzz524, zzz31, Succ(Succ(zzz6900)), h) → new_mkVBalBranch3MkVBalBranch26(zzz340, zzz341, Succ(Succ(zzz3420000)), zzz343, zzz344, zzz520, zzz521, zzz523, zzz524, zzz31, Succ(zzz3420000), Succ(zzz6900), h)
new_mkVBalBranch(zzz31, Branch(zzz520, zzz521, Neg(Zero), zzz523, zzz524), Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), h) → new_mkVBalBranch3MkVBalBranch13(zzz340, zzz341, zzz34200, zzz343, zzz344, zzz520, zzz521, zzz523, zzz524, zzz31, new_primPlusNat2(new_primMulNat0(zzz34200), Succ(zzz34200)), h)
new_mkVBalBranch3MkVBalBranch27(zzz340, zzz341, zzz3420, zzz343, zzz344, zzz520, zzz521, zzz52200, zzz523, zzz524, zzz31, h) → new_mkVBalBranch(zzz31, Branch(zzz520, zzz521, Neg(Succ(zzz52200)), zzz523, zzz524), zzz343, h)
new_mkVBalBranch3MkVBalBranch24(zzz340, zzz341, Pos(zzz3420), zzz343, zzz344, zzz520, zzz521, zzz52200, zzz523, zzz524, zzz31, Succ(zzz690), h) → new_mkVBalBranch(zzz31, Branch(zzz520, zzz521, Neg(Succ(zzz52200)), zzz523, zzz524), zzz343, h)
new_mkVBalBranch3MkVBalBranch12(zzz340, zzz341, zzz34200, zzz343, zzz344, zzz520, zzz521, zzz523, zzz524, zzz31, Succ(zzz1250), h) → new_mkVBalBranch(zzz31, zzz524, Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), h)
new_mkVBalBranch3MkVBalBranch28(zzz340, zzz341, zzz343, zzz344, zzz520, zzz521, zzz52200, zzz523, zzz524, zzz31, h) → new_mkVBalBranch(zzz31, Branch(zzz520, zzz521, Neg(Succ(zzz52200)), zzz523, zzz524), zzz343, h)
new_mkVBalBranch3MkVBalBranch24(zzz340, zzz341, Neg(Succ(Succ(Zero))), zzz343, zzz344, zzz520, zzz521, Zero, zzz523, zzz524, zzz31, Succ(Succ(zzz6900)), h) → new_mkVBalBranch3MkVBalBranch26(zzz340, zzz341, Succ(Zero), zzz343, zzz344, zzz520, zzz521, zzz523, zzz524, zzz31, Zero, Succ(zzz6900), h)
new_mkVBalBranch(zzz31, Branch(zzz520, zzz521, Pos(Zero), zzz523, zzz524), Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), h) → new_mkVBalBranch3MkVBalBranch12(zzz340, zzz341, zzz34200, zzz343, zzz344, zzz520, zzz521, zzz523, zzz524, zzz31, new_primPlusNat2(new_primMulNat0(zzz34200), Succ(zzz34200)), h)
new_mkVBalBranch3MkVBalBranch22(zzz340, zzz341, Zero, zzz343, zzz344, zzz520, zzz521, zzz52200, zzz523, zzz524, zzz31, h) → new_mkVBalBranch(zzz31, zzz524, Branch(zzz340, zzz341, Neg(Zero), zzz343, zzz344), h)
new_mkVBalBranch3MkVBalBranch1(zzz340, zzz341, zzz34200, zzz343, zzz344, zzz520, zzz521, zzz52200, zzz523, zzz524, zzz31, Succ(zzz1430), h) → new_mkVBalBranch(zzz31, zzz524, Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), h)
new_mkVBalBranch3MkVBalBranch24(zzz340, zzz341, Neg(Succ(Zero)), zzz343, zzz344, zzz520, zzz521, zzz52200, zzz523, zzz524, zzz31, Succ(zzz690), h) → new_mkVBalBranch(zzz31, Branch(zzz520, zzz521, Neg(Succ(zzz52200)), zzz523, zzz524), zzz343, h)
new_mkVBalBranch3MkVBalBranch13(zzz340, zzz341, zzz34200, zzz343, zzz344, zzz520, zzz521, zzz523, zzz524, zzz31, Succ(zzz1290), h) → new_mkVBalBranch(zzz31, zzz524, Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), h)
new_mkVBalBranch3MkVBalBranch2(zzz340, zzz341, Pos(Succ(zzz34200)), zzz343, zzz344, zzz520, zzz521, zzz52200, zzz523, zzz524, zzz31, Succ(zzz680), h) → new_mkVBalBranch3MkVBalBranch20(zzz340, zzz341, zzz34200, zzz343, zzz344, zzz520, zzz521, zzz52200, zzz523, zzz524, zzz31, Succ(new_primPlusNat2(zzz680, zzz52200)), zzz34200, h)
new_mkVBalBranch(zzz31, Branch(zzz520, zzz521, Neg(Zero), zzz523, zzz524), Branch(zzz340, zzz341, Pos(Succ(zzz34200)), zzz343, zzz344), h) → new_mkVBalBranch(zzz31, Branch(zzz520, zzz521, Neg(Zero), zzz523, zzz524), zzz343, h)
new_mkVBalBranch3MkVBalBranch24(zzz340, zzz341, Neg(Zero), zzz343, zzz344, zzz520, zzz521, zzz52200, zzz523, zzz524, zzz31, Succ(zzz690), h) → new_mkVBalBranch(zzz31, Branch(zzz520, zzz521, Neg(Succ(zzz52200)), zzz523, zzz524), zzz343, h)
new_mkVBalBranch3MkVBalBranch1(zzz340, zzz341, zzz34200, zzz343, zzz344, zzz520, zzz521, zzz52200, zzz523, zzz524, zzz31, Zero, h) → new_mkVBalBranch3MkVBalBranch17(zzz340, zzz341, zzz34200, zzz343, zzz344, zzz520, zzz521, zzz52200, zzz523, zzz524, zzz31, h)
new_mkVBalBranch3MkVBalBranch16(zzz1702, zzz1703, zzz1704, zzz1705, zzz1706, zzz1707, zzz1708, zzz1709, zzz1710, zzz1711, zzz1712, Succ(zzz17130), Succ(zzz17140), bd) → new_mkVBalBranch3MkVBalBranch16(zzz1702, zzz1703, zzz1704, zzz1705, zzz1706, zzz1707, zzz1708, zzz1709, zzz1710, zzz1711, zzz1712, zzz17130, zzz17140, bd)
new_mkVBalBranch3MkVBalBranch25(zzz537, zzz538, zzz539, zzz540, zzz541, zzz542, zzz543, zzz544, zzz545, zzz546, zzz547, Zero, Succ(zzz5490), bc) → new_mkVBalBranch(zzz547, Branch(zzz542, zzz543, Neg(Succ(Succ(zzz544))), zzz545, zzz546), zzz540, bc)
new_mkVBalBranch3MkVBalBranch212(zzz818, zzz819, zzz820, zzz821, zzz822, zzz823, zzz824, zzz825, zzz826, zzz827, bf) → new_mkVBalBranch3MkVBalBranch14(zzz818, zzz819, zzz820, zzz821, zzz822, zzz823, zzz824, zzz825, zzz826, zzz827, new_primPlusNat2(new_primMulNat0(zzz820), Succ(zzz820)), bf)
new_mkVBalBranch3MkVBalBranch10(zzz929, zzz930, zzz931, zzz932, zzz933, zzz934, zzz935, zzz936, zzz937, zzz938, zzz939, Succ(zzz10020), ba) → new_mkVBalBranch3MkVBalBranch11(zzz929, zzz930, zzz931, zzz932, zzz933, zzz934, zzz935, zzz936, zzz937, zzz938, zzz939, Succ(zzz10020), Succ(zzz936), ba)
new_mkVBalBranch3MkVBalBranch14(zzz818, zzz819, zzz820, zzz821, zzz822, zzz823, zzz824, zzz825, zzz826, zzz827, Succ(zzz8960), bf) → new_mkVBalBranch3MkVBalBranch16(zzz818, zzz819, zzz820, zzz821, zzz822, zzz823, zzz824, Zero, zzz825, zzz826, zzz827, Succ(Zero), Succ(zzz8960), bf)
new_mkVBalBranch3MkVBalBranch24(zzz340, zzz341, Neg(Succ(Succ(Succ(zzz3420000)))), zzz343, zzz344, zzz520, zzz521, Succ(zzz522000), zzz523, zzz524, zzz31, Succ(Succ(zzz6900)), h) → new_mkVBalBranch3MkVBalBranch25(zzz340, zzz341, Succ(Succ(zzz3420000)), zzz343, zzz344, zzz520, zzz521, zzz522000, zzz523, zzz524, zzz31, Succ(zzz3420000), Succ(Succ(new_primPlusNat2(zzz6900, zzz522000))), h)
new_mkVBalBranch3MkVBalBranch2(zzz340, zzz341, Pos(Succ(zzz34200)), zzz343, zzz344, zzz520, zzz521, zzz52200, zzz523, zzz524, zzz31, Zero, h) → new_mkVBalBranch3MkVBalBranch20(zzz340, zzz341, zzz34200, zzz343, zzz344, zzz520, zzz521, zzz52200, zzz523, zzz524, zzz31, zzz52200, zzz34200, h)
new_mkVBalBranch3MkVBalBranch24(zzz340, zzz341, Neg(Zero), zzz343, zzz344, zzz520, zzz521, zzz52200, zzz523, zzz524, zzz31, Zero, h) → new_mkVBalBranch3MkVBalBranch210(zzz340, zzz341, zzz343, zzz344, zzz520, zzz521, zzz52200, zzz523, zzz524, zzz31, h)
new_mkVBalBranch3MkVBalBranch24(zzz340, zzz341, Neg(Succ(Succ(Zero))), zzz343, zzz344, zzz520, zzz521, Succ(zzz522000), zzz523, zzz524, zzz31, Succ(Succ(zzz6900)), h) → new_mkVBalBranch3MkVBalBranch25(zzz340, zzz341, Succ(Zero), zzz343, zzz344, zzz520, zzz521, zzz522000, zzz523, zzz524, zzz31, Zero, Succ(Succ(new_primPlusNat2(zzz6900, zzz522000))), h)
new_mkVBalBranch3MkVBalBranch23(zzz929, zzz930, zzz931, zzz932, zzz933, zzz934, zzz935, zzz936, zzz937, zzz938, zzz939, ba) → new_mkVBalBranch3MkVBalBranch10(zzz929, zzz930, zzz931, zzz932, zzz933, zzz934, zzz935, zzz936, zzz937, zzz938, zzz939, new_primPlusNat2(new_primMulNat0(zzz931), Succ(zzz931)), ba)
new_mkVBalBranch3MkVBalBranch2(zzz340, zzz341, Neg(Zero), zzz343, zzz344, zzz520, zzz521, zzz52200, zzz523, zzz524, zzz31, Succ(zzz680), h) → new_mkVBalBranch(zzz31, zzz524, Branch(zzz340, zzz341, Neg(Zero), zzz343, zzz344), h)
new_mkVBalBranch3MkVBalBranch16(zzz1702, zzz1703, zzz1704, zzz1705, zzz1706, zzz1707, zzz1708, zzz1709, zzz1710, zzz1711, zzz1712, Zero, Succ(zzz17140), bd) → new_mkVBalBranch(zzz1712, zzz1711, Branch(zzz1702, zzz1703, Neg(Succ(zzz1704)), zzz1705, zzz1706), bd)
new_mkVBalBranch3MkVBalBranch10(zzz929, zzz930, zzz931, zzz932, zzz933, zzz934, zzz935, zzz936, zzz937, zzz938, zzz939, Zero, ba) → new_mkVBalBranch3MkVBalBranch11(zzz929, zzz930, zzz931, zzz932, zzz933, zzz934, zzz935, zzz936, zzz937, zzz938, zzz939, Zero, Succ(zzz936), ba)
new_mkVBalBranch3MkVBalBranch22(zzz340, zzz341, Succ(zzz34200), zzz343, zzz344, zzz520, zzz521, zzz52200, zzz523, zzz524, zzz31, h) → new_mkVBalBranch3MkVBalBranch1(zzz340, zzz341, zzz34200, zzz343, zzz344, zzz520, zzz521, zzz52200, zzz523, zzz524, zzz31, new_primPlusNat2(new_primPlusNat3(Succ(new_primPlusNat3(new_primPlusNat1(zzz34200), zzz34200)), Succ(zzz34200)), Succ(zzz34200)), h)
new_mkVBalBranch3MkVBalBranch25(zzz537, zzz538, zzz539, zzz540, zzz541, zzz542, zzz543, zzz544, zzz545, zzz546, zzz547, Zero, Zero, bc) → new_mkVBalBranch3MkVBalBranch211(zzz537, zzz538, zzz539, zzz540, zzz541, zzz542, zzz543, zzz544, zzz545, zzz546, zzz547, bc)
new_mkVBalBranch3MkVBalBranch2(zzz340, zzz341, Pos(Zero), zzz343, zzz344, zzz520, zzz521, zzz52200, zzz523, zzz524, zzz31, Zero, h) → new_mkVBalBranch3MkVBalBranch21(zzz340, zzz341, zzz343, zzz344, zzz520, zzz521, zzz52200, zzz523, zzz524, zzz31, h)

The TRS R consists of the following rules:

new_primPlusNat1(Zero) → Zero
new_primMulNat0(zzz6200) → new_primPlusNat3(Succ(new_primPlusNat3(new_primPlusNat1(zzz6200), zzz6200)), Succ(zzz6200))
new_primPlusNat2(Succ(zzz900), Succ(zzz9100)) → Succ(Succ(new_primPlusNat2(zzz900, zzz9100)))
new_primPlusNat3(zzz90, Succ(zzz910)) → Succ(Succ(new_primPlusNat2(zzz90, zzz910)))
new_primPlusNat3(zzz90, Zero) → Succ(zzz90)
new_primMulNat1(zzz34200) → new_primPlusNat2(new_primMulNat0(zzz34200), Succ(zzz34200))
new_primPlusNat2(Zero, Zero) → Zero
new_primPlusNat1(Succ(zzz62000)) → Succ(Succ(new_primPlusNat1(zzz62000)))
new_primPlusNat2(Succ(zzz900), Zero) → Succ(zzz900)
new_primPlusNat2(Zero, Succ(zzz9100)) → Succ(zzz9100)

The set Q consists of the following terms:

new_primPlusNat2(Zero, Succ(x0))
new_primMulNat1(x0)
new_primMulNat0(x0)
new_primPlusNat3(x0, Succ(x1))
new_primPlusNat2(Succ(x0), Succ(x1))
new_primPlusNat3(x0, Zero)
new_primPlusNat1(Zero)
new_primPlusNat2(Zero, Zero)
new_primPlusNat1(Succ(x0))
new_primPlusNat2(Succ(x0), Zero)

We have to consider all minimal (P,Q,R)-chains.
By rewriting [15] the rule new_mkVBalBranch3MkVBalBranch211(zzz537, zzz538, zzz539, zzz540, zzz541, zzz542, zzz543, zzz544, zzz545, zzz546, zzz547, bc) → new_mkVBalBranch3MkVBalBranch15(zzz537, zzz538, zzz539, zzz540, zzz541, zzz542, zzz543, zzz544, zzz545, zzz546, zzz547, new_primMulNat1(zzz539), bc) at position [11] we obtained the following new rules:

new_mkVBalBranch3MkVBalBranch211(zzz537, zzz538, zzz539, zzz540, zzz541, zzz542, zzz543, zzz544, zzz545, zzz546, zzz547, bc) → new_mkVBalBranch3MkVBalBranch15(zzz537, zzz538, zzz539, zzz540, zzz541, zzz542, zzz543, zzz544, zzz545, zzz546, zzz547, new_primPlusNat2(new_primMulNat0(zzz539), Succ(zzz539)), bc)



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

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

new_mkVBalBranch3MkVBalBranch211(zzz537, zzz538, zzz539, zzz540, zzz541, zzz542, zzz543, zzz544, zzz545, zzz546, zzz547, bc) → new_mkVBalBranch3MkVBalBranch15(zzz537, zzz538, zzz539, zzz540, zzz541, zzz542, zzz543, zzz544, zzz545, zzz546, zzz547, new_primPlusNat2(new_primMulNat0(zzz539), Succ(zzz539)), bc)
new_mkVBalBranch3MkVBalBranch11(zzz2033, zzz2034, zzz2035, zzz2036, zzz2037, zzz2038, zzz2039, zzz2040, zzz2041, zzz2042, zzz2043, Zero, Succ(zzz20450), bb) → new_mkVBalBranch(zzz2043, zzz2042, Branch(zzz2033, zzz2034, Pos(Succ(zzz2035)), zzz2036, zzz2037), bb)
new_mkVBalBranch3MkVBalBranch2(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344, zzz520, zzz521, zzz52200, zzz523, zzz524, zzz31, Succ(zzz680), h) → new_mkVBalBranch3MkVBalBranch1(zzz340, zzz341, zzz34200, zzz343, zzz344, zzz520, zzz521, zzz52200, zzz523, zzz524, zzz31, new_primPlusNat2(new_primPlusNat3(Succ(new_primPlusNat3(new_primPlusNat1(zzz34200), zzz34200)), Succ(zzz34200)), Succ(zzz34200)), h)
new_mkVBalBranch3MkVBalBranch26(zzz1133, zzz1134, zzz1135, zzz1136, zzz1137, zzz1138, zzz1139, zzz1140, zzz1141, zzz1142, Succ(zzz11430), Succ(zzz11440), be) → new_mkVBalBranch3MkVBalBranch26(zzz1133, zzz1134, zzz1135, zzz1136, zzz1137, zzz1138, zzz1139, zzz1140, zzz1141, zzz1142, zzz11430, zzz11440, be)
new_mkVBalBranch3MkVBalBranch24(zzz340, zzz341, Neg(Succ(Succ(Succ(zzz3420000)))), zzz343, zzz344, zzz520, zzz521, Zero, zzz523, zzz524, zzz31, Succ(Zero), h) → new_mkVBalBranch3MkVBalBranch26(zzz340, zzz341, Succ(Succ(zzz3420000)), zzz343, zzz344, zzz520, zzz521, zzz523, zzz524, zzz31, Succ(zzz3420000), Zero, h)
new_mkVBalBranch3MkVBalBranch24(zzz340, zzz341, Neg(Succ(Zero)), zzz343, zzz344, zzz520, zzz521, Zero, zzz523, zzz524, zzz31, Zero, h) → new_mkVBalBranch3MkVBalBranch29(zzz340, zzz341, Zero, zzz343, zzz344, zzz520, zzz521, zzz523, zzz524, zzz31, h)
new_mkVBalBranch3MkVBalBranch25(zzz537, zzz538, zzz539, zzz540, zzz541, zzz542, zzz543, zzz544, zzz545, zzz546, zzz547, Succ(zzz5480), Zero, bc) → new_mkVBalBranch3MkVBalBranch15(zzz537, zzz538, zzz539, zzz540, zzz541, zzz542, zzz543, zzz544, zzz545, zzz546, zzz547, new_primPlusNat2(new_primMulNat0(zzz539), Succ(zzz539)), bc)
new_mkVBalBranch3MkVBalBranch20(zzz929, zzz930, zzz931, zzz932, zzz933, zzz934, zzz935, zzz936, zzz937, zzz938, zzz939, Zero, Succ(zzz9410), ba) → new_mkVBalBranch(zzz939, Branch(zzz934, zzz935, Pos(Succ(zzz936)), zzz937, zzz938), zzz932, ba)
new_mkVBalBranch3MkVBalBranch17(zzz340, zzz341, zzz34200, zzz343, zzz344, zzz520, zzz521, zzz52200, zzz523, zzz524, zzz31, h) → new_mkVBalBranch(zzz31, zzz524, Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), h)
new_mkVBalBranch3MkVBalBranch26(zzz1133, zzz1134, zzz1135, zzz1136, zzz1137, zzz1138, zzz1139, zzz1140, zzz1141, zzz1142, Zero, Zero, be) → new_mkVBalBranch3MkVBalBranch29(zzz1133, zzz1134, zzz1135, zzz1136, zzz1137, zzz1138, zzz1139, zzz1140, zzz1141, zzz1142, be)
new_mkVBalBranch3MkVBalBranch20(zzz929, zzz930, zzz931, zzz932, zzz933, zzz934, zzz935, zzz936, zzz937, zzz938, zzz939, Zero, Zero, ba) → new_mkVBalBranch3MkVBalBranch23(zzz929, zzz930, zzz931, zzz932, zzz933, zzz934, zzz935, zzz936, zzz937, zzz938, zzz939, ba)
new_mkVBalBranch3MkVBalBranch20(zzz929, zzz930, zzz931, zzz932, zzz933, zzz934, zzz935, zzz936, zzz937, zzz938, zzz939, Succ(zzz9400), Zero, ba) → new_mkVBalBranch3MkVBalBranch10(zzz929, zzz930, zzz931, zzz932, zzz933, zzz934, zzz935, zzz936, zzz937, zzz938, zzz939, new_primPlusNat2(new_primMulNat0(zzz931), Succ(zzz931)), ba)
new_mkVBalBranch3MkVBalBranch24(zzz340, zzz341, Neg(Succ(Succ(Zero))), zzz343, zzz344, zzz520, zzz521, Succ(zzz522000), zzz523, zzz524, zzz31, Succ(Zero), h) → new_mkVBalBranch3MkVBalBranch25(zzz340, zzz341, Succ(Zero), zzz343, zzz344, zzz520, zzz521, zzz522000, zzz523, zzz524, zzz31, Zero, Succ(zzz522000), h)
new_mkVBalBranch3MkVBalBranch20(zzz929, zzz930, zzz931, zzz932, zzz933, zzz934, zzz935, zzz936, zzz937, zzz938, zzz939, Succ(zzz9400), Succ(zzz9410), ba) → new_mkVBalBranch3MkVBalBranch20(zzz929, zzz930, zzz931, zzz932, zzz933, zzz934, zzz935, zzz936, zzz937, zzz938, zzz939, zzz9400, zzz9410, ba)
new_mkVBalBranch3MkVBalBranch24(zzz340, zzz341, Neg(Succ(Succ(Succ(zzz3420000)))), zzz343, zzz344, zzz520, zzz521, Succ(zzz522000), zzz523, zzz524, zzz31, Succ(Zero), h) → new_mkVBalBranch3MkVBalBranch25(zzz340, zzz341, Succ(Succ(zzz3420000)), zzz343, zzz344, zzz520, zzz521, zzz522000, zzz523, zzz524, zzz31, Succ(zzz3420000), Succ(zzz522000), h)
new_mkVBalBranch3MkVBalBranch26(zzz1133, zzz1134, zzz1135, zzz1136, zzz1137, zzz1138, zzz1139, zzz1140, zzz1141, zzz1142, Succ(zzz11430), Zero, be) → new_mkVBalBranch3MkVBalBranch212(zzz1133, zzz1134, zzz1135, zzz1136, zzz1137, zzz1138, zzz1139, zzz1140, zzz1141, zzz1142, be)
new_mkVBalBranch3MkVBalBranch24(zzz340, zzz341, Neg(Succ(Succ(zzz342000))), zzz343, zzz344, zzz520, zzz521, Succ(zzz522000), zzz523, zzz524, zzz31, Zero, h) → new_mkVBalBranch3MkVBalBranch25(zzz340, zzz341, Succ(zzz342000), zzz343, zzz344, zzz520, zzz521, zzz522000, zzz523, zzz524, zzz31, zzz342000, zzz522000, h)
new_mkVBalBranch(zzz31, Branch(zzz520, zzz521, Pos(Succ(zzz52200)), zzz523, zzz524), Branch(zzz340, zzz341, zzz342, zzz343, zzz344), h) → new_mkVBalBranch3MkVBalBranch2(zzz340, zzz341, zzz342, zzz343, zzz344, zzz520, zzz521, zzz52200, zzz523, zzz524, zzz31, new_primPlusNat3(Succ(new_primPlusNat3(new_primPlusNat1(zzz52200), zzz52200)), Succ(zzz52200)), h)
new_mkVBalBranch3MkVBalBranch29(zzz818, zzz819, zzz820, zzz821, zzz822, zzz823, zzz824, zzz825, zzz826, zzz827, bf) → new_mkVBalBranch3MkVBalBranch14(zzz818, zzz819, zzz820, zzz821, zzz822, zzz823, zzz824, zzz825, zzz826, zzz827, new_primPlusNat2(new_primMulNat0(zzz820), Succ(zzz820)), bf)
new_mkVBalBranch3MkVBalBranch11(zzz2033, zzz2034, zzz2035, zzz2036, zzz2037, zzz2038, zzz2039, zzz2040, zzz2041, zzz2042, zzz2043, Succ(zzz20440), Succ(zzz20450), bb) → new_mkVBalBranch3MkVBalBranch11(zzz2033, zzz2034, zzz2035, zzz2036, zzz2037, zzz2038, zzz2039, zzz2040, zzz2041, zzz2042, zzz2043, zzz20440, zzz20450, bb)
new_mkVBalBranch3MkVBalBranch2(zzz340, zzz341, Neg(zzz3420), zzz343, zzz344, zzz520, zzz521, zzz52200, zzz523, zzz524, zzz31, Zero, h) → new_mkVBalBranch3MkVBalBranch22(zzz340, zzz341, zzz3420, zzz343, zzz344, zzz520, zzz521, zzz52200, zzz523, zzz524, zzz31, h)
new_mkVBalBranch3MkVBalBranch25(zzz537, zzz538, zzz539, zzz540, zzz541, zzz542, zzz543, zzz544, zzz545, zzz546, zzz547, Succ(zzz5480), Succ(zzz5490), bc) → new_mkVBalBranch3MkVBalBranch25(zzz537, zzz538, zzz539, zzz540, zzz541, zzz542, zzz543, zzz544, zzz545, zzz546, zzz547, zzz5480, zzz5490, bc)
new_mkVBalBranch(zzz31, Branch(zzz520, zzz521, Neg(Succ(zzz52200)), zzz523, zzz524), Branch(zzz340, zzz341, zzz342, zzz343, zzz344), h) → new_mkVBalBranch3MkVBalBranch24(zzz340, zzz341, zzz342, zzz343, zzz344, zzz520, zzz521, zzz52200, zzz523, zzz524, zzz31, new_primPlusNat3(Succ(new_primPlusNat3(new_primPlusNat1(zzz52200), zzz52200)), Succ(zzz52200)), h)
new_mkVBalBranch3MkVBalBranch24(zzz340, zzz341, Neg(Succ(Zero)), zzz343, zzz344, zzz520, zzz521, Succ(zzz522000), zzz523, zzz524, zzz31, Zero, h) → new_mkVBalBranch3MkVBalBranch28(zzz340, zzz341, zzz343, zzz344, zzz520, zzz521, Succ(zzz522000), zzz523, zzz524, zzz31, h)
new_mkVBalBranch3MkVBalBranch210(zzz340, zzz341, zzz343, zzz344, zzz520, zzz521, zzz52200, zzz523, zzz524, zzz31, h) → new_mkVBalBranch(zzz31, Branch(zzz520, zzz521, Neg(Succ(zzz52200)), zzz523, zzz524), zzz343, h)
new_mkVBalBranch3MkVBalBranch24(zzz340, zzz341, Neg(Succ(Succ(zzz342000))), zzz343, zzz344, zzz520, zzz521, Zero, zzz523, zzz524, zzz31, Zero, h) → new_mkVBalBranch3MkVBalBranch14(zzz340, zzz341, Succ(zzz342000), zzz343, zzz344, zzz520, zzz521, zzz523, zzz524, zzz31, new_primMulNat1(Succ(zzz342000)), h)
new_mkVBalBranch3MkVBalBranch26(zzz1133, zzz1134, zzz1135, zzz1136, zzz1137, zzz1138, zzz1139, zzz1140, zzz1141, zzz1142, Zero, Succ(zzz11440), be) → new_mkVBalBranch(zzz1142, Branch(zzz1138, zzz1139, Neg(Succ(Zero)), zzz1140, zzz1141), zzz1136, be)
new_mkVBalBranch3MkVBalBranch24(zzz340, zzz341, Neg(Succ(Succ(Zero))), zzz343, zzz344, zzz520, zzz521, Zero, zzz523, zzz524, zzz31, Succ(Zero), h) → new_mkVBalBranch3MkVBalBranch26(zzz340, zzz341, Succ(Zero), zzz343, zzz344, zzz520, zzz521, zzz523, zzz524, zzz31, Zero, Zero, h)
new_mkVBalBranch(zzz31, Branch(zzz520, zzz521, Pos(Zero), zzz523, zzz524), Branch(zzz340, zzz341, Pos(Succ(zzz34200)), zzz343, zzz344), h) → new_mkVBalBranch(zzz31, Branch(zzz520, zzz521, Pos(Zero), zzz523, zzz524), zzz343, h)
new_mkVBalBranch3MkVBalBranch2(zzz340, zzz341, Pos(Zero), zzz343, zzz344, zzz520, zzz521, zzz52200, zzz523, zzz524, zzz31, Succ(zzz680), h) → new_mkVBalBranch(zzz31, zzz524, Branch(zzz340, zzz341, Pos(Zero), zzz343, zzz344), h)
new_mkVBalBranch3MkVBalBranch21(zzz340, zzz341, zzz343, zzz344, zzz520, zzz521, zzz52200, zzz523, zzz524, zzz31, h) → new_mkVBalBranch(zzz31, zzz524, Branch(zzz340, zzz341, Pos(Zero), zzz343, zzz344), h)
new_mkVBalBranch3MkVBalBranch24(zzz340, zzz341, Pos(zzz3420), zzz343, zzz344, zzz520, zzz521, zzz52200, zzz523, zzz524, zzz31, Zero, h) → new_mkVBalBranch3MkVBalBranch27(zzz340, zzz341, zzz3420, zzz343, zzz344, zzz520, zzz521, zzz52200, zzz523, zzz524, zzz31, h)
new_mkVBalBranch3MkVBalBranch24(zzz340, zzz341, Neg(Succ(Succ(Succ(zzz3420000)))), zzz343, zzz344, zzz520, zzz521, Zero, zzz523, zzz524, zzz31, Succ(Succ(zzz6900)), h) → new_mkVBalBranch3MkVBalBranch26(zzz340, zzz341, Succ(Succ(zzz3420000)), zzz343, zzz344, zzz520, zzz521, zzz523, zzz524, zzz31, Succ(zzz3420000), Succ(zzz6900), h)
new_mkVBalBranch3MkVBalBranch15(zzz537, zzz538, zzz539, zzz540, zzz541, zzz542, zzz543, zzz544, zzz545, zzz546, zzz547, Succ(zzz6990), bc) → new_mkVBalBranch3MkVBalBranch16(zzz537, zzz538, zzz539, zzz540, zzz541, zzz542, zzz543, Succ(zzz544), zzz545, zzz546, zzz547, Succ(Succ(zzz544)), Succ(zzz6990), bc)
new_mkVBalBranch(zzz31, Branch(zzz520, zzz521, Neg(Zero), zzz523, zzz524), Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), h) → new_mkVBalBranch3MkVBalBranch13(zzz340, zzz341, zzz34200, zzz343, zzz344, zzz520, zzz521, zzz523, zzz524, zzz31, new_primPlusNat2(new_primMulNat0(zzz34200), Succ(zzz34200)), h)
new_mkVBalBranch3MkVBalBranch27(zzz340, zzz341, zzz3420, zzz343, zzz344, zzz520, zzz521, zzz52200, zzz523, zzz524, zzz31, h) → new_mkVBalBranch(zzz31, Branch(zzz520, zzz521, Neg(Succ(zzz52200)), zzz523, zzz524), zzz343, h)
new_mkVBalBranch3MkVBalBranch24(zzz340, zzz341, Pos(zzz3420), zzz343, zzz344, zzz520, zzz521, zzz52200, zzz523, zzz524, zzz31, Succ(zzz690), h) → new_mkVBalBranch(zzz31, Branch(zzz520, zzz521, Neg(Succ(zzz52200)), zzz523, zzz524), zzz343, h)
new_mkVBalBranch3MkVBalBranch12(zzz340, zzz341, zzz34200, zzz343, zzz344, zzz520, zzz521, zzz523, zzz524, zzz31, Succ(zzz1250), h) → new_mkVBalBranch(zzz31, zzz524, Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), h)
new_mkVBalBranch3MkVBalBranch28(zzz340, zzz341, zzz343, zzz344, zzz520, zzz521, zzz52200, zzz523, zzz524, zzz31, h) → new_mkVBalBranch(zzz31, Branch(zzz520, zzz521, Neg(Succ(zzz52200)), zzz523, zzz524), zzz343, h)
new_mkVBalBranch3MkVBalBranch24(zzz340, zzz341, Neg(Succ(Succ(Zero))), zzz343, zzz344, zzz520, zzz521, Zero, zzz523, zzz524, zzz31, Succ(Succ(zzz6900)), h) → new_mkVBalBranch3MkVBalBranch26(zzz340, zzz341, Succ(Zero), zzz343, zzz344, zzz520, zzz521, zzz523, zzz524, zzz31, Zero, Succ(zzz6900), h)
new_mkVBalBranch3MkVBalBranch1(zzz340, zzz341, zzz34200, zzz343, zzz344, zzz520, zzz521, zzz52200, zzz523, zzz524, zzz31, Succ(zzz1430), h) → new_mkVBalBranch(zzz31, zzz524, Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), h)
new_mkVBalBranch3MkVBalBranch22(zzz340, zzz341, Zero, zzz343, zzz344, zzz520, zzz521, zzz52200, zzz523, zzz524, zzz31, h) → new_mkVBalBranch(zzz31, zzz524, Branch(zzz340, zzz341, Neg(Zero), zzz343, zzz344), h)
new_mkVBalBranch(zzz31, Branch(zzz520, zzz521, Pos(Zero), zzz523, zzz524), Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), h) → new_mkVBalBranch3MkVBalBranch12(zzz340, zzz341, zzz34200, zzz343, zzz344, zzz520, zzz521, zzz523, zzz524, zzz31, new_primPlusNat2(new_primMulNat0(zzz34200), Succ(zzz34200)), h)
new_mkVBalBranch3MkVBalBranch24(zzz340, zzz341, Neg(Succ(Zero)), zzz343, zzz344, zzz520, zzz521, zzz52200, zzz523, zzz524, zzz31, Succ(zzz690), h) → new_mkVBalBranch(zzz31, Branch(zzz520, zzz521, Neg(Succ(zzz52200)), zzz523, zzz524), zzz343, h)
new_mkVBalBranch3MkVBalBranch13(zzz340, zzz341, zzz34200, zzz343, zzz344, zzz520, zzz521, zzz523, zzz524, zzz31, Succ(zzz1290), h) → new_mkVBalBranch(zzz31, zzz524, Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), h)
new_mkVBalBranch3MkVBalBranch2(zzz340, zzz341, Pos(Succ(zzz34200)), zzz343, zzz344, zzz520, zzz521, zzz52200, zzz523, zzz524, zzz31, Succ(zzz680), h) → new_mkVBalBranch3MkVBalBranch20(zzz340, zzz341, zzz34200, zzz343, zzz344, zzz520, zzz521, zzz52200, zzz523, zzz524, zzz31, Succ(new_primPlusNat2(zzz680, zzz52200)), zzz34200, h)
new_mkVBalBranch3MkVBalBranch24(zzz340, zzz341, Neg(Zero), zzz343, zzz344, zzz520, zzz521, zzz52200, zzz523, zzz524, zzz31, Succ(zzz690), h) → new_mkVBalBranch(zzz31, Branch(zzz520, zzz521, Neg(Succ(zzz52200)), zzz523, zzz524), zzz343, h)
new_mkVBalBranch(zzz31, Branch(zzz520, zzz521, Neg(Zero), zzz523, zzz524), Branch(zzz340, zzz341, Pos(Succ(zzz34200)), zzz343, zzz344), h) → new_mkVBalBranch(zzz31, Branch(zzz520, zzz521, Neg(Zero), zzz523, zzz524), zzz343, h)
new_mkVBalBranch3MkVBalBranch1(zzz340, zzz341, zzz34200, zzz343, zzz344, zzz520, zzz521, zzz52200, zzz523, zzz524, zzz31, Zero, h) → new_mkVBalBranch3MkVBalBranch17(zzz340, zzz341, zzz34200, zzz343, zzz344, zzz520, zzz521, zzz52200, zzz523, zzz524, zzz31, h)
new_mkVBalBranch3MkVBalBranch16(zzz1702, zzz1703, zzz1704, zzz1705, zzz1706, zzz1707, zzz1708, zzz1709, zzz1710, zzz1711, zzz1712, Succ(zzz17130), Succ(zzz17140), bd) → new_mkVBalBranch3MkVBalBranch16(zzz1702, zzz1703, zzz1704, zzz1705, zzz1706, zzz1707, zzz1708, zzz1709, zzz1710, zzz1711, zzz1712, zzz17130, zzz17140, bd)
new_mkVBalBranch3MkVBalBranch25(zzz537, zzz538, zzz539, zzz540, zzz541, zzz542, zzz543, zzz544, zzz545, zzz546, zzz547, Zero, Succ(zzz5490), bc) → new_mkVBalBranch(zzz547, Branch(zzz542, zzz543, Neg(Succ(Succ(zzz544))), zzz545, zzz546), zzz540, bc)
new_mkVBalBranch3MkVBalBranch10(zzz929, zzz930, zzz931, zzz932, zzz933, zzz934, zzz935, zzz936, zzz937, zzz938, zzz939, Succ(zzz10020), ba) → new_mkVBalBranch3MkVBalBranch11(zzz929, zzz930, zzz931, zzz932, zzz933, zzz934, zzz935, zzz936, zzz937, zzz938, zzz939, Succ(zzz10020), Succ(zzz936), ba)
new_mkVBalBranch3MkVBalBranch212(zzz818, zzz819, zzz820, zzz821, zzz822, zzz823, zzz824, zzz825, zzz826, zzz827, bf) → new_mkVBalBranch3MkVBalBranch14(zzz818, zzz819, zzz820, zzz821, zzz822, zzz823, zzz824, zzz825, zzz826, zzz827, new_primPlusNat2(new_primMulNat0(zzz820), Succ(zzz820)), bf)
new_mkVBalBranch3MkVBalBranch14(zzz818, zzz819, zzz820, zzz821, zzz822, zzz823, zzz824, zzz825, zzz826, zzz827, Succ(zzz8960), bf) → new_mkVBalBranch3MkVBalBranch16(zzz818, zzz819, zzz820, zzz821, zzz822, zzz823, zzz824, Zero, zzz825, zzz826, zzz827, Succ(Zero), Succ(zzz8960), bf)
new_mkVBalBranch3MkVBalBranch24(zzz340, zzz341, Neg(Succ(Succ(Succ(zzz3420000)))), zzz343, zzz344, zzz520, zzz521, Succ(zzz522000), zzz523, zzz524, zzz31, Succ(Succ(zzz6900)), h) → new_mkVBalBranch3MkVBalBranch25(zzz340, zzz341, Succ(Succ(zzz3420000)), zzz343, zzz344, zzz520, zzz521, zzz522000, zzz523, zzz524, zzz31, Succ(zzz3420000), Succ(Succ(new_primPlusNat2(zzz6900, zzz522000))), h)
new_mkVBalBranch3MkVBalBranch2(zzz340, zzz341, Pos(Succ(zzz34200)), zzz343, zzz344, zzz520, zzz521, zzz52200, zzz523, zzz524, zzz31, Zero, h) → new_mkVBalBranch3MkVBalBranch20(zzz340, zzz341, zzz34200, zzz343, zzz344, zzz520, zzz521, zzz52200, zzz523, zzz524, zzz31, zzz52200, zzz34200, h)
new_mkVBalBranch3MkVBalBranch24(zzz340, zzz341, Neg(Zero), zzz343, zzz344, zzz520, zzz521, zzz52200, zzz523, zzz524, zzz31, Zero, h) → new_mkVBalBranch3MkVBalBranch210(zzz340, zzz341, zzz343, zzz344, zzz520, zzz521, zzz52200, zzz523, zzz524, zzz31, h)
new_mkVBalBranch3MkVBalBranch24(zzz340, zzz341, Neg(Succ(Succ(Zero))), zzz343, zzz344, zzz520, zzz521, Succ(zzz522000), zzz523, zzz524, zzz31, Succ(Succ(zzz6900)), h) → new_mkVBalBranch3MkVBalBranch25(zzz340, zzz341, Succ(Zero), zzz343, zzz344, zzz520, zzz521, zzz522000, zzz523, zzz524, zzz31, Zero, Succ(Succ(new_primPlusNat2(zzz6900, zzz522000))), h)
new_mkVBalBranch3MkVBalBranch23(zzz929, zzz930, zzz931, zzz932, zzz933, zzz934, zzz935, zzz936, zzz937, zzz938, zzz939, ba) → new_mkVBalBranch3MkVBalBranch10(zzz929, zzz930, zzz931, zzz932, zzz933, zzz934, zzz935, zzz936, zzz937, zzz938, zzz939, new_primPlusNat2(new_primMulNat0(zzz931), Succ(zzz931)), ba)
new_mkVBalBranch3MkVBalBranch2(zzz340, zzz341, Neg(Zero), zzz343, zzz344, zzz520, zzz521, zzz52200, zzz523, zzz524, zzz31, Succ(zzz680), h) → new_mkVBalBranch(zzz31, zzz524, Branch(zzz340, zzz341, Neg(Zero), zzz343, zzz344), h)
new_mkVBalBranch3MkVBalBranch16(zzz1702, zzz1703, zzz1704, zzz1705, zzz1706, zzz1707, zzz1708, zzz1709, zzz1710, zzz1711, zzz1712, Zero, Succ(zzz17140), bd) → new_mkVBalBranch(zzz1712, zzz1711, Branch(zzz1702, zzz1703, Neg(Succ(zzz1704)), zzz1705, zzz1706), bd)
new_mkVBalBranch3MkVBalBranch10(zzz929, zzz930, zzz931, zzz932, zzz933, zzz934, zzz935, zzz936, zzz937, zzz938, zzz939, Zero, ba) → new_mkVBalBranch3MkVBalBranch11(zzz929, zzz930, zzz931, zzz932, zzz933, zzz934, zzz935, zzz936, zzz937, zzz938, zzz939, Zero, Succ(zzz936), ba)
new_mkVBalBranch3MkVBalBranch2(zzz340, zzz341, Pos(Zero), zzz343, zzz344, zzz520, zzz521, zzz52200, zzz523, zzz524, zzz31, Zero, h) → new_mkVBalBranch3MkVBalBranch21(zzz340, zzz341, zzz343, zzz344, zzz520, zzz521, zzz52200, zzz523, zzz524, zzz31, h)
new_mkVBalBranch3MkVBalBranch25(zzz537, zzz538, zzz539, zzz540, zzz541, zzz542, zzz543, zzz544, zzz545, zzz546, zzz547, Zero, Zero, bc) → new_mkVBalBranch3MkVBalBranch211(zzz537, zzz538, zzz539, zzz540, zzz541, zzz542, zzz543, zzz544, zzz545, zzz546, zzz547, bc)
new_mkVBalBranch3MkVBalBranch22(zzz340, zzz341, Succ(zzz34200), zzz343, zzz344, zzz520, zzz521, zzz52200, zzz523, zzz524, zzz31, h) → new_mkVBalBranch3MkVBalBranch1(zzz340, zzz341, zzz34200, zzz343, zzz344, zzz520, zzz521, zzz52200, zzz523, zzz524, zzz31, new_primPlusNat2(new_primPlusNat3(Succ(new_primPlusNat3(new_primPlusNat1(zzz34200), zzz34200)), Succ(zzz34200)), Succ(zzz34200)), h)

The TRS R consists of the following rules:

new_primPlusNat1(Zero) → Zero
new_primMulNat0(zzz6200) → new_primPlusNat3(Succ(new_primPlusNat3(new_primPlusNat1(zzz6200), zzz6200)), Succ(zzz6200))
new_primPlusNat2(Succ(zzz900), Succ(zzz9100)) → Succ(Succ(new_primPlusNat2(zzz900, zzz9100)))
new_primPlusNat3(zzz90, Succ(zzz910)) → Succ(Succ(new_primPlusNat2(zzz90, zzz910)))
new_primPlusNat3(zzz90, Zero) → Succ(zzz90)
new_primMulNat1(zzz34200) → new_primPlusNat2(new_primMulNat0(zzz34200), Succ(zzz34200))
new_primPlusNat2(Zero, Zero) → Zero
new_primPlusNat1(Succ(zzz62000)) → Succ(Succ(new_primPlusNat1(zzz62000)))
new_primPlusNat2(Succ(zzz900), Zero) → Succ(zzz900)
new_primPlusNat2(Zero, Succ(zzz9100)) → Succ(zzz9100)

The set Q consists of the following terms:

new_primPlusNat2(Zero, Succ(x0))
new_primMulNat1(x0)
new_primMulNat0(x0)
new_primPlusNat3(x0, Succ(x1))
new_primPlusNat2(Succ(x0), Succ(x1))
new_primPlusNat3(x0, Zero)
new_primPlusNat1(Zero)
new_primPlusNat2(Zero, Zero)
new_primPlusNat1(Succ(x0))
new_primPlusNat2(Succ(x0), Zero)

We have to consider all minimal (P,Q,R)-chains.
By rewriting [15] the rule new_mkVBalBranch3MkVBalBranch24(zzz340, zzz341, Neg(Succ(Succ(zzz342000))), zzz343, zzz344, zzz520, zzz521, Zero, zzz523, zzz524, zzz31, Zero, h) → new_mkVBalBranch3MkVBalBranch14(zzz340, zzz341, Succ(zzz342000), zzz343, zzz344, zzz520, zzz521, zzz523, zzz524, zzz31, new_primMulNat1(Succ(zzz342000)), h) at position [10] we obtained the following new rules:

new_mkVBalBranch3MkVBalBranch24(zzz340, zzz341, Neg(Succ(Succ(zzz342000))), zzz343, zzz344, zzz520, zzz521, Zero, zzz523, zzz524, zzz31, Zero, h) → new_mkVBalBranch3MkVBalBranch14(zzz340, zzz341, Succ(zzz342000), zzz343, zzz344, zzz520, zzz521, zzz523, zzz524, zzz31, new_primPlusNat2(new_primMulNat0(Succ(zzz342000)), Succ(Succ(zzz342000))), 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
                                    ↳ DependencyGraphProof
                                      ↳ QDP
                                        ↳ Rewriting
                                          ↳ QDP
                                            ↳ Rewriting
                                              ↳ QDP
                                                ↳ Rewriting
                                                  ↳ QDP
                                                    ↳ Rewriting
                                                      ↳ QDP
                                                        ↳ Rewriting
                                                          ↳ QDP
                                                            ↳ Rewriting
                                                              ↳ QDP
                                                                ↳ Rewriting
                                                                  ↳ QDP
                                                                    ↳ Rewriting
                                                                      ↳ QDP
                                                                        ↳ Rewriting
                                                                          ↳ QDP
                                                                            ↳ Rewriting
                                                                              ↳ QDP
                                                                                ↳ Rewriting
                                                                                  ↳ QDP
                                                                                    ↳ Rewriting
                                                                                      ↳ QDP
                                                                                        ↳ Rewriting
                                                                                          ↳ QDP
                                                                                            ↳ UsableRulesProof
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP

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

new_mkVBalBranch3MkVBalBranch11(zzz2033, zzz2034, zzz2035, zzz2036, zzz2037, zzz2038, zzz2039, zzz2040, zzz2041, zzz2042, zzz2043, Zero, Succ(zzz20450), bb) → new_mkVBalBranch(zzz2043, zzz2042, Branch(zzz2033, zzz2034, Pos(Succ(zzz2035)), zzz2036, zzz2037), bb)
new_mkVBalBranch3MkVBalBranch211(zzz537, zzz538, zzz539, zzz540, zzz541, zzz542, zzz543, zzz544, zzz545, zzz546, zzz547, bc) → new_mkVBalBranch3MkVBalBranch15(zzz537, zzz538, zzz539, zzz540, zzz541, zzz542, zzz543, zzz544, zzz545, zzz546, zzz547, new_primPlusNat2(new_primMulNat0(zzz539), Succ(zzz539)), bc)
new_mkVBalBranch3MkVBalBranch2(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344, zzz520, zzz521, zzz52200, zzz523, zzz524, zzz31, Succ(zzz680), h) → new_mkVBalBranch3MkVBalBranch1(zzz340, zzz341, zzz34200, zzz343, zzz344, zzz520, zzz521, zzz52200, zzz523, zzz524, zzz31, new_primPlusNat2(new_primPlusNat3(Succ(new_primPlusNat3(new_primPlusNat1(zzz34200), zzz34200)), Succ(zzz34200)), Succ(zzz34200)), h)
new_mkVBalBranch3MkVBalBranch26(zzz1133, zzz1134, zzz1135, zzz1136, zzz1137, zzz1138, zzz1139, zzz1140, zzz1141, zzz1142, Succ(zzz11430), Succ(zzz11440), be) → new_mkVBalBranch3MkVBalBranch26(zzz1133, zzz1134, zzz1135, zzz1136, zzz1137, zzz1138, zzz1139, zzz1140, zzz1141, zzz1142, zzz11430, zzz11440, be)
new_mkVBalBranch3MkVBalBranch24(zzz340, zzz341, Neg(Succ(Succ(zzz342000))), zzz343, zzz344, zzz520, zzz521, Zero, zzz523, zzz524, zzz31, Zero, h) → new_mkVBalBranch3MkVBalBranch14(zzz340, zzz341, Succ(zzz342000), zzz343, zzz344, zzz520, zzz521, zzz523, zzz524, zzz31, new_primPlusNat2(new_primMulNat0(Succ(zzz342000)), Succ(Succ(zzz342000))), h)
new_mkVBalBranch3MkVBalBranch24(zzz340, zzz341, Neg(Succ(Succ(Succ(zzz3420000)))), zzz343, zzz344, zzz520, zzz521, Zero, zzz523, zzz524, zzz31, Succ(Zero), h) → new_mkVBalBranch3MkVBalBranch26(zzz340, zzz341, Succ(Succ(zzz3420000)), zzz343, zzz344, zzz520, zzz521, zzz523, zzz524, zzz31, Succ(zzz3420000), Zero, h)
new_mkVBalBranch3MkVBalBranch25(zzz537, zzz538, zzz539, zzz540, zzz541, zzz542, zzz543, zzz544, zzz545, zzz546, zzz547, Succ(zzz5480), Zero, bc) → new_mkVBalBranch3MkVBalBranch15(zzz537, zzz538, zzz539, zzz540, zzz541, zzz542, zzz543, zzz544, zzz545, zzz546, zzz547, new_primPlusNat2(new_primMulNat0(zzz539), Succ(zzz539)), bc)
new_mkVBalBranch3MkVBalBranch24(zzz340, zzz341, Neg(Succ(Zero)), zzz343, zzz344, zzz520, zzz521, Zero, zzz523, zzz524, zzz31, Zero, h) → new_mkVBalBranch3MkVBalBranch29(zzz340, zzz341, Zero, zzz343, zzz344, zzz520, zzz521, zzz523, zzz524, zzz31, h)
new_mkVBalBranch3MkVBalBranch20(zzz929, zzz930, zzz931, zzz932, zzz933, zzz934, zzz935, zzz936, zzz937, zzz938, zzz939, Zero, Succ(zzz9410), ba) → new_mkVBalBranch(zzz939, Branch(zzz934, zzz935, Pos(Succ(zzz936)), zzz937, zzz938), zzz932, ba)
new_mkVBalBranch3MkVBalBranch17(zzz340, zzz341, zzz34200, zzz343, zzz344, zzz520, zzz521, zzz52200, zzz523, zzz524, zzz31, h) → new_mkVBalBranch(zzz31, zzz524, Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), h)
new_mkVBalBranch3MkVBalBranch26(zzz1133, zzz1134, zzz1135, zzz1136, zzz1137, zzz1138, zzz1139, zzz1140, zzz1141, zzz1142, Zero, Zero, be) → new_mkVBalBranch3MkVBalBranch29(zzz1133, zzz1134, zzz1135, zzz1136, zzz1137, zzz1138, zzz1139, zzz1140, zzz1141, zzz1142, be)
new_mkVBalBranch3MkVBalBranch20(zzz929, zzz930, zzz931, zzz932, zzz933, zzz934, zzz935, zzz936, zzz937, zzz938, zzz939, Zero, Zero, ba) → new_mkVBalBranch3MkVBalBranch23(zzz929, zzz930, zzz931, zzz932, zzz933, zzz934, zzz935, zzz936, zzz937, zzz938, zzz939, ba)
new_mkVBalBranch3MkVBalBranch20(zzz929, zzz930, zzz931, zzz932, zzz933, zzz934, zzz935, zzz936, zzz937, zzz938, zzz939, Succ(zzz9400), Zero, ba) → new_mkVBalBranch3MkVBalBranch10(zzz929, zzz930, zzz931, zzz932, zzz933, zzz934, zzz935, zzz936, zzz937, zzz938, zzz939, new_primPlusNat2(new_primMulNat0(zzz931), Succ(zzz931)), ba)
new_mkVBalBranch3MkVBalBranch24(zzz340, zzz341, Neg(Succ(Succ(Zero))), zzz343, zzz344, zzz520, zzz521, Succ(zzz522000), zzz523, zzz524, zzz31, Succ(Zero), h) → new_mkVBalBranch3MkVBalBranch25(zzz340, zzz341, Succ(Zero), zzz343, zzz344, zzz520, zzz521, zzz522000, zzz523, zzz524, zzz31, Zero, Succ(zzz522000), h)
new_mkVBalBranch3MkVBalBranch24(zzz340, zzz341, Neg(Succ(Succ(Succ(zzz3420000)))), zzz343, zzz344, zzz520, zzz521, Succ(zzz522000), zzz523, zzz524, zzz31, Succ(Zero), h) → new_mkVBalBranch3MkVBalBranch25(zzz340, zzz341, Succ(Succ(zzz3420000)), zzz343, zzz344, zzz520, zzz521, zzz522000, zzz523, zzz524, zzz31, Succ(zzz3420000), Succ(zzz522000), h)
new_mkVBalBranch3MkVBalBranch20(zzz929, zzz930, zzz931, zzz932, zzz933, zzz934, zzz935, zzz936, zzz937, zzz938, zzz939, Succ(zzz9400), Succ(zzz9410), ba) → new_mkVBalBranch3MkVBalBranch20(zzz929, zzz930, zzz931, zzz932, zzz933, zzz934, zzz935, zzz936, zzz937, zzz938, zzz939, zzz9400, zzz9410, ba)
new_mkVBalBranch3MkVBalBranch24(zzz340, zzz341, Neg(Succ(Succ(zzz342000))), zzz343, zzz344, zzz520, zzz521, Succ(zzz522000), zzz523, zzz524, zzz31, Zero, h) → new_mkVBalBranch3MkVBalBranch25(zzz340, zzz341, Succ(zzz342000), zzz343, zzz344, zzz520, zzz521, zzz522000, zzz523, zzz524, zzz31, zzz342000, zzz522000, h)
new_mkVBalBranch3MkVBalBranch26(zzz1133, zzz1134, zzz1135, zzz1136, zzz1137, zzz1138, zzz1139, zzz1140, zzz1141, zzz1142, Succ(zzz11430), Zero, be) → new_mkVBalBranch3MkVBalBranch212(zzz1133, zzz1134, zzz1135, zzz1136, zzz1137, zzz1138, zzz1139, zzz1140, zzz1141, zzz1142, be)
new_mkVBalBranch(zzz31, Branch(zzz520, zzz521, Pos(Succ(zzz52200)), zzz523, zzz524), Branch(zzz340, zzz341, zzz342, zzz343, zzz344), h) → new_mkVBalBranch3MkVBalBranch2(zzz340, zzz341, zzz342, zzz343, zzz344, zzz520, zzz521, zzz52200, zzz523, zzz524, zzz31, new_primPlusNat3(Succ(new_primPlusNat3(new_primPlusNat1(zzz52200), zzz52200)), Succ(zzz52200)), h)
new_mkVBalBranch3MkVBalBranch29(zzz818, zzz819, zzz820, zzz821, zzz822, zzz823, zzz824, zzz825, zzz826, zzz827, bf) → new_mkVBalBranch3MkVBalBranch14(zzz818, zzz819, zzz820, zzz821, zzz822, zzz823, zzz824, zzz825, zzz826, zzz827, new_primPlusNat2(new_primMulNat0(zzz820), Succ(zzz820)), bf)
new_mkVBalBranch3MkVBalBranch11(zzz2033, zzz2034, zzz2035, zzz2036, zzz2037, zzz2038, zzz2039, zzz2040, zzz2041, zzz2042, zzz2043, Succ(zzz20440), Succ(zzz20450), bb) → new_mkVBalBranch3MkVBalBranch11(zzz2033, zzz2034, zzz2035, zzz2036, zzz2037, zzz2038, zzz2039, zzz2040, zzz2041, zzz2042, zzz2043, zzz20440, zzz20450, bb)
new_mkVBalBranch3MkVBalBranch25(zzz537, zzz538, zzz539, zzz540, zzz541, zzz542, zzz543, zzz544, zzz545, zzz546, zzz547, Succ(zzz5480), Succ(zzz5490), bc) → new_mkVBalBranch3MkVBalBranch25(zzz537, zzz538, zzz539, zzz540, zzz541, zzz542, zzz543, zzz544, zzz545, zzz546, zzz547, zzz5480, zzz5490, bc)
new_mkVBalBranch3MkVBalBranch2(zzz340, zzz341, Neg(zzz3420), zzz343, zzz344, zzz520, zzz521, zzz52200, zzz523, zzz524, zzz31, Zero, h) → new_mkVBalBranch3MkVBalBranch22(zzz340, zzz341, zzz3420, zzz343, zzz344, zzz520, zzz521, zzz52200, zzz523, zzz524, zzz31, h)
new_mkVBalBranch(zzz31, Branch(zzz520, zzz521, Neg(Succ(zzz52200)), zzz523, zzz524), Branch(zzz340, zzz341, zzz342, zzz343, zzz344), h) → new_mkVBalBranch3MkVBalBranch24(zzz340, zzz341, zzz342, zzz343, zzz344, zzz520, zzz521, zzz52200, zzz523, zzz524, zzz31, new_primPlusNat3(Succ(new_primPlusNat3(new_primPlusNat1(zzz52200), zzz52200)), Succ(zzz52200)), h)
new_mkVBalBranch3MkVBalBranch24(zzz340, zzz341, Neg(Succ(Zero)), zzz343, zzz344, zzz520, zzz521, Succ(zzz522000), zzz523, zzz524, zzz31, Zero, h) → new_mkVBalBranch3MkVBalBranch28(zzz340, zzz341, zzz343, zzz344, zzz520, zzz521, Succ(zzz522000), zzz523, zzz524, zzz31, h)
new_mkVBalBranch3MkVBalBranch210(zzz340, zzz341, zzz343, zzz344, zzz520, zzz521, zzz52200, zzz523, zzz524, zzz31, h) → new_mkVBalBranch(zzz31, Branch(zzz520, zzz521, Neg(Succ(zzz52200)), zzz523, zzz524), zzz343, h)
new_mkVBalBranch3MkVBalBranch26(zzz1133, zzz1134, zzz1135, zzz1136, zzz1137, zzz1138, zzz1139, zzz1140, zzz1141, zzz1142, Zero, Succ(zzz11440), be) → new_mkVBalBranch(zzz1142, Branch(zzz1138, zzz1139, Neg(Succ(Zero)), zzz1140, zzz1141), zzz1136, be)
new_mkVBalBranch3MkVBalBranch24(zzz340, zzz341, Neg(Succ(Succ(Zero))), zzz343, zzz344, zzz520, zzz521, Zero, zzz523, zzz524, zzz31, Succ(Zero), h) → new_mkVBalBranch3MkVBalBranch26(zzz340, zzz341, Succ(Zero), zzz343, zzz344, zzz520, zzz521, zzz523, zzz524, zzz31, Zero, Zero, h)
new_mkVBalBranch(zzz31, Branch(zzz520, zzz521, Pos(Zero), zzz523, zzz524), Branch(zzz340, zzz341, Pos(Succ(zzz34200)), zzz343, zzz344), h) → new_mkVBalBranch(zzz31, Branch(zzz520, zzz521, Pos(Zero), zzz523, zzz524), zzz343, h)
new_mkVBalBranch3MkVBalBranch2(zzz340, zzz341, Pos(Zero), zzz343, zzz344, zzz520, zzz521, zzz52200, zzz523, zzz524, zzz31, Succ(zzz680), h) → new_mkVBalBranch(zzz31, zzz524, Branch(zzz340, zzz341, Pos(Zero), zzz343, zzz344), h)
new_mkVBalBranch3MkVBalBranch21(zzz340, zzz341, zzz343, zzz344, zzz520, zzz521, zzz52200, zzz523, zzz524, zzz31, h) → new_mkVBalBranch(zzz31, zzz524, Branch(zzz340, zzz341, Pos(Zero), zzz343, zzz344), h)
new_mkVBalBranch3MkVBalBranch24(zzz340, zzz341, Pos(zzz3420), zzz343, zzz344, zzz520, zzz521, zzz52200, zzz523, zzz524, zzz31, Zero, h) → new_mkVBalBranch3MkVBalBranch27(zzz340, zzz341, zzz3420, zzz343, zzz344, zzz520, zzz521, zzz52200, zzz523, zzz524, zzz31, h)
new_mkVBalBranch3MkVBalBranch15(zzz537, zzz538, zzz539, zzz540, zzz541, zzz542, zzz543, zzz544, zzz545, zzz546, zzz547, Succ(zzz6990), bc) → new_mkVBalBranch3MkVBalBranch16(zzz537, zzz538, zzz539, zzz540, zzz541, zzz542, zzz543, Succ(zzz544), zzz545, zzz546, zzz547, Succ(Succ(zzz544)), Succ(zzz6990), bc)
new_mkVBalBranch3MkVBalBranch24(zzz340, zzz341, Neg(Succ(Succ(Succ(zzz3420000)))), zzz343, zzz344, zzz520, zzz521, Zero, zzz523, zzz524, zzz31, Succ(Succ(zzz6900)), h) → new_mkVBalBranch3MkVBalBranch26(zzz340, zzz341, Succ(Succ(zzz3420000)), zzz343, zzz344, zzz520, zzz521, zzz523, zzz524, zzz31, Succ(zzz3420000), Succ(zzz6900), h)
new_mkVBalBranch(zzz31, Branch(zzz520, zzz521, Neg(Zero), zzz523, zzz524), Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), h) → new_mkVBalBranch3MkVBalBranch13(zzz340, zzz341, zzz34200, zzz343, zzz344, zzz520, zzz521, zzz523, zzz524, zzz31, new_primPlusNat2(new_primMulNat0(zzz34200), Succ(zzz34200)), h)
new_mkVBalBranch3MkVBalBranch27(zzz340, zzz341, zzz3420, zzz343, zzz344, zzz520, zzz521, zzz52200, zzz523, zzz524, zzz31, h) → new_mkVBalBranch(zzz31, Branch(zzz520, zzz521, Neg(Succ(zzz52200)), zzz523, zzz524), zzz343, h)
new_mkVBalBranch3MkVBalBranch24(zzz340, zzz341, Pos(zzz3420), zzz343, zzz344, zzz520, zzz521, zzz52200, zzz523, zzz524, zzz31, Succ(zzz690), h) → new_mkVBalBranch(zzz31, Branch(zzz520, zzz521, Neg(Succ(zzz52200)), zzz523, zzz524), zzz343, h)
new_mkVBalBranch3MkVBalBranch12(zzz340, zzz341, zzz34200, zzz343, zzz344, zzz520, zzz521, zzz523, zzz524, zzz31, Succ(zzz1250), h) → new_mkVBalBranch(zzz31, zzz524, Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), h)
new_mkVBalBranch3MkVBalBranch28(zzz340, zzz341, zzz343, zzz344, zzz520, zzz521, zzz52200, zzz523, zzz524, zzz31, h) → new_mkVBalBranch(zzz31, Branch(zzz520, zzz521, Neg(Succ(zzz52200)), zzz523, zzz524), zzz343, h)
new_mkVBalBranch3MkVBalBranch24(zzz340, zzz341, Neg(Succ(Succ(Zero))), zzz343, zzz344, zzz520, zzz521, Zero, zzz523, zzz524, zzz31, Succ(Succ(zzz6900)), h) → new_mkVBalBranch3MkVBalBranch26(zzz340, zzz341, Succ(Zero), zzz343, zzz344, zzz520, zzz521, zzz523, zzz524, zzz31, Zero, Succ(zzz6900), h)
new_mkVBalBranch(zzz31, Branch(zzz520, zzz521, Pos(Zero), zzz523, zzz524), Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), h) → new_mkVBalBranch3MkVBalBranch12(zzz340, zzz341, zzz34200, zzz343, zzz344, zzz520, zzz521, zzz523, zzz524, zzz31, new_primPlusNat2(new_primMulNat0(zzz34200), Succ(zzz34200)), h)
new_mkVBalBranch3MkVBalBranch22(zzz340, zzz341, Zero, zzz343, zzz344, zzz520, zzz521, zzz52200, zzz523, zzz524, zzz31, h) → new_mkVBalBranch(zzz31, zzz524, Branch(zzz340, zzz341, Neg(Zero), zzz343, zzz344), h)
new_mkVBalBranch3MkVBalBranch1(zzz340, zzz341, zzz34200, zzz343, zzz344, zzz520, zzz521, zzz52200, zzz523, zzz524, zzz31, Succ(zzz1430), h) → new_mkVBalBranch(zzz31, zzz524, Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), h)
new_mkVBalBranch3MkVBalBranch24(zzz340, zzz341, Neg(Succ(Zero)), zzz343, zzz344, zzz520, zzz521, zzz52200, zzz523, zzz524, zzz31, Succ(zzz690), h) → new_mkVBalBranch(zzz31, Branch(zzz520, zzz521, Neg(Succ(zzz52200)), zzz523, zzz524), zzz343, h)
new_mkVBalBranch3MkVBalBranch13(zzz340, zzz341, zzz34200, zzz343, zzz344, zzz520, zzz521, zzz523, zzz524, zzz31, Succ(zzz1290), h) → new_mkVBalBranch(zzz31, zzz524, Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), h)
new_mkVBalBranch3MkVBalBranch2(zzz340, zzz341, Pos(Succ(zzz34200)), zzz343, zzz344, zzz520, zzz521, zzz52200, zzz523, zzz524, zzz31, Succ(zzz680), h) → new_mkVBalBranch3MkVBalBranch20(zzz340, zzz341, zzz34200, zzz343, zzz344, zzz520, zzz521, zzz52200, zzz523, zzz524, zzz31, Succ(new_primPlusNat2(zzz680, zzz52200)), zzz34200, h)
new_mkVBalBranch(zzz31, Branch(zzz520, zzz521, Neg(Zero), zzz523, zzz524), Branch(zzz340, zzz341, Pos(Succ(zzz34200)), zzz343, zzz344), h) → new_mkVBalBranch(zzz31, Branch(zzz520, zzz521, Neg(Zero), zzz523, zzz524), zzz343, h)
new_mkVBalBranch3MkVBalBranch24(zzz340, zzz341, Neg(Zero), zzz343, zzz344, zzz520, zzz521, zzz52200, zzz523, zzz524, zzz31, Succ(zzz690), h) → new_mkVBalBranch(zzz31, Branch(zzz520, zzz521, Neg(Succ(zzz52200)), zzz523, zzz524), zzz343, h)
new_mkVBalBranch3MkVBalBranch1(zzz340, zzz341, zzz34200, zzz343, zzz344, zzz520, zzz521, zzz52200, zzz523, zzz524, zzz31, Zero, h) → new_mkVBalBranch3MkVBalBranch17(zzz340, zzz341, zzz34200, zzz343, zzz344, zzz520, zzz521, zzz52200, zzz523, zzz524, zzz31, h)
new_mkVBalBranch3MkVBalBranch16(zzz1702, zzz1703, zzz1704, zzz1705, zzz1706, zzz1707, zzz1708, zzz1709, zzz1710, zzz1711, zzz1712, Succ(zzz17130), Succ(zzz17140), bd) → new_mkVBalBranch3MkVBalBranch16(zzz1702, zzz1703, zzz1704, zzz1705, zzz1706, zzz1707, zzz1708, zzz1709, zzz1710, zzz1711, zzz1712, zzz17130, zzz17140, bd)
new_mkVBalBranch3MkVBalBranch25(zzz537, zzz538, zzz539, zzz540, zzz541, zzz542, zzz543, zzz544, zzz545, zzz546, zzz547, Zero, Succ(zzz5490), bc) → new_mkVBalBranch(zzz547, Branch(zzz542, zzz543, Neg(Succ(Succ(zzz544))), zzz545, zzz546), zzz540, bc)
new_mkVBalBranch3MkVBalBranch212(zzz818, zzz819, zzz820, zzz821, zzz822, zzz823, zzz824, zzz825, zzz826, zzz827, bf) → new_mkVBalBranch3MkVBalBranch14(zzz818, zzz819, zzz820, zzz821, zzz822, zzz823, zzz824, zzz825, zzz826, zzz827, new_primPlusNat2(new_primMulNat0(zzz820), Succ(zzz820)), bf)
new_mkVBalBranch3MkVBalBranch10(zzz929, zzz930, zzz931, zzz932, zzz933, zzz934, zzz935, zzz936, zzz937, zzz938, zzz939, Succ(zzz10020), ba) → new_mkVBalBranch3MkVBalBranch11(zzz929, zzz930, zzz931, zzz932, zzz933, zzz934, zzz935, zzz936, zzz937, zzz938, zzz939, Succ(zzz10020), Succ(zzz936), ba)
new_mkVBalBranch3MkVBalBranch14(zzz818, zzz819, zzz820, zzz821, zzz822, zzz823, zzz824, zzz825, zzz826, zzz827, Succ(zzz8960), bf) → new_mkVBalBranch3MkVBalBranch16(zzz818, zzz819, zzz820, zzz821, zzz822, zzz823, zzz824, Zero, zzz825, zzz826, zzz827, Succ(Zero), Succ(zzz8960), bf)
new_mkVBalBranch3MkVBalBranch24(zzz340, zzz341, Neg(Succ(Succ(Succ(zzz3420000)))), zzz343, zzz344, zzz520, zzz521, Succ(zzz522000), zzz523, zzz524, zzz31, Succ(Succ(zzz6900)), h) → new_mkVBalBranch3MkVBalBranch25(zzz340, zzz341, Succ(Succ(zzz3420000)), zzz343, zzz344, zzz520, zzz521, zzz522000, zzz523, zzz524, zzz31, Succ(zzz3420000), Succ(Succ(new_primPlusNat2(zzz6900, zzz522000))), h)
new_mkVBalBranch3MkVBalBranch2(zzz340, zzz341, Pos(Succ(zzz34200)), zzz343, zzz344, zzz520, zzz521, zzz52200, zzz523, zzz524, zzz31, Zero, h) → new_mkVBalBranch3MkVBalBranch20(zzz340, zzz341, zzz34200, zzz343, zzz344, zzz520, zzz521, zzz52200, zzz523, zzz524, zzz31, zzz52200, zzz34200, h)
new_mkVBalBranch3MkVBalBranch24(zzz340, zzz341, Neg(Zero), zzz343, zzz344, zzz520, zzz521, zzz52200, zzz523, zzz524, zzz31, Zero, h) → new_mkVBalBranch3MkVBalBranch210(zzz340, zzz341, zzz343, zzz344, zzz520, zzz521, zzz52200, zzz523, zzz524, zzz31, h)
new_mkVBalBranch3MkVBalBranch24(zzz340, zzz341, Neg(Succ(Succ(Zero))), zzz343, zzz344, zzz520, zzz521, Succ(zzz522000), zzz523, zzz524, zzz31, Succ(Succ(zzz6900)), h) → new_mkVBalBranch3MkVBalBranch25(zzz340, zzz341, Succ(Zero), zzz343, zzz344, zzz520, zzz521, zzz522000, zzz523, zzz524, zzz31, Zero, Succ(Succ(new_primPlusNat2(zzz6900, zzz522000))), h)
new_mkVBalBranch3MkVBalBranch23(zzz929, zzz930, zzz931, zzz932, zzz933, zzz934, zzz935, zzz936, zzz937, zzz938, zzz939, ba) → new_mkVBalBranch3MkVBalBranch10(zzz929, zzz930, zzz931, zzz932, zzz933, zzz934, zzz935, zzz936, zzz937, zzz938, zzz939, new_primPlusNat2(new_primMulNat0(zzz931), Succ(zzz931)), ba)
new_mkVBalBranch3MkVBalBranch2(zzz340, zzz341, Neg(Zero), zzz343, zzz344, zzz520, zzz521, zzz52200, zzz523, zzz524, zzz31, Succ(zzz680), h) → new_mkVBalBranch(zzz31, zzz524, Branch(zzz340, zzz341, Neg(Zero), zzz343, zzz344), h)
new_mkVBalBranch3MkVBalBranch16(zzz1702, zzz1703, zzz1704, zzz1705, zzz1706, zzz1707, zzz1708, zzz1709, zzz1710, zzz1711, zzz1712, Zero, Succ(zzz17140), bd) → new_mkVBalBranch(zzz1712, zzz1711, Branch(zzz1702, zzz1703, Neg(Succ(zzz1704)), zzz1705, zzz1706), bd)
new_mkVBalBranch3MkVBalBranch10(zzz929, zzz930, zzz931, zzz932, zzz933, zzz934, zzz935, zzz936, zzz937, zzz938, zzz939, Zero, ba) → new_mkVBalBranch3MkVBalBranch11(zzz929, zzz930, zzz931, zzz932, zzz933, zzz934, zzz935, zzz936, zzz937, zzz938, zzz939, Zero, Succ(zzz936), ba)
new_mkVBalBranch3MkVBalBranch22(zzz340, zzz341, Succ(zzz34200), zzz343, zzz344, zzz520, zzz521, zzz52200, zzz523, zzz524, zzz31, h) → new_mkVBalBranch3MkVBalBranch1(zzz340, zzz341, zzz34200, zzz343, zzz344, zzz520, zzz521, zzz52200, zzz523, zzz524, zzz31, new_primPlusNat2(new_primPlusNat3(Succ(new_primPlusNat3(new_primPlusNat1(zzz34200), zzz34200)), Succ(zzz34200)), Succ(zzz34200)), h)
new_mkVBalBranch3MkVBalBranch25(zzz537, zzz538, zzz539, zzz540, zzz541, zzz542, zzz543, zzz544, zzz545, zzz546, zzz547, Zero, Zero, bc) → new_mkVBalBranch3MkVBalBranch211(zzz537, zzz538, zzz539, zzz540, zzz541, zzz542, zzz543, zzz544, zzz545, zzz546, zzz547, bc)
new_mkVBalBranch3MkVBalBranch2(zzz340, zzz341, Pos(Zero), zzz343, zzz344, zzz520, zzz521, zzz52200, zzz523, zzz524, zzz31, Zero, h) → new_mkVBalBranch3MkVBalBranch21(zzz340, zzz341, zzz343, zzz344, zzz520, zzz521, zzz52200, zzz523, zzz524, zzz31, h)

The TRS R consists of the following rules:

new_primPlusNat1(Zero) → Zero
new_primMulNat0(zzz6200) → new_primPlusNat3(Succ(new_primPlusNat3(new_primPlusNat1(zzz6200), zzz6200)), Succ(zzz6200))
new_primPlusNat2(Succ(zzz900), Succ(zzz9100)) → Succ(Succ(new_primPlusNat2(zzz900, zzz9100)))
new_primPlusNat3(zzz90, Succ(zzz910)) → Succ(Succ(new_primPlusNat2(zzz90, zzz910)))
new_primPlusNat3(zzz90, Zero) → Succ(zzz90)
new_primMulNat1(zzz34200) → new_primPlusNat2(new_primMulNat0(zzz34200), Succ(zzz34200))
new_primPlusNat2(Zero, Zero) → Zero
new_primPlusNat1(Succ(zzz62000)) → Succ(Succ(new_primPlusNat1(zzz62000)))
new_primPlusNat2(Succ(zzz900), Zero) → Succ(zzz900)
new_primPlusNat2(Zero, Succ(zzz9100)) → Succ(zzz9100)

The set Q consists of the following terms:

new_primPlusNat2(Zero, Succ(x0))
new_primMulNat1(x0)
new_primMulNat0(x0)
new_primPlusNat3(x0, Succ(x1))
new_primPlusNat2(Succ(x0), Succ(x1))
new_primPlusNat3(x0, Zero)
new_primPlusNat1(Zero)
new_primPlusNat2(Zero, Zero)
new_primPlusNat1(Succ(x0))
new_primPlusNat2(Succ(x0), Zero)

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

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

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

new_mkVBalBranch3MkVBalBranch211(zzz537, zzz538, zzz539, zzz540, zzz541, zzz542, zzz543, zzz544, zzz545, zzz546, zzz547, bc) → new_mkVBalBranch3MkVBalBranch15(zzz537, zzz538, zzz539, zzz540, zzz541, zzz542, zzz543, zzz544, zzz545, zzz546, zzz547, new_primPlusNat2(new_primMulNat0(zzz539), Succ(zzz539)), bc)
new_mkVBalBranch3MkVBalBranch11(zzz2033, zzz2034, zzz2035, zzz2036, zzz2037, zzz2038, zzz2039, zzz2040, zzz2041, zzz2042, zzz2043, Zero, Succ(zzz20450), bb) → new_mkVBalBranch(zzz2043, zzz2042, Branch(zzz2033, zzz2034, Pos(Succ(zzz2035)), zzz2036, zzz2037), bb)
new_mkVBalBranch3MkVBalBranch2(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344, zzz520, zzz521, zzz52200, zzz523, zzz524, zzz31, Succ(zzz680), h) → new_mkVBalBranch3MkVBalBranch1(zzz340, zzz341, zzz34200, zzz343, zzz344, zzz520, zzz521, zzz52200, zzz523, zzz524, zzz31, new_primPlusNat2(new_primPlusNat3(Succ(new_primPlusNat3(new_primPlusNat1(zzz34200), zzz34200)), Succ(zzz34200)), Succ(zzz34200)), h)
new_mkVBalBranch3MkVBalBranch26(zzz1133, zzz1134, zzz1135, zzz1136, zzz1137, zzz1138, zzz1139, zzz1140, zzz1141, zzz1142, Succ(zzz11430), Succ(zzz11440), be) → new_mkVBalBranch3MkVBalBranch26(zzz1133, zzz1134, zzz1135, zzz1136, zzz1137, zzz1138, zzz1139, zzz1140, zzz1141, zzz1142, zzz11430, zzz11440, be)
new_mkVBalBranch3MkVBalBranch24(zzz340, zzz341, Neg(Succ(Succ(zzz342000))), zzz343, zzz344, zzz520, zzz521, Zero, zzz523, zzz524, zzz31, Zero, h) → new_mkVBalBranch3MkVBalBranch14(zzz340, zzz341, Succ(zzz342000), zzz343, zzz344, zzz520, zzz521, zzz523, zzz524, zzz31, new_primPlusNat2(new_primMulNat0(Succ(zzz342000)), Succ(Succ(zzz342000))), h)
new_mkVBalBranch3MkVBalBranch24(zzz340, zzz341, Neg(Succ(Succ(Succ(zzz3420000)))), zzz343, zzz344, zzz520, zzz521, Zero, zzz523, zzz524, zzz31, Succ(Zero), h) → new_mkVBalBranch3MkVBalBranch26(zzz340, zzz341, Succ(Succ(zzz3420000)), zzz343, zzz344, zzz520, zzz521, zzz523, zzz524, zzz31, Succ(zzz3420000), Zero, h)
new_mkVBalBranch3MkVBalBranch25(zzz537, zzz538, zzz539, zzz540, zzz541, zzz542, zzz543, zzz544, zzz545, zzz546, zzz547, Succ(zzz5480), Zero, bc) → new_mkVBalBranch3MkVBalBranch15(zzz537, zzz538, zzz539, zzz540, zzz541, zzz542, zzz543, zzz544, zzz545, zzz546, zzz547, new_primPlusNat2(new_primMulNat0(zzz539), Succ(zzz539)), bc)
new_mkVBalBranch3MkVBalBranch24(zzz340, zzz341, Neg(Succ(Zero)), zzz343, zzz344, zzz520, zzz521, Zero, zzz523, zzz524, zzz31, Zero, h) → new_mkVBalBranch3MkVBalBranch29(zzz340, zzz341, Zero, zzz343, zzz344, zzz520, zzz521, zzz523, zzz524, zzz31, h)
new_mkVBalBranch3MkVBalBranch20(zzz929, zzz930, zzz931, zzz932, zzz933, zzz934, zzz935, zzz936, zzz937, zzz938, zzz939, Zero, Succ(zzz9410), ba) → new_mkVBalBranch(zzz939, Branch(zzz934, zzz935, Pos(Succ(zzz936)), zzz937, zzz938), zzz932, ba)
new_mkVBalBranch3MkVBalBranch17(zzz340, zzz341, zzz34200, zzz343, zzz344, zzz520, zzz521, zzz52200, zzz523, zzz524, zzz31, h) → new_mkVBalBranch(zzz31, zzz524, Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), h)
new_mkVBalBranch3MkVBalBranch26(zzz1133, zzz1134, zzz1135, zzz1136, zzz1137, zzz1138, zzz1139, zzz1140, zzz1141, zzz1142, Zero, Zero, be) → new_mkVBalBranch3MkVBalBranch29(zzz1133, zzz1134, zzz1135, zzz1136, zzz1137, zzz1138, zzz1139, zzz1140, zzz1141, zzz1142, be)
new_mkVBalBranch3MkVBalBranch20(zzz929, zzz930, zzz931, zzz932, zzz933, zzz934, zzz935, zzz936, zzz937, zzz938, zzz939, Zero, Zero, ba) → new_mkVBalBranch3MkVBalBranch23(zzz929, zzz930, zzz931, zzz932, zzz933, zzz934, zzz935, zzz936, zzz937, zzz938, zzz939, ba)
new_mkVBalBranch3MkVBalBranch20(zzz929, zzz930, zzz931, zzz932, zzz933, zzz934, zzz935, zzz936, zzz937, zzz938, zzz939, Succ(zzz9400), Zero, ba) → new_mkVBalBranch3MkVBalBranch10(zzz929, zzz930, zzz931, zzz932, zzz933, zzz934, zzz935, zzz936, zzz937, zzz938, zzz939, new_primPlusNat2(new_primMulNat0(zzz931), Succ(zzz931)), ba)
new_mkVBalBranch3MkVBalBranch24(zzz340, zzz341, Neg(Succ(Succ(Zero))), zzz343, zzz344, zzz520, zzz521, Succ(zzz522000), zzz523, zzz524, zzz31, Succ(Zero), h) → new_mkVBalBranch3MkVBalBranch25(zzz340, zzz341, Succ(Zero), zzz343, zzz344, zzz520, zzz521, zzz522000, zzz523, zzz524, zzz31, Zero, Succ(zzz522000), h)
new_mkVBalBranch3MkVBalBranch20(zzz929, zzz930, zzz931, zzz932, zzz933, zzz934, zzz935, zzz936, zzz937, zzz938, zzz939, Succ(zzz9400), Succ(zzz9410), ba) → new_mkVBalBranch3MkVBalBranch20(zzz929, zzz930, zzz931, zzz932, zzz933, zzz934, zzz935, zzz936, zzz937, zzz938, zzz939, zzz9400, zzz9410, ba)
new_mkVBalBranch3MkVBalBranch24(zzz340, zzz341, Neg(Succ(Succ(Succ(zzz3420000)))), zzz343, zzz344, zzz520, zzz521, Succ(zzz522000), zzz523, zzz524, zzz31, Succ(Zero), h) → new_mkVBalBranch3MkVBalBranch25(zzz340, zzz341, Succ(Succ(zzz3420000)), zzz343, zzz344, zzz520, zzz521, zzz522000, zzz523, zzz524, zzz31, Succ(zzz3420000), Succ(zzz522000), h)
new_mkVBalBranch3MkVBalBranch26(zzz1133, zzz1134, zzz1135, zzz1136, zzz1137, zzz1138, zzz1139, zzz1140, zzz1141, zzz1142, Succ(zzz11430), Zero, be) → new_mkVBalBranch3MkVBalBranch212(zzz1133, zzz1134, zzz1135, zzz1136, zzz1137, zzz1138, zzz1139, zzz1140, zzz1141, zzz1142, be)
new_mkVBalBranch3MkVBalBranch24(zzz340, zzz341, Neg(Succ(Succ(zzz342000))), zzz343, zzz344, zzz520, zzz521, Succ(zzz522000), zzz523, zzz524, zzz31, Zero, h) → new_mkVBalBranch3MkVBalBranch25(zzz340, zzz341, Succ(zzz342000), zzz343, zzz344, zzz520, zzz521, zzz522000, zzz523, zzz524, zzz31, zzz342000, zzz522000, h)
new_mkVBalBranch(zzz31, Branch(zzz520, zzz521, Pos(Succ(zzz52200)), zzz523, zzz524), Branch(zzz340, zzz341, zzz342, zzz343, zzz344), h) → new_mkVBalBranch3MkVBalBranch2(zzz340, zzz341, zzz342, zzz343, zzz344, zzz520, zzz521, zzz52200, zzz523, zzz524, zzz31, new_primPlusNat3(Succ(new_primPlusNat3(new_primPlusNat1(zzz52200), zzz52200)), Succ(zzz52200)), h)
new_mkVBalBranch3MkVBalBranch29(zzz818, zzz819, zzz820, zzz821, zzz822, zzz823, zzz824, zzz825, zzz826, zzz827, bf) → new_mkVBalBranch3MkVBalBranch14(zzz818, zzz819, zzz820, zzz821, zzz822, zzz823, zzz824, zzz825, zzz826, zzz827, new_primPlusNat2(new_primMulNat0(zzz820), Succ(zzz820)), bf)
new_mkVBalBranch3MkVBalBranch11(zzz2033, zzz2034, zzz2035, zzz2036, zzz2037, zzz2038, zzz2039, zzz2040, zzz2041, zzz2042, zzz2043, Succ(zzz20440), Succ(zzz20450), bb) → new_mkVBalBranch3MkVBalBranch11(zzz2033, zzz2034, zzz2035, zzz2036, zzz2037, zzz2038, zzz2039, zzz2040, zzz2041, zzz2042, zzz2043, zzz20440, zzz20450, bb)
new_mkVBalBranch3MkVBalBranch2(zzz340, zzz341, Neg(zzz3420), zzz343, zzz344, zzz520, zzz521, zzz52200, zzz523, zzz524, zzz31, Zero, h) → new_mkVBalBranch3MkVBalBranch22(zzz340, zzz341, zzz3420, zzz343, zzz344, zzz520, zzz521, zzz52200, zzz523, zzz524, zzz31, h)
new_mkVBalBranch3MkVBalBranch25(zzz537, zzz538, zzz539, zzz540, zzz541, zzz542, zzz543, zzz544, zzz545, zzz546, zzz547, Succ(zzz5480), Succ(zzz5490), bc) → new_mkVBalBranch3MkVBalBranch25(zzz537, zzz538, zzz539, zzz540, zzz541, zzz542, zzz543, zzz544, zzz545, zzz546, zzz547, zzz5480, zzz5490, bc)
new_mkVBalBranch(zzz31, Branch(zzz520, zzz521, Neg(Succ(zzz52200)), zzz523, zzz524), Branch(zzz340, zzz341, zzz342, zzz343, zzz344), h) → new_mkVBalBranch3MkVBalBranch24(zzz340, zzz341, zzz342, zzz343, zzz344, zzz520, zzz521, zzz52200, zzz523, zzz524, zzz31, new_primPlusNat3(Succ(new_primPlusNat3(new_primPlusNat1(zzz52200), zzz52200)), Succ(zzz52200)), h)
new_mkVBalBranch3MkVBalBranch24(zzz340, zzz341, Neg(Succ(Zero)), zzz343, zzz344, zzz520, zzz521, Succ(zzz522000), zzz523, zzz524, zzz31, Zero, h) → new_mkVBalBranch3MkVBalBranch28(zzz340, zzz341, zzz343, zzz344, zzz520, zzz521, Succ(zzz522000), zzz523, zzz524, zzz31, h)
new_mkVBalBranch3MkVBalBranch210(zzz340, zzz341, zzz343, zzz344, zzz520, zzz521, zzz52200, zzz523, zzz524, zzz31, h) → new_mkVBalBranch(zzz31, Branch(zzz520, zzz521, Neg(Succ(zzz52200)), zzz523, zzz524), zzz343, h)
new_mkVBalBranch3MkVBalBranch26(zzz1133, zzz1134, zzz1135, zzz1136, zzz1137, zzz1138, zzz1139, zzz1140, zzz1141, zzz1142, Zero, Succ(zzz11440), be) → new_mkVBalBranch(zzz1142, Branch(zzz1138, zzz1139, Neg(Succ(Zero)), zzz1140, zzz1141), zzz1136, be)
new_mkVBalBranch3MkVBalBranch24(zzz340, zzz341, Neg(Succ(Succ(Zero))), zzz343, zzz344, zzz520, zzz521, Zero, zzz523, zzz524, zzz31, Succ(Zero), h) → new_mkVBalBranch3MkVBalBranch26(zzz340, zzz341, Succ(Zero), zzz343, zzz344, zzz520, zzz521, zzz523, zzz524, zzz31, Zero, Zero, h)
new_mkVBalBranch(zzz31, Branch(zzz520, zzz521, Pos(Zero), zzz523, zzz524), Branch(zzz340, zzz341, Pos(Succ(zzz34200)), zzz343, zzz344), h) → new_mkVBalBranch(zzz31, Branch(zzz520, zzz521, Pos(Zero), zzz523, zzz524), zzz343, h)
new_mkVBalBranch3MkVBalBranch2(zzz340, zzz341, Pos(Zero), zzz343, zzz344, zzz520, zzz521, zzz52200, zzz523, zzz524, zzz31, Succ(zzz680), h) → new_mkVBalBranch(zzz31, zzz524, Branch(zzz340, zzz341, Pos(Zero), zzz343, zzz344), h)
new_mkVBalBranch3MkVBalBranch21(zzz340, zzz341, zzz343, zzz344, zzz520, zzz521, zzz52200, zzz523, zzz524, zzz31, h) → new_mkVBalBranch(zzz31, zzz524, Branch(zzz340, zzz341, Pos(Zero), zzz343, zzz344), h)
new_mkVBalBranch3MkVBalBranch24(zzz340, zzz341, Pos(zzz3420), zzz343, zzz344, zzz520, zzz521, zzz52200, zzz523, zzz524, zzz31, Zero, h) → new_mkVBalBranch3MkVBalBranch27(zzz340, zzz341, zzz3420, zzz343, zzz344, zzz520, zzz521, zzz52200, zzz523, zzz524, zzz31, h)
new_mkVBalBranch3MkVBalBranch15(zzz537, zzz538, zzz539, zzz540, zzz541, zzz542, zzz543, zzz544, zzz545, zzz546, zzz547, Succ(zzz6990), bc) → new_mkVBalBranch3MkVBalBranch16(zzz537, zzz538, zzz539, zzz540, zzz541, zzz542, zzz543, Succ(zzz544), zzz545, zzz546, zzz547, Succ(Succ(zzz544)), Succ(zzz6990), bc)
new_mkVBalBranch3MkVBalBranch24(zzz340, zzz341, Neg(Succ(Succ(Succ(zzz3420000)))), zzz343, zzz344, zzz520, zzz521, Zero, zzz523, zzz524, zzz31, Succ(Succ(zzz6900)), h) → new_mkVBalBranch3MkVBalBranch26(zzz340, zzz341, Succ(Succ(zzz3420000)), zzz343, zzz344, zzz520, zzz521, zzz523, zzz524, zzz31, Succ(zzz3420000), Succ(zzz6900), h)
new_mkVBalBranch(zzz31, Branch(zzz520, zzz521, Neg(Zero), zzz523, zzz524), Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), h) → new_mkVBalBranch3MkVBalBranch13(zzz340, zzz341, zzz34200, zzz343, zzz344, zzz520, zzz521, zzz523, zzz524, zzz31, new_primPlusNat2(new_primMulNat0(zzz34200), Succ(zzz34200)), h)
new_mkVBalBranch3MkVBalBranch27(zzz340, zzz341, zzz3420, zzz343, zzz344, zzz520, zzz521, zzz52200, zzz523, zzz524, zzz31, h) → new_mkVBalBranch(zzz31, Branch(zzz520, zzz521, Neg(Succ(zzz52200)), zzz523, zzz524), zzz343, h)
new_mkVBalBranch3MkVBalBranch24(zzz340, zzz341, Pos(zzz3420), zzz343, zzz344, zzz520, zzz521, zzz52200, zzz523, zzz524, zzz31, Succ(zzz690), h) → new_mkVBalBranch(zzz31, Branch(zzz520, zzz521, Neg(Succ(zzz52200)), zzz523, zzz524), zzz343, h)
new_mkVBalBranch3MkVBalBranch12(zzz340, zzz341, zzz34200, zzz343, zzz344, zzz520, zzz521, zzz523, zzz524, zzz31, Succ(zzz1250), h) → new_mkVBalBranch(zzz31, zzz524, Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), h)
new_mkVBalBranch3MkVBalBranch28(zzz340, zzz341, zzz343, zzz344, zzz520, zzz521, zzz52200, zzz523, zzz524, zzz31, h) → new_mkVBalBranch(zzz31, Branch(zzz520, zzz521, Neg(Succ(zzz52200)), zzz523, zzz524), zzz343, h)
new_mkVBalBranch3MkVBalBranch24(zzz340, zzz341, Neg(Succ(Succ(Zero))), zzz343, zzz344, zzz520, zzz521, Zero, zzz523, zzz524, zzz31, Succ(Succ(zzz6900)), h) → new_mkVBalBranch3MkVBalBranch26(zzz340, zzz341, Succ(Zero), zzz343, zzz344, zzz520, zzz521, zzz523, zzz524, zzz31, Zero, Succ(zzz6900), h)
new_mkVBalBranch(zzz31, Branch(zzz520, zzz521, Pos(Zero), zzz523, zzz524), Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), h) → new_mkVBalBranch3MkVBalBranch12(zzz340, zzz341, zzz34200, zzz343, zzz344, zzz520, zzz521, zzz523, zzz524, zzz31, new_primPlusNat2(new_primMulNat0(zzz34200), Succ(zzz34200)), h)
new_mkVBalBranch3MkVBalBranch22(zzz340, zzz341, Zero, zzz343, zzz344, zzz520, zzz521, zzz52200, zzz523, zzz524, zzz31, h) → new_mkVBalBranch(zzz31, zzz524, Branch(zzz340, zzz341, Neg(Zero), zzz343, zzz344), h)
new_mkVBalBranch3MkVBalBranch1(zzz340, zzz341, zzz34200, zzz343, zzz344, zzz520, zzz521, zzz52200, zzz523, zzz524, zzz31, Succ(zzz1430), h) → new_mkVBalBranch(zzz31, zzz524, Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), h)
new_mkVBalBranch3MkVBalBranch24(zzz340, zzz341, Neg(Succ(Zero)), zzz343, zzz344, zzz520, zzz521, zzz52200, zzz523, zzz524, zzz31, Succ(zzz690), h) → new_mkVBalBranch(zzz31, Branch(zzz520, zzz521, Neg(Succ(zzz52200)), zzz523, zzz524), zzz343, h)
new_mkVBalBranch3MkVBalBranch13(zzz340, zzz341, zzz34200, zzz343, zzz344, zzz520, zzz521, zzz523, zzz524, zzz31, Succ(zzz1290), h) → new_mkVBalBranch(zzz31, zzz524, Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), h)
new_mkVBalBranch3MkVBalBranch2(zzz340, zzz341, Pos(Succ(zzz34200)), zzz343, zzz344, zzz520, zzz521, zzz52200, zzz523, zzz524, zzz31, Succ(zzz680), h) → new_mkVBalBranch3MkVBalBranch20(zzz340, zzz341, zzz34200, zzz343, zzz344, zzz520, zzz521, zzz52200, zzz523, zzz524, zzz31, Succ(new_primPlusNat2(zzz680, zzz52200)), zzz34200, h)
new_mkVBalBranch(zzz31, Branch(zzz520, zzz521, Neg(Zero), zzz523, zzz524), Branch(zzz340, zzz341, Pos(Succ(zzz34200)), zzz343, zzz344), h) → new_mkVBalBranch(zzz31, Branch(zzz520, zzz521, Neg(Zero), zzz523, zzz524), zzz343, h)
new_mkVBalBranch3MkVBalBranch24(zzz340, zzz341, Neg(Zero), zzz343, zzz344, zzz520, zzz521, zzz52200, zzz523, zzz524, zzz31, Succ(zzz690), h) → new_mkVBalBranch(zzz31, Branch(zzz520, zzz521, Neg(Succ(zzz52200)), zzz523, zzz524), zzz343, h)
new_mkVBalBranch3MkVBalBranch1(zzz340, zzz341, zzz34200, zzz343, zzz344, zzz520, zzz521, zzz52200, zzz523, zzz524, zzz31, Zero, h) → new_mkVBalBranch3MkVBalBranch17(zzz340, zzz341, zzz34200, zzz343, zzz344, zzz520, zzz521, zzz52200, zzz523, zzz524, zzz31, h)
new_mkVBalBranch3MkVBalBranch16(zzz1702, zzz1703, zzz1704, zzz1705, zzz1706, zzz1707, zzz1708, zzz1709, zzz1710, zzz1711, zzz1712, Succ(zzz17130), Succ(zzz17140), bd) → new_mkVBalBranch3MkVBalBranch16(zzz1702, zzz1703, zzz1704, zzz1705, zzz1706, zzz1707, zzz1708, zzz1709, zzz1710, zzz1711, zzz1712, zzz17130, zzz17140, bd)
new_mkVBalBranch3MkVBalBranch25(zzz537, zzz538, zzz539, zzz540, zzz541, zzz542, zzz543, zzz544, zzz545, zzz546, zzz547, Zero, Succ(zzz5490), bc) → new_mkVBalBranch(zzz547, Branch(zzz542, zzz543, Neg(Succ(Succ(zzz544))), zzz545, zzz546), zzz540, bc)
new_mkVBalBranch3MkVBalBranch212(zzz818, zzz819, zzz820, zzz821, zzz822, zzz823, zzz824, zzz825, zzz826, zzz827, bf) → new_mkVBalBranch3MkVBalBranch14(zzz818, zzz819, zzz820, zzz821, zzz822, zzz823, zzz824, zzz825, zzz826, zzz827, new_primPlusNat2(new_primMulNat0(zzz820), Succ(zzz820)), bf)
new_mkVBalBranch3MkVBalBranch10(zzz929, zzz930, zzz931, zzz932, zzz933, zzz934, zzz935, zzz936, zzz937, zzz938, zzz939, Succ(zzz10020), ba) → new_mkVBalBranch3MkVBalBranch11(zzz929, zzz930, zzz931, zzz932, zzz933, zzz934, zzz935, zzz936, zzz937, zzz938, zzz939, Succ(zzz10020), Succ(zzz936), ba)
new_mkVBalBranch3MkVBalBranch14(zzz818, zzz819, zzz820, zzz821, zzz822, zzz823, zzz824, zzz825, zzz826, zzz827, Succ(zzz8960), bf) → new_mkVBalBranch3MkVBalBranch16(zzz818, zzz819, zzz820, zzz821, zzz822, zzz823, zzz824, Zero, zzz825, zzz826, zzz827, Succ(Zero), Succ(zzz8960), bf)
new_mkVBalBranch3MkVBalBranch24(zzz340, zzz341, Neg(Succ(Succ(Succ(zzz3420000)))), zzz343, zzz344, zzz520, zzz521, Succ(zzz522000), zzz523, zzz524, zzz31, Succ(Succ(zzz6900)), h) → new_mkVBalBranch3MkVBalBranch25(zzz340, zzz341, Succ(Succ(zzz3420000)), zzz343, zzz344, zzz520, zzz521, zzz522000, zzz523, zzz524, zzz31, Succ(zzz3420000), Succ(Succ(new_primPlusNat2(zzz6900, zzz522000))), h)
new_mkVBalBranch3MkVBalBranch2(zzz340, zzz341, Pos(Succ(zzz34200)), zzz343, zzz344, zzz520, zzz521, zzz52200, zzz523, zzz524, zzz31, Zero, h) → new_mkVBalBranch3MkVBalBranch20(zzz340, zzz341, zzz34200, zzz343, zzz344, zzz520, zzz521, zzz52200, zzz523, zzz524, zzz31, zzz52200, zzz34200, h)
new_mkVBalBranch3MkVBalBranch24(zzz340, zzz341, Neg(Zero), zzz343, zzz344, zzz520, zzz521, zzz52200, zzz523, zzz524, zzz31, Zero, h) → new_mkVBalBranch3MkVBalBranch210(zzz340, zzz341, zzz343, zzz344, zzz520, zzz521, zzz52200, zzz523, zzz524, zzz31, h)
new_mkVBalBranch3MkVBalBranch24(zzz340, zzz341, Neg(Succ(Succ(Zero))), zzz343, zzz344, zzz520, zzz521, Succ(zzz522000), zzz523, zzz524, zzz31, Succ(Succ(zzz6900)), h) → new_mkVBalBranch3MkVBalBranch25(zzz340, zzz341, Succ(Zero), zzz343, zzz344, zzz520, zzz521, zzz522000, zzz523, zzz524, zzz31, Zero, Succ(Succ(new_primPlusNat2(zzz6900, zzz522000))), h)
new_mkVBalBranch3MkVBalBranch23(zzz929, zzz930, zzz931, zzz932, zzz933, zzz934, zzz935, zzz936, zzz937, zzz938, zzz939, ba) → new_mkVBalBranch3MkVBalBranch10(zzz929, zzz930, zzz931, zzz932, zzz933, zzz934, zzz935, zzz936, zzz937, zzz938, zzz939, new_primPlusNat2(new_primMulNat0(zzz931), Succ(zzz931)), ba)
new_mkVBalBranch3MkVBalBranch2(zzz340, zzz341, Neg(Zero), zzz343, zzz344, zzz520, zzz521, zzz52200, zzz523, zzz524, zzz31, Succ(zzz680), h) → new_mkVBalBranch(zzz31, zzz524, Branch(zzz340, zzz341, Neg(Zero), zzz343, zzz344), h)
new_mkVBalBranch3MkVBalBranch16(zzz1702, zzz1703, zzz1704, zzz1705, zzz1706, zzz1707, zzz1708, zzz1709, zzz1710, zzz1711, zzz1712, Zero, Succ(zzz17140), bd) → new_mkVBalBranch(zzz1712, zzz1711, Branch(zzz1702, zzz1703, Neg(Succ(zzz1704)), zzz1705, zzz1706), bd)
new_mkVBalBranch3MkVBalBranch10(zzz929, zzz930, zzz931, zzz932, zzz933, zzz934, zzz935, zzz936, zzz937, zzz938, zzz939, Zero, ba) → new_mkVBalBranch3MkVBalBranch11(zzz929, zzz930, zzz931, zzz932, zzz933, zzz934, zzz935, zzz936, zzz937, zzz938, zzz939, Zero, Succ(zzz936), ba)
new_mkVBalBranch3MkVBalBranch22(zzz340, zzz341, Succ(zzz34200), zzz343, zzz344, zzz520, zzz521, zzz52200, zzz523, zzz524, zzz31, h) → new_mkVBalBranch3MkVBalBranch1(zzz340, zzz341, zzz34200, zzz343, zzz344, zzz520, zzz521, zzz52200, zzz523, zzz524, zzz31, new_primPlusNat2(new_primPlusNat3(Succ(new_primPlusNat3(new_primPlusNat1(zzz34200), zzz34200)), Succ(zzz34200)), Succ(zzz34200)), h)
new_mkVBalBranch3MkVBalBranch2(zzz340, zzz341, Pos(Zero), zzz343, zzz344, zzz520, zzz521, zzz52200, zzz523, zzz524, zzz31, Zero, h) → new_mkVBalBranch3MkVBalBranch21(zzz340, zzz341, zzz343, zzz344, zzz520, zzz521, zzz52200, zzz523, zzz524, zzz31, h)
new_mkVBalBranch3MkVBalBranch25(zzz537, zzz538, zzz539, zzz540, zzz541, zzz542, zzz543, zzz544, zzz545, zzz546, zzz547, Zero, Zero, bc) → new_mkVBalBranch3MkVBalBranch211(zzz537, zzz538, zzz539, zzz540, zzz541, zzz542, zzz543, zzz544, zzz545, zzz546, zzz547, bc)

The TRS R consists of the following rules:

new_primMulNat0(zzz6200) → new_primPlusNat3(Succ(new_primPlusNat3(new_primPlusNat1(zzz6200), zzz6200)), Succ(zzz6200))
new_primPlusNat2(Succ(zzz900), Succ(zzz9100)) → Succ(Succ(new_primPlusNat2(zzz900, zzz9100)))
new_primPlusNat2(Zero, Succ(zzz9100)) → Succ(zzz9100)
new_primPlusNat2(Zero, Zero) → Zero
new_primPlusNat2(Succ(zzz900), Zero) → Succ(zzz900)
new_primPlusNat1(Zero) → Zero
new_primPlusNat1(Succ(zzz62000)) → Succ(Succ(new_primPlusNat1(zzz62000)))
new_primPlusNat3(zzz90, Succ(zzz910)) → Succ(Succ(new_primPlusNat2(zzz90, zzz910)))
new_primPlusNat3(zzz90, Zero) → Succ(zzz90)

The set Q consists of the following terms:

new_primPlusNat2(Zero, Succ(x0))
new_primMulNat1(x0)
new_primMulNat0(x0)
new_primPlusNat3(x0, Succ(x1))
new_primPlusNat2(Succ(x0), Succ(x1))
new_primPlusNat3(x0, Zero)
new_primPlusNat1(Zero)
new_primPlusNat2(Zero, Zero)
new_primPlusNat1(Succ(x0))
new_primPlusNat2(Succ(x0), Zero)

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

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

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

new_mkVBalBranch3MkVBalBranch211(zzz537, zzz538, zzz539, zzz540, zzz541, zzz542, zzz543, zzz544, zzz545, zzz546, zzz547, bc) → new_mkVBalBranch3MkVBalBranch15(zzz537, zzz538, zzz539, zzz540, zzz541, zzz542, zzz543, zzz544, zzz545, zzz546, zzz547, new_primPlusNat2(new_primMulNat0(zzz539), Succ(zzz539)), bc)
new_mkVBalBranch3MkVBalBranch11(zzz2033, zzz2034, zzz2035, zzz2036, zzz2037, zzz2038, zzz2039, zzz2040, zzz2041, zzz2042, zzz2043, Zero, Succ(zzz20450), bb) → new_mkVBalBranch(zzz2043, zzz2042, Branch(zzz2033, zzz2034, Pos(Succ(zzz2035)), zzz2036, zzz2037), bb)
new_mkVBalBranch3MkVBalBranch2(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344, zzz520, zzz521, zzz52200, zzz523, zzz524, zzz31, Succ(zzz680), h) → new_mkVBalBranch3MkVBalBranch1(zzz340, zzz341, zzz34200, zzz343, zzz344, zzz520, zzz521, zzz52200, zzz523, zzz524, zzz31, new_primPlusNat2(new_primPlusNat3(Succ(new_primPlusNat3(new_primPlusNat1(zzz34200), zzz34200)), Succ(zzz34200)), Succ(zzz34200)), h)
new_mkVBalBranch3MkVBalBranch26(zzz1133, zzz1134, zzz1135, zzz1136, zzz1137, zzz1138, zzz1139, zzz1140, zzz1141, zzz1142, Succ(zzz11430), Succ(zzz11440), be) → new_mkVBalBranch3MkVBalBranch26(zzz1133, zzz1134, zzz1135, zzz1136, zzz1137, zzz1138, zzz1139, zzz1140, zzz1141, zzz1142, zzz11430, zzz11440, be)
new_mkVBalBranch3MkVBalBranch24(zzz340, zzz341, Neg(Succ(Succ(zzz342000))), zzz343, zzz344, zzz520, zzz521, Zero, zzz523, zzz524, zzz31, Zero, h) → new_mkVBalBranch3MkVBalBranch14(zzz340, zzz341, Succ(zzz342000), zzz343, zzz344, zzz520, zzz521, zzz523, zzz524, zzz31, new_primPlusNat2(new_primMulNat0(Succ(zzz342000)), Succ(Succ(zzz342000))), h)
new_mkVBalBranch3MkVBalBranch24(zzz340, zzz341, Neg(Succ(Succ(Succ(zzz3420000)))), zzz343, zzz344, zzz520, zzz521, Zero, zzz523, zzz524, zzz31, Succ(Zero), h) → new_mkVBalBranch3MkVBalBranch26(zzz340, zzz341, Succ(Succ(zzz3420000)), zzz343, zzz344, zzz520, zzz521, zzz523, zzz524, zzz31, Succ(zzz3420000), Zero, h)
new_mkVBalBranch3MkVBalBranch25(zzz537, zzz538, zzz539, zzz540, zzz541, zzz542, zzz543, zzz544, zzz545, zzz546, zzz547, Succ(zzz5480), Zero, bc) → new_mkVBalBranch3MkVBalBranch15(zzz537, zzz538, zzz539, zzz540, zzz541, zzz542, zzz543, zzz544, zzz545, zzz546, zzz547, new_primPlusNat2(new_primMulNat0(zzz539), Succ(zzz539)), bc)
new_mkVBalBranch3MkVBalBranch24(zzz340, zzz341, Neg(Succ(Zero)), zzz343, zzz344, zzz520, zzz521, Zero, zzz523, zzz524, zzz31, Zero, h) → new_mkVBalBranch3MkVBalBranch29(zzz340, zzz341, Zero, zzz343, zzz344, zzz520, zzz521, zzz523, zzz524, zzz31, h)
new_mkVBalBranch3MkVBalBranch20(zzz929, zzz930, zzz931, zzz932, zzz933, zzz934, zzz935, zzz936, zzz937, zzz938, zzz939, Zero, Succ(zzz9410), ba) → new_mkVBalBranch(zzz939, Branch(zzz934, zzz935, Pos(Succ(zzz936)), zzz937, zzz938), zzz932, ba)
new_mkVBalBranch3MkVBalBranch17(zzz340, zzz341, zzz34200, zzz343, zzz344, zzz520, zzz521, zzz52200, zzz523, zzz524, zzz31, h) → new_mkVBalBranch(zzz31, zzz524, Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), h)
new_mkVBalBranch3MkVBalBranch26(zzz1133, zzz1134, zzz1135, zzz1136, zzz1137, zzz1138, zzz1139, zzz1140, zzz1141, zzz1142, Zero, Zero, be) → new_mkVBalBranch3MkVBalBranch29(zzz1133, zzz1134, zzz1135, zzz1136, zzz1137, zzz1138, zzz1139, zzz1140, zzz1141, zzz1142, be)
new_mkVBalBranch3MkVBalBranch20(zzz929, zzz930, zzz931, zzz932, zzz933, zzz934, zzz935, zzz936, zzz937, zzz938, zzz939, Zero, Zero, ba) → new_mkVBalBranch3MkVBalBranch23(zzz929, zzz930, zzz931, zzz932, zzz933, zzz934, zzz935, zzz936, zzz937, zzz938, zzz939, ba)
new_mkVBalBranch3MkVBalBranch20(zzz929, zzz930, zzz931, zzz932, zzz933, zzz934, zzz935, zzz936, zzz937, zzz938, zzz939, Succ(zzz9400), Zero, ba) → new_mkVBalBranch3MkVBalBranch10(zzz929, zzz930, zzz931, zzz932, zzz933, zzz934, zzz935, zzz936, zzz937, zzz938, zzz939, new_primPlusNat2(new_primMulNat0(zzz931), Succ(zzz931)), ba)
new_mkVBalBranch3MkVBalBranch24(zzz340, zzz341, Neg(Succ(Succ(Zero))), zzz343, zzz344, zzz520, zzz521, Succ(zzz522000), zzz523, zzz524, zzz31, Succ(Zero), h) → new_mkVBalBranch3MkVBalBranch25(zzz340, zzz341, Succ(Zero), zzz343, zzz344, zzz520, zzz521, zzz522000, zzz523, zzz524, zzz31, Zero, Succ(zzz522000), h)
new_mkVBalBranch3MkVBalBranch24(zzz340, zzz341, Neg(Succ(Succ(Succ(zzz3420000)))), zzz343, zzz344, zzz520, zzz521, Succ(zzz522000), zzz523, zzz524, zzz31, Succ(Zero), h) → new_mkVBalBranch3MkVBalBranch25(zzz340, zzz341, Succ(Succ(zzz3420000)), zzz343, zzz344, zzz520, zzz521, zzz522000, zzz523, zzz524, zzz31, Succ(zzz3420000), Succ(zzz522000), h)
new_mkVBalBranch3MkVBalBranch20(zzz929, zzz930, zzz931, zzz932, zzz933, zzz934, zzz935, zzz936, zzz937, zzz938, zzz939, Succ(zzz9400), Succ(zzz9410), ba) → new_mkVBalBranch3MkVBalBranch20(zzz929, zzz930, zzz931, zzz932, zzz933, zzz934, zzz935, zzz936, zzz937, zzz938, zzz939, zzz9400, zzz9410, ba)
new_mkVBalBranch3MkVBalBranch24(zzz340, zzz341, Neg(Succ(Succ(zzz342000))), zzz343, zzz344, zzz520, zzz521, Succ(zzz522000), zzz523, zzz524, zzz31, Zero, h) → new_mkVBalBranch3MkVBalBranch25(zzz340, zzz341, Succ(zzz342000), zzz343, zzz344, zzz520, zzz521, zzz522000, zzz523, zzz524, zzz31, zzz342000, zzz522000, h)
new_mkVBalBranch3MkVBalBranch26(zzz1133, zzz1134, zzz1135, zzz1136, zzz1137, zzz1138, zzz1139, zzz1140, zzz1141, zzz1142, Succ(zzz11430), Zero, be) → new_mkVBalBranch3MkVBalBranch212(zzz1133, zzz1134, zzz1135, zzz1136, zzz1137, zzz1138, zzz1139, zzz1140, zzz1141, zzz1142, be)
new_mkVBalBranch(zzz31, Branch(zzz520, zzz521, Pos(Succ(zzz52200)), zzz523, zzz524), Branch(zzz340, zzz341, zzz342, zzz343, zzz344), h) → new_mkVBalBranch3MkVBalBranch2(zzz340, zzz341, zzz342, zzz343, zzz344, zzz520, zzz521, zzz52200, zzz523, zzz524, zzz31, new_primPlusNat3(Succ(new_primPlusNat3(new_primPlusNat1(zzz52200), zzz52200)), Succ(zzz52200)), h)
new_mkVBalBranch3MkVBalBranch29(zzz818, zzz819, zzz820, zzz821, zzz822, zzz823, zzz824, zzz825, zzz826, zzz827, bf) → new_mkVBalBranch3MkVBalBranch14(zzz818, zzz819, zzz820, zzz821, zzz822, zzz823, zzz824, zzz825, zzz826, zzz827, new_primPlusNat2(new_primMulNat0(zzz820), Succ(zzz820)), bf)
new_mkVBalBranch3MkVBalBranch11(zzz2033, zzz2034, zzz2035, zzz2036, zzz2037, zzz2038, zzz2039, zzz2040, zzz2041, zzz2042, zzz2043, Succ(zzz20440), Succ(zzz20450), bb) → new_mkVBalBranch3MkVBalBranch11(zzz2033, zzz2034, zzz2035, zzz2036, zzz2037, zzz2038, zzz2039, zzz2040, zzz2041, zzz2042, zzz2043, zzz20440, zzz20450, bb)
new_mkVBalBranch3MkVBalBranch25(zzz537, zzz538, zzz539, zzz540, zzz541, zzz542, zzz543, zzz544, zzz545, zzz546, zzz547, Succ(zzz5480), Succ(zzz5490), bc) → new_mkVBalBranch3MkVBalBranch25(zzz537, zzz538, zzz539, zzz540, zzz541, zzz542, zzz543, zzz544, zzz545, zzz546, zzz547, zzz5480, zzz5490, bc)
new_mkVBalBranch3MkVBalBranch2(zzz340, zzz341, Neg(zzz3420), zzz343, zzz344, zzz520, zzz521, zzz52200, zzz523, zzz524, zzz31, Zero, h) → new_mkVBalBranch3MkVBalBranch22(zzz340, zzz341, zzz3420, zzz343, zzz344, zzz520, zzz521, zzz52200, zzz523, zzz524, zzz31, h)
new_mkVBalBranch(zzz31, Branch(zzz520, zzz521, Neg(Succ(zzz52200)), zzz523, zzz524), Branch(zzz340, zzz341, zzz342, zzz343, zzz344), h) → new_mkVBalBranch3MkVBalBranch24(zzz340, zzz341, zzz342, zzz343, zzz344, zzz520, zzz521, zzz52200, zzz523, zzz524, zzz31, new_primPlusNat3(Succ(new_primPlusNat3(new_primPlusNat1(zzz52200), zzz52200)), Succ(zzz52200)), h)
new_mkVBalBranch3MkVBalBranch24(zzz340, zzz341, Neg(Succ(Zero)), zzz343, zzz344, zzz520, zzz521, Succ(zzz522000), zzz523, zzz524, zzz31, Zero, h) → new_mkVBalBranch3MkVBalBranch28(zzz340, zzz341, zzz343, zzz344, zzz520, zzz521, Succ(zzz522000), zzz523, zzz524, zzz31, h)
new_mkVBalBranch3MkVBalBranch210(zzz340, zzz341, zzz343, zzz344, zzz520, zzz521, zzz52200, zzz523, zzz524, zzz31, h) → new_mkVBalBranch(zzz31, Branch(zzz520, zzz521, Neg(Succ(zzz52200)), zzz523, zzz524), zzz343, h)
new_mkVBalBranch3MkVBalBranch26(zzz1133, zzz1134, zzz1135, zzz1136, zzz1137, zzz1138, zzz1139, zzz1140, zzz1141, zzz1142, Zero, Succ(zzz11440), be) → new_mkVBalBranch(zzz1142, Branch(zzz1138, zzz1139, Neg(Succ(Zero)), zzz1140, zzz1141), zzz1136, be)
new_mkVBalBranch3MkVBalBranch24(zzz340, zzz341, Neg(Succ(Succ(Zero))), zzz343, zzz344, zzz520, zzz521, Zero, zzz523, zzz524, zzz31, Succ(Zero), h) → new_mkVBalBranch3MkVBalBranch26(zzz340, zzz341, Succ(Zero), zzz343, zzz344, zzz520, zzz521, zzz523, zzz524, zzz31, Zero, Zero, h)
new_mkVBalBranch(zzz31, Branch(zzz520, zzz521, Pos(Zero), zzz523, zzz524), Branch(zzz340, zzz341, Pos(Succ(zzz34200)), zzz343, zzz344), h) → new_mkVBalBranch(zzz31, Branch(zzz520, zzz521, Pos(Zero), zzz523, zzz524), zzz343, h)
new_mkVBalBranch3MkVBalBranch2(zzz340, zzz341, Pos(Zero), zzz343, zzz344, zzz520, zzz521, zzz52200, zzz523, zzz524, zzz31, Succ(zzz680), h) → new_mkVBalBranch(zzz31, zzz524, Branch(zzz340, zzz341, Pos(Zero), zzz343, zzz344), h)
new_mkVBalBranch3MkVBalBranch21(zzz340, zzz341, zzz343, zzz344, zzz520, zzz521, zzz52200, zzz523, zzz524, zzz31, h) → new_mkVBalBranch(zzz31, zzz524, Branch(zzz340, zzz341, Pos(Zero), zzz343, zzz344), h)
new_mkVBalBranch3MkVBalBranch24(zzz340, zzz341, Pos(zzz3420), zzz343, zzz344, zzz520, zzz521, zzz52200, zzz523, zzz524, zzz31, Zero, h) → new_mkVBalBranch3MkVBalBranch27(zzz340, zzz341, zzz3420, zzz343, zzz344, zzz520, zzz521, zzz52200, zzz523, zzz524, zzz31, h)
new_mkVBalBranch3MkVBalBranch15(zzz537, zzz538, zzz539, zzz540, zzz541, zzz542, zzz543, zzz544, zzz545, zzz546, zzz547, Succ(zzz6990), bc) → new_mkVBalBranch3MkVBalBranch16(zzz537, zzz538, zzz539, zzz540, zzz541, zzz542, zzz543, Succ(zzz544), zzz545, zzz546, zzz547, Succ(Succ(zzz544)), Succ(zzz6990), bc)
new_mkVBalBranch3MkVBalBranch24(zzz340, zzz341, Neg(Succ(Succ(Succ(zzz3420000)))), zzz343, zzz344, zzz520, zzz521, Zero, zzz523, zzz524, zzz31, Succ(Succ(zzz6900)), h) → new_mkVBalBranch3MkVBalBranch26(zzz340, zzz341, Succ(Succ(zzz3420000)), zzz343, zzz344, zzz520, zzz521, zzz523, zzz524, zzz31, Succ(zzz3420000), Succ(zzz6900), h)
new_mkVBalBranch(zzz31, Branch(zzz520, zzz521, Neg(Zero), zzz523, zzz524), Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), h) → new_mkVBalBranch3MkVBalBranch13(zzz340, zzz341, zzz34200, zzz343, zzz344, zzz520, zzz521, zzz523, zzz524, zzz31, new_primPlusNat2(new_primMulNat0(zzz34200), Succ(zzz34200)), h)
new_mkVBalBranch3MkVBalBranch27(zzz340, zzz341, zzz3420, zzz343, zzz344, zzz520, zzz521, zzz52200, zzz523, zzz524, zzz31, h) → new_mkVBalBranch(zzz31, Branch(zzz520, zzz521, Neg(Succ(zzz52200)), zzz523, zzz524), zzz343, h)
new_mkVBalBranch3MkVBalBranch24(zzz340, zzz341, Pos(zzz3420), zzz343, zzz344, zzz520, zzz521, zzz52200, zzz523, zzz524, zzz31, Succ(zzz690), h) → new_mkVBalBranch(zzz31, Branch(zzz520, zzz521, Neg(Succ(zzz52200)), zzz523, zzz524), zzz343, h)
new_mkVBalBranch3MkVBalBranch12(zzz340, zzz341, zzz34200, zzz343, zzz344, zzz520, zzz521, zzz523, zzz524, zzz31, Succ(zzz1250), h) → new_mkVBalBranch(zzz31, zzz524, Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), h)
new_mkVBalBranch3MkVBalBranch28(zzz340, zzz341, zzz343, zzz344, zzz520, zzz521, zzz52200, zzz523, zzz524, zzz31, h) → new_mkVBalBranch(zzz31, Branch(zzz520, zzz521, Neg(Succ(zzz52200)), zzz523, zzz524), zzz343, h)
new_mkVBalBranch3MkVBalBranch24(zzz340, zzz341, Neg(Succ(Succ(Zero))), zzz343, zzz344, zzz520, zzz521, Zero, zzz523, zzz524, zzz31, Succ(Succ(zzz6900)), h) → new_mkVBalBranch3MkVBalBranch26(zzz340, zzz341, Succ(Zero), zzz343, zzz344, zzz520, zzz521, zzz523, zzz524, zzz31, Zero, Succ(zzz6900), h)
new_mkVBalBranch(zzz31, Branch(zzz520, zzz521, Pos(Zero), zzz523, zzz524), Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), h) → new_mkVBalBranch3MkVBalBranch12(zzz340, zzz341, zzz34200, zzz343, zzz344, zzz520, zzz521, zzz523, zzz524, zzz31, new_primPlusNat2(new_primMulNat0(zzz34200), Succ(zzz34200)), h)
new_mkVBalBranch3MkVBalBranch22(zzz340, zzz341, Zero, zzz343, zzz344, zzz520, zzz521, zzz52200, zzz523, zzz524, zzz31, h) → new_mkVBalBranch(zzz31, zzz524, Branch(zzz340, zzz341, Neg(Zero), zzz343, zzz344), h)
new_mkVBalBranch3MkVBalBranch1(zzz340, zzz341, zzz34200, zzz343, zzz344, zzz520, zzz521, zzz52200, zzz523, zzz524, zzz31, Succ(zzz1430), h) → new_mkVBalBranch(zzz31, zzz524, Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), h)
new_mkVBalBranch3MkVBalBranch24(zzz340, zzz341, Neg(Succ(Zero)), zzz343, zzz344, zzz520, zzz521, zzz52200, zzz523, zzz524, zzz31, Succ(zzz690), h) → new_mkVBalBranch(zzz31, Branch(zzz520, zzz521, Neg(Succ(zzz52200)), zzz523, zzz524), zzz343, h)
new_mkVBalBranch3MkVBalBranch13(zzz340, zzz341, zzz34200, zzz343, zzz344, zzz520, zzz521, zzz523, zzz524, zzz31, Succ(zzz1290), h) → new_mkVBalBranch(zzz31, zzz524, Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), h)
new_mkVBalBranch3MkVBalBranch2(zzz340, zzz341, Pos(Succ(zzz34200)), zzz343, zzz344, zzz520, zzz521, zzz52200, zzz523, zzz524, zzz31, Succ(zzz680), h) → new_mkVBalBranch3MkVBalBranch20(zzz340, zzz341, zzz34200, zzz343, zzz344, zzz520, zzz521, zzz52200, zzz523, zzz524, zzz31, Succ(new_primPlusNat2(zzz680, zzz52200)), zzz34200, h)
new_mkVBalBranch(zzz31, Branch(zzz520, zzz521, Neg(Zero), zzz523, zzz524), Branch(zzz340, zzz341, Pos(Succ(zzz34200)), zzz343, zzz344), h) → new_mkVBalBranch(zzz31, Branch(zzz520, zzz521, Neg(Zero), zzz523, zzz524), zzz343, h)
new_mkVBalBranch3MkVBalBranch24(zzz340, zzz341, Neg(Zero), zzz343, zzz344, zzz520, zzz521, zzz52200, zzz523, zzz524, zzz31, Succ(zzz690), h) → new_mkVBalBranch(zzz31, Branch(zzz520, zzz521, Neg(Succ(zzz52200)), zzz523, zzz524), zzz343, h)
new_mkVBalBranch3MkVBalBranch1(zzz340, zzz341, zzz34200, zzz343, zzz344, zzz520, zzz521, zzz52200, zzz523, zzz524, zzz31, Zero, h) → new_mkVBalBranch3MkVBalBranch17(zzz340, zzz341, zzz34200, zzz343, zzz344, zzz520, zzz521, zzz52200, zzz523, zzz524, zzz31, h)
new_mkVBalBranch3MkVBalBranch16(zzz1702, zzz1703, zzz1704, zzz1705, zzz1706, zzz1707, zzz1708, zzz1709, zzz1710, zzz1711, zzz1712, Succ(zzz17130), Succ(zzz17140), bd) → new_mkVBalBranch3MkVBalBranch16(zzz1702, zzz1703, zzz1704, zzz1705, zzz1706, zzz1707, zzz1708, zzz1709, zzz1710, zzz1711, zzz1712, zzz17130, zzz17140, bd)
new_mkVBalBranch3MkVBalBranch25(zzz537, zzz538, zzz539, zzz540, zzz541, zzz542, zzz543, zzz544, zzz545, zzz546, zzz547, Zero, Succ(zzz5490), bc) → new_mkVBalBranch(zzz547, Branch(zzz542, zzz543, Neg(Succ(Succ(zzz544))), zzz545, zzz546), zzz540, bc)
new_mkVBalBranch3MkVBalBranch10(zzz929, zzz930, zzz931, zzz932, zzz933, zzz934, zzz935, zzz936, zzz937, zzz938, zzz939, Succ(zzz10020), ba) → new_mkVBalBranch3MkVBalBranch11(zzz929, zzz930, zzz931, zzz932, zzz933, zzz934, zzz935, zzz936, zzz937, zzz938, zzz939, Succ(zzz10020), Succ(zzz936), ba)
new_mkVBalBranch3MkVBalBranch212(zzz818, zzz819, zzz820, zzz821, zzz822, zzz823, zzz824, zzz825, zzz826, zzz827, bf) → new_mkVBalBranch3MkVBalBranch14(zzz818, zzz819, zzz820, zzz821, zzz822, zzz823, zzz824, zzz825, zzz826, zzz827, new_primPlusNat2(new_primMulNat0(zzz820), Succ(zzz820)), bf)
new_mkVBalBranch3MkVBalBranch14(zzz818, zzz819, zzz820, zzz821, zzz822, zzz823, zzz824, zzz825, zzz826, zzz827, Succ(zzz8960), bf) → new_mkVBalBranch3MkVBalBranch16(zzz818, zzz819, zzz820, zzz821, zzz822, zzz823, zzz824, Zero, zzz825, zzz826, zzz827, Succ(Zero), Succ(zzz8960), bf)
new_mkVBalBranch3MkVBalBranch24(zzz340, zzz341, Neg(Succ(Succ(Succ(zzz3420000)))), zzz343, zzz344, zzz520, zzz521, Succ(zzz522000), zzz523, zzz524, zzz31, Succ(Succ(zzz6900)), h) → new_mkVBalBranch3MkVBalBranch25(zzz340, zzz341, Succ(Succ(zzz3420000)), zzz343, zzz344, zzz520, zzz521, zzz522000, zzz523, zzz524, zzz31, Succ(zzz3420000), Succ(Succ(new_primPlusNat2(zzz6900, zzz522000))), h)
new_mkVBalBranch3MkVBalBranch2(zzz340, zzz341, Pos(Succ(zzz34200)), zzz343, zzz344, zzz520, zzz521, zzz52200, zzz523, zzz524, zzz31, Zero, h) → new_mkVBalBranch3MkVBalBranch20(zzz340, zzz341, zzz34200, zzz343, zzz344, zzz520, zzz521, zzz52200, zzz523, zzz524, zzz31, zzz52200, zzz34200, h)
new_mkVBalBranch3MkVBalBranch24(zzz340, zzz341, Neg(Zero), zzz343, zzz344, zzz520, zzz521, zzz52200, zzz523, zzz524, zzz31, Zero, h) → new_mkVBalBranch3MkVBalBranch210(zzz340, zzz341, zzz343, zzz344, zzz520, zzz521, zzz52200, zzz523, zzz524, zzz31, h)
new_mkVBalBranch3MkVBalBranch24(zzz340, zzz341, Neg(Succ(Succ(Zero))), zzz343, zzz344, zzz520, zzz521, Succ(zzz522000), zzz523, zzz524, zzz31, Succ(Succ(zzz6900)), h) → new_mkVBalBranch3MkVBalBranch25(zzz340, zzz341, Succ(Zero), zzz343, zzz344, zzz520, zzz521, zzz522000, zzz523, zzz524, zzz31, Zero, Succ(Succ(new_primPlusNat2(zzz6900, zzz522000))), h)
new_mkVBalBranch3MkVBalBranch23(zzz929, zzz930, zzz931, zzz932, zzz933, zzz934, zzz935, zzz936, zzz937, zzz938, zzz939, ba) → new_mkVBalBranch3MkVBalBranch10(zzz929, zzz930, zzz931, zzz932, zzz933, zzz934, zzz935, zzz936, zzz937, zzz938, zzz939, new_primPlusNat2(new_primMulNat0(zzz931), Succ(zzz931)), ba)
new_mkVBalBranch3MkVBalBranch2(zzz340, zzz341, Neg(Zero), zzz343, zzz344, zzz520, zzz521, zzz52200, zzz523, zzz524, zzz31, Succ(zzz680), h) → new_mkVBalBranch(zzz31, zzz524, Branch(zzz340, zzz341, Neg(Zero), zzz343, zzz344), h)
new_mkVBalBranch3MkVBalBranch16(zzz1702, zzz1703, zzz1704, zzz1705, zzz1706, zzz1707, zzz1708, zzz1709, zzz1710, zzz1711, zzz1712, Zero, Succ(zzz17140), bd) → new_mkVBalBranch(zzz1712, zzz1711, Branch(zzz1702, zzz1703, Neg(Succ(zzz1704)), zzz1705, zzz1706), bd)
new_mkVBalBranch3MkVBalBranch10(zzz929, zzz930, zzz931, zzz932, zzz933, zzz934, zzz935, zzz936, zzz937, zzz938, zzz939, Zero, ba) → new_mkVBalBranch3MkVBalBranch11(zzz929, zzz930, zzz931, zzz932, zzz933, zzz934, zzz935, zzz936, zzz937, zzz938, zzz939, Zero, Succ(zzz936), ba)
new_mkVBalBranch3MkVBalBranch25(zzz537, zzz538, zzz539, zzz540, zzz541, zzz542, zzz543, zzz544, zzz545, zzz546, zzz547, Zero, Zero, bc) → new_mkVBalBranch3MkVBalBranch211(zzz537, zzz538, zzz539, zzz540, zzz541, zzz542, zzz543, zzz544, zzz545, zzz546, zzz547, bc)
new_mkVBalBranch3MkVBalBranch2(zzz340, zzz341, Pos(Zero), zzz343, zzz344, zzz520, zzz521, zzz52200, zzz523, zzz524, zzz31, Zero, h) → new_mkVBalBranch3MkVBalBranch21(zzz340, zzz341, zzz343, zzz344, zzz520, zzz521, zzz52200, zzz523, zzz524, zzz31, h)
new_mkVBalBranch3MkVBalBranch22(zzz340, zzz341, Succ(zzz34200), zzz343, zzz344, zzz520, zzz521, zzz52200, zzz523, zzz524, zzz31, h) → new_mkVBalBranch3MkVBalBranch1(zzz340, zzz341, zzz34200, zzz343, zzz344, zzz520, zzz521, zzz52200, zzz523, zzz524, zzz31, new_primPlusNat2(new_primPlusNat3(Succ(new_primPlusNat3(new_primPlusNat1(zzz34200), zzz34200)), Succ(zzz34200)), Succ(zzz34200)), h)

The TRS R consists of the following rules:

new_primMulNat0(zzz6200) → new_primPlusNat3(Succ(new_primPlusNat3(new_primPlusNat1(zzz6200), zzz6200)), Succ(zzz6200))
new_primPlusNat2(Succ(zzz900), Succ(zzz9100)) → Succ(Succ(new_primPlusNat2(zzz900, zzz9100)))
new_primPlusNat2(Zero, Succ(zzz9100)) → Succ(zzz9100)
new_primPlusNat2(Zero, Zero) → Zero
new_primPlusNat2(Succ(zzz900), Zero) → Succ(zzz900)
new_primPlusNat1(Zero) → Zero
new_primPlusNat1(Succ(zzz62000)) → Succ(Succ(new_primPlusNat1(zzz62000)))
new_primPlusNat3(zzz90, Succ(zzz910)) → Succ(Succ(new_primPlusNat2(zzz90, zzz910)))
new_primPlusNat3(zzz90, Zero) → Succ(zzz90)

The set Q consists of the following terms:

new_primPlusNat2(Zero, Succ(x0))
new_primMulNat0(x0)
new_primPlusNat3(x0, Succ(x1))
new_primPlusNat2(Succ(x0), Succ(x1))
new_primPlusNat3(x0, Zero)
new_primPlusNat1(Zero)
new_primPlusNat2(Zero, Zero)
new_primPlusNat1(Succ(x0))
new_primPlusNat2(Succ(x0), Zero)

We have to consider all minimal (P,Q,R)-chains.
By rewriting [15] the rule new_mkVBalBranch3MkVBalBranch211(zzz537, zzz538, zzz539, zzz540, zzz541, zzz542, zzz543, zzz544, zzz545, zzz546, zzz547, bc) → new_mkVBalBranch3MkVBalBranch15(zzz537, zzz538, zzz539, zzz540, zzz541, zzz542, zzz543, zzz544, zzz545, zzz546, zzz547, new_primPlusNat2(new_primMulNat0(zzz539), Succ(zzz539)), bc) at position [11,0] we obtained the following new rules:

new_mkVBalBranch3MkVBalBranch211(zzz537, zzz538, zzz539, zzz540, zzz541, zzz542, zzz543, zzz544, zzz545, zzz546, zzz547, bc) → new_mkVBalBranch3MkVBalBranch15(zzz537, zzz538, zzz539, zzz540, zzz541, zzz542, zzz543, zzz544, zzz545, zzz546, zzz547, new_primPlusNat2(new_primPlusNat3(Succ(new_primPlusNat3(new_primPlusNat1(zzz539), zzz539)), Succ(zzz539)), Succ(zzz539)), bc)



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

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

new_mkVBalBranch3MkVBalBranch11(zzz2033, zzz2034, zzz2035, zzz2036, zzz2037, zzz2038, zzz2039, zzz2040, zzz2041, zzz2042, zzz2043, Zero, Succ(zzz20450), bb) → new_mkVBalBranch(zzz2043, zzz2042, Branch(zzz2033, zzz2034, Pos(Succ(zzz2035)), zzz2036, zzz2037), bb)
new_mkVBalBranch3MkVBalBranch2(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344, zzz520, zzz521, zzz52200, zzz523, zzz524, zzz31, Succ(zzz680), h) → new_mkVBalBranch3MkVBalBranch1(zzz340, zzz341, zzz34200, zzz343, zzz344, zzz520, zzz521, zzz52200, zzz523, zzz524, zzz31, new_primPlusNat2(new_primPlusNat3(Succ(new_primPlusNat3(new_primPlusNat1(zzz34200), zzz34200)), Succ(zzz34200)), Succ(zzz34200)), h)
new_mkVBalBranch3MkVBalBranch26(zzz1133, zzz1134, zzz1135, zzz1136, zzz1137, zzz1138, zzz1139, zzz1140, zzz1141, zzz1142, Succ(zzz11430), Succ(zzz11440), be) → new_mkVBalBranch3MkVBalBranch26(zzz1133, zzz1134, zzz1135, zzz1136, zzz1137, zzz1138, zzz1139, zzz1140, zzz1141, zzz1142, zzz11430, zzz11440, be)
new_mkVBalBranch3MkVBalBranch24(zzz340, zzz341, Neg(Succ(Succ(zzz342000))), zzz343, zzz344, zzz520, zzz521, Zero, zzz523, zzz524, zzz31, Zero, h) → new_mkVBalBranch3MkVBalBranch14(zzz340, zzz341, Succ(zzz342000), zzz343, zzz344, zzz520, zzz521, zzz523, zzz524, zzz31, new_primPlusNat2(new_primMulNat0(Succ(zzz342000)), Succ(Succ(zzz342000))), h)
new_mkVBalBranch3MkVBalBranch24(zzz340, zzz341, Neg(Succ(Succ(Succ(zzz3420000)))), zzz343, zzz344, zzz520, zzz521, Zero, zzz523, zzz524, zzz31, Succ(Zero), h) → new_mkVBalBranch3MkVBalBranch26(zzz340, zzz341, Succ(Succ(zzz3420000)), zzz343, zzz344, zzz520, zzz521, zzz523, zzz524, zzz31, Succ(zzz3420000), Zero, h)
new_mkVBalBranch3MkVBalBranch24(zzz340, zzz341, Neg(Succ(Zero)), zzz343, zzz344, zzz520, zzz521, Zero, zzz523, zzz524, zzz31, Zero, h) → new_mkVBalBranch3MkVBalBranch29(zzz340, zzz341, Zero, zzz343, zzz344, zzz520, zzz521, zzz523, zzz524, zzz31, h)
new_mkVBalBranch3MkVBalBranch25(zzz537, zzz538, zzz539, zzz540, zzz541, zzz542, zzz543, zzz544, zzz545, zzz546, zzz547, Succ(zzz5480), Zero, bc) → new_mkVBalBranch3MkVBalBranch15(zzz537, zzz538, zzz539, zzz540, zzz541, zzz542, zzz543, zzz544, zzz545, zzz546, zzz547, new_primPlusNat2(new_primMulNat0(zzz539), Succ(zzz539)), bc)
new_mkVBalBranch3MkVBalBranch20(zzz929, zzz930, zzz931, zzz932, zzz933, zzz934, zzz935, zzz936, zzz937, zzz938, zzz939, Zero, Succ(zzz9410), ba) → new_mkVBalBranch(zzz939, Branch(zzz934, zzz935, Pos(Succ(zzz936)), zzz937, zzz938), zzz932, ba)
new_mkVBalBranch3MkVBalBranch17(zzz340, zzz341, zzz34200, zzz343, zzz344, zzz520, zzz521, zzz52200, zzz523, zzz524, zzz31, h) → new_mkVBalBranch(zzz31, zzz524, Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), h)
new_mkVBalBranch3MkVBalBranch26(zzz1133, zzz1134, zzz1135, zzz1136, zzz1137, zzz1138, zzz1139, zzz1140, zzz1141, zzz1142, Zero, Zero, be) → new_mkVBalBranch3MkVBalBranch29(zzz1133, zzz1134, zzz1135, zzz1136, zzz1137, zzz1138, zzz1139, zzz1140, zzz1141, zzz1142, be)
new_mkVBalBranch3MkVBalBranch20(zzz929, zzz930, zzz931, zzz932, zzz933, zzz934, zzz935, zzz936, zzz937, zzz938, zzz939, Zero, Zero, ba) → new_mkVBalBranch3MkVBalBranch23(zzz929, zzz930, zzz931, zzz932, zzz933, zzz934, zzz935, zzz936, zzz937, zzz938, zzz939, ba)
new_mkVBalBranch3MkVBalBranch20(zzz929, zzz930, zzz931, zzz932, zzz933, zzz934, zzz935, zzz936, zzz937, zzz938, zzz939, Succ(zzz9400), Zero, ba) → new_mkVBalBranch3MkVBalBranch10(zzz929, zzz930, zzz931, zzz932, zzz933, zzz934, zzz935, zzz936, zzz937, zzz938, zzz939, new_primPlusNat2(new_primMulNat0(zzz931), Succ(zzz931)), ba)
new_mkVBalBranch3MkVBalBranch24(zzz340, zzz341, Neg(Succ(Succ(Zero))), zzz343, zzz344, zzz520, zzz521, Succ(zzz522000), zzz523, zzz524, zzz31, Succ(Zero), h) → new_mkVBalBranch3MkVBalBranch25(zzz340, zzz341, Succ(Zero), zzz343, zzz344, zzz520, zzz521, zzz522000, zzz523, zzz524, zzz31, Zero, Succ(zzz522000), h)
new_mkVBalBranch3MkVBalBranch20(zzz929, zzz930, zzz931, zzz932, zzz933, zzz934, zzz935, zzz936, zzz937, zzz938, zzz939, Succ(zzz9400), Succ(zzz9410), ba) → new_mkVBalBranch3MkVBalBranch20(zzz929, zzz930, zzz931, zzz932, zzz933, zzz934, zzz935, zzz936, zzz937, zzz938, zzz939, zzz9400, zzz9410, ba)
new_mkVBalBranch3MkVBalBranch24(zzz340, zzz341, Neg(Succ(Succ(Succ(zzz3420000)))), zzz343, zzz344, zzz520, zzz521, Succ(zzz522000), zzz523, zzz524, zzz31, Succ(Zero), h) → new_mkVBalBranch3MkVBalBranch25(zzz340, zzz341, Succ(Succ(zzz3420000)), zzz343, zzz344, zzz520, zzz521, zzz522000, zzz523, zzz524, zzz31, Succ(zzz3420000), Succ(zzz522000), h)
new_mkVBalBranch3MkVBalBranch26(zzz1133, zzz1134, zzz1135, zzz1136, zzz1137, zzz1138, zzz1139, zzz1140, zzz1141, zzz1142, Succ(zzz11430), Zero, be) → new_mkVBalBranch3MkVBalBranch212(zzz1133, zzz1134, zzz1135, zzz1136, zzz1137, zzz1138, zzz1139, zzz1140, zzz1141, zzz1142, be)
new_mkVBalBranch3MkVBalBranch24(zzz340, zzz341, Neg(Succ(Succ(zzz342000))), zzz343, zzz344, zzz520, zzz521, Succ(zzz522000), zzz523, zzz524, zzz31, Zero, h) → new_mkVBalBranch3MkVBalBranch25(zzz340, zzz341, Succ(zzz342000), zzz343, zzz344, zzz520, zzz521, zzz522000, zzz523, zzz524, zzz31, zzz342000, zzz522000, h)
new_mkVBalBranch(zzz31, Branch(zzz520, zzz521, Pos(Succ(zzz52200)), zzz523, zzz524), Branch(zzz340, zzz341, zzz342, zzz343, zzz344), h) → new_mkVBalBranch3MkVBalBranch2(zzz340, zzz341, zzz342, zzz343, zzz344, zzz520, zzz521, zzz52200, zzz523, zzz524, zzz31, new_primPlusNat3(Succ(new_primPlusNat3(new_primPlusNat1(zzz52200), zzz52200)), Succ(zzz52200)), h)
new_mkVBalBranch3MkVBalBranch29(zzz818, zzz819, zzz820, zzz821, zzz822, zzz823, zzz824, zzz825, zzz826, zzz827, bf) → new_mkVBalBranch3MkVBalBranch14(zzz818, zzz819, zzz820, zzz821, zzz822, zzz823, zzz824, zzz825, zzz826, zzz827, new_primPlusNat2(new_primMulNat0(zzz820), Succ(zzz820)), bf)
new_mkVBalBranch3MkVBalBranch11(zzz2033, zzz2034, zzz2035, zzz2036, zzz2037, zzz2038, zzz2039, zzz2040, zzz2041, zzz2042, zzz2043, Succ(zzz20440), Succ(zzz20450), bb) → new_mkVBalBranch3MkVBalBranch11(zzz2033, zzz2034, zzz2035, zzz2036, zzz2037, zzz2038, zzz2039, zzz2040, zzz2041, zzz2042, zzz2043, zzz20440, zzz20450, bb)
new_mkVBalBranch3MkVBalBranch2(zzz340, zzz341, Neg(zzz3420), zzz343, zzz344, zzz520, zzz521, zzz52200, zzz523, zzz524, zzz31, Zero, h) → new_mkVBalBranch3MkVBalBranch22(zzz340, zzz341, zzz3420, zzz343, zzz344, zzz520, zzz521, zzz52200, zzz523, zzz524, zzz31, h)
new_mkVBalBranch3MkVBalBranch25(zzz537, zzz538, zzz539, zzz540, zzz541, zzz542, zzz543, zzz544, zzz545, zzz546, zzz547, Succ(zzz5480), Succ(zzz5490), bc) → new_mkVBalBranch3MkVBalBranch25(zzz537, zzz538, zzz539, zzz540, zzz541, zzz542, zzz543, zzz544, zzz545, zzz546, zzz547, zzz5480, zzz5490, bc)
new_mkVBalBranch(zzz31, Branch(zzz520, zzz521, Neg(Succ(zzz52200)), zzz523, zzz524), Branch(zzz340, zzz341, zzz342, zzz343, zzz344), h) → new_mkVBalBranch3MkVBalBranch24(zzz340, zzz341, zzz342, zzz343, zzz344, zzz520, zzz521, zzz52200, zzz523, zzz524, zzz31, new_primPlusNat3(Succ(new_primPlusNat3(new_primPlusNat1(zzz52200), zzz52200)), Succ(zzz52200)), h)
new_mkVBalBranch3MkVBalBranch24(zzz340, zzz341, Neg(Succ(Zero)), zzz343, zzz344, zzz520, zzz521, Succ(zzz522000), zzz523, zzz524, zzz31, Zero, h) → new_mkVBalBranch3MkVBalBranch28(zzz340, zzz341, zzz343, zzz344, zzz520, zzz521, Succ(zzz522000), zzz523, zzz524, zzz31, h)
new_mkVBalBranch3MkVBalBranch210(zzz340, zzz341, zzz343, zzz344, zzz520, zzz521, zzz52200, zzz523, zzz524, zzz31, h) → new_mkVBalBranch(zzz31, Branch(zzz520, zzz521, Neg(Succ(zzz52200)), zzz523, zzz524), zzz343, h)
new_mkVBalBranch3MkVBalBranch26(zzz1133, zzz1134, zzz1135, zzz1136, zzz1137, zzz1138, zzz1139, zzz1140, zzz1141, zzz1142, Zero, Succ(zzz11440), be) → new_mkVBalBranch(zzz1142, Branch(zzz1138, zzz1139, Neg(Succ(Zero)), zzz1140, zzz1141), zzz1136, be)
new_mkVBalBranch3MkVBalBranch24(zzz340, zzz341, Neg(Succ(Succ(Zero))), zzz343, zzz344, zzz520, zzz521, Zero, zzz523, zzz524, zzz31, Succ(Zero), h) → new_mkVBalBranch3MkVBalBranch26(zzz340, zzz341, Succ(Zero), zzz343, zzz344, zzz520, zzz521, zzz523, zzz524, zzz31, Zero, Zero, h)
new_mkVBalBranch(zzz31, Branch(zzz520, zzz521, Pos(Zero), zzz523, zzz524), Branch(zzz340, zzz341, Pos(Succ(zzz34200)), zzz343, zzz344), h) → new_mkVBalBranch(zzz31, Branch(zzz520, zzz521, Pos(Zero), zzz523, zzz524), zzz343, h)
new_mkVBalBranch3MkVBalBranch2(zzz340, zzz341, Pos(Zero), zzz343, zzz344, zzz520, zzz521, zzz52200, zzz523, zzz524, zzz31, Succ(zzz680), h) → new_mkVBalBranch(zzz31, zzz524, Branch(zzz340, zzz341, Pos(Zero), zzz343, zzz344), h)
new_mkVBalBranch3MkVBalBranch21(zzz340, zzz341, zzz343, zzz344, zzz520, zzz521, zzz52200, zzz523, zzz524, zzz31, h) → new_mkVBalBranch(zzz31, zzz524, Branch(zzz340, zzz341, Pos(Zero), zzz343, zzz344), h)
new_mkVBalBranch3MkVBalBranch24(zzz340, zzz341, Pos(zzz3420), zzz343, zzz344, zzz520, zzz521, zzz52200, zzz523, zzz524, zzz31, Zero, h) → new_mkVBalBranch3MkVBalBranch27(zzz340, zzz341, zzz3420, zzz343, zzz344, zzz520, zzz521, zzz52200, zzz523, zzz524, zzz31, h)
new_mkVBalBranch3MkVBalBranch24(zzz340, zzz341, Neg(Succ(Succ(Succ(zzz3420000)))), zzz343, zzz344, zzz520, zzz521, Zero, zzz523, zzz524, zzz31, Succ(Succ(zzz6900)), h) → new_mkVBalBranch3MkVBalBranch26(zzz340, zzz341, Succ(Succ(zzz3420000)), zzz343, zzz344, zzz520, zzz521, zzz523, zzz524, zzz31, Succ(zzz3420000), Succ(zzz6900), h)
new_mkVBalBranch3MkVBalBranch15(zzz537, zzz538, zzz539, zzz540, zzz541, zzz542, zzz543, zzz544, zzz545, zzz546, zzz547, Succ(zzz6990), bc) → new_mkVBalBranch3MkVBalBranch16(zzz537, zzz538, zzz539, zzz540, zzz541, zzz542, zzz543, Succ(zzz544), zzz545, zzz546, zzz547, Succ(Succ(zzz544)), Succ(zzz6990), bc)
new_mkVBalBranch(zzz31, Branch(zzz520, zzz521, Neg(Zero), zzz523, zzz524), Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), h) → new_mkVBalBranch3MkVBalBranch13(zzz340, zzz341, zzz34200, zzz343, zzz344, zzz520, zzz521, zzz523, zzz524, zzz31, new_primPlusNat2(new_primMulNat0(zzz34200), Succ(zzz34200)), h)
new_mkVBalBranch3MkVBalBranch27(zzz340, zzz341, zzz3420, zzz343, zzz344, zzz520, zzz521, zzz52200, zzz523, zzz524, zzz31, h) → new_mkVBalBranch(zzz31, Branch(zzz520, zzz521, Neg(Succ(zzz52200)), zzz523, zzz524), zzz343, h)
new_mkVBalBranch3MkVBalBranch24(zzz340, zzz341, Pos(zzz3420), zzz343, zzz344, zzz520, zzz521, zzz52200, zzz523, zzz524, zzz31, Succ(zzz690), h) → new_mkVBalBranch(zzz31, Branch(zzz520, zzz521, Neg(Succ(zzz52200)), zzz523, zzz524), zzz343, h)
new_mkVBalBranch3MkVBalBranch12(zzz340, zzz341, zzz34200, zzz343, zzz344, zzz520, zzz521, zzz523, zzz524, zzz31, Succ(zzz1250), h) → new_mkVBalBranch(zzz31, zzz524, Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), h)
new_mkVBalBranch3MkVBalBranch28(zzz340, zzz341, zzz343, zzz344, zzz520, zzz521, zzz52200, zzz523, zzz524, zzz31, h) → new_mkVBalBranch(zzz31, Branch(zzz520, zzz521, Neg(Succ(zzz52200)), zzz523, zzz524), zzz343, h)
new_mkVBalBranch3MkVBalBranch24(zzz340, zzz341, Neg(Succ(Succ(Zero))), zzz343, zzz344, zzz520, zzz521, Zero, zzz523, zzz524, zzz31, Succ(Succ(zzz6900)), h) → new_mkVBalBranch3MkVBalBranch26(zzz340, zzz341, Succ(Zero), zzz343, zzz344, zzz520, zzz521, zzz523, zzz524, zzz31, Zero, Succ(zzz6900), h)
new_mkVBalBranch3MkVBalBranch211(zzz537, zzz538, zzz539, zzz540, zzz541, zzz542, zzz543, zzz544, zzz545, zzz546, zzz547, bc) → new_mkVBalBranch3MkVBalBranch15(zzz537, zzz538, zzz539, zzz540, zzz541, zzz542, zzz543, zzz544, zzz545, zzz546, zzz547, new_primPlusNat2(new_primPlusNat3(Succ(new_primPlusNat3(new_primPlusNat1(zzz539), zzz539)), Succ(zzz539)), Succ(zzz539)), bc)
new_mkVBalBranch3MkVBalBranch1(zzz340, zzz341, zzz34200, zzz343, zzz344, zzz520, zzz521, zzz52200, zzz523, zzz524, zzz31, Succ(zzz1430), h) → new_mkVBalBranch(zzz31, zzz524, Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), h)
new_mkVBalBranch3MkVBalBranch22(zzz340, zzz341, Zero, zzz343, zzz344, zzz520, zzz521, zzz52200, zzz523, zzz524, zzz31, h) → new_mkVBalBranch(zzz31, zzz524, Branch(zzz340, zzz341, Neg(Zero), zzz343, zzz344), h)
new_mkVBalBranch(zzz31, Branch(zzz520, zzz521, Pos(Zero), zzz523, zzz524), Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), h) → new_mkVBalBranch3MkVBalBranch12(zzz340, zzz341, zzz34200, zzz343, zzz344, zzz520, zzz521, zzz523, zzz524, zzz31, new_primPlusNat2(new_primMulNat0(zzz34200), Succ(zzz34200)), h)
new_mkVBalBranch3MkVBalBranch24(zzz340, zzz341, Neg(Succ(Zero)), zzz343, zzz344, zzz520, zzz521, zzz52200, zzz523, zzz524, zzz31, Succ(zzz690), h) → new_mkVBalBranch(zzz31, Branch(zzz520, zzz521, Neg(Succ(zzz52200)), zzz523, zzz524), zzz343, h)
new_mkVBalBranch3MkVBalBranch13(zzz340, zzz341, zzz34200, zzz343, zzz344, zzz520, zzz521, zzz523, zzz524, zzz31, Succ(zzz1290), h) → new_mkVBalBranch(zzz31, zzz524, Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), h)
new_mkVBalBranch3MkVBalBranch2(zzz340, zzz341, Pos(Succ(zzz34200)), zzz343, zzz344, zzz520, zzz521, zzz52200, zzz523, zzz524, zzz31, Succ(zzz680), h) → new_mkVBalBranch3MkVBalBranch20(zzz340, zzz341, zzz34200, zzz343, zzz344, zzz520, zzz521, zzz52200, zzz523, zzz524, zzz31, Succ(new_primPlusNat2(zzz680, zzz52200)), zzz34200, h)
new_mkVBalBranch3MkVBalBranch24(zzz340, zzz341, Neg(Zero), zzz343, zzz344, zzz520, zzz521, zzz52200, zzz523, zzz524, zzz31, Succ(zzz690), h) → new_mkVBalBranch(zzz31, Branch(zzz520, zzz521, Neg(Succ(zzz52200)), zzz523, zzz524), zzz343, h)
new_mkVBalBranch(zzz31, Branch(zzz520, zzz521, Neg(Zero), zzz523, zzz524), Branch(zzz340, zzz341, Pos(Succ(zzz34200)), zzz343, zzz344), h) → new_mkVBalBranch(zzz31, Branch(zzz520, zzz521, Neg(Zero), zzz523, zzz524), zzz343, h)
new_mkVBalBranch3MkVBalBranch1(zzz340, zzz341, zzz34200, zzz343, zzz344, zzz520, zzz521, zzz52200, zzz523, zzz524, zzz31, Zero, h) → new_mkVBalBranch3MkVBalBranch17(zzz340, zzz341, zzz34200, zzz343, zzz344, zzz520, zzz521, zzz52200, zzz523, zzz524, zzz31, h)
new_mkVBalBranch3MkVBalBranch16(zzz1702, zzz1703, zzz1704, zzz1705, zzz1706, zzz1707, zzz1708, zzz1709, zzz1710, zzz1711, zzz1712, Succ(zzz17130), Succ(zzz17140), bd) → new_mkVBalBranch3MkVBalBranch16(zzz1702, zzz1703, zzz1704, zzz1705, zzz1706, zzz1707, zzz1708, zzz1709, zzz1710, zzz1711, zzz1712, zzz17130, zzz17140, bd)
new_mkVBalBranch3MkVBalBranch25(zzz537, zzz538, zzz539, zzz540, zzz541, zzz542, zzz543, zzz544, zzz545, zzz546, zzz547, Zero, Succ(zzz5490), bc) → new_mkVBalBranch(zzz547, Branch(zzz542, zzz543, Neg(Succ(Succ(zzz544))), zzz545, zzz546), zzz540, bc)
new_mkVBalBranch3MkVBalBranch212(zzz818, zzz819, zzz820, zzz821, zzz822, zzz823, zzz824, zzz825, zzz826, zzz827, bf) → new_mkVBalBranch3MkVBalBranch14(zzz818, zzz819, zzz820, zzz821, zzz822, zzz823, zzz824, zzz825, zzz826, zzz827, new_primPlusNat2(new_primMulNat0(zzz820), Succ(zzz820)), bf)
new_mkVBalBranch3MkVBalBranch10(zzz929, zzz930, zzz931, zzz932, zzz933, zzz934, zzz935, zzz936, zzz937, zzz938, zzz939, Succ(zzz10020), ba) → new_mkVBalBranch3MkVBalBranch11(zzz929, zzz930, zzz931, zzz932, zzz933, zzz934, zzz935, zzz936, zzz937, zzz938, zzz939, Succ(zzz10020), Succ(zzz936), ba)
new_mkVBalBranch3MkVBalBranch14(zzz818, zzz819, zzz820, zzz821, zzz822, zzz823, zzz824, zzz825, zzz826, zzz827, Succ(zzz8960), bf) → new_mkVBalBranch3MkVBalBranch16(zzz818, zzz819, zzz820, zzz821, zzz822, zzz823, zzz824, Zero, zzz825, zzz826, zzz827, Succ(Zero), Succ(zzz8960), bf)
new_mkVBalBranch3MkVBalBranch24(zzz340, zzz341, Neg(Succ(Succ(Succ(zzz3420000)))), zzz343, zzz344, zzz520, zzz521, Succ(zzz522000), zzz523, zzz524, zzz31, Succ(Succ(zzz6900)), h) → new_mkVBalBranch3MkVBalBranch25(zzz340, zzz341, Succ(Succ(zzz3420000)), zzz343, zzz344, zzz520, zzz521, zzz522000, zzz523, zzz524, zzz31, Succ(zzz3420000), Succ(Succ(new_primPlusNat2(zzz6900, zzz522000))), h)
new_mkVBalBranch3MkVBalBranch2(zzz340, zzz341, Pos(Succ(zzz34200)), zzz343, zzz344, zzz520, zzz521, zzz52200, zzz523, zzz524, zzz31, Zero, h) → new_mkVBalBranch3MkVBalBranch20(zzz340, zzz341, zzz34200, zzz343, zzz344, zzz520, zzz521, zzz52200, zzz523, zzz524, zzz31, zzz52200, zzz34200, h)
new_mkVBalBranch3MkVBalBranch24(zzz340, zzz341, Neg(Zero), zzz343, zzz344, zzz520, zzz521, zzz52200, zzz523, zzz524, zzz31, Zero, h) → new_mkVBalBranch3MkVBalBranch210(zzz340, zzz341, zzz343, zzz344, zzz520, zzz521, zzz52200, zzz523, zzz524, zzz31, h)
new_mkVBalBranch3MkVBalBranch24(zzz340, zzz341, Neg(Succ(Succ(Zero))), zzz343, zzz344, zzz520, zzz521, Succ(zzz522000), zzz523, zzz524, zzz31, Succ(Succ(zzz6900)), h) → new_mkVBalBranch3MkVBalBranch25(zzz340, zzz341, Succ(Zero), zzz343, zzz344, zzz520, zzz521, zzz522000, zzz523, zzz524, zzz31, Zero, Succ(Succ(new_primPlusNat2(zzz6900, zzz522000))), h)
new_mkVBalBranch3MkVBalBranch23(zzz929, zzz930, zzz931, zzz932, zzz933, zzz934, zzz935, zzz936, zzz937, zzz938, zzz939, ba) → new_mkVBalBranch3MkVBalBranch10(zzz929, zzz930, zzz931, zzz932, zzz933, zzz934, zzz935, zzz936, zzz937, zzz938, zzz939, new_primPlusNat2(new_primMulNat0(zzz931), Succ(zzz931)), ba)
new_mkVBalBranch3MkVBalBranch2(zzz340, zzz341, Neg(Zero), zzz343, zzz344, zzz520, zzz521, zzz52200, zzz523, zzz524, zzz31, Succ(zzz680), h) → new_mkVBalBranch(zzz31, zzz524, Branch(zzz340, zzz341, Neg(Zero), zzz343, zzz344), h)
new_mkVBalBranch3MkVBalBranch16(zzz1702, zzz1703, zzz1704, zzz1705, zzz1706, zzz1707, zzz1708, zzz1709, zzz1710, zzz1711, zzz1712, Zero, Succ(zzz17140), bd) → new_mkVBalBranch(zzz1712, zzz1711, Branch(zzz1702, zzz1703, Neg(Succ(zzz1704)), zzz1705, zzz1706), bd)
new_mkVBalBranch3MkVBalBranch10(zzz929, zzz930, zzz931, zzz932, zzz933, zzz934, zzz935, zzz936, zzz937, zzz938, zzz939, Zero, ba) → new_mkVBalBranch3MkVBalBranch11(zzz929, zzz930, zzz931, zzz932, zzz933, zzz934, zzz935, zzz936, zzz937, zzz938, zzz939, Zero, Succ(zzz936), ba)
new_mkVBalBranch3MkVBalBranch22(zzz340, zzz341, Succ(zzz34200), zzz343, zzz344, zzz520, zzz521, zzz52200, zzz523, zzz524, zzz31, h) → new_mkVBalBranch3MkVBalBranch1(zzz340, zzz341, zzz34200, zzz343, zzz344, zzz520, zzz521, zzz52200, zzz523, zzz524, zzz31, new_primPlusNat2(new_primPlusNat3(Succ(new_primPlusNat3(new_primPlusNat1(zzz34200), zzz34200)), Succ(zzz34200)), Succ(zzz34200)), h)
new_mkVBalBranch3MkVBalBranch2(zzz340, zzz341, Pos(Zero), zzz343, zzz344, zzz520, zzz521, zzz52200, zzz523, zzz524, zzz31, Zero, h) → new_mkVBalBranch3MkVBalBranch21(zzz340, zzz341, zzz343, zzz344, zzz520, zzz521, zzz52200, zzz523, zzz524, zzz31, h)
new_mkVBalBranch3MkVBalBranch25(zzz537, zzz538, zzz539, zzz540, zzz541, zzz542, zzz543, zzz544, zzz545, zzz546, zzz547, Zero, Zero, bc) → new_mkVBalBranch3MkVBalBranch211(zzz537, zzz538, zzz539, zzz540, zzz541, zzz542, zzz543, zzz544, zzz545, zzz546, zzz547, bc)

The TRS R consists of the following rules:

new_primMulNat0(zzz6200) → new_primPlusNat3(Succ(new_primPlusNat3(new_primPlusNat1(zzz6200), zzz6200)), Succ(zzz6200))
new_primPlusNat2(Succ(zzz900), Succ(zzz9100)) → Succ(Succ(new_primPlusNat2(zzz900, zzz9100)))
new_primPlusNat2(Zero, Succ(zzz9100)) → Succ(zzz9100)
new_primPlusNat2(Zero, Zero) → Zero
new_primPlusNat2(Succ(zzz900), Zero) → Succ(zzz900)
new_primPlusNat1(Zero) → Zero
new_primPlusNat1(Succ(zzz62000)) → Succ(Succ(new_primPlusNat1(zzz62000)))
new_primPlusNat3(zzz90, Succ(zzz910)) → Succ(Succ(new_primPlusNat2(zzz90, zzz910)))
new_primPlusNat3(zzz90, Zero) → Succ(zzz90)

The set Q consists of the following terms:

new_primPlusNat2(Zero, Succ(x0))
new_primMulNat0(x0)
new_primPlusNat3(x0, Succ(x1))
new_primPlusNat2(Succ(x0), Succ(x1))
new_primPlusNat3(x0, Zero)
new_primPlusNat1(Zero)
new_primPlusNat2(Zero, Zero)
new_primPlusNat1(Succ(x0))
new_primPlusNat2(Succ(x0), Zero)

We have to consider all minimal (P,Q,R)-chains.
By rewriting [15] the rule new_mkVBalBranch3MkVBalBranch2(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344, zzz520, zzz521, zzz52200, zzz523, zzz524, zzz31, Succ(zzz680), h) → new_mkVBalBranch3MkVBalBranch1(zzz340, zzz341, zzz34200, zzz343, zzz344, zzz520, zzz521, zzz52200, zzz523, zzz524, zzz31, new_primPlusNat2(new_primPlusNat3(Succ(new_primPlusNat3(new_primPlusNat1(zzz34200), zzz34200)), Succ(zzz34200)), Succ(zzz34200)), h) at position [11,0] we obtained the following new rules:

new_mkVBalBranch3MkVBalBranch2(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344, zzz520, zzz521, zzz52200, zzz523, zzz524, zzz31, Succ(zzz680), h) → new_mkVBalBranch3MkVBalBranch1(zzz340, zzz341, zzz34200, zzz343, zzz344, zzz520, zzz521, zzz52200, zzz523, zzz524, zzz31, new_primPlusNat2(Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat3(new_primPlusNat1(zzz34200), zzz34200)), 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
                                    ↳ DependencyGraphProof
                                      ↳ QDP
                                        ↳ Rewriting
                                          ↳ QDP
                                            ↳ Rewriting
                                              ↳ QDP
                                                ↳ Rewriting
                                                  ↳ QDP
                                                    ↳ Rewriting
                                                      ↳ QDP
                                                        ↳ Rewriting
                                                          ↳ QDP
                                                            ↳ Rewriting
                                                              ↳ QDP
                                                                ↳ Rewriting
                                                                  ↳ QDP
                                                                    ↳ Rewriting
                                                                      ↳ QDP
                                                                        ↳ Rewriting
                                                                          ↳ QDP
                                                                            ↳ Rewriting
                                                                              ↳ QDP
                                                                                ↳ Rewriting
                                                                                  ↳ QDP
                                                                                    ↳ Rewriting
                                                                                      ↳ QDP
                                                                                        ↳ Rewriting
                                                                                          ↳ QDP
                                                                                            ↳ UsableRulesProof
                                                                                              ↳ QDP
                                                                                                ↳ QReductionProof
                                                                                                  ↳ QDP
                                                                                                    ↳ Rewriting
                                                                                                      ↳ QDP
                                                                                                        ↳ Rewriting
                                                                                                          ↳ QDP
                                                                                                            ↳ Rewriting
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP

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

new_mkVBalBranch3MkVBalBranch11(zzz2033, zzz2034, zzz2035, zzz2036, zzz2037, zzz2038, zzz2039, zzz2040, zzz2041, zzz2042, zzz2043, Zero, Succ(zzz20450), bb) → new_mkVBalBranch(zzz2043, zzz2042, Branch(zzz2033, zzz2034, Pos(Succ(zzz2035)), zzz2036, zzz2037), bb)
new_mkVBalBranch3MkVBalBranch26(zzz1133, zzz1134, zzz1135, zzz1136, zzz1137, zzz1138, zzz1139, zzz1140, zzz1141, zzz1142, Succ(zzz11430), Succ(zzz11440), be) → new_mkVBalBranch3MkVBalBranch26(zzz1133, zzz1134, zzz1135, zzz1136, zzz1137, zzz1138, zzz1139, zzz1140, zzz1141, zzz1142, zzz11430, zzz11440, be)
new_mkVBalBranch3MkVBalBranch24(zzz340, zzz341, Neg(Succ(Succ(zzz342000))), zzz343, zzz344, zzz520, zzz521, Zero, zzz523, zzz524, zzz31, Zero, h) → new_mkVBalBranch3MkVBalBranch14(zzz340, zzz341, Succ(zzz342000), zzz343, zzz344, zzz520, zzz521, zzz523, zzz524, zzz31, new_primPlusNat2(new_primMulNat0(Succ(zzz342000)), Succ(Succ(zzz342000))), h)
new_mkVBalBranch3MkVBalBranch24(zzz340, zzz341, Neg(Succ(Succ(Succ(zzz3420000)))), zzz343, zzz344, zzz520, zzz521, Zero, zzz523, zzz524, zzz31, Succ(Zero), h) → new_mkVBalBranch3MkVBalBranch26(zzz340, zzz341, Succ(Succ(zzz3420000)), zzz343, zzz344, zzz520, zzz521, zzz523, zzz524, zzz31, Succ(zzz3420000), Zero, h)
new_mkVBalBranch3MkVBalBranch25(zzz537, zzz538, zzz539, zzz540, zzz541, zzz542, zzz543, zzz544, zzz545, zzz546, zzz547, Succ(zzz5480), Zero, bc) → new_mkVBalBranch3MkVBalBranch15(zzz537, zzz538, zzz539, zzz540, zzz541, zzz542, zzz543, zzz544, zzz545, zzz546, zzz547, new_primPlusNat2(new_primMulNat0(zzz539), Succ(zzz539)), bc)
new_mkVBalBranch3MkVBalBranch24(zzz340, zzz341, Neg(Succ(Zero)), zzz343, zzz344, zzz520, zzz521, Zero, zzz523, zzz524, zzz31, Zero, h) → new_mkVBalBranch3MkVBalBranch29(zzz340, zzz341, Zero, zzz343, zzz344, zzz520, zzz521, zzz523, zzz524, zzz31, h)
new_mkVBalBranch3MkVBalBranch20(zzz929, zzz930, zzz931, zzz932, zzz933, zzz934, zzz935, zzz936, zzz937, zzz938, zzz939, Zero, Succ(zzz9410), ba) → new_mkVBalBranch(zzz939, Branch(zzz934, zzz935, Pos(Succ(zzz936)), zzz937, zzz938), zzz932, ba)
new_mkVBalBranch3MkVBalBranch17(zzz340, zzz341, zzz34200, zzz343, zzz344, zzz520, zzz521, zzz52200, zzz523, zzz524, zzz31, h) → new_mkVBalBranch(zzz31, zzz524, Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), h)
new_mkVBalBranch3MkVBalBranch26(zzz1133, zzz1134, zzz1135, zzz1136, zzz1137, zzz1138, zzz1139, zzz1140, zzz1141, zzz1142, Zero, Zero, be) → new_mkVBalBranch3MkVBalBranch29(zzz1133, zzz1134, zzz1135, zzz1136, zzz1137, zzz1138, zzz1139, zzz1140, zzz1141, zzz1142, be)
new_mkVBalBranch3MkVBalBranch20(zzz929, zzz930, zzz931, zzz932, zzz933, zzz934, zzz935, zzz936, zzz937, zzz938, zzz939, Zero, Zero, ba) → new_mkVBalBranch3MkVBalBranch23(zzz929, zzz930, zzz931, zzz932, zzz933, zzz934, zzz935, zzz936, zzz937, zzz938, zzz939, ba)
new_mkVBalBranch3MkVBalBranch20(zzz929, zzz930, zzz931, zzz932, zzz933, zzz934, zzz935, zzz936, zzz937, zzz938, zzz939, Succ(zzz9400), Zero, ba) → new_mkVBalBranch3MkVBalBranch10(zzz929, zzz930, zzz931, zzz932, zzz933, zzz934, zzz935, zzz936, zzz937, zzz938, zzz939, new_primPlusNat2(new_primMulNat0(zzz931), Succ(zzz931)), ba)
new_mkVBalBranch3MkVBalBranch24(zzz340, zzz341, Neg(Succ(Succ(Zero))), zzz343, zzz344, zzz520, zzz521, Succ(zzz522000), zzz523, zzz524, zzz31, Succ(Zero), h) → new_mkVBalBranch3MkVBalBranch25(zzz340, zzz341, Succ(Zero), zzz343, zzz344, zzz520, zzz521, zzz522000, zzz523, zzz524, zzz31, Zero, Succ(zzz522000), h)
new_mkVBalBranch3MkVBalBranch24(zzz340, zzz341, Neg(Succ(Succ(Succ(zzz3420000)))), zzz343, zzz344, zzz520, zzz521, Succ(zzz522000), zzz523, zzz524, zzz31, Succ(Zero), h) → new_mkVBalBranch3MkVBalBranch25(zzz340, zzz341, Succ(Succ(zzz3420000)), zzz343, zzz344, zzz520, zzz521, zzz522000, zzz523, zzz524, zzz31, Succ(zzz3420000), Succ(zzz522000), h)
new_mkVBalBranch3MkVBalBranch20(zzz929, zzz930, zzz931, zzz932, zzz933, zzz934, zzz935, zzz936, zzz937, zzz938, zzz939, Succ(zzz9400), Succ(zzz9410), ba) → new_mkVBalBranch3MkVBalBranch20(zzz929, zzz930, zzz931, zzz932, zzz933, zzz934, zzz935, zzz936, zzz937, zzz938, zzz939, zzz9400, zzz9410, ba)
new_mkVBalBranch3MkVBalBranch24(zzz340, zzz341, Neg(Succ(Succ(zzz342000))), zzz343, zzz344, zzz520, zzz521, Succ(zzz522000), zzz523, zzz524, zzz31, Zero, h) → new_mkVBalBranch3MkVBalBranch25(zzz340, zzz341, Succ(zzz342000), zzz343, zzz344, zzz520, zzz521, zzz522000, zzz523, zzz524, zzz31, zzz342000, zzz522000, h)
new_mkVBalBranch3MkVBalBranch26(zzz1133, zzz1134, zzz1135, zzz1136, zzz1137, zzz1138, zzz1139, zzz1140, zzz1141, zzz1142, Succ(zzz11430), Zero, be) → new_mkVBalBranch3MkVBalBranch212(zzz1133, zzz1134, zzz1135, zzz1136, zzz1137, zzz1138, zzz1139, zzz1140, zzz1141, zzz1142, be)
new_mkVBalBranch(zzz31, Branch(zzz520, zzz521, Pos(Succ(zzz52200)), zzz523, zzz524), Branch(zzz340, zzz341, zzz342, zzz343, zzz344), h) → new_mkVBalBranch3MkVBalBranch2(zzz340, zzz341, zzz342, zzz343, zzz344, zzz520, zzz521, zzz52200, zzz523, zzz524, zzz31, new_primPlusNat3(Succ(new_primPlusNat3(new_primPlusNat1(zzz52200), zzz52200)), Succ(zzz52200)), h)
new_mkVBalBranch3MkVBalBranch29(zzz818, zzz819, zzz820, zzz821, zzz822, zzz823, zzz824, zzz825, zzz826, zzz827, bf) → new_mkVBalBranch3MkVBalBranch14(zzz818, zzz819, zzz820, zzz821, zzz822, zzz823, zzz824, zzz825, zzz826, zzz827, new_primPlusNat2(new_primMulNat0(zzz820), Succ(zzz820)), bf)
new_mkVBalBranch3MkVBalBranch11(zzz2033, zzz2034, zzz2035, zzz2036, zzz2037, zzz2038, zzz2039, zzz2040, zzz2041, zzz2042, zzz2043, Succ(zzz20440), Succ(zzz20450), bb) → new_mkVBalBranch3MkVBalBranch11(zzz2033, zzz2034, zzz2035, zzz2036, zzz2037, zzz2038, zzz2039, zzz2040, zzz2041, zzz2042, zzz2043, zzz20440, zzz20450, bb)
new_mkVBalBranch3MkVBalBranch25(zzz537, zzz538, zzz539, zzz540, zzz541, zzz542, zzz543, zzz544, zzz545, zzz546, zzz547, Succ(zzz5480), Succ(zzz5490), bc) → new_mkVBalBranch3MkVBalBranch25(zzz537, zzz538, zzz539, zzz540, zzz541, zzz542, zzz543, zzz544, zzz545, zzz546, zzz547, zzz5480, zzz5490, bc)
new_mkVBalBranch3MkVBalBranch2(zzz340, zzz341, Neg(zzz3420), zzz343, zzz344, zzz520, zzz521, zzz52200, zzz523, zzz524, zzz31, Zero, h) → new_mkVBalBranch3MkVBalBranch22(zzz340, zzz341, zzz3420, zzz343, zzz344, zzz520, zzz521, zzz52200, zzz523, zzz524, zzz31, h)
new_mkVBalBranch(zzz31, Branch(zzz520, zzz521, Neg(Succ(zzz52200)), zzz523, zzz524), Branch(zzz340, zzz341, zzz342, zzz343, zzz344), h) → new_mkVBalBranch3MkVBalBranch24(zzz340, zzz341, zzz342, zzz343, zzz344, zzz520, zzz521, zzz52200, zzz523, zzz524, zzz31, new_primPlusNat3(Succ(new_primPlusNat3(new_primPlusNat1(zzz52200), zzz52200)), Succ(zzz52200)), h)
new_mkVBalBranch3MkVBalBranch24(zzz340, zzz341, Neg(Succ(Zero)), zzz343, zzz344, zzz520, zzz521, Succ(zzz522000), zzz523, zzz524, zzz31, Zero, h) → new_mkVBalBranch3MkVBalBranch28(zzz340, zzz341, zzz343, zzz344, zzz520, zzz521, Succ(zzz522000), zzz523, zzz524, zzz31, h)
new_mkVBalBranch3MkVBalBranch210(zzz340, zzz341, zzz343, zzz344, zzz520, zzz521, zzz52200, zzz523, zzz524, zzz31, h) → new_mkVBalBranch(zzz31, Branch(zzz520, zzz521, Neg(Succ(zzz52200)), zzz523, zzz524), zzz343, h)
new_mkVBalBranch3MkVBalBranch26(zzz1133, zzz1134, zzz1135, zzz1136, zzz1137, zzz1138, zzz1139, zzz1140, zzz1141, zzz1142, Zero, Succ(zzz11440), be) → new_mkVBalBranch(zzz1142, Branch(zzz1138, zzz1139, Neg(Succ(Zero)), zzz1140, zzz1141), zzz1136, be)
new_mkVBalBranch3MkVBalBranch24(zzz340, zzz341, Neg(Succ(Succ(Zero))), zzz343, zzz344, zzz520, zzz521, Zero, zzz523, zzz524, zzz31, Succ(Zero), h) → new_mkVBalBranch3MkVBalBranch26(zzz340, zzz341, Succ(Zero), zzz343, zzz344, zzz520, zzz521, zzz523, zzz524, zzz31, Zero, Zero, h)
new_mkVBalBranch(zzz31, Branch(zzz520, zzz521, Pos(Zero), zzz523, zzz524), Branch(zzz340, zzz341, Pos(Succ(zzz34200)), zzz343, zzz344), h) → new_mkVBalBranch(zzz31, Branch(zzz520, zzz521, Pos(Zero), zzz523, zzz524), zzz343, h)
new_mkVBalBranch3MkVBalBranch2(zzz340, zzz341, Pos(Zero), zzz343, zzz344, zzz520, zzz521, zzz52200, zzz523, zzz524, zzz31, Succ(zzz680), h) → new_mkVBalBranch(zzz31, zzz524, Branch(zzz340, zzz341, Pos(Zero), zzz343, zzz344), h)
new_mkVBalBranch3MkVBalBranch21(zzz340, zzz341, zzz343, zzz344, zzz520, zzz521, zzz52200, zzz523, zzz524, zzz31, h) → new_mkVBalBranch(zzz31, zzz524, Branch(zzz340, zzz341, Pos(Zero), zzz343, zzz344), h)
new_mkVBalBranch3MkVBalBranch24(zzz340, zzz341, Pos(zzz3420), zzz343, zzz344, zzz520, zzz521, zzz52200, zzz523, zzz524, zzz31, Zero, h) → new_mkVBalBranch3MkVBalBranch27(zzz340, zzz341, zzz3420, zzz343, zzz344, zzz520, zzz521, zzz52200, zzz523, zzz524, zzz31, h)
new_mkVBalBranch3MkVBalBranch15(zzz537, zzz538, zzz539, zzz540, zzz541, zzz542, zzz543, zzz544, zzz545, zzz546, zzz547, Succ(zzz6990), bc) → new_mkVBalBranch3MkVBalBranch16(zzz537, zzz538, zzz539, zzz540, zzz541, zzz542, zzz543, Succ(zzz544), zzz545, zzz546, zzz547, Succ(Succ(zzz544)), Succ(zzz6990), bc)
new_mkVBalBranch3MkVBalBranch24(zzz340, zzz341, Neg(Succ(Succ(Succ(zzz3420000)))), zzz343, zzz344, zzz520, zzz521, Zero, zzz523, zzz524, zzz31, Succ(Succ(zzz6900)), h) → new_mkVBalBranch3MkVBalBranch26(zzz340, zzz341, Succ(Succ(zzz3420000)), zzz343, zzz344, zzz520, zzz521, zzz523, zzz524, zzz31, Succ(zzz3420000), Succ(zzz6900), h)
new_mkVBalBranch(zzz31, Branch(zzz520, zzz521, Neg(Zero), zzz523, zzz524), Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), h) → new_mkVBalBranch3MkVBalBranch13(zzz340, zzz341, zzz34200, zzz343, zzz344, zzz520, zzz521, zzz523, zzz524, zzz31, new_primPlusNat2(new_primMulNat0(zzz34200), Succ(zzz34200)), h)
new_mkVBalBranch3MkVBalBranch27(zzz340, zzz341, zzz3420, zzz343, zzz344, zzz520, zzz521, zzz52200, zzz523, zzz524, zzz31, h) → new_mkVBalBranch(zzz31, Branch(zzz520, zzz521, Neg(Succ(zzz52200)), zzz523, zzz524), zzz343, h)
new_mkVBalBranch3MkVBalBranch24(zzz340, zzz341, Pos(zzz3420), zzz343, zzz344, zzz520, zzz521, zzz52200, zzz523, zzz524, zzz31, Succ(zzz690), h) → new_mkVBalBranch(zzz31, Branch(zzz520, zzz521, Neg(Succ(zzz52200)), zzz523, zzz524), zzz343, h)
new_mkVBalBranch3MkVBalBranch12(zzz340, zzz341, zzz34200, zzz343, zzz344, zzz520, zzz521, zzz523, zzz524, zzz31, Succ(zzz1250), h) → new_mkVBalBranch(zzz31, zzz524, Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), h)
new_mkVBalBranch3MkVBalBranch28(zzz340, zzz341, zzz343, zzz344, zzz520, zzz521, zzz52200, zzz523, zzz524, zzz31, h) → new_mkVBalBranch(zzz31, Branch(zzz520, zzz521, Neg(Succ(zzz52200)), zzz523, zzz524), zzz343, h)
new_mkVBalBranch3MkVBalBranch24(zzz340, zzz341, Neg(Succ(Succ(Zero))), zzz343, zzz344, zzz520, zzz521, Zero, zzz523, zzz524, zzz31, Succ(Succ(zzz6900)), h) → new_mkVBalBranch3MkVBalBranch26(zzz340, zzz341, Succ(Zero), zzz343, zzz344, zzz520, zzz521, zzz523, zzz524, zzz31, Zero, Succ(zzz6900), h)
new_mkVBalBranch3MkVBalBranch211(zzz537, zzz538, zzz539, zzz540, zzz541, zzz542, zzz543, zzz544, zzz545, zzz546, zzz547, bc) → new_mkVBalBranch3MkVBalBranch15(zzz537, zzz538, zzz539, zzz540, zzz541, zzz542, zzz543, zzz544, zzz545, zzz546, zzz547, new_primPlusNat2(new_primPlusNat3(Succ(new_primPlusNat3(new_primPlusNat1(zzz539), zzz539)), Succ(zzz539)), Succ(zzz539)), bc)
new_mkVBalBranch(zzz31, Branch(zzz520, zzz521, Pos(Zero), zzz523, zzz524), Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), h) → new_mkVBalBranch3MkVBalBranch12(zzz340, zzz341, zzz34200, zzz343, zzz344, zzz520, zzz521, zzz523, zzz524, zzz31, new_primPlusNat2(new_primMulNat0(zzz34200), Succ(zzz34200)), h)
new_mkVBalBranch3MkVBalBranch22(zzz340, zzz341, Zero, zzz343, zzz344, zzz520, zzz521, zzz52200, zzz523, zzz524, zzz31, h) → new_mkVBalBranch(zzz31, zzz524, Branch(zzz340, zzz341, Neg(Zero), zzz343, zzz344), h)
new_mkVBalBranch3MkVBalBranch1(zzz340, zzz341, zzz34200, zzz343, zzz344, zzz520, zzz521, zzz52200, zzz523, zzz524, zzz31, Succ(zzz1430), h) → new_mkVBalBranch(zzz31, zzz524, Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), h)
new_mkVBalBranch3MkVBalBranch24(zzz340, zzz341, Neg(Succ(Zero)), zzz343, zzz344, zzz520, zzz521, zzz52200, zzz523, zzz524, zzz31, Succ(zzz690), h) → new_mkVBalBranch(zzz31, Branch(zzz520, zzz521, Neg(Succ(zzz52200)), zzz523, zzz524), zzz343, h)
new_mkVBalBranch3MkVBalBranch13(zzz340, zzz341, zzz34200, zzz343, zzz344, zzz520, zzz521, zzz523, zzz524, zzz31, Succ(zzz1290), h) → new_mkVBalBranch(zzz31, zzz524, Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), h)
new_mkVBalBranch3MkVBalBranch2(zzz340, zzz341, Pos(Succ(zzz34200)), zzz343, zzz344, zzz520, zzz521, zzz52200, zzz523, zzz524, zzz31, Succ(zzz680), h) → new_mkVBalBranch3MkVBalBranch20(zzz340, zzz341, zzz34200, zzz343, zzz344, zzz520, zzz521, zzz52200, zzz523, zzz524, zzz31, Succ(new_primPlusNat2(zzz680, zzz52200)), zzz34200, h)
new_mkVBalBranch(zzz31, Branch(zzz520, zzz521, Neg(Zero), zzz523, zzz524), Branch(zzz340, zzz341, Pos(Succ(zzz34200)), zzz343, zzz344), h) → new_mkVBalBranch(zzz31, Branch(zzz520, zzz521, Neg(Zero), zzz523, zzz524), zzz343, h)
new_mkVBalBranch3MkVBalBranch24(zzz340, zzz341, Neg(Zero), zzz343, zzz344, zzz520, zzz521, zzz52200, zzz523, zzz524, zzz31, Succ(zzz690), h) → new_mkVBalBranch(zzz31, Branch(zzz520, zzz521, Neg(Succ(zzz52200)), zzz523, zzz524), zzz343, h)
new_mkVBalBranch3MkVBalBranch1(zzz340, zzz341, zzz34200, zzz343, zzz344, zzz520, zzz521, zzz52200, zzz523, zzz524, zzz31, Zero, h) → new_mkVBalBranch3MkVBalBranch17(zzz340, zzz341, zzz34200, zzz343, zzz344, zzz520, zzz521, zzz52200, zzz523, zzz524, zzz31, h)
new_mkVBalBranch3MkVBalBranch16(zzz1702, zzz1703, zzz1704, zzz1705, zzz1706, zzz1707, zzz1708, zzz1709, zzz1710, zzz1711, zzz1712, Succ(zzz17130), Succ(zzz17140), bd) → new_mkVBalBranch3MkVBalBranch16(zzz1702, zzz1703, zzz1704, zzz1705, zzz1706, zzz1707, zzz1708, zzz1709, zzz1710, zzz1711, zzz1712, zzz17130, zzz17140, bd)
new_mkVBalBranch3MkVBalBranch25(zzz537, zzz538, zzz539, zzz540, zzz541, zzz542, zzz543, zzz544, zzz545, zzz546, zzz547, Zero, Succ(zzz5490), bc) → new_mkVBalBranch(zzz547, Branch(zzz542, zzz543, Neg(Succ(Succ(zzz544))), zzz545, zzz546), zzz540, bc)
new_mkVBalBranch3MkVBalBranch10(zzz929, zzz930, zzz931, zzz932, zzz933, zzz934, zzz935, zzz936, zzz937, zzz938, zzz939, Succ(zzz10020), ba) → new_mkVBalBranch3MkVBalBranch11(zzz929, zzz930, zzz931, zzz932, zzz933, zzz934, zzz935, zzz936, zzz937, zzz938, zzz939, Succ(zzz10020), Succ(zzz936), ba)
new_mkVBalBranch3MkVBalBranch212(zzz818, zzz819, zzz820, zzz821, zzz822, zzz823, zzz824, zzz825, zzz826, zzz827, bf) → new_mkVBalBranch3MkVBalBranch14(zzz818, zzz819, zzz820, zzz821, zzz822, zzz823, zzz824, zzz825, zzz826, zzz827, new_primPlusNat2(new_primMulNat0(zzz820), Succ(zzz820)), bf)
new_mkVBalBranch3MkVBalBranch14(zzz818, zzz819, zzz820, zzz821, zzz822, zzz823, zzz824, zzz825, zzz826, zzz827, Succ(zzz8960), bf) → new_mkVBalBranch3MkVBalBranch16(zzz818, zzz819, zzz820, zzz821, zzz822, zzz823, zzz824, Zero, zzz825, zzz826, zzz827, Succ(Zero), Succ(zzz8960), bf)
new_mkVBalBranch3MkVBalBranch24(zzz340, zzz341, Neg(Succ(Succ(Succ(zzz3420000)))), zzz343, zzz344, zzz520, zzz521, Succ(zzz522000), zzz523, zzz524, zzz31, Succ(Succ(zzz6900)), h) → new_mkVBalBranch3MkVBalBranch25(zzz340, zzz341, Succ(Succ(zzz3420000)), zzz343, zzz344, zzz520, zzz521, zzz522000, zzz523, zzz524, zzz31, Succ(zzz3420000), Succ(Succ(new_primPlusNat2(zzz6900, zzz522000))), h)
new_mkVBalBranch3MkVBalBranch2(zzz340, zzz341, Pos(Succ(zzz34200)), zzz343, zzz344, zzz520, zzz521, zzz52200, zzz523, zzz524, zzz31, Zero, h) → new_mkVBalBranch3MkVBalBranch20(zzz340, zzz341, zzz34200, zzz343, zzz344, zzz520, zzz521, zzz52200, zzz523, zzz524, zzz31, zzz52200, zzz34200, h)
new_mkVBalBranch3MkVBalBranch24(zzz340, zzz341, Neg(Zero), zzz343, zzz344, zzz520, zzz521, zzz52200, zzz523, zzz524, zzz31, Zero, h) → new_mkVBalBranch3MkVBalBranch210(zzz340, zzz341, zzz343, zzz344, zzz520, zzz521, zzz52200, zzz523, zzz524, zzz31, h)
new_mkVBalBranch3MkVBalBranch24(zzz340, zzz341, Neg(Succ(Succ(Zero))), zzz343, zzz344, zzz520, zzz521, Succ(zzz522000), zzz523, zzz524, zzz31, Succ(Succ(zzz6900)), h) → new_mkVBalBranch3MkVBalBranch25(zzz340, zzz341, Succ(Zero), zzz343, zzz344, zzz520, zzz521, zzz522000, zzz523, zzz524, zzz31, Zero, Succ(Succ(new_primPlusNat2(zzz6900, zzz522000))), h)
new_mkVBalBranch3MkVBalBranch23(zzz929, zzz930, zzz931, zzz932, zzz933, zzz934, zzz935, zzz936, zzz937, zzz938, zzz939, ba) → new_mkVBalBranch3MkVBalBranch10(zzz929, zzz930, zzz931, zzz932, zzz933, zzz934, zzz935, zzz936, zzz937, zzz938, zzz939, new_primPlusNat2(new_primMulNat0(zzz931), Succ(zzz931)), ba)
new_mkVBalBranch3MkVBalBranch2(zzz340, zzz341, Neg(Zero), zzz343, zzz344, zzz520, zzz521, zzz52200, zzz523, zzz524, zzz31, Succ(zzz680), h) → new_mkVBalBranch(zzz31, zzz524, Branch(zzz340, zzz341, Neg(Zero), zzz343, zzz344), h)
new_mkVBalBranch3MkVBalBranch2(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344, zzz520, zzz521, zzz52200, zzz523, zzz524, zzz31, Succ(zzz680), h) → new_mkVBalBranch3MkVBalBranch1(zzz340, zzz341, zzz34200, zzz343, zzz344, zzz520, zzz521, zzz52200, zzz523, zzz524, zzz31, new_primPlusNat2(Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat3(new_primPlusNat1(zzz34200), zzz34200)), zzz34200))), Succ(zzz34200)), h)
new_mkVBalBranch3MkVBalBranch16(zzz1702, zzz1703, zzz1704, zzz1705, zzz1706, zzz1707, zzz1708, zzz1709, zzz1710, zzz1711, zzz1712, Zero, Succ(zzz17140), bd) → new_mkVBalBranch(zzz1712, zzz1711, Branch(zzz1702, zzz1703, Neg(Succ(zzz1704)), zzz1705, zzz1706), bd)
new_mkVBalBranch3MkVBalBranch10(zzz929, zzz930, zzz931, zzz932, zzz933, zzz934, zzz935, zzz936, zzz937, zzz938, zzz939, Zero, ba) → new_mkVBalBranch3MkVBalBranch11(zzz929, zzz930, zzz931, zzz932, zzz933, zzz934, zzz935, zzz936, zzz937, zzz938, zzz939, Zero, Succ(zzz936), ba)
new_mkVBalBranch3MkVBalBranch25(zzz537, zzz538, zzz539, zzz540, zzz541, zzz542, zzz543, zzz544, zzz545, zzz546, zzz547, Zero, Zero, bc) → new_mkVBalBranch3MkVBalBranch211(zzz537, zzz538, zzz539, zzz540, zzz541, zzz542, zzz543, zzz544, zzz545, zzz546, zzz547, bc)
new_mkVBalBranch3MkVBalBranch2(zzz340, zzz341, Pos(Zero), zzz343, zzz344, zzz520, zzz521, zzz52200, zzz523, zzz524, zzz31, Zero, h) → new_mkVBalBranch3MkVBalBranch21(zzz340, zzz341, zzz343, zzz344, zzz520, zzz521, zzz52200, zzz523, zzz524, zzz31, h)
new_mkVBalBranch3MkVBalBranch22(zzz340, zzz341, Succ(zzz34200), zzz343, zzz344, zzz520, zzz521, zzz52200, zzz523, zzz524, zzz31, h) → new_mkVBalBranch3MkVBalBranch1(zzz340, zzz341, zzz34200, zzz343, zzz344, zzz520, zzz521, zzz52200, zzz523, zzz524, zzz31, new_primPlusNat2(new_primPlusNat3(Succ(new_primPlusNat3(new_primPlusNat1(zzz34200), zzz34200)), Succ(zzz34200)), Succ(zzz34200)), h)

The TRS R consists of the following rules:

new_primMulNat0(zzz6200) → new_primPlusNat3(Succ(new_primPlusNat3(new_primPlusNat1(zzz6200), zzz6200)), Succ(zzz6200))
new_primPlusNat2(Succ(zzz900), Succ(zzz9100)) → Succ(Succ(new_primPlusNat2(zzz900, zzz9100)))
new_primPlusNat2(Zero, Succ(zzz9100)) → Succ(zzz9100)
new_primPlusNat2(Zero, Zero) → Zero
new_primPlusNat2(Succ(zzz900), Zero) → Succ(zzz900)
new_primPlusNat1(Zero) → Zero
new_primPlusNat1(Succ(zzz62000)) → Succ(Succ(new_primPlusNat1(zzz62000)))
new_primPlusNat3(zzz90, Succ(zzz910)) → Succ(Succ(new_primPlusNat2(zzz90, zzz910)))
new_primPlusNat3(zzz90, Zero) → Succ(zzz90)

The set Q consists of the following terms:

new_primPlusNat2(Zero, Succ(x0))
new_primMulNat0(x0)
new_primPlusNat3(x0, Succ(x1))
new_primPlusNat2(Succ(x0), Succ(x1))
new_primPlusNat3(x0, Zero)
new_primPlusNat1(Zero)
new_primPlusNat2(Zero, Zero)
new_primPlusNat1(Succ(x0))
new_primPlusNat2(Succ(x0), Zero)

We have to consider all minimal (P,Q,R)-chains.
By rewriting [15] the rule new_mkVBalBranch3MkVBalBranch24(zzz340, zzz341, Neg(Succ(Succ(zzz342000))), zzz343, zzz344, zzz520, zzz521, Zero, zzz523, zzz524, zzz31, Zero, h) → new_mkVBalBranch3MkVBalBranch14(zzz340, zzz341, Succ(zzz342000), zzz343, zzz344, zzz520, zzz521, zzz523, zzz524, zzz31, new_primPlusNat2(new_primMulNat0(Succ(zzz342000)), Succ(Succ(zzz342000))), h) at position [10,0] we obtained the following new rules:

new_mkVBalBranch3MkVBalBranch24(zzz340, zzz341, Neg(Succ(Succ(zzz342000))), zzz343, zzz344, zzz520, zzz521, Zero, zzz523, zzz524, zzz31, Zero, h) → new_mkVBalBranch3MkVBalBranch14(zzz340, zzz341, Succ(zzz342000), zzz343, zzz344, zzz520, zzz521, zzz523, zzz524, zzz31, new_primPlusNat2(new_primPlusNat3(Succ(new_primPlusNat3(new_primPlusNat1(Succ(zzz342000)), Succ(zzz342000))), Succ(Succ(zzz342000))), Succ(Succ(zzz342000))), 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
                                    ↳ DependencyGraphProof
                                      ↳ QDP
                                        ↳ Rewriting
                                          ↳ QDP
                                            ↳ Rewriting
                                              ↳ QDP
                                                ↳ Rewriting
                                                  ↳ QDP
                                                    ↳ Rewriting
                                                      ↳ QDP
                                                        ↳ Rewriting
                                                          ↳ QDP
                                                            ↳ Rewriting
                                                              ↳ QDP
                                                                ↳ Rewriting
                                                                  ↳ QDP
                                                                    ↳ Rewriting
                                                                      ↳ QDP
                                                                        ↳ Rewriting
                                                                          ↳ QDP
                                                                            ↳ Rewriting
                                                                              ↳ QDP
                                                                                ↳ Rewriting
                                                                                  ↳ QDP
                                                                                    ↳ Rewriting
                                                                                      ↳ QDP
                                                                                        ↳ Rewriting
                                                                                          ↳ QDP
                                                                                            ↳ UsableRulesProof
                                                                                              ↳ QDP
                                                                                                ↳ QReductionProof
                                                                                                  ↳ QDP
                                                                                                    ↳ Rewriting
                                                                                                      ↳ QDP
                                                                                                        ↳ Rewriting
                                                                                                          ↳ QDP
                                                                                                            ↳ Rewriting
                                                                                                              ↳ QDP
                                                                                                                ↳ Rewriting
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP

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

new_mkVBalBranch3MkVBalBranch11(zzz2033, zzz2034, zzz2035, zzz2036, zzz2037, zzz2038, zzz2039, zzz2040, zzz2041, zzz2042, zzz2043, Zero, Succ(zzz20450), bb) → new_mkVBalBranch(zzz2043, zzz2042, Branch(zzz2033, zzz2034, Pos(Succ(zzz2035)), zzz2036, zzz2037), bb)
new_mkVBalBranch3MkVBalBranch26(zzz1133, zzz1134, zzz1135, zzz1136, zzz1137, zzz1138, zzz1139, zzz1140, zzz1141, zzz1142, Succ(zzz11430), Succ(zzz11440), be) → new_mkVBalBranch3MkVBalBranch26(zzz1133, zzz1134, zzz1135, zzz1136, zzz1137, zzz1138, zzz1139, zzz1140, zzz1141, zzz1142, zzz11430, zzz11440, be)
new_mkVBalBranch3MkVBalBranch24(zzz340, zzz341, Neg(Succ(Succ(Succ(zzz3420000)))), zzz343, zzz344, zzz520, zzz521, Zero, zzz523, zzz524, zzz31, Succ(Zero), h) → new_mkVBalBranch3MkVBalBranch26(zzz340, zzz341, Succ(Succ(zzz3420000)), zzz343, zzz344, zzz520, zzz521, zzz523, zzz524, zzz31, Succ(zzz3420000), Zero, h)
new_mkVBalBranch3MkVBalBranch24(zzz340, zzz341, Neg(Succ(Zero)), zzz343, zzz344, zzz520, zzz521, Zero, zzz523, zzz524, zzz31, Zero, h) → new_mkVBalBranch3MkVBalBranch29(zzz340, zzz341, Zero, zzz343, zzz344, zzz520, zzz521, zzz523, zzz524, zzz31, h)
new_mkVBalBranch3MkVBalBranch25(zzz537, zzz538, zzz539, zzz540, zzz541, zzz542, zzz543, zzz544, zzz545, zzz546, zzz547, Succ(zzz5480), Zero, bc) → new_mkVBalBranch3MkVBalBranch15(zzz537, zzz538, zzz539, zzz540, zzz541, zzz542, zzz543, zzz544, zzz545, zzz546, zzz547, new_primPlusNat2(new_primMulNat0(zzz539), Succ(zzz539)), bc)
new_mkVBalBranch3MkVBalBranch20(zzz929, zzz930, zzz931, zzz932, zzz933, zzz934, zzz935, zzz936, zzz937, zzz938, zzz939, Zero, Succ(zzz9410), ba) → new_mkVBalBranch(zzz939, Branch(zzz934, zzz935, Pos(Succ(zzz936)), zzz937, zzz938), zzz932, ba)
new_mkVBalBranch3MkVBalBranch17(zzz340, zzz341, zzz34200, zzz343, zzz344, zzz520, zzz521, zzz52200, zzz523, zzz524, zzz31, h) → new_mkVBalBranch(zzz31, zzz524, Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), h)
new_mkVBalBranch3MkVBalBranch26(zzz1133, zzz1134, zzz1135, zzz1136, zzz1137, zzz1138, zzz1139, zzz1140, zzz1141, zzz1142, Zero, Zero, be) → new_mkVBalBranch3MkVBalBranch29(zzz1133, zzz1134, zzz1135, zzz1136, zzz1137, zzz1138, zzz1139, zzz1140, zzz1141, zzz1142, be)
new_mkVBalBranch3MkVBalBranch20(zzz929, zzz930, zzz931, zzz932, zzz933, zzz934, zzz935, zzz936, zzz937, zzz938, zzz939, Zero, Zero, ba) → new_mkVBalBranch3MkVBalBranch23(zzz929, zzz930, zzz931, zzz932, zzz933, zzz934, zzz935, zzz936, zzz937, zzz938, zzz939, ba)
new_mkVBalBranch3MkVBalBranch20(zzz929, zzz930, zzz931, zzz932, zzz933, zzz934, zzz935, zzz936, zzz937, zzz938, zzz939, Succ(zzz9400), Zero, ba) → new_mkVBalBranch3MkVBalBranch10(zzz929, zzz930, zzz931, zzz932, zzz933, zzz934, zzz935, zzz936, zzz937, zzz938, zzz939, new_primPlusNat2(new_primMulNat0(zzz931), Succ(zzz931)), ba)
new_mkVBalBranch3MkVBalBranch24(zzz340, zzz341, Neg(Succ(Succ(Zero))), zzz343, zzz344, zzz520, zzz521, Succ(zzz522000), zzz523, zzz524, zzz31, Succ(Zero), h) → new_mkVBalBranch3MkVBalBranch25(zzz340, zzz341, Succ(Zero), zzz343, zzz344, zzz520, zzz521, zzz522000, zzz523, zzz524, zzz31, Zero, Succ(zzz522000), h)
new_mkVBalBranch3MkVBalBranch20(zzz929, zzz930, zzz931, zzz932, zzz933, zzz934, zzz935, zzz936, zzz937, zzz938, zzz939, Succ(zzz9400), Succ(zzz9410), ba) → new_mkVBalBranch3MkVBalBranch20(zzz929, zzz930, zzz931, zzz932, zzz933, zzz934, zzz935, zzz936, zzz937, zzz938, zzz939, zzz9400, zzz9410, ba)
new_mkVBalBranch3MkVBalBranch24(zzz340, zzz341, Neg(Succ(Succ(Succ(zzz3420000)))), zzz343, zzz344, zzz520, zzz521, Succ(zzz522000), zzz523, zzz524, zzz31, Succ(Zero), h) → new_mkVBalBranch3MkVBalBranch25(zzz340, zzz341, Succ(Succ(zzz3420000)), zzz343, zzz344, zzz520, zzz521, zzz522000, zzz523, zzz524, zzz31, Succ(zzz3420000), Succ(zzz522000), h)
new_mkVBalBranch3MkVBalBranch26(zzz1133, zzz1134, zzz1135, zzz1136, zzz1137, zzz1138, zzz1139, zzz1140, zzz1141, zzz1142, Succ(zzz11430), Zero, be) → new_mkVBalBranch3MkVBalBranch212(zzz1133, zzz1134, zzz1135, zzz1136, zzz1137, zzz1138, zzz1139, zzz1140, zzz1141, zzz1142, be)
new_mkVBalBranch3MkVBalBranch24(zzz340, zzz341, Neg(Succ(Succ(zzz342000))), zzz343, zzz344, zzz520, zzz521, Succ(zzz522000), zzz523, zzz524, zzz31, Zero, h) → new_mkVBalBranch3MkVBalBranch25(zzz340, zzz341, Succ(zzz342000), zzz343, zzz344, zzz520, zzz521, zzz522000, zzz523, zzz524, zzz31, zzz342000, zzz522000, h)
new_mkVBalBranch(zzz31, Branch(zzz520, zzz521, Pos(Succ(zzz52200)), zzz523, zzz524), Branch(zzz340, zzz341, zzz342, zzz343, zzz344), h) → new_mkVBalBranch3MkVBalBranch2(zzz340, zzz341, zzz342, zzz343, zzz344, zzz520, zzz521, zzz52200, zzz523, zzz524, zzz31, new_primPlusNat3(Succ(new_primPlusNat3(new_primPlusNat1(zzz52200), zzz52200)), Succ(zzz52200)), h)
new_mkVBalBranch3MkVBalBranch29(zzz818, zzz819, zzz820, zzz821, zzz822, zzz823, zzz824, zzz825, zzz826, zzz827, bf) → new_mkVBalBranch3MkVBalBranch14(zzz818, zzz819, zzz820, zzz821, zzz822, zzz823, zzz824, zzz825, zzz826, zzz827, new_primPlusNat2(new_primMulNat0(zzz820), Succ(zzz820)), bf)
new_mkVBalBranch3MkVBalBranch11(zzz2033, zzz2034, zzz2035, zzz2036, zzz2037, zzz2038, zzz2039, zzz2040, zzz2041, zzz2042, zzz2043, Succ(zzz20440), Succ(zzz20450), bb) → new_mkVBalBranch3MkVBalBranch11(zzz2033, zzz2034, zzz2035, zzz2036, zzz2037, zzz2038, zzz2039, zzz2040, zzz2041, zzz2042, zzz2043, zzz20440, zzz20450, bb)
new_mkVBalBranch3MkVBalBranch2(zzz340, zzz341, Neg(zzz3420), zzz343, zzz344, zzz520, zzz521, zzz52200, zzz523, zzz524, zzz31, Zero, h) → new_mkVBalBranch3MkVBalBranch22(zzz340, zzz341, zzz3420, zzz343, zzz344, zzz520, zzz521, zzz52200, zzz523, zzz524, zzz31, h)
new_mkVBalBranch3MkVBalBranch25(zzz537, zzz538, zzz539, zzz540, zzz541, zzz542, zzz543, zzz544, zzz545, zzz546, zzz547, Succ(zzz5480), Succ(zzz5490), bc) → new_mkVBalBranch3MkVBalBranch25(zzz537, zzz538, zzz539, zzz540, zzz541, zzz542, zzz543, zzz544, zzz545, zzz546, zzz547, zzz5480, zzz5490, bc)
new_mkVBalBranch(zzz31, Branch(zzz520, zzz521, Neg(Succ(zzz52200)), zzz523, zzz524), Branch(zzz340, zzz341, zzz342, zzz343, zzz344), h) → new_mkVBalBranch3MkVBalBranch24(zzz340, zzz341, zzz342, zzz343, zzz344, zzz520, zzz521, zzz52200, zzz523, zzz524, zzz31, new_primPlusNat3(Succ(new_primPlusNat3(new_primPlusNat1(zzz52200), zzz52200)), Succ(zzz52200)), h)
new_mkVBalBranch3MkVBalBranch24(zzz340, zzz341, Neg(Succ(Zero)), zzz343, zzz344, zzz520, zzz521, Succ(zzz522000), zzz523, zzz524, zzz31, Zero, h) → new_mkVBalBranch3MkVBalBranch28(zzz340, zzz341, zzz343, zzz344, zzz520, zzz521, Succ(zzz522000), zzz523, zzz524, zzz31, h)
new_mkVBalBranch3MkVBalBranch210(zzz340, zzz341, zzz343, zzz344, zzz520, zzz521, zzz52200, zzz523, zzz524, zzz31, h) → new_mkVBalBranch(zzz31, Branch(zzz520, zzz521, Neg(Succ(zzz52200)), zzz523, zzz524), zzz343, h)
new_mkVBalBranch3MkVBalBranch26(zzz1133, zzz1134, zzz1135, zzz1136, zzz1137, zzz1138, zzz1139, zzz1140, zzz1141, zzz1142, Zero, Succ(zzz11440), be) → new_mkVBalBranch(zzz1142, Branch(zzz1138, zzz1139, Neg(Succ(Zero)), zzz1140, zzz1141), zzz1136, be)
new_mkVBalBranch3MkVBalBranch24(zzz340, zzz341, Neg(Succ(Succ(Zero))), zzz343, zzz344, zzz520, zzz521, Zero, zzz523, zzz524, zzz31, Succ(Zero), h) → new_mkVBalBranch3MkVBalBranch26(zzz340, zzz341, Succ(Zero), zzz343, zzz344, zzz520, zzz521, zzz523, zzz524, zzz31, Zero, Zero, h)
new_mkVBalBranch(zzz31, Branch(zzz520, zzz521, Pos(Zero), zzz523, zzz524), Branch(zzz340, zzz341, Pos(Succ(zzz34200)), zzz343, zzz344), h) → new_mkVBalBranch(zzz31, Branch(zzz520, zzz521, Pos(Zero), zzz523, zzz524), zzz343, h)
new_mkVBalBranch3MkVBalBranch2(zzz340, zzz341, Pos(Zero), zzz343, zzz344, zzz520, zzz521, zzz52200, zzz523, zzz524, zzz31, Succ(zzz680), h) → new_mkVBalBranch(zzz31, zzz524, Branch(zzz340, zzz341, Pos(Zero), zzz343, zzz344), h)
new_mkVBalBranch3MkVBalBranch21(zzz340, zzz341, zzz343, zzz344, zzz520, zzz521, zzz52200, zzz523, zzz524, zzz31, h) → new_mkVBalBranch(zzz31, zzz524, Branch(zzz340, zzz341, Pos(Zero), zzz343, zzz344), h)
new_mkVBalBranch3MkVBalBranch24(zzz340, zzz341, Pos(zzz3420), zzz343, zzz344, zzz520, zzz521, zzz52200, zzz523, zzz524, zzz31, Zero, h) → new_mkVBalBranch3MkVBalBranch27(zzz340, zzz341, zzz3420, zzz343, zzz344, zzz520, zzz521, zzz52200, zzz523, zzz524, zzz31, h)
new_mkVBalBranch3MkVBalBranch24(zzz340, zzz341, Neg(Succ(Succ(Succ(zzz3420000)))), zzz343, zzz344, zzz520, zzz521, Zero, zzz523, zzz524, zzz31, Succ(Succ(zzz6900)), h) → new_mkVBalBranch3MkVBalBranch26(zzz340, zzz341, Succ(Succ(zzz3420000)), zzz343, zzz344, zzz520, zzz521, zzz523, zzz524, zzz31, Succ(zzz3420000), Succ(zzz6900), h)
new_mkVBalBranch3MkVBalBranch15(zzz537, zzz538, zzz539, zzz540, zzz541, zzz542, zzz543, zzz544, zzz545, zzz546, zzz547, Succ(zzz6990), bc) → new_mkVBalBranch3MkVBalBranch16(zzz537, zzz538, zzz539, zzz540, zzz541, zzz542, zzz543, Succ(zzz544), zzz545, zzz546, zzz547, Succ(Succ(zzz544)), Succ(zzz6990), bc)
new_mkVBalBranch(zzz31, Branch(zzz520, zzz521, Neg(Zero), zzz523, zzz524), Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), h) → new_mkVBalBranch3MkVBalBranch13(zzz340, zzz341, zzz34200, zzz343, zzz344, zzz520, zzz521, zzz523, zzz524, zzz31, new_primPlusNat2(new_primMulNat0(zzz34200), Succ(zzz34200)), h)
new_mkVBalBranch3MkVBalBranch27(zzz340, zzz341, zzz3420, zzz343, zzz344, zzz520, zzz521, zzz52200, zzz523, zzz524, zzz31, h) → new_mkVBalBranch(zzz31, Branch(zzz520, zzz521, Neg(Succ(zzz52200)), zzz523, zzz524), zzz343, h)
new_mkVBalBranch3MkVBalBranch24(zzz340, zzz341, Pos(zzz3420), zzz343, zzz344, zzz520, zzz521, zzz52200, zzz523, zzz524, zzz31, Succ(zzz690), h) → new_mkVBalBranch(zzz31, Branch(zzz520, zzz521, Neg(Succ(zzz52200)), zzz523, zzz524), zzz343, h)
new_mkVBalBranch3MkVBalBranch12(zzz340, zzz341, zzz34200, zzz343, zzz344, zzz520, zzz521, zzz523, zzz524, zzz31, Succ(zzz1250), h) → new_mkVBalBranch(zzz31, zzz524, Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), h)
new_mkVBalBranch3MkVBalBranch28(zzz340, zzz341, zzz343, zzz344, zzz520, zzz521, zzz52200, zzz523, zzz524, zzz31, h) → new_mkVBalBranch(zzz31, Branch(zzz520, zzz521, Neg(Succ(zzz52200)), zzz523, zzz524), zzz343, h)
new_mkVBalBranch3MkVBalBranch24(zzz340, zzz341, Neg(Succ(Succ(Zero))), zzz343, zzz344, zzz520, zzz521, Zero, zzz523, zzz524, zzz31, Succ(Succ(zzz6900)), h) → new_mkVBalBranch3MkVBalBranch26(zzz340, zzz341, Succ(Zero), zzz343, zzz344, zzz520, zzz521, zzz523, zzz524, zzz31, Zero, Succ(zzz6900), h)
new_mkVBalBranch3MkVBalBranch211(zzz537, zzz538, zzz539, zzz540, zzz541, zzz542, zzz543, zzz544, zzz545, zzz546, zzz547, bc) → new_mkVBalBranch3MkVBalBranch15(zzz537, zzz538, zzz539, zzz540, zzz541, zzz542, zzz543, zzz544, zzz545, zzz546, zzz547, new_primPlusNat2(new_primPlusNat3(Succ(new_primPlusNat3(new_primPlusNat1(zzz539), zzz539)), Succ(zzz539)), Succ(zzz539)), bc)
new_mkVBalBranch3MkVBalBranch1(zzz340, zzz341, zzz34200, zzz343, zzz344, zzz520, zzz521, zzz52200, zzz523, zzz524, zzz31, Succ(zzz1430), h) → new_mkVBalBranch(zzz31, zzz524, Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), h)
new_mkVBalBranch3MkVBalBranch22(zzz340, zzz341, Zero, zzz343, zzz344, zzz520, zzz521, zzz52200, zzz523, zzz524, zzz31, h) → new_mkVBalBranch(zzz31, zzz524, Branch(zzz340, zzz341, Neg(Zero), zzz343, zzz344), h)
new_mkVBalBranch(zzz31, Branch(zzz520, zzz521, Pos(Zero), zzz523, zzz524), Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), h) → new_mkVBalBranch3MkVBalBranch12(zzz340, zzz341, zzz34200, zzz343, zzz344, zzz520, zzz521, zzz523, zzz524, zzz31, new_primPlusNat2(new_primMulNat0(zzz34200), Succ(zzz34200)), h)
new_mkVBalBranch3MkVBalBranch24(zzz340, zzz341, Neg(Succ(Zero)), zzz343, zzz344, zzz520, zzz521, zzz52200, zzz523, zzz524, zzz31, Succ(zzz690), h) → new_mkVBalBranch(zzz31, Branch(zzz520, zzz521, Neg(Succ(zzz52200)), zzz523, zzz524), zzz343, h)
new_mkVBalBranch3MkVBalBranch13(zzz340, zzz341, zzz34200, zzz343, zzz344, zzz520, zzz521, zzz523, zzz524, zzz31, Succ(zzz1290), h) → new_mkVBalBranch(zzz31, zzz524, Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), h)
new_mkVBalBranch3MkVBalBranch2(zzz340, zzz341, Pos(Succ(zzz34200)), zzz343, zzz344, zzz520, zzz521, zzz52200, zzz523, zzz524, zzz31, Succ(zzz680), h) → new_mkVBalBranch3MkVBalBranch20(zzz340, zzz341, zzz34200, zzz343, zzz344, zzz520, zzz521, zzz52200, zzz523, zzz524, zzz31, Succ(new_primPlusNat2(zzz680, zzz52200)), zzz34200, h)
new_mkVBalBranch3MkVBalBranch24(zzz340, zzz341, Neg(Zero), zzz343, zzz344, zzz520, zzz521, zzz52200, zzz523, zzz524, zzz31, Succ(zzz690), h) → new_mkVBalBranch(zzz31, Branch(zzz520, zzz521, Neg(Succ(zzz52200)), zzz523, zzz524), zzz343, h)
new_mkVBalBranch(zzz31, Branch(zzz520, zzz521, Neg(Zero), zzz523, zzz524), Branch(zzz340, zzz341, Pos(Succ(zzz34200)), zzz343, zzz344), h) → new_mkVBalBranch(zzz31, Branch(zzz520, zzz521, Neg(Zero), zzz523, zzz524), zzz343, h)
new_mkVBalBranch3MkVBalBranch24(zzz340, zzz341, Neg(Succ(Succ(zzz342000))), zzz343, zzz344, zzz520, zzz521, Zero, zzz523, zzz524, zzz31, Zero, h) → new_mkVBalBranch3MkVBalBranch14(zzz340, zzz341, Succ(zzz342000), zzz343, zzz344, zzz520, zzz521, zzz523, zzz524, zzz31, new_primPlusNat2(new_primPlusNat3(Succ(new_primPlusNat3(new_primPlusNat1(Succ(zzz342000)), Succ(zzz342000))), Succ(Succ(zzz342000))), Succ(Succ(zzz342000))), h)
new_mkVBalBranch3MkVBalBranch1(zzz340, zzz341, zzz34200, zzz343, zzz344, zzz520, zzz521, zzz52200, zzz523, zzz524, zzz31, Zero, h) → new_mkVBalBranch3MkVBalBranch17(zzz340, zzz341, zzz34200, zzz343, zzz344, zzz520, zzz521, zzz52200, zzz523, zzz524, zzz31, h)
new_mkVBalBranch3MkVBalBranch16(zzz1702, zzz1703, zzz1704, zzz1705, zzz1706, zzz1707, zzz1708, zzz1709, zzz1710, zzz1711, zzz1712, Succ(zzz17130), Succ(zzz17140), bd) → new_mkVBalBranch3MkVBalBranch16(zzz1702, zzz1703, zzz1704, zzz1705, zzz1706, zzz1707, zzz1708, zzz1709, zzz1710, zzz1711, zzz1712, zzz17130, zzz17140, bd)
new_mkVBalBranch3MkVBalBranch25(zzz537, zzz538, zzz539, zzz540, zzz541, zzz542, zzz543, zzz544, zzz545, zzz546, zzz547, Zero, Succ(zzz5490), bc) → new_mkVBalBranch(zzz547, Branch(zzz542, zzz543, Neg(Succ(Succ(zzz544))), zzz545, zzz546), zzz540, bc)
new_mkVBalBranch3MkVBalBranch212(zzz818, zzz819, zzz820, zzz821, zzz822, zzz823, zzz824, zzz825, zzz826, zzz827, bf) → new_mkVBalBranch3MkVBalBranch14(zzz818, zzz819, zzz820, zzz821, zzz822, zzz823, zzz824, zzz825, zzz826, zzz827, new_primPlusNat2(new_primMulNat0(zzz820), Succ(zzz820)), bf)
new_mkVBalBranch3MkVBalBranch10(zzz929, zzz930, zzz931, zzz932, zzz933, zzz934, zzz935, zzz936, zzz937, zzz938, zzz939, Succ(zzz10020), ba) → new_mkVBalBranch3MkVBalBranch11(zzz929, zzz930, zzz931, zzz932, zzz933, zzz934, zzz935, zzz936, zzz937, zzz938, zzz939, Succ(zzz10020), Succ(zzz936), ba)
new_mkVBalBranch3MkVBalBranch14(zzz818, zzz819, zzz820, zzz821, zzz822, zzz823, zzz824, zzz825, zzz826, zzz827, Succ(zzz8960), bf) → new_mkVBalBranch3MkVBalBranch16(zzz818, zzz819, zzz820, zzz821, zzz822, zzz823, zzz824, Zero, zzz825, zzz826, zzz827, Succ(Zero), Succ(zzz8960), bf)
new_mkVBalBranch3MkVBalBranch24(zzz340, zzz341, Neg(Succ(Succ(Succ(zzz3420000)))), zzz343, zzz344, zzz520, zzz521, Succ(zzz522000), zzz523, zzz524, zzz31, Succ(Succ(zzz6900)), h) → new_mkVBalBranch3MkVBalBranch25(zzz340, zzz341, Succ(Succ(zzz3420000)), zzz343, zzz344, zzz520, zzz521, zzz522000, zzz523, zzz524, zzz31, Succ(zzz3420000), Succ(Succ(new_primPlusNat2(zzz6900, zzz522000))), h)
new_mkVBalBranch3MkVBalBranch2(zzz340, zzz341, Pos(Succ(zzz34200)), zzz343, zzz344, zzz520, zzz521, zzz52200, zzz523, zzz524, zzz31, Zero, h) → new_mkVBalBranch3MkVBalBranch20(zzz340, zzz341, zzz34200, zzz343, zzz344, zzz520, zzz521, zzz52200, zzz523, zzz524, zzz31, zzz52200, zzz34200, h)
new_mkVBalBranch3MkVBalBranch24(zzz340, zzz341, Neg(Zero), zzz343, zzz344, zzz520, zzz521, zzz52200, zzz523, zzz524, zzz31, Zero, h) → new_mkVBalBranch3MkVBalBranch210(zzz340, zzz341, zzz343, zzz344, zzz520, zzz521, zzz52200, zzz523, zzz524, zzz31, h)
new_mkVBalBranch3MkVBalBranch24(zzz340, zzz341, Neg(Succ(Succ(Zero))), zzz343, zzz344, zzz520, zzz521, Succ(zzz522000), zzz523, zzz524, zzz31, Succ(Succ(zzz6900)), h) → new_mkVBalBranch3MkVBalBranch25(zzz340, zzz341, Succ(Zero), zzz343, zzz344, zzz520, zzz521, zzz522000, zzz523, zzz524, zzz31, Zero, Succ(Succ(new_primPlusNat2(zzz6900, zzz522000))), h)
new_mkVBalBranch3MkVBalBranch23(zzz929, zzz930, zzz931, zzz932, zzz933, zzz934, zzz935, zzz936, zzz937, zzz938, zzz939, ba) → new_mkVBalBranch3MkVBalBranch10(zzz929, zzz930, zzz931, zzz932, zzz933, zzz934, zzz935, zzz936, zzz937, zzz938, zzz939, new_primPlusNat2(new_primMulNat0(zzz931), Succ(zzz931)), ba)
new_mkVBalBranch3MkVBalBranch2(zzz340, zzz341, Neg(Zero), zzz343, zzz344, zzz520, zzz521, zzz52200, zzz523, zzz524, zzz31, Succ(zzz680), h) → new_mkVBalBranch(zzz31, zzz524, Branch(zzz340, zzz341, Neg(Zero), zzz343, zzz344), h)
new_mkVBalBranch3MkVBalBranch2(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344, zzz520, zzz521, zzz52200, zzz523, zzz524, zzz31, Succ(zzz680), h) → new_mkVBalBranch3MkVBalBranch1(zzz340, zzz341, zzz34200, zzz343, zzz344, zzz520, zzz521, zzz52200, zzz523, zzz524, zzz31, new_primPlusNat2(Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat3(new_primPlusNat1(zzz34200), zzz34200)), zzz34200))), Succ(zzz34200)), h)
new_mkVBalBranch3MkVBalBranch16(zzz1702, zzz1703, zzz1704, zzz1705, zzz1706, zzz1707, zzz1708, zzz1709, zzz1710, zzz1711, zzz1712, Zero, Succ(zzz17140), bd) → new_mkVBalBranch(zzz1712, zzz1711, Branch(zzz1702, zzz1703, Neg(Succ(zzz1704)), zzz1705, zzz1706), bd)
new_mkVBalBranch3MkVBalBranch10(zzz929, zzz930, zzz931, zzz932, zzz933, zzz934, zzz935, zzz936, zzz937, zzz938, zzz939, Zero, ba) → new_mkVBalBranch3MkVBalBranch11(zzz929, zzz930, zzz931, zzz932, zzz933, zzz934, zzz935, zzz936, zzz937, zzz938, zzz939, Zero, Succ(zzz936), ba)
new_mkVBalBranch3MkVBalBranch22(zzz340, zzz341, Succ(zzz34200), zzz343, zzz344, zzz520, zzz521, zzz52200, zzz523, zzz524, zzz31, h) → new_mkVBalBranch3MkVBalBranch1(zzz340, zzz341, zzz34200, zzz343, zzz344, zzz520, zzz521, zzz52200, zzz523, zzz524, zzz31, new_primPlusNat2(new_primPlusNat3(Succ(new_primPlusNat3(new_primPlusNat1(zzz34200), zzz34200)), Succ(zzz34200)), Succ(zzz34200)), h)
new_mkVBalBranch3MkVBalBranch2(zzz340, zzz341, Pos(Zero), zzz343, zzz344, zzz520, zzz521, zzz52200, zzz523, zzz524, zzz31, Zero, h) → new_mkVBalBranch3MkVBalBranch21(zzz340, zzz341, zzz343, zzz344, zzz520, zzz521, zzz52200, zzz523, zzz524, zzz31, h)
new_mkVBalBranch3MkVBalBranch25(zzz537, zzz538, zzz539, zzz540, zzz541, zzz542, zzz543, zzz544, zzz545, zzz546, zzz547, Zero, Zero, bc) → new_mkVBalBranch3MkVBalBranch211(zzz537, zzz538, zzz539, zzz540, zzz541, zzz542, zzz543, zzz544, zzz545, zzz546, zzz547, bc)

The TRS R consists of the following rules:

new_primMulNat0(zzz6200) → new_primPlusNat3(Succ(new_primPlusNat3(new_primPlusNat1(zzz6200), zzz6200)), Succ(zzz6200))
new_primPlusNat2(Succ(zzz900), Succ(zzz9100)) → Succ(Succ(new_primPlusNat2(zzz900, zzz9100)))
new_primPlusNat2(Zero, Succ(zzz9100)) → Succ(zzz9100)
new_primPlusNat2(Zero, Zero) → Zero
new_primPlusNat2(Succ(zzz900), Zero) → Succ(zzz900)
new_primPlusNat1(Zero) → Zero
new_primPlusNat1(Succ(zzz62000)) → Succ(Succ(new_primPlusNat1(zzz62000)))
new_primPlusNat3(zzz90, Succ(zzz910)) → Succ(Succ(new_primPlusNat2(zzz90, zzz910)))
new_primPlusNat3(zzz90, Zero) → Succ(zzz90)

The set Q consists of the following terms:

new_primPlusNat2(Zero, Succ(x0))
new_primMulNat0(x0)
new_primPlusNat3(x0, Succ(x1))
new_primPlusNat2(Succ(x0), Succ(x1))
new_primPlusNat3(x0, Zero)
new_primPlusNat1(Zero)
new_primPlusNat2(Zero, Zero)
new_primPlusNat1(Succ(x0))
new_primPlusNat2(Succ(x0), Zero)

We have to consider all minimal (P,Q,R)-chains.
By rewriting [15] the rule new_mkVBalBranch3MkVBalBranch25(zzz537, zzz538, zzz539, zzz540, zzz541, zzz542, zzz543, zzz544, zzz545, zzz546, zzz547, Succ(zzz5480), Zero, bc) → new_mkVBalBranch3MkVBalBranch15(zzz537, zzz538, zzz539, zzz540, zzz541, zzz542, zzz543, zzz544, zzz545, zzz546, zzz547, new_primPlusNat2(new_primMulNat0(zzz539), Succ(zzz539)), bc) at position [11,0] we obtained the following new rules:

new_mkVBalBranch3MkVBalBranch25(zzz537, zzz538, zzz539, zzz540, zzz541, zzz542, zzz543, zzz544, zzz545, zzz546, zzz547, Succ(zzz5480), Zero, bc) → new_mkVBalBranch3MkVBalBranch15(zzz537, zzz538, zzz539, zzz540, zzz541, zzz542, zzz543, zzz544, zzz545, zzz546, zzz547, new_primPlusNat2(new_primPlusNat3(Succ(new_primPlusNat3(new_primPlusNat1(zzz539), zzz539)), Succ(zzz539)), Succ(zzz539)), bc)



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

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

new_mkVBalBranch3MkVBalBranch11(zzz2033, zzz2034, zzz2035, zzz2036, zzz2037, zzz2038, zzz2039, zzz2040, zzz2041, zzz2042, zzz2043, Zero, Succ(zzz20450), bb) → new_mkVBalBranch(zzz2043, zzz2042, Branch(zzz2033, zzz2034, Pos(Succ(zzz2035)), zzz2036, zzz2037), bb)
new_mkVBalBranch3MkVBalBranch26(zzz1133, zzz1134, zzz1135, zzz1136, zzz1137, zzz1138, zzz1139, zzz1140, zzz1141, zzz1142, Succ(zzz11430), Succ(zzz11440), be) → new_mkVBalBranch3MkVBalBranch26(zzz1133, zzz1134, zzz1135, zzz1136, zzz1137, zzz1138, zzz1139, zzz1140, zzz1141, zzz1142, zzz11430, zzz11440, be)
new_mkVBalBranch3MkVBalBranch25(zzz537, zzz538, zzz539, zzz540, zzz541, zzz542, zzz543, zzz544, zzz545, zzz546, zzz547, Succ(zzz5480), Zero, bc) → new_mkVBalBranch3MkVBalBranch15(zzz537, zzz538, zzz539, zzz540, zzz541, zzz542, zzz543, zzz544, zzz545, zzz546, zzz547, new_primPlusNat2(new_primPlusNat3(Succ(new_primPlusNat3(new_primPlusNat1(zzz539), zzz539)), Succ(zzz539)), Succ(zzz539)), bc)
new_mkVBalBranch3MkVBalBranch24(zzz340, zzz341, Neg(Succ(Succ(Succ(zzz3420000)))), zzz343, zzz344, zzz520, zzz521, Zero, zzz523, zzz524, zzz31, Succ(Zero), h) → new_mkVBalBranch3MkVBalBranch26(zzz340, zzz341, Succ(Succ(zzz3420000)), zzz343, zzz344, zzz520, zzz521, zzz523, zzz524, zzz31, Succ(zzz3420000), Zero, h)
new_mkVBalBranch3MkVBalBranch24(zzz340, zzz341, Neg(Succ(Zero)), zzz343, zzz344, zzz520, zzz521, Zero, zzz523, zzz524, zzz31, Zero, h) → new_mkVBalBranch3MkVBalBranch29(zzz340, zzz341, Zero, zzz343, zzz344, zzz520, zzz521, zzz523, zzz524, zzz31, h)
new_mkVBalBranch3MkVBalBranch20(zzz929, zzz930, zzz931, zzz932, zzz933, zzz934, zzz935, zzz936, zzz937, zzz938, zzz939, Zero, Succ(zzz9410), ba) → new_mkVBalBranch(zzz939, Branch(zzz934, zzz935, Pos(Succ(zzz936)), zzz937, zzz938), zzz932, ba)
new_mkVBalBranch3MkVBalBranch17(zzz340, zzz341, zzz34200, zzz343, zzz344, zzz520, zzz521, zzz52200, zzz523, zzz524, zzz31, h) → new_mkVBalBranch(zzz31, zzz524, Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), h)
new_mkVBalBranch3MkVBalBranch26(zzz1133, zzz1134, zzz1135, zzz1136, zzz1137, zzz1138, zzz1139, zzz1140, zzz1141, zzz1142, Zero, Zero, be) → new_mkVBalBranch3MkVBalBranch29(zzz1133, zzz1134, zzz1135, zzz1136, zzz1137, zzz1138, zzz1139, zzz1140, zzz1141, zzz1142, be)
new_mkVBalBranch3MkVBalBranch20(zzz929, zzz930, zzz931, zzz932, zzz933, zzz934, zzz935, zzz936, zzz937, zzz938, zzz939, Zero, Zero, ba) → new_mkVBalBranch3MkVBalBranch23(zzz929, zzz930, zzz931, zzz932, zzz933, zzz934, zzz935, zzz936, zzz937, zzz938, zzz939, ba)
new_mkVBalBranch3MkVBalBranch20(zzz929, zzz930, zzz931, zzz932, zzz933, zzz934, zzz935, zzz936, zzz937, zzz938, zzz939, Succ(zzz9400), Zero, ba) → new_mkVBalBranch3MkVBalBranch10(zzz929, zzz930, zzz931, zzz932, zzz933, zzz934, zzz935, zzz936, zzz937, zzz938, zzz939, new_primPlusNat2(new_primMulNat0(zzz931), Succ(zzz931)), ba)
new_mkVBalBranch3MkVBalBranch24(zzz340, zzz341, Neg(Succ(Succ(Zero))), zzz343, zzz344, zzz520, zzz521, Succ(zzz522000), zzz523, zzz524, zzz31, Succ(Zero), h) → new_mkVBalBranch3MkVBalBranch25(zzz340, zzz341, Succ(Zero), zzz343, zzz344, zzz520, zzz521, zzz522000, zzz523, zzz524, zzz31, Zero, Succ(zzz522000), h)
new_mkVBalBranch3MkVBalBranch24(zzz340, zzz341, Neg(Succ(Succ(Succ(zzz3420000)))), zzz343, zzz344, zzz520, zzz521, Succ(zzz522000), zzz523, zzz524, zzz31, Succ(Zero), h) → new_mkVBalBranch3MkVBalBranch25(zzz340, zzz341, Succ(Succ(zzz3420000)), zzz343, zzz344, zzz520, zzz521, zzz522000, zzz523, zzz524, zzz31, Succ(zzz3420000), Succ(zzz522000), h)
new_mkVBalBranch3MkVBalBranch20(zzz929, zzz930, zzz931, zzz932, zzz933, zzz934, zzz935, zzz936, zzz937, zzz938, zzz939, Succ(zzz9400), Succ(zzz9410), ba) → new_mkVBalBranch3MkVBalBranch20(zzz929, zzz930, zzz931, zzz932, zzz933, zzz934, zzz935, zzz936, zzz937, zzz938, zzz939, zzz9400, zzz9410, ba)
new_mkVBalBranch3MkVBalBranch24(zzz340, zzz341, Neg(Succ(Succ(zzz342000))), zzz343, zzz344, zzz520, zzz521, Succ(zzz522000), zzz523, zzz524, zzz31, Zero, h) → new_mkVBalBranch3MkVBalBranch25(zzz340, zzz341, Succ(zzz342000), zzz343, zzz344, zzz520, zzz521, zzz522000, zzz523, zzz524, zzz31, zzz342000, zzz522000, h)
new_mkVBalBranch3MkVBalBranch26(zzz1133, zzz1134, zzz1135, zzz1136, zzz1137, zzz1138, zzz1139, zzz1140, zzz1141, zzz1142, Succ(zzz11430), Zero, be) → new_mkVBalBranch3MkVBalBranch212(zzz1133, zzz1134, zzz1135, zzz1136, zzz1137, zzz1138, zzz1139, zzz1140, zzz1141, zzz1142, be)
new_mkVBalBranch(zzz31, Branch(zzz520, zzz521, Pos(Succ(zzz52200)), zzz523, zzz524), Branch(zzz340, zzz341, zzz342, zzz343, zzz344), h) → new_mkVBalBranch3MkVBalBranch2(zzz340, zzz341, zzz342, zzz343, zzz344, zzz520, zzz521, zzz52200, zzz523, zzz524, zzz31, new_primPlusNat3(Succ(new_primPlusNat3(new_primPlusNat1(zzz52200), zzz52200)), Succ(zzz52200)), h)
new_mkVBalBranch3MkVBalBranch29(zzz818, zzz819, zzz820, zzz821, zzz822, zzz823, zzz824, zzz825, zzz826, zzz827, bf) → new_mkVBalBranch3MkVBalBranch14(zzz818, zzz819, zzz820, zzz821, zzz822, zzz823, zzz824, zzz825, zzz826, zzz827, new_primPlusNat2(new_primMulNat0(zzz820), Succ(zzz820)), bf)
new_mkVBalBranch3MkVBalBranch11(zzz2033, zzz2034, zzz2035, zzz2036, zzz2037, zzz2038, zzz2039, zzz2040, zzz2041, zzz2042, zzz2043, Succ(zzz20440), Succ(zzz20450), bb) → new_mkVBalBranch3MkVBalBranch11(zzz2033, zzz2034, zzz2035, zzz2036, zzz2037, zzz2038, zzz2039, zzz2040, zzz2041, zzz2042, zzz2043, zzz20440, zzz20450, bb)
new_mkVBalBranch3MkVBalBranch25(zzz537, zzz538, zzz539, zzz540, zzz541, zzz542, zzz543, zzz544, zzz545, zzz546, zzz547, Succ(zzz5480), Succ(zzz5490), bc) → new_mkVBalBranch3MkVBalBranch25(zzz537, zzz538, zzz539, zzz540, zzz541, zzz542, zzz543, zzz544, zzz545, zzz546, zzz547, zzz5480, zzz5490, bc)
new_mkVBalBranch3MkVBalBranch2(zzz340, zzz341, Neg(zzz3420), zzz343, zzz344, zzz520, zzz521, zzz52200, zzz523, zzz524, zzz31, Zero, h) → new_mkVBalBranch3MkVBalBranch22(zzz340, zzz341, zzz3420, zzz343, zzz344, zzz520, zzz521, zzz52200, zzz523, zzz524, zzz31, h)
new_mkVBalBranch(zzz31, Branch(zzz520, zzz521, Neg(Succ(zzz52200)), zzz523, zzz524), Branch(zzz340, zzz341, zzz342, zzz343, zzz344), h) → new_mkVBalBranch3MkVBalBranch24(zzz340, zzz341, zzz342, zzz343, zzz344, zzz520, zzz521, zzz52200, zzz523, zzz524, zzz31, new_primPlusNat3(Succ(new_primPlusNat3(new_primPlusNat1(zzz52200), zzz52200)), Succ(zzz52200)), h)
new_mkVBalBranch3MkVBalBranch24(zzz340, zzz341, Neg(Succ(Zero)), zzz343, zzz344, zzz520, zzz521, Succ(zzz522000), zzz523, zzz524, zzz31, Zero, h) → new_mkVBalBranch3MkVBalBranch28(zzz340, zzz341, zzz343, zzz344, zzz520, zzz521, Succ(zzz522000), zzz523, zzz524, zzz31, h)
new_mkVBalBranch3MkVBalBranch210(zzz340, zzz341, zzz343, zzz344, zzz520, zzz521, zzz52200, zzz523, zzz524, zzz31, h) → new_mkVBalBranch(zzz31, Branch(zzz520, zzz521, Neg(Succ(zzz52200)), zzz523, zzz524), zzz343, h)
new_mkVBalBranch3MkVBalBranch26(zzz1133, zzz1134, zzz1135, zzz1136, zzz1137, zzz1138, zzz1139, zzz1140, zzz1141, zzz1142, Zero, Succ(zzz11440), be) → new_mkVBalBranch(zzz1142, Branch(zzz1138, zzz1139, Neg(Succ(Zero)), zzz1140, zzz1141), zzz1136, be)
new_mkVBalBranch3MkVBalBranch24(zzz340, zzz341, Neg(Succ(Succ(Zero))), zzz343, zzz344, zzz520, zzz521, Zero, zzz523, zzz524, zzz31, Succ(Zero), h) → new_mkVBalBranch3MkVBalBranch26(zzz340, zzz341, Succ(Zero), zzz343, zzz344, zzz520, zzz521, zzz523, zzz524, zzz31, Zero, Zero, h)
new_mkVBalBranch(zzz31, Branch(zzz520, zzz521, Pos(Zero), zzz523, zzz524), Branch(zzz340, zzz341, Pos(Succ(zzz34200)), zzz343, zzz344), h) → new_mkVBalBranch(zzz31, Branch(zzz520, zzz521, Pos(Zero), zzz523, zzz524), zzz343, h)
new_mkVBalBranch3MkVBalBranch2(zzz340, zzz341, Pos(Zero), zzz343, zzz344, zzz520, zzz521, zzz52200, zzz523, zzz524, zzz31, Succ(zzz680), h) → new_mkVBalBranch(zzz31, zzz524, Branch(zzz340, zzz341, Pos(Zero), zzz343, zzz344), h)
new_mkVBalBranch3MkVBalBranch21(zzz340, zzz341, zzz343, zzz344, zzz520, zzz521, zzz52200, zzz523, zzz524, zzz31, h) → new_mkVBalBranch(zzz31, zzz524, Branch(zzz340, zzz341, Pos(Zero), zzz343, zzz344), h)
new_mkVBalBranch3MkVBalBranch24(zzz340, zzz341, Pos(zzz3420), zzz343, zzz344, zzz520, zzz521, zzz52200, zzz523, zzz524, zzz31, Zero, h) → new_mkVBalBranch3MkVBalBranch27(zzz340, zzz341, zzz3420, zzz343, zzz344, zzz520, zzz521, zzz52200, zzz523, zzz524, zzz31, h)
new_mkVBalBranch3MkVBalBranch15(zzz537, zzz538, zzz539, zzz540, zzz541, zzz542, zzz543, zzz544, zzz545, zzz546, zzz547, Succ(zzz6990), bc) → new_mkVBalBranch3MkVBalBranch16(zzz537, zzz538, zzz539, zzz540, zzz541, zzz542, zzz543, Succ(zzz544), zzz545, zzz546, zzz547, Succ(Succ(zzz544)), Succ(zzz6990), bc)
new_mkVBalBranch3MkVBalBranch24(zzz340, zzz341, Neg(Succ(Succ(Succ(zzz3420000)))), zzz343, zzz344, zzz520, zzz521, Zero, zzz523, zzz524, zzz31, Succ(Succ(zzz6900)), h) → new_mkVBalBranch3MkVBalBranch26(zzz340, zzz341, Succ(Succ(zzz3420000)), zzz343, zzz344, zzz520, zzz521, zzz523, zzz524, zzz31, Succ(zzz3420000), Succ(zzz6900), h)
new_mkVBalBranch(zzz31, Branch(zzz520, zzz521, Neg(Zero), zzz523, zzz524), Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), h) → new_mkVBalBranch3MkVBalBranch13(zzz340, zzz341, zzz34200, zzz343, zzz344, zzz520, zzz521, zzz523, zzz524, zzz31, new_primPlusNat2(new_primMulNat0(zzz34200), Succ(zzz34200)), h)
new_mkVBalBranch3MkVBalBranch27(zzz340, zzz341, zzz3420, zzz343, zzz344, zzz520, zzz521, zzz52200, zzz523, zzz524, zzz31, h) → new_mkVBalBranch(zzz31, Branch(zzz520, zzz521, Neg(Succ(zzz52200)), zzz523, zzz524), zzz343, h)
new_mkVBalBranch3MkVBalBranch24(zzz340, zzz341, Pos(zzz3420), zzz343, zzz344, zzz520, zzz521, zzz52200, zzz523, zzz524, zzz31, Succ(zzz690), h) → new_mkVBalBranch(zzz31, Branch(zzz520, zzz521, Neg(Succ(zzz52200)), zzz523, zzz524), zzz343, h)
new_mkVBalBranch3MkVBalBranch12(zzz340, zzz341, zzz34200, zzz343, zzz344, zzz520, zzz521, zzz523, zzz524, zzz31, Succ(zzz1250), h) → new_mkVBalBranch(zzz31, zzz524, Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), h)
new_mkVBalBranch3MkVBalBranch28(zzz340, zzz341, zzz343, zzz344, zzz520, zzz521, zzz52200, zzz523, zzz524, zzz31, h) → new_mkVBalBranch(zzz31, Branch(zzz520, zzz521, Neg(Succ(zzz52200)), zzz523, zzz524), zzz343, h)
new_mkVBalBranch3MkVBalBranch24(zzz340, zzz341, Neg(Succ(Succ(Zero))), zzz343, zzz344, zzz520, zzz521, Zero, zzz523, zzz524, zzz31, Succ(Succ(zzz6900)), h) → new_mkVBalBranch3MkVBalBranch26(zzz340, zzz341, Succ(Zero), zzz343, zzz344, zzz520, zzz521, zzz523, zzz524, zzz31, Zero, Succ(zzz6900), h)
new_mkVBalBranch3MkVBalBranch211(zzz537, zzz538, zzz539, zzz540, zzz541, zzz542, zzz543, zzz544, zzz545, zzz546, zzz547, bc) → new_mkVBalBranch3MkVBalBranch15(zzz537, zzz538, zzz539, zzz540, zzz541, zzz542, zzz543, zzz544, zzz545, zzz546, zzz547, new_primPlusNat2(new_primPlusNat3(Succ(new_primPlusNat3(new_primPlusNat1(zzz539), zzz539)), Succ(zzz539)), Succ(zzz539)), bc)
new_mkVBalBranch(zzz31, Branch(zzz520, zzz521, Pos(Zero), zzz523, zzz524), Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), h) → new_mkVBalBranch3MkVBalBranch12(zzz340, zzz341, zzz34200, zzz343, zzz344, zzz520, zzz521, zzz523, zzz524, zzz31, new_primPlusNat2(new_primMulNat0(zzz34200), Succ(zzz34200)), h)
new_mkVBalBranch3MkVBalBranch22(zzz340, zzz341, Zero, zzz343, zzz344, zzz520, zzz521, zzz52200, zzz523, zzz524, zzz31, h) → new_mkVBalBranch(zzz31, zzz524, Branch(zzz340, zzz341, Neg(Zero), zzz343, zzz344), h)
new_mkVBalBranch3MkVBalBranch1(zzz340, zzz341, zzz34200, zzz343, zzz344, zzz520, zzz521, zzz52200, zzz523, zzz524, zzz31, Succ(zzz1430), h) → new_mkVBalBranch(zzz31, zzz524, Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), h)
new_mkVBalBranch3MkVBalBranch24(zzz340, zzz341, Neg(Succ(Zero)), zzz343, zzz344, zzz520, zzz521, zzz52200, zzz523, zzz524, zzz31, Succ(zzz690), h) → new_mkVBalBranch(zzz31, Branch(zzz520, zzz521, Neg(Succ(zzz52200)), zzz523, zzz524), zzz343, h)
new_mkVBalBranch3MkVBalBranch13(zzz340, zzz341, zzz34200, zzz343, zzz344, zzz520, zzz521, zzz523, zzz524, zzz31, Succ(zzz1290), h) → new_mkVBalBranch(zzz31, zzz524, Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), h)
new_mkVBalBranch3MkVBalBranch2(zzz340, zzz341, Pos(Succ(zzz34200)), zzz343, zzz344, zzz520, zzz521, zzz52200, zzz523, zzz524, zzz31, Succ(zzz680), h) → new_mkVBalBranch3MkVBalBranch20(zzz340, zzz341, zzz34200, zzz343, zzz344, zzz520, zzz521, zzz52200, zzz523, zzz524, zzz31, Succ(new_primPlusNat2(zzz680, zzz52200)), zzz34200, h)
new_mkVBalBranch(zzz31, Branch(zzz520, zzz521, Neg(Zero), zzz523, zzz524), Branch(zzz340, zzz341, Pos(Succ(zzz34200)), zzz343, zzz344), h) → new_mkVBalBranch(zzz31, Branch(zzz520, zzz521, Neg(Zero), zzz523, zzz524), zzz343, h)
new_mkVBalBranch3MkVBalBranch24(zzz340, zzz341, Neg(Zero), zzz343, zzz344, zzz520, zzz521, zzz52200, zzz523, zzz524, zzz31, Succ(zzz690), h) → new_mkVBalBranch(zzz31, Branch(zzz520, zzz521, Neg(Succ(zzz52200)), zzz523, zzz524), zzz343, h)
new_mkVBalBranch3MkVBalBranch24(zzz340, zzz341, Neg(Succ(Succ(zzz342000))), zzz343, zzz344, zzz520, zzz521, Zero, zzz523, zzz524, zzz31, Zero, h) → new_mkVBalBranch3MkVBalBranch14(zzz340, zzz341, Succ(zzz342000), zzz343, zzz344, zzz520, zzz521, zzz523, zzz524, zzz31, new_primPlusNat2(new_primPlusNat3(Succ(new_primPlusNat3(new_primPlusNat1(Succ(zzz342000)), Succ(zzz342000))), Succ(Succ(zzz342000))), Succ(Succ(zzz342000))), h)
new_mkVBalBranch3MkVBalBranch1(zzz340, zzz341, zzz34200, zzz343, zzz344, zzz520, zzz521, zzz52200, zzz523, zzz524, zzz31, Zero, h) → new_mkVBalBranch3MkVBalBranch17(zzz340, zzz341, zzz34200, zzz343, zzz344, zzz520, zzz521, zzz52200, zzz523, zzz524, zzz31, h)
new_mkVBalBranch3MkVBalBranch16(zzz1702, zzz1703, zzz1704, zzz1705, zzz1706, zzz1707, zzz1708, zzz1709, zzz1710, zzz1711, zzz1712, Succ(zzz17130), Succ(zzz17140), bd) → new_mkVBalBranch3MkVBalBranch16(zzz1702, zzz1703, zzz1704, zzz1705, zzz1706, zzz1707, zzz1708, zzz1709, zzz1710, zzz1711, zzz1712, zzz17130, zzz17140, bd)
new_mkVBalBranch3MkVBalBranch25(zzz537, zzz538, zzz539, zzz540, zzz541, zzz542, zzz543, zzz544, zzz545, zzz546, zzz547, Zero, Succ(zzz5490), bc) → new_mkVBalBranch(zzz547, Branch(zzz542, zzz543, Neg(Succ(Succ(zzz544))), zzz545, zzz546), zzz540, bc)
new_mkVBalBranch3MkVBalBranch10(zzz929, zzz930, zzz931, zzz932, zzz933, zzz934, zzz935, zzz936, zzz937, zzz938, zzz939, Succ(zzz10020), ba) → new_mkVBalBranch3MkVBalBranch11(zzz929, zzz930, zzz931, zzz932, zzz933, zzz934, zzz935, zzz936, zzz937, zzz938, zzz939, Succ(zzz10020), Succ(zzz936), ba)
new_mkVBalBranch3MkVBalBranch212(zzz818, zzz819, zzz820, zzz821, zzz822, zzz823, zzz824, zzz825, zzz826, zzz827, bf) → new_mkVBalBranch3MkVBalBranch14(zzz818, zzz819, zzz820, zzz821, zzz822, zzz823, zzz824, zzz825, zzz826, zzz827, new_primPlusNat2(new_primMulNat0(zzz820), Succ(zzz820)), bf)
new_mkVBalBranch3MkVBalBranch14(zzz818, zzz819, zzz820, zzz821, zzz822, zzz823, zzz824, zzz825, zzz826, zzz827, Succ(zzz8960), bf) → new_mkVBalBranch3MkVBalBranch16(zzz818, zzz819, zzz820, zzz821, zzz822, zzz823, zzz824, Zero, zzz825, zzz826, zzz827, Succ(Zero), Succ(zzz8960), bf)
new_mkVBalBranch3MkVBalBranch24(zzz340, zzz341, Neg(Succ(Succ(Succ(zzz3420000)))), zzz343, zzz344, zzz520, zzz521, Succ(zzz522000), zzz523, zzz524, zzz31, Succ(Succ(zzz6900)), h) → new_mkVBalBranch3MkVBalBranch25(zzz340, zzz341, Succ(Succ(zzz3420000)), zzz343, zzz344, zzz520, zzz521, zzz522000, zzz523, zzz524, zzz31, Succ(zzz3420000), Succ(Succ(new_primPlusNat2(zzz6900, zzz522000))), h)
new_mkVBalBranch3MkVBalBranch2(zzz340, zzz341, Pos(Succ(zzz34200)), zzz343, zzz344, zzz520, zzz521, zzz52200, zzz523, zzz524, zzz31, Zero, h) → new_mkVBalBranch3MkVBalBranch20(zzz340, zzz341, zzz34200, zzz343, zzz344, zzz520, zzz521, zzz52200, zzz523, zzz524, zzz31, zzz52200, zzz34200, h)
new_mkVBalBranch3MkVBalBranch24(zzz340, zzz341, Neg(Zero), zzz343, zzz344, zzz520, zzz521, zzz52200, zzz523, zzz524, zzz31, Zero, h) → new_mkVBalBranch3MkVBalBranch210(zzz340, zzz341, zzz343, zzz344, zzz520, zzz521, zzz52200, zzz523, zzz524, zzz31, h)
new_mkVBalBranch3MkVBalBranch24(zzz340, zzz341, Neg(Succ(Succ(Zero))), zzz343, zzz344, zzz520, zzz521, Succ(zzz522000), zzz523, zzz524, zzz31, Succ(Succ(zzz6900)), h) → new_mkVBalBranch3MkVBalBranch25(zzz340, zzz341, Succ(Zero), zzz343, zzz344, zzz520, zzz521, zzz522000, zzz523, zzz524, zzz31, Zero, Succ(Succ(new_primPlusNat2(zzz6900, zzz522000))), h)
new_mkVBalBranch3MkVBalBranch23(zzz929, zzz930, zzz931, zzz932, zzz933, zzz934, zzz935, zzz936, zzz937, zzz938, zzz939, ba) → new_mkVBalBranch3MkVBalBranch10(zzz929, zzz930, zzz931, zzz932, zzz933, zzz934, zzz935, zzz936, zzz937, zzz938, zzz939, new_primPlusNat2(new_primMulNat0(zzz931), Succ(zzz931)), ba)
new_mkVBalBranch3MkVBalBranch2(zzz340, zzz341, Neg(Zero), zzz343, zzz344, zzz520, zzz521, zzz52200, zzz523, zzz524, zzz31, Succ(zzz680), h) → new_mkVBalBranch(zzz31, zzz524, Branch(zzz340, zzz341, Neg(Zero), zzz343, zzz344), h)
new_mkVBalBranch3MkVBalBranch2(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344, zzz520, zzz521, zzz52200, zzz523, zzz524, zzz31, Succ(zzz680), h) → new_mkVBalBranch3MkVBalBranch1(zzz340, zzz341, zzz34200, zzz343, zzz344, zzz520, zzz521, zzz52200, zzz523, zzz524, zzz31, new_primPlusNat2(Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat3(new_primPlusNat1(zzz34200), zzz34200)), zzz34200))), Succ(zzz34200)), h)
new_mkVBalBranch3MkVBalBranch16(zzz1702, zzz1703, zzz1704, zzz1705, zzz1706, zzz1707, zzz1708, zzz1709, zzz1710, zzz1711, zzz1712, Zero, Succ(zzz17140), bd) → new_mkVBalBranch(zzz1712, zzz1711, Branch(zzz1702, zzz1703, Neg(Succ(zzz1704)), zzz1705, zzz1706), bd)
new_mkVBalBranch3MkVBalBranch10(zzz929, zzz930, zzz931, zzz932, zzz933, zzz934, zzz935, zzz936, zzz937, zzz938, zzz939, Zero, ba) → new_mkVBalBranch3MkVBalBranch11(zzz929, zzz930, zzz931, zzz932, zzz933, zzz934, zzz935, zzz936, zzz937, zzz938, zzz939, Zero, Succ(zzz936), ba)
new_mkVBalBranch3MkVBalBranch25(zzz537, zzz538, zzz539, zzz540, zzz541, zzz542, zzz543, zzz544, zzz545, zzz546, zzz547, Zero, Zero, bc) → new_mkVBalBranch3MkVBalBranch211(zzz537, zzz538, zzz539, zzz540, zzz541, zzz542, zzz543, zzz544, zzz545, zzz546, zzz547, bc)
new_mkVBalBranch3MkVBalBranch2(zzz340, zzz341, Pos(Zero), zzz343, zzz344, zzz520, zzz521, zzz52200, zzz523, zzz524, zzz31, Zero, h) → new_mkVBalBranch3MkVBalBranch21(zzz340, zzz341, zzz343, zzz344, zzz520, zzz521, zzz52200, zzz523, zzz524, zzz31, h)
new_mkVBalBranch3MkVBalBranch22(zzz340, zzz341, Succ(zzz34200), zzz343, zzz344, zzz520, zzz521, zzz52200, zzz523, zzz524, zzz31, h) → new_mkVBalBranch3MkVBalBranch1(zzz340, zzz341, zzz34200, zzz343, zzz344, zzz520, zzz521, zzz52200, zzz523, zzz524, zzz31, new_primPlusNat2(new_primPlusNat3(Succ(new_primPlusNat3(new_primPlusNat1(zzz34200), zzz34200)), Succ(zzz34200)), Succ(zzz34200)), h)

The TRS R consists of the following rules:

new_primMulNat0(zzz6200) → new_primPlusNat3(Succ(new_primPlusNat3(new_primPlusNat1(zzz6200), zzz6200)), Succ(zzz6200))
new_primPlusNat2(Succ(zzz900), Succ(zzz9100)) → Succ(Succ(new_primPlusNat2(zzz900, zzz9100)))
new_primPlusNat2(Zero, Succ(zzz9100)) → Succ(zzz9100)
new_primPlusNat2(Zero, Zero) → Zero
new_primPlusNat2(Succ(zzz900), Zero) → Succ(zzz900)
new_primPlusNat1(Zero) → Zero
new_primPlusNat1(Succ(zzz62000)) → Succ(Succ(new_primPlusNat1(zzz62000)))
new_primPlusNat3(zzz90, Succ(zzz910)) → Succ(Succ(new_primPlusNat2(zzz90, zzz910)))
new_primPlusNat3(zzz90, Zero) → Succ(zzz90)

The set Q consists of the following terms:

new_primPlusNat2(Zero, Succ(x0))
new_primMulNat0(x0)
new_primPlusNat3(x0, Succ(x1))
new_primPlusNat2(Succ(x0), Succ(x1))
new_primPlusNat3(x0, Zero)
new_primPlusNat1(Zero)
new_primPlusNat2(Zero, Zero)
new_primPlusNat1(Succ(x0))
new_primPlusNat2(Succ(x0), Zero)

We have to consider all minimal (P,Q,R)-chains.
By rewriting [15] the rule new_mkVBalBranch3MkVBalBranch20(zzz929, zzz930, zzz931, zzz932, zzz933, zzz934, zzz935, zzz936, zzz937, zzz938, zzz939, Succ(zzz9400), Zero, ba) → new_mkVBalBranch3MkVBalBranch10(zzz929, zzz930, zzz931, zzz932, zzz933, zzz934, zzz935, zzz936, zzz937, zzz938, zzz939, new_primPlusNat2(new_primMulNat0(zzz931), Succ(zzz931)), ba) at position [11,0] we obtained the following new rules:

new_mkVBalBranch3MkVBalBranch20(zzz929, zzz930, zzz931, zzz932, zzz933, zzz934, zzz935, zzz936, zzz937, zzz938, zzz939, Succ(zzz9400), Zero, ba) → new_mkVBalBranch3MkVBalBranch10(zzz929, zzz930, zzz931, zzz932, zzz933, zzz934, zzz935, zzz936, zzz937, zzz938, zzz939, new_primPlusNat2(new_primPlusNat3(Succ(new_primPlusNat3(new_primPlusNat1(zzz931), zzz931)), Succ(zzz931)), Succ(zzz931)), 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
                                    ↳ DependencyGraphProof
                                      ↳ QDP
                                        ↳ Rewriting
                                          ↳ QDP
                                            ↳ Rewriting
                                              ↳ QDP
                                                ↳ Rewriting
                                                  ↳ QDP
                                                    ↳ Rewriting
                                                      ↳ QDP
                                                        ↳ Rewriting
                                                          ↳ QDP
                                                            ↳ Rewriting
                                                              ↳ QDP
                                                                ↳ Rewriting
                                                                  ↳ QDP
                                                                    ↳ Rewriting
                                                                      ↳ QDP
                                                                        ↳ Rewriting
                                                                          ↳ QDP
                                                                            ↳ Rewriting
                                                                              ↳ QDP
                                                                                ↳ Rewriting
                                                                                  ↳ QDP
                                                                                    ↳ Rewriting
                                                                                      ↳ QDP
                                                                                        ↳ Rewriting
                                                                                          ↳ QDP
                                                                                            ↳ UsableRulesProof
                                                                                              ↳ QDP
                                                                                                ↳ QReductionProof
                                                                                                  ↳ QDP
                                                                                                    ↳ Rewriting
                                                                                                      ↳ QDP
                                                                                                        ↳ Rewriting
                                                                                                          ↳ QDP
                                                                                                            ↳ Rewriting
                                                                                                              ↳ QDP
                                                                                                                ↳ Rewriting
                                                                                                                  ↳ QDP
                                                                                                                    ↳ Rewriting
                                                                                                                      ↳ QDP
                                                                                                                        ↳ Rewriting
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP

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

new_mkVBalBranch3MkVBalBranch11(zzz2033, zzz2034, zzz2035, zzz2036, zzz2037, zzz2038, zzz2039, zzz2040, zzz2041, zzz2042, zzz2043, Zero, Succ(zzz20450), bb) → new_mkVBalBranch(zzz2043, zzz2042, Branch(zzz2033, zzz2034, Pos(Succ(zzz2035)), zzz2036, zzz2037), bb)
new_mkVBalBranch3MkVBalBranch26(zzz1133, zzz1134, zzz1135, zzz1136, zzz1137, zzz1138, zzz1139, zzz1140, zzz1141, zzz1142, Succ(zzz11430), Succ(zzz11440), be) → new_mkVBalBranch3MkVBalBranch26(zzz1133, zzz1134, zzz1135, zzz1136, zzz1137, zzz1138, zzz1139, zzz1140, zzz1141, zzz1142, zzz11430, zzz11440, be)
new_mkVBalBranch3MkVBalBranch25(zzz537, zzz538, zzz539, zzz540, zzz541, zzz542, zzz543, zzz544, zzz545, zzz546, zzz547, Succ(zzz5480), Zero, bc) → new_mkVBalBranch3MkVBalBranch15(zzz537, zzz538, zzz539, zzz540, zzz541, zzz542, zzz543, zzz544, zzz545, zzz546, zzz547, new_primPlusNat2(new_primPlusNat3(Succ(new_primPlusNat3(new_primPlusNat1(zzz539), zzz539)), Succ(zzz539)), Succ(zzz539)), bc)
new_mkVBalBranch3MkVBalBranch24(zzz340, zzz341, Neg(Succ(Succ(Succ(zzz3420000)))), zzz343, zzz344, zzz520, zzz521, Zero, zzz523, zzz524, zzz31, Succ(Zero), h) → new_mkVBalBranch3MkVBalBranch26(zzz340, zzz341, Succ(Succ(zzz3420000)), zzz343, zzz344, zzz520, zzz521, zzz523, zzz524, zzz31, Succ(zzz3420000), Zero, h)
new_mkVBalBranch3MkVBalBranch24(zzz340, zzz341, Neg(Succ(Zero)), zzz343, zzz344, zzz520, zzz521, Zero, zzz523, zzz524, zzz31, Zero, h) → new_mkVBalBranch3MkVBalBranch29(zzz340, zzz341, Zero, zzz343, zzz344, zzz520, zzz521, zzz523, zzz524, zzz31, h)
new_mkVBalBranch3MkVBalBranch20(zzz929, zzz930, zzz931, zzz932, zzz933, zzz934, zzz935, zzz936, zzz937, zzz938, zzz939, Zero, Succ(zzz9410), ba) → new_mkVBalBranch(zzz939, Branch(zzz934, zzz935, Pos(Succ(zzz936)), zzz937, zzz938), zzz932, ba)
new_mkVBalBranch3MkVBalBranch17(zzz340, zzz341, zzz34200, zzz343, zzz344, zzz520, zzz521, zzz52200, zzz523, zzz524, zzz31, h) → new_mkVBalBranch(zzz31, zzz524, Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), h)
new_mkVBalBranch3MkVBalBranch26(zzz1133, zzz1134, zzz1135, zzz1136, zzz1137, zzz1138, zzz1139, zzz1140, zzz1141, zzz1142, Zero, Zero, be) → new_mkVBalBranch3MkVBalBranch29(zzz1133, zzz1134, zzz1135, zzz1136, zzz1137, zzz1138, zzz1139, zzz1140, zzz1141, zzz1142, be)
new_mkVBalBranch3MkVBalBranch20(zzz929, zzz930, zzz931, zzz932, zzz933, zzz934, zzz935, zzz936, zzz937, zzz938, zzz939, Zero, Zero, ba) → new_mkVBalBranch3MkVBalBranch23(zzz929, zzz930, zzz931, zzz932, zzz933, zzz934, zzz935, zzz936, zzz937, zzz938, zzz939, ba)
new_mkVBalBranch3MkVBalBranch24(zzz340, zzz341, Neg(Succ(Succ(Zero))), zzz343, zzz344, zzz520, zzz521, Succ(zzz522000), zzz523, zzz524, zzz31, Succ(Zero), h) → new_mkVBalBranch3MkVBalBranch25(zzz340, zzz341, Succ(Zero), zzz343, zzz344, zzz520, zzz521, zzz522000, zzz523, zzz524, zzz31, Zero, Succ(zzz522000), h)
new_mkVBalBranch3MkVBalBranch20(zzz929, zzz930, zzz931, zzz932, zzz933, zzz934, zzz935, zzz936, zzz937, zzz938, zzz939, Succ(zzz9400), Succ(zzz9410), ba) → new_mkVBalBranch3MkVBalBranch20(zzz929, zzz930, zzz931, zzz932, zzz933, zzz934, zzz935, zzz936, zzz937, zzz938, zzz939, zzz9400, zzz9410, ba)
new_mkVBalBranch3MkVBalBranch24(zzz340, zzz341, Neg(Succ(Succ(Succ(zzz3420000)))), zzz343, zzz344, zzz520, zzz521, Succ(zzz522000), zzz523, zzz524, zzz31, Succ(Zero), h) → new_mkVBalBranch3MkVBalBranch25(zzz340, zzz341, Succ(Succ(zzz3420000)), zzz343, zzz344, zzz520, zzz521, zzz522000, zzz523, zzz524, zzz31, Succ(zzz3420000), Succ(zzz522000), h)
new_mkVBalBranch3MkVBalBranch26(zzz1133, zzz1134, zzz1135, zzz1136, zzz1137, zzz1138, zzz1139, zzz1140, zzz1141, zzz1142, Succ(zzz11430), Zero, be) → new_mkVBalBranch3MkVBalBranch212(zzz1133, zzz1134, zzz1135, zzz1136, zzz1137, zzz1138, zzz1139, zzz1140, zzz1141, zzz1142, be)
new_mkVBalBranch3MkVBalBranch24(zzz340, zzz341, Neg(Succ(Succ(zzz342000))), zzz343, zzz344, zzz520, zzz521, Succ(zzz522000), zzz523, zzz524, zzz31, Zero, h) → new_mkVBalBranch3MkVBalBranch25(zzz340, zzz341, Succ(zzz342000), zzz343, zzz344, zzz520, zzz521, zzz522000, zzz523, zzz524, zzz31, zzz342000, zzz522000, h)
new_mkVBalBranch(zzz31, Branch(zzz520, zzz521, Pos(Succ(zzz52200)), zzz523, zzz524), Branch(zzz340, zzz341, zzz342, zzz343, zzz344), h) → new_mkVBalBranch3MkVBalBranch2(zzz340, zzz341, zzz342, zzz343, zzz344, zzz520, zzz521, zzz52200, zzz523, zzz524, zzz31, new_primPlusNat3(Succ(new_primPlusNat3(new_primPlusNat1(zzz52200), zzz52200)), Succ(zzz52200)), h)
new_mkVBalBranch3MkVBalBranch29(zzz818, zzz819, zzz820, zzz821, zzz822, zzz823, zzz824, zzz825, zzz826, zzz827, bf) → new_mkVBalBranch3MkVBalBranch14(zzz818, zzz819, zzz820, zzz821, zzz822, zzz823, zzz824, zzz825, zzz826, zzz827, new_primPlusNat2(new_primMulNat0(zzz820), Succ(zzz820)), bf)
new_mkVBalBranch3MkVBalBranch11(zzz2033, zzz2034, zzz2035, zzz2036, zzz2037, zzz2038, zzz2039, zzz2040, zzz2041, zzz2042, zzz2043, Succ(zzz20440), Succ(zzz20450), bb) → new_mkVBalBranch3MkVBalBranch11(zzz2033, zzz2034, zzz2035, zzz2036, zzz2037, zzz2038, zzz2039, zzz2040, zzz2041, zzz2042, zzz2043, zzz20440, zzz20450, bb)
new_mkVBalBranch3MkVBalBranch2(zzz340, zzz341, Neg(zzz3420), zzz343, zzz344, zzz520, zzz521, zzz52200, zzz523, zzz524, zzz31, Zero, h) → new_mkVBalBranch3MkVBalBranch22(zzz340, zzz341, zzz3420, zzz343, zzz344, zzz520, zzz521, zzz52200, zzz523, zzz524, zzz31, h)
new_mkVBalBranch3MkVBalBranch25(zzz537, zzz538, zzz539, zzz540, zzz541, zzz542, zzz543, zzz544, zzz545, zzz546, zzz547, Succ(zzz5480), Succ(zzz5490), bc) → new_mkVBalBranch3MkVBalBranch25(zzz537, zzz538, zzz539, zzz540, zzz541, zzz542, zzz543, zzz544, zzz545, zzz546, zzz547, zzz5480, zzz5490, bc)
new_mkVBalBranch(zzz31, Branch(zzz520, zzz521, Neg(Succ(zzz52200)), zzz523, zzz524), Branch(zzz340, zzz341, zzz342, zzz343, zzz344), h) → new_mkVBalBranch3MkVBalBranch24(zzz340, zzz341, zzz342, zzz343, zzz344, zzz520, zzz521, zzz52200, zzz523, zzz524, zzz31, new_primPlusNat3(Succ(new_primPlusNat3(new_primPlusNat1(zzz52200), zzz52200)), Succ(zzz52200)), h)
new_mkVBalBranch3MkVBalBranch24(zzz340, zzz341, Neg(Succ(Zero)), zzz343, zzz344, zzz520, zzz521, Succ(zzz522000), zzz523, zzz524, zzz31, Zero, h) → new_mkVBalBranch3MkVBalBranch28(zzz340, zzz341, zzz343, zzz344, zzz520, zzz521, Succ(zzz522000), zzz523, zzz524, zzz31, h)
new_mkVBalBranch3MkVBalBranch210(zzz340, zzz341, zzz343, zzz344, zzz520, zzz521, zzz52200, zzz523, zzz524, zzz31, h) → new_mkVBalBranch(zzz31, Branch(zzz520, zzz521, Neg(Succ(zzz52200)), zzz523, zzz524), zzz343, h)
new_mkVBalBranch3MkVBalBranch26(zzz1133, zzz1134, zzz1135, zzz1136, zzz1137, zzz1138, zzz1139, zzz1140, zzz1141, zzz1142, Zero, Succ(zzz11440), be) → new_mkVBalBranch(zzz1142, Branch(zzz1138, zzz1139, Neg(Succ(Zero)), zzz1140, zzz1141), zzz1136, be)
new_mkVBalBranch3MkVBalBranch24(zzz340, zzz341, Neg(Succ(Succ(Zero))), zzz343, zzz344, zzz520, zzz521, Zero, zzz523, zzz524, zzz31, Succ(Zero), h) → new_mkVBalBranch3MkVBalBranch26(zzz340, zzz341, Succ(Zero), zzz343, zzz344, zzz520, zzz521, zzz523, zzz524, zzz31, Zero, Zero, h)
new_mkVBalBranch(zzz31, Branch(zzz520, zzz521, Pos(Zero), zzz523, zzz524), Branch(zzz340, zzz341, Pos(Succ(zzz34200)), zzz343, zzz344), h) → new_mkVBalBranch(zzz31, Branch(zzz520, zzz521, Pos(Zero), zzz523, zzz524), zzz343, h)
new_mkVBalBranch3MkVBalBranch2(zzz340, zzz341, Pos(Zero), zzz343, zzz344, zzz520, zzz521, zzz52200, zzz523, zzz524, zzz31, Succ(zzz680), h) → new_mkVBalBranch(zzz31, zzz524, Branch(zzz340, zzz341, Pos(Zero), zzz343, zzz344), h)
new_mkVBalBranch3MkVBalBranch21(zzz340, zzz341, zzz343, zzz344, zzz520, zzz521, zzz52200, zzz523, zzz524, zzz31, h) → new_mkVBalBranch(zzz31, zzz524, Branch(zzz340, zzz341, Pos(Zero), zzz343, zzz344), h)
new_mkVBalBranch3MkVBalBranch24(zzz340, zzz341, Pos(zzz3420), zzz343, zzz344, zzz520, zzz521, zzz52200, zzz523, zzz524, zzz31, Zero, h) → new_mkVBalBranch3MkVBalBranch27(zzz340, zzz341, zzz3420, zzz343, zzz344, zzz520, zzz521, zzz52200, zzz523, zzz524, zzz31, h)
new_mkVBalBranch3MkVBalBranch24(zzz340, zzz341, Neg(Succ(Succ(Succ(zzz3420000)))), zzz343, zzz344, zzz520, zzz521, Zero, zzz523, zzz524, zzz31, Succ(Succ(zzz6900)), h) → new_mkVBalBranch3MkVBalBranch26(zzz340, zzz341, Succ(Succ(zzz3420000)), zzz343, zzz344, zzz520, zzz521, zzz523, zzz524, zzz31, Succ(zzz3420000), Succ(zzz6900), h)
new_mkVBalBranch3MkVBalBranch15(zzz537, zzz538, zzz539, zzz540, zzz541, zzz542, zzz543, zzz544, zzz545, zzz546, zzz547, Succ(zzz6990), bc) → new_mkVBalBranch3MkVBalBranch16(zzz537, zzz538, zzz539, zzz540, zzz541, zzz542, zzz543, Succ(zzz544), zzz545, zzz546, zzz547, Succ(Succ(zzz544)), Succ(zzz6990), bc)
new_mkVBalBranch(zzz31, Branch(zzz520, zzz521, Neg(Zero), zzz523, zzz524), Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), h) → new_mkVBalBranch3MkVBalBranch13(zzz340, zzz341, zzz34200, zzz343, zzz344, zzz520, zzz521, zzz523, zzz524, zzz31, new_primPlusNat2(new_primMulNat0(zzz34200), Succ(zzz34200)), h)
new_mkVBalBranch3MkVBalBranch27(zzz340, zzz341, zzz3420, zzz343, zzz344, zzz520, zzz521, zzz52200, zzz523, zzz524, zzz31, h) → new_mkVBalBranch(zzz31, Branch(zzz520, zzz521, Neg(Succ(zzz52200)), zzz523, zzz524), zzz343, h)
new_mkVBalBranch3MkVBalBranch24(zzz340, zzz341, Pos(zzz3420), zzz343, zzz344, zzz520, zzz521, zzz52200, zzz523, zzz524, zzz31, Succ(zzz690), h) → new_mkVBalBranch(zzz31, Branch(zzz520, zzz521, Neg(Succ(zzz52200)), zzz523, zzz524), zzz343, h)
new_mkVBalBranch3MkVBalBranch12(zzz340, zzz341, zzz34200, zzz343, zzz344, zzz520, zzz521, zzz523, zzz524, zzz31, Succ(zzz1250), h) → new_mkVBalBranch(zzz31, zzz524, Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), h)
new_mkVBalBranch3MkVBalBranch28(zzz340, zzz341, zzz343, zzz344, zzz520, zzz521, zzz52200, zzz523, zzz524, zzz31, h) → new_mkVBalBranch(zzz31, Branch(zzz520, zzz521, Neg(Succ(zzz52200)), zzz523, zzz524), zzz343, h)
new_mkVBalBranch3MkVBalBranch24(zzz340, zzz341, Neg(Succ(Succ(Zero))), zzz343, zzz344, zzz520, zzz521, Zero, zzz523, zzz524, zzz31, Succ(Succ(zzz6900)), h) → new_mkVBalBranch3MkVBalBranch26(zzz340, zzz341, Succ(Zero), zzz343, zzz344, zzz520, zzz521, zzz523, zzz524, zzz31, Zero, Succ(zzz6900), h)
new_mkVBalBranch3MkVBalBranch211(zzz537, zzz538, zzz539, zzz540, zzz541, zzz542, zzz543, zzz544, zzz545, zzz546, zzz547, bc) → new_mkVBalBranch3MkVBalBranch15(zzz537, zzz538, zzz539, zzz540, zzz541, zzz542, zzz543, zzz544, zzz545, zzz546, zzz547, new_primPlusNat2(new_primPlusNat3(Succ(new_primPlusNat3(new_primPlusNat1(zzz539), zzz539)), Succ(zzz539)), Succ(zzz539)), bc)
new_mkVBalBranch3MkVBalBranch1(zzz340, zzz341, zzz34200, zzz343, zzz344, zzz520, zzz521, zzz52200, zzz523, zzz524, zzz31, Succ(zzz1430), h) → new_mkVBalBranch(zzz31, zzz524, Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), h)
new_mkVBalBranch3MkVBalBranch22(zzz340, zzz341, Zero, zzz343, zzz344, zzz520, zzz521, zzz52200, zzz523, zzz524, zzz31, h) → new_mkVBalBranch(zzz31, zzz524, Branch(zzz340, zzz341, Neg(Zero), zzz343, zzz344), h)
new_mkVBalBranch(zzz31, Branch(zzz520, zzz521, Pos(Zero), zzz523, zzz524), Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), h) → new_mkVBalBranch3MkVBalBranch12(zzz340, zzz341, zzz34200, zzz343, zzz344, zzz520, zzz521, zzz523, zzz524, zzz31, new_primPlusNat2(new_primMulNat0(zzz34200), Succ(zzz34200)), h)
new_mkVBalBranch3MkVBalBranch24(zzz340, zzz341, Neg(Succ(Zero)), zzz343, zzz344, zzz520, zzz521, zzz52200, zzz523, zzz524, zzz31, Succ(zzz690), h) → new_mkVBalBranch(zzz31, Branch(zzz520, zzz521, Neg(Succ(zzz52200)), zzz523, zzz524), zzz343, h)
new_mkVBalBranch3MkVBalBranch13(zzz340, zzz341, zzz34200, zzz343, zzz344, zzz520, zzz521, zzz523, zzz524, zzz31, Succ(zzz1290), h) → new_mkVBalBranch(zzz31, zzz524, Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), h)
new_mkVBalBranch3MkVBalBranch2(zzz340, zzz341, Pos(Succ(zzz34200)), zzz343, zzz344, zzz520, zzz521, zzz52200, zzz523, zzz524, zzz31, Succ(zzz680), h) → new_mkVBalBranch3MkVBalBranch20(zzz340, zzz341, zzz34200, zzz343, zzz344, zzz520, zzz521, zzz52200, zzz523, zzz524, zzz31, Succ(new_primPlusNat2(zzz680, zzz52200)), zzz34200, h)
new_mkVBalBranch3MkVBalBranch24(zzz340, zzz341, Neg(Zero), zzz343, zzz344, zzz520, zzz521, zzz52200, zzz523, zzz524, zzz31, Succ(zzz690), h) → new_mkVBalBranch(zzz31, Branch(zzz520, zzz521, Neg(Succ(zzz52200)), zzz523, zzz524), zzz343, h)
new_mkVBalBranch(zzz31, Branch(zzz520, zzz521, Neg(Zero), zzz523, zzz524), Branch(zzz340, zzz341, Pos(Succ(zzz34200)), zzz343, zzz344), h) → new_mkVBalBranch(zzz31, Branch(zzz520, zzz521, Neg(Zero), zzz523, zzz524), zzz343, h)
new_mkVBalBranch3MkVBalBranch24(zzz340, zzz341, Neg(Succ(Succ(zzz342000))), zzz343, zzz344, zzz520, zzz521, Zero, zzz523, zzz524, zzz31, Zero, h) → new_mkVBalBranch3MkVBalBranch14(zzz340, zzz341, Succ(zzz342000), zzz343, zzz344, zzz520, zzz521, zzz523, zzz524, zzz31, new_primPlusNat2(new_primPlusNat3(Succ(new_primPlusNat3(new_primPlusNat1(Succ(zzz342000)), Succ(zzz342000))), Succ(Succ(zzz342000))), Succ(Succ(zzz342000))), h)
new_mkVBalBranch3MkVBalBranch1(zzz340, zzz341, zzz34200, zzz343, zzz344, zzz520, zzz521, zzz52200, zzz523, zzz524, zzz31, Zero, h) → new_mkVBalBranch3MkVBalBranch17(zzz340, zzz341, zzz34200, zzz343, zzz344, zzz520, zzz521, zzz52200, zzz523, zzz524, zzz31, h)
new_mkVBalBranch3MkVBalBranch16(zzz1702, zzz1703, zzz1704, zzz1705, zzz1706, zzz1707, zzz1708, zzz1709, zzz1710, zzz1711, zzz1712, Succ(zzz17130), Succ(zzz17140), bd) → new_mkVBalBranch3MkVBalBranch16(zzz1702, zzz1703, zzz1704, zzz1705, zzz1706, zzz1707, zzz1708, zzz1709, zzz1710, zzz1711, zzz1712, zzz17130, zzz17140, bd)
new_mkVBalBranch3MkVBalBranch25(zzz537, zzz538, zzz539, zzz540, zzz541, zzz542, zzz543, zzz544, zzz545, zzz546, zzz547, Zero, Succ(zzz5490), bc) → new_mkVBalBranch(zzz547, Branch(zzz542, zzz543, Neg(Succ(Succ(zzz544))), zzz545, zzz546), zzz540, bc)
new_mkVBalBranch3MkVBalBranch212(zzz818, zzz819, zzz820, zzz821, zzz822, zzz823, zzz824, zzz825, zzz826, zzz827, bf) → new_mkVBalBranch3MkVBalBranch14(zzz818, zzz819, zzz820, zzz821, zzz822, zzz823, zzz824, zzz825, zzz826, zzz827, new_primPlusNat2(new_primMulNat0(zzz820), Succ(zzz820)), bf)
new_mkVBalBranch3MkVBalBranch10(zzz929, zzz930, zzz931, zzz932, zzz933, zzz934, zzz935, zzz936, zzz937, zzz938, zzz939, Succ(zzz10020), ba) → new_mkVBalBranch3MkVBalBranch11(zzz929, zzz930, zzz931, zzz932, zzz933, zzz934, zzz935, zzz936, zzz937, zzz938, zzz939, Succ(zzz10020), Succ(zzz936), ba)
new_mkVBalBranch3MkVBalBranch14(zzz818, zzz819, zzz820, zzz821, zzz822, zzz823, zzz824, zzz825, zzz826, zzz827, Succ(zzz8960), bf) → new_mkVBalBranch3MkVBalBranch16(zzz818, zzz819, zzz820, zzz821, zzz822, zzz823, zzz824, Zero, zzz825, zzz826, zzz827, Succ(Zero), Succ(zzz8960), bf)
new_mkVBalBranch3MkVBalBranch24(zzz340, zzz341, Neg(Succ(Succ(Succ(zzz3420000)))), zzz343, zzz344, zzz520, zzz521, Succ(zzz522000), zzz523, zzz524, zzz31, Succ(Succ(zzz6900)), h) → new_mkVBalBranch3MkVBalBranch25(zzz340, zzz341, Succ(Succ(zzz3420000)), zzz343, zzz344, zzz520, zzz521, zzz522000, zzz523, zzz524, zzz31, Succ(zzz3420000), Succ(Succ(new_primPlusNat2(zzz6900, zzz522000))), h)
new_mkVBalBranch3MkVBalBranch2(zzz340, zzz341, Pos(Succ(zzz34200)), zzz343, zzz344, zzz520, zzz521, zzz52200, zzz523, zzz524, zzz31, Zero, h) → new_mkVBalBranch3MkVBalBranch20(zzz340, zzz341, zzz34200, zzz343, zzz344, zzz520, zzz521, zzz52200, zzz523, zzz524, zzz31, zzz52200, zzz34200, h)
new_mkVBalBranch3MkVBalBranch24(zzz340, zzz341, Neg(Zero), zzz343, zzz344, zzz520, zzz521, zzz52200, zzz523, zzz524, zzz31, Zero, h) → new_mkVBalBranch3MkVBalBranch210(zzz340, zzz341, zzz343, zzz344, zzz520, zzz521, zzz52200, zzz523, zzz524, zzz31, h)
new_mkVBalBranch3MkVBalBranch24(zzz340, zzz341, Neg(Succ(Succ(Zero))), zzz343, zzz344, zzz520, zzz521, Succ(zzz522000), zzz523, zzz524, zzz31, Succ(Succ(zzz6900)), h) → new_mkVBalBranch3MkVBalBranch25(zzz340, zzz341, Succ(Zero), zzz343, zzz344, zzz520, zzz521, zzz522000, zzz523, zzz524, zzz31, Zero, Succ(Succ(new_primPlusNat2(zzz6900, zzz522000))), h)
new_mkVBalBranch3MkVBalBranch20(zzz929, zzz930, zzz931, zzz932, zzz933, zzz934, zzz935, zzz936, zzz937, zzz938, zzz939, Succ(zzz9400), Zero, ba) → new_mkVBalBranch3MkVBalBranch10(zzz929, zzz930, zzz931, zzz932, zzz933, zzz934, zzz935, zzz936, zzz937, zzz938, zzz939, new_primPlusNat2(new_primPlusNat3(Succ(new_primPlusNat3(new_primPlusNat1(zzz931), zzz931)), Succ(zzz931)), Succ(zzz931)), ba)
new_mkVBalBranch3MkVBalBranch23(zzz929, zzz930, zzz931, zzz932, zzz933, zzz934, zzz935, zzz936, zzz937, zzz938, zzz939, ba) → new_mkVBalBranch3MkVBalBranch10(zzz929, zzz930, zzz931, zzz932, zzz933, zzz934, zzz935, zzz936, zzz937, zzz938, zzz939, new_primPlusNat2(new_primMulNat0(zzz931), Succ(zzz931)), ba)
new_mkVBalBranch3MkVBalBranch2(zzz340, zzz341, Neg(Zero), zzz343, zzz344, zzz520, zzz521, zzz52200, zzz523, zzz524, zzz31, Succ(zzz680), h) → new_mkVBalBranch(zzz31, zzz524, Branch(zzz340, zzz341, Neg(Zero), zzz343, zzz344), h)
new_mkVBalBranch3MkVBalBranch2(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344, zzz520, zzz521, zzz52200, zzz523, zzz524, zzz31, Succ(zzz680), h) → new_mkVBalBranch3MkVBalBranch1(zzz340, zzz341, zzz34200, zzz343, zzz344, zzz520, zzz521, zzz52200, zzz523, zzz524, zzz31, new_primPlusNat2(Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat3(new_primPlusNat1(zzz34200), zzz34200)), zzz34200))), Succ(zzz34200)), h)
new_mkVBalBranch3MkVBalBranch16(zzz1702, zzz1703, zzz1704, zzz1705, zzz1706, zzz1707, zzz1708, zzz1709, zzz1710, zzz1711, zzz1712, Zero, Succ(zzz17140), bd) → new_mkVBalBranch(zzz1712, zzz1711, Branch(zzz1702, zzz1703, Neg(Succ(zzz1704)), zzz1705, zzz1706), bd)
new_mkVBalBranch3MkVBalBranch10(zzz929, zzz930, zzz931, zzz932, zzz933, zzz934, zzz935, zzz936, zzz937, zzz938, zzz939, Zero, ba) → new_mkVBalBranch3MkVBalBranch11(zzz929, zzz930, zzz931, zzz932, zzz933, zzz934, zzz935, zzz936, zzz937, zzz938, zzz939, Zero, Succ(zzz936), ba)
new_mkVBalBranch3MkVBalBranch22(zzz340, zzz341, Succ(zzz34200), zzz343, zzz344, zzz520, zzz521, zzz52200, zzz523, zzz524, zzz31, h) → new_mkVBalBranch3MkVBalBranch1(zzz340, zzz341, zzz34200, zzz343, zzz344, zzz520, zzz521, zzz52200, zzz523, zzz524, zzz31, new_primPlusNat2(new_primPlusNat3(Succ(new_primPlusNat3(new_primPlusNat1(zzz34200), zzz34200)), Succ(zzz34200)), Succ(zzz34200)), h)
new_mkVBalBranch3MkVBalBranch2(zzz340, zzz341, Pos(Zero), zzz343, zzz344, zzz520, zzz521, zzz52200, zzz523, zzz524, zzz31, Zero, h) → new_mkVBalBranch3MkVBalBranch21(zzz340, zzz341, zzz343, zzz344, zzz520, zzz521, zzz52200, zzz523, zzz524, zzz31, h)
new_mkVBalBranch3MkVBalBranch25(zzz537, zzz538, zzz539, zzz540, zzz541, zzz542, zzz543, zzz544, zzz545, zzz546, zzz547, Zero, Zero, bc) → new_mkVBalBranch3MkVBalBranch211(zzz537, zzz538, zzz539, zzz540, zzz541, zzz542, zzz543, zzz544, zzz545, zzz546, zzz547, bc)

The TRS R consists of the following rules:

new_primMulNat0(zzz6200) → new_primPlusNat3(Succ(new_primPlusNat3(new_primPlusNat1(zzz6200), zzz6200)), Succ(zzz6200))
new_primPlusNat2(Succ(zzz900), Succ(zzz9100)) → Succ(Succ(new_primPlusNat2(zzz900, zzz9100)))
new_primPlusNat2(Zero, Succ(zzz9100)) → Succ(zzz9100)
new_primPlusNat2(Zero, Zero) → Zero
new_primPlusNat2(Succ(zzz900), Zero) → Succ(zzz900)
new_primPlusNat1(Zero) → Zero
new_primPlusNat1(Succ(zzz62000)) → Succ(Succ(new_primPlusNat1(zzz62000)))
new_primPlusNat3(zzz90, Succ(zzz910)) → Succ(Succ(new_primPlusNat2(zzz90, zzz910)))
new_primPlusNat3(zzz90, Zero) → Succ(zzz90)

The set Q consists of the following terms:

new_primPlusNat2(Zero, Succ(x0))
new_primMulNat0(x0)
new_primPlusNat3(x0, Succ(x1))
new_primPlusNat2(Succ(x0), Succ(x1))
new_primPlusNat3(x0, Zero)
new_primPlusNat1(Zero)
new_primPlusNat2(Zero, Zero)
new_primPlusNat1(Succ(x0))
new_primPlusNat2(Succ(x0), Zero)

We have to consider all minimal (P,Q,R)-chains.
By rewriting [15] the rule new_mkVBalBranch(zzz31, Branch(zzz520, zzz521, Pos(Succ(zzz52200)), zzz523, zzz524), Branch(zzz340, zzz341, zzz342, zzz343, zzz344), h) → new_mkVBalBranch3MkVBalBranch2(zzz340, zzz341, zzz342, zzz343, zzz344, zzz520, zzz521, zzz52200, zzz523, zzz524, zzz31, new_primPlusNat3(Succ(new_primPlusNat3(new_primPlusNat1(zzz52200), zzz52200)), Succ(zzz52200)), h) at position [11] we obtained the following new rules:

new_mkVBalBranch(zzz31, Branch(zzz520, zzz521, Pos(Succ(zzz52200)), zzz523, zzz524), Branch(zzz340, zzz341, zzz342, zzz343, zzz344), h) → new_mkVBalBranch3MkVBalBranch2(zzz340, zzz341, zzz342, zzz343, zzz344, zzz520, zzz521, zzz52200, zzz523, zzz524, zzz31, Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat3(new_primPlusNat1(zzz52200), zzz52200)), zzz52200))), 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
                                    ↳ DependencyGraphProof
                                      ↳ QDP
                                        ↳ Rewriting
                                          ↳ QDP
                                            ↳ Rewriting
                                              ↳ QDP
                                                ↳ Rewriting
                                                  ↳ QDP
                                                    ↳ Rewriting
                                                      ↳ QDP
                                                        ↳ Rewriting
                                                          ↳ QDP
                                                            ↳ Rewriting
                                                              ↳ QDP
                                                                ↳ Rewriting
                                                                  ↳ QDP
                                                                    ↳ Rewriting
                                                                      ↳ QDP
                                                                        ↳ Rewriting
                                                                          ↳ QDP
                                                                            ↳ Rewriting
                                                                              ↳ QDP
                                                                                ↳ Rewriting
                                                                                  ↳ QDP
                                                                                    ↳ Rewriting
                                                                                      ↳ QDP
                                                                                        ↳ Rewriting
                                                                                          ↳ QDP
                                                                                            ↳ UsableRulesProof
                                                                                              ↳ QDP
                                                                                                ↳ QReductionProof
                                                                                                  ↳ QDP
                                                                                                    ↳ Rewriting
                                                                                                      ↳ QDP
                                                                                                        ↳ Rewriting
                                                                                                          ↳ QDP
                                                                                                            ↳ Rewriting
                                                                                                              ↳ QDP
                                                                                                                ↳ Rewriting
                                                                                                                  ↳ QDP
                                                                                                                    ↳ Rewriting
                                                                                                                      ↳ QDP
                                                                                                                        ↳ Rewriting
                                                                                                                          ↳ QDP
                                                                                                                            ↳ DependencyGraphProof
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP

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

new_mkVBalBranch3MkVBalBranch11(zzz2033, zzz2034, zzz2035, zzz2036, zzz2037, zzz2038, zzz2039, zzz2040, zzz2041, zzz2042, zzz2043, Zero, Succ(zzz20450), bb) → new_mkVBalBranch(zzz2043, zzz2042, Branch(zzz2033, zzz2034, Pos(Succ(zzz2035)), zzz2036, zzz2037), bb)
new_mkVBalBranch3MkVBalBranch26(zzz1133, zzz1134, zzz1135, zzz1136, zzz1137, zzz1138, zzz1139, zzz1140, zzz1141, zzz1142, Succ(zzz11430), Succ(zzz11440), be) → new_mkVBalBranch3MkVBalBranch26(zzz1133, zzz1134, zzz1135, zzz1136, zzz1137, zzz1138, zzz1139, zzz1140, zzz1141, zzz1142, zzz11430, zzz11440, be)
new_mkVBalBranch3MkVBalBranch25(zzz537, zzz538, zzz539, zzz540, zzz541, zzz542, zzz543, zzz544, zzz545, zzz546, zzz547, Succ(zzz5480), Zero, bc) → new_mkVBalBranch3MkVBalBranch15(zzz537, zzz538, zzz539, zzz540, zzz541, zzz542, zzz543, zzz544, zzz545, zzz546, zzz547, new_primPlusNat2(new_primPlusNat3(Succ(new_primPlusNat3(new_primPlusNat1(zzz539), zzz539)), Succ(zzz539)), Succ(zzz539)), bc)
new_mkVBalBranch3MkVBalBranch24(zzz340, zzz341, Neg(Succ(Succ(Succ(zzz3420000)))), zzz343, zzz344, zzz520, zzz521, Zero, zzz523, zzz524, zzz31, Succ(Zero), h) → new_mkVBalBranch3MkVBalBranch26(zzz340, zzz341, Succ(Succ(zzz3420000)), zzz343, zzz344, zzz520, zzz521, zzz523, zzz524, zzz31, Succ(zzz3420000), Zero, h)
new_mkVBalBranch3MkVBalBranch24(zzz340, zzz341, Neg(Succ(Zero)), zzz343, zzz344, zzz520, zzz521, Zero, zzz523, zzz524, zzz31, Zero, h) → new_mkVBalBranch3MkVBalBranch29(zzz340, zzz341, Zero, zzz343, zzz344, zzz520, zzz521, zzz523, zzz524, zzz31, h)
new_mkVBalBranch3MkVBalBranch20(zzz929, zzz930, zzz931, zzz932, zzz933, zzz934, zzz935, zzz936, zzz937, zzz938, zzz939, Zero, Succ(zzz9410), ba) → new_mkVBalBranch(zzz939, Branch(zzz934, zzz935, Pos(Succ(zzz936)), zzz937, zzz938), zzz932, ba)
new_mkVBalBranch3MkVBalBranch17(zzz340, zzz341, zzz34200, zzz343, zzz344, zzz520, zzz521, zzz52200, zzz523, zzz524, zzz31, h) → new_mkVBalBranch(zzz31, zzz524, Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), h)
new_mkVBalBranch3MkVBalBranch26(zzz1133, zzz1134, zzz1135, zzz1136, zzz1137, zzz1138, zzz1139, zzz1140, zzz1141, zzz1142, Zero, Zero, be) → new_mkVBalBranch3MkVBalBranch29(zzz1133, zzz1134, zzz1135, zzz1136, zzz1137, zzz1138, zzz1139, zzz1140, zzz1141, zzz1142, be)
new_mkVBalBranch3MkVBalBranch20(zzz929, zzz930, zzz931, zzz932, zzz933, zzz934, zzz935, zzz936, zzz937, zzz938, zzz939, Zero, Zero, ba) → new_mkVBalBranch3MkVBalBranch23(zzz929, zzz930, zzz931, zzz932, zzz933, zzz934, zzz935, zzz936, zzz937, zzz938, zzz939, ba)
new_mkVBalBranch3MkVBalBranch24(zzz340, zzz341, Neg(Succ(Succ(Zero))), zzz343, zzz344, zzz520, zzz521, Succ(zzz522000), zzz523, zzz524, zzz31, Succ(Zero), h) → new_mkVBalBranch3MkVBalBranch25(zzz340, zzz341, Succ(Zero), zzz343, zzz344, zzz520, zzz521, zzz522000, zzz523, zzz524, zzz31, Zero, Succ(zzz522000), h)
new_mkVBalBranch3MkVBalBranch24(zzz340, zzz341, Neg(Succ(Succ(Succ(zzz3420000)))), zzz343, zzz344, zzz520, zzz521, Succ(zzz522000), zzz523, zzz524, zzz31, Succ(Zero), h) → new_mkVBalBranch3MkVBalBranch25(zzz340, zzz341, Succ(Succ(zzz3420000)), zzz343, zzz344, zzz520, zzz521, zzz522000, zzz523, zzz524, zzz31, Succ(zzz3420000), Succ(zzz522000), h)
new_mkVBalBranch3MkVBalBranch20(zzz929, zzz930, zzz931, zzz932, zzz933, zzz934, zzz935, zzz936, zzz937, zzz938, zzz939, Succ(zzz9400), Succ(zzz9410), ba) → new_mkVBalBranch3MkVBalBranch20(zzz929, zzz930, zzz931, zzz932, zzz933, zzz934, zzz935, zzz936, zzz937, zzz938, zzz939, zzz9400, zzz9410, ba)
new_mkVBalBranch3MkVBalBranch24(zzz340, zzz341, Neg(Succ(Succ(zzz342000))), zzz343, zzz344, zzz520, zzz521, Succ(zzz522000), zzz523, zzz524, zzz31, Zero, h) → new_mkVBalBranch3MkVBalBranch25(zzz340, zzz341, Succ(zzz342000), zzz343, zzz344, zzz520, zzz521, zzz522000, zzz523, zzz524, zzz31, zzz342000, zzz522000, h)
new_mkVBalBranch3MkVBalBranch26(zzz1133, zzz1134, zzz1135, zzz1136, zzz1137, zzz1138, zzz1139, zzz1140, zzz1141, zzz1142, Succ(zzz11430), Zero, be) → new_mkVBalBranch3MkVBalBranch212(zzz1133, zzz1134, zzz1135, zzz1136, zzz1137, zzz1138, zzz1139, zzz1140, zzz1141, zzz1142, be)
new_mkVBalBranch3MkVBalBranch29(zzz818, zzz819, zzz820, zzz821, zzz822, zzz823, zzz824, zzz825, zzz826, zzz827, bf) → new_mkVBalBranch3MkVBalBranch14(zzz818, zzz819, zzz820, zzz821, zzz822, zzz823, zzz824, zzz825, zzz826, zzz827, new_primPlusNat2(new_primMulNat0(zzz820), Succ(zzz820)), bf)
new_mkVBalBranch3MkVBalBranch11(zzz2033, zzz2034, zzz2035, zzz2036, zzz2037, zzz2038, zzz2039, zzz2040, zzz2041, zzz2042, zzz2043, Succ(zzz20440), Succ(zzz20450), bb) → new_mkVBalBranch3MkVBalBranch11(zzz2033, zzz2034, zzz2035, zzz2036, zzz2037, zzz2038, zzz2039, zzz2040, zzz2041, zzz2042, zzz2043, zzz20440, zzz20450, bb)
new_mkVBalBranch3MkVBalBranch25(zzz537, zzz538, zzz539, zzz540, zzz541, zzz542, zzz543, zzz544, zzz545, zzz546, zzz547, Succ(zzz5480), Succ(zzz5490), bc) → new_mkVBalBranch3MkVBalBranch25(zzz537, zzz538, zzz539, zzz540, zzz541, zzz542, zzz543, zzz544, zzz545, zzz546, zzz547, zzz5480, zzz5490, bc)
new_mkVBalBranch3MkVBalBranch2(zzz340, zzz341, Neg(zzz3420), zzz343, zzz344, zzz520, zzz521, zzz52200, zzz523, zzz524, zzz31, Zero, h) → new_mkVBalBranch3MkVBalBranch22(zzz340, zzz341, zzz3420, zzz343, zzz344, zzz520, zzz521, zzz52200, zzz523, zzz524, zzz31, h)
new_mkVBalBranch(zzz31, Branch(zzz520, zzz521, Neg(Succ(zzz52200)), zzz523, zzz524), Branch(zzz340, zzz341, zzz342, zzz343, zzz344), h) → new_mkVBalBranch3MkVBalBranch24(zzz340, zzz341, zzz342, zzz343, zzz344, zzz520, zzz521, zzz52200, zzz523, zzz524, zzz31, new_primPlusNat3(Succ(new_primPlusNat3(new_primPlusNat1(zzz52200), zzz52200)), Succ(zzz52200)), h)
new_mkVBalBranch3MkVBalBranch24(zzz340, zzz341, Neg(Succ(Zero)), zzz343, zzz344, zzz520, zzz521, Succ(zzz522000), zzz523, zzz524, zzz31, Zero, h) → new_mkVBalBranch3MkVBalBranch28(zzz340, zzz341, zzz343, zzz344, zzz520, zzz521, Succ(zzz522000), zzz523, zzz524, zzz31, h)
new_mkVBalBranch(zzz31, Branch(zzz520, zzz521, Pos(Succ(zzz52200)), zzz523, zzz524), Branch(zzz340, zzz341, zzz342, zzz343, zzz344), h) → new_mkVBalBranch3MkVBalBranch2(zzz340, zzz341, zzz342, zzz343, zzz344, zzz520, zzz521, zzz52200, zzz523, zzz524, zzz31, Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat3(new_primPlusNat1(zzz52200), zzz52200)), zzz52200))), h)
new_mkVBalBranch3MkVBalBranch210(zzz340, zzz341, zzz343, zzz344, zzz520, zzz521, zzz52200, zzz523, zzz524, zzz31, h) → new_mkVBalBranch(zzz31, Branch(zzz520, zzz521, Neg(Succ(zzz52200)), zzz523, zzz524), zzz343, h)
new_mkVBalBranch3MkVBalBranch26(zzz1133, zzz1134, zzz1135, zzz1136, zzz1137, zzz1138, zzz1139, zzz1140, zzz1141, zzz1142, Zero, Succ(zzz11440), be) → new_mkVBalBranch(zzz1142, Branch(zzz1138, zzz1139, Neg(Succ(Zero)), zzz1140, zzz1141), zzz1136, be)
new_mkVBalBranch3MkVBalBranch24(zzz340, zzz341, Neg(Succ(Succ(Zero))), zzz343, zzz344, zzz520, zzz521, Zero, zzz523, zzz524, zzz31, Succ(Zero), h) → new_mkVBalBranch3MkVBalBranch26(zzz340, zzz341, Succ(Zero), zzz343, zzz344, zzz520, zzz521, zzz523, zzz524, zzz31, Zero, Zero, h)
new_mkVBalBranch(zzz31, Branch(zzz520, zzz521, Pos(Zero), zzz523, zzz524), Branch(zzz340, zzz341, Pos(Succ(zzz34200)), zzz343, zzz344), h) → new_mkVBalBranch(zzz31, Branch(zzz520, zzz521, Pos(Zero), zzz523, zzz524), zzz343, h)
new_mkVBalBranch3MkVBalBranch2(zzz340, zzz341, Pos(Zero), zzz343, zzz344, zzz520, zzz521, zzz52200, zzz523, zzz524, zzz31, Succ(zzz680), h) → new_mkVBalBranch(zzz31, zzz524, Branch(zzz340, zzz341, Pos(Zero), zzz343, zzz344), h)
new_mkVBalBranch3MkVBalBranch21(zzz340, zzz341, zzz343, zzz344, zzz520, zzz521, zzz52200, zzz523, zzz524, zzz31, h) → new_mkVBalBranch(zzz31, zzz524, Branch(zzz340, zzz341, Pos(Zero), zzz343, zzz344), h)
new_mkVBalBranch3MkVBalBranch24(zzz340, zzz341, Pos(zzz3420), zzz343, zzz344, zzz520, zzz521, zzz52200, zzz523, zzz524, zzz31, Zero, h) → new_mkVBalBranch3MkVBalBranch27(zzz340, zzz341, zzz3420, zzz343, zzz344, zzz520, zzz521, zzz52200, zzz523, zzz524, zzz31, h)
new_mkVBalBranch3MkVBalBranch15(zzz537, zzz538, zzz539, zzz540, zzz541, zzz542, zzz543, zzz544, zzz545, zzz546, zzz547, Succ(zzz6990), bc) → new_mkVBalBranch3MkVBalBranch16(zzz537, zzz538, zzz539, zzz540, zzz541, zzz542, zzz543, Succ(zzz544), zzz545, zzz546, zzz547, Succ(Succ(zzz544)), Succ(zzz6990), bc)
new_mkVBalBranch3MkVBalBranch24(zzz340, zzz341, Neg(Succ(Succ(Succ(zzz3420000)))), zzz343, zzz344, zzz520, zzz521, Zero, zzz523, zzz524, zzz31, Succ(Succ(zzz6900)), h) → new_mkVBalBranch3MkVBalBranch26(zzz340, zzz341, Succ(Succ(zzz3420000)), zzz343, zzz344, zzz520, zzz521, zzz523, zzz524, zzz31, Succ(zzz3420000), Succ(zzz6900), h)
new_mkVBalBranch(zzz31, Branch(zzz520, zzz521, Neg(Zero), zzz523, zzz524), Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), h) → new_mkVBalBranch3MkVBalBranch13(zzz340, zzz341, zzz34200, zzz343, zzz344, zzz520, zzz521, zzz523, zzz524, zzz31, new_primPlusNat2(new_primMulNat0(zzz34200), Succ(zzz34200)), h)
new_mkVBalBranch3MkVBalBranch27(zzz340, zzz341, zzz3420, zzz343, zzz344, zzz520, zzz521, zzz52200, zzz523, zzz524, zzz31, h) → new_mkVBalBranch(zzz31, Branch(zzz520, zzz521, Neg(Succ(zzz52200)), zzz523, zzz524), zzz343, h)
new_mkVBalBranch3MkVBalBranch24(zzz340, zzz341, Pos(zzz3420), zzz343, zzz344, zzz520, zzz521, zzz52200, zzz523, zzz524, zzz31, Succ(zzz690), h) → new_mkVBalBranch(zzz31, Branch(zzz520, zzz521, Neg(Succ(zzz52200)), zzz523, zzz524), zzz343, h)
new_mkVBalBranch3MkVBalBranch12(zzz340, zzz341, zzz34200, zzz343, zzz344, zzz520, zzz521, zzz523, zzz524, zzz31, Succ(zzz1250), h) → new_mkVBalBranch(zzz31, zzz524, Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), h)
new_mkVBalBranch3MkVBalBranch28(zzz340, zzz341, zzz343, zzz344, zzz520, zzz521, zzz52200, zzz523, zzz524, zzz31, h) → new_mkVBalBranch(zzz31, Branch(zzz520, zzz521, Neg(Succ(zzz52200)), zzz523, zzz524), zzz343, h)
new_mkVBalBranch3MkVBalBranch24(zzz340, zzz341, Neg(Succ(Succ(Zero))), zzz343, zzz344, zzz520, zzz521, Zero, zzz523, zzz524, zzz31, Succ(Succ(zzz6900)), h) → new_mkVBalBranch3MkVBalBranch26(zzz340, zzz341, Succ(Zero), zzz343, zzz344, zzz520, zzz521, zzz523, zzz524, zzz31, Zero, Succ(zzz6900), h)
new_mkVBalBranch3MkVBalBranch211(zzz537, zzz538, zzz539, zzz540, zzz541, zzz542, zzz543, zzz544, zzz545, zzz546, zzz547, bc) → new_mkVBalBranch3MkVBalBranch15(zzz537, zzz538, zzz539, zzz540, zzz541, zzz542, zzz543, zzz544, zzz545, zzz546, zzz547, new_primPlusNat2(new_primPlusNat3(Succ(new_primPlusNat3(new_primPlusNat1(zzz539), zzz539)), Succ(zzz539)), Succ(zzz539)), bc)
new_mkVBalBranch(zzz31, Branch(zzz520, zzz521, Pos(Zero), zzz523, zzz524), Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), h) → new_mkVBalBranch3MkVBalBranch12(zzz340, zzz341, zzz34200, zzz343, zzz344, zzz520, zzz521, zzz523, zzz524, zzz31, new_primPlusNat2(new_primMulNat0(zzz34200), Succ(zzz34200)), h)
new_mkVBalBranch3MkVBalBranch22(zzz340, zzz341, Zero, zzz343, zzz344, zzz520, zzz521, zzz52200, zzz523, zzz524, zzz31, h) → new_mkVBalBranch(zzz31, zzz524, Branch(zzz340, zzz341, Neg(Zero), zzz343, zzz344), h)
new_mkVBalBranch3MkVBalBranch1(zzz340, zzz341, zzz34200, zzz343, zzz344, zzz520, zzz521, zzz52200, zzz523, zzz524, zzz31, Succ(zzz1430), h) → new_mkVBalBranch(zzz31, zzz524, Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), h)
new_mkVBalBranch3MkVBalBranch24(zzz340, zzz341, Neg(Succ(Zero)), zzz343, zzz344, zzz520, zzz521, zzz52200, zzz523, zzz524, zzz31, Succ(zzz690), h) → new_mkVBalBranch(zzz31, Branch(zzz520, zzz521, Neg(Succ(zzz52200)), zzz523, zzz524), zzz343, h)
new_mkVBalBranch3MkVBalBranch13(zzz340, zzz341, zzz34200, zzz343, zzz344, zzz520, zzz521, zzz523, zzz524, zzz31, Succ(zzz1290), h) → new_mkVBalBranch(zzz31, zzz524, Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), h)
new_mkVBalBranch3MkVBalBranch2(zzz340, zzz341, Pos(Succ(zzz34200)), zzz343, zzz344, zzz520, zzz521, zzz52200, zzz523, zzz524, zzz31, Succ(zzz680), h) → new_mkVBalBranch3MkVBalBranch20(zzz340, zzz341, zzz34200, zzz343, zzz344, zzz520, zzz521, zzz52200, zzz523, zzz524, zzz31, Succ(new_primPlusNat2(zzz680, zzz52200)), zzz34200, h)
new_mkVBalBranch(zzz31, Branch(zzz520, zzz521, Neg(Zero), zzz523, zzz524), Branch(zzz340, zzz341, Pos(Succ(zzz34200)), zzz343, zzz344), h) → new_mkVBalBranch(zzz31, Branch(zzz520, zzz521, Neg(Zero), zzz523, zzz524), zzz343, h)
new_mkVBalBranch3MkVBalBranch24(zzz340, zzz341, Neg(Zero), zzz343, zzz344, zzz520, zzz521, zzz52200, zzz523, zzz524, zzz31, Succ(zzz690), h) → new_mkVBalBranch(zzz31, Branch(zzz520, zzz521, Neg(Succ(zzz52200)), zzz523, zzz524), zzz343, h)
new_mkVBalBranch3MkVBalBranch24(zzz340, zzz341, Neg(Succ(Succ(zzz342000))), zzz343, zzz344, zzz520, zzz521, Zero, zzz523, zzz524, zzz31, Zero, h) → new_mkVBalBranch3MkVBalBranch14(zzz340, zzz341, Succ(zzz342000), zzz343, zzz344, zzz520, zzz521, zzz523, zzz524, zzz31, new_primPlusNat2(new_primPlusNat3(Succ(new_primPlusNat3(new_primPlusNat1(Succ(zzz342000)), Succ(zzz342000))), Succ(Succ(zzz342000))), Succ(Succ(zzz342000))), h)
new_mkVBalBranch3MkVBalBranch1(zzz340, zzz341, zzz34200, zzz343, zzz344, zzz520, zzz521, zzz52200, zzz523, zzz524, zzz31, Zero, h) → new_mkVBalBranch3MkVBalBranch17(zzz340, zzz341, zzz34200, zzz343, zzz344, zzz520, zzz521, zzz52200, zzz523, zzz524, zzz31, h)
new_mkVBalBranch3MkVBalBranch16(zzz1702, zzz1703, zzz1704, zzz1705, zzz1706, zzz1707, zzz1708, zzz1709, zzz1710, zzz1711, zzz1712, Succ(zzz17130), Succ(zzz17140), bd) → new_mkVBalBranch3MkVBalBranch16(zzz1702, zzz1703, zzz1704, zzz1705, zzz1706, zzz1707, zzz1708, zzz1709, zzz1710, zzz1711, zzz1712, zzz17130, zzz17140, bd)
new_mkVBalBranch3MkVBalBranch25(zzz537, zzz538, zzz539, zzz540, zzz541, zzz542, zzz543, zzz544, zzz545, zzz546, zzz547, Zero, Succ(zzz5490), bc) → new_mkVBalBranch(zzz547, Branch(zzz542, zzz543, Neg(Succ(Succ(zzz544))), zzz545, zzz546), zzz540, bc)
new_mkVBalBranch3MkVBalBranch10(zzz929, zzz930, zzz931, zzz932, zzz933, zzz934, zzz935, zzz936, zzz937, zzz938, zzz939, Succ(zzz10020), ba) → new_mkVBalBranch3MkVBalBranch11(zzz929, zzz930, zzz931, zzz932, zzz933, zzz934, zzz935, zzz936, zzz937, zzz938, zzz939, Succ(zzz10020), Succ(zzz936), ba)
new_mkVBalBranch3MkVBalBranch212(zzz818, zzz819, zzz820, zzz821, zzz822, zzz823, zzz824, zzz825, zzz826, zzz827, bf) → new_mkVBalBranch3MkVBalBranch14(zzz818, zzz819, zzz820, zzz821, zzz822, zzz823, zzz824, zzz825, zzz826, zzz827, new_primPlusNat2(new_primMulNat0(zzz820), Succ(zzz820)), bf)
new_mkVBalBranch3MkVBalBranch14(zzz818, zzz819, zzz820, zzz821, zzz822, zzz823, zzz824, zzz825, zzz826, zzz827, Succ(zzz8960), bf) → new_mkVBalBranch3MkVBalBranch16(zzz818, zzz819, zzz820, zzz821, zzz822, zzz823, zzz824, Zero, zzz825, zzz826, zzz827, Succ(Zero), Succ(zzz8960), bf)
new_mkVBalBranch3MkVBalBranch24(zzz340, zzz341, Neg(Succ(Succ(Succ(zzz3420000)))), zzz343, zzz344, zzz520, zzz521, Succ(zzz522000), zzz523, zzz524, zzz31, Succ(Succ(zzz6900)), h) → new_mkVBalBranch3MkVBalBranch25(zzz340, zzz341, Succ(Succ(zzz3420000)), zzz343, zzz344, zzz520, zzz521, zzz522000, zzz523, zzz524, zzz31, Succ(zzz3420000), Succ(Succ(new_primPlusNat2(zzz6900, zzz522000))), h)
new_mkVBalBranch3MkVBalBranch2(zzz340, zzz341, Pos(Succ(zzz34200)), zzz343, zzz344, zzz520, zzz521, zzz52200, zzz523, zzz524, zzz31, Zero, h) → new_mkVBalBranch3MkVBalBranch20(zzz340, zzz341, zzz34200, zzz343, zzz344, zzz520, zzz521, zzz52200, zzz523, zzz524, zzz31, zzz52200, zzz34200, h)
new_mkVBalBranch3MkVBalBranch24(zzz340, zzz341, Neg(Zero), zzz343, zzz344, zzz520, zzz521, zzz52200, zzz523, zzz524, zzz31, Zero, h) → new_mkVBalBranch3MkVBalBranch210(zzz340, zzz341, zzz343, zzz344, zzz520, zzz521, zzz52200, zzz523, zzz524, zzz31, h)
new_mkVBalBranch3MkVBalBranch24(zzz340, zzz341, Neg(Succ(Succ(Zero))), zzz343, zzz344, zzz520, zzz521, Succ(zzz522000), zzz523, zzz524, zzz31, Succ(Succ(zzz6900)), h) → new_mkVBalBranch3MkVBalBranch25(zzz340, zzz341, Succ(Zero), zzz343, zzz344, zzz520, zzz521, zzz522000, zzz523, zzz524, zzz31, Zero, Succ(Succ(new_primPlusNat2(zzz6900, zzz522000))), h)
new_mkVBalBranch3MkVBalBranch20(zzz929, zzz930, zzz931, zzz932, zzz933, zzz934, zzz935, zzz936, zzz937, zzz938, zzz939, Succ(zzz9400), Zero, ba) → new_mkVBalBranch3MkVBalBranch10(zzz929, zzz930, zzz931, zzz932, zzz933, zzz934, zzz935, zzz936, zzz937, zzz938, zzz939, new_primPlusNat2(new_primPlusNat3(Succ(new_primPlusNat3(new_primPlusNat1(zzz931), zzz931)), Succ(zzz931)), Succ(zzz931)), ba)
new_mkVBalBranch3MkVBalBranch23(zzz929, zzz930, zzz931, zzz932, zzz933, zzz934, zzz935, zzz936, zzz937, zzz938, zzz939, ba) → new_mkVBalBranch3MkVBalBranch10(zzz929, zzz930, zzz931, zzz932, zzz933, zzz934, zzz935, zzz936, zzz937, zzz938, zzz939, new_primPlusNat2(new_primMulNat0(zzz931), Succ(zzz931)), ba)
new_mkVBalBranch3MkVBalBranch2(zzz340, zzz341, Neg(Zero), zzz343, zzz344, zzz520, zzz521, zzz52200, zzz523, zzz524, zzz31, Succ(zzz680), h) → new_mkVBalBranch(zzz31, zzz524, Branch(zzz340, zzz341, Neg(Zero), zzz343, zzz344), h)
new_mkVBalBranch3MkVBalBranch2(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344, zzz520, zzz521, zzz52200, zzz523, zzz524, zzz31, Succ(zzz680), h) → new_mkVBalBranch3MkVBalBranch1(zzz340, zzz341, zzz34200, zzz343, zzz344, zzz520, zzz521, zzz52200, zzz523, zzz524, zzz31, new_primPlusNat2(Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat3(new_primPlusNat1(zzz34200), zzz34200)), zzz34200))), Succ(zzz34200)), h)
new_mkVBalBranch3MkVBalBranch16(zzz1702, zzz1703, zzz1704, zzz1705, zzz1706, zzz1707, zzz1708, zzz1709, zzz1710, zzz1711, zzz1712, Zero, Succ(zzz17140), bd) → new_mkVBalBranch(zzz1712, zzz1711, Branch(zzz1702, zzz1703, Neg(Succ(zzz1704)), zzz1705, zzz1706), bd)
new_mkVBalBranch3MkVBalBranch10(zzz929, zzz930, zzz931, zzz932, zzz933, zzz934, zzz935, zzz936, zzz937, zzz938, zzz939, Zero, ba) → new_mkVBalBranch3MkVBalBranch11(zzz929, zzz930, zzz931, zzz932, zzz933, zzz934, zzz935, zzz936, zzz937, zzz938, zzz939, Zero, Succ(zzz936), ba)
new_mkVBalBranch3MkVBalBranch25(zzz537, zzz538, zzz539, zzz540, zzz541, zzz542, zzz543, zzz544, zzz545, zzz546, zzz547, Zero, Zero, bc) → new_mkVBalBranch3MkVBalBranch211(zzz537, zzz538, zzz539, zzz540, zzz541, zzz542, zzz543, zzz544, zzz545, zzz546, zzz547, bc)
new_mkVBalBranch3MkVBalBranch2(zzz340, zzz341, Pos(Zero), zzz343, zzz344, zzz520, zzz521, zzz52200, zzz523, zzz524, zzz31, Zero, h) → new_mkVBalBranch3MkVBalBranch21(zzz340, zzz341, zzz343, zzz344, zzz520, zzz521, zzz52200, zzz523, zzz524, zzz31, h)
new_mkVBalBranch3MkVBalBranch22(zzz340, zzz341, Succ(zzz34200), zzz343, zzz344, zzz520, zzz521, zzz52200, zzz523, zzz524, zzz31, h) → new_mkVBalBranch3MkVBalBranch1(zzz340, zzz341, zzz34200, zzz343, zzz344, zzz520, zzz521, zzz52200, zzz523, zzz524, zzz31, new_primPlusNat2(new_primPlusNat3(Succ(new_primPlusNat3(new_primPlusNat1(zzz34200), zzz34200)), Succ(zzz34200)), Succ(zzz34200)), h)

The TRS R consists of the following rules:

new_primMulNat0(zzz6200) → new_primPlusNat3(Succ(new_primPlusNat3(new_primPlusNat1(zzz6200), zzz6200)), Succ(zzz6200))
new_primPlusNat2(Succ(zzz900), Succ(zzz9100)) → Succ(Succ(new_primPlusNat2(zzz900, zzz9100)))
new_primPlusNat2(Zero, Succ(zzz9100)) → Succ(zzz9100)
new_primPlusNat2(Zero, Zero) → Zero
new_primPlusNat2(Succ(zzz900), Zero) → Succ(zzz900)
new_primPlusNat1(Zero) → Zero
new_primPlusNat1(Succ(zzz62000)) → Succ(Succ(new_primPlusNat1(zzz62000)))
new_primPlusNat3(zzz90, Succ(zzz910)) → Succ(Succ(new_primPlusNat2(zzz90, zzz910)))
new_primPlusNat3(zzz90, Zero) → Succ(zzz90)

The set Q consists of the following terms:

new_primPlusNat2(Zero, Succ(x0))
new_primMulNat0(x0)
new_primPlusNat3(x0, Succ(x1))
new_primPlusNat2(Succ(x0), Succ(x1))
new_primPlusNat3(x0, Zero)
new_primPlusNat1(Zero)
new_primPlusNat2(Zero, Zero)
new_primPlusNat1(Succ(x0))
new_primPlusNat2(Succ(x0), Zero)

We have to consider all minimal (P,Q,R)-chains.
The approximation of the Dependency Graph [15,17,22] contains 1 SCC with 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
                                    ↳ DependencyGraphProof
                                      ↳ QDP
                                        ↳ Rewriting
                                          ↳ QDP
                                            ↳ Rewriting
                                              ↳ QDP
                                                ↳ Rewriting
                                                  ↳ QDP
                                                    ↳ Rewriting
                                                      ↳ QDP
                                                        ↳ Rewriting
                                                          ↳ QDP
                                                            ↳ Rewriting
                                                              ↳ QDP
                                                                ↳ Rewriting
                                                                  ↳ QDP
                                                                    ↳ Rewriting
                                                                      ↳ QDP
                                                                        ↳ Rewriting
                                                                          ↳ QDP
                                                                            ↳ Rewriting
                                                                              ↳ QDP
                                                                                ↳ Rewriting
                                                                                  ↳ QDP
                                                                                    ↳ Rewriting
                                                                                      ↳ QDP
                                                                                        ↳ Rewriting
                                                                                          ↳ QDP
                                                                                            ↳ UsableRulesProof
                                                                                              ↳ QDP
                                                                                                ↳ QReductionProof
                                                                                                  ↳ QDP
                                                                                                    ↳ Rewriting
                                                                                                      ↳ QDP
                                                                                                        ↳ Rewriting
                                                                                                          ↳ QDP
                                                                                                            ↳ Rewriting
                                                                                                              ↳ QDP
                                                                                                                ↳ Rewriting
                                                                                                                  ↳ QDP
                                                                                                                    ↳ Rewriting
                                                                                                                      ↳ QDP
                                                                                                                        ↳ Rewriting
                                                                                                                          ↳ QDP
                                                                                                                            ↳ DependencyGraphProof
                                                                                                                              ↳ QDP
                                                                                                                                ↳ Rewriting
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP

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

new_mkVBalBranch3MkVBalBranch11(zzz2033, zzz2034, zzz2035, zzz2036, zzz2037, zzz2038, zzz2039, zzz2040, zzz2041, zzz2042, zzz2043, Zero, Succ(zzz20450), bb) → new_mkVBalBranch(zzz2043, zzz2042, Branch(zzz2033, zzz2034, Pos(Succ(zzz2035)), zzz2036, zzz2037), bb)
new_mkVBalBranch3MkVBalBranch26(zzz1133, zzz1134, zzz1135, zzz1136, zzz1137, zzz1138, zzz1139, zzz1140, zzz1141, zzz1142, Succ(zzz11430), Succ(zzz11440), be) → new_mkVBalBranch3MkVBalBranch26(zzz1133, zzz1134, zzz1135, zzz1136, zzz1137, zzz1138, zzz1139, zzz1140, zzz1141, zzz1142, zzz11430, zzz11440, be)
new_mkVBalBranch3MkVBalBranch25(zzz537, zzz538, zzz539, zzz540, zzz541, zzz542, zzz543, zzz544, zzz545, zzz546, zzz547, Succ(zzz5480), Zero, bc) → new_mkVBalBranch3MkVBalBranch15(zzz537, zzz538, zzz539, zzz540, zzz541, zzz542, zzz543, zzz544, zzz545, zzz546, zzz547, new_primPlusNat2(new_primPlusNat3(Succ(new_primPlusNat3(new_primPlusNat1(zzz539), zzz539)), Succ(zzz539)), Succ(zzz539)), bc)
new_mkVBalBranch3MkVBalBranch24(zzz340, zzz341, Neg(Succ(Succ(Succ(zzz3420000)))), zzz343, zzz344, zzz520, zzz521, Zero, zzz523, zzz524, zzz31, Succ(Zero), h) → new_mkVBalBranch3MkVBalBranch26(zzz340, zzz341, Succ(Succ(zzz3420000)), zzz343, zzz344, zzz520, zzz521, zzz523, zzz524, zzz31, Succ(zzz3420000), Zero, h)
new_mkVBalBranch3MkVBalBranch24(zzz340, zzz341, Neg(Succ(Zero)), zzz343, zzz344, zzz520, zzz521, Zero, zzz523, zzz524, zzz31, Zero, h) → new_mkVBalBranch3MkVBalBranch29(zzz340, zzz341, Zero, zzz343, zzz344, zzz520, zzz521, zzz523, zzz524, zzz31, h)
new_mkVBalBranch3MkVBalBranch20(zzz929, zzz930, zzz931, zzz932, zzz933, zzz934, zzz935, zzz936, zzz937, zzz938, zzz939, Zero, Succ(zzz9410), ba) → new_mkVBalBranch(zzz939, Branch(zzz934, zzz935, Pos(Succ(zzz936)), zzz937, zzz938), zzz932, ba)
new_mkVBalBranch3MkVBalBranch17(zzz340, zzz341, zzz34200, zzz343, zzz344, zzz520, zzz521, zzz52200, zzz523, zzz524, zzz31, h) → new_mkVBalBranch(zzz31, zzz524, Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), h)
new_mkVBalBranch3MkVBalBranch26(zzz1133, zzz1134, zzz1135, zzz1136, zzz1137, zzz1138, zzz1139, zzz1140, zzz1141, zzz1142, Zero, Zero, be) → new_mkVBalBranch3MkVBalBranch29(zzz1133, zzz1134, zzz1135, zzz1136, zzz1137, zzz1138, zzz1139, zzz1140, zzz1141, zzz1142, be)
new_mkVBalBranch3MkVBalBranch20(zzz929, zzz930, zzz931, zzz932, zzz933, zzz934, zzz935, zzz936, zzz937, zzz938, zzz939, Zero, Zero, ba) → new_mkVBalBranch3MkVBalBranch23(zzz929, zzz930, zzz931, zzz932, zzz933, zzz934, zzz935, zzz936, zzz937, zzz938, zzz939, ba)
new_mkVBalBranch3MkVBalBranch24(zzz340, zzz341, Neg(Succ(Succ(Zero))), zzz343, zzz344, zzz520, zzz521, Succ(zzz522000), zzz523, zzz524, zzz31, Succ(Zero), h) → new_mkVBalBranch3MkVBalBranch25(zzz340, zzz341, Succ(Zero), zzz343, zzz344, zzz520, zzz521, zzz522000, zzz523, zzz524, zzz31, Zero, Succ(zzz522000), h)
new_mkVBalBranch3MkVBalBranch20(zzz929, zzz930, zzz931, zzz932, zzz933, zzz934, zzz935, zzz936, zzz937, zzz938, zzz939, Succ(zzz9400), Succ(zzz9410), ba) → new_mkVBalBranch3MkVBalBranch20(zzz929, zzz930, zzz931, zzz932, zzz933, zzz934, zzz935, zzz936, zzz937, zzz938, zzz939, zzz9400, zzz9410, ba)
new_mkVBalBranch3MkVBalBranch24(zzz340, zzz341, Neg(Succ(Succ(Succ(zzz3420000)))), zzz343, zzz344, zzz520, zzz521, Succ(zzz522000), zzz523, zzz524, zzz31, Succ(Zero), h) → new_mkVBalBranch3MkVBalBranch25(zzz340, zzz341, Succ(Succ(zzz3420000)), zzz343, zzz344, zzz520, zzz521, zzz522000, zzz523, zzz524, zzz31, Succ(zzz3420000), Succ(zzz522000), h)
new_mkVBalBranch3MkVBalBranch26(zzz1133, zzz1134, zzz1135, zzz1136, zzz1137, zzz1138, zzz1139, zzz1140, zzz1141, zzz1142, Succ(zzz11430), Zero, be) → new_mkVBalBranch3MkVBalBranch212(zzz1133, zzz1134, zzz1135, zzz1136, zzz1137, zzz1138, zzz1139, zzz1140, zzz1141, zzz1142, be)
new_mkVBalBranch3MkVBalBranch24(zzz340, zzz341, Neg(Succ(Succ(zzz342000))), zzz343, zzz344, zzz520, zzz521, Succ(zzz522000), zzz523, zzz524, zzz31, Zero, h) → new_mkVBalBranch3MkVBalBranch25(zzz340, zzz341, Succ(zzz342000), zzz343, zzz344, zzz520, zzz521, zzz522000, zzz523, zzz524, zzz31, zzz342000, zzz522000, h)
new_mkVBalBranch3MkVBalBranch29(zzz818, zzz819, zzz820, zzz821, zzz822, zzz823, zzz824, zzz825, zzz826, zzz827, bf) → new_mkVBalBranch3MkVBalBranch14(zzz818, zzz819, zzz820, zzz821, zzz822, zzz823, zzz824, zzz825, zzz826, zzz827, new_primPlusNat2(new_primMulNat0(zzz820), Succ(zzz820)), bf)
new_mkVBalBranch3MkVBalBranch11(zzz2033, zzz2034, zzz2035, zzz2036, zzz2037, zzz2038, zzz2039, zzz2040, zzz2041, zzz2042, zzz2043, Succ(zzz20440), Succ(zzz20450), bb) → new_mkVBalBranch3MkVBalBranch11(zzz2033, zzz2034, zzz2035, zzz2036, zzz2037, zzz2038, zzz2039, zzz2040, zzz2041, zzz2042, zzz2043, zzz20440, zzz20450, bb)
new_mkVBalBranch3MkVBalBranch25(zzz537, zzz538, zzz539, zzz540, zzz541, zzz542, zzz543, zzz544, zzz545, zzz546, zzz547, Succ(zzz5480), Succ(zzz5490), bc) → new_mkVBalBranch3MkVBalBranch25(zzz537, zzz538, zzz539, zzz540, zzz541, zzz542, zzz543, zzz544, zzz545, zzz546, zzz547, zzz5480, zzz5490, bc)
new_mkVBalBranch(zzz31, Branch(zzz520, zzz521, Neg(Succ(zzz52200)), zzz523, zzz524), Branch(zzz340, zzz341, zzz342, zzz343, zzz344), h) → new_mkVBalBranch3MkVBalBranch24(zzz340, zzz341, zzz342, zzz343, zzz344, zzz520, zzz521, zzz52200, zzz523, zzz524, zzz31, new_primPlusNat3(Succ(new_primPlusNat3(new_primPlusNat1(zzz52200), zzz52200)), Succ(zzz52200)), h)
new_mkVBalBranch3MkVBalBranch24(zzz340, zzz341, Neg(Succ(Zero)), zzz343, zzz344, zzz520, zzz521, Succ(zzz522000), zzz523, zzz524, zzz31, Zero, h) → new_mkVBalBranch3MkVBalBranch28(zzz340, zzz341, zzz343, zzz344, zzz520, zzz521, Succ(zzz522000), zzz523, zzz524, zzz31, h)
new_mkVBalBranch3MkVBalBranch210(zzz340, zzz341, zzz343, zzz344, zzz520, zzz521, zzz52200, zzz523, zzz524, zzz31, h) → new_mkVBalBranch(zzz31, Branch(zzz520, zzz521, Neg(Succ(zzz52200)), zzz523, zzz524), zzz343, h)
new_mkVBalBranch(zzz31, Branch(zzz520, zzz521, Pos(Succ(zzz52200)), zzz523, zzz524), Branch(zzz340, zzz341, zzz342, zzz343, zzz344), h) → new_mkVBalBranch3MkVBalBranch2(zzz340, zzz341, zzz342, zzz343, zzz344, zzz520, zzz521, zzz52200, zzz523, zzz524, zzz31, Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat3(new_primPlusNat1(zzz52200), zzz52200)), zzz52200))), h)
new_mkVBalBranch3MkVBalBranch26(zzz1133, zzz1134, zzz1135, zzz1136, zzz1137, zzz1138, zzz1139, zzz1140, zzz1141, zzz1142, Zero, Succ(zzz11440), be) → new_mkVBalBranch(zzz1142, Branch(zzz1138, zzz1139, Neg(Succ(Zero)), zzz1140, zzz1141), zzz1136, be)
new_mkVBalBranch3MkVBalBranch24(zzz340, zzz341, Neg(Succ(Succ(Zero))), zzz343, zzz344, zzz520, zzz521, Zero, zzz523, zzz524, zzz31, Succ(Zero), h) → new_mkVBalBranch3MkVBalBranch26(zzz340, zzz341, Succ(Zero), zzz343, zzz344, zzz520, zzz521, zzz523, zzz524, zzz31, Zero, Zero, h)
new_mkVBalBranch(zzz31, Branch(zzz520, zzz521, Pos(Zero), zzz523, zzz524), Branch(zzz340, zzz341, Pos(Succ(zzz34200)), zzz343, zzz344), h) → new_mkVBalBranch(zzz31, Branch(zzz520, zzz521, Pos(Zero), zzz523, zzz524), zzz343, h)
new_mkVBalBranch3MkVBalBranch2(zzz340, zzz341, Pos(Zero), zzz343, zzz344, zzz520, zzz521, zzz52200, zzz523, zzz524, zzz31, Succ(zzz680), h) → new_mkVBalBranch(zzz31, zzz524, Branch(zzz340, zzz341, Pos(Zero), zzz343, zzz344), h)
new_mkVBalBranch3MkVBalBranch24(zzz340, zzz341, Pos(zzz3420), zzz343, zzz344, zzz520, zzz521, zzz52200, zzz523, zzz524, zzz31, Zero, h) → new_mkVBalBranch3MkVBalBranch27(zzz340, zzz341, zzz3420, zzz343, zzz344, zzz520, zzz521, zzz52200, zzz523, zzz524, zzz31, h)
new_mkVBalBranch3MkVBalBranch15(zzz537, zzz538, zzz539, zzz540, zzz541, zzz542, zzz543, zzz544, zzz545, zzz546, zzz547, Succ(zzz6990), bc) → new_mkVBalBranch3MkVBalBranch16(zzz537, zzz538, zzz539, zzz540, zzz541, zzz542, zzz543, Succ(zzz544), zzz545, zzz546, zzz547, Succ(Succ(zzz544)), Succ(zzz6990), bc)
new_mkVBalBranch3MkVBalBranch24(zzz340, zzz341, Neg(Succ(Succ(Succ(zzz3420000)))), zzz343, zzz344, zzz520, zzz521, Zero, zzz523, zzz524, zzz31, Succ(Succ(zzz6900)), h) → new_mkVBalBranch3MkVBalBranch26(zzz340, zzz341, Succ(Succ(zzz3420000)), zzz343, zzz344, zzz520, zzz521, zzz523, zzz524, zzz31, Succ(zzz3420000), Succ(zzz6900), h)
new_mkVBalBranch(zzz31, Branch(zzz520, zzz521, Neg(Zero), zzz523, zzz524), Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), h) → new_mkVBalBranch3MkVBalBranch13(zzz340, zzz341, zzz34200, zzz343, zzz344, zzz520, zzz521, zzz523, zzz524, zzz31, new_primPlusNat2(new_primMulNat0(zzz34200), Succ(zzz34200)), h)
new_mkVBalBranch3MkVBalBranch27(zzz340, zzz341, zzz3420, zzz343, zzz344, zzz520, zzz521, zzz52200, zzz523, zzz524, zzz31, h) → new_mkVBalBranch(zzz31, Branch(zzz520, zzz521, Neg(Succ(zzz52200)), zzz523, zzz524), zzz343, h)
new_mkVBalBranch3MkVBalBranch24(zzz340, zzz341, Pos(zzz3420), zzz343, zzz344, zzz520, zzz521, zzz52200, zzz523, zzz524, zzz31, Succ(zzz690), h) → new_mkVBalBranch(zzz31, Branch(zzz520, zzz521, Neg(Succ(zzz52200)), zzz523, zzz524), zzz343, h)
new_mkVBalBranch3MkVBalBranch12(zzz340, zzz341, zzz34200, zzz343, zzz344, zzz520, zzz521, zzz523, zzz524, zzz31, Succ(zzz1250), h) → new_mkVBalBranch(zzz31, zzz524, Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), h)
new_mkVBalBranch3MkVBalBranch28(zzz340, zzz341, zzz343, zzz344, zzz520, zzz521, zzz52200, zzz523, zzz524, zzz31, h) → new_mkVBalBranch(zzz31, Branch(zzz520, zzz521, Neg(Succ(zzz52200)), zzz523, zzz524), zzz343, h)
new_mkVBalBranch3MkVBalBranch24(zzz340, zzz341, Neg(Succ(Succ(Zero))), zzz343, zzz344, zzz520, zzz521, Zero, zzz523, zzz524, zzz31, Succ(Succ(zzz6900)), h) → new_mkVBalBranch3MkVBalBranch26(zzz340, zzz341, Succ(Zero), zzz343, zzz344, zzz520, zzz521, zzz523, zzz524, zzz31, Zero, Succ(zzz6900), h)
new_mkVBalBranch3MkVBalBranch211(zzz537, zzz538, zzz539, zzz540, zzz541, zzz542, zzz543, zzz544, zzz545, zzz546, zzz547, bc) → new_mkVBalBranch3MkVBalBranch15(zzz537, zzz538, zzz539, zzz540, zzz541, zzz542, zzz543, zzz544, zzz545, zzz546, zzz547, new_primPlusNat2(new_primPlusNat3(Succ(new_primPlusNat3(new_primPlusNat1(zzz539), zzz539)), Succ(zzz539)), Succ(zzz539)), bc)
new_mkVBalBranch(zzz31, Branch(zzz520, zzz521, Pos(Zero), zzz523, zzz524), Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), h) → new_mkVBalBranch3MkVBalBranch12(zzz340, zzz341, zzz34200, zzz343, zzz344, zzz520, zzz521, zzz523, zzz524, zzz31, new_primPlusNat2(new_primMulNat0(zzz34200), Succ(zzz34200)), h)
new_mkVBalBranch3MkVBalBranch1(zzz340, zzz341, zzz34200, zzz343, zzz344, zzz520, zzz521, zzz52200, zzz523, zzz524, zzz31, Succ(zzz1430), h) → new_mkVBalBranch(zzz31, zzz524, Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), h)
new_mkVBalBranch3MkVBalBranch24(zzz340, zzz341, Neg(Succ(Zero)), zzz343, zzz344, zzz520, zzz521, zzz52200, zzz523, zzz524, zzz31, Succ(zzz690), h) → new_mkVBalBranch(zzz31, Branch(zzz520, zzz521, Neg(Succ(zzz52200)), zzz523, zzz524), zzz343, h)
new_mkVBalBranch3MkVBalBranch13(zzz340, zzz341, zzz34200, zzz343, zzz344, zzz520, zzz521, zzz523, zzz524, zzz31, Succ(zzz1290), h) → new_mkVBalBranch(zzz31, zzz524, Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), h)
new_mkVBalBranch3MkVBalBranch2(zzz340, zzz341, Pos(Succ(zzz34200)), zzz343, zzz344, zzz520, zzz521, zzz52200, zzz523, zzz524, zzz31, Succ(zzz680), h) → new_mkVBalBranch3MkVBalBranch20(zzz340, zzz341, zzz34200, zzz343, zzz344, zzz520, zzz521, zzz52200, zzz523, zzz524, zzz31, Succ(new_primPlusNat2(zzz680, zzz52200)), zzz34200, h)
new_mkVBalBranch3MkVBalBranch24(zzz340, zzz341, Neg(Zero), zzz343, zzz344, zzz520, zzz521, zzz52200, zzz523, zzz524, zzz31, Succ(zzz690), h) → new_mkVBalBranch(zzz31, Branch(zzz520, zzz521, Neg(Succ(zzz52200)), zzz523, zzz524), zzz343, h)
new_mkVBalBranch(zzz31, Branch(zzz520, zzz521, Neg(Zero), zzz523, zzz524), Branch(zzz340, zzz341, Pos(Succ(zzz34200)), zzz343, zzz344), h) → new_mkVBalBranch(zzz31, Branch(zzz520, zzz521, Neg(Zero), zzz523, zzz524), zzz343, h)
new_mkVBalBranch3MkVBalBranch24(zzz340, zzz341, Neg(Succ(Succ(zzz342000))), zzz343, zzz344, zzz520, zzz521, Zero, zzz523, zzz524, zzz31, Zero, h) → new_mkVBalBranch3MkVBalBranch14(zzz340, zzz341, Succ(zzz342000), zzz343, zzz344, zzz520, zzz521, zzz523, zzz524, zzz31, new_primPlusNat2(new_primPlusNat3(Succ(new_primPlusNat3(new_primPlusNat1(Succ(zzz342000)), Succ(zzz342000))), Succ(Succ(zzz342000))), Succ(Succ(zzz342000))), h)
new_mkVBalBranch3MkVBalBranch1(zzz340, zzz341, zzz34200, zzz343, zzz344, zzz520, zzz521, zzz52200, zzz523, zzz524, zzz31, Zero, h) → new_mkVBalBranch3MkVBalBranch17(zzz340, zzz341, zzz34200, zzz343, zzz344, zzz520, zzz521, zzz52200, zzz523, zzz524, zzz31, h)
new_mkVBalBranch3MkVBalBranch16(zzz1702, zzz1703, zzz1704, zzz1705, zzz1706, zzz1707, zzz1708, zzz1709, zzz1710, zzz1711, zzz1712, Succ(zzz17130), Succ(zzz17140), bd) → new_mkVBalBranch3MkVBalBranch16(zzz1702, zzz1703, zzz1704, zzz1705, zzz1706, zzz1707, zzz1708, zzz1709, zzz1710, zzz1711, zzz1712, zzz17130, zzz17140, bd)
new_mkVBalBranch3MkVBalBranch25(zzz537, zzz538, zzz539, zzz540, zzz541, zzz542, zzz543, zzz544, zzz545, zzz546, zzz547, Zero, Succ(zzz5490), bc) → new_mkVBalBranch(zzz547, Branch(zzz542, zzz543, Neg(Succ(Succ(zzz544))), zzz545, zzz546), zzz540, bc)
new_mkVBalBranch3MkVBalBranch10(zzz929, zzz930, zzz931, zzz932, zzz933, zzz934, zzz935, zzz936, zzz937, zzz938, zzz939, Succ(zzz10020), ba) → new_mkVBalBranch3MkVBalBranch11(zzz929, zzz930, zzz931, zzz932, zzz933, zzz934, zzz935, zzz936, zzz937, zzz938, zzz939, Succ(zzz10020), Succ(zzz936), ba)
new_mkVBalBranch3MkVBalBranch212(zzz818, zzz819, zzz820, zzz821, zzz822, zzz823, zzz824, zzz825, zzz826, zzz827, bf) → new_mkVBalBranch3MkVBalBranch14(zzz818, zzz819, zzz820, zzz821, zzz822, zzz823, zzz824, zzz825, zzz826, zzz827, new_primPlusNat2(new_primMulNat0(zzz820), Succ(zzz820)), bf)
new_mkVBalBranch3MkVBalBranch14(zzz818, zzz819, zzz820, zzz821, zzz822, zzz823, zzz824, zzz825, zzz826, zzz827, Succ(zzz8960), bf) → new_mkVBalBranch3MkVBalBranch16(zzz818, zzz819, zzz820, zzz821, zzz822, zzz823, zzz824, Zero, zzz825, zzz826, zzz827, Succ(Zero), Succ(zzz8960), bf)
new_mkVBalBranch3MkVBalBranch24(zzz340, zzz341, Neg(Succ(Succ(Succ(zzz3420000)))), zzz343, zzz344, zzz520, zzz521, Succ(zzz522000), zzz523, zzz524, zzz31, Succ(Succ(zzz6900)), h) → new_mkVBalBranch3MkVBalBranch25(zzz340, zzz341, Succ(Succ(zzz3420000)), zzz343, zzz344, zzz520, zzz521, zzz522000, zzz523, zzz524, zzz31, Succ(zzz3420000), Succ(Succ(new_primPlusNat2(zzz6900, zzz522000))), h)
new_mkVBalBranch3MkVBalBranch24(zzz340, zzz341, Neg(Zero), zzz343, zzz344, zzz520, zzz521, zzz52200, zzz523, zzz524, zzz31, Zero, h) → new_mkVBalBranch3MkVBalBranch210(zzz340, zzz341, zzz343, zzz344, zzz520, zzz521, zzz52200, zzz523, zzz524, zzz31, h)
new_mkVBalBranch3MkVBalBranch24(zzz340, zzz341, Neg(Succ(Succ(Zero))), zzz343, zzz344, zzz520, zzz521, Succ(zzz522000), zzz523, zzz524, zzz31, Succ(Succ(zzz6900)), h) → new_mkVBalBranch3MkVBalBranch25(zzz340, zzz341, Succ(Zero), zzz343, zzz344, zzz520, zzz521, zzz522000, zzz523, zzz524, zzz31, Zero, Succ(Succ(new_primPlusNat2(zzz6900, zzz522000))), h)
new_mkVBalBranch3MkVBalBranch20(zzz929, zzz930, zzz931, zzz932, zzz933, zzz934, zzz935, zzz936, zzz937, zzz938, zzz939, Succ(zzz9400), Zero, ba) → new_mkVBalBranch3MkVBalBranch10(zzz929, zzz930, zzz931, zzz932, zzz933, zzz934, zzz935, zzz936, zzz937, zzz938, zzz939, new_primPlusNat2(new_primPlusNat3(Succ(new_primPlusNat3(new_primPlusNat1(zzz931), zzz931)), Succ(zzz931)), Succ(zzz931)), ba)
new_mkVBalBranch3MkVBalBranch23(zzz929, zzz930, zzz931, zzz932, zzz933, zzz934, zzz935, zzz936, zzz937, zzz938, zzz939, ba) → new_mkVBalBranch3MkVBalBranch10(zzz929, zzz930, zzz931, zzz932, zzz933, zzz934, zzz935, zzz936, zzz937, zzz938, zzz939, new_primPlusNat2(new_primMulNat0(zzz931), Succ(zzz931)), ba)
new_mkVBalBranch3MkVBalBranch2(zzz340, zzz341, Neg(Zero), zzz343, zzz344, zzz520, zzz521, zzz52200, zzz523, zzz524, zzz31, Succ(zzz680), h) → new_mkVBalBranch(zzz31, zzz524, Branch(zzz340, zzz341, Neg(Zero), zzz343, zzz344), h)
new_mkVBalBranch3MkVBalBranch2(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344, zzz520, zzz521, zzz52200, zzz523, zzz524, zzz31, Succ(zzz680), h) → new_mkVBalBranch3MkVBalBranch1(zzz340, zzz341, zzz34200, zzz343, zzz344, zzz520, zzz521, zzz52200, zzz523, zzz524, zzz31, new_primPlusNat2(Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat3(new_primPlusNat1(zzz34200), zzz34200)), zzz34200))), Succ(zzz34200)), h)
new_mkVBalBranch3MkVBalBranch16(zzz1702, zzz1703, zzz1704, zzz1705, zzz1706, zzz1707, zzz1708, zzz1709, zzz1710, zzz1711, zzz1712, Zero, Succ(zzz17140), bd) → new_mkVBalBranch(zzz1712, zzz1711, Branch(zzz1702, zzz1703, Neg(Succ(zzz1704)), zzz1705, zzz1706), bd)
new_mkVBalBranch3MkVBalBranch10(zzz929, zzz930, zzz931, zzz932, zzz933, zzz934, zzz935, zzz936, zzz937, zzz938, zzz939, Zero, ba) → new_mkVBalBranch3MkVBalBranch11(zzz929, zzz930, zzz931, zzz932, zzz933, zzz934, zzz935, zzz936, zzz937, zzz938, zzz939, Zero, Succ(zzz936), ba)
new_mkVBalBranch3MkVBalBranch25(zzz537, zzz538, zzz539, zzz540, zzz541, zzz542, zzz543, zzz544, zzz545, zzz546, zzz547, Zero, Zero, bc) → new_mkVBalBranch3MkVBalBranch211(zzz537, zzz538, zzz539, zzz540, zzz541, zzz542, zzz543, zzz544, zzz545, zzz546, zzz547, bc)

The TRS R consists of the following rules:

new_primMulNat0(zzz6200) → new_primPlusNat3(Succ(new_primPlusNat3(new_primPlusNat1(zzz6200), zzz6200)), Succ(zzz6200))
new_primPlusNat2(Succ(zzz900), Succ(zzz9100)) → Succ(Succ(new_primPlusNat2(zzz900, zzz9100)))
new_primPlusNat2(Zero, Succ(zzz9100)) → Succ(zzz9100)
new_primPlusNat2(Zero, Zero) → Zero
new_primPlusNat2(Succ(zzz900), Zero) → Succ(zzz900)
new_primPlusNat1(Zero) → Zero
new_primPlusNat1(Succ(zzz62000)) → Succ(Succ(new_primPlusNat1(zzz62000)))
new_primPlusNat3(zzz90, Succ(zzz910)) → Succ(Succ(new_primPlusNat2(zzz90, zzz910)))
new_primPlusNat3(zzz90, Zero) → Succ(zzz90)

The set Q consists of the following terms:

new_primPlusNat2(Zero, Succ(x0))
new_primMulNat0(x0)
new_primPlusNat3(x0, Succ(x1))
new_primPlusNat2(Succ(x0), Succ(x1))
new_primPlusNat3(x0, Zero)
new_primPlusNat1(Zero)
new_primPlusNat2(Zero, Zero)
new_primPlusNat1(Succ(x0))
new_primPlusNat2(Succ(x0), Zero)

We have to consider all minimal (P,Q,R)-chains.
By rewriting [15] the rule new_mkVBalBranch(zzz31, Branch(zzz520, zzz521, Pos(Zero), zzz523, zzz524), Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), h) → new_mkVBalBranch3MkVBalBranch12(zzz340, zzz341, zzz34200, zzz343, zzz344, zzz520, zzz521, zzz523, zzz524, zzz31, new_primPlusNat2(new_primMulNat0(zzz34200), Succ(zzz34200)), h) at position [10,0] we obtained the following new rules:

new_mkVBalBranch(zzz31, Branch(zzz520, zzz521, Pos(Zero), zzz523, zzz524), Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), h) → new_mkVBalBranch3MkVBalBranch12(zzz340, zzz341, zzz34200, zzz343, zzz344, zzz520, zzz521, zzz523, zzz524, zzz31, new_primPlusNat2(new_primPlusNat3(Succ(new_primPlusNat3(new_primPlusNat1(zzz34200), zzz34200)), Succ(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
                                    ↳ DependencyGraphProof
                                      ↳ QDP
                                        ↳ Rewriting
                                          ↳ QDP
                                            ↳ Rewriting
                                              ↳ QDP
                                                ↳ Rewriting
                                                  ↳ QDP
                                                    ↳ Rewriting
                                                      ↳ QDP
                                                        ↳ Rewriting
                                                          ↳ QDP
                                                            ↳ Rewriting
                                                              ↳ QDP
                                                                ↳ Rewriting
                                                                  ↳ QDP
                                                                    ↳ Rewriting
                                                                      ↳ QDP
                                                                        ↳ Rewriting
                                                                          ↳ QDP
                                                                            ↳ Rewriting
                                                                              ↳ QDP
                                                                                ↳ Rewriting
                                                                                  ↳ QDP
                                                                                    ↳ Rewriting
                                                                                      ↳ QDP
                                                                                        ↳ Rewriting
                                                                                          ↳ QDP
                                                                                            ↳ UsableRulesProof
                                                                                              ↳ QDP
                                                                                                ↳ QReductionProof
                                                                                                  ↳ QDP
                                                                                                    ↳ Rewriting
                                                                                                      ↳ QDP
                                                                                                        ↳ Rewriting
                                                                                                          ↳ QDP
                                                                                                            ↳ Rewriting
                                                                                                              ↳ QDP
                                                                                                                ↳ Rewriting
                                                                                                                  ↳ QDP
                                                                                                                    ↳ Rewriting
                                                                                                                      ↳ QDP
                                                                                                                        ↳ Rewriting
                                                                                                                          ↳ QDP
                                                                                                                            ↳ DependencyGraphProof
                                                                                                                              ↳ QDP
                                                                                                                                ↳ Rewriting
                                                                                                                                  ↳ QDP
                                                                                                                                    ↳ Rewriting
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP

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

new_mkVBalBranch3MkVBalBranch11(zzz2033, zzz2034, zzz2035, zzz2036, zzz2037, zzz2038, zzz2039, zzz2040, zzz2041, zzz2042, zzz2043, Zero, Succ(zzz20450), bb) → new_mkVBalBranch(zzz2043, zzz2042, Branch(zzz2033, zzz2034, Pos(Succ(zzz2035)), zzz2036, zzz2037), bb)
new_mkVBalBranch3MkVBalBranch26(zzz1133, zzz1134, zzz1135, zzz1136, zzz1137, zzz1138, zzz1139, zzz1140, zzz1141, zzz1142, Succ(zzz11430), Succ(zzz11440), be) → new_mkVBalBranch3MkVBalBranch26(zzz1133, zzz1134, zzz1135, zzz1136, zzz1137, zzz1138, zzz1139, zzz1140, zzz1141, zzz1142, zzz11430, zzz11440, be)
new_mkVBalBranch3MkVBalBranch25(zzz537, zzz538, zzz539, zzz540, zzz541, zzz542, zzz543, zzz544, zzz545, zzz546, zzz547, Succ(zzz5480), Zero, bc) → new_mkVBalBranch3MkVBalBranch15(zzz537, zzz538, zzz539, zzz540, zzz541, zzz542, zzz543, zzz544, zzz545, zzz546, zzz547, new_primPlusNat2(new_primPlusNat3(Succ(new_primPlusNat3(new_primPlusNat1(zzz539), zzz539)), Succ(zzz539)), Succ(zzz539)), bc)
new_mkVBalBranch3MkVBalBranch24(zzz340, zzz341, Neg(Succ(Succ(Succ(zzz3420000)))), zzz343, zzz344, zzz520, zzz521, Zero, zzz523, zzz524, zzz31, Succ(Zero), h) → new_mkVBalBranch3MkVBalBranch26(zzz340, zzz341, Succ(Succ(zzz3420000)), zzz343, zzz344, zzz520, zzz521, zzz523, zzz524, zzz31, Succ(zzz3420000), Zero, h)
new_mkVBalBranch3MkVBalBranch24(zzz340, zzz341, Neg(Succ(Zero)), zzz343, zzz344, zzz520, zzz521, Zero, zzz523, zzz524, zzz31, Zero, h) → new_mkVBalBranch3MkVBalBranch29(zzz340, zzz341, Zero, zzz343, zzz344, zzz520, zzz521, zzz523, zzz524, zzz31, h)
new_mkVBalBranch3MkVBalBranch20(zzz929, zzz930, zzz931, zzz932, zzz933, zzz934, zzz935, zzz936, zzz937, zzz938, zzz939, Zero, Succ(zzz9410), ba) → new_mkVBalBranch(zzz939, Branch(zzz934, zzz935, Pos(Succ(zzz936)), zzz937, zzz938), zzz932, ba)
new_mkVBalBranch3MkVBalBranch17(zzz340, zzz341, zzz34200, zzz343, zzz344, zzz520, zzz521, zzz52200, zzz523, zzz524, zzz31, h) → new_mkVBalBranch(zzz31, zzz524, Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), h)
new_mkVBalBranch3MkVBalBranch26(zzz1133, zzz1134, zzz1135, zzz1136, zzz1137, zzz1138, zzz1139, zzz1140, zzz1141, zzz1142, Zero, Zero, be) → new_mkVBalBranch3MkVBalBranch29(zzz1133, zzz1134, zzz1135, zzz1136, zzz1137, zzz1138, zzz1139, zzz1140, zzz1141, zzz1142, be)
new_mkVBalBranch3MkVBalBranch20(zzz929, zzz930, zzz931, zzz932, zzz933, zzz934, zzz935, zzz936, zzz937, zzz938, zzz939, Zero, Zero, ba) → new_mkVBalBranch3MkVBalBranch23(zzz929, zzz930, zzz931, zzz932, zzz933, zzz934, zzz935, zzz936, zzz937, zzz938, zzz939, ba)
new_mkVBalBranch3MkVBalBranch24(zzz340, zzz341, Neg(Succ(Succ(Zero))), zzz343, zzz344, zzz520, zzz521, Succ(zzz522000), zzz523, zzz524, zzz31, Succ(Zero), h) → new_mkVBalBranch3MkVBalBranch25(zzz340, zzz341, Succ(Zero), zzz343, zzz344, zzz520, zzz521, zzz522000, zzz523, zzz524, zzz31, Zero, Succ(zzz522000), h)
new_mkVBalBranch3MkVBalBranch24(zzz340, zzz341, Neg(Succ(Succ(Succ(zzz3420000)))), zzz343, zzz344, zzz520, zzz521, Succ(zzz522000), zzz523, zzz524, zzz31, Succ(Zero), h) → new_mkVBalBranch3MkVBalBranch25(zzz340, zzz341, Succ(Succ(zzz3420000)), zzz343, zzz344, zzz520, zzz521, zzz522000, zzz523, zzz524, zzz31, Succ(zzz3420000), Succ(zzz522000), h)
new_mkVBalBranch3MkVBalBranch20(zzz929, zzz930, zzz931, zzz932, zzz933, zzz934, zzz935, zzz936, zzz937, zzz938, zzz939, Succ(zzz9400), Succ(zzz9410), ba) → new_mkVBalBranch3MkVBalBranch20(zzz929, zzz930, zzz931, zzz932, zzz933, zzz934, zzz935, zzz936, zzz937, zzz938, zzz939, zzz9400, zzz9410, ba)
new_mkVBalBranch3MkVBalBranch24(zzz340, zzz341, Neg(Succ(Succ(zzz342000))), zzz343, zzz344, zzz520, zzz521, Succ(zzz522000), zzz523, zzz524, zzz31, Zero, h) → new_mkVBalBranch3MkVBalBranch25(zzz340, zzz341, Succ(zzz342000), zzz343, zzz344, zzz520, zzz521, zzz522000, zzz523, zzz524, zzz31, zzz342000, zzz522000, h)
new_mkVBalBranch3MkVBalBranch26(zzz1133, zzz1134, zzz1135, zzz1136, zzz1137, zzz1138, zzz1139, zzz1140, zzz1141, zzz1142, Succ(zzz11430), Zero, be) → new_mkVBalBranch3MkVBalBranch212(zzz1133, zzz1134, zzz1135, zzz1136, zzz1137, zzz1138, zzz1139, zzz1140, zzz1141, zzz1142, be)
new_mkVBalBranch3MkVBalBranch29(zzz818, zzz819, zzz820, zzz821, zzz822, zzz823, zzz824, zzz825, zzz826, zzz827, bf) → new_mkVBalBranch3MkVBalBranch14(zzz818, zzz819, zzz820, zzz821, zzz822, zzz823, zzz824, zzz825, zzz826, zzz827, new_primPlusNat2(new_primMulNat0(zzz820), Succ(zzz820)), bf)
new_mkVBalBranch3MkVBalBranch11(zzz2033, zzz2034, zzz2035, zzz2036, zzz2037, zzz2038, zzz2039, zzz2040, zzz2041, zzz2042, zzz2043, Succ(zzz20440), Succ(zzz20450), bb) → new_mkVBalBranch3MkVBalBranch11(zzz2033, zzz2034, zzz2035, zzz2036, zzz2037, zzz2038, zzz2039, zzz2040, zzz2041, zzz2042, zzz2043, zzz20440, zzz20450, bb)
new_mkVBalBranch3MkVBalBranch25(zzz537, zzz538, zzz539, zzz540, zzz541, zzz542, zzz543, zzz544, zzz545, zzz546, zzz547, Succ(zzz5480), Succ(zzz5490), bc) → new_mkVBalBranch3MkVBalBranch25(zzz537, zzz538, zzz539, zzz540, zzz541, zzz542, zzz543, zzz544, zzz545, zzz546, zzz547, zzz5480, zzz5490, bc)
new_mkVBalBranch(zzz31, Branch(zzz520, zzz521, Neg(Succ(zzz52200)), zzz523, zzz524), Branch(zzz340, zzz341, zzz342, zzz343, zzz344), h) → new_mkVBalBranch3MkVBalBranch24(zzz340, zzz341, zzz342, zzz343, zzz344, zzz520, zzz521, zzz52200, zzz523, zzz524, zzz31, new_primPlusNat3(Succ(new_primPlusNat3(new_primPlusNat1(zzz52200), zzz52200)), Succ(zzz52200)), h)
new_mkVBalBranch3MkVBalBranch24(zzz340, zzz341, Neg(Succ(Zero)), zzz343, zzz344, zzz520, zzz521, Succ(zzz522000), zzz523, zzz524, zzz31, Zero, h) → new_mkVBalBranch3MkVBalBranch28(zzz340, zzz341, zzz343, zzz344, zzz520, zzz521, Succ(zzz522000), zzz523, zzz524, zzz31, h)
new_mkVBalBranch(zzz31, Branch(zzz520, zzz521, Pos(Succ(zzz52200)), zzz523, zzz524), Branch(zzz340, zzz341, zzz342, zzz343, zzz344), h) → new_mkVBalBranch3MkVBalBranch2(zzz340, zzz341, zzz342, zzz343, zzz344, zzz520, zzz521, zzz52200, zzz523, zzz524, zzz31, Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat3(new_primPlusNat1(zzz52200), zzz52200)), zzz52200))), h)
new_mkVBalBranch3MkVBalBranch210(zzz340, zzz341, zzz343, zzz344, zzz520, zzz521, zzz52200, zzz523, zzz524, zzz31, h) → new_mkVBalBranch(zzz31, Branch(zzz520, zzz521, Neg(Succ(zzz52200)), zzz523, zzz524), zzz343, h)
new_mkVBalBranch3MkVBalBranch26(zzz1133, zzz1134, zzz1135, zzz1136, zzz1137, zzz1138, zzz1139, zzz1140, zzz1141, zzz1142, Zero, Succ(zzz11440), be) → new_mkVBalBranch(zzz1142, Branch(zzz1138, zzz1139, Neg(Succ(Zero)), zzz1140, zzz1141), zzz1136, be)
new_mkVBalBranch3MkVBalBranch24(zzz340, zzz341, Neg(Succ(Succ(Zero))), zzz343, zzz344, zzz520, zzz521, Zero, zzz523, zzz524, zzz31, Succ(Zero), h) → new_mkVBalBranch3MkVBalBranch26(zzz340, zzz341, Succ(Zero), zzz343, zzz344, zzz520, zzz521, zzz523, zzz524, zzz31, Zero, Zero, h)
new_mkVBalBranch(zzz31, Branch(zzz520, zzz521, Pos(Zero), zzz523, zzz524), Branch(zzz340, zzz341, Pos(Succ(zzz34200)), zzz343, zzz344), h) → new_mkVBalBranch(zzz31, Branch(zzz520, zzz521, Pos(Zero), zzz523, zzz524), zzz343, h)
new_mkVBalBranch3MkVBalBranch2(zzz340, zzz341, Pos(Zero), zzz343, zzz344, zzz520, zzz521, zzz52200, zzz523, zzz524, zzz31, Succ(zzz680), h) → new_mkVBalBranch(zzz31, zzz524, Branch(zzz340, zzz341, Pos(Zero), zzz343, zzz344), h)
new_mkVBalBranch3MkVBalBranch24(zzz340, zzz341, Pos(zzz3420), zzz343, zzz344, zzz520, zzz521, zzz52200, zzz523, zzz524, zzz31, Zero, h) → new_mkVBalBranch3MkVBalBranch27(zzz340, zzz341, zzz3420, zzz343, zzz344, zzz520, zzz521, zzz52200, zzz523, zzz524, zzz31, h)
new_mkVBalBranch3MkVBalBranch24(zzz340, zzz341, Neg(Succ(Succ(Succ(zzz3420000)))), zzz343, zzz344, zzz520, zzz521, Zero, zzz523, zzz524, zzz31, Succ(Succ(zzz6900)), h) → new_mkVBalBranch3MkVBalBranch26(zzz340, zzz341, Succ(Succ(zzz3420000)), zzz343, zzz344, zzz520, zzz521, zzz523, zzz524, zzz31, Succ(zzz3420000), Succ(zzz6900), h)
new_mkVBalBranch3MkVBalBranch15(zzz537, zzz538, zzz539, zzz540, zzz541, zzz542, zzz543, zzz544, zzz545, zzz546, zzz547, Succ(zzz6990), bc) → new_mkVBalBranch3MkVBalBranch16(zzz537, zzz538, zzz539, zzz540, zzz541, zzz542, zzz543, Succ(zzz544), zzz545, zzz546, zzz547, Succ(Succ(zzz544)), Succ(zzz6990), bc)
new_mkVBalBranch(zzz31, Branch(zzz520, zzz521, Neg(Zero), zzz523, zzz524), Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), h) → new_mkVBalBranch3MkVBalBranch13(zzz340, zzz341, zzz34200, zzz343, zzz344, zzz520, zzz521, zzz523, zzz524, zzz31, new_primPlusNat2(new_primMulNat0(zzz34200), Succ(zzz34200)), h)
new_mkVBalBranch3MkVBalBranch27(zzz340, zzz341, zzz3420, zzz343, zzz344, zzz520, zzz521, zzz52200, zzz523, zzz524, zzz31, h) → new_mkVBalBranch(zzz31, Branch(zzz520, zzz521, Neg(Succ(zzz52200)), zzz523, zzz524), zzz343, h)
new_mkVBalBranch3MkVBalBranch24(zzz340, zzz341, Pos(zzz3420), zzz343, zzz344, zzz520, zzz521, zzz52200, zzz523, zzz524, zzz31, Succ(zzz690), h) → new_mkVBalBranch(zzz31, Branch(zzz520, zzz521, Neg(Succ(zzz52200)), zzz523, zzz524), zzz343, h)
new_mkVBalBranch3MkVBalBranch12(zzz340, zzz341, zzz34200, zzz343, zzz344, zzz520, zzz521, zzz523, zzz524, zzz31, Succ(zzz1250), h) → new_mkVBalBranch(zzz31, zzz524, Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), h)
new_mkVBalBranch3MkVBalBranch28(zzz340, zzz341, zzz343, zzz344, zzz520, zzz521, zzz52200, zzz523, zzz524, zzz31, h) → new_mkVBalBranch(zzz31, Branch(zzz520, zzz521, Neg(Succ(zzz52200)), zzz523, zzz524), zzz343, h)
new_mkVBalBranch(zzz31, Branch(zzz520, zzz521, Pos(Zero), zzz523, zzz524), Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), h) → new_mkVBalBranch3MkVBalBranch12(zzz340, zzz341, zzz34200, zzz343, zzz344, zzz520, zzz521, zzz523, zzz524, zzz31, new_primPlusNat2(new_primPlusNat3(Succ(new_primPlusNat3(new_primPlusNat1(zzz34200), zzz34200)), Succ(zzz34200)), Succ(zzz34200)), h)
new_mkVBalBranch3MkVBalBranch24(zzz340, zzz341, Neg(Succ(Succ(Zero))), zzz343, zzz344, zzz520, zzz521, Zero, zzz523, zzz524, zzz31, Succ(Succ(zzz6900)), h) → new_mkVBalBranch3MkVBalBranch26(zzz340, zzz341, Succ(Zero), zzz343, zzz344, zzz520, zzz521, zzz523, zzz524, zzz31, Zero, Succ(zzz6900), h)
new_mkVBalBranch3MkVBalBranch211(zzz537, zzz538, zzz539, zzz540, zzz541, zzz542, zzz543, zzz544, zzz545, zzz546, zzz547, bc) → new_mkVBalBranch3MkVBalBranch15(zzz537, zzz538, zzz539, zzz540, zzz541, zzz542, zzz543, zzz544, zzz545, zzz546, zzz547, new_primPlusNat2(new_primPlusNat3(Succ(new_primPlusNat3(new_primPlusNat1(zzz539), zzz539)), Succ(zzz539)), Succ(zzz539)), bc)
new_mkVBalBranch3MkVBalBranch1(zzz340, zzz341, zzz34200, zzz343, zzz344, zzz520, zzz521, zzz52200, zzz523, zzz524, zzz31, Succ(zzz1430), h) → new_mkVBalBranch(zzz31, zzz524, Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), h)
new_mkVBalBranch3MkVBalBranch24(zzz340, zzz341, Neg(Succ(Zero)), zzz343, zzz344, zzz520, zzz521, zzz52200, zzz523, zzz524, zzz31, Succ(zzz690), h) → new_mkVBalBranch(zzz31, Branch(zzz520, zzz521, Neg(Succ(zzz52200)), zzz523, zzz524), zzz343, h)
new_mkVBalBranch3MkVBalBranch13(zzz340, zzz341, zzz34200, zzz343, zzz344, zzz520, zzz521, zzz523, zzz524, zzz31, Succ(zzz1290), h) → new_mkVBalBranch(zzz31, zzz524, Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), h)
new_mkVBalBranch3MkVBalBranch2(zzz340, zzz341, Pos(Succ(zzz34200)), zzz343, zzz344, zzz520, zzz521, zzz52200, zzz523, zzz524, zzz31, Succ(zzz680), h) → new_mkVBalBranch3MkVBalBranch20(zzz340, zzz341, zzz34200, zzz343, zzz344, zzz520, zzz521, zzz52200, zzz523, zzz524, zzz31, Succ(new_primPlusNat2(zzz680, zzz52200)), zzz34200, h)
new_mkVBalBranch(zzz31, Branch(zzz520, zzz521, Neg(Zero), zzz523, zzz524), Branch(zzz340, zzz341, Pos(Succ(zzz34200)), zzz343, zzz344), h) → new_mkVBalBranch(zzz31, Branch(zzz520, zzz521, Neg(Zero), zzz523, zzz524), zzz343, h)
new_mkVBalBranch3MkVBalBranch24(zzz340, zzz341, Neg(Zero), zzz343, zzz344, zzz520, zzz521, zzz52200, zzz523, zzz524, zzz31, Succ(zzz690), h) → new_mkVBalBranch(zzz31, Branch(zzz520, zzz521, Neg(Succ(zzz52200)), zzz523, zzz524), zzz343, h)
new_mkVBalBranch3MkVBalBranch24(zzz340, zzz341, Neg(Succ(Succ(zzz342000))), zzz343, zzz344, zzz520, zzz521, Zero, zzz523, zzz524, zzz31, Zero, h) → new_mkVBalBranch3MkVBalBranch14(zzz340, zzz341, Succ(zzz342000), zzz343, zzz344, zzz520, zzz521, zzz523, zzz524, zzz31, new_primPlusNat2(new_primPlusNat3(Succ(new_primPlusNat3(new_primPlusNat1(Succ(zzz342000)), Succ(zzz342000))), Succ(Succ(zzz342000))), Succ(Succ(zzz342000))), h)
new_mkVBalBranch3MkVBalBranch1(zzz340, zzz341, zzz34200, zzz343, zzz344, zzz520, zzz521, zzz52200, zzz523, zzz524, zzz31, Zero, h) → new_mkVBalBranch3MkVBalBranch17(zzz340, zzz341, zzz34200, zzz343, zzz344, zzz520, zzz521, zzz52200, zzz523, zzz524, zzz31, h)
new_mkVBalBranch3MkVBalBranch16(zzz1702, zzz1703, zzz1704, zzz1705, zzz1706, zzz1707, zzz1708, zzz1709, zzz1710, zzz1711, zzz1712, Succ(zzz17130), Succ(zzz17140), bd) → new_mkVBalBranch3MkVBalBranch16(zzz1702, zzz1703, zzz1704, zzz1705, zzz1706, zzz1707, zzz1708, zzz1709, zzz1710, zzz1711, zzz1712, zzz17130, zzz17140, bd)
new_mkVBalBranch3MkVBalBranch25(zzz537, zzz538, zzz539, zzz540, zzz541, zzz542, zzz543, zzz544, zzz545, zzz546, zzz547, Zero, Succ(zzz5490), bc) → new_mkVBalBranch(zzz547, Branch(zzz542, zzz543, Neg(Succ(Succ(zzz544))), zzz545, zzz546), zzz540, bc)
new_mkVBalBranch3MkVBalBranch212(zzz818, zzz819, zzz820, zzz821, zzz822, zzz823, zzz824, zzz825, zzz826, zzz827, bf) → new_mkVBalBranch3MkVBalBranch14(zzz818, zzz819, zzz820, zzz821, zzz822, zzz823, zzz824, zzz825, zzz826, zzz827, new_primPlusNat2(new_primMulNat0(zzz820), Succ(zzz820)), bf)
new_mkVBalBranch3MkVBalBranch10(zzz929, zzz930, zzz931, zzz932, zzz933, zzz934, zzz935, zzz936, zzz937, zzz938, zzz939, Succ(zzz10020), ba) → new_mkVBalBranch3MkVBalBranch11(zzz929, zzz930, zzz931, zzz932, zzz933, zzz934, zzz935, zzz936, zzz937, zzz938, zzz939, Succ(zzz10020), Succ(zzz936), ba)
new_mkVBalBranch3MkVBalBranch14(zzz818, zzz819, zzz820, zzz821, zzz822, zzz823, zzz824, zzz825, zzz826, zzz827, Succ(zzz8960), bf) → new_mkVBalBranch3MkVBalBranch16(zzz818, zzz819, zzz820, zzz821, zzz822, zzz823, zzz824, Zero, zzz825, zzz826, zzz827, Succ(Zero), Succ(zzz8960), bf)
new_mkVBalBranch3MkVBalBranch24(zzz340, zzz341, Neg(Succ(Succ(Succ(zzz3420000)))), zzz343, zzz344, zzz520, zzz521, Succ(zzz522000), zzz523, zzz524, zzz31, Succ(Succ(zzz6900)), h) → new_mkVBalBranch3MkVBalBranch25(zzz340, zzz341, Succ(Succ(zzz3420000)), zzz343, zzz344, zzz520, zzz521, zzz522000, zzz523, zzz524, zzz31, Succ(zzz3420000), Succ(Succ(new_primPlusNat2(zzz6900, zzz522000))), h)
new_mkVBalBranch3MkVBalBranch24(zzz340, zzz341, Neg(Zero), zzz343, zzz344, zzz520, zzz521, zzz52200, zzz523, zzz524, zzz31, Zero, h) → new_mkVBalBranch3MkVBalBranch210(zzz340, zzz341, zzz343, zzz344, zzz520, zzz521, zzz52200, zzz523, zzz524, zzz31, h)
new_mkVBalBranch3MkVBalBranch24(zzz340, zzz341, Neg(Succ(Succ(Zero))), zzz343, zzz344, zzz520, zzz521, Succ(zzz522000), zzz523, zzz524, zzz31, Succ(Succ(zzz6900)), h) → new_mkVBalBranch3MkVBalBranch25(zzz340, zzz341, Succ(Zero), zzz343, zzz344, zzz520, zzz521, zzz522000, zzz523, zzz524, zzz31, Zero, Succ(Succ(new_primPlusNat2(zzz6900, zzz522000))), h)
new_mkVBalBranch3MkVBalBranch20(zzz929, zzz930, zzz931, zzz932, zzz933, zzz934, zzz935, zzz936, zzz937, zzz938, zzz939, Succ(zzz9400), Zero, ba) → new_mkVBalBranch3MkVBalBranch10(zzz929, zzz930, zzz931, zzz932, zzz933, zzz934, zzz935, zzz936, zzz937, zzz938, zzz939, new_primPlusNat2(new_primPlusNat3(Succ(new_primPlusNat3(new_primPlusNat1(zzz931), zzz931)), Succ(zzz931)), Succ(zzz931)), ba)
new_mkVBalBranch3MkVBalBranch23(zzz929, zzz930, zzz931, zzz932, zzz933, zzz934, zzz935, zzz936, zzz937, zzz938, zzz939, ba) → new_mkVBalBranch3MkVBalBranch10(zzz929, zzz930, zzz931, zzz932, zzz933, zzz934, zzz935, zzz936, zzz937, zzz938, zzz939, new_primPlusNat2(new_primMulNat0(zzz931), Succ(zzz931)), ba)
new_mkVBalBranch3MkVBalBranch2(zzz340, zzz341, Neg(Zero), zzz343, zzz344, zzz520, zzz521, zzz52200, zzz523, zzz524, zzz31, Succ(zzz680), h) → new_mkVBalBranch(zzz31, zzz524, Branch(zzz340, zzz341, Neg(Zero), zzz343, zzz344), h)
new_mkVBalBranch3MkVBalBranch2(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344, zzz520, zzz521, zzz52200, zzz523, zzz524, zzz31, Succ(zzz680), h) → new_mkVBalBranch3MkVBalBranch1(zzz340, zzz341, zzz34200, zzz343, zzz344, zzz520, zzz521, zzz52200, zzz523, zzz524, zzz31, new_primPlusNat2(Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat3(new_primPlusNat1(zzz34200), zzz34200)), zzz34200))), Succ(zzz34200)), h)
new_mkVBalBranch3MkVBalBranch16(zzz1702, zzz1703, zzz1704, zzz1705, zzz1706, zzz1707, zzz1708, zzz1709, zzz1710, zzz1711, zzz1712, Zero, Succ(zzz17140), bd) → new_mkVBalBranch(zzz1712, zzz1711, Branch(zzz1702, zzz1703, Neg(Succ(zzz1704)), zzz1705, zzz1706), bd)
new_mkVBalBranch3MkVBalBranch10(zzz929, zzz930, zzz931, zzz932, zzz933, zzz934, zzz935, zzz936, zzz937, zzz938, zzz939, Zero, ba) → new_mkVBalBranch3MkVBalBranch11(zzz929, zzz930, zzz931, zzz932, zzz933, zzz934, zzz935, zzz936, zzz937, zzz938, zzz939, Zero, Succ(zzz936), ba)
new_mkVBalBranch3MkVBalBranch25(zzz537, zzz538, zzz539, zzz540, zzz541, zzz542, zzz543, zzz544, zzz545, zzz546, zzz547, Zero, Zero, bc) → new_mkVBalBranch3MkVBalBranch211(zzz537, zzz538, zzz539, zzz540, zzz541, zzz542, zzz543, zzz544, zzz545, zzz546, zzz547, bc)

The TRS R consists of the following rules:

new_primMulNat0(zzz6200) → new_primPlusNat3(Succ(new_primPlusNat3(new_primPlusNat1(zzz6200), zzz6200)), Succ(zzz6200))
new_primPlusNat2(Succ(zzz900), Succ(zzz9100)) → Succ(Succ(new_primPlusNat2(zzz900, zzz9100)))
new_primPlusNat2(Zero, Succ(zzz9100)) → Succ(zzz9100)
new_primPlusNat2(Zero, Zero) → Zero
new_primPlusNat2(Succ(zzz900), Zero) → Succ(zzz900)
new_primPlusNat1(Zero) → Zero
new_primPlusNat1(Succ(zzz62000)) → Succ(Succ(new_primPlusNat1(zzz62000)))
new_primPlusNat3(zzz90, Succ(zzz910)) → Succ(Succ(new_primPlusNat2(zzz90, zzz910)))
new_primPlusNat3(zzz90, Zero) → Succ(zzz90)

The set Q consists of the following terms:

new_primPlusNat2(Zero, Succ(x0))
new_primMulNat0(x0)
new_primPlusNat3(x0, Succ(x1))
new_primPlusNat2(Succ(x0), Succ(x1))
new_primPlusNat3(x0, Zero)
new_primPlusNat1(Zero)
new_primPlusNat2(Zero, Zero)
new_primPlusNat1(Succ(x0))
new_primPlusNat2(Succ(x0), Zero)

We have to consider all minimal (P,Q,R)-chains.
By rewriting [15] the rule new_mkVBalBranch(zzz31, Branch(zzz520, zzz521, Neg(Succ(zzz52200)), zzz523, zzz524), Branch(zzz340, zzz341, zzz342, zzz343, zzz344), h) → new_mkVBalBranch3MkVBalBranch24(zzz340, zzz341, zzz342, zzz343, zzz344, zzz520, zzz521, zzz52200, zzz523, zzz524, zzz31, new_primPlusNat3(Succ(new_primPlusNat3(new_primPlusNat1(zzz52200), zzz52200)), Succ(zzz52200)), h) at position [11] we obtained the following new rules:

new_mkVBalBranch(zzz31, Branch(zzz520, zzz521, Neg(Succ(zzz52200)), zzz523, zzz524), Branch(zzz340, zzz341, zzz342, zzz343, zzz344), h) → new_mkVBalBranch3MkVBalBranch24(zzz340, zzz341, zzz342, zzz343, zzz344, zzz520, zzz521, zzz52200, zzz523, zzz524, zzz31, Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat3(new_primPlusNat1(zzz52200), zzz52200)), zzz52200))), 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
                                    ↳ DependencyGraphProof
                                      ↳ QDP
                                        ↳ Rewriting
                                          ↳ QDP
                                            ↳ Rewriting
                                              ↳ QDP
                                                ↳ Rewriting
                                                  ↳ QDP
                                                    ↳ Rewriting
                                                      ↳ QDP
                                                        ↳ Rewriting
                                                          ↳ QDP
                                                            ↳ Rewriting
                                                              ↳ QDP
                                                                ↳ Rewriting
                                                                  ↳ QDP
                                                                    ↳ Rewriting
                                                                      ↳ QDP
                                                                        ↳ Rewriting
                                                                          ↳ QDP
                                                                            ↳ Rewriting
                                                                              ↳ QDP
                                                                                ↳ Rewriting
                                                                                  ↳ QDP
                                                                                    ↳ Rewriting
                                                                                      ↳ QDP
                                                                                        ↳ Rewriting
                                                                                          ↳ QDP
                                                                                            ↳ UsableRulesProof
                                                                                              ↳ QDP
                                                                                                ↳ QReductionProof
                                                                                                  ↳ QDP
                                                                                                    ↳ Rewriting
                                                                                                      ↳ QDP
                                                                                                        ↳ Rewriting
                                                                                                          ↳ QDP
                                                                                                            ↳ Rewriting
                                                                                                              ↳ QDP
                                                                                                                ↳ Rewriting
                                                                                                                  ↳ QDP
                                                                                                                    ↳ Rewriting
                                                                                                                      ↳ QDP
                                                                                                                        ↳ Rewriting
                                                                                                                          ↳ QDP
                                                                                                                            ↳ DependencyGraphProof
                                                                                                                              ↳ QDP
                                                                                                                                ↳ Rewriting
                                                                                                                                  ↳ QDP
                                                                                                                                    ↳ Rewriting
                                                                                                                                      ↳ QDP
                                                                                                                                        ↳ DependencyGraphProof
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP

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

new_mkVBalBranch(zzz31, Branch(zzz520, zzz521, Neg(Succ(zzz52200)), zzz523, zzz524), Branch(zzz340, zzz341, zzz342, zzz343, zzz344), h) → new_mkVBalBranch3MkVBalBranch24(zzz340, zzz341, zzz342, zzz343, zzz344, zzz520, zzz521, zzz52200, zzz523, zzz524, zzz31, Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat3(new_primPlusNat1(zzz52200), zzz52200)), zzz52200))), h)
new_mkVBalBranch3MkVBalBranch11(zzz2033, zzz2034, zzz2035, zzz2036, zzz2037, zzz2038, zzz2039, zzz2040, zzz2041, zzz2042, zzz2043, Zero, Succ(zzz20450), bb) → new_mkVBalBranch(zzz2043, zzz2042, Branch(zzz2033, zzz2034, Pos(Succ(zzz2035)), zzz2036, zzz2037), bb)
new_mkVBalBranch3MkVBalBranch26(zzz1133, zzz1134, zzz1135, zzz1136, zzz1137, zzz1138, zzz1139, zzz1140, zzz1141, zzz1142, Succ(zzz11430), Succ(zzz11440), be) → new_mkVBalBranch3MkVBalBranch26(zzz1133, zzz1134, zzz1135, zzz1136, zzz1137, zzz1138, zzz1139, zzz1140, zzz1141, zzz1142, zzz11430, zzz11440, be)
new_mkVBalBranch3MkVBalBranch25(zzz537, zzz538, zzz539, zzz540, zzz541, zzz542, zzz543, zzz544, zzz545, zzz546, zzz547, Succ(zzz5480), Zero, bc) → new_mkVBalBranch3MkVBalBranch15(zzz537, zzz538, zzz539, zzz540, zzz541, zzz542, zzz543, zzz544, zzz545, zzz546, zzz547, new_primPlusNat2(new_primPlusNat3(Succ(new_primPlusNat3(new_primPlusNat1(zzz539), zzz539)), Succ(zzz539)), Succ(zzz539)), bc)
new_mkVBalBranch3MkVBalBranch24(zzz340, zzz341, Neg(Succ(Succ(Succ(zzz3420000)))), zzz343, zzz344, zzz520, zzz521, Zero, zzz523, zzz524, zzz31, Succ(Zero), h) → new_mkVBalBranch3MkVBalBranch26(zzz340, zzz341, Succ(Succ(zzz3420000)), zzz343, zzz344, zzz520, zzz521, zzz523, zzz524, zzz31, Succ(zzz3420000), Zero, h)
new_mkVBalBranch3MkVBalBranch24(zzz340, zzz341, Neg(Succ(Zero)), zzz343, zzz344, zzz520, zzz521, Zero, zzz523, zzz524, zzz31, Zero, h) → new_mkVBalBranch3MkVBalBranch29(zzz340, zzz341, Zero, zzz343, zzz344, zzz520, zzz521, zzz523, zzz524, zzz31, h)
new_mkVBalBranch3MkVBalBranch20(zzz929, zzz930, zzz931, zzz932, zzz933, zzz934, zzz935, zzz936, zzz937, zzz938, zzz939, Zero, Succ(zzz9410), ba) → new_mkVBalBranch(zzz939, Branch(zzz934, zzz935, Pos(Succ(zzz936)), zzz937, zzz938), zzz932, ba)
new_mkVBalBranch3MkVBalBranch17(zzz340, zzz341, zzz34200, zzz343, zzz344, zzz520, zzz521, zzz52200, zzz523, zzz524, zzz31, h) → new_mkVBalBranch(zzz31, zzz524, Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), h)
new_mkVBalBranch3MkVBalBranch26(zzz1133, zzz1134, zzz1135, zzz1136, zzz1137, zzz1138, zzz1139, zzz1140, zzz1141, zzz1142, Zero, Zero, be) → new_mkVBalBranch3MkVBalBranch29(zzz1133, zzz1134, zzz1135, zzz1136, zzz1137, zzz1138, zzz1139, zzz1140, zzz1141, zzz1142, be)
new_mkVBalBranch3MkVBalBranch20(zzz929, zzz930, zzz931, zzz932, zzz933, zzz934, zzz935, zzz936, zzz937, zzz938, zzz939, Zero, Zero, ba) → new_mkVBalBranch3MkVBalBranch23(zzz929, zzz930, zzz931, zzz932, zzz933, zzz934, zzz935, zzz936, zzz937, zzz938, zzz939, ba)
new_mkVBalBranch3MkVBalBranch24(zzz340, zzz341, Neg(Succ(Succ(Zero))), zzz343, zzz344, zzz520, zzz521, Succ(zzz522000), zzz523, zzz524, zzz31, Succ(Zero), h) → new_mkVBalBranch3MkVBalBranch25(zzz340, zzz341, Succ(Zero), zzz343, zzz344, zzz520, zzz521, zzz522000, zzz523, zzz524, zzz31, Zero, Succ(zzz522000), h)
new_mkVBalBranch3MkVBalBranch20(zzz929, zzz930, zzz931, zzz932, zzz933, zzz934, zzz935, zzz936, zzz937, zzz938, zzz939, Succ(zzz9400), Succ(zzz9410), ba) → new_mkVBalBranch3MkVBalBranch20(zzz929, zzz930, zzz931, zzz932, zzz933, zzz934, zzz935, zzz936, zzz937, zzz938, zzz939, zzz9400, zzz9410, ba)
new_mkVBalBranch3MkVBalBranch24(zzz340, zzz341, Neg(Succ(Succ(Succ(zzz3420000)))), zzz343, zzz344, zzz520, zzz521, Succ(zzz522000), zzz523, zzz524, zzz31, Succ(Zero), h) → new_mkVBalBranch3MkVBalBranch25(zzz340, zzz341, Succ(Succ(zzz3420000)), zzz343, zzz344, zzz520, zzz521, zzz522000, zzz523, zzz524, zzz31, Succ(zzz3420000), Succ(zzz522000), h)
new_mkVBalBranch3MkVBalBranch26(zzz1133, zzz1134, zzz1135, zzz1136, zzz1137, zzz1138, zzz1139, zzz1140, zzz1141, zzz1142, Succ(zzz11430), Zero, be) → new_mkVBalBranch3MkVBalBranch212(zzz1133, zzz1134, zzz1135, zzz1136, zzz1137, zzz1138, zzz1139, zzz1140, zzz1141, zzz1142, be)
new_mkVBalBranch3MkVBalBranch24(zzz340, zzz341, Neg(Succ(Succ(zzz342000))), zzz343, zzz344, zzz520, zzz521, Succ(zzz522000), zzz523, zzz524, zzz31, Zero, h) → new_mkVBalBranch3MkVBalBranch25(zzz340, zzz341, Succ(zzz342000), zzz343, zzz344, zzz520, zzz521, zzz522000, zzz523, zzz524, zzz31, zzz342000, zzz522000, h)
new_mkVBalBranch3MkVBalBranch29(zzz818, zzz819, zzz820, zzz821, zzz822, zzz823, zzz824, zzz825, zzz826, zzz827, bf) → new_mkVBalBranch3MkVBalBranch14(zzz818, zzz819, zzz820, zzz821, zzz822, zzz823, zzz824, zzz825, zzz826, zzz827, new_primPlusNat2(new_primMulNat0(zzz820), Succ(zzz820)), bf)
new_mkVBalBranch3MkVBalBranch11(zzz2033, zzz2034, zzz2035, zzz2036, zzz2037, zzz2038, zzz2039, zzz2040, zzz2041, zzz2042, zzz2043, Succ(zzz20440), Succ(zzz20450), bb) → new_mkVBalBranch3MkVBalBranch11(zzz2033, zzz2034, zzz2035, zzz2036, zzz2037, zzz2038, zzz2039, zzz2040, zzz2041, zzz2042, zzz2043, zzz20440, zzz20450, bb)
new_mkVBalBranch3MkVBalBranch25(zzz537, zzz538, zzz539, zzz540, zzz541, zzz542, zzz543, zzz544, zzz545, zzz546, zzz547, Succ(zzz5480), Succ(zzz5490), bc) → new_mkVBalBranch3MkVBalBranch25(zzz537, zzz538, zzz539, zzz540, zzz541, zzz542, zzz543, zzz544, zzz545, zzz546, zzz547, zzz5480, zzz5490, bc)
new_mkVBalBranch3MkVBalBranch24(zzz340, zzz341, Neg(Succ(Zero)), zzz343, zzz344, zzz520, zzz521, Succ(zzz522000), zzz523, zzz524, zzz31, Zero, h) → new_mkVBalBranch3MkVBalBranch28(zzz340, zzz341, zzz343, zzz344, zzz520, zzz521, Succ(zzz522000), zzz523, zzz524, zzz31, h)
new_mkVBalBranch3MkVBalBranch210(zzz340, zzz341, zzz343, zzz344, zzz520, zzz521, zzz52200, zzz523, zzz524, zzz31, h) → new_mkVBalBranch(zzz31, Branch(zzz520, zzz521, Neg(Succ(zzz52200)), zzz523, zzz524), zzz343, h)
new_mkVBalBranch(zzz31, Branch(zzz520, zzz521, Pos(Succ(zzz52200)), zzz523, zzz524), Branch(zzz340, zzz341, zzz342, zzz343, zzz344), h) → new_mkVBalBranch3MkVBalBranch2(zzz340, zzz341, zzz342, zzz343, zzz344, zzz520, zzz521, zzz52200, zzz523, zzz524, zzz31, Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat3(new_primPlusNat1(zzz52200), zzz52200)), zzz52200))), h)
new_mkVBalBranch3MkVBalBranch26(zzz1133, zzz1134, zzz1135, zzz1136, zzz1137, zzz1138, zzz1139, zzz1140, zzz1141, zzz1142, Zero, Succ(zzz11440), be) → new_mkVBalBranch(zzz1142, Branch(zzz1138, zzz1139, Neg(Succ(Zero)), zzz1140, zzz1141), zzz1136, be)
new_mkVBalBranch3MkVBalBranch24(zzz340, zzz341, Neg(Succ(Succ(Zero))), zzz343, zzz344, zzz520, zzz521, Zero, zzz523, zzz524, zzz31, Succ(Zero), h) → new_mkVBalBranch3MkVBalBranch26(zzz340, zzz341, Succ(Zero), zzz343, zzz344, zzz520, zzz521, zzz523, zzz524, zzz31, Zero, Zero, h)
new_mkVBalBranch(zzz31, Branch(zzz520, zzz521, Pos(Zero), zzz523, zzz524), Branch(zzz340, zzz341, Pos(Succ(zzz34200)), zzz343, zzz344), h) → new_mkVBalBranch(zzz31, Branch(zzz520, zzz521, Pos(Zero), zzz523, zzz524), zzz343, h)
new_mkVBalBranch3MkVBalBranch2(zzz340, zzz341, Pos(Zero), zzz343, zzz344, zzz520, zzz521, zzz52200, zzz523, zzz524, zzz31, Succ(zzz680), h) → new_mkVBalBranch(zzz31, zzz524, Branch(zzz340, zzz341, Pos(Zero), zzz343, zzz344), h)
new_mkVBalBranch3MkVBalBranch24(zzz340, zzz341, Pos(zzz3420), zzz343, zzz344, zzz520, zzz521, zzz52200, zzz523, zzz524, zzz31, Zero, h) → new_mkVBalBranch3MkVBalBranch27(zzz340, zzz341, zzz3420, zzz343, zzz344, zzz520, zzz521, zzz52200, zzz523, zzz524, zzz31, h)
new_mkVBalBranch3MkVBalBranch15(zzz537, zzz538, zzz539, zzz540, zzz541, zzz542, zzz543, zzz544, zzz545, zzz546, zzz547, Succ(zzz6990), bc) → new_mkVBalBranch3MkVBalBranch16(zzz537, zzz538, zzz539, zzz540, zzz541, zzz542, zzz543, Succ(zzz544), zzz545, zzz546, zzz547, Succ(Succ(zzz544)), Succ(zzz6990), bc)
new_mkVBalBranch3MkVBalBranch24(zzz340, zzz341, Neg(Succ(Succ(Succ(zzz3420000)))), zzz343, zzz344, zzz520, zzz521, Zero, zzz523, zzz524, zzz31, Succ(Succ(zzz6900)), h) → new_mkVBalBranch3MkVBalBranch26(zzz340, zzz341, Succ(Succ(zzz3420000)), zzz343, zzz344, zzz520, zzz521, zzz523, zzz524, zzz31, Succ(zzz3420000), Succ(zzz6900), h)
new_mkVBalBranch(zzz31, Branch(zzz520, zzz521, Neg(Zero), zzz523, zzz524), Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), h) → new_mkVBalBranch3MkVBalBranch13(zzz340, zzz341, zzz34200, zzz343, zzz344, zzz520, zzz521, zzz523, zzz524, zzz31, new_primPlusNat2(new_primMulNat0(zzz34200), Succ(zzz34200)), h)
new_mkVBalBranch3MkVBalBranch27(zzz340, zzz341, zzz3420, zzz343, zzz344, zzz520, zzz521, zzz52200, zzz523, zzz524, zzz31, h) → new_mkVBalBranch(zzz31, Branch(zzz520, zzz521, Neg(Succ(zzz52200)), zzz523, zzz524), zzz343, h)
new_mkVBalBranch3MkVBalBranch24(zzz340, zzz341, Pos(zzz3420), zzz343, zzz344, zzz520, zzz521, zzz52200, zzz523, zzz524, zzz31, Succ(zzz690), h) → new_mkVBalBranch(zzz31, Branch(zzz520, zzz521, Neg(Succ(zzz52200)), zzz523, zzz524), zzz343, h)
new_mkVBalBranch3MkVBalBranch12(zzz340, zzz341, zzz34200, zzz343, zzz344, zzz520, zzz521, zzz523, zzz524, zzz31, Succ(zzz1250), h) → new_mkVBalBranch(zzz31, zzz524, Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), h)
new_mkVBalBranch3MkVBalBranch28(zzz340, zzz341, zzz343, zzz344, zzz520, zzz521, zzz52200, zzz523, zzz524, zzz31, h) → new_mkVBalBranch(zzz31, Branch(zzz520, zzz521, Neg(Succ(zzz52200)), zzz523, zzz524), zzz343, h)
new_mkVBalBranch3MkVBalBranch24(zzz340, zzz341, Neg(Succ(Succ(Zero))), zzz343, zzz344, zzz520, zzz521, Zero, zzz523, zzz524, zzz31, Succ(Succ(zzz6900)), h) → new_mkVBalBranch3MkVBalBranch26(zzz340, zzz341, Succ(Zero), zzz343, zzz344, zzz520, zzz521, zzz523, zzz524, zzz31, Zero, Succ(zzz6900), h)
new_mkVBalBranch(zzz31, Branch(zzz520, zzz521, Pos(Zero), zzz523, zzz524), Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), h) → new_mkVBalBranch3MkVBalBranch12(zzz340, zzz341, zzz34200, zzz343, zzz344, zzz520, zzz521, zzz523, zzz524, zzz31, new_primPlusNat2(new_primPlusNat3(Succ(new_primPlusNat3(new_primPlusNat1(zzz34200), zzz34200)), Succ(zzz34200)), Succ(zzz34200)), h)
new_mkVBalBranch3MkVBalBranch211(zzz537, zzz538, zzz539, zzz540, zzz541, zzz542, zzz543, zzz544, zzz545, zzz546, zzz547, bc) → new_mkVBalBranch3MkVBalBranch15(zzz537, zzz538, zzz539, zzz540, zzz541, zzz542, zzz543, zzz544, zzz545, zzz546, zzz547, new_primPlusNat2(new_primPlusNat3(Succ(new_primPlusNat3(new_primPlusNat1(zzz539), zzz539)), Succ(zzz539)), Succ(zzz539)), bc)
new_mkVBalBranch3MkVBalBranch1(zzz340, zzz341, zzz34200, zzz343, zzz344, zzz520, zzz521, zzz52200, zzz523, zzz524, zzz31, Succ(zzz1430), h) → new_mkVBalBranch(zzz31, zzz524, Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), h)
new_mkVBalBranch3MkVBalBranch24(zzz340, zzz341, Neg(Succ(Zero)), zzz343, zzz344, zzz520, zzz521, zzz52200, zzz523, zzz524, zzz31, Succ(zzz690), h) → new_mkVBalBranch(zzz31, Branch(zzz520, zzz521, Neg(Succ(zzz52200)), zzz523, zzz524), zzz343, h)
new_mkVBalBranch3MkVBalBranch13(zzz340, zzz341, zzz34200, zzz343, zzz344, zzz520, zzz521, zzz523, zzz524, zzz31, Succ(zzz1290), h) → new_mkVBalBranch(zzz31, zzz524, Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), h)
new_mkVBalBranch3MkVBalBranch2(zzz340, zzz341, Pos(Succ(zzz34200)), zzz343, zzz344, zzz520, zzz521, zzz52200, zzz523, zzz524, zzz31, Succ(zzz680), h) → new_mkVBalBranch3MkVBalBranch20(zzz340, zzz341, zzz34200, zzz343, zzz344, zzz520, zzz521, zzz52200, zzz523, zzz524, zzz31, Succ(new_primPlusNat2(zzz680, zzz52200)), zzz34200, h)
new_mkVBalBranch3MkVBalBranch24(zzz340, zzz341, Neg(Zero), zzz343, zzz344, zzz520, zzz521, zzz52200, zzz523, zzz524, zzz31, Succ(zzz690), h) → new_mkVBalBranch(zzz31, Branch(zzz520, zzz521, Neg(Succ(zzz52200)), zzz523, zzz524), zzz343, h)
new_mkVBalBranch(zzz31, Branch(zzz520, zzz521, Neg(Zero), zzz523, zzz524), Branch(zzz340, zzz341, Pos(Succ(zzz34200)), zzz343, zzz344), h) → new_mkVBalBranch(zzz31, Branch(zzz520, zzz521, Neg(Zero), zzz523, zzz524), zzz343, h)
new_mkVBalBranch3MkVBalBranch24(zzz340, zzz341, Neg(Succ(Succ(zzz342000))), zzz343, zzz344, zzz520, zzz521, Zero, zzz523, zzz524, zzz31, Zero, h) → new_mkVBalBranch3MkVBalBranch14(zzz340, zzz341, Succ(zzz342000), zzz343, zzz344, zzz520, zzz521, zzz523, zzz524, zzz31, new_primPlusNat2(new_primPlusNat3(Succ(new_primPlusNat3(new_primPlusNat1(Succ(zzz342000)), Succ(zzz342000))), Succ(Succ(zzz342000))), Succ(Succ(zzz342000))), h)
new_mkVBalBranch3MkVBalBranch1(zzz340, zzz341, zzz34200, zzz343, zzz344, zzz520, zzz521, zzz52200, zzz523, zzz524, zzz31, Zero, h) → new_mkVBalBranch3MkVBalBranch17(zzz340, zzz341, zzz34200, zzz343, zzz344, zzz520, zzz521, zzz52200, zzz523, zzz524, zzz31, h)
new_mkVBalBranch3MkVBalBranch16(zzz1702, zzz1703, zzz1704, zzz1705, zzz1706, zzz1707, zzz1708, zzz1709, zzz1710, zzz1711, zzz1712, Succ(zzz17130), Succ(zzz17140), bd) → new_mkVBalBranch3MkVBalBranch16(zzz1702, zzz1703, zzz1704, zzz1705, zzz1706, zzz1707, zzz1708, zzz1709, zzz1710, zzz1711, zzz1712, zzz17130, zzz17140, bd)
new_mkVBalBranch3MkVBalBranch25(zzz537, zzz538, zzz539, zzz540, zzz541, zzz542, zzz543, zzz544, zzz545, zzz546, zzz547, Zero, Succ(zzz5490), bc) → new_mkVBalBranch(zzz547, Branch(zzz542, zzz543, Neg(Succ(Succ(zzz544))), zzz545, zzz546), zzz540, bc)
new_mkVBalBranch3MkVBalBranch10(zzz929, zzz930, zzz931, zzz932, zzz933, zzz934, zzz935, zzz936, zzz937, zzz938, zzz939, Succ(zzz10020), ba) → new_mkVBalBranch3MkVBalBranch11(zzz929, zzz930, zzz931, zzz932, zzz933, zzz934, zzz935, zzz936, zzz937, zzz938, zzz939, Succ(zzz10020), Succ(zzz936), ba)
new_mkVBalBranch3MkVBalBranch212(zzz818, zzz819, zzz820, zzz821, zzz822, zzz823, zzz824, zzz825, zzz826, zzz827, bf) → new_mkVBalBranch3MkVBalBranch14(zzz818, zzz819, zzz820, zzz821, zzz822, zzz823, zzz824, zzz825, zzz826, zzz827, new_primPlusNat2(new_primMulNat0(zzz820), Succ(zzz820)), bf)
new_mkVBalBranch3MkVBalBranch14(zzz818, zzz819, zzz820, zzz821, zzz822, zzz823, zzz824, zzz825, zzz826, zzz827, Succ(zzz8960), bf) → new_mkVBalBranch3MkVBalBranch16(zzz818, zzz819, zzz820, zzz821, zzz822, zzz823, zzz824, Zero, zzz825, zzz826, zzz827, Succ(Zero), Succ(zzz8960), bf)
new_mkVBalBranch3MkVBalBranch24(zzz340, zzz341, Neg(Succ(Succ(Succ(zzz3420000)))), zzz343, zzz344, zzz520, zzz521, Succ(zzz522000), zzz523, zzz524, zzz31, Succ(Succ(zzz6900)), h) → new_mkVBalBranch3MkVBalBranch25(zzz340, zzz341, Succ(Succ(zzz3420000)), zzz343, zzz344, zzz520, zzz521, zzz522000, zzz523, zzz524, zzz31, Succ(zzz3420000), Succ(Succ(new_primPlusNat2(zzz6900, zzz522000))), h)
new_mkVBalBranch3MkVBalBranch24(zzz340, zzz341, Neg(Zero), zzz343, zzz344, zzz520, zzz521, zzz52200, zzz523, zzz524, zzz31, Zero, h) → new_mkVBalBranch3MkVBalBranch210(zzz340, zzz341, zzz343, zzz344, zzz520, zzz521, zzz52200, zzz523, zzz524, zzz31, h)
new_mkVBalBranch3MkVBalBranch24(zzz340, zzz341, Neg(Succ(Succ(Zero))), zzz343, zzz344, zzz520, zzz521, Succ(zzz522000), zzz523, zzz524, zzz31, Succ(Succ(zzz6900)), h) → new_mkVBalBranch3MkVBalBranch25(zzz340, zzz341, Succ(Zero), zzz343, zzz344, zzz520, zzz521, zzz522000, zzz523, zzz524, zzz31, Zero, Succ(Succ(new_primPlusNat2(zzz6900, zzz522000))), h)
new_mkVBalBranch3MkVBalBranch20(zzz929, zzz930, zzz931, zzz932, zzz933, zzz934, zzz935, zzz936, zzz937, zzz938, zzz939, Succ(zzz9400), Zero, ba) → new_mkVBalBranch3MkVBalBranch10(zzz929, zzz930, zzz931, zzz932, zzz933, zzz934, zzz935, zzz936, zzz937, zzz938, zzz939, new_primPlusNat2(new_primPlusNat3(Succ(new_primPlusNat3(new_primPlusNat1(zzz931), zzz931)), Succ(zzz931)), Succ(zzz931)), ba)
new_mkVBalBranch3MkVBalBranch23(zzz929, zzz930, zzz931, zzz932, zzz933, zzz934, zzz935, zzz936, zzz937, zzz938, zzz939, ba) → new_mkVBalBranch3MkVBalBranch10(zzz929, zzz930, zzz931, zzz932, zzz933, zzz934, zzz935, zzz936, zzz937, zzz938, zzz939, new_primPlusNat2(new_primMulNat0(zzz931), Succ(zzz931)), ba)
new_mkVBalBranch3MkVBalBranch2(zzz340, zzz341, Neg(Zero), zzz343, zzz344, zzz520, zzz521, zzz52200, zzz523, zzz524, zzz31, Succ(zzz680), h) → new_mkVBalBranch(zzz31, zzz524, Branch(zzz340, zzz341, Neg(Zero), zzz343, zzz344), h)
new_mkVBalBranch3MkVBalBranch2(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344, zzz520, zzz521, zzz52200, zzz523, zzz524, zzz31, Succ(zzz680), h) → new_mkVBalBranch3MkVBalBranch1(zzz340, zzz341, zzz34200, zzz343, zzz344, zzz520, zzz521, zzz52200, zzz523, zzz524, zzz31, new_primPlusNat2(Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat3(new_primPlusNat1(zzz34200), zzz34200)), zzz34200))), Succ(zzz34200)), h)
new_mkVBalBranch3MkVBalBranch16(zzz1702, zzz1703, zzz1704, zzz1705, zzz1706, zzz1707, zzz1708, zzz1709, zzz1710, zzz1711, zzz1712, Zero, Succ(zzz17140), bd) → new_mkVBalBranch(zzz1712, zzz1711, Branch(zzz1702, zzz1703, Neg(Succ(zzz1704)), zzz1705, zzz1706), bd)
new_mkVBalBranch3MkVBalBranch10(zzz929, zzz930, zzz931, zzz932, zzz933, zzz934, zzz935, zzz936, zzz937, zzz938, zzz939, Zero, ba) → new_mkVBalBranch3MkVBalBranch11(zzz929, zzz930, zzz931, zzz932, zzz933, zzz934, zzz935, zzz936, zzz937, zzz938, zzz939, Zero, Succ(zzz936), ba)
new_mkVBalBranch3MkVBalBranch25(zzz537, zzz538, zzz539, zzz540, zzz541, zzz542, zzz543, zzz544, zzz545, zzz546, zzz547, Zero, Zero, bc) → new_mkVBalBranch3MkVBalBranch211(zzz537, zzz538, zzz539, zzz540, zzz541, zzz542, zzz543, zzz544, zzz545, zzz546, zzz547, bc)

The TRS R consists of the following rules:

new_primMulNat0(zzz6200) → new_primPlusNat3(Succ(new_primPlusNat3(new_primPlusNat1(zzz6200), zzz6200)), Succ(zzz6200))
new_primPlusNat2(Succ(zzz900), Succ(zzz9100)) → Succ(Succ(new_primPlusNat2(zzz900, zzz9100)))
new_primPlusNat2(Zero, Succ(zzz9100)) → Succ(zzz9100)
new_primPlusNat2(Zero, Zero) → Zero
new_primPlusNat2(Succ(zzz900), Zero) → Succ(zzz900)
new_primPlusNat1(Zero) → Zero
new_primPlusNat1(Succ(zzz62000)) → Succ(Succ(new_primPlusNat1(zzz62000)))
new_primPlusNat3(zzz90, Succ(zzz910)) → Succ(Succ(new_primPlusNat2(zzz90, zzz910)))
new_primPlusNat3(zzz90, Zero) → Succ(zzz90)

The set Q consists of the following terms:

new_primPlusNat2(Zero, Succ(x0))
new_primMulNat0(x0)
new_primPlusNat3(x0, Succ(x1))
new_primPlusNat2(Succ(x0), Succ(x1))
new_primPlusNat3(x0, Zero)
new_primPlusNat1(Zero)
new_primPlusNat2(Zero, Zero)
new_primPlusNat1(Succ(x0))
new_primPlusNat2(Succ(x0), Zero)

We have to consider all minimal (P,Q,R)-chains.
The approximation of the Dependency Graph [15,17,22] contains 1 SCC with 13 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
                                    ↳ DependencyGraphProof
                                      ↳ QDP
                                        ↳ Rewriting
                                          ↳ QDP
                                            ↳ Rewriting
                                              ↳ QDP
                                                ↳ Rewriting
                                                  ↳ QDP
                                                    ↳ Rewriting
                                                      ↳ QDP
                                                        ↳ Rewriting
                                                          ↳ QDP
                                                            ↳ Rewriting
                                                              ↳ QDP
                                                                ↳ Rewriting
                                                                  ↳ QDP
                                                                    ↳ Rewriting
                                                                      ↳ QDP
                                                                        ↳ Rewriting
                                                                          ↳ QDP
                                                                            ↳ Rewriting
                                                                              ↳ QDP
                                                                                ↳ Rewriting
                                                                                  ↳ QDP
                                                                                    ↳ Rewriting
                                                                                      ↳ QDP
                                                                                        ↳ Rewriting
                                                                                          ↳ QDP
                                                                                            ↳ UsableRulesProof
                                                                                              ↳ QDP
                                                                                                ↳ QReductionProof
                                                                                                  ↳ QDP
                                                                                                    ↳ Rewriting
                                                                                                      ↳ QDP
                                                                                                        ↳ Rewriting
                                                                                                          ↳ QDP
                                                                                                            ↳ Rewriting
                                                                                                              ↳ QDP
                                                                                                                ↳ Rewriting
                                                                                                                  ↳ QDP
                                                                                                                    ↳ Rewriting
                                                                                                                      ↳ QDP
                                                                                                                        ↳ Rewriting
                                                                                                                          ↳ QDP
                                                                                                                            ↳ DependencyGraphProof
                                                                                                                              ↳ QDP
                                                                                                                                ↳ Rewriting
                                                                                                                                  ↳ QDP
                                                                                                                                    ↳ Rewriting
                                                                                                                                      ↳ QDP
                                                                                                                                        ↳ DependencyGraphProof
                                                                                                                                          ↳ QDP
                                                                                                                                            ↳ Rewriting
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP

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

new_mkVBalBranch(zzz31, Branch(zzz520, zzz521, Neg(Zero), zzz523, zzz524), Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), h) → new_mkVBalBranch3MkVBalBranch13(zzz340, zzz341, zzz34200, zzz343, zzz344, zzz520, zzz521, zzz523, zzz524, zzz31, new_primPlusNat2(new_primMulNat0(zzz34200), Succ(zzz34200)), h)
new_mkVBalBranch3MkVBalBranch11(zzz2033, zzz2034, zzz2035, zzz2036, zzz2037, zzz2038, zzz2039, zzz2040, zzz2041, zzz2042, zzz2043, Zero, Succ(zzz20450), bb) → new_mkVBalBranch(zzz2043, zzz2042, Branch(zzz2033, zzz2034, Pos(Succ(zzz2035)), zzz2036, zzz2037), bb)
new_mkVBalBranch(zzz31, Branch(zzz520, zzz521, Neg(Succ(zzz52200)), zzz523, zzz524), Branch(zzz340, zzz341, zzz342, zzz343, zzz344), h) → new_mkVBalBranch3MkVBalBranch24(zzz340, zzz341, zzz342, zzz343, zzz344, zzz520, zzz521, zzz52200, zzz523, zzz524, zzz31, Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat3(new_primPlusNat1(zzz52200), zzz52200)), zzz52200))), h)
new_mkVBalBranch3MkVBalBranch26(zzz1133, zzz1134, zzz1135, zzz1136, zzz1137, zzz1138, zzz1139, zzz1140, zzz1141, zzz1142, Succ(zzz11430), Succ(zzz11440), be) → new_mkVBalBranch3MkVBalBranch26(zzz1133, zzz1134, zzz1135, zzz1136, zzz1137, zzz1138, zzz1139, zzz1140, zzz1141, zzz1142, zzz11430, zzz11440, be)
new_mkVBalBranch3MkVBalBranch24(zzz340, zzz341, Pos(zzz3420), zzz343, zzz344, zzz520, zzz521, zzz52200, zzz523, zzz524, zzz31, Succ(zzz690), h) → new_mkVBalBranch(zzz31, Branch(zzz520, zzz521, Neg(Succ(zzz52200)), zzz523, zzz524), zzz343, h)
new_mkVBalBranch3MkVBalBranch25(zzz537, zzz538, zzz539, zzz540, zzz541, zzz542, zzz543, zzz544, zzz545, zzz546, zzz547, Succ(zzz5480), Zero, bc) → new_mkVBalBranch3MkVBalBranch15(zzz537, zzz538, zzz539, zzz540, zzz541, zzz542, zzz543, zzz544, zzz545, zzz546, zzz547, new_primPlusNat2(new_primPlusNat3(Succ(new_primPlusNat3(new_primPlusNat1(zzz539), zzz539)), Succ(zzz539)), Succ(zzz539)), bc)
new_mkVBalBranch3MkVBalBranch12(zzz340, zzz341, zzz34200, zzz343, zzz344, zzz520, zzz521, zzz523, zzz524, zzz31, Succ(zzz1250), h) → new_mkVBalBranch(zzz31, zzz524, Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), h)
new_mkVBalBranch3MkVBalBranch20(zzz929, zzz930, zzz931, zzz932, zzz933, zzz934, zzz935, zzz936, zzz937, zzz938, zzz939, Zero, Succ(zzz9410), ba) → new_mkVBalBranch(zzz939, Branch(zzz934, zzz935, Pos(Succ(zzz936)), zzz937, zzz938), zzz932, ba)
new_mkVBalBranch(zzz31, Branch(zzz520, zzz521, Pos(Zero), zzz523, zzz524), Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), h) → new_mkVBalBranch3MkVBalBranch12(zzz340, zzz341, zzz34200, zzz343, zzz344, zzz520, zzz521, zzz523, zzz524, zzz31, new_primPlusNat2(new_primPlusNat3(Succ(new_primPlusNat3(new_primPlusNat1(zzz34200), zzz34200)), Succ(zzz34200)), Succ(zzz34200)), h)
new_mkVBalBranch3MkVBalBranch24(zzz340, zzz341, Neg(Succ(Succ(Zero))), zzz343, zzz344, zzz520, zzz521, Zero, zzz523, zzz524, zzz31, Succ(Succ(zzz6900)), h) → new_mkVBalBranch3MkVBalBranch26(zzz340, zzz341, Succ(Zero), zzz343, zzz344, zzz520, zzz521, zzz523, zzz524, zzz31, Zero, Succ(zzz6900), h)
new_mkVBalBranch3MkVBalBranch17(zzz340, zzz341, zzz34200, zzz343, zzz344, zzz520, zzz521, zzz52200, zzz523, zzz524, zzz31, h) → new_mkVBalBranch(zzz31, zzz524, Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), h)
new_mkVBalBranch3MkVBalBranch211(zzz537, zzz538, zzz539, zzz540, zzz541, zzz542, zzz543, zzz544, zzz545, zzz546, zzz547, bc) → new_mkVBalBranch3MkVBalBranch15(zzz537, zzz538, zzz539, zzz540, zzz541, zzz542, zzz543, zzz544, zzz545, zzz546, zzz547, new_primPlusNat2(new_primPlusNat3(Succ(new_primPlusNat3(new_primPlusNat1(zzz539), zzz539)), Succ(zzz539)), Succ(zzz539)), bc)
new_mkVBalBranch3MkVBalBranch1(zzz340, zzz341, zzz34200, zzz343, zzz344, zzz520, zzz521, zzz52200, zzz523, zzz524, zzz31, Succ(zzz1430), h) → new_mkVBalBranch(zzz31, zzz524, Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), h)
new_mkVBalBranch3MkVBalBranch26(zzz1133, zzz1134, zzz1135, zzz1136, zzz1137, zzz1138, zzz1139, zzz1140, zzz1141, zzz1142, Zero, Zero, be) → new_mkVBalBranch3MkVBalBranch29(zzz1133, zzz1134, zzz1135, zzz1136, zzz1137, zzz1138, zzz1139, zzz1140, zzz1141, zzz1142, be)
new_mkVBalBranch3MkVBalBranch20(zzz929, zzz930, zzz931, zzz932, zzz933, zzz934, zzz935, zzz936, zzz937, zzz938, zzz939, Zero, Zero, ba) → new_mkVBalBranch3MkVBalBranch23(zzz929, zzz930, zzz931, zzz932, zzz933, zzz934, zzz935, zzz936, zzz937, zzz938, zzz939, ba)
new_mkVBalBranch3MkVBalBranch24(zzz340, zzz341, Neg(Succ(Zero)), zzz343, zzz344, zzz520, zzz521, zzz52200, zzz523, zzz524, zzz31, Succ(zzz690), h) → new_mkVBalBranch(zzz31, Branch(zzz520, zzz521, Neg(Succ(zzz52200)), zzz523, zzz524), zzz343, h)
new_mkVBalBranch3MkVBalBranch13(zzz340, zzz341, zzz34200, zzz343, zzz344, zzz520, zzz521, zzz523, zzz524, zzz31, Succ(zzz1290), h) → new_mkVBalBranch(zzz31, zzz524, Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), h)
new_mkVBalBranch3MkVBalBranch2(zzz340, zzz341, Pos(Succ(zzz34200)), zzz343, zzz344, zzz520, zzz521, zzz52200, zzz523, zzz524, zzz31, Succ(zzz680), h) → new_mkVBalBranch3MkVBalBranch20(zzz340, zzz341, zzz34200, zzz343, zzz344, zzz520, zzz521, zzz52200, zzz523, zzz524, zzz31, Succ(new_primPlusNat2(zzz680, zzz52200)), zzz34200, h)
new_mkVBalBranch(zzz31, Branch(zzz520, zzz521, Neg(Zero), zzz523, zzz524), Branch(zzz340, zzz341, Pos(Succ(zzz34200)), zzz343, zzz344), h) → new_mkVBalBranch(zzz31, Branch(zzz520, zzz521, Neg(Zero), zzz523, zzz524), zzz343, h)
new_mkVBalBranch3MkVBalBranch24(zzz340, zzz341, Neg(Zero), zzz343, zzz344, zzz520, zzz521, zzz52200, zzz523, zzz524, zzz31, Succ(zzz690), h) → new_mkVBalBranch(zzz31, Branch(zzz520, zzz521, Neg(Succ(zzz52200)), zzz523, zzz524), zzz343, h)
new_mkVBalBranch3MkVBalBranch20(zzz929, zzz930, zzz931, zzz932, zzz933, zzz934, zzz935, zzz936, zzz937, zzz938, zzz939, Succ(zzz9400), Succ(zzz9410), ba) → new_mkVBalBranch3MkVBalBranch20(zzz929, zzz930, zzz931, zzz932, zzz933, zzz934, zzz935, zzz936, zzz937, zzz938, zzz939, zzz9400, zzz9410, ba)
new_mkVBalBranch3MkVBalBranch1(zzz340, zzz341, zzz34200, zzz343, zzz344, zzz520, zzz521, zzz52200, zzz523, zzz524, zzz31, Zero, h) → new_mkVBalBranch3MkVBalBranch17(zzz340, zzz341, zzz34200, zzz343, zzz344, zzz520, zzz521, zzz52200, zzz523, zzz524, zzz31, h)
new_mkVBalBranch3MkVBalBranch26(zzz1133, zzz1134, zzz1135, zzz1136, zzz1137, zzz1138, zzz1139, zzz1140, zzz1141, zzz1142, Succ(zzz11430), Zero, be) → new_mkVBalBranch3MkVBalBranch212(zzz1133, zzz1134, zzz1135, zzz1136, zzz1137, zzz1138, zzz1139, zzz1140, zzz1141, zzz1142, be)
new_mkVBalBranch3MkVBalBranch16(zzz1702, zzz1703, zzz1704, zzz1705, zzz1706, zzz1707, zzz1708, zzz1709, zzz1710, zzz1711, zzz1712, Succ(zzz17130), Succ(zzz17140), bd) → new_mkVBalBranch3MkVBalBranch16(zzz1702, zzz1703, zzz1704, zzz1705, zzz1706, zzz1707, zzz1708, zzz1709, zzz1710, zzz1711, zzz1712, zzz17130, zzz17140, bd)
new_mkVBalBranch3MkVBalBranch29(zzz818, zzz819, zzz820, zzz821, zzz822, zzz823, zzz824, zzz825, zzz826, zzz827, bf) → new_mkVBalBranch3MkVBalBranch14(zzz818, zzz819, zzz820, zzz821, zzz822, zzz823, zzz824, zzz825, zzz826, zzz827, new_primPlusNat2(new_primMulNat0(zzz820), Succ(zzz820)), bf)
new_mkVBalBranch3MkVBalBranch25(zzz537, zzz538, zzz539, zzz540, zzz541, zzz542, zzz543, zzz544, zzz545, zzz546, zzz547, Zero, Succ(zzz5490), bc) → new_mkVBalBranch(zzz547, Branch(zzz542, zzz543, Neg(Succ(Succ(zzz544))), zzz545, zzz546), zzz540, bc)
new_mkVBalBranch3MkVBalBranch11(zzz2033, zzz2034, zzz2035, zzz2036, zzz2037, zzz2038, zzz2039, zzz2040, zzz2041, zzz2042, zzz2043, Succ(zzz20440), Succ(zzz20450), bb) → new_mkVBalBranch3MkVBalBranch11(zzz2033, zzz2034, zzz2035, zzz2036, zzz2037, zzz2038, zzz2039, zzz2040, zzz2041, zzz2042, zzz2043, zzz20440, zzz20450, bb)
new_mkVBalBranch3MkVBalBranch25(zzz537, zzz538, zzz539, zzz540, zzz541, zzz542, zzz543, zzz544, zzz545, zzz546, zzz547, Succ(zzz5480), Succ(zzz5490), bc) → new_mkVBalBranch3MkVBalBranch25(zzz537, zzz538, zzz539, zzz540, zzz541, zzz542, zzz543, zzz544, zzz545, zzz546, zzz547, zzz5480, zzz5490, bc)
new_mkVBalBranch3MkVBalBranch10(zzz929, zzz930, zzz931, zzz932, zzz933, zzz934, zzz935, zzz936, zzz937, zzz938, zzz939, Succ(zzz10020), ba) → new_mkVBalBranch3MkVBalBranch11(zzz929, zzz930, zzz931, zzz932, zzz933, zzz934, zzz935, zzz936, zzz937, zzz938, zzz939, Succ(zzz10020), Succ(zzz936), ba)
new_mkVBalBranch(zzz31, Branch(zzz520, zzz521, Pos(Succ(zzz52200)), zzz523, zzz524), Branch(zzz340, zzz341, zzz342, zzz343, zzz344), h) → new_mkVBalBranch3MkVBalBranch2(zzz340, zzz341, zzz342, zzz343, zzz344, zzz520, zzz521, zzz52200, zzz523, zzz524, zzz31, Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat3(new_primPlusNat1(zzz52200), zzz52200)), zzz52200))), h)
new_mkVBalBranch3MkVBalBranch212(zzz818, zzz819, zzz820, zzz821, zzz822, zzz823, zzz824, zzz825, zzz826, zzz827, bf) → new_mkVBalBranch3MkVBalBranch14(zzz818, zzz819, zzz820, zzz821, zzz822, zzz823, zzz824, zzz825, zzz826, zzz827, new_primPlusNat2(new_primMulNat0(zzz820), Succ(zzz820)), bf)
new_mkVBalBranch3MkVBalBranch14(zzz818, zzz819, zzz820, zzz821, zzz822, zzz823, zzz824, zzz825, zzz826, zzz827, Succ(zzz8960), bf) → new_mkVBalBranch3MkVBalBranch16(zzz818, zzz819, zzz820, zzz821, zzz822, zzz823, zzz824, Zero, zzz825, zzz826, zzz827, Succ(Zero), Succ(zzz8960), bf)
new_mkVBalBranch3MkVBalBranch26(zzz1133, zzz1134, zzz1135, zzz1136, zzz1137, zzz1138, zzz1139, zzz1140, zzz1141, zzz1142, Zero, Succ(zzz11440), be) → new_mkVBalBranch(zzz1142, Branch(zzz1138, zzz1139, Neg(Succ(Zero)), zzz1140, zzz1141), zzz1136, be)
new_mkVBalBranch3MkVBalBranch24(zzz340, zzz341, Neg(Succ(Succ(Succ(zzz3420000)))), zzz343, zzz344, zzz520, zzz521, Succ(zzz522000), zzz523, zzz524, zzz31, Succ(Succ(zzz6900)), h) → new_mkVBalBranch3MkVBalBranch25(zzz340, zzz341, Succ(Succ(zzz3420000)), zzz343, zzz344, zzz520, zzz521, zzz522000, zzz523, zzz524, zzz31, Succ(zzz3420000), Succ(Succ(new_primPlusNat2(zzz6900, zzz522000))), h)
new_mkVBalBranch3MkVBalBranch24(zzz340, zzz341, Neg(Succ(Succ(Zero))), zzz343, zzz344, zzz520, zzz521, Succ(zzz522000), zzz523, zzz524, zzz31, Succ(Succ(zzz6900)), h) → new_mkVBalBranch3MkVBalBranch25(zzz340, zzz341, Succ(Zero), zzz343, zzz344, zzz520, zzz521, zzz522000, zzz523, zzz524, zzz31, Zero, Succ(Succ(new_primPlusNat2(zzz6900, zzz522000))), h)
new_mkVBalBranch3MkVBalBranch20(zzz929, zzz930, zzz931, zzz932, zzz933, zzz934, zzz935, zzz936, zzz937, zzz938, zzz939, Succ(zzz9400), Zero, ba) → new_mkVBalBranch3MkVBalBranch10(zzz929, zzz930, zzz931, zzz932, zzz933, zzz934, zzz935, zzz936, zzz937, zzz938, zzz939, new_primPlusNat2(new_primPlusNat3(Succ(new_primPlusNat3(new_primPlusNat1(zzz931), zzz931)), Succ(zzz931)), Succ(zzz931)), ba)
new_mkVBalBranch(zzz31, Branch(zzz520, zzz521, Pos(Zero), zzz523, zzz524), Branch(zzz340, zzz341, Pos(Succ(zzz34200)), zzz343, zzz344), h) → new_mkVBalBranch(zzz31, Branch(zzz520, zzz521, Pos(Zero), zzz523, zzz524), zzz343, h)
new_mkVBalBranch3MkVBalBranch23(zzz929, zzz930, zzz931, zzz932, zzz933, zzz934, zzz935, zzz936, zzz937, zzz938, zzz939, ba) → new_mkVBalBranch3MkVBalBranch10(zzz929, zzz930, zzz931, zzz932, zzz933, zzz934, zzz935, zzz936, zzz937, zzz938, zzz939, new_primPlusNat2(new_primMulNat0(zzz931), Succ(zzz931)), ba)
new_mkVBalBranch3MkVBalBranch2(zzz340, zzz341, Pos(Zero), zzz343, zzz344, zzz520, zzz521, zzz52200, zzz523, zzz524, zzz31, Succ(zzz680), h) → new_mkVBalBranch(zzz31, zzz524, Branch(zzz340, zzz341, Pos(Zero), zzz343, zzz344), h)
new_mkVBalBranch3MkVBalBranch2(zzz340, zzz341, Neg(Zero), zzz343, zzz344, zzz520, zzz521, zzz52200, zzz523, zzz524, zzz31, Succ(zzz680), h) → new_mkVBalBranch(zzz31, zzz524, Branch(zzz340, zzz341, Neg(Zero), zzz343, zzz344), h)
new_mkVBalBranch3MkVBalBranch2(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344, zzz520, zzz521, zzz52200, zzz523, zzz524, zzz31, Succ(zzz680), h) → new_mkVBalBranch3MkVBalBranch1(zzz340, zzz341, zzz34200, zzz343, zzz344, zzz520, zzz521, zzz52200, zzz523, zzz524, zzz31, new_primPlusNat2(Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat3(new_primPlusNat1(zzz34200), zzz34200)), zzz34200))), Succ(zzz34200)), h)
new_mkVBalBranch3MkVBalBranch16(zzz1702, zzz1703, zzz1704, zzz1705, zzz1706, zzz1707, zzz1708, zzz1709, zzz1710, zzz1711, zzz1712, Zero, Succ(zzz17140), bd) → new_mkVBalBranch(zzz1712, zzz1711, Branch(zzz1702, zzz1703, Neg(Succ(zzz1704)), zzz1705, zzz1706), bd)
new_mkVBalBranch3MkVBalBranch10(zzz929, zzz930, zzz931, zzz932, zzz933, zzz934, zzz935, zzz936, zzz937, zzz938, zzz939, Zero, ba) → new_mkVBalBranch3MkVBalBranch11(zzz929, zzz930, zzz931, zzz932, zzz933, zzz934, zzz935, zzz936, zzz937, zzz938, zzz939, Zero, Succ(zzz936), ba)
new_mkVBalBranch3MkVBalBranch15(zzz537, zzz538, zzz539, zzz540, zzz541, zzz542, zzz543, zzz544, zzz545, zzz546, zzz547, Succ(zzz6990), bc) → new_mkVBalBranch3MkVBalBranch16(zzz537, zzz538, zzz539, zzz540, zzz541, zzz542, zzz543, Succ(zzz544), zzz545, zzz546, zzz547, Succ(Succ(zzz544)), Succ(zzz6990), bc)
new_mkVBalBranch3MkVBalBranch24(zzz340, zzz341, Neg(Succ(Succ(Succ(zzz3420000)))), zzz343, zzz344, zzz520, zzz521, Zero, zzz523, zzz524, zzz31, Succ(Succ(zzz6900)), h) → new_mkVBalBranch3MkVBalBranch26(zzz340, zzz341, Succ(Succ(zzz3420000)), zzz343, zzz344, zzz520, zzz521, zzz523, zzz524, zzz31, Succ(zzz3420000), Succ(zzz6900), h)
new_mkVBalBranch3MkVBalBranch25(zzz537, zzz538, zzz539, zzz540, zzz541, zzz542, zzz543, zzz544, zzz545, zzz546, zzz547, Zero, Zero, bc) → new_mkVBalBranch3MkVBalBranch211(zzz537, zzz538, zzz539, zzz540, zzz541, zzz542, zzz543, zzz544, zzz545, zzz546, zzz547, bc)

The TRS R consists of the following rules:

new_primMulNat0(zzz6200) → new_primPlusNat3(Succ(new_primPlusNat3(new_primPlusNat1(zzz6200), zzz6200)), Succ(zzz6200))
new_primPlusNat2(Succ(zzz900), Succ(zzz9100)) → Succ(Succ(new_primPlusNat2(zzz900, zzz9100)))
new_primPlusNat2(Zero, Succ(zzz9100)) → Succ(zzz9100)
new_primPlusNat2(Zero, Zero) → Zero
new_primPlusNat2(Succ(zzz900), Zero) → Succ(zzz900)
new_primPlusNat1(Zero) → Zero
new_primPlusNat1(Succ(zzz62000)) → Succ(Succ(new_primPlusNat1(zzz62000)))
new_primPlusNat3(zzz90, Succ(zzz910)) → Succ(Succ(new_primPlusNat2(zzz90, zzz910)))
new_primPlusNat3(zzz90, Zero) → Succ(zzz90)

The set Q consists of the following terms:

new_primPlusNat2(Zero, Succ(x0))
new_primMulNat0(x0)
new_primPlusNat3(x0, Succ(x1))
new_primPlusNat2(Succ(x0), Succ(x1))
new_primPlusNat3(x0, Zero)
new_primPlusNat1(Zero)
new_primPlusNat2(Zero, Zero)
new_primPlusNat1(Succ(x0))
new_primPlusNat2(Succ(x0), Zero)

We have to consider all minimal (P,Q,R)-chains.
By rewriting [15] the rule new_mkVBalBranch(zzz31, Branch(zzz520, zzz521, Pos(Zero), zzz523, zzz524), Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), h) → new_mkVBalBranch3MkVBalBranch12(zzz340, zzz341, zzz34200, zzz343, zzz344, zzz520, zzz521, zzz523, zzz524, zzz31, new_primPlusNat2(new_primPlusNat3(Succ(new_primPlusNat3(new_primPlusNat1(zzz34200), zzz34200)), Succ(zzz34200)), Succ(zzz34200)), h) at position [10,0] we obtained the following new rules:

new_mkVBalBranch(zzz31, Branch(zzz520, zzz521, Pos(Zero), zzz523, zzz524), Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), h) → new_mkVBalBranch3MkVBalBranch12(zzz340, zzz341, zzz34200, zzz343, zzz344, zzz520, zzz521, zzz523, zzz524, zzz31, new_primPlusNat2(Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat3(new_primPlusNat1(zzz34200), zzz34200)), 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
                                    ↳ DependencyGraphProof
                                      ↳ QDP
                                        ↳ Rewriting
                                          ↳ QDP
                                            ↳ Rewriting
                                              ↳ QDP
                                                ↳ Rewriting
                                                  ↳ QDP
                                                    ↳ Rewriting
                                                      ↳ QDP
                                                        ↳ Rewriting
                                                          ↳ QDP
                                                            ↳ Rewriting
                                                              ↳ QDP
                                                                ↳ Rewriting
                                                                  ↳ QDP
                                                                    ↳ Rewriting
                                                                      ↳ QDP
                                                                        ↳ Rewriting
                                                                          ↳ QDP
                                                                            ↳ Rewriting
                                                                              ↳ QDP
                                                                                ↳ Rewriting
                                                                                  ↳ QDP
                                                                                    ↳ Rewriting
                                                                                      ↳ QDP
                                                                                        ↳ Rewriting
                                                                                          ↳ QDP
                                                                                            ↳ UsableRulesProof
                                                                                              ↳ QDP
                                                                                                ↳ QReductionProof
                                                                                                  ↳ QDP
                                                                                                    ↳ Rewriting
                                                                                                      ↳ QDP
                                                                                                        ↳ Rewriting
                                                                                                          ↳ QDP
                                                                                                            ↳ Rewriting
                                                                                                              ↳ QDP
                                                                                                                ↳ Rewriting
                                                                                                                  ↳ QDP
                                                                                                                    ↳ Rewriting
                                                                                                                      ↳ QDP
                                                                                                                        ↳ Rewriting
                                                                                                                          ↳ QDP
                                                                                                                            ↳ DependencyGraphProof
                                                                                                                              ↳ QDP
                                                                                                                                ↳ Rewriting
                                                                                                                                  ↳ QDP
                                                                                                                                    ↳ Rewriting
                                                                                                                                      ↳ QDP
                                                                                                                                        ↳ DependencyGraphProof
                                                                                                                                          ↳ QDP
                                                                                                                                            ↳ Rewriting
                                                                                                                                              ↳ QDP
                                                                                                                                                ↳ Rewriting
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP

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

new_mkVBalBranch(zzz31, Branch(zzz520, zzz521, Neg(Zero), zzz523, zzz524), Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), h) → new_mkVBalBranch3MkVBalBranch13(zzz340, zzz341, zzz34200, zzz343, zzz344, zzz520, zzz521, zzz523, zzz524, zzz31, new_primPlusNat2(new_primMulNat0(zzz34200), Succ(zzz34200)), h)
new_mkVBalBranch(zzz31, Branch(zzz520, zzz521, Neg(Succ(zzz52200)), zzz523, zzz524), Branch(zzz340, zzz341, zzz342, zzz343, zzz344), h) → new_mkVBalBranch3MkVBalBranch24(zzz340, zzz341, zzz342, zzz343, zzz344, zzz520, zzz521, zzz52200, zzz523, zzz524, zzz31, Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat3(new_primPlusNat1(zzz52200), zzz52200)), zzz52200))), h)
new_mkVBalBranch3MkVBalBranch11(zzz2033, zzz2034, zzz2035, zzz2036, zzz2037, zzz2038, zzz2039, zzz2040, zzz2041, zzz2042, zzz2043, Zero, Succ(zzz20450), bb) → new_mkVBalBranch(zzz2043, zzz2042, Branch(zzz2033, zzz2034, Pos(Succ(zzz2035)), zzz2036, zzz2037), bb)
new_mkVBalBranch3MkVBalBranch26(zzz1133, zzz1134, zzz1135, zzz1136, zzz1137, zzz1138, zzz1139, zzz1140, zzz1141, zzz1142, Succ(zzz11430), Succ(zzz11440), be) → new_mkVBalBranch3MkVBalBranch26(zzz1133, zzz1134, zzz1135, zzz1136, zzz1137, zzz1138, zzz1139, zzz1140, zzz1141, zzz1142, zzz11430, zzz11440, be)
new_mkVBalBranch3MkVBalBranch24(zzz340, zzz341, Pos(zzz3420), zzz343, zzz344, zzz520, zzz521, zzz52200, zzz523, zzz524, zzz31, Succ(zzz690), h) → new_mkVBalBranch(zzz31, Branch(zzz520, zzz521, Neg(Succ(zzz52200)), zzz523, zzz524), zzz343, h)
new_mkVBalBranch3MkVBalBranch25(zzz537, zzz538, zzz539, zzz540, zzz541, zzz542, zzz543, zzz544, zzz545, zzz546, zzz547, Succ(zzz5480), Zero, bc) → new_mkVBalBranch3MkVBalBranch15(zzz537, zzz538, zzz539, zzz540, zzz541, zzz542, zzz543, zzz544, zzz545, zzz546, zzz547, new_primPlusNat2(new_primPlusNat3(Succ(new_primPlusNat3(new_primPlusNat1(zzz539), zzz539)), Succ(zzz539)), Succ(zzz539)), bc)
new_mkVBalBranch3MkVBalBranch12(zzz340, zzz341, zzz34200, zzz343, zzz344, zzz520, zzz521, zzz523, zzz524, zzz31, Succ(zzz1250), h) → new_mkVBalBranch(zzz31, zzz524, Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), h)
new_mkVBalBranch3MkVBalBranch20(zzz929, zzz930, zzz931, zzz932, zzz933, zzz934, zzz935, zzz936, zzz937, zzz938, zzz939, Zero, Succ(zzz9410), ba) → new_mkVBalBranch(zzz939, Branch(zzz934, zzz935, Pos(Succ(zzz936)), zzz937, zzz938), zzz932, ba)
new_mkVBalBranch3MkVBalBranch24(zzz340, zzz341, Neg(Succ(Succ(Zero))), zzz343, zzz344, zzz520, zzz521, Zero, zzz523, zzz524, zzz31, Succ(Succ(zzz6900)), h) → new_mkVBalBranch3MkVBalBranch26(zzz340, zzz341, Succ(Zero), zzz343, zzz344, zzz520, zzz521, zzz523, zzz524, zzz31, Zero, Succ(zzz6900), h)
new_mkVBalBranch3MkVBalBranch211(zzz537, zzz538, zzz539, zzz540, zzz541, zzz542, zzz543, zzz544, zzz545, zzz546, zzz547, bc) → new_mkVBalBranch3MkVBalBranch15(zzz537, zzz538, zzz539, zzz540, zzz541, zzz542, zzz543, zzz544, zzz545, zzz546, zzz547, new_primPlusNat2(new_primPlusNat3(Succ(new_primPlusNat3(new_primPlusNat1(zzz539), zzz539)), Succ(zzz539)), Succ(zzz539)), bc)
new_mkVBalBranch3MkVBalBranch17(zzz340, zzz341, zzz34200, zzz343, zzz344, zzz520, zzz521, zzz52200, zzz523, zzz524, zzz31, h) → new_mkVBalBranch(zzz31, zzz524, Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), h)
new_mkVBalBranch3MkVBalBranch26(zzz1133, zzz1134, zzz1135, zzz1136, zzz1137, zzz1138, zzz1139, zzz1140, zzz1141, zzz1142, Zero, Zero, be) → new_mkVBalBranch3MkVBalBranch29(zzz1133, zzz1134, zzz1135, zzz1136, zzz1137, zzz1138, zzz1139, zzz1140, zzz1141, zzz1142, be)
new_mkVBalBranch3MkVBalBranch1(zzz340, zzz341, zzz34200, zzz343, zzz344, zzz520, zzz521, zzz52200, zzz523, zzz524, zzz31, Succ(zzz1430), h) → new_mkVBalBranch(zzz31, zzz524, Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), h)
new_mkVBalBranch3MkVBalBranch24(zzz340, zzz341, Neg(Succ(Zero)), zzz343, zzz344, zzz520, zzz521, zzz52200, zzz523, zzz524, zzz31, Succ(zzz690), h) → new_mkVBalBranch(zzz31, Branch(zzz520, zzz521, Neg(Succ(zzz52200)), zzz523, zzz524), zzz343, h)
new_mkVBalBranch3MkVBalBranch20(zzz929, zzz930, zzz931, zzz932, zzz933, zzz934, zzz935, zzz936, zzz937, zzz938, zzz939, Zero, Zero, ba) → new_mkVBalBranch3MkVBalBranch23(zzz929, zzz930, zzz931, zzz932, zzz933, zzz934, zzz935, zzz936, zzz937, zzz938, zzz939, ba)
new_mkVBalBranch3MkVBalBranch13(zzz340, zzz341, zzz34200, zzz343, zzz344, zzz520, zzz521, zzz523, zzz524, zzz31, Succ(zzz1290), h) → new_mkVBalBranch(zzz31, zzz524, Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), h)
new_mkVBalBranch3MkVBalBranch2(zzz340, zzz341, Pos(Succ(zzz34200)), zzz343, zzz344, zzz520, zzz521, zzz52200, zzz523, zzz524, zzz31, Succ(zzz680), h) → new_mkVBalBranch3MkVBalBranch20(zzz340, zzz341, zzz34200, zzz343, zzz344, zzz520, zzz521, zzz52200, zzz523, zzz524, zzz31, Succ(new_primPlusNat2(zzz680, zzz52200)), zzz34200, h)
new_mkVBalBranch3MkVBalBranch24(zzz340, zzz341, Neg(Zero), zzz343, zzz344, zzz520, zzz521, zzz52200, zzz523, zzz524, zzz31, Succ(zzz690), h) → new_mkVBalBranch(zzz31, Branch(zzz520, zzz521, Neg(Succ(zzz52200)), zzz523, zzz524), zzz343, h)
new_mkVBalBranch(zzz31, Branch(zzz520, zzz521, Neg(Zero), zzz523, zzz524), Branch(zzz340, zzz341, Pos(Succ(zzz34200)), zzz343, zzz344), h) → new_mkVBalBranch(zzz31, Branch(zzz520, zzz521, Neg(Zero), zzz523, zzz524), zzz343, h)
new_mkVBalBranch3MkVBalBranch20(zzz929, zzz930, zzz931, zzz932, zzz933, zzz934, zzz935, zzz936, zzz937, zzz938, zzz939, Succ(zzz9400), Succ(zzz9410), ba) → new_mkVBalBranch3MkVBalBranch20(zzz929, zzz930, zzz931, zzz932, zzz933, zzz934, zzz935, zzz936, zzz937, zzz938, zzz939, zzz9400, zzz9410, ba)
new_mkVBalBranch3MkVBalBranch26(zzz1133, zzz1134, zzz1135, zzz1136, zzz1137, zzz1138, zzz1139, zzz1140, zzz1141, zzz1142, Succ(zzz11430), Zero, be) → new_mkVBalBranch3MkVBalBranch212(zzz1133, zzz1134, zzz1135, zzz1136, zzz1137, zzz1138, zzz1139, zzz1140, zzz1141, zzz1142, be)
new_mkVBalBranch3MkVBalBranch1(zzz340, zzz341, zzz34200, zzz343, zzz344, zzz520, zzz521, zzz52200, zzz523, zzz524, zzz31, Zero, h) → new_mkVBalBranch3MkVBalBranch17(zzz340, zzz341, zzz34200, zzz343, zzz344, zzz520, zzz521, zzz52200, zzz523, zzz524, zzz31, h)
new_mkVBalBranch3MkVBalBranch16(zzz1702, zzz1703, zzz1704, zzz1705, zzz1706, zzz1707, zzz1708, zzz1709, zzz1710, zzz1711, zzz1712, Succ(zzz17130), Succ(zzz17140), bd) → new_mkVBalBranch3MkVBalBranch16(zzz1702, zzz1703, zzz1704, zzz1705, zzz1706, zzz1707, zzz1708, zzz1709, zzz1710, zzz1711, zzz1712, zzz17130, zzz17140, bd)
new_mkVBalBranch3MkVBalBranch29(zzz818, zzz819, zzz820, zzz821, zzz822, zzz823, zzz824, zzz825, zzz826, zzz827, bf) → new_mkVBalBranch3MkVBalBranch14(zzz818, zzz819, zzz820, zzz821, zzz822, zzz823, zzz824, zzz825, zzz826, zzz827, new_primPlusNat2(new_primMulNat0(zzz820), Succ(zzz820)), bf)
new_mkVBalBranch3MkVBalBranch25(zzz537, zzz538, zzz539, zzz540, zzz541, zzz542, zzz543, zzz544, zzz545, zzz546, zzz547, Zero, Succ(zzz5490), bc) → new_mkVBalBranch(zzz547, Branch(zzz542, zzz543, Neg(Succ(Succ(zzz544))), zzz545, zzz546), zzz540, bc)
new_mkVBalBranch3MkVBalBranch11(zzz2033, zzz2034, zzz2035, zzz2036, zzz2037, zzz2038, zzz2039, zzz2040, zzz2041, zzz2042, zzz2043, Succ(zzz20440), Succ(zzz20450), bb) → new_mkVBalBranch3MkVBalBranch11(zzz2033, zzz2034, zzz2035, zzz2036, zzz2037, zzz2038, zzz2039, zzz2040, zzz2041, zzz2042, zzz2043, zzz20440, zzz20450, bb)
new_mkVBalBranch3MkVBalBranch25(zzz537, zzz538, zzz539, zzz540, zzz541, zzz542, zzz543, zzz544, zzz545, zzz546, zzz547, Succ(zzz5480), Succ(zzz5490), bc) → new_mkVBalBranch3MkVBalBranch25(zzz537, zzz538, zzz539, zzz540, zzz541, zzz542, zzz543, zzz544, zzz545, zzz546, zzz547, zzz5480, zzz5490, bc)
new_mkVBalBranch3MkVBalBranch212(zzz818, zzz819, zzz820, zzz821, zzz822, zzz823, zzz824, zzz825, zzz826, zzz827, bf) → new_mkVBalBranch3MkVBalBranch14(zzz818, zzz819, zzz820, zzz821, zzz822, zzz823, zzz824, zzz825, zzz826, zzz827, new_primPlusNat2(new_primMulNat0(zzz820), Succ(zzz820)), bf)
new_mkVBalBranch(zzz31, Branch(zzz520, zzz521, Pos(Succ(zzz52200)), zzz523, zzz524), Branch(zzz340, zzz341, zzz342, zzz343, zzz344), h) → new_mkVBalBranch3MkVBalBranch2(zzz340, zzz341, zzz342, zzz343, zzz344, zzz520, zzz521, zzz52200, zzz523, zzz524, zzz31, Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat3(new_primPlusNat1(zzz52200), zzz52200)), zzz52200))), h)
new_mkVBalBranch3MkVBalBranch10(zzz929, zzz930, zzz931, zzz932, zzz933, zzz934, zzz935, zzz936, zzz937, zzz938, zzz939, Succ(zzz10020), ba) → new_mkVBalBranch3MkVBalBranch11(zzz929, zzz930, zzz931, zzz932, zzz933, zzz934, zzz935, zzz936, zzz937, zzz938, zzz939, Succ(zzz10020), Succ(zzz936), ba)
new_mkVBalBranch3MkVBalBranch14(zzz818, zzz819, zzz820, zzz821, zzz822, zzz823, zzz824, zzz825, zzz826, zzz827, Succ(zzz8960), bf) → new_mkVBalBranch3MkVBalBranch16(zzz818, zzz819, zzz820, zzz821, zzz822, zzz823, zzz824, Zero, zzz825, zzz826, zzz827, Succ(Zero), Succ(zzz8960), bf)
new_mkVBalBranch3MkVBalBranch24(zzz340, zzz341, Neg(Succ(Succ(Succ(zzz3420000)))), zzz343, zzz344, zzz520, zzz521, Succ(zzz522000), zzz523, zzz524, zzz31, Succ(Succ(zzz6900)), h) → new_mkVBalBranch3MkVBalBranch25(zzz340, zzz341, Succ(Succ(zzz3420000)), zzz343, zzz344, zzz520, zzz521, zzz522000, zzz523, zzz524, zzz31, Succ(zzz3420000), Succ(Succ(new_primPlusNat2(zzz6900, zzz522000))), h)
new_mkVBalBranch3MkVBalBranch26(zzz1133, zzz1134, zzz1135, zzz1136, zzz1137, zzz1138, zzz1139, zzz1140, zzz1141, zzz1142, Zero, Succ(zzz11440), be) → new_mkVBalBranch(zzz1142, Branch(zzz1138, zzz1139, Neg(Succ(Zero)), zzz1140, zzz1141), zzz1136, be)
new_mkVBalBranch3MkVBalBranch24(zzz340, zzz341, Neg(Succ(Succ(Zero))), zzz343, zzz344, zzz520, zzz521, Succ(zzz522000), zzz523, zzz524, zzz31, Succ(Succ(zzz6900)), h) → new_mkVBalBranch3MkVBalBranch25(zzz340, zzz341, Succ(Zero), zzz343, zzz344, zzz520, zzz521, zzz522000, zzz523, zzz524, zzz31, Zero, Succ(Succ(new_primPlusNat2(zzz6900, zzz522000))), h)
new_mkVBalBranch(zzz31, Branch(zzz520, zzz521, Pos(Zero), zzz523, zzz524), Branch(zzz340, zzz341, Pos(Succ(zzz34200)), zzz343, zzz344), h) → new_mkVBalBranch(zzz31, Branch(zzz520, zzz521, Pos(Zero), zzz523, zzz524), zzz343, h)
new_mkVBalBranch3MkVBalBranch20(zzz929, zzz930, zzz931, zzz932, zzz933, zzz934, zzz935, zzz936, zzz937, zzz938, zzz939, Succ(zzz9400), Zero, ba) → new_mkVBalBranch3MkVBalBranch10(zzz929, zzz930, zzz931, zzz932, zzz933, zzz934, zzz935, zzz936, zzz937, zzz938, zzz939, new_primPlusNat2(new_primPlusNat3(Succ(new_primPlusNat3(new_primPlusNat1(zzz931), zzz931)), Succ(zzz931)), Succ(zzz931)), ba)
new_mkVBalBranch(zzz31, Branch(zzz520, zzz521, Pos(Zero), zzz523, zzz524), Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), h) → new_mkVBalBranch3MkVBalBranch12(zzz340, zzz341, zzz34200, zzz343, zzz344, zzz520, zzz521, zzz523, zzz524, zzz31, new_primPlusNat2(Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat3(new_primPlusNat1(zzz34200), zzz34200)), zzz34200))), Succ(zzz34200)), h)
new_mkVBalBranch3MkVBalBranch2(zzz340, zzz341, Pos(Zero), zzz343, zzz344, zzz520, zzz521, zzz52200, zzz523, zzz524, zzz31, Succ(zzz680), h) → new_mkVBalBranch(zzz31, zzz524, Branch(zzz340, zzz341, Pos(Zero), zzz343, zzz344), h)
new_mkVBalBranch3MkVBalBranch23(zzz929, zzz930, zzz931, zzz932, zzz933, zzz934, zzz935, zzz936, zzz937, zzz938, zzz939, ba) → new_mkVBalBranch3MkVBalBranch10(zzz929, zzz930, zzz931, zzz932, zzz933, zzz934, zzz935, zzz936, zzz937, zzz938, zzz939, new_primPlusNat2(new_primMulNat0(zzz931), Succ(zzz931)), ba)
new_mkVBalBranch3MkVBalBranch2(zzz340, zzz341, Neg(Zero), zzz343, zzz344, zzz520, zzz521, zzz52200, zzz523, zzz524, zzz31, Succ(zzz680), h) → new_mkVBalBranch(zzz31, zzz524, Branch(zzz340, zzz341, Neg(Zero), zzz343, zzz344), h)
new_mkVBalBranch3MkVBalBranch2(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344, zzz520, zzz521, zzz52200, zzz523, zzz524, zzz31, Succ(zzz680), h) → new_mkVBalBranch3MkVBalBranch1(zzz340, zzz341, zzz34200, zzz343, zzz344, zzz520, zzz521, zzz52200, zzz523, zzz524, zzz31, new_primPlusNat2(Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat3(new_primPlusNat1(zzz34200), zzz34200)), zzz34200))), Succ(zzz34200)), h)
new_mkVBalBranch3MkVBalBranch16(zzz1702, zzz1703, zzz1704, zzz1705, zzz1706, zzz1707, zzz1708, zzz1709, zzz1710, zzz1711, zzz1712, Zero, Succ(zzz17140), bd) → new_mkVBalBranch(zzz1712, zzz1711, Branch(zzz1702, zzz1703, Neg(Succ(zzz1704)), zzz1705, zzz1706), bd)
new_mkVBalBranch3MkVBalBranch24(zzz340, zzz341, Neg(Succ(Succ(Succ(zzz3420000)))), zzz343, zzz344, zzz520, zzz521, Zero, zzz523, zzz524, zzz31, Succ(Succ(zzz6900)), h) → new_mkVBalBranch3MkVBalBranch26(zzz340, zzz341, Succ(Succ(zzz3420000)), zzz343, zzz344, zzz520, zzz521, zzz523, zzz524, zzz31, Succ(zzz3420000), Succ(zzz6900), h)
new_mkVBalBranch3MkVBalBranch15(zzz537, zzz538, zzz539, zzz540, zzz541, zzz542, zzz543, zzz544, zzz545, zzz546, zzz547, Succ(zzz6990), bc) → new_mkVBalBranch3MkVBalBranch16(zzz537, zzz538, zzz539, zzz540, zzz541, zzz542, zzz543, Succ(zzz544), zzz545, zzz546, zzz547, Succ(Succ(zzz544)), Succ(zzz6990), bc)
new_mkVBalBranch3MkVBalBranch10(zzz929, zzz930, zzz931, zzz932, zzz933, zzz934, zzz935, zzz936, zzz937, zzz938, zzz939, Zero, ba) → new_mkVBalBranch3MkVBalBranch11(zzz929, zzz930, zzz931, zzz932, zzz933, zzz934, zzz935, zzz936, zzz937, zzz938, zzz939, Zero, Succ(zzz936), ba)
new_mkVBalBranch3MkVBalBranch25(zzz537, zzz538, zzz539, zzz540, zzz541, zzz542, zzz543, zzz544, zzz545, zzz546, zzz547, Zero, Zero, bc) → new_mkVBalBranch3MkVBalBranch211(zzz537, zzz538, zzz539, zzz540, zzz541, zzz542, zzz543, zzz544, zzz545, zzz546, zzz547, bc)

The TRS R consists of the following rules:

new_primMulNat0(zzz6200) → new_primPlusNat3(Succ(new_primPlusNat3(new_primPlusNat1(zzz6200), zzz6200)), Succ(zzz6200))
new_primPlusNat2(Succ(zzz900), Succ(zzz9100)) → Succ(Succ(new_primPlusNat2(zzz900, zzz9100)))
new_primPlusNat2(Zero, Succ(zzz9100)) → Succ(zzz9100)
new_primPlusNat2(Zero, Zero) → Zero
new_primPlusNat2(Succ(zzz900), Zero) → Succ(zzz900)
new_primPlusNat1(Zero) → Zero
new_primPlusNat1(Succ(zzz62000)) → Succ(Succ(new_primPlusNat1(zzz62000)))
new_primPlusNat3(zzz90, Succ(zzz910)) → Succ(Succ(new_primPlusNat2(zzz90, zzz910)))
new_primPlusNat3(zzz90, Zero) → Succ(zzz90)

The set Q consists of the following terms:

new_primPlusNat2(Zero, Succ(x0))
new_primMulNat0(x0)
new_primPlusNat3(x0, Succ(x1))
new_primPlusNat2(Succ(x0), Succ(x1))
new_primPlusNat3(x0, Zero)
new_primPlusNat1(Zero)
new_primPlusNat2(Zero, Zero)
new_primPlusNat1(Succ(x0))
new_primPlusNat2(Succ(x0), Zero)

We have to consider all minimal (P,Q,R)-chains.
By rewriting [15] the rule new_mkVBalBranch(zzz31, Branch(zzz520, zzz521, Neg(Zero), zzz523, zzz524), Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), h) → new_mkVBalBranch3MkVBalBranch13(zzz340, zzz341, zzz34200, zzz343, zzz344, zzz520, zzz521, zzz523, zzz524, zzz31, new_primPlusNat2(new_primMulNat0(zzz34200), Succ(zzz34200)), h) at position [10,0] we obtained the following new rules:

new_mkVBalBranch(zzz31, Branch(zzz520, zzz521, Neg(Zero), zzz523, zzz524), Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), h) → new_mkVBalBranch3MkVBalBranch13(zzz340, zzz341, zzz34200, zzz343, zzz344, zzz520, zzz521, zzz523, zzz524, zzz31, new_primPlusNat2(new_primPlusNat3(Succ(new_primPlusNat3(new_primPlusNat1(zzz34200), zzz34200)), Succ(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
                                    ↳ DependencyGraphProof
                                      ↳ QDP
                                        ↳ Rewriting
                                          ↳ QDP
                                            ↳ Rewriting
                                              ↳ QDP
                                                ↳ Rewriting
                                                  ↳ QDP
                                                    ↳ Rewriting
                                                      ↳ QDP
                                                        ↳ Rewriting
                                                          ↳ QDP
                                                            ↳ Rewriting
                                                              ↳ QDP
                                                                ↳ Rewriting
                                                                  ↳ QDP
                                                                    ↳ Rewriting
                                                                      ↳ QDP
                                                                        ↳ Rewriting
                                                                          ↳ QDP
                                                                            ↳ Rewriting
                                                                              ↳ QDP
                                                                                ↳ Rewriting
                                                                                  ↳ QDP
                                                                                    ↳ Rewriting
                                                                                      ↳ QDP
                                                                                        ↳ Rewriting
                                                                                          ↳ QDP
                                                                                            ↳ UsableRulesProof
                                                                                              ↳ QDP
                                                                                                ↳ QReductionProof
                                                                                                  ↳ QDP
                                                                                                    ↳ Rewriting
                                                                                                      ↳ QDP
                                                                                                        ↳ Rewriting
                                                                                                          ↳ QDP
                                                                                                            ↳ Rewriting
                                                                                                              ↳ QDP
                                                                                                                ↳ Rewriting
                                                                                                                  ↳ QDP
                                                                                                                    ↳ Rewriting
                                                                                                                      ↳ QDP
                                                                                                                        ↳ Rewriting
                                                                                                                          ↳ QDP
                                                                                                                            ↳ DependencyGraphProof
                                                                                                                              ↳ QDP
                                                                                                                                ↳ Rewriting
                                                                                                                                  ↳ QDP
                                                                                                                                    ↳ Rewriting
                                                                                                                                      ↳ QDP
                                                                                                                                        ↳ DependencyGraphProof
                                                                                                                                          ↳ QDP
                                                                                                                                            ↳ Rewriting
                                                                                                                                              ↳ QDP
                                                                                                                                                ↳ Rewriting
                                                                                                                                                  ↳ QDP
                                                                                                                                                    ↳ Rewriting
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP

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

new_mkVBalBranch3MkVBalBranch11(zzz2033, zzz2034, zzz2035, zzz2036, zzz2037, zzz2038, zzz2039, zzz2040, zzz2041, zzz2042, zzz2043, Zero, Succ(zzz20450), bb) → new_mkVBalBranch(zzz2043, zzz2042, Branch(zzz2033, zzz2034, Pos(Succ(zzz2035)), zzz2036, zzz2037), bb)
new_mkVBalBranch(zzz31, Branch(zzz520, zzz521, Neg(Succ(zzz52200)), zzz523, zzz524), Branch(zzz340, zzz341, zzz342, zzz343, zzz344), h) → new_mkVBalBranch3MkVBalBranch24(zzz340, zzz341, zzz342, zzz343, zzz344, zzz520, zzz521, zzz52200, zzz523, zzz524, zzz31, Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat3(new_primPlusNat1(zzz52200), zzz52200)), zzz52200))), h)
new_mkVBalBranch3MkVBalBranch26(zzz1133, zzz1134, zzz1135, zzz1136, zzz1137, zzz1138, zzz1139, zzz1140, zzz1141, zzz1142, Succ(zzz11430), Succ(zzz11440), be) → new_mkVBalBranch3MkVBalBranch26(zzz1133, zzz1134, zzz1135, zzz1136, zzz1137, zzz1138, zzz1139, zzz1140, zzz1141, zzz1142, zzz11430, zzz11440, be)
new_mkVBalBranch3MkVBalBranch24(zzz340, zzz341, Pos(zzz3420), zzz343, zzz344, zzz520, zzz521, zzz52200, zzz523, zzz524, zzz31, Succ(zzz690), h) → new_mkVBalBranch(zzz31, Branch(zzz520, zzz521, Neg(Succ(zzz52200)), zzz523, zzz524), zzz343, h)
new_mkVBalBranch3MkVBalBranch25(zzz537, zzz538, zzz539, zzz540, zzz541, zzz542, zzz543, zzz544, zzz545, zzz546, zzz547, Succ(zzz5480), Zero, bc) → new_mkVBalBranch3MkVBalBranch15(zzz537, zzz538, zzz539, zzz540, zzz541, zzz542, zzz543, zzz544, zzz545, zzz546, zzz547, new_primPlusNat2(new_primPlusNat3(Succ(new_primPlusNat3(new_primPlusNat1(zzz539), zzz539)), Succ(zzz539)), Succ(zzz539)), bc)
new_mkVBalBranch3MkVBalBranch12(zzz340, zzz341, zzz34200, zzz343, zzz344, zzz520, zzz521, zzz523, zzz524, zzz31, Succ(zzz1250), h) → new_mkVBalBranch(zzz31, zzz524, Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), h)
new_mkVBalBranch3MkVBalBranch20(zzz929, zzz930, zzz931, zzz932, zzz933, zzz934, zzz935, zzz936, zzz937, zzz938, zzz939, Zero, Succ(zzz9410), ba) → new_mkVBalBranch(zzz939, Branch(zzz934, zzz935, Pos(Succ(zzz936)), zzz937, zzz938), zzz932, ba)
new_mkVBalBranch3MkVBalBranch24(zzz340, zzz341, Neg(Succ(Succ(Zero))), zzz343, zzz344, zzz520, zzz521, Zero, zzz523, zzz524, zzz31, Succ(Succ(zzz6900)), h) → new_mkVBalBranch3MkVBalBranch26(zzz340, zzz341, Succ(Zero), zzz343, zzz344, zzz520, zzz521, zzz523, zzz524, zzz31, Zero, Succ(zzz6900), h)
new_mkVBalBranch3MkVBalBranch17(zzz340, zzz341, zzz34200, zzz343, zzz344, zzz520, zzz521, zzz52200, zzz523, zzz524, zzz31, h) → new_mkVBalBranch(zzz31, zzz524, Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), h)
new_mkVBalBranch3MkVBalBranch211(zzz537, zzz538, zzz539, zzz540, zzz541, zzz542, zzz543, zzz544, zzz545, zzz546, zzz547, bc) → new_mkVBalBranch3MkVBalBranch15(zzz537, zzz538, zzz539, zzz540, zzz541, zzz542, zzz543, zzz544, zzz545, zzz546, zzz547, new_primPlusNat2(new_primPlusNat3(Succ(new_primPlusNat3(new_primPlusNat1(zzz539), zzz539)), Succ(zzz539)), Succ(zzz539)), bc)
new_mkVBalBranch3MkVBalBranch1(zzz340, zzz341, zzz34200, zzz343, zzz344, zzz520, zzz521, zzz52200, zzz523, zzz524, zzz31, Succ(zzz1430), h) → new_mkVBalBranch(zzz31, zzz524, Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), h)
new_mkVBalBranch3MkVBalBranch26(zzz1133, zzz1134, zzz1135, zzz1136, zzz1137, zzz1138, zzz1139, zzz1140, zzz1141, zzz1142, Zero, Zero, be) → new_mkVBalBranch3MkVBalBranch29(zzz1133, zzz1134, zzz1135, zzz1136, zzz1137, zzz1138, zzz1139, zzz1140, zzz1141, zzz1142, be)
new_mkVBalBranch3MkVBalBranch20(zzz929, zzz930, zzz931, zzz932, zzz933, zzz934, zzz935, zzz936, zzz937, zzz938, zzz939, Zero, Zero, ba) → new_mkVBalBranch3MkVBalBranch23(zzz929, zzz930, zzz931, zzz932, zzz933, zzz934, zzz935, zzz936, zzz937, zzz938, zzz939, ba)
new_mkVBalBranch3MkVBalBranch24(zzz340, zzz341, Neg(Succ(Zero)), zzz343, zzz344, zzz520, zzz521, zzz52200, zzz523, zzz524, zzz31, Succ(zzz690), h) → new_mkVBalBranch(zzz31, Branch(zzz520, zzz521, Neg(Succ(zzz52200)), zzz523, zzz524), zzz343, h)
new_mkVBalBranch3MkVBalBranch13(zzz340, zzz341, zzz34200, zzz343, zzz344, zzz520, zzz521, zzz523, zzz524, zzz31, Succ(zzz1290), h) → new_mkVBalBranch(zzz31, zzz524, Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), h)
new_mkVBalBranch3MkVBalBranch2(zzz340, zzz341, Pos(Succ(zzz34200)), zzz343, zzz344, zzz520, zzz521, zzz52200, zzz523, zzz524, zzz31, Succ(zzz680), h) → new_mkVBalBranch3MkVBalBranch20(zzz340, zzz341, zzz34200, zzz343, zzz344, zzz520, zzz521, zzz52200, zzz523, zzz524, zzz31, Succ(new_primPlusNat2(zzz680, zzz52200)), zzz34200, h)
new_mkVBalBranch(zzz31, Branch(zzz520, zzz521, Neg(Zero), zzz523, zzz524), Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), h) → new_mkVBalBranch3MkVBalBranch13(zzz340, zzz341, zzz34200, zzz343, zzz344, zzz520, zzz521, zzz523, zzz524, zzz31, new_primPlusNat2(new_primPlusNat3(Succ(new_primPlusNat3(new_primPlusNat1(zzz34200), zzz34200)), Succ(zzz34200)), Succ(zzz34200)), h)
new_mkVBalBranch(zzz31, Branch(zzz520, zzz521, Neg(Zero), zzz523, zzz524), Branch(zzz340, zzz341, Pos(Succ(zzz34200)), zzz343, zzz344), h) → new_mkVBalBranch(zzz31, Branch(zzz520, zzz521, Neg(Zero), zzz523, zzz524), zzz343, h)
new_mkVBalBranch3MkVBalBranch24(zzz340, zzz341, Neg(Zero), zzz343, zzz344, zzz520, zzz521, zzz52200, zzz523, zzz524, zzz31, Succ(zzz690), h) → new_mkVBalBranch(zzz31, Branch(zzz520, zzz521, Neg(Succ(zzz52200)), zzz523, zzz524), zzz343, h)
new_mkVBalBranch3MkVBalBranch20(zzz929, zzz930, zzz931, zzz932, zzz933, zzz934, zzz935, zzz936, zzz937, zzz938, zzz939, Succ(zzz9400), Succ(zzz9410), ba) → new_mkVBalBranch3MkVBalBranch20(zzz929, zzz930, zzz931, zzz932, zzz933, zzz934, zzz935, zzz936, zzz937, zzz938, zzz939, zzz9400, zzz9410, ba)
new_mkVBalBranch3MkVBalBranch1(zzz340, zzz341, zzz34200, zzz343, zzz344, zzz520, zzz521, zzz52200, zzz523, zzz524, zzz31, Zero, h) → new_mkVBalBranch3MkVBalBranch17(zzz340, zzz341, zzz34200, zzz343, zzz344, zzz520, zzz521, zzz52200, zzz523, zzz524, zzz31, h)
new_mkVBalBranch3MkVBalBranch26(zzz1133, zzz1134, zzz1135, zzz1136, zzz1137, zzz1138, zzz1139, zzz1140, zzz1141, zzz1142, Succ(zzz11430), Zero, be) → new_mkVBalBranch3MkVBalBranch212(zzz1133, zzz1134, zzz1135, zzz1136, zzz1137, zzz1138, zzz1139, zzz1140, zzz1141, zzz1142, be)
new_mkVBalBranch3MkVBalBranch16(zzz1702, zzz1703, zzz1704, zzz1705, zzz1706, zzz1707, zzz1708, zzz1709, zzz1710, zzz1711, zzz1712, Succ(zzz17130), Succ(zzz17140), bd) → new_mkVBalBranch3MkVBalBranch16(zzz1702, zzz1703, zzz1704, zzz1705, zzz1706, zzz1707, zzz1708, zzz1709, zzz1710, zzz1711, zzz1712, zzz17130, zzz17140, bd)
new_mkVBalBranch3MkVBalBranch29(zzz818, zzz819, zzz820, zzz821, zzz822, zzz823, zzz824, zzz825, zzz826, zzz827, bf) → new_mkVBalBranch3MkVBalBranch14(zzz818, zzz819, zzz820, zzz821, zzz822, zzz823, zzz824, zzz825, zzz826, zzz827, new_primPlusNat2(new_primMulNat0(zzz820), Succ(zzz820)), bf)
new_mkVBalBranch3MkVBalBranch25(zzz537, zzz538, zzz539, zzz540, zzz541, zzz542, zzz543, zzz544, zzz545, zzz546, zzz547, Zero, Succ(zzz5490), bc) → new_mkVBalBranch(zzz547, Branch(zzz542, zzz543, Neg(Succ(Succ(zzz544))), zzz545, zzz546), zzz540, bc)
new_mkVBalBranch3MkVBalBranch11(zzz2033, zzz2034, zzz2035, zzz2036, zzz2037, zzz2038, zzz2039, zzz2040, zzz2041, zzz2042, zzz2043, Succ(zzz20440), Succ(zzz20450), bb) → new_mkVBalBranch3MkVBalBranch11(zzz2033, zzz2034, zzz2035, zzz2036, zzz2037, zzz2038, zzz2039, zzz2040, zzz2041, zzz2042, zzz2043, zzz20440, zzz20450, bb)
new_mkVBalBranch3MkVBalBranch25(zzz537, zzz538, zzz539, zzz540, zzz541, zzz542, zzz543, zzz544, zzz545, zzz546, zzz547, Succ(zzz5480), Succ(zzz5490), bc) → new_mkVBalBranch3MkVBalBranch25(zzz537, zzz538, zzz539, zzz540, zzz541, zzz542, zzz543, zzz544, zzz545, zzz546, zzz547, zzz5480, zzz5490, bc)
new_mkVBalBranch3MkVBalBranch10(zzz929, zzz930, zzz931, zzz932, zzz933, zzz934, zzz935, zzz936, zzz937, zzz938, zzz939, Succ(zzz10020), ba) → new_mkVBalBranch3MkVBalBranch11(zzz929, zzz930, zzz931, zzz932, zzz933, zzz934, zzz935, zzz936, zzz937, zzz938, zzz939, Succ(zzz10020), Succ(zzz936), ba)
new_mkVBalBranch(zzz31, Branch(zzz520, zzz521, Pos(Succ(zzz52200)), zzz523, zzz524), Branch(zzz340, zzz341, zzz342, zzz343, zzz344), h) → new_mkVBalBranch3MkVBalBranch2(zzz340, zzz341, zzz342, zzz343, zzz344, zzz520, zzz521, zzz52200, zzz523, zzz524, zzz31, Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat3(new_primPlusNat1(zzz52200), zzz52200)), zzz52200))), h)
new_mkVBalBranch3MkVBalBranch212(zzz818, zzz819, zzz820, zzz821, zzz822, zzz823, zzz824, zzz825, zzz826, zzz827, bf) → new_mkVBalBranch3MkVBalBranch14(zzz818, zzz819, zzz820, zzz821, zzz822, zzz823, zzz824, zzz825, zzz826, zzz827, new_primPlusNat2(new_primMulNat0(zzz820), Succ(zzz820)), bf)
new_mkVBalBranch3MkVBalBranch14(zzz818, zzz819, zzz820, zzz821, zzz822, zzz823, zzz824, zzz825, zzz826, zzz827, Succ(zzz8960), bf) → new_mkVBalBranch3MkVBalBranch16(zzz818, zzz819, zzz820, zzz821, zzz822, zzz823, zzz824, Zero, zzz825, zzz826, zzz827, Succ(Zero), Succ(zzz8960), bf)
new_mkVBalBranch3MkVBalBranch26(zzz1133, zzz1134, zzz1135, zzz1136, zzz1137, zzz1138, zzz1139, zzz1140, zzz1141, zzz1142, Zero, Succ(zzz11440), be) → new_mkVBalBranch(zzz1142, Branch(zzz1138, zzz1139, Neg(Succ(Zero)), zzz1140, zzz1141), zzz1136, be)
new_mkVBalBranch3MkVBalBranch24(zzz340, zzz341, Neg(Succ(Succ(Succ(zzz3420000)))), zzz343, zzz344, zzz520, zzz521, Succ(zzz522000), zzz523, zzz524, zzz31, Succ(Succ(zzz6900)), h) → new_mkVBalBranch3MkVBalBranch25(zzz340, zzz341, Succ(Succ(zzz3420000)), zzz343, zzz344, zzz520, zzz521, zzz522000, zzz523, zzz524, zzz31, Succ(zzz3420000), Succ(Succ(new_primPlusNat2(zzz6900, zzz522000))), h)
new_mkVBalBranch3MkVBalBranch24(zzz340, zzz341, Neg(Succ(Succ(Zero))), zzz343, zzz344, zzz520, zzz521, Succ(zzz522000), zzz523, zzz524, zzz31, Succ(Succ(zzz6900)), h) → new_mkVBalBranch3MkVBalBranch25(zzz340, zzz341, Succ(Zero), zzz343, zzz344, zzz520, zzz521, zzz522000, zzz523, zzz524, zzz31, Zero, Succ(Succ(new_primPlusNat2(zzz6900, zzz522000))), h)
new_mkVBalBranch3MkVBalBranch20(zzz929, zzz930, zzz931, zzz932, zzz933, zzz934, zzz935, zzz936, zzz937, zzz938, zzz939, Succ(zzz9400), Zero, ba) → new_mkVBalBranch3MkVBalBranch10(zzz929, zzz930, zzz931, zzz932, zzz933, zzz934, zzz935, zzz936, zzz937, zzz938, zzz939, new_primPlusNat2(new_primPlusNat3(Succ(new_primPlusNat3(new_primPlusNat1(zzz931), zzz931)), Succ(zzz931)), Succ(zzz931)), ba)
new_mkVBalBranch(zzz31, Branch(zzz520, zzz521, Pos(Zero), zzz523, zzz524), Branch(zzz340, zzz341, Pos(Succ(zzz34200)), zzz343, zzz344), h) → new_mkVBalBranch(zzz31, Branch(zzz520, zzz521, Pos(Zero), zzz523, zzz524), zzz343, h)
new_mkVBalBranch(zzz31, Branch(zzz520, zzz521, Pos(Zero), zzz523, zzz524), Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), h) → new_mkVBalBranch3MkVBalBranch12(zzz340, zzz341, zzz34200, zzz343, zzz344, zzz520, zzz521, zzz523, zzz524, zzz31, new_primPlusNat2(Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat3(new_primPlusNat1(zzz34200), zzz34200)), zzz34200))), Succ(zzz34200)), h)
new_mkVBalBranch3MkVBalBranch23(zzz929, zzz930, zzz931, zzz932, zzz933, zzz934, zzz935, zzz936, zzz937, zzz938, zzz939, ba) → new_mkVBalBranch3MkVBalBranch10(zzz929, zzz930, zzz931, zzz932, zzz933, zzz934, zzz935, zzz936, zzz937, zzz938, zzz939, new_primPlusNat2(new_primMulNat0(zzz931), Succ(zzz931)), ba)
new_mkVBalBranch3MkVBalBranch2(zzz340, zzz341, Pos(Zero), zzz343, zzz344, zzz520, zzz521, zzz52200, zzz523, zzz524, zzz31, Succ(zzz680), h) → new_mkVBalBranch(zzz31, zzz524, Branch(zzz340, zzz341, Pos(Zero), zzz343, zzz344), h)
new_mkVBalBranch3MkVBalBranch2(zzz340, zzz341, Neg(Zero), zzz343, zzz344, zzz520, zzz521, zzz52200, zzz523, zzz524, zzz31, Succ(zzz680), h) → new_mkVBalBranch(zzz31, zzz524, Branch(zzz340, zzz341, Neg(Zero), zzz343, zzz344), h)
new_mkVBalBranch3MkVBalBranch2(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344, zzz520, zzz521, zzz52200, zzz523, zzz524, zzz31, Succ(zzz680), h) → new_mkVBalBranch3MkVBalBranch1(zzz340, zzz341, zzz34200, zzz343, zzz344, zzz520, zzz521, zzz52200, zzz523, zzz524, zzz31, new_primPlusNat2(Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat3(new_primPlusNat1(zzz34200), zzz34200)), zzz34200))), Succ(zzz34200)), h)
new_mkVBalBranch3MkVBalBranch16(zzz1702, zzz1703, zzz1704, zzz1705, zzz1706, zzz1707, zzz1708, zzz1709, zzz1710, zzz1711, zzz1712, Zero, Succ(zzz17140), bd) → new_mkVBalBranch(zzz1712, zzz1711, Branch(zzz1702, zzz1703, Neg(Succ(zzz1704)), zzz1705, zzz1706), bd)
new_mkVBalBranch3MkVBalBranch10(zzz929, zzz930, zzz931, zzz932, zzz933, zzz934, zzz935, zzz936, zzz937, zzz938, zzz939, Zero, ba) → new_mkVBalBranch3MkVBalBranch11(zzz929, zzz930, zzz931, zzz932, zzz933, zzz934, zzz935, zzz936, zzz937, zzz938, zzz939, Zero, Succ(zzz936), ba)
new_mkVBalBranch3MkVBalBranch15(zzz537, zzz538, zzz539, zzz540, zzz541, zzz542, zzz543, zzz544, zzz545, zzz546, zzz547, Succ(zzz6990), bc) → new_mkVBalBranch3MkVBalBranch16(zzz537, zzz538, zzz539, zzz540, zzz541, zzz542, zzz543, Succ(zzz544), zzz545, zzz546, zzz547, Succ(Succ(zzz544)), Succ(zzz6990), bc)
new_mkVBalBranch3MkVBalBranch24(zzz340, zzz341, Neg(Succ(Succ(Succ(zzz3420000)))), zzz343, zzz344, zzz520, zzz521, Zero, zzz523, zzz524, zzz31, Succ(Succ(zzz6900)), h) → new_mkVBalBranch3MkVBalBranch26(zzz340, zzz341, Succ(Succ(zzz3420000)), zzz343, zzz344, zzz520, zzz521, zzz523, zzz524, zzz31, Succ(zzz3420000), Succ(zzz6900), h)
new_mkVBalBranch3MkVBalBranch25(zzz537, zzz538, zzz539, zzz540, zzz541, zzz542, zzz543, zzz544, zzz545, zzz546, zzz547, Zero, Zero, bc) → new_mkVBalBranch3MkVBalBranch211(zzz537, zzz538, zzz539, zzz540, zzz541, zzz542, zzz543, zzz544, zzz545, zzz546, zzz547, bc)

The TRS R consists of the following rules:

new_primMulNat0(zzz6200) → new_primPlusNat3(Succ(new_primPlusNat3(new_primPlusNat1(zzz6200), zzz6200)), Succ(zzz6200))
new_primPlusNat2(Succ(zzz900), Succ(zzz9100)) → Succ(Succ(new_primPlusNat2(zzz900, zzz9100)))
new_primPlusNat2(Zero, Succ(zzz9100)) → Succ(zzz9100)
new_primPlusNat2(Zero, Zero) → Zero
new_primPlusNat2(Succ(zzz900), Zero) → Succ(zzz900)
new_primPlusNat1(Zero) → Zero
new_primPlusNat1(Succ(zzz62000)) → Succ(Succ(new_primPlusNat1(zzz62000)))
new_primPlusNat3(zzz90, Succ(zzz910)) → Succ(Succ(new_primPlusNat2(zzz90, zzz910)))
new_primPlusNat3(zzz90, Zero) → Succ(zzz90)

The set Q consists of the following terms:

new_primPlusNat2(Zero, Succ(x0))
new_primMulNat0(x0)
new_primPlusNat3(x0, Succ(x1))
new_primPlusNat2(Succ(x0), Succ(x1))
new_primPlusNat3(x0, Zero)
new_primPlusNat1(Zero)
new_primPlusNat2(Zero, Zero)
new_primPlusNat1(Succ(x0))
new_primPlusNat2(Succ(x0), Zero)

We have to consider all minimal (P,Q,R)-chains.
By rewriting [15] the rule new_mkVBalBranch3MkVBalBranch29(zzz818, zzz819, zzz820, zzz821, zzz822, zzz823, zzz824, zzz825, zzz826, zzz827, bf) → new_mkVBalBranch3MkVBalBranch14(zzz818, zzz819, zzz820, zzz821, zzz822, zzz823, zzz824, zzz825, zzz826, zzz827, new_primPlusNat2(new_primMulNat0(zzz820), Succ(zzz820)), bf) at position [10,0] we obtained the following new rules:

new_mkVBalBranch3MkVBalBranch29(zzz818, zzz819, zzz820, zzz821, zzz822, zzz823, zzz824, zzz825, zzz826, zzz827, bf) → new_mkVBalBranch3MkVBalBranch14(zzz818, zzz819, zzz820, zzz821, zzz822, zzz823, zzz824, zzz825, zzz826, zzz827, new_primPlusNat2(new_primPlusNat3(Succ(new_primPlusNat3(new_primPlusNat1(zzz820), zzz820)), Succ(zzz820)), Succ(zzz820)), bf)



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

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

new_mkVBalBranch(zzz31, Branch(zzz520, zzz521, Neg(Succ(zzz52200)), zzz523, zzz524), Branch(zzz340, zzz341, zzz342, zzz343, zzz344), h) → new_mkVBalBranch3MkVBalBranch24(zzz340, zzz341, zzz342, zzz343, zzz344, zzz520, zzz521, zzz52200, zzz523, zzz524, zzz31, Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat3(new_primPlusNat1(zzz52200), zzz52200)), zzz52200))), h)
new_mkVBalBranch3MkVBalBranch11(zzz2033, zzz2034, zzz2035, zzz2036, zzz2037, zzz2038, zzz2039, zzz2040, zzz2041, zzz2042, zzz2043, Zero, Succ(zzz20450), bb) → new_mkVBalBranch(zzz2043, zzz2042, Branch(zzz2033, zzz2034, Pos(Succ(zzz2035)), zzz2036, zzz2037), bb)
new_mkVBalBranch3MkVBalBranch26(zzz1133, zzz1134, zzz1135, zzz1136, zzz1137, zzz1138, zzz1139, zzz1140, zzz1141, zzz1142, Succ(zzz11430), Succ(zzz11440), be) → new_mkVBalBranch3MkVBalBranch26(zzz1133, zzz1134, zzz1135, zzz1136, zzz1137, zzz1138, zzz1139, zzz1140, zzz1141, zzz1142, zzz11430, zzz11440, be)
new_mkVBalBranch3MkVBalBranch24(zzz340, zzz341, Pos(zzz3420), zzz343, zzz344, zzz520, zzz521, zzz52200, zzz523, zzz524, zzz31, Succ(zzz690), h) → new_mkVBalBranch(zzz31, Branch(zzz520, zzz521, Neg(Succ(zzz52200)), zzz523, zzz524), zzz343, h)
new_mkVBalBranch3MkVBalBranch25(zzz537, zzz538, zzz539, zzz540, zzz541, zzz542, zzz543, zzz544, zzz545, zzz546, zzz547, Succ(zzz5480), Zero, bc) → new_mkVBalBranch3MkVBalBranch15(zzz537, zzz538, zzz539, zzz540, zzz541, zzz542, zzz543, zzz544, zzz545, zzz546, zzz547, new_primPlusNat2(new_primPlusNat3(Succ(new_primPlusNat3(new_primPlusNat1(zzz539), zzz539)), Succ(zzz539)), Succ(zzz539)), bc)
new_mkVBalBranch3MkVBalBranch12(zzz340, zzz341, zzz34200, zzz343, zzz344, zzz520, zzz521, zzz523, zzz524, zzz31, Succ(zzz1250), h) → new_mkVBalBranch(zzz31, zzz524, Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), h)
new_mkVBalBranch3MkVBalBranch20(zzz929, zzz930, zzz931, zzz932, zzz933, zzz934, zzz935, zzz936, zzz937, zzz938, zzz939, Zero, Succ(zzz9410), ba) → new_mkVBalBranch(zzz939, Branch(zzz934, zzz935, Pos(Succ(zzz936)), zzz937, zzz938), zzz932, ba)
new_mkVBalBranch3MkVBalBranch24(zzz340, zzz341, Neg(Succ(Succ(Zero))), zzz343, zzz344, zzz520, zzz521, Zero, zzz523, zzz524, zzz31, Succ(Succ(zzz6900)), h) → new_mkVBalBranch3MkVBalBranch26(zzz340, zzz341, Succ(Zero), zzz343, zzz344, zzz520, zzz521, zzz523, zzz524, zzz31, Zero, Succ(zzz6900), h)
new_mkVBalBranch3MkVBalBranch211(zzz537, zzz538, zzz539, zzz540, zzz541, zzz542, zzz543, zzz544, zzz545, zzz546, zzz547, bc) → new_mkVBalBranch3MkVBalBranch15(zzz537, zzz538, zzz539, zzz540, zzz541, zzz542, zzz543, zzz544, zzz545, zzz546, zzz547, new_primPlusNat2(new_primPlusNat3(Succ(new_primPlusNat3(new_primPlusNat1(zzz539), zzz539)), Succ(zzz539)), Succ(zzz539)), bc)
new_mkVBalBranch3MkVBalBranch17(zzz340, zzz341, zzz34200, zzz343, zzz344, zzz520, zzz521, zzz52200, zzz523, zzz524, zzz31, h) → new_mkVBalBranch(zzz31, zzz524, Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), h)
new_mkVBalBranch3MkVBalBranch26(zzz1133, zzz1134, zzz1135, zzz1136, zzz1137, zzz1138, zzz1139, zzz1140, zzz1141, zzz1142, Zero, Zero, be) → new_mkVBalBranch3MkVBalBranch29(zzz1133, zzz1134, zzz1135, zzz1136, zzz1137, zzz1138, zzz1139, zzz1140, zzz1141, zzz1142, be)
new_mkVBalBranch3MkVBalBranch1(zzz340, zzz341, zzz34200, zzz343, zzz344, zzz520, zzz521, zzz52200, zzz523, zzz524, zzz31, Succ(zzz1430), h) → new_mkVBalBranch(zzz31, zzz524, Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), h)
new_mkVBalBranch3MkVBalBranch24(zzz340, zzz341, Neg(Succ(Zero)), zzz343, zzz344, zzz520, zzz521, zzz52200, zzz523, zzz524, zzz31, Succ(zzz690), h) → new_mkVBalBranch(zzz31, Branch(zzz520, zzz521, Neg(Succ(zzz52200)), zzz523, zzz524), zzz343, h)
new_mkVBalBranch3MkVBalBranch20(zzz929, zzz930, zzz931, zzz932, zzz933, zzz934, zzz935, zzz936, zzz937, zzz938, zzz939, Zero, Zero, ba) → new_mkVBalBranch3MkVBalBranch23(zzz929, zzz930, zzz931, zzz932, zzz933, zzz934, zzz935, zzz936, zzz937, zzz938, zzz939, ba)
new_mkVBalBranch3MkVBalBranch13(zzz340, zzz341, zzz34200, zzz343, zzz344, zzz520, zzz521, zzz523, zzz524, zzz31, Succ(zzz1290), h) → new_mkVBalBranch(zzz31, zzz524, Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), h)
new_mkVBalBranch3MkVBalBranch2(zzz340, zzz341, Pos(Succ(zzz34200)), zzz343, zzz344, zzz520, zzz521, zzz52200, zzz523, zzz524, zzz31, Succ(zzz680), h) → new_mkVBalBranch3MkVBalBranch20(zzz340, zzz341, zzz34200, zzz343, zzz344, zzz520, zzz521, zzz52200, zzz523, zzz524, zzz31, Succ(new_primPlusNat2(zzz680, zzz52200)), zzz34200, h)
new_mkVBalBranch(zzz31, Branch(zzz520, zzz521, Neg(Zero), zzz523, zzz524), Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), h) → new_mkVBalBranch3MkVBalBranch13(zzz340, zzz341, zzz34200, zzz343, zzz344, zzz520, zzz521, zzz523, zzz524, zzz31, new_primPlusNat2(new_primPlusNat3(Succ(new_primPlusNat3(new_primPlusNat1(zzz34200), zzz34200)), Succ(zzz34200)), Succ(zzz34200)), h)
new_mkVBalBranch3MkVBalBranch24(zzz340, zzz341, Neg(Zero), zzz343, zzz344, zzz520, zzz521, zzz52200, zzz523, zzz524, zzz31, Succ(zzz690), h) → new_mkVBalBranch(zzz31, Branch(zzz520, zzz521, Neg(Succ(zzz52200)), zzz523, zzz524), zzz343, h)
new_mkVBalBranch(zzz31, Branch(zzz520, zzz521, Neg(Zero), zzz523, zzz524), Branch(zzz340, zzz341, Pos(Succ(zzz34200)), zzz343, zzz344), h) → new_mkVBalBranch(zzz31, Branch(zzz520, zzz521, Neg(Zero), zzz523, zzz524), zzz343, h)
new_mkVBalBranch3MkVBalBranch20(zzz929, zzz930, zzz931, zzz932, zzz933, zzz934, zzz935, zzz936, zzz937, zzz938, zzz939, Succ(zzz9400), Succ(zzz9410), ba) → new_mkVBalBranch3MkVBalBranch20(zzz929, zzz930, zzz931, zzz932, zzz933, zzz934, zzz935, zzz936, zzz937, zzz938, zzz939, zzz9400, zzz9410, ba)
new_mkVBalBranch3MkVBalBranch26(zzz1133, zzz1134, zzz1135, zzz1136, zzz1137, zzz1138, zzz1139, zzz1140, zzz1141, zzz1142, Succ(zzz11430), Zero, be) → new_mkVBalBranch3MkVBalBranch212(zzz1133, zzz1134, zzz1135, zzz1136, zzz1137, zzz1138, zzz1139, zzz1140, zzz1141, zzz1142, be)
new_mkVBalBranch3MkVBalBranch1(zzz340, zzz341, zzz34200, zzz343, zzz344, zzz520, zzz521, zzz52200, zzz523, zzz524, zzz31, Zero, h) → new_mkVBalBranch3MkVBalBranch17(zzz340, zzz341, zzz34200, zzz343, zzz344, zzz520, zzz521, zzz52200, zzz523, zzz524, zzz31, h)
new_mkVBalBranch3MkVBalBranch16(zzz1702, zzz1703, zzz1704, zzz1705, zzz1706, zzz1707, zzz1708, zzz1709, zzz1710, zzz1711, zzz1712, Succ(zzz17130), Succ(zzz17140), bd) → new_mkVBalBranch3MkVBalBranch16(zzz1702, zzz1703, zzz1704, zzz1705, zzz1706, zzz1707, zzz1708, zzz1709, zzz1710, zzz1711, zzz1712, zzz17130, zzz17140, bd)
new_mkVBalBranch3MkVBalBranch25(zzz537, zzz538, zzz539, zzz540, zzz541, zzz542, zzz543, zzz544, zzz545, zzz546, zzz547, Zero, Succ(zzz5490), bc) → new_mkVBalBranch(zzz547, Branch(zzz542, zzz543, Neg(Succ(Succ(zzz544))), zzz545, zzz546), zzz540, bc)
new_mkVBalBranch3MkVBalBranch11(zzz2033, zzz2034, zzz2035, zzz2036, zzz2037, zzz2038, zzz2039, zzz2040, zzz2041, zzz2042, zzz2043, Succ(zzz20440), Succ(zzz20450), bb) → new_mkVBalBranch3MkVBalBranch11(zzz2033, zzz2034, zzz2035, zzz2036, zzz2037, zzz2038, zzz2039, zzz2040, zzz2041, zzz2042, zzz2043, zzz20440, zzz20450, bb)
new_mkVBalBranch3MkVBalBranch25(zzz537, zzz538, zzz539, zzz540, zzz541, zzz542, zzz543, zzz544, zzz545, zzz546, zzz547, Succ(zzz5480), Succ(zzz5490), bc) → new_mkVBalBranch3MkVBalBranch25(zzz537, zzz538, zzz539, zzz540, zzz541, zzz542, zzz543, zzz544, zzz545, zzz546, zzz547, zzz5480, zzz5490, bc)
new_mkVBalBranch3MkVBalBranch29(zzz818, zzz819, zzz820, zzz821, zzz822, zzz823, zzz824, zzz825, zzz826, zzz827, bf) → new_mkVBalBranch3MkVBalBranch14(zzz818, zzz819, zzz820, zzz821, zzz822, zzz823, zzz824, zzz825, zzz826, zzz827, new_primPlusNat2(new_primPlusNat3(Succ(new_primPlusNat3(new_primPlusNat1(zzz820), zzz820)), Succ(zzz820)), Succ(zzz820)), bf)
new_mkVBalBranch3MkVBalBranch212(zzz818, zzz819, zzz820, zzz821, zzz822, zzz823, zzz824, zzz825, zzz826, zzz827, bf) → new_mkVBalBranch3MkVBalBranch14(zzz818, zzz819, zzz820, zzz821, zzz822, zzz823, zzz824, zzz825, zzz826, zzz827, new_primPlusNat2(new_primMulNat0(zzz820), Succ(zzz820)), bf)
new_mkVBalBranch(zzz31, Branch(zzz520, zzz521, Pos(Succ(zzz52200)), zzz523, zzz524), Branch(zzz340, zzz341, zzz342, zzz343, zzz344), h) → new_mkVBalBranch3MkVBalBranch2(zzz340, zzz341, zzz342, zzz343, zzz344, zzz520, zzz521, zzz52200, zzz523, zzz524, zzz31, Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat3(new_primPlusNat1(zzz52200), zzz52200)), zzz52200))), h)
new_mkVBalBranch3MkVBalBranch10(zzz929, zzz930, zzz931, zzz932, zzz933, zzz934, zzz935, zzz936, zzz937, zzz938, zzz939, Succ(zzz10020), ba) → new_mkVBalBranch3MkVBalBranch11(zzz929, zzz930, zzz931, zzz932, zzz933, zzz934, zzz935, zzz936, zzz937, zzz938, zzz939, Succ(zzz10020), Succ(zzz936), ba)
new_mkVBalBranch3MkVBalBranch14(zzz818, zzz819, zzz820, zzz821, zzz822, zzz823, zzz824, zzz825, zzz826, zzz827, Succ(zzz8960), bf) → new_mkVBalBranch3MkVBalBranch16(zzz818, zzz819, zzz820, zzz821, zzz822, zzz823, zzz824, Zero, zzz825, zzz826, zzz827, Succ(Zero), Succ(zzz8960), bf)
new_mkVBalBranch3MkVBalBranch24(zzz340, zzz341, Neg(Succ(Succ(Succ(zzz3420000)))), zzz343, zzz344, zzz520, zzz521, Succ(zzz522000), zzz523, zzz524, zzz31, Succ(Succ(zzz6900)), h) → new_mkVBalBranch3MkVBalBranch25(zzz340, zzz341, Succ(Succ(zzz3420000)), zzz343, zzz344, zzz520, zzz521, zzz522000, zzz523, zzz524, zzz31, Succ(zzz3420000), Succ(Succ(new_primPlusNat2(zzz6900, zzz522000))), h)
new_mkVBalBranch3MkVBalBranch26(zzz1133, zzz1134, zzz1135, zzz1136, zzz1137, zzz1138, zzz1139, zzz1140, zzz1141, zzz1142, Zero, Succ(zzz11440), be) → new_mkVBalBranch(zzz1142, Branch(zzz1138, zzz1139, Neg(Succ(Zero)), zzz1140, zzz1141), zzz1136, be)
new_mkVBalBranch3MkVBalBranch24(zzz340, zzz341, Neg(Succ(Succ(Zero))), zzz343, zzz344, zzz520, zzz521, Succ(zzz522000), zzz523, zzz524, zzz31, Succ(Succ(zzz6900)), h) → new_mkVBalBranch3MkVBalBranch25(zzz340, zzz341, Succ(Zero), zzz343, zzz344, zzz520, zzz521, zzz522000, zzz523, zzz524, zzz31, Zero, Succ(Succ(new_primPlusNat2(zzz6900, zzz522000))), h)
new_mkVBalBranch(zzz31, Branch(zzz520, zzz521, Pos(Zero), zzz523, zzz524), Branch(zzz340, zzz341, Pos(Succ(zzz34200)), zzz343, zzz344), h) → new_mkVBalBranch(zzz31, Branch(zzz520, zzz521, Pos(Zero), zzz523, zzz524), zzz343, h)
new_mkVBalBranch3MkVBalBranch20(zzz929, zzz930, zzz931, zzz932, zzz933, zzz934, zzz935, zzz936, zzz937, zzz938, zzz939, Succ(zzz9400), Zero, ba) → new_mkVBalBranch3MkVBalBranch10(zzz929, zzz930, zzz931, zzz932, zzz933, zzz934, zzz935, zzz936, zzz937, zzz938, zzz939, new_primPlusNat2(new_primPlusNat3(Succ(new_primPlusNat3(new_primPlusNat1(zzz931), zzz931)), Succ(zzz931)), Succ(zzz931)), ba)
new_mkVBalBranch(zzz31, Branch(zzz520, zzz521, Pos(Zero), zzz523, zzz524), Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), h) → new_mkVBalBranch3MkVBalBranch12(zzz340, zzz341, zzz34200, zzz343, zzz344, zzz520, zzz521, zzz523, zzz524, zzz31, new_primPlusNat2(Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat3(new_primPlusNat1(zzz34200), zzz34200)), zzz34200))), Succ(zzz34200)), h)
new_mkVBalBranch3MkVBalBranch2(zzz340, zzz341, Pos(Zero), zzz343, zzz344, zzz520, zzz521, zzz52200, zzz523, zzz524, zzz31, Succ(zzz680), h) → new_mkVBalBranch(zzz31, zzz524, Branch(zzz340, zzz341, Pos(Zero), zzz343, zzz344), h)
new_mkVBalBranch3MkVBalBranch23(zzz929, zzz930, zzz931, zzz932, zzz933, zzz934, zzz935, zzz936, zzz937, zzz938, zzz939, ba) → new_mkVBalBranch3MkVBalBranch10(zzz929, zzz930, zzz931, zzz932, zzz933, zzz934, zzz935, zzz936, zzz937, zzz938, zzz939, new_primPlusNat2(new_primMulNat0(zzz931), Succ(zzz931)), ba)
new_mkVBalBranch3MkVBalBranch2(zzz340, zzz341, Neg(Zero), zzz343, zzz344, zzz520, zzz521, zzz52200, zzz523, zzz524, zzz31, Succ(zzz680), h) → new_mkVBalBranch(zzz31, zzz524, Branch(zzz340, zzz341, Neg(Zero), zzz343, zzz344), h)
new_mkVBalBranch3MkVBalBranch2(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344, zzz520, zzz521, zzz52200, zzz523, zzz524, zzz31, Succ(zzz680), h) → new_mkVBalBranch3MkVBalBranch1(zzz340, zzz341, zzz34200, zzz343, zzz344, zzz520, zzz521, zzz52200, zzz523, zzz524, zzz31, new_primPlusNat2(Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat3(new_primPlusNat1(zzz34200), zzz34200)), zzz34200))), Succ(zzz34200)), h)
new_mkVBalBranch3MkVBalBranch16(zzz1702, zzz1703, zzz1704, zzz1705, zzz1706, zzz1707, zzz1708, zzz1709, zzz1710, zzz1711, zzz1712, Zero, Succ(zzz17140), bd) → new_mkVBalBranch(zzz1712, zzz1711, Branch(zzz1702, zzz1703, Neg(Succ(zzz1704)), zzz1705, zzz1706), bd)
new_mkVBalBranch3MkVBalBranch24(zzz340, zzz341, Neg(Succ(Succ(Succ(zzz3420000)))), zzz343, zzz344, zzz520, zzz521, Zero, zzz523, zzz524, zzz31, Succ(Succ(zzz6900)), h) → new_mkVBalBranch3MkVBalBranch26(zzz340, zzz341, Succ(Succ(zzz3420000)), zzz343, zzz344, zzz520, zzz521, zzz523, zzz524, zzz31, Succ(zzz3420000), Succ(zzz6900), h)
new_mkVBalBranch3MkVBalBranch15(zzz537, zzz538, zzz539, zzz540, zzz541, zzz542, zzz543, zzz544, zzz545, zzz546, zzz547, Succ(zzz6990), bc) → new_mkVBalBranch3MkVBalBranch16(zzz537, zzz538, zzz539, zzz540, zzz541, zzz542, zzz543, Succ(zzz544), zzz545, zzz546, zzz547, Succ(Succ(zzz544)), Succ(zzz6990), bc)
new_mkVBalBranch3MkVBalBranch10(zzz929, zzz930, zzz931, zzz932, zzz933, zzz934, zzz935, zzz936, zzz937, zzz938, zzz939, Zero, ba) → new_mkVBalBranch3MkVBalBranch11(zzz929, zzz930, zzz931, zzz932, zzz933, zzz934, zzz935, zzz936, zzz937, zzz938, zzz939, Zero, Succ(zzz936), ba)
new_mkVBalBranch3MkVBalBranch25(zzz537, zzz538, zzz539, zzz540, zzz541, zzz542, zzz543, zzz544, zzz545, zzz546, zzz547, Zero, Zero, bc) → new_mkVBalBranch3MkVBalBranch211(zzz537, zzz538, zzz539, zzz540, zzz541, zzz542, zzz543, zzz544, zzz545, zzz546, zzz547, bc)

The TRS R consists of the following rules:

new_primMulNat0(zzz6200) → new_primPlusNat3(Succ(new_primPlusNat3(new_primPlusNat1(zzz6200), zzz6200)), Succ(zzz6200))
new_primPlusNat2(Succ(zzz900), Succ(zzz9100)) → Succ(Succ(new_primPlusNat2(zzz900, zzz9100)))
new_primPlusNat2(Zero, Succ(zzz9100)) → Succ(zzz9100)
new_primPlusNat2(Zero, Zero) → Zero
new_primPlusNat2(Succ(zzz900), Zero) → Succ(zzz900)
new_primPlusNat1(Zero) → Zero
new_primPlusNat1(Succ(zzz62000)) → Succ(Succ(new_primPlusNat1(zzz62000)))
new_primPlusNat3(zzz90, Succ(zzz910)) → Succ(Succ(new_primPlusNat2(zzz90, zzz910)))
new_primPlusNat3(zzz90, Zero) → Succ(zzz90)

The set Q consists of the following terms:

new_primPlusNat2(Zero, Succ(x0))
new_primMulNat0(x0)
new_primPlusNat3(x0, Succ(x1))
new_primPlusNat2(Succ(x0), Succ(x1))
new_primPlusNat3(x0, Zero)
new_primPlusNat1(Zero)
new_primPlusNat2(Zero, Zero)
new_primPlusNat1(Succ(x0))
new_primPlusNat2(Succ(x0), Zero)

We have to consider all minimal (P,Q,R)-chains.
By rewriting [15] the rule new_mkVBalBranch3MkVBalBranch212(zzz818, zzz819, zzz820, zzz821, zzz822, zzz823, zzz824, zzz825, zzz826, zzz827, bf) → new_mkVBalBranch3MkVBalBranch14(zzz818, zzz819, zzz820, zzz821, zzz822, zzz823, zzz824, zzz825, zzz826, zzz827, new_primPlusNat2(new_primMulNat0(zzz820), Succ(zzz820)), bf) at position [10,0] we obtained the following new rules:

new_mkVBalBranch3MkVBalBranch212(zzz818, zzz819, zzz820, zzz821, zzz822, zzz823, zzz824, zzz825, zzz826, zzz827, bf) → new_mkVBalBranch3MkVBalBranch14(zzz818, zzz819, zzz820, zzz821, zzz822, zzz823, zzz824, zzz825, zzz826, zzz827, new_primPlusNat2(new_primPlusNat3(Succ(new_primPlusNat3(new_primPlusNat1(zzz820), zzz820)), Succ(zzz820)), Succ(zzz820)), bf)



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

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

new_mkVBalBranch3MkVBalBranch11(zzz2033, zzz2034, zzz2035, zzz2036, zzz2037, zzz2038, zzz2039, zzz2040, zzz2041, zzz2042, zzz2043, Zero, Succ(zzz20450), bb) → new_mkVBalBranch(zzz2043, zzz2042, Branch(zzz2033, zzz2034, Pos(Succ(zzz2035)), zzz2036, zzz2037), bb)
new_mkVBalBranch(zzz31, Branch(zzz520, zzz521, Neg(Succ(zzz52200)), zzz523, zzz524), Branch(zzz340, zzz341, zzz342, zzz343, zzz344), h) → new_mkVBalBranch3MkVBalBranch24(zzz340, zzz341, zzz342, zzz343, zzz344, zzz520, zzz521, zzz52200, zzz523, zzz524, zzz31, Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat3(new_primPlusNat1(zzz52200), zzz52200)), zzz52200))), h)
new_mkVBalBranch3MkVBalBranch26(zzz1133, zzz1134, zzz1135, zzz1136, zzz1137, zzz1138, zzz1139, zzz1140, zzz1141, zzz1142, Succ(zzz11430), Succ(zzz11440), be) → new_mkVBalBranch3MkVBalBranch26(zzz1133, zzz1134, zzz1135, zzz1136, zzz1137, zzz1138, zzz1139, zzz1140, zzz1141, zzz1142, zzz11430, zzz11440, be)
new_mkVBalBranch3MkVBalBranch24(zzz340, zzz341, Pos(zzz3420), zzz343, zzz344, zzz520, zzz521, zzz52200, zzz523, zzz524, zzz31, Succ(zzz690), h) → new_mkVBalBranch(zzz31, Branch(zzz520, zzz521, Neg(Succ(zzz52200)), zzz523, zzz524), zzz343, h)
new_mkVBalBranch3MkVBalBranch25(zzz537, zzz538, zzz539, zzz540, zzz541, zzz542, zzz543, zzz544, zzz545, zzz546, zzz547, Succ(zzz5480), Zero, bc) → new_mkVBalBranch3MkVBalBranch15(zzz537, zzz538, zzz539, zzz540, zzz541, zzz542, zzz543, zzz544, zzz545, zzz546, zzz547, new_primPlusNat2(new_primPlusNat3(Succ(new_primPlusNat3(new_primPlusNat1(zzz539), zzz539)), Succ(zzz539)), Succ(zzz539)), bc)
new_mkVBalBranch3MkVBalBranch12(zzz340, zzz341, zzz34200, zzz343, zzz344, zzz520, zzz521, zzz523, zzz524, zzz31, Succ(zzz1250), h) → new_mkVBalBranch(zzz31, zzz524, Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), h)
new_mkVBalBranch3MkVBalBranch20(zzz929, zzz930, zzz931, zzz932, zzz933, zzz934, zzz935, zzz936, zzz937, zzz938, zzz939, Zero, Succ(zzz9410), ba) → new_mkVBalBranch(zzz939, Branch(zzz934, zzz935, Pos(Succ(zzz936)), zzz937, zzz938), zzz932, ba)
new_mkVBalBranch3MkVBalBranch24(zzz340, zzz341, Neg(Succ(Succ(Zero))), zzz343, zzz344, zzz520, zzz521, Zero, zzz523, zzz524, zzz31, Succ(Succ(zzz6900)), h) → new_mkVBalBranch3MkVBalBranch26(zzz340, zzz341, Succ(Zero), zzz343, zzz344, zzz520, zzz521, zzz523, zzz524, zzz31, Zero, Succ(zzz6900), h)
new_mkVBalBranch3MkVBalBranch17(zzz340, zzz341, zzz34200, zzz343, zzz344, zzz520, zzz521, zzz52200, zzz523, zzz524, zzz31, h) → new_mkVBalBranch(zzz31, zzz524, Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), h)
new_mkVBalBranch3MkVBalBranch211(zzz537, zzz538, zzz539, zzz540, zzz541, zzz542, zzz543, zzz544, zzz545, zzz546, zzz547, bc) → new_mkVBalBranch3MkVBalBranch15(zzz537, zzz538, zzz539, zzz540, zzz541, zzz542, zzz543, zzz544, zzz545, zzz546, zzz547, new_primPlusNat2(new_primPlusNat3(Succ(new_primPlusNat3(new_primPlusNat1(zzz539), zzz539)), Succ(zzz539)), Succ(zzz539)), bc)
new_mkVBalBranch3MkVBalBranch1(zzz340, zzz341, zzz34200, zzz343, zzz344, zzz520, zzz521, zzz52200, zzz523, zzz524, zzz31, Succ(zzz1430), h) → new_mkVBalBranch(zzz31, zzz524, Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), h)
new_mkVBalBranch3MkVBalBranch26(zzz1133, zzz1134, zzz1135, zzz1136, zzz1137, zzz1138, zzz1139, zzz1140, zzz1141, zzz1142, Zero, Zero, be) → new_mkVBalBranch3MkVBalBranch29(zzz1133, zzz1134, zzz1135, zzz1136, zzz1137, zzz1138, zzz1139, zzz1140, zzz1141, zzz1142, be)
new_mkVBalBranch3MkVBalBranch20(zzz929, zzz930, zzz931, zzz932, zzz933, zzz934, zzz935, zzz936, zzz937, zzz938, zzz939, Zero, Zero, ba) → new_mkVBalBranch3MkVBalBranch23(zzz929, zzz930, zzz931, zzz932, zzz933, zzz934, zzz935, zzz936, zzz937, zzz938, zzz939, ba)
new_mkVBalBranch3MkVBalBranch24(zzz340, zzz341, Neg(Succ(Zero)), zzz343, zzz344, zzz520, zzz521, zzz52200, zzz523, zzz524, zzz31, Succ(zzz690), h) → new_mkVBalBranch(zzz31, Branch(zzz520, zzz521, Neg(Succ(zzz52200)), zzz523, zzz524), zzz343, h)
new_mkVBalBranch3MkVBalBranch13(zzz340, zzz341, zzz34200, zzz343, zzz344, zzz520, zzz521, zzz523, zzz524, zzz31, Succ(zzz1290), h) → new_mkVBalBranch(zzz31, zzz524, Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), h)
new_mkVBalBranch3MkVBalBranch2(zzz340, zzz341, Pos(Succ(zzz34200)), zzz343, zzz344, zzz520, zzz521, zzz52200, zzz523, zzz524, zzz31, Succ(zzz680), h) → new_mkVBalBranch3MkVBalBranch20(zzz340, zzz341, zzz34200, zzz343, zzz344, zzz520, zzz521, zzz52200, zzz523, zzz524, zzz31, Succ(new_primPlusNat2(zzz680, zzz52200)), zzz34200, h)
new_mkVBalBranch(zzz31, Branch(zzz520, zzz521, Neg(Zero), zzz523, zzz524), Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), h) → new_mkVBalBranch3MkVBalBranch13(zzz340, zzz341, zzz34200, zzz343, zzz344, zzz520, zzz521, zzz523, zzz524, zzz31, new_primPlusNat2(new_primPlusNat3(Succ(new_primPlusNat3(new_primPlusNat1(zzz34200), zzz34200)), Succ(zzz34200)), Succ(zzz34200)), h)
new_mkVBalBranch(zzz31, Branch(zzz520, zzz521, Neg(Zero), zzz523, zzz524), Branch(zzz340, zzz341, Pos(Succ(zzz34200)), zzz343, zzz344), h) → new_mkVBalBranch(zzz31, Branch(zzz520, zzz521, Neg(Zero), zzz523, zzz524), zzz343, h)
new_mkVBalBranch3MkVBalBranch24(zzz340, zzz341, Neg(Zero), zzz343, zzz344, zzz520, zzz521, zzz52200, zzz523, zzz524, zzz31, Succ(zzz690), h) → new_mkVBalBranch(zzz31, Branch(zzz520, zzz521, Neg(Succ(zzz52200)), zzz523, zzz524), zzz343, h)
new_mkVBalBranch3MkVBalBranch212(zzz818, zzz819, zzz820, zzz821, zzz822, zzz823, zzz824, zzz825, zzz826, zzz827, bf) → new_mkVBalBranch3MkVBalBranch14(zzz818, zzz819, zzz820, zzz821, zzz822, zzz823, zzz824, zzz825, zzz826, zzz827, new_primPlusNat2(new_primPlusNat3(Succ(new_primPlusNat3(new_primPlusNat1(zzz820), zzz820)), Succ(zzz820)), Succ(zzz820)), bf)
new_mkVBalBranch3MkVBalBranch20(zzz929, zzz930, zzz931, zzz932, zzz933, zzz934, zzz935, zzz936, zzz937, zzz938, zzz939, Succ(zzz9400), Succ(zzz9410), ba) → new_mkVBalBranch3MkVBalBranch20(zzz929, zzz930, zzz931, zzz932, zzz933, zzz934, zzz935, zzz936, zzz937, zzz938, zzz939, zzz9400, zzz9410, ba)
new_mkVBalBranch3MkVBalBranch1(zzz340, zzz341, zzz34200, zzz343, zzz344, zzz520, zzz521, zzz52200, zzz523, zzz524, zzz31, Zero, h) → new_mkVBalBranch3MkVBalBranch17(zzz340, zzz341, zzz34200, zzz343, zzz344, zzz520, zzz521, zzz52200, zzz523, zzz524, zzz31, h)
new_mkVBalBranch3MkVBalBranch26(zzz1133, zzz1134, zzz1135, zzz1136, zzz1137, zzz1138, zzz1139, zzz1140, zzz1141, zzz1142, Succ(zzz11430), Zero, be) → new_mkVBalBranch3MkVBalBranch212(zzz1133, zzz1134, zzz1135, zzz1136, zzz1137, zzz1138, zzz1139, zzz1140, zzz1141, zzz1142, be)
new_mkVBalBranch3MkVBalBranch16(zzz1702, zzz1703, zzz1704, zzz1705, zzz1706, zzz1707, zzz1708, zzz1709, zzz1710, zzz1711, zzz1712, Succ(zzz17130), Succ(zzz17140), bd) → new_mkVBalBranch3MkVBalBranch16(zzz1702, zzz1703, zzz1704, zzz1705, zzz1706, zzz1707, zzz1708, zzz1709, zzz1710, zzz1711, zzz1712, zzz17130, zzz17140, bd)
new_mkVBalBranch3MkVBalBranch25(zzz537, zzz538, zzz539, zzz540, zzz541, zzz542, zzz543, zzz544, zzz545, zzz546, zzz547, Zero, Succ(zzz5490), bc) → new_mkVBalBranch(zzz547, Branch(zzz542, zzz543, Neg(Succ(Succ(zzz544))), zzz545, zzz546), zzz540, bc)
new_mkVBalBranch3MkVBalBranch11(zzz2033, zzz2034, zzz2035, zzz2036, zzz2037, zzz2038, zzz2039, zzz2040, zzz2041, zzz2042, zzz2043, Succ(zzz20440), Succ(zzz20450), bb) → new_mkVBalBranch3MkVBalBranch11(zzz2033, zzz2034, zzz2035, zzz2036, zzz2037, zzz2038, zzz2039, zzz2040, zzz2041, zzz2042, zzz2043, zzz20440, zzz20450, bb)
new_mkVBalBranch3MkVBalBranch25(zzz537, zzz538, zzz539, zzz540, zzz541, zzz542, zzz543, zzz544, zzz545, zzz546, zzz547, Succ(zzz5480), Succ(zzz5490), bc) → new_mkVBalBranch3MkVBalBranch25(zzz537, zzz538, zzz539, zzz540, zzz541, zzz542, zzz543, zzz544, zzz545, zzz546, zzz547, zzz5480, zzz5490, bc)
new_mkVBalBranch3MkVBalBranch29(zzz818, zzz819, zzz820, zzz821, zzz822, zzz823, zzz824, zzz825, zzz826, zzz827, bf) → new_mkVBalBranch3MkVBalBranch14(zzz818, zzz819, zzz820, zzz821, zzz822, zzz823, zzz824, zzz825, zzz826, zzz827, new_primPlusNat2(new_primPlusNat3(Succ(new_primPlusNat3(new_primPlusNat1(zzz820), zzz820)), Succ(zzz820)), Succ(zzz820)), bf)
new_mkVBalBranch3MkVBalBranch10(zzz929, zzz930, zzz931, zzz932, zzz933, zzz934, zzz935, zzz936, zzz937, zzz938, zzz939, Succ(zzz10020), ba) → new_mkVBalBranch3MkVBalBranch11(zzz929, zzz930, zzz931, zzz932, zzz933, zzz934, zzz935, zzz936, zzz937, zzz938, zzz939, Succ(zzz10020), Succ(zzz936), ba)
new_mkVBalBranch(zzz31, Branch(zzz520, zzz521, Pos(Succ(zzz52200)), zzz523, zzz524), Branch(zzz340, zzz341, zzz342, zzz343, zzz344), h) → new_mkVBalBranch3MkVBalBranch2(zzz340, zzz341, zzz342, zzz343, zzz344, zzz520, zzz521, zzz52200, zzz523, zzz524, zzz31, Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat3(new_primPlusNat1(zzz52200), zzz52200)), zzz52200))), h)
new_mkVBalBranch3MkVBalBranch14(zzz818, zzz819, zzz820, zzz821, zzz822, zzz823, zzz824, zzz825, zzz826, zzz827, Succ(zzz8960), bf) → new_mkVBalBranch3MkVBalBranch16(zzz818, zzz819, zzz820, zzz821, zzz822, zzz823, zzz824, Zero, zzz825, zzz826, zzz827, Succ(Zero), Succ(zzz8960), bf)
new_mkVBalBranch3MkVBalBranch26(zzz1133, zzz1134, zzz1135, zzz1136, zzz1137, zzz1138, zzz1139, zzz1140, zzz1141, zzz1142, Zero, Succ(zzz11440), be) → new_mkVBalBranch(zzz1142, Branch(zzz1138, zzz1139, Neg(Succ(Zero)), zzz1140, zzz1141), zzz1136, be)
new_mkVBalBranch3MkVBalBranch24(zzz340, zzz341, Neg(Succ(Succ(Succ(zzz3420000)))), zzz343, zzz344, zzz520, zzz521, Succ(zzz522000), zzz523, zzz524, zzz31, Succ(Succ(zzz6900)), h) → new_mkVBalBranch3MkVBalBranch25(zzz340, zzz341, Succ(Succ(zzz3420000)), zzz343, zzz344, zzz520, zzz521, zzz522000, zzz523, zzz524, zzz31, Succ(zzz3420000), Succ(Succ(new_primPlusNat2(zzz6900, zzz522000))), h)
new_mkVBalBranch3MkVBalBranch24(zzz340, zzz341, Neg(Succ(Succ(Zero))), zzz343, zzz344, zzz520, zzz521, Succ(zzz522000), zzz523, zzz524, zzz31, Succ(Succ(zzz6900)), h) → new_mkVBalBranch3MkVBalBranch25(zzz340, zzz341, Succ(Zero), zzz343, zzz344, zzz520, zzz521, zzz522000, zzz523, zzz524, zzz31, Zero, Succ(Succ(new_primPlusNat2(zzz6900, zzz522000))), h)
new_mkVBalBranch3MkVBalBranch20(zzz929, zzz930, zzz931, zzz932, zzz933, zzz934, zzz935, zzz936, zzz937, zzz938, zzz939, Succ(zzz9400), Zero, ba) → new_mkVBalBranch3MkVBalBranch10(zzz929, zzz930, zzz931, zzz932, zzz933, zzz934, zzz935, zzz936, zzz937, zzz938, zzz939, new_primPlusNat2(new_primPlusNat3(Succ(new_primPlusNat3(new_primPlusNat1(zzz931), zzz931)), Succ(zzz931)), Succ(zzz931)), ba)
new_mkVBalBranch(zzz31, Branch(zzz520, zzz521, Pos(Zero), zzz523, zzz524), Branch(zzz340, zzz341, Pos(Succ(zzz34200)), zzz343, zzz344), h) → new_mkVBalBranch(zzz31, Branch(zzz520, zzz521, Pos(Zero), zzz523, zzz524), zzz343, h)
new_mkVBalBranch(zzz31, Branch(zzz520, zzz521, Pos(Zero), zzz523, zzz524), Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), h) → new_mkVBalBranch3MkVBalBranch12(zzz340, zzz341, zzz34200, zzz343, zzz344, zzz520, zzz521, zzz523, zzz524, zzz31, new_primPlusNat2(Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat3(new_primPlusNat1(zzz34200), zzz34200)), zzz34200))), Succ(zzz34200)), h)
new_mkVBalBranch3MkVBalBranch23(zzz929, zzz930, zzz931, zzz932, zzz933, zzz934, zzz935, zzz936, zzz937, zzz938, zzz939, ba) → new_mkVBalBranch3MkVBalBranch10(zzz929, zzz930, zzz931, zzz932, zzz933, zzz934, zzz935, zzz936, zzz937, zzz938, zzz939, new_primPlusNat2(new_primMulNat0(zzz931), Succ(zzz931)), ba)
new_mkVBalBranch3MkVBalBranch2(zzz340, zzz341, Pos(Zero), zzz343, zzz344, zzz520, zzz521, zzz52200, zzz523, zzz524, zzz31, Succ(zzz680), h) → new_mkVBalBranch(zzz31, zzz524, Branch(zzz340, zzz341, Pos(Zero), zzz343, zzz344), h)
new_mkVBalBranch3MkVBalBranch2(zzz340, zzz341, Neg(Zero), zzz343, zzz344, zzz520, zzz521, zzz52200, zzz523, zzz524, zzz31, Succ(zzz680), h) → new_mkVBalBranch(zzz31, zzz524, Branch(zzz340, zzz341, Neg(Zero), zzz343, zzz344), h)
new_mkVBalBranch3MkVBalBranch2(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344, zzz520, zzz521, zzz52200, zzz523, zzz524, zzz31, Succ(zzz680), h) → new_mkVBalBranch3MkVBalBranch1(zzz340, zzz341, zzz34200, zzz343, zzz344, zzz520, zzz521, zzz52200, zzz523, zzz524, zzz31, new_primPlusNat2(Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat3(new_primPlusNat1(zzz34200), zzz34200)), zzz34200))), Succ(zzz34200)), h)
new_mkVBalBranch3MkVBalBranch16(zzz1702, zzz1703, zzz1704, zzz1705, zzz1706, zzz1707, zzz1708, zzz1709, zzz1710, zzz1711, zzz1712, Zero, Succ(zzz17140), bd) → new_mkVBalBranch(zzz1712, zzz1711, Branch(zzz1702, zzz1703, Neg(Succ(zzz1704)), zzz1705, zzz1706), bd)
new_mkVBalBranch3MkVBalBranch10(zzz929, zzz930, zzz931, zzz932, zzz933, zzz934, zzz935, zzz936, zzz937, zzz938, zzz939, Zero, ba) → new_mkVBalBranch3MkVBalBranch11(zzz929, zzz930, zzz931, zzz932, zzz933, zzz934, zzz935, zzz936, zzz937, zzz938, zzz939, Zero, Succ(zzz936), ba)
new_mkVBalBranch3MkVBalBranch15(zzz537, zzz538, zzz539, zzz540, zzz541, zzz542, zzz543, zzz544, zzz545, zzz546, zzz547, Succ(zzz6990), bc) → new_mkVBalBranch3MkVBalBranch16(zzz537, zzz538, zzz539, zzz540, zzz541, zzz542, zzz543, Succ(zzz544), zzz545, zzz546, zzz547, Succ(Succ(zzz544)), Succ(zzz6990), bc)
new_mkVBalBranch3MkVBalBranch24(zzz340, zzz341, Neg(Succ(Succ(Succ(zzz3420000)))), zzz343, zzz344, zzz520, zzz521, Zero, zzz523, zzz524, zzz31, Succ(Succ(zzz6900)), h) → new_mkVBalBranch3MkVBalBranch26(zzz340, zzz341, Succ(Succ(zzz3420000)), zzz343, zzz344, zzz520, zzz521, zzz523, zzz524, zzz31, Succ(zzz3420000), Succ(zzz6900), h)
new_mkVBalBranch3MkVBalBranch25(zzz537, zzz538, zzz539, zzz540, zzz541, zzz542, zzz543, zzz544, zzz545, zzz546, zzz547, Zero, Zero, bc) → new_mkVBalBranch3MkVBalBranch211(zzz537, zzz538, zzz539, zzz540, zzz541, zzz542, zzz543, zzz544, zzz545, zzz546, zzz547, bc)

The TRS R consists of the following rules:

new_primMulNat0(zzz6200) → new_primPlusNat3(Succ(new_primPlusNat3(new_primPlusNat1(zzz6200), zzz6200)), Succ(zzz6200))
new_primPlusNat2(Succ(zzz900), Succ(zzz9100)) → Succ(Succ(new_primPlusNat2(zzz900, zzz9100)))
new_primPlusNat2(Zero, Succ(zzz9100)) → Succ(zzz9100)
new_primPlusNat2(Zero, Zero) → Zero
new_primPlusNat2(Succ(zzz900), Zero) → Succ(zzz900)
new_primPlusNat1(Zero) → Zero
new_primPlusNat1(Succ(zzz62000)) → Succ(Succ(new_primPlusNat1(zzz62000)))
new_primPlusNat3(zzz90, Succ(zzz910)) → Succ(Succ(new_primPlusNat2(zzz90, zzz910)))
new_primPlusNat3(zzz90, Zero) → Succ(zzz90)

The set Q consists of the following terms:

new_primPlusNat2(Zero, Succ(x0))
new_primMulNat0(x0)
new_primPlusNat3(x0, Succ(x1))
new_primPlusNat2(Succ(x0), Succ(x1))
new_primPlusNat3(x0, Zero)
new_primPlusNat1(Zero)
new_primPlusNat2(Zero, Zero)
new_primPlusNat1(Succ(x0))
new_primPlusNat2(Succ(x0), Zero)

We have to consider all minimal (P,Q,R)-chains.
By rewriting [15] the rule new_mkVBalBranch3MkVBalBranch211(zzz537, zzz538, zzz539, zzz540, zzz541, zzz542, zzz543, zzz544, zzz545, zzz546, zzz547, bc) → new_mkVBalBranch3MkVBalBranch15(zzz537, zzz538, zzz539, zzz540, zzz541, zzz542, zzz543, zzz544, zzz545, zzz546, zzz547, new_primPlusNat2(new_primPlusNat3(Succ(new_primPlusNat3(new_primPlusNat1(zzz539), zzz539)), Succ(zzz539)), Succ(zzz539)), bc) at position [11,0] we obtained the following new rules:

new_mkVBalBranch3MkVBalBranch211(zzz537, zzz538, zzz539, zzz540, zzz541, zzz542, zzz543, zzz544, zzz545, zzz546, zzz547, bc) → new_mkVBalBranch3MkVBalBranch15(zzz537, zzz538, zzz539, zzz540, zzz541, zzz542, zzz543, zzz544, zzz545, zzz546, zzz547, new_primPlusNat2(Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat3(new_primPlusNat1(zzz539), zzz539)), zzz539))), Succ(zzz539)), bc)



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

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

new_mkVBalBranch(zzz31, Branch(zzz520, zzz521, Neg(Succ(zzz52200)), zzz523, zzz524), Branch(zzz340, zzz341, zzz342, zzz343, zzz344), h) → new_mkVBalBranch3MkVBalBranch24(zzz340, zzz341, zzz342, zzz343, zzz344, zzz520, zzz521, zzz52200, zzz523, zzz524, zzz31, Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat3(new_primPlusNat1(zzz52200), zzz52200)), zzz52200))), h)
new_mkVBalBranch3MkVBalBranch11(zzz2033, zzz2034, zzz2035, zzz2036, zzz2037, zzz2038, zzz2039, zzz2040, zzz2041, zzz2042, zzz2043, Zero, Succ(zzz20450), bb) → new_mkVBalBranch(zzz2043, zzz2042, Branch(zzz2033, zzz2034, Pos(Succ(zzz2035)), zzz2036, zzz2037), bb)
new_mkVBalBranch3MkVBalBranch26(zzz1133, zzz1134, zzz1135, zzz1136, zzz1137, zzz1138, zzz1139, zzz1140, zzz1141, zzz1142, Succ(zzz11430), Succ(zzz11440), be) → new_mkVBalBranch3MkVBalBranch26(zzz1133, zzz1134, zzz1135, zzz1136, zzz1137, zzz1138, zzz1139, zzz1140, zzz1141, zzz1142, zzz11430, zzz11440, be)
new_mkVBalBranch3MkVBalBranch24(zzz340, zzz341, Pos(zzz3420), zzz343, zzz344, zzz520, zzz521, zzz52200, zzz523, zzz524, zzz31, Succ(zzz690), h) → new_mkVBalBranch(zzz31, Branch(zzz520, zzz521, Neg(Succ(zzz52200)), zzz523, zzz524), zzz343, h)
new_mkVBalBranch3MkVBalBranch25(zzz537, zzz538, zzz539, zzz540, zzz541, zzz542, zzz543, zzz544, zzz545, zzz546, zzz547, Succ(zzz5480), Zero, bc) → new_mkVBalBranch3MkVBalBranch15(zzz537, zzz538, zzz539, zzz540, zzz541, zzz542, zzz543, zzz544, zzz545, zzz546, zzz547, new_primPlusNat2(new_primPlusNat3(Succ(new_primPlusNat3(new_primPlusNat1(zzz539), zzz539)), Succ(zzz539)), Succ(zzz539)), bc)
new_mkVBalBranch3MkVBalBranch12(zzz340, zzz341, zzz34200, zzz343, zzz344, zzz520, zzz521, zzz523, zzz524, zzz31, Succ(zzz1250), h) → new_mkVBalBranch(zzz31, zzz524, Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), h)
new_mkVBalBranch3MkVBalBranch20(zzz929, zzz930, zzz931, zzz932, zzz933, zzz934, zzz935, zzz936, zzz937, zzz938, zzz939, Zero, Succ(zzz9410), ba) → new_mkVBalBranch(zzz939, Branch(zzz934, zzz935, Pos(Succ(zzz936)), zzz937, zzz938), zzz932, ba)
new_mkVBalBranch3MkVBalBranch24(zzz340, zzz341, Neg(Succ(Succ(Zero))), zzz343, zzz344, zzz520, zzz521, Zero, zzz523, zzz524, zzz31, Succ(Succ(zzz6900)), h) → new_mkVBalBranch3MkVBalBranch26(zzz340, zzz341, Succ(Zero), zzz343, zzz344, zzz520, zzz521, zzz523, zzz524, zzz31, Zero, Succ(zzz6900), h)
new_mkVBalBranch3MkVBalBranch17(zzz340, zzz341, zzz34200, zzz343, zzz344, zzz520, zzz521, zzz52200, zzz523, zzz524, zzz31, h) → new_mkVBalBranch(zzz31, zzz524, Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), h)
new_mkVBalBranch3MkVBalBranch26(zzz1133, zzz1134, zzz1135, zzz1136, zzz1137, zzz1138, zzz1139, zzz1140, zzz1141, zzz1142, Zero, Zero, be) → new_mkVBalBranch3MkVBalBranch29(zzz1133, zzz1134, zzz1135, zzz1136, zzz1137, zzz1138, zzz1139, zzz1140, zzz1141, zzz1142, be)
new_mkVBalBranch3MkVBalBranch1(zzz340, zzz341, zzz34200, zzz343, zzz344, zzz520, zzz521, zzz52200, zzz523, zzz524, zzz31, Succ(zzz1430), h) → new_mkVBalBranch(zzz31, zzz524, Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), h)
new_mkVBalBranch3MkVBalBranch24(zzz340, zzz341, Neg(Succ(Zero)), zzz343, zzz344, zzz520, zzz521, zzz52200, zzz523, zzz524, zzz31, Succ(zzz690), h) → new_mkVBalBranch(zzz31, Branch(zzz520, zzz521, Neg(Succ(zzz52200)), zzz523, zzz524), zzz343, h)
new_mkVBalBranch3MkVBalBranch20(zzz929, zzz930, zzz931, zzz932, zzz933, zzz934, zzz935, zzz936, zzz937, zzz938, zzz939, Zero, Zero, ba) → new_mkVBalBranch3MkVBalBranch23(zzz929, zzz930, zzz931, zzz932, zzz933, zzz934, zzz935, zzz936, zzz937, zzz938, zzz939, ba)
new_mkVBalBranch3MkVBalBranch13(zzz340, zzz341, zzz34200, zzz343, zzz344, zzz520, zzz521, zzz523, zzz524, zzz31, Succ(zzz1290), h) → new_mkVBalBranch(zzz31, zzz524, Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), h)
new_mkVBalBranch3MkVBalBranch2(zzz340, zzz341, Pos(Succ(zzz34200)), zzz343, zzz344, zzz520, zzz521, zzz52200, zzz523, zzz524, zzz31, Succ(zzz680), h) → new_mkVBalBranch3MkVBalBranch20(zzz340, zzz341, zzz34200, zzz343, zzz344, zzz520, zzz521, zzz52200, zzz523, zzz524, zzz31, Succ(new_primPlusNat2(zzz680, zzz52200)), zzz34200, h)
new_mkVBalBranch(zzz31, Branch(zzz520, zzz521, Neg(Zero), zzz523, zzz524), Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), h) → new_mkVBalBranch3MkVBalBranch13(zzz340, zzz341, zzz34200, zzz343, zzz344, zzz520, zzz521, zzz523, zzz524, zzz31, new_primPlusNat2(new_primPlusNat3(Succ(new_primPlusNat3(new_primPlusNat1(zzz34200), zzz34200)), Succ(zzz34200)), Succ(zzz34200)), h)
new_mkVBalBranch3MkVBalBranch24(zzz340, zzz341, Neg(Zero), zzz343, zzz344, zzz520, zzz521, zzz52200, zzz523, zzz524, zzz31, Succ(zzz690), h) → new_mkVBalBranch(zzz31, Branch(zzz520, zzz521, Neg(Succ(zzz52200)), zzz523, zzz524), zzz343, h)
new_mkVBalBranch(zzz31, Branch(zzz520, zzz521, Neg(Zero), zzz523, zzz524), Branch(zzz340, zzz341, Pos(Succ(zzz34200)), zzz343, zzz344), h) → new_mkVBalBranch(zzz31, Branch(zzz520, zzz521, Neg(Zero), zzz523, zzz524), zzz343, h)
new_mkVBalBranch3MkVBalBranch212(zzz818, zzz819, zzz820, zzz821, zzz822, zzz823, zzz824, zzz825, zzz826, zzz827, bf) → new_mkVBalBranch3MkVBalBranch14(zzz818, zzz819, zzz820, zzz821, zzz822, zzz823, zzz824, zzz825, zzz826, zzz827, new_primPlusNat2(new_primPlusNat3(Succ(new_primPlusNat3(new_primPlusNat1(zzz820), zzz820)), Succ(zzz820)), Succ(zzz820)), bf)
new_mkVBalBranch3MkVBalBranch20(zzz929, zzz930, zzz931, zzz932, zzz933, zzz934, zzz935, zzz936, zzz937, zzz938, zzz939, Succ(zzz9400), Succ(zzz9410), ba) → new_mkVBalBranch3MkVBalBranch20(zzz929, zzz930, zzz931, zzz932, zzz933, zzz934, zzz935, zzz936, zzz937, zzz938, zzz939, zzz9400, zzz9410, ba)
new_mkVBalBranch3MkVBalBranch26(zzz1133, zzz1134, zzz1135, zzz1136, zzz1137, zzz1138, zzz1139, zzz1140, zzz1141, zzz1142, Succ(zzz11430), Zero, be) → new_mkVBalBranch3MkVBalBranch212(zzz1133, zzz1134, zzz1135, zzz1136, zzz1137, zzz1138, zzz1139, zzz1140, zzz1141, zzz1142, be)
new_mkVBalBranch3MkVBalBranch1(zzz340, zzz341, zzz34200, zzz343, zzz344, zzz520, zzz521, zzz52200, zzz523, zzz524, zzz31, Zero, h) → new_mkVBalBranch3MkVBalBranch17(zzz340, zzz341, zzz34200, zzz343, zzz344, zzz520, zzz521, zzz52200, zzz523, zzz524, zzz31, h)
new_mkVBalBranch3MkVBalBranch211(zzz537, zzz538, zzz539, zzz540, zzz541, zzz542, zzz543, zzz544, zzz545, zzz546, zzz547, bc) → new_mkVBalBranch3MkVBalBranch15(zzz537, zzz538, zzz539, zzz540, zzz541, zzz542, zzz543, zzz544, zzz545, zzz546, zzz547, new_primPlusNat2(Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat3(new_primPlusNat1(zzz539), zzz539)), zzz539))), Succ(zzz539)), bc)
new_mkVBalBranch3MkVBalBranch16(zzz1702, zzz1703, zzz1704, zzz1705, zzz1706, zzz1707, zzz1708, zzz1709, zzz1710, zzz1711, zzz1712, Succ(zzz17130), Succ(zzz17140), bd) → new_mkVBalBranch3MkVBalBranch16(zzz1702, zzz1703, zzz1704, zzz1705, zzz1706, zzz1707, zzz1708, zzz1709, zzz1710, zzz1711, zzz1712, zzz17130, zzz17140, bd)
new_mkVBalBranch3MkVBalBranch25(zzz537, zzz538, zzz539, zzz540, zzz541, zzz542, zzz543, zzz544, zzz545, zzz546, zzz547, Zero, Succ(zzz5490), bc) → new_mkVBalBranch(zzz547, Branch(zzz542, zzz543, Neg(Succ(Succ(zzz544))), zzz545, zzz546), zzz540, bc)
new_mkVBalBranch3MkVBalBranch11(zzz2033, zzz2034, zzz2035, zzz2036, zzz2037, zzz2038, zzz2039, zzz2040, zzz2041, zzz2042, zzz2043, Succ(zzz20440), Succ(zzz20450), bb) → new_mkVBalBranch3MkVBalBranch11(zzz2033, zzz2034, zzz2035, zzz2036, zzz2037, zzz2038, zzz2039, zzz2040, zzz2041, zzz2042, zzz2043, zzz20440, zzz20450, bb)
new_mkVBalBranch3MkVBalBranch25(zzz537, zzz538, zzz539, zzz540, zzz541, zzz542, zzz543, zzz544, zzz545, zzz546, zzz547, Succ(zzz5480), Succ(zzz5490), bc) → new_mkVBalBranch3MkVBalBranch25(zzz537, zzz538, zzz539, zzz540, zzz541, zzz542, zzz543, zzz544, zzz545, zzz546, zzz547, zzz5480, zzz5490, bc)
new_mkVBalBranch3MkVBalBranch29(zzz818, zzz819, zzz820, zzz821, zzz822, zzz823, zzz824, zzz825, zzz826, zzz827, bf) → new_mkVBalBranch3MkVBalBranch14(zzz818, zzz819, zzz820, zzz821, zzz822, zzz823, zzz824, zzz825, zzz826, zzz827, new_primPlusNat2(new_primPlusNat3(Succ(new_primPlusNat3(new_primPlusNat1(zzz820), zzz820)), Succ(zzz820)), Succ(zzz820)), bf)
new_mkVBalBranch(zzz31, Branch(zzz520, zzz521, Pos(Succ(zzz52200)), zzz523, zzz524), Branch(zzz340, zzz341, zzz342, zzz343, zzz344), h) → new_mkVBalBranch3MkVBalBranch2(zzz340, zzz341, zzz342, zzz343, zzz344, zzz520, zzz521, zzz52200, zzz523, zzz524, zzz31, Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat3(new_primPlusNat1(zzz52200), zzz52200)), zzz52200))), h)
new_mkVBalBranch3MkVBalBranch10(zzz929, zzz930, zzz931, zzz932, zzz933, zzz934, zzz935, zzz936, zzz937, zzz938, zzz939, Succ(zzz10020), ba) → new_mkVBalBranch3MkVBalBranch11(zzz929, zzz930, zzz931, zzz932, zzz933, zzz934, zzz935, zzz936, zzz937, zzz938, zzz939, Succ(zzz10020), Succ(zzz936), ba)
new_mkVBalBranch3MkVBalBranch14(zzz818, zzz819, zzz820, zzz821, zzz822, zzz823, zzz824, zzz825, zzz826, zzz827, Succ(zzz8960), bf) → new_mkVBalBranch3MkVBalBranch16(zzz818, zzz819, zzz820, zzz821, zzz822, zzz823, zzz824, Zero, zzz825, zzz826, zzz827, Succ(Zero), Succ(zzz8960), bf)
new_mkVBalBranch3MkVBalBranch24(zzz340, zzz341, Neg(Succ(Succ(Succ(zzz3420000)))), zzz343, zzz344, zzz520, zzz521, Succ(zzz522000), zzz523, zzz524, zzz31, Succ(Succ(zzz6900)), h) → new_mkVBalBranch3MkVBalBranch25(zzz340, zzz341, Succ(Succ(zzz3420000)), zzz343, zzz344, zzz520, zzz521, zzz522000, zzz523, zzz524, zzz31, Succ(zzz3420000), Succ(Succ(new_primPlusNat2(zzz6900, zzz522000))), h)
new_mkVBalBranch3MkVBalBranch26(zzz1133, zzz1134, zzz1135, zzz1136, zzz1137, zzz1138, zzz1139, zzz1140, zzz1141, zzz1142, Zero, Succ(zzz11440), be) → new_mkVBalBranch(zzz1142, Branch(zzz1138, zzz1139, Neg(Succ(Zero)), zzz1140, zzz1141), zzz1136, be)
new_mkVBalBranch3MkVBalBranch24(zzz340, zzz341, Neg(Succ(Succ(Zero))), zzz343, zzz344, zzz520, zzz521, Succ(zzz522000), zzz523, zzz524, zzz31, Succ(Succ(zzz6900)), h) → new_mkVBalBranch3MkVBalBranch25(zzz340, zzz341, Succ(Zero), zzz343, zzz344, zzz520, zzz521, zzz522000, zzz523, zzz524, zzz31, Zero, Succ(Succ(new_primPlusNat2(zzz6900, zzz522000))), h)
new_mkVBalBranch(zzz31, Branch(zzz520, zzz521, Pos(Zero), zzz523, zzz524), Branch(zzz340, zzz341, Pos(Succ(zzz34200)), zzz343, zzz344), h) → new_mkVBalBranch(zzz31, Branch(zzz520, zzz521, Pos(Zero), zzz523, zzz524), zzz343, h)
new_mkVBalBranch3MkVBalBranch20(zzz929, zzz930, zzz931, zzz932, zzz933, zzz934, zzz935, zzz936, zzz937, zzz938, zzz939, Succ(zzz9400), Zero, ba) → new_mkVBalBranch3MkVBalBranch10(zzz929, zzz930, zzz931, zzz932, zzz933, zzz934, zzz935, zzz936, zzz937, zzz938, zzz939, new_primPlusNat2(new_primPlusNat3(Succ(new_primPlusNat3(new_primPlusNat1(zzz931), zzz931)), Succ(zzz931)), Succ(zzz931)), ba)
new_mkVBalBranch(zzz31, Branch(zzz520, zzz521, Pos(Zero), zzz523, zzz524), Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), h) → new_mkVBalBranch3MkVBalBranch12(zzz340, zzz341, zzz34200, zzz343, zzz344, zzz520, zzz521, zzz523, zzz524, zzz31, new_primPlusNat2(Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat3(new_primPlusNat1(zzz34200), zzz34200)), zzz34200))), Succ(zzz34200)), h)
new_mkVBalBranch3MkVBalBranch2(zzz340, zzz341, Pos(Zero), zzz343, zzz344, zzz520, zzz521, zzz52200, zzz523, zzz524, zzz31, Succ(zzz680), h) → new_mkVBalBranch(zzz31, zzz524, Branch(zzz340, zzz341, Pos(Zero), zzz343, zzz344), h)
new_mkVBalBranch3MkVBalBranch23(zzz929, zzz930, zzz931, zzz932, zzz933, zzz934, zzz935, zzz936, zzz937, zzz938, zzz939, ba) → new_mkVBalBranch3MkVBalBranch10(zzz929, zzz930, zzz931, zzz932, zzz933, zzz934, zzz935, zzz936, zzz937, zzz938, zzz939, new_primPlusNat2(new_primMulNat0(zzz931), Succ(zzz931)), ba)
new_mkVBalBranch3MkVBalBranch2(zzz340, zzz341, Neg(Zero), zzz343, zzz344, zzz520, zzz521, zzz52200, zzz523, zzz524, zzz31, Succ(zzz680), h) → new_mkVBalBranch(zzz31, zzz524, Branch(zzz340, zzz341, Neg(Zero), zzz343, zzz344), h)
new_mkVBalBranch3MkVBalBranch2(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344, zzz520, zzz521, zzz52200, zzz523, zzz524, zzz31, Succ(zzz680), h) → new_mkVBalBranch3MkVBalBranch1(zzz340, zzz341, zzz34200, zzz343, zzz344, zzz520, zzz521, zzz52200, zzz523, zzz524, zzz31, new_primPlusNat2(Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat3(new_primPlusNat1(zzz34200), zzz34200)), zzz34200))), Succ(zzz34200)), h)
new_mkVBalBranch3MkVBalBranch16(zzz1702, zzz1703, zzz1704, zzz1705, zzz1706, zzz1707, zzz1708, zzz1709, zzz1710, zzz1711, zzz1712, Zero, Succ(zzz17140), bd) → new_mkVBalBranch(zzz1712, zzz1711, Branch(zzz1702, zzz1703, Neg(Succ(zzz1704)), zzz1705, zzz1706), bd)
new_mkVBalBranch3MkVBalBranch24(zzz340, zzz341, Neg(Succ(Succ(Succ(zzz3420000)))), zzz343, zzz344, zzz520, zzz521, Zero, zzz523, zzz524, zzz31, Succ(Succ(zzz6900)), h) → new_mkVBalBranch3MkVBalBranch26(zzz340, zzz341, Succ(Succ(zzz3420000)), zzz343, zzz344, zzz520, zzz521, zzz523, zzz524, zzz31, Succ(zzz3420000), Succ(zzz6900), h)
new_mkVBalBranch3MkVBalBranch15(zzz537, zzz538, zzz539, zzz540, zzz541, zzz542, zzz543, zzz544, zzz545, zzz546, zzz547, Succ(zzz6990), bc) → new_mkVBalBranch3MkVBalBranch16(zzz537, zzz538, zzz539, zzz540, zzz541, zzz542, zzz543, Succ(zzz544), zzz545, zzz546, zzz547, Succ(Succ(zzz544)), Succ(zzz6990), bc)
new_mkVBalBranch3MkVBalBranch10(zzz929, zzz930, zzz931, zzz932, zzz933, zzz934, zzz935, zzz936, zzz937, zzz938, zzz939, Zero, ba) → new_mkVBalBranch3MkVBalBranch11(zzz929, zzz930, zzz931, zzz932, zzz933, zzz934, zzz935, zzz936, zzz937, zzz938, zzz939, Zero, Succ(zzz936), ba)
new_mkVBalBranch3MkVBalBranch25(zzz537, zzz538, zzz539, zzz540, zzz541, zzz542, zzz543, zzz544, zzz545, zzz546, zzz547, Zero, Zero, bc) → new_mkVBalBranch3MkVBalBranch211(zzz537, zzz538, zzz539, zzz540, zzz541, zzz542, zzz543, zzz544, zzz545, zzz546, zzz547, bc)

The TRS R consists of the following rules:

new_primMulNat0(zzz6200) → new_primPlusNat3(Succ(new_primPlusNat3(new_primPlusNat1(zzz6200), zzz6200)), Succ(zzz6200))
new_primPlusNat2(Succ(zzz900), Succ(zzz9100)) → Succ(Succ(new_primPlusNat2(zzz900, zzz9100)))
new_primPlusNat2(Zero, Succ(zzz9100)) → Succ(zzz9100)
new_primPlusNat2(Zero, Zero) → Zero
new_primPlusNat2(Succ(zzz900), Zero) → Succ(zzz900)
new_primPlusNat1(Zero) → Zero
new_primPlusNat1(Succ(zzz62000)) → Succ(Succ(new_primPlusNat1(zzz62000)))
new_primPlusNat3(zzz90, Succ(zzz910)) → Succ(Succ(new_primPlusNat2(zzz90, zzz910)))
new_primPlusNat3(zzz90, Zero) → Succ(zzz90)

The set Q consists of the following terms:

new_primPlusNat2(Zero, Succ(x0))
new_primMulNat0(x0)
new_primPlusNat3(x0, Succ(x1))
new_primPlusNat2(Succ(x0), Succ(x1))
new_primPlusNat3(x0, Zero)
new_primPlusNat1(Zero)
new_primPlusNat2(Zero, Zero)
new_primPlusNat1(Succ(x0))
new_primPlusNat2(Succ(x0), Zero)

We have to consider all minimal (P,Q,R)-chains.
By rewriting [15] the rule new_mkVBalBranch3MkVBalBranch25(zzz537, zzz538, zzz539, zzz540, zzz541, zzz542, zzz543, zzz544, zzz545, zzz546, zzz547, Succ(zzz5480), Zero, bc) → new_mkVBalBranch3MkVBalBranch15(zzz537, zzz538, zzz539, zzz540, zzz541, zzz542, zzz543, zzz544, zzz545, zzz546, zzz547, new_primPlusNat2(new_primPlusNat3(Succ(new_primPlusNat3(new_primPlusNat1(zzz539), zzz539)), Succ(zzz539)), Succ(zzz539)), bc) at position [11,0] we obtained the following new rules:

new_mkVBalBranch3MkVBalBranch25(zzz537, zzz538, zzz539, zzz540, zzz541, zzz542, zzz543, zzz544, zzz545, zzz546, zzz547, Succ(zzz5480), Zero, bc) → new_mkVBalBranch3MkVBalBranch15(zzz537, zzz538, zzz539, zzz540, zzz541, zzz542, zzz543, zzz544, zzz545, zzz546, zzz547, new_primPlusNat2(Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat3(new_primPlusNat1(zzz539), zzz539)), zzz539))), Succ(zzz539)), bc)



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

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

new_mkVBalBranch3MkVBalBranch11(zzz2033, zzz2034, zzz2035, zzz2036, zzz2037, zzz2038, zzz2039, zzz2040, zzz2041, zzz2042, zzz2043, Zero, Succ(zzz20450), bb) → new_mkVBalBranch(zzz2043, zzz2042, Branch(zzz2033, zzz2034, Pos(Succ(zzz2035)), zzz2036, zzz2037), bb)
new_mkVBalBranch(zzz31, Branch(zzz520, zzz521, Neg(Succ(zzz52200)), zzz523, zzz524), Branch(zzz340, zzz341, zzz342, zzz343, zzz344), h) → new_mkVBalBranch3MkVBalBranch24(zzz340, zzz341, zzz342, zzz343, zzz344, zzz520, zzz521, zzz52200, zzz523, zzz524, zzz31, Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat3(new_primPlusNat1(zzz52200), zzz52200)), zzz52200))), h)
new_mkVBalBranch3MkVBalBranch26(zzz1133, zzz1134, zzz1135, zzz1136, zzz1137, zzz1138, zzz1139, zzz1140, zzz1141, zzz1142, Succ(zzz11430), Succ(zzz11440), be) → new_mkVBalBranch3MkVBalBranch26(zzz1133, zzz1134, zzz1135, zzz1136, zzz1137, zzz1138, zzz1139, zzz1140, zzz1141, zzz1142, zzz11430, zzz11440, be)
new_mkVBalBranch3MkVBalBranch24(zzz340, zzz341, Pos(zzz3420), zzz343, zzz344, zzz520, zzz521, zzz52200, zzz523, zzz524, zzz31, Succ(zzz690), h) → new_mkVBalBranch(zzz31, Branch(zzz520, zzz521, Neg(Succ(zzz52200)), zzz523, zzz524), zzz343, h)
new_mkVBalBranch3MkVBalBranch12(zzz340, zzz341, zzz34200, zzz343, zzz344, zzz520, zzz521, zzz523, zzz524, zzz31, Succ(zzz1250), h) → new_mkVBalBranch(zzz31, zzz524, Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), h)
new_mkVBalBranch3MkVBalBranch20(zzz929, zzz930, zzz931, zzz932, zzz933, zzz934, zzz935, zzz936, zzz937, zzz938, zzz939, Zero, Succ(zzz9410), ba) → new_mkVBalBranch(zzz939, Branch(zzz934, zzz935, Pos(Succ(zzz936)), zzz937, zzz938), zzz932, ba)
new_mkVBalBranch3MkVBalBranch24(zzz340, zzz341, Neg(Succ(Succ(Zero))), zzz343, zzz344, zzz520, zzz521, Zero, zzz523, zzz524, zzz31, Succ(Succ(zzz6900)), h) → new_mkVBalBranch3MkVBalBranch26(zzz340, zzz341, Succ(Zero), zzz343, zzz344, zzz520, zzz521, zzz523, zzz524, zzz31, Zero, Succ(zzz6900), h)
new_mkVBalBranch3MkVBalBranch17(zzz340, zzz341, zzz34200, zzz343, zzz344, zzz520, zzz521, zzz52200, zzz523, zzz524, zzz31, h) → new_mkVBalBranch(zzz31, zzz524, Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), h)
new_mkVBalBranch3MkVBalBranch1(zzz340, zzz341, zzz34200, zzz343, zzz344, zzz520, zzz521, zzz52200, zzz523, zzz524, zzz31, Succ(zzz1430), h) → new_mkVBalBranch(zzz31, zzz524, Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), h)
new_mkVBalBranch3MkVBalBranch26(zzz1133, zzz1134, zzz1135, zzz1136, zzz1137, zzz1138, zzz1139, zzz1140, zzz1141, zzz1142, Zero, Zero, be) → new_mkVBalBranch3MkVBalBranch29(zzz1133, zzz1134, zzz1135, zzz1136, zzz1137, zzz1138, zzz1139, zzz1140, zzz1141, zzz1142, be)
new_mkVBalBranch3MkVBalBranch20(zzz929, zzz930, zzz931, zzz932, zzz933, zzz934, zzz935, zzz936, zzz937, zzz938, zzz939, Zero, Zero, ba) → new_mkVBalBranch3MkVBalBranch23(zzz929, zzz930, zzz931, zzz932, zzz933, zzz934, zzz935, zzz936, zzz937, zzz938, zzz939, ba)
new_mkVBalBranch3MkVBalBranch24(zzz340, zzz341, Neg(Succ(Zero)), zzz343, zzz344, zzz520, zzz521, zzz52200, zzz523, zzz524, zzz31, Succ(zzz690), h) → new_mkVBalBranch(zzz31, Branch(zzz520, zzz521, Neg(Succ(zzz52200)), zzz523, zzz524), zzz343, h)
new_mkVBalBranch3MkVBalBranch13(zzz340, zzz341, zzz34200, zzz343, zzz344, zzz520, zzz521, zzz523, zzz524, zzz31, Succ(zzz1290), h) → new_mkVBalBranch(zzz31, zzz524, Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), h)
new_mkVBalBranch3MkVBalBranch2(zzz340, zzz341, Pos(Succ(zzz34200)), zzz343, zzz344, zzz520, zzz521, zzz52200, zzz523, zzz524, zzz31, Succ(zzz680), h) → new_mkVBalBranch3MkVBalBranch20(zzz340, zzz341, zzz34200, zzz343, zzz344, zzz520, zzz521, zzz52200, zzz523, zzz524, zzz31, Succ(new_primPlusNat2(zzz680, zzz52200)), zzz34200, h)
new_mkVBalBranch(zzz31, Branch(zzz520, zzz521, Neg(Zero), zzz523, zzz524), Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), h) → new_mkVBalBranch3MkVBalBranch13(zzz340, zzz341, zzz34200, zzz343, zzz344, zzz520, zzz521, zzz523, zzz524, zzz31, new_primPlusNat2(new_primPlusNat3(Succ(new_primPlusNat3(new_primPlusNat1(zzz34200), zzz34200)), Succ(zzz34200)), Succ(zzz34200)), h)
new_mkVBalBranch(zzz31, Branch(zzz520, zzz521, Neg(Zero), zzz523, zzz524), Branch(zzz340, zzz341, Pos(Succ(zzz34200)), zzz343, zzz344), h) → new_mkVBalBranch(zzz31, Branch(zzz520, zzz521, Neg(Zero), zzz523, zzz524), zzz343, h)
new_mkVBalBranch3MkVBalBranch24(zzz340, zzz341, Neg(Zero), zzz343, zzz344, zzz520, zzz521, zzz52200, zzz523, zzz524, zzz31, Succ(zzz690), h) → new_mkVBalBranch(zzz31, Branch(zzz520, zzz521, Neg(Succ(zzz52200)), zzz523, zzz524), zzz343, h)
new_mkVBalBranch3MkVBalBranch212(zzz818, zzz819, zzz820, zzz821, zzz822, zzz823, zzz824, zzz825, zzz826, zzz827, bf) → new_mkVBalBranch3MkVBalBranch14(zzz818, zzz819, zzz820, zzz821, zzz822, zzz823, zzz824, zzz825, zzz826, zzz827, new_primPlusNat2(new_primPlusNat3(Succ(new_primPlusNat3(new_primPlusNat1(zzz820), zzz820)), Succ(zzz820)), Succ(zzz820)), bf)
new_mkVBalBranch3MkVBalBranch20(zzz929, zzz930, zzz931, zzz932, zzz933, zzz934, zzz935, zzz936, zzz937, zzz938, zzz939, Succ(zzz9400), Succ(zzz9410), ba) → new_mkVBalBranch3MkVBalBranch20(zzz929, zzz930, zzz931, zzz932, zzz933, zzz934, zzz935, zzz936, zzz937, zzz938, zzz939, zzz9400, zzz9410, ba)
new_mkVBalBranch3MkVBalBranch1(zzz340, zzz341, zzz34200, zzz343, zzz344, zzz520, zzz521, zzz52200, zzz523, zzz524, zzz31, Zero, h) → new_mkVBalBranch3MkVBalBranch17(zzz340, zzz341, zzz34200, zzz343, zzz344, zzz520, zzz521, zzz52200, zzz523, zzz524, zzz31, h)
new_mkVBalBranch3MkVBalBranch26(zzz1133, zzz1134, zzz1135, zzz1136, zzz1137, zzz1138, zzz1139, zzz1140, zzz1141, zzz1142, Succ(zzz11430), Zero, be) → new_mkVBalBranch3MkVBalBranch212(zzz1133, zzz1134, zzz1135, zzz1136, zzz1137, zzz1138, zzz1139, zzz1140, zzz1141, zzz1142, be)
new_mkVBalBranch3MkVBalBranch211(zzz537, zzz538, zzz539, zzz540, zzz541, zzz542, zzz543, zzz544, zzz545, zzz546, zzz547, bc) → new_mkVBalBranch3MkVBalBranch15(zzz537, zzz538, zzz539, zzz540, zzz541, zzz542, zzz543, zzz544, zzz545, zzz546, zzz547, new_primPlusNat2(Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat3(new_primPlusNat1(zzz539), zzz539)), zzz539))), Succ(zzz539)), bc)
new_mkVBalBranch3MkVBalBranch16(zzz1702, zzz1703, zzz1704, zzz1705, zzz1706, zzz1707, zzz1708, zzz1709, zzz1710, zzz1711, zzz1712, Succ(zzz17130), Succ(zzz17140), bd) → new_mkVBalBranch3MkVBalBranch16(zzz1702, zzz1703, zzz1704, zzz1705, zzz1706, zzz1707, zzz1708, zzz1709, zzz1710, zzz1711, zzz1712, zzz17130, zzz17140, bd)
new_mkVBalBranch3MkVBalBranch25(zzz537, zzz538, zzz539, zzz540, zzz541, zzz542, zzz543, zzz544, zzz545, zzz546, zzz547, Zero, Succ(zzz5490), bc) → new_mkVBalBranch(zzz547, Branch(zzz542, zzz543, Neg(Succ(Succ(zzz544))), zzz545, zzz546), zzz540, bc)
new_mkVBalBranch3MkVBalBranch25(zzz537, zzz538, zzz539, zzz540, zzz541, zzz542, zzz543, zzz544, zzz545, zzz546, zzz547, Succ(zzz5480), Zero, bc) → new_mkVBalBranch3MkVBalBranch15(zzz537, zzz538, zzz539, zzz540, zzz541, zzz542, zzz543, zzz544, zzz545, zzz546, zzz547, new_primPlusNat2(Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat3(new_primPlusNat1(zzz539), zzz539)), zzz539))), Succ(zzz539)), bc)
new_mkVBalBranch3MkVBalBranch11(zzz2033, zzz2034, zzz2035, zzz2036, zzz2037, zzz2038, zzz2039, zzz2040, zzz2041, zzz2042, zzz2043, Succ(zzz20440), Succ(zzz20450), bb) → new_mkVBalBranch3MkVBalBranch11(zzz2033, zzz2034, zzz2035, zzz2036, zzz2037, zzz2038, zzz2039, zzz2040, zzz2041, zzz2042, zzz2043, zzz20440, zzz20450, bb)
new_mkVBalBranch3MkVBalBranch25(zzz537, zzz538, zzz539, zzz540, zzz541, zzz542, zzz543, zzz544, zzz545, zzz546, zzz547, Succ(zzz5480), Succ(zzz5490), bc) → new_mkVBalBranch3MkVBalBranch25(zzz537, zzz538, zzz539, zzz540, zzz541, zzz542, zzz543, zzz544, zzz545, zzz546, zzz547, zzz5480, zzz5490, bc)
new_mkVBalBranch3MkVBalBranch29(zzz818, zzz819, zzz820, zzz821, zzz822, zzz823, zzz824, zzz825, zzz826, zzz827, bf) → new_mkVBalBranch3MkVBalBranch14(zzz818, zzz819, zzz820, zzz821, zzz822, zzz823, zzz824, zzz825, zzz826, zzz827, new_primPlusNat2(new_primPlusNat3(Succ(new_primPlusNat3(new_primPlusNat1(zzz820), zzz820)), Succ(zzz820)), Succ(zzz820)), bf)
new_mkVBalBranch3MkVBalBranch10(zzz929, zzz930, zzz931, zzz932, zzz933, zzz934, zzz935, zzz936, zzz937, zzz938, zzz939, Succ(zzz10020), ba) → new_mkVBalBranch3MkVBalBranch11(zzz929, zzz930, zzz931, zzz932, zzz933, zzz934, zzz935, zzz936, zzz937, zzz938, zzz939, Succ(zzz10020), Succ(zzz936), ba)
new_mkVBalBranch(zzz31, Branch(zzz520, zzz521, Pos(Succ(zzz52200)), zzz523, zzz524), Branch(zzz340, zzz341, zzz342, zzz343, zzz344), h) → new_mkVBalBranch3MkVBalBranch2(zzz340, zzz341, zzz342, zzz343, zzz344, zzz520, zzz521, zzz52200, zzz523, zzz524, zzz31, Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat3(new_primPlusNat1(zzz52200), zzz52200)), zzz52200))), h)
new_mkVBalBranch3MkVBalBranch14(zzz818, zzz819, zzz820, zzz821, zzz822, zzz823, zzz824, zzz825, zzz826, zzz827, Succ(zzz8960), bf) → new_mkVBalBranch3MkVBalBranch16(zzz818, zzz819, zzz820, zzz821, zzz822, zzz823, zzz824, Zero, zzz825, zzz826, zzz827, Succ(Zero), Succ(zzz8960), bf)
new_mkVBalBranch3MkVBalBranch26(zzz1133, zzz1134, zzz1135, zzz1136, zzz1137, zzz1138, zzz1139, zzz1140, zzz1141, zzz1142, Zero, Succ(zzz11440), be) → new_mkVBalBranch(zzz1142, Branch(zzz1138, zzz1139, Neg(Succ(Zero)), zzz1140, zzz1141), zzz1136, be)
new_mkVBalBranch3MkVBalBranch24(zzz340, zzz341, Neg(Succ(Succ(Succ(zzz3420000)))), zzz343, zzz344, zzz520, zzz521, Succ(zzz522000), zzz523, zzz524, zzz31, Succ(Succ(zzz6900)), h) → new_mkVBalBranch3MkVBalBranch25(zzz340, zzz341, Succ(Succ(zzz3420000)), zzz343, zzz344, zzz520, zzz521, zzz522000, zzz523, zzz524, zzz31, Succ(zzz3420000), Succ(Succ(new_primPlusNat2(zzz6900, zzz522000))), h)
new_mkVBalBranch3MkVBalBranch24(zzz340, zzz341, Neg(Succ(Succ(Zero))), zzz343, zzz344, zzz520, zzz521, Succ(zzz522000), zzz523, zzz524, zzz31, Succ(Succ(zzz6900)), h) → new_mkVBalBranch3MkVBalBranch25(zzz340, zzz341, Succ(Zero), zzz343, zzz344, zzz520, zzz521, zzz522000, zzz523, zzz524, zzz31, Zero, Succ(Succ(new_primPlusNat2(zzz6900, zzz522000))), h)
new_mkVBalBranch3MkVBalBranch20(zzz929, zzz930, zzz931, zzz932, zzz933, zzz934, zzz935, zzz936, zzz937, zzz938, zzz939, Succ(zzz9400), Zero, ba) → new_mkVBalBranch3MkVBalBranch10(zzz929, zzz930, zzz931, zzz932, zzz933, zzz934, zzz935, zzz936, zzz937, zzz938, zzz939, new_primPlusNat2(new_primPlusNat3(Succ(new_primPlusNat3(new_primPlusNat1(zzz931), zzz931)), Succ(zzz931)), Succ(zzz931)), ba)
new_mkVBalBranch(zzz31, Branch(zzz520, zzz521, Pos(Zero), zzz523, zzz524), Branch(zzz340, zzz341, Pos(Succ(zzz34200)), zzz343, zzz344), h) → new_mkVBalBranch(zzz31, Branch(zzz520, zzz521, Pos(Zero), zzz523, zzz524), zzz343, h)
new_mkVBalBranch(zzz31, Branch(zzz520, zzz521, Pos(Zero), zzz523, zzz524), Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), h) → new_mkVBalBranch3MkVBalBranch12(zzz340, zzz341, zzz34200, zzz343, zzz344, zzz520, zzz521, zzz523, zzz524, zzz31, new_primPlusNat2(Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat3(new_primPlusNat1(zzz34200), zzz34200)), zzz34200))), Succ(zzz34200)), h)
new_mkVBalBranch3MkVBalBranch23(zzz929, zzz930, zzz931, zzz932, zzz933, zzz934, zzz935, zzz936, zzz937, zzz938, zzz939, ba) → new_mkVBalBranch3MkVBalBranch10(zzz929, zzz930, zzz931, zzz932, zzz933, zzz934, zzz935, zzz936, zzz937, zzz938, zzz939, new_primPlusNat2(new_primMulNat0(zzz931), Succ(zzz931)), ba)
new_mkVBalBranch3MkVBalBranch2(zzz340, zzz341, Pos(Zero), zzz343, zzz344, zzz520, zzz521, zzz52200, zzz523, zzz524, zzz31, Succ(zzz680), h) → new_mkVBalBranch(zzz31, zzz524, Branch(zzz340, zzz341, Pos(Zero), zzz343, zzz344), h)
new_mkVBalBranch3MkVBalBranch2(zzz340, zzz341, Neg(Zero), zzz343, zzz344, zzz520, zzz521, zzz52200, zzz523, zzz524, zzz31, Succ(zzz680), h) → new_mkVBalBranch(zzz31, zzz524, Branch(zzz340, zzz341, Neg(Zero), zzz343, zzz344), h)
new_mkVBalBranch3MkVBalBranch2(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344, zzz520, zzz521, zzz52200, zzz523, zzz524, zzz31, Succ(zzz680), h) → new_mkVBalBranch3MkVBalBranch1(zzz340, zzz341, zzz34200, zzz343, zzz344, zzz520, zzz521, zzz52200, zzz523, zzz524, zzz31, new_primPlusNat2(Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat3(new_primPlusNat1(zzz34200), zzz34200)), zzz34200))), Succ(zzz34200)), h)
new_mkVBalBranch3MkVBalBranch16(zzz1702, zzz1703, zzz1704, zzz1705, zzz1706, zzz1707, zzz1708, zzz1709, zzz1710, zzz1711, zzz1712, Zero, Succ(zzz17140), bd) → new_mkVBalBranch(zzz1712, zzz1711, Branch(zzz1702, zzz1703, Neg(Succ(zzz1704)), zzz1705, zzz1706), bd)
new_mkVBalBranch3MkVBalBranch10(zzz929, zzz930, zzz931, zzz932, zzz933, zzz934, zzz935, zzz936, zzz937, zzz938, zzz939, Zero, ba) → new_mkVBalBranch3MkVBalBranch11(zzz929, zzz930, zzz931, zzz932, zzz933, zzz934, zzz935, zzz936, zzz937, zzz938, zzz939, Zero, Succ(zzz936), ba)
new_mkVBalBranch3MkVBalBranch15(zzz537, zzz538, zzz539, zzz540, zzz541, zzz542, zzz543, zzz544, zzz545, zzz546, zzz547, Succ(zzz6990), bc) → new_mkVBalBranch3MkVBalBranch16(zzz537, zzz538, zzz539, zzz540, zzz541, zzz542, zzz543, Succ(zzz544), zzz545, zzz546, zzz547, Succ(Succ(zzz544)), Succ(zzz6990), bc)
new_mkVBalBranch3MkVBalBranch24(zzz340, zzz341, Neg(Succ(Succ(Succ(zzz3420000)))), zzz343, zzz344, zzz520, zzz521, Zero, zzz523, zzz524, zzz31, Succ(Succ(zzz6900)), h) → new_mkVBalBranch3MkVBalBranch26(zzz340, zzz341, Succ(Succ(zzz3420000)), zzz343, zzz344, zzz520, zzz521, zzz523, zzz524, zzz31, Succ(zzz3420000), Succ(zzz6900), h)
new_mkVBalBranch3MkVBalBranch25(zzz537, zzz538, zzz539, zzz540, zzz541, zzz542, zzz543, zzz544, zzz545, zzz546, zzz547, Zero, Zero, bc) → new_mkVBalBranch3MkVBalBranch211(zzz537, zzz538, zzz539, zzz540, zzz541, zzz542, zzz543, zzz544, zzz545, zzz546, zzz547, bc)

The TRS R consists of the following rules:

new_primMulNat0(zzz6200) → new_primPlusNat3(Succ(new_primPlusNat3(new_primPlusNat1(zzz6200), zzz6200)), Succ(zzz6200))
new_primPlusNat2(Succ(zzz900), Succ(zzz9100)) → Succ(Succ(new_primPlusNat2(zzz900, zzz9100)))
new_primPlusNat2(Zero, Succ(zzz9100)) → Succ(zzz9100)
new_primPlusNat2(Zero, Zero) → Zero
new_primPlusNat2(Succ(zzz900), Zero) → Succ(zzz900)
new_primPlusNat1(Zero) → Zero
new_primPlusNat1(Succ(zzz62000)) → Succ(Succ(new_primPlusNat1(zzz62000)))
new_primPlusNat3(zzz90, Succ(zzz910)) → Succ(Succ(new_primPlusNat2(zzz90, zzz910)))
new_primPlusNat3(zzz90, Zero) → Succ(zzz90)

The set Q consists of the following terms:

new_primPlusNat2(Zero, Succ(x0))
new_primMulNat0(x0)
new_primPlusNat3(x0, Succ(x1))
new_primPlusNat2(Succ(x0), Succ(x1))
new_primPlusNat3(x0, Zero)
new_primPlusNat1(Zero)
new_primPlusNat2(Zero, Zero)
new_primPlusNat1(Succ(x0))
new_primPlusNat2(Succ(x0), Zero)

We have to consider all minimal (P,Q,R)-chains.
By rewriting [15] the rule new_mkVBalBranch3MkVBalBranch23(zzz929, zzz930, zzz931, zzz932, zzz933, zzz934, zzz935, zzz936, zzz937, zzz938, zzz939, ba) → new_mkVBalBranch3MkVBalBranch10(zzz929, zzz930, zzz931, zzz932, zzz933, zzz934, zzz935, zzz936, zzz937, zzz938, zzz939, new_primPlusNat2(new_primMulNat0(zzz931), Succ(zzz931)), ba) at position [11,0] we obtained the following new rules:

new_mkVBalBranch3MkVBalBranch23(zzz929, zzz930, zzz931, zzz932, zzz933, zzz934, zzz935, zzz936, zzz937, zzz938, zzz939, ba) → new_mkVBalBranch3MkVBalBranch10(zzz929, zzz930, zzz931, zzz932, zzz933, zzz934, zzz935, zzz936, zzz937, zzz938, zzz939, new_primPlusNat2(new_primPlusNat3(Succ(new_primPlusNat3(new_primPlusNat1(zzz931), zzz931)), Succ(zzz931)), Succ(zzz931)), 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
                                    ↳ DependencyGraphProof
                                      ↳ QDP
                                        ↳ Rewriting
                                          ↳ QDP
                                            ↳ Rewriting
                                              ↳ QDP
                                                ↳ Rewriting
                                                  ↳ QDP
                                                    ↳ Rewriting
                                                      ↳ QDP
                                                        ↳ Rewriting
                                                          ↳ QDP
                                                            ↳ Rewriting
                                                              ↳ QDP
                                                                ↳ Rewriting
                                                                  ↳ QDP
                                                                    ↳ Rewriting
                                                                      ↳ QDP
                                                                        ↳ Rewriting
                                                                          ↳ QDP
                                                                            ↳ Rewriting
                                                                              ↳ QDP
                                                                                ↳ Rewriting
                                                                                  ↳ QDP
                                                                                    ↳ Rewriting
                                                                                      ↳ QDP
                                                                                        ↳ Rewriting
                                                                                          ↳ QDP
                                                                                            ↳ UsableRulesProof
                                                                                              ↳ QDP
                                                                                                ↳ QReductionProof
                                                                                                  ↳ QDP
                                                                                                    ↳ Rewriting
                                                                                                      ↳ QDP
                                                                                                        ↳ Rewriting
                                                                                                          ↳ QDP
                                                                                                            ↳ Rewriting
                                                                                                              ↳ QDP
                                                                                                                ↳ Rewriting
                                                                                                                  ↳ QDP
                                                                                                                    ↳ Rewriting
                                                                                                                      ↳ QDP
                                                                                                                        ↳ Rewriting
                                                                                                                          ↳ QDP
                                                                                                                            ↳ DependencyGraphProof
                                                                                                                              ↳ QDP
                                                                                                                                ↳ Rewriting
                                                                                                                                  ↳ QDP
                                                                                                                                    ↳ Rewriting
                                                                                                                                      ↳ QDP
                                                                                                                                        ↳ DependencyGraphProof
                                                                                                                                          ↳ QDP
                                                                                                                                            ↳ Rewriting
                                                                                                                                              ↳ QDP
                                                                                                                                                ↳ Rewriting
                                                                                                                                                  ↳ QDP
                                                                                                                                                    ↳ Rewriting
                                                                                                                                                      ↳ QDP
                                                                                                                                                        ↳ Rewriting
                                                                                                                                                          ↳ QDP
                                                                                                                                                            ↳ Rewriting
                                                                                                                                                              ↳ QDP
                                                                                                                                                                ↳ Rewriting
                                                                                                                                                                  ↳ QDP
                                                                                                                                                                    ↳ Rewriting
                                                                                                                                                                      ↳ QDP
                                                                                                                                                                        ↳ UsableRulesProof
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP

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

new_mkVBalBranch(zzz31, Branch(zzz520, zzz521, Neg(Succ(zzz52200)), zzz523, zzz524), Branch(zzz340, zzz341, zzz342, zzz343, zzz344), h) → new_mkVBalBranch3MkVBalBranch24(zzz340, zzz341, zzz342, zzz343, zzz344, zzz520, zzz521, zzz52200, zzz523, zzz524, zzz31, Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat3(new_primPlusNat1(zzz52200), zzz52200)), zzz52200))), h)
new_mkVBalBranch3MkVBalBranch11(zzz2033, zzz2034, zzz2035, zzz2036, zzz2037, zzz2038, zzz2039, zzz2040, zzz2041, zzz2042, zzz2043, Zero, Succ(zzz20450), bb) → new_mkVBalBranch(zzz2043, zzz2042, Branch(zzz2033, zzz2034, Pos(Succ(zzz2035)), zzz2036, zzz2037), bb)
new_mkVBalBranch3MkVBalBranch26(zzz1133, zzz1134, zzz1135, zzz1136, zzz1137, zzz1138, zzz1139, zzz1140, zzz1141, zzz1142, Succ(zzz11430), Succ(zzz11440), be) → new_mkVBalBranch3MkVBalBranch26(zzz1133, zzz1134, zzz1135, zzz1136, zzz1137, zzz1138, zzz1139, zzz1140, zzz1141, zzz1142, zzz11430, zzz11440, be)
new_mkVBalBranch3MkVBalBranch24(zzz340, zzz341, Pos(zzz3420), zzz343, zzz344, zzz520, zzz521, zzz52200, zzz523, zzz524, zzz31, Succ(zzz690), h) → new_mkVBalBranch(zzz31, Branch(zzz520, zzz521, Neg(Succ(zzz52200)), zzz523, zzz524), zzz343, h)
new_mkVBalBranch3MkVBalBranch12(zzz340, zzz341, zzz34200, zzz343, zzz344, zzz520, zzz521, zzz523, zzz524, zzz31, Succ(zzz1250), h) → new_mkVBalBranch(zzz31, zzz524, Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), h)
new_mkVBalBranch3MkVBalBranch20(zzz929, zzz930, zzz931, zzz932, zzz933, zzz934, zzz935, zzz936, zzz937, zzz938, zzz939, Zero, Succ(zzz9410), ba) → new_mkVBalBranch(zzz939, Branch(zzz934, zzz935, Pos(Succ(zzz936)), zzz937, zzz938), zzz932, ba)
new_mkVBalBranch3MkVBalBranch24(zzz340, zzz341, Neg(Succ(Succ(Zero))), zzz343, zzz344, zzz520, zzz521, Zero, zzz523, zzz524, zzz31, Succ(Succ(zzz6900)), h) → new_mkVBalBranch3MkVBalBranch26(zzz340, zzz341, Succ(Zero), zzz343, zzz344, zzz520, zzz521, zzz523, zzz524, zzz31, Zero, Succ(zzz6900), h)
new_mkVBalBranch3MkVBalBranch17(zzz340, zzz341, zzz34200, zzz343, zzz344, zzz520, zzz521, zzz52200, zzz523, zzz524, zzz31, h) → new_mkVBalBranch(zzz31, zzz524, Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), h)
new_mkVBalBranch3MkVBalBranch26(zzz1133, zzz1134, zzz1135, zzz1136, zzz1137, zzz1138, zzz1139, zzz1140, zzz1141, zzz1142, Zero, Zero, be) → new_mkVBalBranch3MkVBalBranch29(zzz1133, zzz1134, zzz1135, zzz1136, zzz1137, zzz1138, zzz1139, zzz1140, zzz1141, zzz1142, be)
new_mkVBalBranch3MkVBalBranch1(zzz340, zzz341, zzz34200, zzz343, zzz344, zzz520, zzz521, zzz52200, zzz523, zzz524, zzz31, Succ(zzz1430), h) → new_mkVBalBranch(zzz31, zzz524, Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), h)
new_mkVBalBranch3MkVBalBranch24(zzz340, zzz341, Neg(Succ(Zero)), zzz343, zzz344, zzz520, zzz521, zzz52200, zzz523, zzz524, zzz31, Succ(zzz690), h) → new_mkVBalBranch(zzz31, Branch(zzz520, zzz521, Neg(Succ(zzz52200)), zzz523, zzz524), zzz343, h)
new_mkVBalBranch3MkVBalBranch20(zzz929, zzz930, zzz931, zzz932, zzz933, zzz934, zzz935, zzz936, zzz937, zzz938, zzz939, Zero, Zero, ba) → new_mkVBalBranch3MkVBalBranch23(zzz929, zzz930, zzz931, zzz932, zzz933, zzz934, zzz935, zzz936, zzz937, zzz938, zzz939, ba)
new_mkVBalBranch3MkVBalBranch13(zzz340, zzz341, zzz34200, zzz343, zzz344, zzz520, zzz521, zzz523, zzz524, zzz31, Succ(zzz1290), h) → new_mkVBalBranch(zzz31, zzz524, Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), h)
new_mkVBalBranch3MkVBalBranch2(zzz340, zzz341, Pos(Succ(zzz34200)), zzz343, zzz344, zzz520, zzz521, zzz52200, zzz523, zzz524, zzz31, Succ(zzz680), h) → new_mkVBalBranch3MkVBalBranch20(zzz340, zzz341, zzz34200, zzz343, zzz344, zzz520, zzz521, zzz52200, zzz523, zzz524, zzz31, Succ(new_primPlusNat2(zzz680, zzz52200)), zzz34200, h)
new_mkVBalBranch(zzz31, Branch(zzz520, zzz521, Neg(Zero), zzz523, zzz524), Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), h) → new_mkVBalBranch3MkVBalBranch13(zzz340, zzz341, zzz34200, zzz343, zzz344, zzz520, zzz521, zzz523, zzz524, zzz31, new_primPlusNat2(new_primPlusNat3(Succ(new_primPlusNat3(new_primPlusNat1(zzz34200), zzz34200)), Succ(zzz34200)), Succ(zzz34200)), h)
new_mkVBalBranch3MkVBalBranch24(zzz340, zzz341, Neg(Zero), zzz343, zzz344, zzz520, zzz521, zzz52200, zzz523, zzz524, zzz31, Succ(zzz690), h) → new_mkVBalBranch(zzz31, Branch(zzz520, zzz521, Neg(Succ(zzz52200)), zzz523, zzz524), zzz343, h)
new_mkVBalBranch(zzz31, Branch(zzz520, zzz521, Neg(Zero), zzz523, zzz524), Branch(zzz340, zzz341, Pos(Succ(zzz34200)), zzz343, zzz344), h) → new_mkVBalBranch(zzz31, Branch(zzz520, zzz521, Neg(Zero), zzz523, zzz524), zzz343, h)
new_mkVBalBranch3MkVBalBranch212(zzz818, zzz819, zzz820, zzz821, zzz822, zzz823, zzz824, zzz825, zzz826, zzz827, bf) → new_mkVBalBranch3MkVBalBranch14(zzz818, zzz819, zzz820, zzz821, zzz822, zzz823, zzz824, zzz825, zzz826, zzz827, new_primPlusNat2(new_primPlusNat3(Succ(new_primPlusNat3(new_primPlusNat1(zzz820), zzz820)), Succ(zzz820)), Succ(zzz820)), bf)
new_mkVBalBranch3MkVBalBranch20(zzz929, zzz930, zzz931, zzz932, zzz933, zzz934, zzz935, zzz936, zzz937, zzz938, zzz939, Succ(zzz9400), Succ(zzz9410), ba) → new_mkVBalBranch3MkVBalBranch20(zzz929, zzz930, zzz931, zzz932, zzz933, zzz934, zzz935, zzz936, zzz937, zzz938, zzz939, zzz9400, zzz9410, ba)
new_mkVBalBranch3MkVBalBranch26(zzz1133, zzz1134, zzz1135, zzz1136, zzz1137, zzz1138, zzz1139, zzz1140, zzz1141, zzz1142, Succ(zzz11430), Zero, be) → new_mkVBalBranch3MkVBalBranch212(zzz1133, zzz1134, zzz1135, zzz1136, zzz1137, zzz1138, zzz1139, zzz1140, zzz1141, zzz1142, be)
new_mkVBalBranch3MkVBalBranch1(zzz340, zzz341, zzz34200, zzz343, zzz344, zzz520, zzz521, zzz52200, zzz523, zzz524, zzz31, Zero, h) → new_mkVBalBranch3MkVBalBranch17(zzz340, zzz341, zzz34200, zzz343, zzz344, zzz520, zzz521, zzz52200, zzz523, zzz524, zzz31, h)
new_mkVBalBranch3MkVBalBranch23(zzz929, zzz930, zzz931, zzz932, zzz933, zzz934, zzz935, zzz936, zzz937, zzz938, zzz939, ba) → new_mkVBalBranch3MkVBalBranch10(zzz929, zzz930, zzz931, zzz932, zzz933, zzz934, zzz935, zzz936, zzz937, zzz938, zzz939, new_primPlusNat2(new_primPlusNat3(Succ(new_primPlusNat3(new_primPlusNat1(zzz931), zzz931)), Succ(zzz931)), Succ(zzz931)), ba)
new_mkVBalBranch3MkVBalBranch211(zzz537, zzz538, zzz539, zzz540, zzz541, zzz542, zzz543, zzz544, zzz545, zzz546, zzz547, bc) → new_mkVBalBranch3MkVBalBranch15(zzz537, zzz538, zzz539, zzz540, zzz541, zzz542, zzz543, zzz544, zzz545, zzz546, zzz547, new_primPlusNat2(Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat3(new_primPlusNat1(zzz539), zzz539)), zzz539))), Succ(zzz539)), bc)
new_mkVBalBranch3MkVBalBranch16(zzz1702, zzz1703, zzz1704, zzz1705, zzz1706, zzz1707, zzz1708, zzz1709, zzz1710, zzz1711, zzz1712, Succ(zzz17130), Succ(zzz17140), bd) → new_mkVBalBranch3MkVBalBranch16(zzz1702, zzz1703, zzz1704, zzz1705, zzz1706, zzz1707, zzz1708, zzz1709, zzz1710, zzz1711, zzz1712, zzz17130, zzz17140, bd)
new_mkVBalBranch3MkVBalBranch25(zzz537, zzz538, zzz539, zzz540, zzz541, zzz542, zzz543, zzz544, zzz545, zzz546, zzz547, Zero, Succ(zzz5490), bc) → new_mkVBalBranch(zzz547, Branch(zzz542, zzz543, Neg(Succ(Succ(zzz544))), zzz545, zzz546), zzz540, bc)
new_mkVBalBranch3MkVBalBranch11(zzz2033, zzz2034, zzz2035, zzz2036, zzz2037, zzz2038, zzz2039, zzz2040, zzz2041, zzz2042, zzz2043, Succ(zzz20440), Succ(zzz20450), bb) → new_mkVBalBranch3MkVBalBranch11(zzz2033, zzz2034, zzz2035, zzz2036, zzz2037, zzz2038, zzz2039, zzz2040, zzz2041, zzz2042, zzz2043, zzz20440, zzz20450, bb)
new_mkVBalBranch3MkVBalBranch25(zzz537, zzz538, zzz539, zzz540, zzz541, zzz542, zzz543, zzz544, zzz545, zzz546, zzz547, Succ(zzz5480), Zero, bc) → new_mkVBalBranch3MkVBalBranch15(zzz537, zzz538, zzz539, zzz540, zzz541, zzz542, zzz543, zzz544, zzz545, zzz546, zzz547, new_primPlusNat2(Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat3(new_primPlusNat1(zzz539), zzz539)), zzz539))), Succ(zzz539)), bc)
new_mkVBalBranch3MkVBalBranch25(zzz537, zzz538, zzz539, zzz540, zzz541, zzz542, zzz543, zzz544, zzz545, zzz546, zzz547, Succ(zzz5480), Succ(zzz5490), bc) → new_mkVBalBranch3MkVBalBranch25(zzz537, zzz538, zzz539, zzz540, zzz541, zzz542, zzz543, zzz544, zzz545, zzz546, zzz547, zzz5480, zzz5490, bc)
new_mkVBalBranch3MkVBalBranch29(zzz818, zzz819, zzz820, zzz821, zzz822, zzz823, zzz824, zzz825, zzz826, zzz827, bf) → new_mkVBalBranch3MkVBalBranch14(zzz818, zzz819, zzz820, zzz821, zzz822, zzz823, zzz824, zzz825, zzz826, zzz827, new_primPlusNat2(new_primPlusNat3(Succ(new_primPlusNat3(new_primPlusNat1(zzz820), zzz820)), Succ(zzz820)), Succ(zzz820)), bf)
new_mkVBalBranch(zzz31, Branch(zzz520, zzz521, Pos(Succ(zzz52200)), zzz523, zzz524), Branch(zzz340, zzz341, zzz342, zzz343, zzz344), h) → new_mkVBalBranch3MkVBalBranch2(zzz340, zzz341, zzz342, zzz343, zzz344, zzz520, zzz521, zzz52200, zzz523, zzz524, zzz31, Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat3(new_primPlusNat1(zzz52200), zzz52200)), zzz52200))), h)
new_mkVBalBranch3MkVBalBranch10(zzz929, zzz930, zzz931, zzz932, zzz933, zzz934, zzz935, zzz936, zzz937, zzz938, zzz939, Succ(zzz10020), ba) → new_mkVBalBranch3MkVBalBranch11(zzz929, zzz930, zzz931, zzz932, zzz933, zzz934, zzz935, zzz936, zzz937, zzz938, zzz939, Succ(zzz10020), Succ(zzz936), ba)
new_mkVBalBranch3MkVBalBranch14(zzz818, zzz819, zzz820, zzz821, zzz822, zzz823, zzz824, zzz825, zzz826, zzz827, Succ(zzz8960), bf) → new_mkVBalBranch3MkVBalBranch16(zzz818, zzz819, zzz820, zzz821, zzz822, zzz823, zzz824, Zero, zzz825, zzz826, zzz827, Succ(Zero), Succ(zzz8960), bf)
new_mkVBalBranch3MkVBalBranch24(zzz340, zzz341, Neg(Succ(Succ(Succ(zzz3420000)))), zzz343, zzz344, zzz520, zzz521, Succ(zzz522000), zzz523, zzz524, zzz31, Succ(Succ(zzz6900)), h) → new_mkVBalBranch3MkVBalBranch25(zzz340, zzz341, Succ(Succ(zzz3420000)), zzz343, zzz344, zzz520, zzz521, zzz522000, zzz523, zzz524, zzz31, Succ(zzz3420000), Succ(Succ(new_primPlusNat2(zzz6900, zzz522000))), h)
new_mkVBalBranch3MkVBalBranch26(zzz1133, zzz1134, zzz1135, zzz1136, zzz1137, zzz1138, zzz1139, zzz1140, zzz1141, zzz1142, Zero, Succ(zzz11440), be) → new_mkVBalBranch(zzz1142, Branch(zzz1138, zzz1139, Neg(Succ(Zero)), zzz1140, zzz1141), zzz1136, be)
new_mkVBalBranch3MkVBalBranch24(zzz340, zzz341, Neg(Succ(Succ(Zero))), zzz343, zzz344, zzz520, zzz521, Succ(zzz522000), zzz523, zzz524, zzz31, Succ(Succ(zzz6900)), h) → new_mkVBalBranch3MkVBalBranch25(zzz340, zzz341, Succ(Zero), zzz343, zzz344, zzz520, zzz521, zzz522000, zzz523, zzz524, zzz31, Zero, Succ(Succ(new_primPlusNat2(zzz6900, zzz522000))), h)
new_mkVBalBranch(zzz31, Branch(zzz520, zzz521, Pos(Zero), zzz523, zzz524), Branch(zzz340, zzz341, Pos(Succ(zzz34200)), zzz343, zzz344), h) → new_mkVBalBranch(zzz31, Branch(zzz520, zzz521, Pos(Zero), zzz523, zzz524), zzz343, h)
new_mkVBalBranch3MkVBalBranch20(zzz929, zzz930, zzz931, zzz932, zzz933, zzz934, zzz935, zzz936, zzz937, zzz938, zzz939, Succ(zzz9400), Zero, ba) → new_mkVBalBranch3MkVBalBranch10(zzz929, zzz930, zzz931, zzz932, zzz933, zzz934, zzz935, zzz936, zzz937, zzz938, zzz939, new_primPlusNat2(new_primPlusNat3(Succ(new_primPlusNat3(new_primPlusNat1(zzz931), zzz931)), Succ(zzz931)), Succ(zzz931)), ba)
new_mkVBalBranch(zzz31, Branch(zzz520, zzz521, Pos(Zero), zzz523, zzz524), Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), h) → new_mkVBalBranch3MkVBalBranch12(zzz340, zzz341, zzz34200, zzz343, zzz344, zzz520, zzz521, zzz523, zzz524, zzz31, new_primPlusNat2(Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat3(new_primPlusNat1(zzz34200), zzz34200)), zzz34200))), Succ(zzz34200)), h)
new_mkVBalBranch3MkVBalBranch2(zzz340, zzz341, Pos(Zero), zzz343, zzz344, zzz520, zzz521, zzz52200, zzz523, zzz524, zzz31, Succ(zzz680), h) → new_mkVBalBranch(zzz31, zzz524, Branch(zzz340, zzz341, Pos(Zero), zzz343, zzz344), h)
new_mkVBalBranch3MkVBalBranch2(zzz340, zzz341, Neg(Zero), zzz343, zzz344, zzz520, zzz521, zzz52200, zzz523, zzz524, zzz31, Succ(zzz680), h) → new_mkVBalBranch(zzz31, zzz524, Branch(zzz340, zzz341, Neg(Zero), zzz343, zzz344), h)
new_mkVBalBranch3MkVBalBranch2(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344, zzz520, zzz521, zzz52200, zzz523, zzz524, zzz31, Succ(zzz680), h) → new_mkVBalBranch3MkVBalBranch1(zzz340, zzz341, zzz34200, zzz343, zzz344, zzz520, zzz521, zzz52200, zzz523, zzz524, zzz31, new_primPlusNat2(Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat3(new_primPlusNat1(zzz34200), zzz34200)), zzz34200))), Succ(zzz34200)), h)
new_mkVBalBranch3MkVBalBranch16(zzz1702, zzz1703, zzz1704, zzz1705, zzz1706, zzz1707, zzz1708, zzz1709, zzz1710, zzz1711, zzz1712, Zero, Succ(zzz17140), bd) → new_mkVBalBranch(zzz1712, zzz1711, Branch(zzz1702, zzz1703, Neg(Succ(zzz1704)), zzz1705, zzz1706), bd)
new_mkVBalBranch3MkVBalBranch24(zzz340, zzz341, Neg(Succ(Succ(Succ(zzz3420000)))), zzz343, zzz344, zzz520, zzz521, Zero, zzz523, zzz524, zzz31, Succ(Succ(zzz6900)), h) → new_mkVBalBranch3MkVBalBranch26(zzz340, zzz341, Succ(Succ(zzz3420000)), zzz343, zzz344, zzz520, zzz521, zzz523, zzz524, zzz31, Succ(zzz3420000), Succ(zzz6900), h)
new_mkVBalBranch3MkVBalBranch15(zzz537, zzz538, zzz539, zzz540, zzz541, zzz542, zzz543, zzz544, zzz545, zzz546, zzz547, Succ(zzz6990), bc) → new_mkVBalBranch3MkVBalBranch16(zzz537, zzz538, zzz539, zzz540, zzz541, zzz542, zzz543, Succ(zzz544), zzz545, zzz546, zzz547, Succ(Succ(zzz544)), Succ(zzz6990), bc)
new_mkVBalBranch3MkVBalBranch10(zzz929, zzz930, zzz931, zzz932, zzz933, zzz934, zzz935, zzz936, zzz937, zzz938, zzz939, Zero, ba) → new_mkVBalBranch3MkVBalBranch11(zzz929, zzz930, zzz931, zzz932, zzz933, zzz934, zzz935, zzz936, zzz937, zzz938, zzz939, Zero, Succ(zzz936), ba)
new_mkVBalBranch3MkVBalBranch25(zzz537, zzz538, zzz539, zzz540, zzz541, zzz542, zzz543, zzz544, zzz545, zzz546, zzz547, Zero, Zero, bc) → new_mkVBalBranch3MkVBalBranch211(zzz537, zzz538, zzz539, zzz540, zzz541, zzz542, zzz543, zzz544, zzz545, zzz546, zzz547, bc)

The TRS R consists of the following rules:

new_primMulNat0(zzz6200) → new_primPlusNat3(Succ(new_primPlusNat3(new_primPlusNat1(zzz6200), zzz6200)), Succ(zzz6200))
new_primPlusNat2(Succ(zzz900), Succ(zzz9100)) → Succ(Succ(new_primPlusNat2(zzz900, zzz9100)))
new_primPlusNat2(Zero, Succ(zzz9100)) → Succ(zzz9100)
new_primPlusNat2(Zero, Zero) → Zero
new_primPlusNat2(Succ(zzz900), Zero) → Succ(zzz900)
new_primPlusNat1(Zero) → Zero
new_primPlusNat1(Succ(zzz62000)) → Succ(Succ(new_primPlusNat1(zzz62000)))
new_primPlusNat3(zzz90, Succ(zzz910)) → Succ(Succ(new_primPlusNat2(zzz90, zzz910)))
new_primPlusNat3(zzz90, Zero) → Succ(zzz90)

The set Q consists of the following terms:

new_primPlusNat2(Zero, Succ(x0))
new_primMulNat0(x0)
new_primPlusNat3(x0, Succ(x1))
new_primPlusNat2(Succ(x0), Succ(x1))
new_primPlusNat3(x0, Zero)
new_primPlusNat1(Zero)
new_primPlusNat2(Zero, Zero)
new_primPlusNat1(Succ(x0))
new_primPlusNat2(Succ(x0), Zero)

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

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

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

new_mkVBalBranch3MkVBalBranch11(zzz2033, zzz2034, zzz2035, zzz2036, zzz2037, zzz2038, zzz2039, zzz2040, zzz2041, zzz2042, zzz2043, Zero, Succ(zzz20450), bb) → new_mkVBalBranch(zzz2043, zzz2042, Branch(zzz2033, zzz2034, Pos(Succ(zzz2035)), zzz2036, zzz2037), bb)
new_mkVBalBranch(zzz31, Branch(zzz520, zzz521, Neg(Succ(zzz52200)), zzz523, zzz524), Branch(zzz340, zzz341, zzz342, zzz343, zzz344), h) → new_mkVBalBranch3MkVBalBranch24(zzz340, zzz341, zzz342, zzz343, zzz344, zzz520, zzz521, zzz52200, zzz523, zzz524, zzz31, Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat3(new_primPlusNat1(zzz52200), zzz52200)), zzz52200))), h)
new_mkVBalBranch3MkVBalBranch26(zzz1133, zzz1134, zzz1135, zzz1136, zzz1137, zzz1138, zzz1139, zzz1140, zzz1141, zzz1142, Succ(zzz11430), Succ(zzz11440), be) → new_mkVBalBranch3MkVBalBranch26(zzz1133, zzz1134, zzz1135, zzz1136, zzz1137, zzz1138, zzz1139, zzz1140, zzz1141, zzz1142, zzz11430, zzz11440, be)
new_mkVBalBranch3MkVBalBranch24(zzz340, zzz341, Pos(zzz3420), zzz343, zzz344, zzz520, zzz521, zzz52200, zzz523, zzz524, zzz31, Succ(zzz690), h) → new_mkVBalBranch(zzz31, Branch(zzz520, zzz521, Neg(Succ(zzz52200)), zzz523, zzz524), zzz343, h)
new_mkVBalBranch3MkVBalBranch12(zzz340, zzz341, zzz34200, zzz343, zzz344, zzz520, zzz521, zzz523, zzz524, zzz31, Succ(zzz1250), h) → new_mkVBalBranch(zzz31, zzz524, Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), h)
new_mkVBalBranch3MkVBalBranch20(zzz929, zzz930, zzz931, zzz932, zzz933, zzz934, zzz935, zzz936, zzz937, zzz938, zzz939, Zero, Succ(zzz9410), ba) → new_mkVBalBranch(zzz939, Branch(zzz934, zzz935, Pos(Succ(zzz936)), zzz937, zzz938), zzz932, ba)
new_mkVBalBranch3MkVBalBranch24(zzz340, zzz341, Neg(Succ(Succ(Zero))), zzz343, zzz344, zzz520, zzz521, Zero, zzz523, zzz524, zzz31, Succ(Succ(zzz6900)), h) → new_mkVBalBranch3MkVBalBranch26(zzz340, zzz341, Succ(Zero), zzz343, zzz344, zzz520, zzz521, zzz523, zzz524, zzz31, Zero, Succ(zzz6900), h)
new_mkVBalBranch3MkVBalBranch17(zzz340, zzz341, zzz34200, zzz343, zzz344, zzz520, zzz521, zzz52200, zzz523, zzz524, zzz31, h) → new_mkVBalBranch(zzz31, zzz524, Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), h)
new_mkVBalBranch3MkVBalBranch1(zzz340, zzz341, zzz34200, zzz343, zzz344, zzz520, zzz521, zzz52200, zzz523, zzz524, zzz31, Succ(zzz1430), h) → new_mkVBalBranch(zzz31, zzz524, Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), h)
new_mkVBalBranch3MkVBalBranch26(zzz1133, zzz1134, zzz1135, zzz1136, zzz1137, zzz1138, zzz1139, zzz1140, zzz1141, zzz1142, Zero, Zero, be) → new_mkVBalBranch3MkVBalBranch29(zzz1133, zzz1134, zzz1135, zzz1136, zzz1137, zzz1138, zzz1139, zzz1140, zzz1141, zzz1142, be)
new_mkVBalBranch3MkVBalBranch20(zzz929, zzz930, zzz931, zzz932, zzz933, zzz934, zzz935, zzz936, zzz937, zzz938, zzz939, Zero, Zero, ba) → new_mkVBalBranch3MkVBalBranch23(zzz929, zzz930, zzz931, zzz932, zzz933, zzz934, zzz935, zzz936, zzz937, zzz938, zzz939, ba)
new_mkVBalBranch3MkVBalBranch24(zzz340, zzz341, Neg(Succ(Zero)), zzz343, zzz344, zzz520, zzz521, zzz52200, zzz523, zzz524, zzz31, Succ(zzz690), h) → new_mkVBalBranch(zzz31, Branch(zzz520, zzz521, Neg(Succ(zzz52200)), zzz523, zzz524), zzz343, h)
new_mkVBalBranch3MkVBalBranch13(zzz340, zzz341, zzz34200, zzz343, zzz344, zzz520, zzz521, zzz523, zzz524, zzz31, Succ(zzz1290), h) → new_mkVBalBranch(zzz31, zzz524, Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), h)
new_mkVBalBranch3MkVBalBranch2(zzz340, zzz341, Pos(Succ(zzz34200)), zzz343, zzz344, zzz520, zzz521, zzz52200, zzz523, zzz524, zzz31, Succ(zzz680), h) → new_mkVBalBranch3MkVBalBranch20(zzz340, zzz341, zzz34200, zzz343, zzz344, zzz520, zzz521, zzz52200, zzz523, zzz524, zzz31, Succ(new_primPlusNat2(zzz680, zzz52200)), zzz34200, h)
new_mkVBalBranch(zzz31, Branch(zzz520, zzz521, Neg(Zero), zzz523, zzz524), Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), h) → new_mkVBalBranch3MkVBalBranch13(zzz340, zzz341, zzz34200, zzz343, zzz344, zzz520, zzz521, zzz523, zzz524, zzz31, new_primPlusNat2(new_primPlusNat3(Succ(new_primPlusNat3(new_primPlusNat1(zzz34200), zzz34200)), Succ(zzz34200)), Succ(zzz34200)), h)
new_mkVBalBranch(zzz31, Branch(zzz520, zzz521, Neg(Zero), zzz523, zzz524), Branch(zzz340, zzz341, Pos(Succ(zzz34200)), zzz343, zzz344), h) → new_mkVBalBranch(zzz31, Branch(zzz520, zzz521, Neg(Zero), zzz523, zzz524), zzz343, h)
new_mkVBalBranch3MkVBalBranch24(zzz340, zzz341, Neg(Zero), zzz343, zzz344, zzz520, zzz521, zzz52200, zzz523, zzz524, zzz31, Succ(zzz690), h) → new_mkVBalBranch(zzz31, Branch(zzz520, zzz521, Neg(Succ(zzz52200)), zzz523, zzz524), zzz343, h)
new_mkVBalBranch3MkVBalBranch212(zzz818, zzz819, zzz820, zzz821, zzz822, zzz823, zzz824, zzz825, zzz826, zzz827, bf) → new_mkVBalBranch3MkVBalBranch14(zzz818, zzz819, zzz820, zzz821, zzz822, zzz823, zzz824, zzz825, zzz826, zzz827, new_primPlusNat2(new_primPlusNat3(Succ(new_primPlusNat3(new_primPlusNat1(zzz820), zzz820)), Succ(zzz820)), Succ(zzz820)), bf)
new_mkVBalBranch3MkVBalBranch20(zzz929, zzz930, zzz931, zzz932, zzz933, zzz934, zzz935, zzz936, zzz937, zzz938, zzz939, Succ(zzz9400), Succ(zzz9410), ba) → new_mkVBalBranch3MkVBalBranch20(zzz929, zzz930, zzz931, zzz932, zzz933, zzz934, zzz935, zzz936, zzz937, zzz938, zzz939, zzz9400, zzz9410, ba)
new_mkVBalBranch3MkVBalBranch1(zzz340, zzz341, zzz34200, zzz343, zzz344, zzz520, zzz521, zzz52200, zzz523, zzz524, zzz31, Zero, h) → new_mkVBalBranch3MkVBalBranch17(zzz340, zzz341, zzz34200, zzz343, zzz344, zzz520, zzz521, zzz52200, zzz523, zzz524, zzz31, h)
new_mkVBalBranch3MkVBalBranch26(zzz1133, zzz1134, zzz1135, zzz1136, zzz1137, zzz1138, zzz1139, zzz1140, zzz1141, zzz1142, Succ(zzz11430), Zero, be) → new_mkVBalBranch3MkVBalBranch212(zzz1133, zzz1134, zzz1135, zzz1136, zzz1137, zzz1138, zzz1139, zzz1140, zzz1141, zzz1142, be)
new_mkVBalBranch3MkVBalBranch23(zzz929, zzz930, zzz931, zzz932, zzz933, zzz934, zzz935, zzz936, zzz937, zzz938, zzz939, ba) → new_mkVBalBranch3MkVBalBranch10(zzz929, zzz930, zzz931, zzz932, zzz933, zzz934, zzz935, zzz936, zzz937, zzz938, zzz939, new_primPlusNat2(new_primPlusNat3(Succ(new_primPlusNat3(new_primPlusNat1(zzz931), zzz931)), Succ(zzz931)), Succ(zzz931)), ba)
new_mkVBalBranch3MkVBalBranch211(zzz537, zzz538, zzz539, zzz540, zzz541, zzz542, zzz543, zzz544, zzz545, zzz546, zzz547, bc) → new_mkVBalBranch3MkVBalBranch15(zzz537, zzz538, zzz539, zzz540, zzz541, zzz542, zzz543, zzz544, zzz545, zzz546, zzz547, new_primPlusNat2(Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat3(new_primPlusNat1(zzz539), zzz539)), zzz539))), Succ(zzz539)), bc)
new_mkVBalBranch3MkVBalBranch16(zzz1702, zzz1703, zzz1704, zzz1705, zzz1706, zzz1707, zzz1708, zzz1709, zzz1710, zzz1711, zzz1712, Succ(zzz17130), Succ(zzz17140), bd) → new_mkVBalBranch3MkVBalBranch16(zzz1702, zzz1703, zzz1704, zzz1705, zzz1706, zzz1707, zzz1708, zzz1709, zzz1710, zzz1711, zzz1712, zzz17130, zzz17140, bd)
new_mkVBalBranch3MkVBalBranch25(zzz537, zzz538, zzz539, zzz540, zzz541, zzz542, zzz543, zzz544, zzz545, zzz546, zzz547, Zero, Succ(zzz5490), bc) → new_mkVBalBranch(zzz547, Branch(zzz542, zzz543, Neg(Succ(Succ(zzz544))), zzz545, zzz546), zzz540, bc)
new_mkVBalBranch3MkVBalBranch25(zzz537, zzz538, zzz539, zzz540, zzz541, zzz542, zzz543, zzz544, zzz545, zzz546, zzz547, Succ(zzz5480), Zero, bc) → new_mkVBalBranch3MkVBalBranch15(zzz537, zzz538, zzz539, zzz540, zzz541, zzz542, zzz543, zzz544, zzz545, zzz546, zzz547, new_primPlusNat2(Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat3(new_primPlusNat1(zzz539), zzz539)), zzz539))), Succ(zzz539)), bc)
new_mkVBalBranch3MkVBalBranch11(zzz2033, zzz2034, zzz2035, zzz2036, zzz2037, zzz2038, zzz2039, zzz2040, zzz2041, zzz2042, zzz2043, Succ(zzz20440), Succ(zzz20450), bb) → new_mkVBalBranch3MkVBalBranch11(zzz2033, zzz2034, zzz2035, zzz2036, zzz2037, zzz2038, zzz2039, zzz2040, zzz2041, zzz2042, zzz2043, zzz20440, zzz20450, bb)
new_mkVBalBranch3MkVBalBranch25(zzz537, zzz538, zzz539, zzz540, zzz541, zzz542, zzz543, zzz544, zzz545, zzz546, zzz547, Succ(zzz5480), Succ(zzz5490), bc) → new_mkVBalBranch3MkVBalBranch25(zzz537, zzz538, zzz539, zzz540, zzz541, zzz542, zzz543, zzz544, zzz545, zzz546, zzz547, zzz5480, zzz5490, bc)
new_mkVBalBranch3MkVBalBranch29(zzz818, zzz819, zzz820, zzz821, zzz822, zzz823, zzz824, zzz825, zzz826, zzz827, bf) → new_mkVBalBranch3MkVBalBranch14(zzz818, zzz819, zzz820, zzz821, zzz822, zzz823, zzz824, zzz825, zzz826, zzz827, new_primPlusNat2(new_primPlusNat3(Succ(new_primPlusNat3(new_primPlusNat1(zzz820), zzz820)), Succ(zzz820)), Succ(zzz820)), bf)
new_mkVBalBranch3MkVBalBranch10(zzz929, zzz930, zzz931, zzz932, zzz933, zzz934, zzz935, zzz936, zzz937, zzz938, zzz939, Succ(zzz10020), ba) → new_mkVBalBranch3MkVBalBranch11(zzz929, zzz930, zzz931, zzz932, zzz933, zzz934, zzz935, zzz936, zzz937, zzz938, zzz939, Succ(zzz10020), Succ(zzz936), ba)
new_mkVBalBranch(zzz31, Branch(zzz520, zzz521, Pos(Succ(zzz52200)), zzz523, zzz524), Branch(zzz340, zzz341, zzz342, zzz343, zzz344), h) → new_mkVBalBranch3MkVBalBranch2(zzz340, zzz341, zzz342, zzz343, zzz344, zzz520, zzz521, zzz52200, zzz523, zzz524, zzz31, Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat3(new_primPlusNat1(zzz52200), zzz52200)), zzz52200))), h)
new_mkVBalBranch3MkVBalBranch14(zzz818, zzz819, zzz820, zzz821, zzz822, zzz823, zzz824, zzz825, zzz826, zzz827, Succ(zzz8960), bf) → new_mkVBalBranch3MkVBalBranch16(zzz818, zzz819, zzz820, zzz821, zzz822, zzz823, zzz824, Zero, zzz825, zzz826, zzz827, Succ(Zero), Succ(zzz8960), bf)
new_mkVBalBranch3MkVBalBranch26(zzz1133, zzz1134, zzz1135, zzz1136, zzz1137, zzz1138, zzz1139, zzz1140, zzz1141, zzz1142, Zero, Succ(zzz11440), be) → new_mkVBalBranch(zzz1142, Branch(zzz1138, zzz1139, Neg(Succ(Zero)), zzz1140, zzz1141), zzz1136, be)
new_mkVBalBranch3MkVBalBranch24(zzz340, zzz341, Neg(Succ(Succ(Succ(zzz3420000)))), zzz343, zzz344, zzz520, zzz521, Succ(zzz522000), zzz523, zzz524, zzz31, Succ(Succ(zzz6900)), h) → new_mkVBalBranch3MkVBalBranch25(zzz340, zzz341, Succ(Succ(zzz3420000)), zzz343, zzz344, zzz520, zzz521, zzz522000, zzz523, zzz524, zzz31, Succ(zzz3420000), Succ(Succ(new_primPlusNat2(zzz6900, zzz522000))), h)
new_mkVBalBranch3MkVBalBranch24(zzz340, zzz341, Neg(Succ(Succ(Zero))), zzz343, zzz344, zzz520, zzz521, Succ(zzz522000), zzz523, zzz524, zzz31, Succ(Succ(zzz6900)), h) → new_mkVBalBranch3MkVBalBranch25(zzz340, zzz341, Succ(Zero), zzz343, zzz344, zzz520, zzz521, zzz522000, zzz523, zzz524, zzz31, Zero, Succ(Succ(new_primPlusNat2(zzz6900, zzz522000))), h)
new_mkVBalBranch3MkVBalBranch20(zzz929, zzz930, zzz931, zzz932, zzz933, zzz934, zzz935, zzz936, zzz937, zzz938, zzz939, Succ(zzz9400), Zero, ba) → new_mkVBalBranch3MkVBalBranch10(zzz929, zzz930, zzz931, zzz932, zzz933, zzz934, zzz935, zzz936, zzz937, zzz938, zzz939, new_primPlusNat2(new_primPlusNat3(Succ(new_primPlusNat3(new_primPlusNat1(zzz931), zzz931)), Succ(zzz931)), Succ(zzz931)), ba)
new_mkVBalBranch(zzz31, Branch(zzz520, zzz521, Pos(Zero), zzz523, zzz524), Branch(zzz340, zzz341, Pos(Succ(zzz34200)), zzz343, zzz344), h) → new_mkVBalBranch(zzz31, Branch(zzz520, zzz521, Pos(Zero), zzz523, zzz524), zzz343, h)
new_mkVBalBranch(zzz31, Branch(zzz520, zzz521, Pos(Zero), zzz523, zzz524), Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), h) → new_mkVBalBranch3MkVBalBranch12(zzz340, zzz341, zzz34200, zzz343, zzz344, zzz520, zzz521, zzz523, zzz524, zzz31, new_primPlusNat2(Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat3(new_primPlusNat1(zzz34200), zzz34200)), zzz34200))), Succ(zzz34200)), h)
new_mkVBalBranch3MkVBalBranch2(zzz340, zzz341, Pos(Zero), zzz343, zzz344, zzz520, zzz521, zzz52200, zzz523, zzz524, zzz31, Succ(zzz680), h) → new_mkVBalBranch(zzz31, zzz524, Branch(zzz340, zzz341, Pos(Zero), zzz343, zzz344), h)
new_mkVBalBranch3MkVBalBranch2(zzz340, zzz341, Neg(Zero), zzz343, zzz344, zzz520, zzz521, zzz52200, zzz523, zzz524, zzz31, Succ(zzz680), h) → new_mkVBalBranch(zzz31, zzz524, Branch(zzz340, zzz341, Neg(Zero), zzz343, zzz344), h)
new_mkVBalBranch3MkVBalBranch2(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344, zzz520, zzz521, zzz52200, zzz523, zzz524, zzz31, Succ(zzz680), h) → new_mkVBalBranch3MkVBalBranch1(zzz340, zzz341, zzz34200, zzz343, zzz344, zzz520, zzz521, zzz52200, zzz523, zzz524, zzz31, new_primPlusNat2(Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat3(new_primPlusNat1(zzz34200), zzz34200)), zzz34200))), Succ(zzz34200)), h)
new_mkVBalBranch3MkVBalBranch16(zzz1702, zzz1703, zzz1704, zzz1705, zzz1706, zzz1707, zzz1708, zzz1709, zzz1710, zzz1711, zzz1712, Zero, Succ(zzz17140), bd) → new_mkVBalBranch(zzz1712, zzz1711, Branch(zzz1702, zzz1703, Neg(Succ(zzz1704)), zzz1705, zzz1706), bd)
new_mkVBalBranch3MkVBalBranch10(zzz929, zzz930, zzz931, zzz932, zzz933, zzz934, zzz935, zzz936, zzz937, zzz938, zzz939, Zero, ba) → new_mkVBalBranch3MkVBalBranch11(zzz929, zzz930, zzz931, zzz932, zzz933, zzz934, zzz935, zzz936, zzz937, zzz938, zzz939, Zero, Succ(zzz936), ba)
new_mkVBalBranch3MkVBalBranch24(zzz340, zzz341, Neg(Succ(Succ(Succ(zzz3420000)))), zzz343, zzz344, zzz520, zzz521, Zero, zzz523, zzz524, zzz31, Succ(Succ(zzz6900)), h) → new_mkVBalBranch3MkVBalBranch26(zzz340, zzz341, Succ(Succ(zzz3420000)), zzz343, zzz344, zzz520, zzz521, zzz523, zzz524, zzz31, Succ(zzz3420000), Succ(zzz6900), h)
new_mkVBalBranch3MkVBalBranch15(zzz537, zzz538, zzz539, zzz540, zzz541, zzz542, zzz543, zzz544, zzz545, zzz546, zzz547, Succ(zzz6990), bc) → new_mkVBalBranch3MkVBalBranch16(zzz537, zzz538, zzz539, zzz540, zzz541, zzz542, zzz543, Succ(zzz544), zzz545, zzz546, zzz547, Succ(Succ(zzz544)), Succ(zzz6990), bc)
new_mkVBalBranch3MkVBalBranch25(zzz537, zzz538, zzz539, zzz540, zzz541, zzz542, zzz543, zzz544, zzz545, zzz546, zzz547, Zero, Zero, bc) → new_mkVBalBranch3MkVBalBranch211(zzz537, zzz538, zzz539, zzz540, zzz541, zzz542, zzz543, zzz544, zzz545, zzz546, zzz547, bc)

The TRS R consists of the following rules:

new_primPlusNat1(Zero) → Zero
new_primPlusNat1(Succ(zzz62000)) → Succ(Succ(new_primPlusNat1(zzz62000)))
new_primPlusNat3(zzz90, Succ(zzz910)) → Succ(Succ(new_primPlusNat2(zzz90, zzz910)))
new_primPlusNat3(zzz90, Zero) → Succ(zzz90)
new_primPlusNat2(Succ(zzz900), Succ(zzz9100)) → Succ(Succ(new_primPlusNat2(zzz900, zzz9100)))
new_primPlusNat2(Zero, Succ(zzz9100)) → Succ(zzz9100)
new_primPlusNat2(Zero, Zero) → Zero
new_primPlusNat2(Succ(zzz900), Zero) → Succ(zzz900)

The set Q consists of the following terms:

new_primPlusNat2(Zero, Succ(x0))
new_primMulNat0(x0)
new_primPlusNat3(x0, Succ(x1))
new_primPlusNat2(Succ(x0), Succ(x1))
new_primPlusNat3(x0, Zero)
new_primPlusNat1(Zero)
new_primPlusNat2(Zero, Zero)
new_primPlusNat1(Succ(x0))
new_primPlusNat2(Succ(x0), Zero)

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

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

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

new_mkVBalBranch(zzz31, Branch(zzz520, zzz521, Neg(Succ(zzz52200)), zzz523, zzz524), Branch(zzz340, zzz341, zzz342, zzz343, zzz344), h) → new_mkVBalBranch3MkVBalBranch24(zzz340, zzz341, zzz342, zzz343, zzz344, zzz520, zzz521, zzz52200, zzz523, zzz524, zzz31, Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat3(new_primPlusNat1(zzz52200), zzz52200)), zzz52200))), h)
new_mkVBalBranch3MkVBalBranch11(zzz2033, zzz2034, zzz2035, zzz2036, zzz2037, zzz2038, zzz2039, zzz2040, zzz2041, zzz2042, zzz2043, Zero, Succ(zzz20450), bb) → new_mkVBalBranch(zzz2043, zzz2042, Branch(zzz2033, zzz2034, Pos(Succ(zzz2035)), zzz2036, zzz2037), bb)
new_mkVBalBranch3MkVBalBranch26(zzz1133, zzz1134, zzz1135, zzz1136, zzz1137, zzz1138, zzz1139, zzz1140, zzz1141, zzz1142, Succ(zzz11430), Succ(zzz11440), be) → new_mkVBalBranch3MkVBalBranch26(zzz1133, zzz1134, zzz1135, zzz1136, zzz1137, zzz1138, zzz1139, zzz1140, zzz1141, zzz1142, zzz11430, zzz11440, be)
new_mkVBalBranch3MkVBalBranch24(zzz340, zzz341, Pos(zzz3420), zzz343, zzz344, zzz520, zzz521, zzz52200, zzz523, zzz524, zzz31, Succ(zzz690), h) → new_mkVBalBranch(zzz31, Branch(zzz520, zzz521, Neg(Succ(zzz52200)), zzz523, zzz524), zzz343, h)
new_mkVBalBranch3MkVBalBranch12(zzz340, zzz341, zzz34200, zzz343, zzz344, zzz520, zzz521, zzz523, zzz524, zzz31, Succ(zzz1250), h) → new_mkVBalBranch(zzz31, zzz524, Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), h)
new_mkVBalBranch3MkVBalBranch20(zzz929, zzz930, zzz931, zzz932, zzz933, zzz934, zzz935, zzz936, zzz937, zzz938, zzz939, Zero, Succ(zzz9410), ba) → new_mkVBalBranch(zzz939, Branch(zzz934, zzz935, Pos(Succ(zzz936)), zzz937, zzz938), zzz932, ba)
new_mkVBalBranch3MkVBalBranch24(zzz340, zzz341, Neg(Succ(Succ(Zero))), zzz343, zzz344, zzz520, zzz521, Zero, zzz523, zzz524, zzz31, Succ(Succ(zzz6900)), h) → new_mkVBalBranch3MkVBalBranch26(zzz340, zzz341, Succ(Zero), zzz343, zzz344, zzz520, zzz521, zzz523, zzz524, zzz31, Zero, Succ(zzz6900), h)
new_mkVBalBranch3MkVBalBranch17(zzz340, zzz341, zzz34200, zzz343, zzz344, zzz520, zzz521, zzz52200, zzz523, zzz524, zzz31, h) → new_mkVBalBranch(zzz31, zzz524, Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), h)
new_mkVBalBranch3MkVBalBranch26(zzz1133, zzz1134, zzz1135, zzz1136, zzz1137, zzz1138, zzz1139, zzz1140, zzz1141, zzz1142, Zero, Zero, be) → new_mkVBalBranch3MkVBalBranch29(zzz1133, zzz1134, zzz1135, zzz1136, zzz1137, zzz1138, zzz1139, zzz1140, zzz1141, zzz1142, be)
new_mkVBalBranch3MkVBalBranch1(zzz340, zzz341, zzz34200, zzz343, zzz344, zzz520, zzz521, zzz52200, zzz523, zzz524, zzz31, Succ(zzz1430), h) → new_mkVBalBranch(zzz31, zzz524, Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), h)
new_mkVBalBranch3MkVBalBranch24(zzz340, zzz341, Neg(Succ(Zero)), zzz343, zzz344, zzz520, zzz521, zzz52200, zzz523, zzz524, zzz31, Succ(zzz690), h) → new_mkVBalBranch(zzz31, Branch(zzz520, zzz521, Neg(Succ(zzz52200)), zzz523, zzz524), zzz343, h)
new_mkVBalBranch3MkVBalBranch20(zzz929, zzz930, zzz931, zzz932, zzz933, zzz934, zzz935, zzz936, zzz937, zzz938, zzz939, Zero, Zero, ba) → new_mkVBalBranch3MkVBalBranch23(zzz929, zzz930, zzz931, zzz932, zzz933, zzz934, zzz935, zzz936, zzz937, zzz938, zzz939, ba)
new_mkVBalBranch3MkVBalBranch13(zzz340, zzz341, zzz34200, zzz343, zzz344, zzz520, zzz521, zzz523, zzz524, zzz31, Succ(zzz1290), h) → new_mkVBalBranch(zzz31, zzz524, Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), h)
new_mkVBalBranch3MkVBalBranch2(zzz340, zzz341, Pos(Succ(zzz34200)), zzz343, zzz344, zzz520, zzz521, zzz52200, zzz523, zzz524, zzz31, Succ(zzz680), h) → new_mkVBalBranch3MkVBalBranch20(zzz340, zzz341, zzz34200, zzz343, zzz344, zzz520, zzz521, zzz52200, zzz523, zzz524, zzz31, Succ(new_primPlusNat2(zzz680, zzz52200)), zzz34200, h)
new_mkVBalBranch(zzz31, Branch(zzz520, zzz521, Neg(Zero), zzz523, zzz524), Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), h) → new_mkVBalBranch3MkVBalBranch13(zzz340, zzz341, zzz34200, zzz343, zzz344, zzz520, zzz521, zzz523, zzz524, zzz31, new_primPlusNat2(new_primPlusNat3(Succ(new_primPlusNat3(new_primPlusNat1(zzz34200), zzz34200)), Succ(zzz34200)), Succ(zzz34200)), h)
new_mkVBalBranch(zzz31, Branch(zzz520, zzz521, Neg(Zero), zzz523, zzz524), Branch(zzz340, zzz341, Pos(Succ(zzz34200)), zzz343, zzz344), h) → new_mkVBalBranch(zzz31, Branch(zzz520, zzz521, Neg(Zero), zzz523, zzz524), zzz343, h)
new_mkVBalBranch3MkVBalBranch24(zzz340, zzz341, Neg(Zero), zzz343, zzz344, zzz520, zzz521, zzz52200, zzz523, zzz524, zzz31, Succ(zzz690), h) → new_mkVBalBranch(zzz31, Branch(zzz520, zzz521, Neg(Succ(zzz52200)), zzz523, zzz524), zzz343, h)
new_mkVBalBranch3MkVBalBranch212(zzz818, zzz819, zzz820, zzz821, zzz822, zzz823, zzz824, zzz825, zzz826, zzz827, bf) → new_mkVBalBranch3MkVBalBranch14(zzz818, zzz819, zzz820, zzz821, zzz822, zzz823, zzz824, zzz825, zzz826, zzz827, new_primPlusNat2(new_primPlusNat3(Succ(new_primPlusNat3(new_primPlusNat1(zzz820), zzz820)), Succ(zzz820)), Succ(zzz820)), bf)
new_mkVBalBranch3MkVBalBranch20(zzz929, zzz930, zzz931, zzz932, zzz933, zzz934, zzz935, zzz936, zzz937, zzz938, zzz939, Succ(zzz9400), Succ(zzz9410), ba) → new_mkVBalBranch3MkVBalBranch20(zzz929, zzz930, zzz931, zzz932, zzz933, zzz934, zzz935, zzz936, zzz937, zzz938, zzz939, zzz9400, zzz9410, ba)
new_mkVBalBranch3MkVBalBranch1(zzz340, zzz341, zzz34200, zzz343, zzz344, zzz520, zzz521, zzz52200, zzz523, zzz524, zzz31, Zero, h) → new_mkVBalBranch3MkVBalBranch17(zzz340, zzz341, zzz34200, zzz343, zzz344, zzz520, zzz521, zzz52200, zzz523, zzz524, zzz31, h)
new_mkVBalBranch3MkVBalBranch26(zzz1133, zzz1134, zzz1135, zzz1136, zzz1137, zzz1138, zzz1139, zzz1140, zzz1141, zzz1142, Succ(zzz11430), Zero, be) → new_mkVBalBranch3MkVBalBranch212(zzz1133, zzz1134, zzz1135, zzz1136, zzz1137, zzz1138, zzz1139, zzz1140, zzz1141, zzz1142, be)
new_mkVBalBranch3MkVBalBranch23(zzz929, zzz930, zzz931, zzz932, zzz933, zzz934, zzz935, zzz936, zzz937, zzz938, zzz939, ba) → new_mkVBalBranch3MkVBalBranch10(zzz929, zzz930, zzz931, zzz932, zzz933, zzz934, zzz935, zzz936, zzz937, zzz938, zzz939, new_primPlusNat2(new_primPlusNat3(Succ(new_primPlusNat3(new_primPlusNat1(zzz931), zzz931)), Succ(zzz931)), Succ(zzz931)), ba)
new_mkVBalBranch3MkVBalBranch211(zzz537, zzz538, zzz539, zzz540, zzz541, zzz542, zzz543, zzz544, zzz545, zzz546, zzz547, bc) → new_mkVBalBranch3MkVBalBranch15(zzz537, zzz538, zzz539, zzz540, zzz541, zzz542, zzz543, zzz544, zzz545, zzz546, zzz547, new_primPlusNat2(Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat3(new_primPlusNat1(zzz539), zzz539)), zzz539))), Succ(zzz539)), bc)
new_mkVBalBranch3MkVBalBranch16(zzz1702, zzz1703, zzz1704, zzz1705, zzz1706, zzz1707, zzz1708, zzz1709, zzz1710, zzz1711, zzz1712, Succ(zzz17130), Succ(zzz17140), bd) → new_mkVBalBranch3MkVBalBranch16(zzz1702, zzz1703, zzz1704, zzz1705, zzz1706, zzz1707, zzz1708, zzz1709, zzz1710, zzz1711, zzz1712, zzz17130, zzz17140, bd)
new_mkVBalBranch3MkVBalBranch25(zzz537, zzz538, zzz539, zzz540, zzz541, zzz542, zzz543, zzz544, zzz545, zzz546, zzz547, Zero, Succ(zzz5490), bc) → new_mkVBalBranch(zzz547, Branch(zzz542, zzz543, Neg(Succ(Succ(zzz544))), zzz545, zzz546), zzz540, bc)
new_mkVBalBranch3MkVBalBranch11(zzz2033, zzz2034, zzz2035, zzz2036, zzz2037, zzz2038, zzz2039, zzz2040, zzz2041, zzz2042, zzz2043, Succ(zzz20440), Succ(zzz20450), bb) → new_mkVBalBranch3MkVBalBranch11(zzz2033, zzz2034, zzz2035, zzz2036, zzz2037, zzz2038, zzz2039, zzz2040, zzz2041, zzz2042, zzz2043, zzz20440, zzz20450, bb)
new_mkVBalBranch3MkVBalBranch25(zzz537, zzz538, zzz539, zzz540, zzz541, zzz542, zzz543, zzz544, zzz545, zzz546, zzz547, Succ(zzz5480), Zero, bc) → new_mkVBalBranch3MkVBalBranch15(zzz537, zzz538, zzz539, zzz540, zzz541, zzz542, zzz543, zzz544, zzz545, zzz546, zzz547, new_primPlusNat2(Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat3(new_primPlusNat1(zzz539), zzz539)), zzz539))), Succ(zzz539)), bc)
new_mkVBalBranch3MkVBalBranch25(zzz537, zzz538, zzz539, zzz540, zzz541, zzz542, zzz543, zzz544, zzz545, zzz546, zzz547, Succ(zzz5480), Succ(zzz5490), bc) → new_mkVBalBranch3MkVBalBranch25(zzz537, zzz538, zzz539, zzz540, zzz541, zzz542, zzz543, zzz544, zzz545, zzz546, zzz547, zzz5480, zzz5490, bc)
new_mkVBalBranch3MkVBalBranch29(zzz818, zzz819, zzz820, zzz821, zzz822, zzz823, zzz824, zzz825, zzz826, zzz827, bf) → new_mkVBalBranch3MkVBalBranch14(zzz818, zzz819, zzz820, zzz821, zzz822, zzz823, zzz824, zzz825, zzz826, zzz827, new_primPlusNat2(new_primPlusNat3(Succ(new_primPlusNat3(new_primPlusNat1(zzz820), zzz820)), Succ(zzz820)), Succ(zzz820)), bf)
new_mkVBalBranch(zzz31, Branch(zzz520, zzz521, Pos(Succ(zzz52200)), zzz523, zzz524), Branch(zzz340, zzz341, zzz342, zzz343, zzz344), h) → new_mkVBalBranch3MkVBalBranch2(zzz340, zzz341, zzz342, zzz343, zzz344, zzz520, zzz521, zzz52200, zzz523, zzz524, zzz31, Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat3(new_primPlusNat1(zzz52200), zzz52200)), zzz52200))), h)
new_mkVBalBranch3MkVBalBranch10(zzz929, zzz930, zzz931, zzz932, zzz933, zzz934, zzz935, zzz936, zzz937, zzz938, zzz939, Succ(zzz10020), ba) → new_mkVBalBranch3MkVBalBranch11(zzz929, zzz930, zzz931, zzz932, zzz933, zzz934, zzz935, zzz936, zzz937, zzz938, zzz939, Succ(zzz10020), Succ(zzz936), ba)
new_mkVBalBranch3MkVBalBranch14(zzz818, zzz819, zzz820, zzz821, zzz822, zzz823, zzz824, zzz825, zzz826, zzz827, Succ(zzz8960), bf) → new_mkVBalBranch3MkVBalBranch16(zzz818, zzz819, zzz820, zzz821, zzz822, zzz823, zzz824, Zero, zzz825, zzz826, zzz827, Succ(Zero), Succ(zzz8960), bf)
new_mkVBalBranch3MkVBalBranch24(zzz340, zzz341, Neg(Succ(Succ(Succ(zzz3420000)))), zzz343, zzz344, zzz520, zzz521, Succ(zzz522000), zzz523, zzz524, zzz31, Succ(Succ(zzz6900)), h) → new_mkVBalBranch3MkVBalBranch25(zzz340, zzz341, Succ(Succ(zzz3420000)), zzz343, zzz344, zzz520, zzz521, zzz522000, zzz523, zzz524, zzz31, Succ(zzz3420000), Succ(Succ(new_primPlusNat2(zzz6900, zzz522000))), h)
new_mkVBalBranch3MkVBalBranch26(zzz1133, zzz1134, zzz1135, zzz1136, zzz1137, zzz1138, zzz1139, zzz1140, zzz1141, zzz1142, Zero, Succ(zzz11440), be) → new_mkVBalBranch(zzz1142, Branch(zzz1138, zzz1139, Neg(Succ(Zero)), zzz1140, zzz1141), zzz1136, be)
new_mkVBalBranch3MkVBalBranch24(zzz340, zzz341, Neg(Succ(Succ(Zero))), zzz343, zzz344, zzz520, zzz521, Succ(zzz522000), zzz523, zzz524, zzz31, Succ(Succ(zzz6900)), h) → new_mkVBalBranch3MkVBalBranch25(zzz340, zzz341, Succ(Zero), zzz343, zzz344, zzz520, zzz521, zzz522000, zzz523, zzz524, zzz31, Zero, Succ(Succ(new_primPlusNat2(zzz6900, zzz522000))), h)
new_mkVBalBranch(zzz31, Branch(zzz520, zzz521, Pos(Zero), zzz523, zzz524), Branch(zzz340, zzz341, Pos(Succ(zzz34200)), zzz343, zzz344), h) → new_mkVBalBranch(zzz31, Branch(zzz520, zzz521, Pos(Zero), zzz523, zzz524), zzz343, h)
new_mkVBalBranch3MkVBalBranch20(zzz929, zzz930, zzz931, zzz932, zzz933, zzz934, zzz935, zzz936, zzz937, zzz938, zzz939, Succ(zzz9400), Zero, ba) → new_mkVBalBranch3MkVBalBranch10(zzz929, zzz930, zzz931, zzz932, zzz933, zzz934, zzz935, zzz936, zzz937, zzz938, zzz939, new_primPlusNat2(new_primPlusNat3(Succ(new_primPlusNat3(new_primPlusNat1(zzz931), zzz931)), Succ(zzz931)), Succ(zzz931)), ba)
new_mkVBalBranch(zzz31, Branch(zzz520, zzz521, Pos(Zero), zzz523, zzz524), Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), h) → new_mkVBalBranch3MkVBalBranch12(zzz340, zzz341, zzz34200, zzz343, zzz344, zzz520, zzz521, zzz523, zzz524, zzz31, new_primPlusNat2(Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat3(new_primPlusNat1(zzz34200), zzz34200)), zzz34200))), Succ(zzz34200)), h)
new_mkVBalBranch3MkVBalBranch2(zzz340, zzz341, Pos(Zero), zzz343, zzz344, zzz520, zzz521, zzz52200, zzz523, zzz524, zzz31, Succ(zzz680), h) → new_mkVBalBranch(zzz31, zzz524, Branch(zzz340, zzz341, Pos(Zero), zzz343, zzz344), h)
new_mkVBalBranch3MkVBalBranch2(zzz340, zzz341, Neg(Zero), zzz343, zzz344, zzz520, zzz521, zzz52200, zzz523, zzz524, zzz31, Succ(zzz680), h) → new_mkVBalBranch(zzz31, zzz524, Branch(zzz340, zzz341, Neg(Zero), zzz343, zzz344), h)
new_mkVBalBranch3MkVBalBranch2(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344, zzz520, zzz521, zzz52200, zzz523, zzz524, zzz31, Succ(zzz680), h) → new_mkVBalBranch3MkVBalBranch1(zzz340, zzz341, zzz34200, zzz343, zzz344, zzz520, zzz521, zzz52200, zzz523, zzz524, zzz31, new_primPlusNat2(Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat3(new_primPlusNat1(zzz34200), zzz34200)), zzz34200))), Succ(zzz34200)), h)
new_mkVBalBranch3MkVBalBranch16(zzz1702, zzz1703, zzz1704, zzz1705, zzz1706, zzz1707, zzz1708, zzz1709, zzz1710, zzz1711, zzz1712, Zero, Succ(zzz17140), bd) → new_mkVBalBranch(zzz1712, zzz1711, Branch(zzz1702, zzz1703, Neg(Succ(zzz1704)), zzz1705, zzz1706), bd)
new_mkVBalBranch3MkVBalBranch15(zzz537, zzz538, zzz539, zzz540, zzz541, zzz542, zzz543, zzz544, zzz545, zzz546, zzz547, Succ(zzz6990), bc) → new_mkVBalBranch3MkVBalBranch16(zzz537, zzz538, zzz539, zzz540, zzz541, zzz542, zzz543, Succ(zzz544), zzz545, zzz546, zzz547, Succ(Succ(zzz544)), Succ(zzz6990), bc)
new_mkVBalBranch3MkVBalBranch24(zzz340, zzz341, Neg(Succ(Succ(Succ(zzz3420000)))), zzz343, zzz344, zzz520, zzz521, Zero, zzz523, zzz524, zzz31, Succ(Succ(zzz6900)), h) → new_mkVBalBranch3MkVBalBranch26(zzz340, zzz341, Succ(Succ(zzz3420000)), zzz343, zzz344, zzz520, zzz521, zzz523, zzz524, zzz31, Succ(zzz3420000), Succ(zzz6900), h)
new_mkVBalBranch3MkVBalBranch10(zzz929, zzz930, zzz931, zzz932, zzz933, zzz934, zzz935, zzz936, zzz937, zzz938, zzz939, Zero, ba) → new_mkVBalBranch3MkVBalBranch11(zzz929, zzz930, zzz931, zzz932, zzz933, zzz934, zzz935, zzz936, zzz937, zzz938, zzz939, Zero, Succ(zzz936), ba)
new_mkVBalBranch3MkVBalBranch25(zzz537, zzz538, zzz539, zzz540, zzz541, zzz542, zzz543, zzz544, zzz545, zzz546, zzz547, Zero, Zero, bc) → new_mkVBalBranch3MkVBalBranch211(zzz537, zzz538, zzz539, zzz540, zzz541, zzz542, zzz543, zzz544, zzz545, zzz546, zzz547, bc)

The TRS R consists of the following rules:

new_primPlusNat1(Zero) → Zero
new_primPlusNat1(Succ(zzz62000)) → Succ(Succ(new_primPlusNat1(zzz62000)))
new_primPlusNat3(zzz90, Succ(zzz910)) → Succ(Succ(new_primPlusNat2(zzz90, zzz910)))
new_primPlusNat3(zzz90, Zero) → Succ(zzz90)
new_primPlusNat2(Succ(zzz900), Succ(zzz9100)) → Succ(Succ(new_primPlusNat2(zzz900, zzz9100)))
new_primPlusNat2(Zero, Succ(zzz9100)) → Succ(zzz9100)
new_primPlusNat2(Zero, Zero) → Zero
new_primPlusNat2(Succ(zzz900), Zero) → Succ(zzz900)

The set Q consists of the following terms:

new_primPlusNat2(Zero, Succ(x0))
new_primPlusNat3(x0, Succ(x1))
new_primPlusNat2(Succ(x0), Succ(x1))
new_primPlusNat3(x0, Zero)
new_primPlusNat1(Zero)
new_primPlusNat2(Zero, Zero)
new_primPlusNat1(Succ(x0))
new_primPlusNat2(Succ(x0), Zero)

We have to consider all minimal (P,Q,R)-chains.
By rewriting [15] the rule new_mkVBalBranch(zzz31, Branch(zzz520, zzz521, Neg(Zero), zzz523, zzz524), Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), h) → new_mkVBalBranch3MkVBalBranch13(zzz340, zzz341, zzz34200, zzz343, zzz344, zzz520, zzz521, zzz523, zzz524, zzz31, new_primPlusNat2(new_primPlusNat3(Succ(new_primPlusNat3(new_primPlusNat1(zzz34200), zzz34200)), Succ(zzz34200)), Succ(zzz34200)), h) at position [10,0] we obtained the following new rules:

new_mkVBalBranch(zzz31, Branch(zzz520, zzz521, Neg(Zero), zzz523, zzz524), Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), h) → new_mkVBalBranch3MkVBalBranch13(zzz340, zzz341, zzz34200, zzz343, zzz344, zzz520, zzz521, zzz523, zzz524, zzz31, new_primPlusNat2(Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat3(new_primPlusNat1(zzz34200), zzz34200)), 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
                                    ↳ DependencyGraphProof
                                      ↳ QDP
                                        ↳ Rewriting
                                          ↳ QDP
                                            ↳ Rewriting
                                              ↳ QDP
                                                ↳ Rewriting
                                                  ↳ QDP
                                                    ↳ Rewriting
                                                      ↳ QDP
                                                        ↳ Rewriting
                                                          ↳ QDP
                                                            ↳ Rewriting
                                                              ↳ QDP
                                                                ↳ Rewriting
                                                                  ↳ QDP
                                                                    ↳ Rewriting
                                                                      ↳ QDP
                                                                        ↳ Rewriting
                                                                          ↳ QDP
                                                                            ↳ Rewriting
                                                                              ↳ QDP
                                                                                ↳ Rewriting
                                                                                  ↳ QDP
                                                                                    ↳ Rewriting
                                                                                      ↳ QDP
                                                                                        ↳ Rewriting
                                                                                          ↳ QDP
                                                                                            ↳ UsableRulesProof
                                                                                              ↳ QDP
                                                                                                ↳ QReductionProof
                                                                                                  ↳ QDP
                                                                                                    ↳ Rewriting
                                                                                                      ↳ QDP
                                                                                                        ↳ Rewriting
                                                                                                          ↳ QDP
                                                                                                            ↳ Rewriting
                                                                                                              ↳ QDP
                                                                                                                ↳ Rewriting
                                                                                                                  ↳ QDP
                                                                                                                    ↳ Rewriting
                                                                                                                      ↳ QDP
                                                                                                                        ↳ Rewriting
                                                                                                                          ↳ QDP
                                                                                                                            ↳ DependencyGraphProof
                                                                                                                              ↳ QDP
                                                                                                                                ↳ Rewriting
                                                                                                                                  ↳ QDP
                                                                                                                                    ↳ Rewriting
                                                                                                                                      ↳ QDP
                                                                                                                                        ↳ DependencyGraphProof
                                                                                                                                          ↳ QDP
                                                                                                                                            ↳ Rewriting
                                                                                                                                              ↳ QDP
                                                                                                                                                ↳ Rewriting
                                                                                                                                                  ↳ QDP
                                                                                                                                                    ↳ Rewriting
                                                                                                                                                      ↳ QDP
                                                                                                                                                        ↳ Rewriting
                                                                                                                                                          ↳ QDP
                                                                                                                                                            ↳ Rewriting
                                                                                                                                                              ↳ QDP
                                                                                                                                                                ↳ Rewriting
                                                                                                                                                                  ↳ QDP
                                                                                                                                                                    ↳ Rewriting
                                                                                                                                                                      ↳ QDP
                                                                                                                                                                        ↳ UsableRulesProof
                                                                                                                                                                          ↳ QDP
                                                                                                                                                                            ↳ QReductionProof
                                                                                                                                                                              ↳ QDP
                                                                                                                                                                                ↳ Rewriting
                                                                                                                                                                                  ↳ QDP
                                                                                                                                                                                    ↳ Rewriting
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP

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

new_mkVBalBranch3MkVBalBranch11(zzz2033, zzz2034, zzz2035, zzz2036, zzz2037, zzz2038, zzz2039, zzz2040, zzz2041, zzz2042, zzz2043, Zero, Succ(zzz20450), bb) → new_mkVBalBranch(zzz2043, zzz2042, Branch(zzz2033, zzz2034, Pos(Succ(zzz2035)), zzz2036, zzz2037), bb)
new_mkVBalBranch(zzz31, Branch(zzz520, zzz521, Neg(Succ(zzz52200)), zzz523, zzz524), Branch(zzz340, zzz341, zzz342, zzz343, zzz344), h) → new_mkVBalBranch3MkVBalBranch24(zzz340, zzz341, zzz342, zzz343, zzz344, zzz520, zzz521, zzz52200, zzz523, zzz524, zzz31, Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat3(new_primPlusNat1(zzz52200), zzz52200)), zzz52200))), h)
new_mkVBalBranch3MkVBalBranch26(zzz1133, zzz1134, zzz1135, zzz1136, zzz1137, zzz1138, zzz1139, zzz1140, zzz1141, zzz1142, Succ(zzz11430), Succ(zzz11440), be) → new_mkVBalBranch3MkVBalBranch26(zzz1133, zzz1134, zzz1135, zzz1136, zzz1137, zzz1138, zzz1139, zzz1140, zzz1141, zzz1142, zzz11430, zzz11440, be)
new_mkVBalBranch3MkVBalBranch24(zzz340, zzz341, Pos(zzz3420), zzz343, zzz344, zzz520, zzz521, zzz52200, zzz523, zzz524, zzz31, Succ(zzz690), h) → new_mkVBalBranch(zzz31, Branch(zzz520, zzz521, Neg(Succ(zzz52200)), zzz523, zzz524), zzz343, h)
new_mkVBalBranch3MkVBalBranch12(zzz340, zzz341, zzz34200, zzz343, zzz344, zzz520, zzz521, zzz523, zzz524, zzz31, Succ(zzz1250), h) → new_mkVBalBranch(zzz31, zzz524, Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), h)
new_mkVBalBranch3MkVBalBranch20(zzz929, zzz930, zzz931, zzz932, zzz933, zzz934, zzz935, zzz936, zzz937, zzz938, zzz939, Zero, Succ(zzz9410), ba) → new_mkVBalBranch(zzz939, Branch(zzz934, zzz935, Pos(Succ(zzz936)), zzz937, zzz938), zzz932, ba)
new_mkVBalBranch3MkVBalBranch24(zzz340, zzz341, Neg(Succ(Succ(Zero))), zzz343, zzz344, zzz520, zzz521, Zero, zzz523, zzz524, zzz31, Succ(Succ(zzz6900)), h) → new_mkVBalBranch3MkVBalBranch26(zzz340, zzz341, Succ(Zero), zzz343, zzz344, zzz520, zzz521, zzz523, zzz524, zzz31, Zero, Succ(zzz6900), h)
new_mkVBalBranch3MkVBalBranch17(zzz340, zzz341, zzz34200, zzz343, zzz344, zzz520, zzz521, zzz52200, zzz523, zzz524, zzz31, h) → new_mkVBalBranch(zzz31, zzz524, Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), h)
new_mkVBalBranch3MkVBalBranch1(zzz340, zzz341, zzz34200, zzz343, zzz344, zzz520, zzz521, zzz52200, zzz523, zzz524, zzz31, Succ(zzz1430), h) → new_mkVBalBranch(zzz31, zzz524, Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), h)
new_mkVBalBranch3MkVBalBranch26(zzz1133, zzz1134, zzz1135, zzz1136, zzz1137, zzz1138, zzz1139, zzz1140, zzz1141, zzz1142, Zero, Zero, be) → new_mkVBalBranch3MkVBalBranch29(zzz1133, zzz1134, zzz1135, zzz1136, zzz1137, zzz1138, zzz1139, zzz1140, zzz1141, zzz1142, be)
new_mkVBalBranch3MkVBalBranch20(zzz929, zzz930, zzz931, zzz932, zzz933, zzz934, zzz935, zzz936, zzz937, zzz938, zzz939, Zero, Zero, ba) → new_mkVBalBranch3MkVBalBranch23(zzz929, zzz930, zzz931, zzz932, zzz933, zzz934, zzz935, zzz936, zzz937, zzz938, zzz939, ba)
new_mkVBalBranch3MkVBalBranch24(zzz340, zzz341, Neg(Succ(Zero)), zzz343, zzz344, zzz520, zzz521, zzz52200, zzz523, zzz524, zzz31, Succ(zzz690), h) → new_mkVBalBranch(zzz31, Branch(zzz520, zzz521, Neg(Succ(zzz52200)), zzz523, zzz524), zzz343, h)
new_mkVBalBranch3MkVBalBranch13(zzz340, zzz341, zzz34200, zzz343, zzz344, zzz520, zzz521, zzz523, zzz524, zzz31, Succ(zzz1290), h) → new_mkVBalBranch(zzz31, zzz524, Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), h)
new_mkVBalBranch3MkVBalBranch2(zzz340, zzz341, Pos(Succ(zzz34200)), zzz343, zzz344, zzz520, zzz521, zzz52200, zzz523, zzz524, zzz31, Succ(zzz680), h) → new_mkVBalBranch3MkVBalBranch20(zzz340, zzz341, zzz34200, zzz343, zzz344, zzz520, zzz521, zzz52200, zzz523, zzz524, zzz31, Succ(new_primPlusNat2(zzz680, zzz52200)), zzz34200, h)
new_mkVBalBranch(zzz31, Branch(zzz520, zzz521, Neg(Zero), zzz523, zzz524), Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), h) → new_mkVBalBranch3MkVBalBranch13(zzz340, zzz341, zzz34200, zzz343, zzz344, zzz520, zzz521, zzz523, zzz524, zzz31, new_primPlusNat2(Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat3(new_primPlusNat1(zzz34200), zzz34200)), zzz34200))), Succ(zzz34200)), h)
new_mkVBalBranch3MkVBalBranch24(zzz340, zzz341, Neg(Zero), zzz343, zzz344, zzz520, zzz521, zzz52200, zzz523, zzz524, zzz31, Succ(zzz690), h) → new_mkVBalBranch(zzz31, Branch(zzz520, zzz521, Neg(Succ(zzz52200)), zzz523, zzz524), zzz343, h)
new_mkVBalBranch(zzz31, Branch(zzz520, zzz521, Neg(Zero), zzz523, zzz524), Branch(zzz340, zzz341, Pos(Succ(zzz34200)), zzz343, zzz344), h) → new_mkVBalBranch(zzz31, Branch(zzz520, zzz521, Neg(Zero), zzz523, zzz524), zzz343, h)
new_mkVBalBranch3MkVBalBranch212(zzz818, zzz819, zzz820, zzz821, zzz822, zzz823, zzz824, zzz825, zzz826, zzz827, bf) → new_mkVBalBranch3MkVBalBranch14(zzz818, zzz819, zzz820, zzz821, zzz822, zzz823, zzz824, zzz825, zzz826, zzz827, new_primPlusNat2(new_primPlusNat3(Succ(new_primPlusNat3(new_primPlusNat1(zzz820), zzz820)), Succ(zzz820)), Succ(zzz820)), bf)
new_mkVBalBranch3MkVBalBranch20(zzz929, zzz930, zzz931, zzz932, zzz933, zzz934, zzz935, zzz936, zzz937, zzz938, zzz939, Succ(zzz9400), Succ(zzz9410), ba) → new_mkVBalBranch3MkVBalBranch20(zzz929, zzz930, zzz931, zzz932, zzz933, zzz934, zzz935, zzz936, zzz937, zzz938, zzz939, zzz9400, zzz9410, ba)
new_mkVBalBranch3MkVBalBranch26(zzz1133, zzz1134, zzz1135, zzz1136, zzz1137, zzz1138, zzz1139, zzz1140, zzz1141, zzz1142, Succ(zzz11430), Zero, be) → new_mkVBalBranch3MkVBalBranch212(zzz1133, zzz1134, zzz1135, zzz1136, zzz1137, zzz1138, zzz1139, zzz1140, zzz1141, zzz1142, be)
new_mkVBalBranch3MkVBalBranch1(zzz340, zzz341, zzz34200, zzz343, zzz344, zzz520, zzz521, zzz52200, zzz523, zzz524, zzz31, Zero, h) → new_mkVBalBranch3MkVBalBranch17(zzz340, zzz341, zzz34200, zzz343, zzz344, zzz520, zzz521, zzz52200, zzz523, zzz524, zzz31, h)
new_mkVBalBranch3MkVBalBranch211(zzz537, zzz538, zzz539, zzz540, zzz541, zzz542, zzz543, zzz544, zzz545, zzz546, zzz547, bc) → new_mkVBalBranch3MkVBalBranch15(zzz537, zzz538, zzz539, zzz540, zzz541, zzz542, zzz543, zzz544, zzz545, zzz546, zzz547, new_primPlusNat2(Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat3(new_primPlusNat1(zzz539), zzz539)), zzz539))), Succ(zzz539)), bc)
new_mkVBalBranch3MkVBalBranch23(zzz929, zzz930, zzz931, zzz932, zzz933, zzz934, zzz935, zzz936, zzz937, zzz938, zzz939, ba) → new_mkVBalBranch3MkVBalBranch10(zzz929, zzz930, zzz931, zzz932, zzz933, zzz934, zzz935, zzz936, zzz937, zzz938, zzz939, new_primPlusNat2(new_primPlusNat3(Succ(new_primPlusNat3(new_primPlusNat1(zzz931), zzz931)), Succ(zzz931)), Succ(zzz931)), ba)
new_mkVBalBranch3MkVBalBranch16(zzz1702, zzz1703, zzz1704, zzz1705, zzz1706, zzz1707, zzz1708, zzz1709, zzz1710, zzz1711, zzz1712, Succ(zzz17130), Succ(zzz17140), bd) → new_mkVBalBranch3MkVBalBranch16(zzz1702, zzz1703, zzz1704, zzz1705, zzz1706, zzz1707, zzz1708, zzz1709, zzz1710, zzz1711, zzz1712, zzz17130, zzz17140, bd)
new_mkVBalBranch3MkVBalBranch25(zzz537, zzz538, zzz539, zzz540, zzz541, zzz542, zzz543, zzz544, zzz545, zzz546, zzz547, Zero, Succ(zzz5490), bc) → new_mkVBalBranch(zzz547, Branch(zzz542, zzz543, Neg(Succ(Succ(zzz544))), zzz545, zzz546), zzz540, bc)
new_mkVBalBranch3MkVBalBranch25(zzz537, zzz538, zzz539, zzz540, zzz541, zzz542, zzz543, zzz544, zzz545, zzz546, zzz547, Succ(zzz5480), Zero, bc) → new_mkVBalBranch3MkVBalBranch15(zzz537, zzz538, zzz539, zzz540, zzz541, zzz542, zzz543, zzz544, zzz545, zzz546, zzz547, new_primPlusNat2(Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat3(new_primPlusNat1(zzz539), zzz539)), zzz539))), Succ(zzz539)), bc)
new_mkVBalBranch3MkVBalBranch11(zzz2033, zzz2034, zzz2035, zzz2036, zzz2037, zzz2038, zzz2039, zzz2040, zzz2041, zzz2042, zzz2043, Succ(zzz20440), Succ(zzz20450), bb) → new_mkVBalBranch3MkVBalBranch11(zzz2033, zzz2034, zzz2035, zzz2036, zzz2037, zzz2038, zzz2039, zzz2040, zzz2041, zzz2042, zzz2043, zzz20440, zzz20450, bb)
new_mkVBalBranch3MkVBalBranch25(zzz537, zzz538, zzz539, zzz540, zzz541, zzz542, zzz543, zzz544, zzz545, zzz546, zzz547, Succ(zzz5480), Succ(zzz5490), bc) → new_mkVBalBranch3MkVBalBranch25(zzz537, zzz538, zzz539, zzz540, zzz541, zzz542, zzz543, zzz544, zzz545, zzz546, zzz547, zzz5480, zzz5490, bc)
new_mkVBalBranch3MkVBalBranch29(zzz818, zzz819, zzz820, zzz821, zzz822, zzz823, zzz824, zzz825, zzz826, zzz827, bf) → new_mkVBalBranch3MkVBalBranch14(zzz818, zzz819, zzz820, zzz821, zzz822, zzz823, zzz824, zzz825, zzz826, zzz827, new_primPlusNat2(new_primPlusNat3(Succ(new_primPlusNat3(new_primPlusNat1(zzz820), zzz820)), Succ(zzz820)), Succ(zzz820)), bf)
new_mkVBalBranch3MkVBalBranch10(zzz929, zzz930, zzz931, zzz932, zzz933, zzz934, zzz935, zzz936, zzz937, zzz938, zzz939, Succ(zzz10020), ba) → new_mkVBalBranch3MkVBalBranch11(zzz929, zzz930, zzz931, zzz932, zzz933, zzz934, zzz935, zzz936, zzz937, zzz938, zzz939, Succ(zzz10020), Succ(zzz936), ba)
new_mkVBalBranch(zzz31, Branch(zzz520, zzz521, Pos(Succ(zzz52200)), zzz523, zzz524), Branch(zzz340, zzz341, zzz342, zzz343, zzz344), h) → new_mkVBalBranch3MkVBalBranch2(zzz340, zzz341, zzz342, zzz343, zzz344, zzz520, zzz521, zzz52200, zzz523, zzz524, zzz31, Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat3(new_primPlusNat1(zzz52200), zzz52200)), zzz52200))), h)
new_mkVBalBranch3MkVBalBranch14(zzz818, zzz819, zzz820, zzz821, zzz822, zzz823, zzz824, zzz825, zzz826, zzz827, Succ(zzz8960), bf) → new_mkVBalBranch3MkVBalBranch16(zzz818, zzz819, zzz820, zzz821, zzz822, zzz823, zzz824, Zero, zzz825, zzz826, zzz827, Succ(Zero), Succ(zzz8960), bf)
new_mkVBalBranch3MkVBalBranch26(zzz1133, zzz1134, zzz1135, zzz1136, zzz1137, zzz1138, zzz1139, zzz1140, zzz1141, zzz1142, Zero, Succ(zzz11440), be) → new_mkVBalBranch(zzz1142, Branch(zzz1138, zzz1139, Neg(Succ(Zero)), zzz1140, zzz1141), zzz1136, be)
new_mkVBalBranch3MkVBalBranch24(zzz340, zzz341, Neg(Succ(Succ(Succ(zzz3420000)))), zzz343, zzz344, zzz520, zzz521, Succ(zzz522000), zzz523, zzz524, zzz31, Succ(Succ(zzz6900)), h) → new_mkVBalBranch3MkVBalBranch25(zzz340, zzz341, Succ(Succ(zzz3420000)), zzz343, zzz344, zzz520, zzz521, zzz522000, zzz523, zzz524, zzz31, Succ(zzz3420000), Succ(Succ(new_primPlusNat2(zzz6900, zzz522000))), h)
new_mkVBalBranch3MkVBalBranch24(zzz340, zzz341, Neg(Succ(Succ(Zero))), zzz343, zzz344, zzz520, zzz521, Succ(zzz522000), zzz523, zzz524, zzz31, Succ(Succ(zzz6900)), h) → new_mkVBalBranch3MkVBalBranch25(zzz340, zzz341, Succ(Zero), zzz343, zzz344, zzz520, zzz521, zzz522000, zzz523, zzz524, zzz31, Zero, Succ(Succ(new_primPlusNat2(zzz6900, zzz522000))), h)
new_mkVBalBranch3MkVBalBranch20(zzz929, zzz930, zzz931, zzz932, zzz933, zzz934, zzz935, zzz936, zzz937, zzz938, zzz939, Succ(zzz9400), Zero, ba) → new_mkVBalBranch3MkVBalBranch10(zzz929, zzz930, zzz931, zzz932, zzz933, zzz934, zzz935, zzz936, zzz937, zzz938, zzz939, new_primPlusNat2(new_primPlusNat3(Succ(new_primPlusNat3(new_primPlusNat1(zzz931), zzz931)), Succ(zzz931)), Succ(zzz931)), ba)
new_mkVBalBranch(zzz31, Branch(zzz520, zzz521, Pos(Zero), zzz523, zzz524), Branch(zzz340, zzz341, Pos(Succ(zzz34200)), zzz343, zzz344), h) → new_mkVBalBranch(zzz31, Branch(zzz520, zzz521, Pos(Zero), zzz523, zzz524), zzz343, h)
new_mkVBalBranch(zzz31, Branch(zzz520, zzz521, Pos(Zero), zzz523, zzz524), Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), h) → new_mkVBalBranch3MkVBalBranch12(zzz340, zzz341, zzz34200, zzz343, zzz344, zzz520, zzz521, zzz523, zzz524, zzz31, new_primPlusNat2(Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat3(new_primPlusNat1(zzz34200), zzz34200)), zzz34200))), Succ(zzz34200)), h)
new_mkVBalBranch3MkVBalBranch2(zzz340, zzz341, Pos(Zero), zzz343, zzz344, zzz520, zzz521, zzz52200, zzz523, zzz524, zzz31, Succ(zzz680), h) → new_mkVBalBranch(zzz31, zzz524, Branch(zzz340, zzz341, Pos(Zero), zzz343, zzz344), h)
new_mkVBalBranch3MkVBalBranch2(zzz340, zzz341, Neg(Zero), zzz343, zzz344, zzz520, zzz521, zzz52200, zzz523, zzz524, zzz31, Succ(zzz680), h) → new_mkVBalBranch(zzz31, zzz524, Branch(zzz340, zzz341, Neg(Zero), zzz343, zzz344), h)
new_mkVBalBranch3MkVBalBranch2(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344, zzz520, zzz521, zzz52200, zzz523, zzz524, zzz31, Succ(zzz680), h) → new_mkVBalBranch3MkVBalBranch1(zzz340, zzz341, zzz34200, zzz343, zzz344, zzz520, zzz521, zzz52200, zzz523, zzz524, zzz31, new_primPlusNat2(Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat3(new_primPlusNat1(zzz34200), zzz34200)), zzz34200))), Succ(zzz34200)), h)
new_mkVBalBranch3MkVBalBranch16(zzz1702, zzz1703, zzz1704, zzz1705, zzz1706, zzz1707, zzz1708, zzz1709, zzz1710, zzz1711, zzz1712, Zero, Succ(zzz17140), bd) → new_mkVBalBranch(zzz1712, zzz1711, Branch(zzz1702, zzz1703, Neg(Succ(zzz1704)), zzz1705, zzz1706), bd)
new_mkVBalBranch3MkVBalBranch10(zzz929, zzz930, zzz931, zzz932, zzz933, zzz934, zzz935, zzz936, zzz937, zzz938, zzz939, Zero, ba) → new_mkVBalBranch3MkVBalBranch11(zzz929, zzz930, zzz931, zzz932, zzz933, zzz934, zzz935, zzz936, zzz937, zzz938, zzz939, Zero, Succ(zzz936), ba)
new_mkVBalBranch3MkVBalBranch24(zzz340, zzz341, Neg(Succ(Succ(Succ(zzz3420000)))), zzz343, zzz344, zzz520, zzz521, Zero, zzz523, zzz524, zzz31, Succ(Succ(zzz6900)), h) → new_mkVBalBranch3MkVBalBranch26(zzz340, zzz341, Succ(Succ(zzz3420000)), zzz343, zzz344, zzz520, zzz521, zzz523, zzz524, zzz31, Succ(zzz3420000), Succ(zzz6900), h)
new_mkVBalBranch3MkVBalBranch15(zzz537, zzz538, zzz539, zzz540, zzz541, zzz542, zzz543, zzz544, zzz545, zzz546, zzz547, Succ(zzz6990), bc) → new_mkVBalBranch3MkVBalBranch16(zzz537, zzz538, zzz539, zzz540, zzz541, zzz542, zzz543, Succ(zzz544), zzz545, zzz546, zzz547, Succ(Succ(zzz544)), Succ(zzz6990), bc)
new_mkVBalBranch3MkVBalBranch25(zzz537, zzz538, zzz539, zzz540, zzz541, zzz542, zzz543, zzz544, zzz545, zzz546, zzz547, Zero, Zero, bc) → new_mkVBalBranch3MkVBalBranch211(zzz537, zzz538, zzz539, zzz540, zzz541, zzz542, zzz543, zzz544, zzz545, zzz546, zzz547, bc)

The TRS R consists of the following rules:

new_primPlusNat1(Zero) → Zero
new_primPlusNat1(Succ(zzz62000)) → Succ(Succ(new_primPlusNat1(zzz62000)))
new_primPlusNat3(zzz90, Succ(zzz910)) → Succ(Succ(new_primPlusNat2(zzz90, zzz910)))
new_primPlusNat3(zzz90, Zero) → Succ(zzz90)
new_primPlusNat2(Succ(zzz900), Succ(zzz9100)) → Succ(Succ(new_primPlusNat2(zzz900, zzz9100)))
new_primPlusNat2(Zero, Succ(zzz9100)) → Succ(zzz9100)
new_primPlusNat2(Zero, Zero) → Zero
new_primPlusNat2(Succ(zzz900), Zero) → Succ(zzz900)

The set Q consists of the following terms:

new_primPlusNat2(Zero, Succ(x0))
new_primPlusNat3(x0, Succ(x1))
new_primPlusNat2(Succ(x0), Succ(x1))
new_primPlusNat3(x0, Zero)
new_primPlusNat1(Zero)
new_primPlusNat2(Zero, Zero)
new_primPlusNat1(Succ(x0))
new_primPlusNat2(Succ(x0), Zero)

We have to consider all minimal (P,Q,R)-chains.
By rewriting [15] the rule new_mkVBalBranch3MkVBalBranch212(zzz818, zzz819, zzz820, zzz821, zzz822, zzz823, zzz824, zzz825, zzz826, zzz827, bf) → new_mkVBalBranch3MkVBalBranch14(zzz818, zzz819, zzz820, zzz821, zzz822, zzz823, zzz824, zzz825, zzz826, zzz827, new_primPlusNat2(new_primPlusNat3(Succ(new_primPlusNat3(new_primPlusNat1(zzz820), zzz820)), Succ(zzz820)), Succ(zzz820)), bf) at position [10,0] we obtained the following new rules:

new_mkVBalBranch3MkVBalBranch212(zzz818, zzz819, zzz820, zzz821, zzz822, zzz823, zzz824, zzz825, zzz826, zzz827, bf) → new_mkVBalBranch3MkVBalBranch14(zzz818, zzz819, zzz820, zzz821, zzz822, zzz823, zzz824, zzz825, zzz826, zzz827, new_primPlusNat2(Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat3(new_primPlusNat1(zzz820), zzz820)), zzz820))), Succ(zzz820)), bf)



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

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

new_mkVBalBranch(zzz31, Branch(zzz520, zzz521, Neg(Succ(zzz52200)), zzz523, zzz524), Branch(zzz340, zzz341, zzz342, zzz343, zzz344), h) → new_mkVBalBranch3MkVBalBranch24(zzz340, zzz341, zzz342, zzz343, zzz344, zzz520, zzz521, zzz52200, zzz523, zzz524, zzz31, Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat3(new_primPlusNat1(zzz52200), zzz52200)), zzz52200))), h)
new_mkVBalBranch3MkVBalBranch11(zzz2033, zzz2034, zzz2035, zzz2036, zzz2037, zzz2038, zzz2039, zzz2040, zzz2041, zzz2042, zzz2043, Zero, Succ(zzz20450), bb) → new_mkVBalBranch(zzz2043, zzz2042, Branch(zzz2033, zzz2034, Pos(Succ(zzz2035)), zzz2036, zzz2037), bb)
new_mkVBalBranch3MkVBalBranch26(zzz1133, zzz1134, zzz1135, zzz1136, zzz1137, zzz1138, zzz1139, zzz1140, zzz1141, zzz1142, Succ(zzz11430), Succ(zzz11440), be) → new_mkVBalBranch3MkVBalBranch26(zzz1133, zzz1134, zzz1135, zzz1136, zzz1137, zzz1138, zzz1139, zzz1140, zzz1141, zzz1142, zzz11430, zzz11440, be)
new_mkVBalBranch3MkVBalBranch24(zzz340, zzz341, Pos(zzz3420), zzz343, zzz344, zzz520, zzz521, zzz52200, zzz523, zzz524, zzz31, Succ(zzz690), h) → new_mkVBalBranch(zzz31, Branch(zzz520, zzz521, Neg(Succ(zzz52200)), zzz523, zzz524), zzz343, h)
new_mkVBalBranch3MkVBalBranch12(zzz340, zzz341, zzz34200, zzz343, zzz344, zzz520, zzz521, zzz523, zzz524, zzz31, Succ(zzz1250), h) → new_mkVBalBranch(zzz31, zzz524, Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), h)
new_mkVBalBranch3MkVBalBranch20(zzz929, zzz930, zzz931, zzz932, zzz933, zzz934, zzz935, zzz936, zzz937, zzz938, zzz939, Zero, Succ(zzz9410), ba) → new_mkVBalBranch(zzz939, Branch(zzz934, zzz935, Pos(Succ(zzz936)), zzz937, zzz938), zzz932, ba)
new_mkVBalBranch3MkVBalBranch24(zzz340, zzz341, Neg(Succ(Succ(Zero))), zzz343, zzz344, zzz520, zzz521, Zero, zzz523, zzz524, zzz31, Succ(Succ(zzz6900)), h) → new_mkVBalBranch3MkVBalBranch26(zzz340, zzz341, Succ(Zero), zzz343, zzz344, zzz520, zzz521, zzz523, zzz524, zzz31, Zero, Succ(zzz6900), h)
new_mkVBalBranch3MkVBalBranch17(zzz340, zzz341, zzz34200, zzz343, zzz344, zzz520, zzz521, zzz52200, zzz523, zzz524, zzz31, h) → new_mkVBalBranch(zzz31, zzz524, Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), h)
new_mkVBalBranch3MkVBalBranch26(zzz1133, zzz1134, zzz1135, zzz1136, zzz1137, zzz1138, zzz1139, zzz1140, zzz1141, zzz1142, Zero, Zero, be) → new_mkVBalBranch3MkVBalBranch29(zzz1133, zzz1134, zzz1135, zzz1136, zzz1137, zzz1138, zzz1139, zzz1140, zzz1141, zzz1142, be)
new_mkVBalBranch3MkVBalBranch1(zzz340, zzz341, zzz34200, zzz343, zzz344, zzz520, zzz521, zzz52200, zzz523, zzz524, zzz31, Succ(zzz1430), h) → new_mkVBalBranch(zzz31, zzz524, Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), h)
new_mkVBalBranch3MkVBalBranch24(zzz340, zzz341, Neg(Succ(Zero)), zzz343, zzz344, zzz520, zzz521, zzz52200, zzz523, zzz524, zzz31, Succ(zzz690), h) → new_mkVBalBranch(zzz31, Branch(zzz520, zzz521, Neg(Succ(zzz52200)), zzz523, zzz524), zzz343, h)
new_mkVBalBranch3MkVBalBranch20(zzz929, zzz930, zzz931, zzz932, zzz933, zzz934, zzz935, zzz936, zzz937, zzz938, zzz939, Zero, Zero, ba) → new_mkVBalBranch3MkVBalBranch23(zzz929, zzz930, zzz931, zzz932, zzz933, zzz934, zzz935, zzz936, zzz937, zzz938, zzz939, ba)
new_mkVBalBranch3MkVBalBranch13(zzz340, zzz341, zzz34200, zzz343, zzz344, zzz520, zzz521, zzz523, zzz524, zzz31, Succ(zzz1290), h) → new_mkVBalBranch(zzz31, zzz524, Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), h)
new_mkVBalBranch3MkVBalBranch2(zzz340, zzz341, Pos(Succ(zzz34200)), zzz343, zzz344, zzz520, zzz521, zzz52200, zzz523, zzz524, zzz31, Succ(zzz680), h) → new_mkVBalBranch3MkVBalBranch20(zzz340, zzz341, zzz34200, zzz343, zzz344, zzz520, zzz521, zzz52200, zzz523, zzz524, zzz31, Succ(new_primPlusNat2(zzz680, zzz52200)), zzz34200, h)
new_mkVBalBranch(zzz31, Branch(zzz520, zzz521, Neg(Zero), zzz523, zzz524), Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), h) → new_mkVBalBranch3MkVBalBranch13(zzz340, zzz341, zzz34200, zzz343, zzz344, zzz520, zzz521, zzz523, zzz524, zzz31, new_primPlusNat2(Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat3(new_primPlusNat1(zzz34200), zzz34200)), zzz34200))), Succ(zzz34200)), h)
new_mkVBalBranch(zzz31, Branch(zzz520, zzz521, Neg(Zero), zzz523, zzz524), Branch(zzz340, zzz341, Pos(Succ(zzz34200)), zzz343, zzz344), h) → new_mkVBalBranch(zzz31, Branch(zzz520, zzz521, Neg(Zero), zzz523, zzz524), zzz343, h)
new_mkVBalBranch3MkVBalBranch24(zzz340, zzz341, Neg(Zero), zzz343, zzz344, zzz520, zzz521, zzz52200, zzz523, zzz524, zzz31, Succ(zzz690), h) → new_mkVBalBranch(zzz31, Branch(zzz520, zzz521, Neg(Succ(zzz52200)), zzz523, zzz524), zzz343, h)
new_mkVBalBranch3MkVBalBranch20(zzz929, zzz930, zzz931, zzz932, zzz933, zzz934, zzz935, zzz936, zzz937, zzz938, zzz939, Succ(zzz9400), Succ(zzz9410), ba) → new_mkVBalBranch3MkVBalBranch20(zzz929, zzz930, zzz931, zzz932, zzz933, zzz934, zzz935, zzz936, zzz937, zzz938, zzz939, zzz9400, zzz9410, ba)
new_mkVBalBranch3MkVBalBranch1(zzz340, zzz341, zzz34200, zzz343, zzz344, zzz520, zzz521, zzz52200, zzz523, zzz524, zzz31, Zero, h) → new_mkVBalBranch3MkVBalBranch17(zzz340, zzz341, zzz34200, zzz343, zzz344, zzz520, zzz521, zzz52200, zzz523, zzz524, zzz31, h)
new_mkVBalBranch3MkVBalBranch26(zzz1133, zzz1134, zzz1135, zzz1136, zzz1137, zzz1138, zzz1139, zzz1140, zzz1141, zzz1142, Succ(zzz11430), Zero, be) → new_mkVBalBranch3MkVBalBranch212(zzz1133, zzz1134, zzz1135, zzz1136, zzz1137, zzz1138, zzz1139, zzz1140, zzz1141, zzz1142, be)
new_mkVBalBranch3MkVBalBranch23(zzz929, zzz930, zzz931, zzz932, zzz933, zzz934, zzz935, zzz936, zzz937, zzz938, zzz939, ba) → new_mkVBalBranch3MkVBalBranch10(zzz929, zzz930, zzz931, zzz932, zzz933, zzz934, zzz935, zzz936, zzz937, zzz938, zzz939, new_primPlusNat2(new_primPlusNat3(Succ(new_primPlusNat3(new_primPlusNat1(zzz931), zzz931)), Succ(zzz931)), Succ(zzz931)), ba)
new_mkVBalBranch3MkVBalBranch211(zzz537, zzz538, zzz539, zzz540, zzz541, zzz542, zzz543, zzz544, zzz545, zzz546, zzz547, bc) → new_mkVBalBranch3MkVBalBranch15(zzz537, zzz538, zzz539, zzz540, zzz541, zzz542, zzz543, zzz544, zzz545, zzz546, zzz547, new_primPlusNat2(Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat3(new_primPlusNat1(zzz539), zzz539)), zzz539))), Succ(zzz539)), bc)
new_mkVBalBranch3MkVBalBranch16(zzz1702, zzz1703, zzz1704, zzz1705, zzz1706, zzz1707, zzz1708, zzz1709, zzz1710, zzz1711, zzz1712, Succ(zzz17130), Succ(zzz17140), bd) → new_mkVBalBranch3MkVBalBranch16(zzz1702, zzz1703, zzz1704, zzz1705, zzz1706, zzz1707, zzz1708, zzz1709, zzz1710, zzz1711, zzz1712, zzz17130, zzz17140, bd)
new_mkVBalBranch3MkVBalBranch25(zzz537, zzz538, zzz539, zzz540, zzz541, zzz542, zzz543, zzz544, zzz545, zzz546, zzz547, Zero, Succ(zzz5490), bc) → new_mkVBalBranch(zzz547, Branch(zzz542, zzz543, Neg(Succ(Succ(zzz544))), zzz545, zzz546), zzz540, bc)
new_mkVBalBranch3MkVBalBranch11(zzz2033, zzz2034, zzz2035, zzz2036, zzz2037, zzz2038, zzz2039, zzz2040, zzz2041, zzz2042, zzz2043, Succ(zzz20440), Succ(zzz20450), bb) → new_mkVBalBranch3MkVBalBranch11(zzz2033, zzz2034, zzz2035, zzz2036, zzz2037, zzz2038, zzz2039, zzz2040, zzz2041, zzz2042, zzz2043, zzz20440, zzz20450, bb)
new_mkVBalBranch3MkVBalBranch25(zzz537, zzz538, zzz539, zzz540, zzz541, zzz542, zzz543, zzz544, zzz545, zzz546, zzz547, Succ(zzz5480), Zero, bc) → new_mkVBalBranch3MkVBalBranch15(zzz537, zzz538, zzz539, zzz540, zzz541, zzz542, zzz543, zzz544, zzz545, zzz546, zzz547, new_primPlusNat2(Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat3(new_primPlusNat1(zzz539), zzz539)), zzz539))), Succ(zzz539)), bc)
new_mkVBalBranch3MkVBalBranch25(zzz537, zzz538, zzz539, zzz540, zzz541, zzz542, zzz543, zzz544, zzz545, zzz546, zzz547, Succ(zzz5480), Succ(zzz5490), bc) → new_mkVBalBranch3MkVBalBranch25(zzz537, zzz538, zzz539, zzz540, zzz541, zzz542, zzz543, zzz544, zzz545, zzz546, zzz547, zzz5480, zzz5490, bc)
new_mkVBalBranch3MkVBalBranch29(zzz818, zzz819, zzz820, zzz821, zzz822, zzz823, zzz824, zzz825, zzz826, zzz827, bf) → new_mkVBalBranch3MkVBalBranch14(zzz818, zzz819, zzz820, zzz821, zzz822, zzz823, zzz824, zzz825, zzz826, zzz827, new_primPlusNat2(new_primPlusNat3(Succ(new_primPlusNat3(new_primPlusNat1(zzz820), zzz820)), Succ(zzz820)), Succ(zzz820)), bf)
new_mkVBalBranch(zzz31, Branch(zzz520, zzz521, Pos(Succ(zzz52200)), zzz523, zzz524), Branch(zzz340, zzz341, zzz342, zzz343, zzz344), h) → new_mkVBalBranch3MkVBalBranch2(zzz340, zzz341, zzz342, zzz343, zzz344, zzz520, zzz521, zzz52200, zzz523, zzz524, zzz31, Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat3(new_primPlusNat1(zzz52200), zzz52200)), zzz52200))), h)
new_mkVBalBranch3MkVBalBranch10(zzz929, zzz930, zzz931, zzz932, zzz933, zzz934, zzz935, zzz936, zzz937, zzz938, zzz939, Succ(zzz10020), ba) → new_mkVBalBranch3MkVBalBranch11(zzz929, zzz930, zzz931, zzz932, zzz933, zzz934, zzz935, zzz936, zzz937, zzz938, zzz939, Succ(zzz10020), Succ(zzz936), ba)
new_mkVBalBranch3MkVBalBranch14(zzz818, zzz819, zzz820, zzz821, zzz822, zzz823, zzz824, zzz825, zzz826, zzz827, Succ(zzz8960), bf) → new_mkVBalBranch3MkVBalBranch16(zzz818, zzz819, zzz820, zzz821, zzz822, zzz823, zzz824, Zero, zzz825, zzz826, zzz827, Succ(Zero), Succ(zzz8960), bf)
new_mkVBalBranch3MkVBalBranch24(zzz340, zzz341, Neg(Succ(Succ(Succ(zzz3420000)))), zzz343, zzz344, zzz520, zzz521, Succ(zzz522000), zzz523, zzz524, zzz31, Succ(Succ(zzz6900)), h) → new_mkVBalBranch3MkVBalBranch25(zzz340, zzz341, Succ(Succ(zzz3420000)), zzz343, zzz344, zzz520, zzz521, zzz522000, zzz523, zzz524, zzz31, Succ(zzz3420000), Succ(Succ(new_primPlusNat2(zzz6900, zzz522000))), h)
new_mkVBalBranch3MkVBalBranch26(zzz1133, zzz1134, zzz1135, zzz1136, zzz1137, zzz1138, zzz1139, zzz1140, zzz1141, zzz1142, Zero, Succ(zzz11440), be) → new_mkVBalBranch(zzz1142, Branch(zzz1138, zzz1139, Neg(Succ(Zero)), zzz1140, zzz1141), zzz1136, be)
new_mkVBalBranch3MkVBalBranch24(zzz340, zzz341, Neg(Succ(Succ(Zero))), zzz343, zzz344, zzz520, zzz521, Succ(zzz522000), zzz523, zzz524, zzz31, Succ(Succ(zzz6900)), h) → new_mkVBalBranch3MkVBalBranch25(zzz340, zzz341, Succ(Zero), zzz343, zzz344, zzz520, zzz521, zzz522000, zzz523, zzz524, zzz31, Zero, Succ(Succ(new_primPlusNat2(zzz6900, zzz522000))), h)
new_mkVBalBranch(zzz31, Branch(zzz520, zzz521, Pos(Zero), zzz523, zzz524), Branch(zzz340, zzz341, Pos(Succ(zzz34200)), zzz343, zzz344), h) → new_mkVBalBranch(zzz31, Branch(zzz520, zzz521, Pos(Zero), zzz523, zzz524), zzz343, h)
new_mkVBalBranch3MkVBalBranch20(zzz929, zzz930, zzz931, zzz932, zzz933, zzz934, zzz935, zzz936, zzz937, zzz938, zzz939, Succ(zzz9400), Zero, ba) → new_mkVBalBranch3MkVBalBranch10(zzz929, zzz930, zzz931, zzz932, zzz933, zzz934, zzz935, zzz936, zzz937, zzz938, zzz939, new_primPlusNat2(new_primPlusNat3(Succ(new_primPlusNat3(new_primPlusNat1(zzz931), zzz931)), Succ(zzz931)), Succ(zzz931)), ba)
new_mkVBalBranch(zzz31, Branch(zzz520, zzz521, Pos(Zero), zzz523, zzz524), Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), h) → new_mkVBalBranch3MkVBalBranch12(zzz340, zzz341, zzz34200, zzz343, zzz344, zzz520, zzz521, zzz523, zzz524, zzz31, new_primPlusNat2(Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat3(new_primPlusNat1(zzz34200), zzz34200)), zzz34200))), Succ(zzz34200)), h)
new_mkVBalBranch3MkVBalBranch2(zzz340, zzz341, Pos(Zero), zzz343, zzz344, zzz520, zzz521, zzz52200, zzz523, zzz524, zzz31, Succ(zzz680), h) → new_mkVBalBranch(zzz31, zzz524, Branch(zzz340, zzz341, Pos(Zero), zzz343, zzz344), h)
new_mkVBalBranch3MkVBalBranch2(zzz340, zzz341, Neg(Zero), zzz343, zzz344, zzz520, zzz521, zzz52200, zzz523, zzz524, zzz31, Succ(zzz680), h) → new_mkVBalBranch(zzz31, zzz524, Branch(zzz340, zzz341, Neg(Zero), zzz343, zzz344), h)
new_mkVBalBranch3MkVBalBranch2(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344, zzz520, zzz521, zzz52200, zzz523, zzz524, zzz31, Succ(zzz680), h) → new_mkVBalBranch3MkVBalBranch1(zzz340, zzz341, zzz34200, zzz343, zzz344, zzz520, zzz521, zzz52200, zzz523, zzz524, zzz31, new_primPlusNat2(Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat3(new_primPlusNat1(zzz34200), zzz34200)), zzz34200))), Succ(zzz34200)), h)
new_mkVBalBranch3MkVBalBranch16(zzz1702, zzz1703, zzz1704, zzz1705, zzz1706, zzz1707, zzz1708, zzz1709, zzz1710, zzz1711, zzz1712, Zero, Succ(zzz17140), bd) → new_mkVBalBranch(zzz1712, zzz1711, Branch(zzz1702, zzz1703, Neg(Succ(zzz1704)), zzz1705, zzz1706), bd)
new_mkVBalBranch3MkVBalBranch15(zzz537, zzz538, zzz539, zzz540, zzz541, zzz542, zzz543, zzz544, zzz545, zzz546, zzz547, Succ(zzz6990), bc) → new_mkVBalBranch3MkVBalBranch16(zzz537, zzz538, zzz539, zzz540, zzz541, zzz542, zzz543, Succ(zzz544), zzz545, zzz546, zzz547, Succ(Succ(zzz544)), Succ(zzz6990), bc)
new_mkVBalBranch3MkVBalBranch24(zzz340, zzz341, Neg(Succ(Succ(Succ(zzz3420000)))), zzz343, zzz344, zzz520, zzz521, Zero, zzz523, zzz524, zzz31, Succ(Succ(zzz6900)), h) → new_mkVBalBranch3MkVBalBranch26(zzz340, zzz341, Succ(Succ(zzz3420000)), zzz343, zzz344, zzz520, zzz521, zzz523, zzz524, zzz31, Succ(zzz3420000), Succ(zzz6900), h)
new_mkVBalBranch3MkVBalBranch10(zzz929, zzz930, zzz931, zzz932, zzz933, zzz934, zzz935, zzz936, zzz937, zzz938, zzz939, Zero, ba) → new_mkVBalBranch3MkVBalBranch11(zzz929, zzz930, zzz931, zzz932, zzz933, zzz934, zzz935, zzz936, zzz937, zzz938, zzz939, Zero, Succ(zzz936), ba)
new_mkVBalBranch3MkVBalBranch25(zzz537, zzz538, zzz539, zzz540, zzz541, zzz542, zzz543, zzz544, zzz545, zzz546, zzz547, Zero, Zero, bc) → new_mkVBalBranch3MkVBalBranch211(zzz537, zzz538, zzz539, zzz540, zzz541, zzz542, zzz543, zzz544, zzz545, zzz546, zzz547, bc)
new_mkVBalBranch3MkVBalBranch212(zzz818, zzz819, zzz820, zzz821, zzz822, zzz823, zzz824, zzz825, zzz826, zzz827, bf) → new_mkVBalBranch3MkVBalBranch14(zzz818, zzz819, zzz820, zzz821, zzz822, zzz823, zzz824, zzz825, zzz826, zzz827, new_primPlusNat2(Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat3(new_primPlusNat1(zzz820), zzz820)), zzz820))), Succ(zzz820)), bf)

The TRS R consists of the following rules:

new_primPlusNat1(Zero) → Zero
new_primPlusNat1(Succ(zzz62000)) → Succ(Succ(new_primPlusNat1(zzz62000)))
new_primPlusNat3(zzz90, Succ(zzz910)) → Succ(Succ(new_primPlusNat2(zzz90, zzz910)))
new_primPlusNat3(zzz90, Zero) → Succ(zzz90)
new_primPlusNat2(Succ(zzz900), Succ(zzz9100)) → Succ(Succ(new_primPlusNat2(zzz900, zzz9100)))
new_primPlusNat2(Zero, Succ(zzz9100)) → Succ(zzz9100)
new_primPlusNat2(Zero, Zero) → Zero
new_primPlusNat2(Succ(zzz900), Zero) → Succ(zzz900)

The set Q consists of the following terms:

new_primPlusNat2(Zero, Succ(x0))
new_primPlusNat3(x0, Succ(x1))
new_primPlusNat2(Succ(x0), Succ(x1))
new_primPlusNat3(x0, Zero)
new_primPlusNat1(Zero)
new_primPlusNat2(Zero, Zero)
new_primPlusNat1(Succ(x0))
new_primPlusNat2(Succ(x0), Zero)

We have to consider all minimal (P,Q,R)-chains.
By rewriting [15] the rule new_mkVBalBranch3MkVBalBranch23(zzz929, zzz930, zzz931, zzz932, zzz933, zzz934, zzz935, zzz936, zzz937, zzz938, zzz939, ba) → new_mkVBalBranch3MkVBalBranch10(zzz929, zzz930, zzz931, zzz932, zzz933, zzz934, zzz935, zzz936, zzz937, zzz938, zzz939, new_primPlusNat2(new_primPlusNat3(Succ(new_primPlusNat3(new_primPlusNat1(zzz931), zzz931)), Succ(zzz931)), Succ(zzz931)), ba) at position [11,0] we obtained the following new rules:

new_mkVBalBranch3MkVBalBranch23(zzz929, zzz930, zzz931, zzz932, zzz933, zzz934, zzz935, zzz936, zzz937, zzz938, zzz939, ba) → new_mkVBalBranch3MkVBalBranch10(zzz929, zzz930, zzz931, zzz932, zzz933, zzz934, zzz935, zzz936, zzz937, zzz938, zzz939, new_primPlusNat2(Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat3(new_primPlusNat1(zzz931), zzz931)), zzz931))), Succ(zzz931)), 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
                                    ↳ DependencyGraphProof
                                      ↳ QDP
                                        ↳ Rewriting
                                          ↳ QDP
                                            ↳ Rewriting
                                              ↳ QDP
                                                ↳ Rewriting
                                                  ↳ QDP
                                                    ↳ Rewriting
                                                      ↳ QDP
                                                        ↳ Rewriting
                                                          ↳ QDP
                                                            ↳ Rewriting
                                                              ↳ QDP
                                                                ↳ Rewriting
                                                                  ↳ QDP
                                                                    ↳ Rewriting
                                                                      ↳ QDP
                                                                        ↳ Rewriting
                                                                          ↳ QDP
                                                                            ↳ Rewriting
                                                                              ↳ QDP
                                                                                ↳ Rewriting
                                                                                  ↳ QDP
                                                                                    ↳ Rewriting
                                                                                      ↳ QDP
                                                                                        ↳ Rewriting
                                                                                          ↳ QDP
                                                                                            ↳ UsableRulesProof
                                                                                              ↳ QDP
                                                                                                ↳ QReductionProof
                                                                                                  ↳ QDP
                                                                                                    ↳ Rewriting
                                                                                                      ↳ QDP
                                                                                                        ↳ Rewriting
                                                                                                          ↳ QDP
                                                                                                            ↳ Rewriting
                                                                                                              ↳ QDP
                                                                                                                ↳ Rewriting
                                                                                                                  ↳ QDP
                                                                                                                    ↳ Rewriting
                                                                                                                      ↳ QDP
                                                                                                                        ↳ Rewriting
                                                                                                                          ↳ QDP
                                                                                                                            ↳ DependencyGraphProof
                                                                                                                              ↳ QDP
                                                                                                                                ↳ Rewriting
                                                                                                                                  ↳ QDP
                                                                                                                                    ↳ Rewriting
                                                                                                                                      ↳ QDP
                                                                                                                                        ↳ DependencyGraphProof
                                                                                                                                          ↳ QDP
                                                                                                                                            ↳ Rewriting
                                                                                                                                              ↳ QDP
                                                                                                                                                ↳ Rewriting
                                                                                                                                                  ↳ QDP
                                                                                                                                                    ↳ Rewriting
                                                                                                                                                      ↳ QDP
                                                                                                                                                        ↳ Rewriting
                                                                                                                                                          ↳ QDP
                                                                                                                                                            ↳ Rewriting
                                                                                                                                                              ↳ QDP
                                                                                                                                                                ↳ Rewriting
                                                                                                                                                                  ↳ QDP
                                                                                                                                                                    ↳ Rewriting
                                                                                                                                                                      ↳ QDP
                                                                                                                                                                        ↳ UsableRulesProof
                                                                                                                                                                          ↳ QDP
                                                                                                                                                                            ↳ QReductionProof
                                                                                                                                                                              ↳ QDP
                                                                                                                                                                                ↳ Rewriting
                                                                                                                                                                                  ↳ QDP
                                                                                                                                                                                    ↳ Rewriting
                                                                                                                                                                                      ↳ QDP
                                                                                                                                                                                        ↳ Rewriting
                                                                                                                                                                                          ↳ QDP
                                                                                                                                                                                            ↳ Rewriting
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP

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

new_mkVBalBranch3MkVBalBranch23(zzz929, zzz930, zzz931, zzz932, zzz933, zzz934, zzz935, zzz936, zzz937, zzz938, zzz939, ba) → new_mkVBalBranch3MkVBalBranch10(zzz929, zzz930, zzz931, zzz932, zzz933, zzz934, zzz935, zzz936, zzz937, zzz938, zzz939, new_primPlusNat2(Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat3(new_primPlusNat1(zzz931), zzz931)), zzz931))), Succ(zzz931)), ba)
new_mkVBalBranch3MkVBalBranch11(zzz2033, zzz2034, zzz2035, zzz2036, zzz2037, zzz2038, zzz2039, zzz2040, zzz2041, zzz2042, zzz2043, Zero, Succ(zzz20450), bb) → new_mkVBalBranch(zzz2043, zzz2042, Branch(zzz2033, zzz2034, Pos(Succ(zzz2035)), zzz2036, zzz2037), bb)
new_mkVBalBranch(zzz31, Branch(zzz520, zzz521, Neg(Succ(zzz52200)), zzz523, zzz524), Branch(zzz340, zzz341, zzz342, zzz343, zzz344), h) → new_mkVBalBranch3MkVBalBranch24(zzz340, zzz341, zzz342, zzz343, zzz344, zzz520, zzz521, zzz52200, zzz523, zzz524, zzz31, Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat3(new_primPlusNat1(zzz52200), zzz52200)), zzz52200))), h)
new_mkVBalBranch3MkVBalBranch26(zzz1133, zzz1134, zzz1135, zzz1136, zzz1137, zzz1138, zzz1139, zzz1140, zzz1141, zzz1142, Succ(zzz11430), Succ(zzz11440), be) → new_mkVBalBranch3MkVBalBranch26(zzz1133, zzz1134, zzz1135, zzz1136, zzz1137, zzz1138, zzz1139, zzz1140, zzz1141, zzz1142, zzz11430, zzz11440, be)
new_mkVBalBranch3MkVBalBranch24(zzz340, zzz341, Pos(zzz3420), zzz343, zzz344, zzz520, zzz521, zzz52200, zzz523, zzz524, zzz31, Succ(zzz690), h) → new_mkVBalBranch(zzz31, Branch(zzz520, zzz521, Neg(Succ(zzz52200)), zzz523, zzz524), zzz343, h)
new_mkVBalBranch3MkVBalBranch12(zzz340, zzz341, zzz34200, zzz343, zzz344, zzz520, zzz521, zzz523, zzz524, zzz31, Succ(zzz1250), h) → new_mkVBalBranch(zzz31, zzz524, Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), h)
new_mkVBalBranch3MkVBalBranch20(zzz929, zzz930, zzz931, zzz932, zzz933, zzz934, zzz935, zzz936, zzz937, zzz938, zzz939, Zero, Succ(zzz9410), ba) → new_mkVBalBranch(zzz939, Branch(zzz934, zzz935, Pos(Succ(zzz936)), zzz937, zzz938), zzz932, ba)
new_mkVBalBranch3MkVBalBranch24(zzz340, zzz341, Neg(Succ(Succ(Zero))), zzz343, zzz344, zzz520, zzz521, Zero, zzz523, zzz524, zzz31, Succ(Succ(zzz6900)), h) → new_mkVBalBranch3MkVBalBranch26(zzz340, zzz341, Succ(Zero), zzz343, zzz344, zzz520, zzz521, zzz523, zzz524, zzz31, Zero, Succ(zzz6900), h)
new_mkVBalBranch3MkVBalBranch17(zzz340, zzz341, zzz34200, zzz343, zzz344, zzz520, zzz521, zzz52200, zzz523, zzz524, zzz31, h) → new_mkVBalBranch(zzz31, zzz524, Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), h)
new_mkVBalBranch3MkVBalBranch1(zzz340, zzz341, zzz34200, zzz343, zzz344, zzz520, zzz521, zzz52200, zzz523, zzz524, zzz31, Succ(zzz1430), h) → new_mkVBalBranch(zzz31, zzz524, Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), h)
new_mkVBalBranch3MkVBalBranch26(zzz1133, zzz1134, zzz1135, zzz1136, zzz1137, zzz1138, zzz1139, zzz1140, zzz1141, zzz1142, Zero, Zero, be) → new_mkVBalBranch3MkVBalBranch29(zzz1133, zzz1134, zzz1135, zzz1136, zzz1137, zzz1138, zzz1139, zzz1140, zzz1141, zzz1142, be)
new_mkVBalBranch3MkVBalBranch20(zzz929, zzz930, zzz931, zzz932, zzz933, zzz934, zzz935, zzz936, zzz937, zzz938, zzz939, Zero, Zero, ba) → new_mkVBalBranch3MkVBalBranch23(zzz929, zzz930, zzz931, zzz932, zzz933, zzz934, zzz935, zzz936, zzz937, zzz938, zzz939, ba)
new_mkVBalBranch3MkVBalBranch24(zzz340, zzz341, Neg(Succ(Zero)), zzz343, zzz344, zzz520, zzz521, zzz52200, zzz523, zzz524, zzz31, Succ(zzz690), h) → new_mkVBalBranch(zzz31, Branch(zzz520, zzz521, Neg(Succ(zzz52200)), zzz523, zzz524), zzz343, h)
new_mkVBalBranch3MkVBalBranch13(zzz340, zzz341, zzz34200, zzz343, zzz344, zzz520, zzz521, zzz523, zzz524, zzz31, Succ(zzz1290), h) → new_mkVBalBranch(zzz31, zzz524, Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), h)
new_mkVBalBranch3MkVBalBranch2(zzz340, zzz341, Pos(Succ(zzz34200)), zzz343, zzz344, zzz520, zzz521, zzz52200, zzz523, zzz524, zzz31, Succ(zzz680), h) → new_mkVBalBranch3MkVBalBranch20(zzz340, zzz341, zzz34200, zzz343, zzz344, zzz520, zzz521, zzz52200, zzz523, zzz524, zzz31, Succ(new_primPlusNat2(zzz680, zzz52200)), zzz34200, h)
new_mkVBalBranch(zzz31, Branch(zzz520, zzz521, Neg(Zero), zzz523, zzz524), Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), h) → new_mkVBalBranch3MkVBalBranch13(zzz340, zzz341, zzz34200, zzz343, zzz344, zzz520, zzz521, zzz523, zzz524, zzz31, new_primPlusNat2(Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat3(new_primPlusNat1(zzz34200), zzz34200)), zzz34200))), Succ(zzz34200)), h)
new_mkVBalBranch3MkVBalBranch24(zzz340, zzz341, Neg(Zero), zzz343, zzz344, zzz520, zzz521, zzz52200, zzz523, zzz524, zzz31, Succ(zzz690), h) → new_mkVBalBranch(zzz31, Branch(zzz520, zzz521, Neg(Succ(zzz52200)), zzz523, zzz524), zzz343, h)
new_mkVBalBranch(zzz31, Branch(zzz520, zzz521, Neg(Zero), zzz523, zzz524), Branch(zzz340, zzz341, Pos(Succ(zzz34200)), zzz343, zzz344), h) → new_mkVBalBranch(zzz31, Branch(zzz520, zzz521, Neg(Zero), zzz523, zzz524), zzz343, h)
new_mkVBalBranch3MkVBalBranch20(zzz929, zzz930, zzz931, zzz932, zzz933, zzz934, zzz935, zzz936, zzz937, zzz938, zzz939, Succ(zzz9400), Succ(zzz9410), ba) → new_mkVBalBranch3MkVBalBranch20(zzz929, zzz930, zzz931, zzz932, zzz933, zzz934, zzz935, zzz936, zzz937, zzz938, zzz939, zzz9400, zzz9410, ba)
new_mkVBalBranch3MkVBalBranch26(zzz1133, zzz1134, zzz1135, zzz1136, zzz1137, zzz1138, zzz1139, zzz1140, zzz1141, zzz1142, Succ(zzz11430), Zero, be) → new_mkVBalBranch3MkVBalBranch212(zzz1133, zzz1134, zzz1135, zzz1136, zzz1137, zzz1138, zzz1139, zzz1140, zzz1141, zzz1142, be)
new_mkVBalBranch3MkVBalBranch1(zzz340, zzz341, zzz34200, zzz343, zzz344, zzz520, zzz521, zzz52200, zzz523, zzz524, zzz31, Zero, h) → new_mkVBalBranch3MkVBalBranch17(zzz340, zzz341, zzz34200, zzz343, zzz344, zzz520, zzz521, zzz52200, zzz523, zzz524, zzz31, h)
new_mkVBalBranch3MkVBalBranch211(zzz537, zzz538, zzz539, zzz540, zzz541, zzz542, zzz543, zzz544, zzz545, zzz546, zzz547, bc) → new_mkVBalBranch3MkVBalBranch15(zzz537, zzz538, zzz539, zzz540, zzz541, zzz542, zzz543, zzz544, zzz545, zzz546, zzz547, new_primPlusNat2(Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat3(new_primPlusNat1(zzz539), zzz539)), zzz539))), Succ(zzz539)), bc)
new_mkVBalBranch3MkVBalBranch16(zzz1702, zzz1703, zzz1704, zzz1705, zzz1706, zzz1707, zzz1708, zzz1709, zzz1710, zzz1711, zzz1712, Succ(zzz17130), Succ(zzz17140), bd) → new_mkVBalBranch3MkVBalBranch16(zzz1702, zzz1703, zzz1704, zzz1705, zzz1706, zzz1707, zzz1708, zzz1709, zzz1710, zzz1711, zzz1712, zzz17130, zzz17140, bd)
new_mkVBalBranch3MkVBalBranch25(zzz537, zzz538, zzz539, zzz540, zzz541, zzz542, zzz543, zzz544, zzz545, zzz546, zzz547, Zero, Succ(zzz5490), bc) → new_mkVBalBranch(zzz547, Branch(zzz542, zzz543, Neg(Succ(Succ(zzz544))), zzz545, zzz546), zzz540, bc)
new_mkVBalBranch3MkVBalBranch25(zzz537, zzz538, zzz539, zzz540, zzz541, zzz542, zzz543, zzz544, zzz545, zzz546, zzz547, Succ(zzz5480), Zero, bc) → new_mkVBalBranch3MkVBalBranch15(zzz537, zzz538, zzz539, zzz540, zzz541, zzz542, zzz543, zzz544, zzz545, zzz546, zzz547, new_primPlusNat2(Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat3(new_primPlusNat1(zzz539), zzz539)), zzz539))), Succ(zzz539)), bc)
new_mkVBalBranch3MkVBalBranch11(zzz2033, zzz2034, zzz2035, zzz2036, zzz2037, zzz2038, zzz2039, zzz2040, zzz2041, zzz2042, zzz2043, Succ(zzz20440), Succ(zzz20450), bb) → new_mkVBalBranch3MkVBalBranch11(zzz2033, zzz2034, zzz2035, zzz2036, zzz2037, zzz2038, zzz2039, zzz2040, zzz2041, zzz2042, zzz2043, zzz20440, zzz20450, bb)
new_mkVBalBranch3MkVBalBranch25(zzz537, zzz538, zzz539, zzz540, zzz541, zzz542, zzz543, zzz544, zzz545, zzz546, zzz547, Succ(zzz5480), Succ(zzz5490), bc) → new_mkVBalBranch3MkVBalBranch25(zzz537, zzz538, zzz539, zzz540, zzz541, zzz542, zzz543, zzz544, zzz545, zzz546, zzz547, zzz5480, zzz5490, bc)
new_mkVBalBranch3MkVBalBranch29(zzz818, zzz819, zzz820, zzz821, zzz822, zzz823, zzz824, zzz825, zzz826, zzz827, bf) → new_mkVBalBranch3MkVBalBranch14(zzz818, zzz819, zzz820, zzz821, zzz822, zzz823, zzz824, zzz825, zzz826, zzz827, new_primPlusNat2(new_primPlusNat3(Succ(new_primPlusNat3(new_primPlusNat1(zzz820), zzz820)), Succ(zzz820)), Succ(zzz820)), bf)
new_mkVBalBranch3MkVBalBranch10(zzz929, zzz930, zzz931, zzz932, zzz933, zzz934, zzz935, zzz936, zzz937, zzz938, zzz939, Succ(zzz10020), ba) → new_mkVBalBranch3MkVBalBranch11(zzz929, zzz930, zzz931, zzz932, zzz933, zzz934, zzz935, zzz936, zzz937, zzz938, zzz939, Succ(zzz10020), Succ(zzz936), ba)
new_mkVBalBranch(zzz31, Branch(zzz520, zzz521, Pos(Succ(zzz52200)), zzz523, zzz524), Branch(zzz340, zzz341, zzz342, zzz343, zzz344), h) → new_mkVBalBranch3MkVBalBranch2(zzz340, zzz341, zzz342, zzz343, zzz344, zzz520, zzz521, zzz52200, zzz523, zzz524, zzz31, Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat3(new_primPlusNat1(zzz52200), zzz52200)), zzz52200))), h)
new_mkVBalBranch3MkVBalBranch14(zzz818, zzz819, zzz820, zzz821, zzz822, zzz823, zzz824, zzz825, zzz826, zzz827, Succ(zzz8960), bf) → new_mkVBalBranch3MkVBalBranch16(zzz818, zzz819, zzz820, zzz821, zzz822, zzz823, zzz824, Zero, zzz825, zzz826, zzz827, Succ(Zero), Succ(zzz8960), bf)
new_mkVBalBranch3MkVBalBranch26(zzz1133, zzz1134, zzz1135, zzz1136, zzz1137, zzz1138, zzz1139, zzz1140, zzz1141, zzz1142, Zero, Succ(zzz11440), be) → new_mkVBalBranch(zzz1142, Branch(zzz1138, zzz1139, Neg(Succ(Zero)), zzz1140, zzz1141), zzz1136, be)
new_mkVBalBranch3MkVBalBranch24(zzz340, zzz341, Neg(Succ(Succ(Succ(zzz3420000)))), zzz343, zzz344, zzz520, zzz521, Succ(zzz522000), zzz523, zzz524, zzz31, Succ(Succ(zzz6900)), h) → new_mkVBalBranch3MkVBalBranch25(zzz340, zzz341, Succ(Succ(zzz3420000)), zzz343, zzz344, zzz520, zzz521, zzz522000, zzz523, zzz524, zzz31, Succ(zzz3420000), Succ(Succ(new_primPlusNat2(zzz6900, zzz522000))), h)
new_mkVBalBranch3MkVBalBranch24(zzz340, zzz341, Neg(Succ(Succ(Zero))), zzz343, zzz344, zzz520, zzz521, Succ(zzz522000), zzz523, zzz524, zzz31, Succ(Succ(zzz6900)), h) → new_mkVBalBranch3MkVBalBranch25(zzz340, zzz341, Succ(Zero), zzz343, zzz344, zzz520, zzz521, zzz522000, zzz523, zzz524, zzz31, Zero, Succ(Succ(new_primPlusNat2(zzz6900, zzz522000))), h)
new_mkVBalBranch3MkVBalBranch20(zzz929, zzz930, zzz931, zzz932, zzz933, zzz934, zzz935, zzz936, zzz937, zzz938, zzz939, Succ(zzz9400), Zero, ba) → new_mkVBalBranch3MkVBalBranch10(zzz929, zzz930, zzz931, zzz932, zzz933, zzz934, zzz935, zzz936, zzz937, zzz938, zzz939, new_primPlusNat2(new_primPlusNat3(Succ(new_primPlusNat3(new_primPlusNat1(zzz931), zzz931)), Succ(zzz931)), Succ(zzz931)), ba)
new_mkVBalBranch(zzz31, Branch(zzz520, zzz521, Pos(Zero), zzz523, zzz524), Branch(zzz340, zzz341, Pos(Succ(zzz34200)), zzz343, zzz344), h) → new_mkVBalBranch(zzz31, Branch(zzz520, zzz521, Pos(Zero), zzz523, zzz524), zzz343, h)
new_mkVBalBranch(zzz31, Branch(zzz520, zzz521, Pos(Zero), zzz523, zzz524), Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), h) → new_mkVBalBranch3MkVBalBranch12(zzz340, zzz341, zzz34200, zzz343, zzz344, zzz520, zzz521, zzz523, zzz524, zzz31, new_primPlusNat2(Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat3(new_primPlusNat1(zzz34200), zzz34200)), zzz34200))), Succ(zzz34200)), h)
new_mkVBalBranch3MkVBalBranch2(zzz340, zzz341, Pos(Zero), zzz343, zzz344, zzz520, zzz521, zzz52200, zzz523, zzz524, zzz31, Succ(zzz680), h) → new_mkVBalBranch(zzz31, zzz524, Branch(zzz340, zzz341, Pos(Zero), zzz343, zzz344), h)
new_mkVBalBranch3MkVBalBranch2(zzz340, zzz341, Neg(Zero), zzz343, zzz344, zzz520, zzz521, zzz52200, zzz523, zzz524, zzz31, Succ(zzz680), h) → new_mkVBalBranch(zzz31, zzz524, Branch(zzz340, zzz341, Neg(Zero), zzz343, zzz344), h)
new_mkVBalBranch3MkVBalBranch2(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344, zzz520, zzz521, zzz52200, zzz523, zzz524, zzz31, Succ(zzz680), h) → new_mkVBalBranch3MkVBalBranch1(zzz340, zzz341, zzz34200, zzz343, zzz344, zzz520, zzz521, zzz52200, zzz523, zzz524, zzz31, new_primPlusNat2(Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat3(new_primPlusNat1(zzz34200), zzz34200)), zzz34200))), Succ(zzz34200)), h)
new_mkVBalBranch3MkVBalBranch16(zzz1702, zzz1703, zzz1704, zzz1705, zzz1706, zzz1707, zzz1708, zzz1709, zzz1710, zzz1711, zzz1712, Zero, Succ(zzz17140), bd) → new_mkVBalBranch(zzz1712, zzz1711, Branch(zzz1702, zzz1703, Neg(Succ(zzz1704)), zzz1705, zzz1706), bd)
new_mkVBalBranch3MkVBalBranch10(zzz929, zzz930, zzz931, zzz932, zzz933, zzz934, zzz935, zzz936, zzz937, zzz938, zzz939, Zero, ba) → new_mkVBalBranch3MkVBalBranch11(zzz929, zzz930, zzz931, zzz932, zzz933, zzz934, zzz935, zzz936, zzz937, zzz938, zzz939, Zero, Succ(zzz936), ba)
new_mkVBalBranch3MkVBalBranch24(zzz340, zzz341, Neg(Succ(Succ(Succ(zzz3420000)))), zzz343, zzz344, zzz520, zzz521, Zero, zzz523, zzz524, zzz31, Succ(Succ(zzz6900)), h) → new_mkVBalBranch3MkVBalBranch26(zzz340, zzz341, Succ(Succ(zzz3420000)), zzz343, zzz344, zzz520, zzz521, zzz523, zzz524, zzz31, Succ(zzz3420000), Succ(zzz6900), h)
new_mkVBalBranch3MkVBalBranch15(zzz537, zzz538, zzz539, zzz540, zzz541, zzz542, zzz543, zzz544, zzz545, zzz546, zzz547, Succ(zzz6990), bc) → new_mkVBalBranch3MkVBalBranch16(zzz537, zzz538, zzz539, zzz540, zzz541, zzz542, zzz543, Succ(zzz544), zzz545, zzz546, zzz547, Succ(Succ(zzz544)), Succ(zzz6990), bc)
new_mkVBalBranch3MkVBalBranch25(zzz537, zzz538, zzz539, zzz540, zzz541, zzz542, zzz543, zzz544, zzz545, zzz546, zzz547, Zero, Zero, bc) → new_mkVBalBranch3MkVBalBranch211(zzz537, zzz538, zzz539, zzz540, zzz541, zzz542, zzz543, zzz544, zzz545, zzz546, zzz547, bc)
new_mkVBalBranch3MkVBalBranch212(zzz818, zzz819, zzz820, zzz821, zzz822, zzz823, zzz824, zzz825, zzz826, zzz827, bf) → new_mkVBalBranch3MkVBalBranch14(zzz818, zzz819, zzz820, zzz821, zzz822, zzz823, zzz824, zzz825, zzz826, zzz827, new_primPlusNat2(Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat3(new_primPlusNat1(zzz820), zzz820)), zzz820))), Succ(zzz820)), bf)

The TRS R consists of the following rules:

new_primPlusNat1(Zero) → Zero
new_primPlusNat1(Succ(zzz62000)) → Succ(Succ(new_primPlusNat1(zzz62000)))
new_primPlusNat3(zzz90, Succ(zzz910)) → Succ(Succ(new_primPlusNat2(zzz90, zzz910)))
new_primPlusNat3(zzz90, Zero) → Succ(zzz90)
new_primPlusNat2(Succ(zzz900), Succ(zzz9100)) → Succ(Succ(new_primPlusNat2(zzz900, zzz9100)))
new_primPlusNat2(Zero, Succ(zzz9100)) → Succ(zzz9100)
new_primPlusNat2(Zero, Zero) → Zero
new_primPlusNat2(Succ(zzz900), Zero) → Succ(zzz900)

The set Q consists of the following terms:

new_primPlusNat2(Zero, Succ(x0))
new_primPlusNat3(x0, Succ(x1))
new_primPlusNat2(Succ(x0), Succ(x1))
new_primPlusNat3(x0, Zero)
new_primPlusNat1(Zero)
new_primPlusNat2(Zero, Zero)
new_primPlusNat1(Succ(x0))
new_primPlusNat2(Succ(x0), Zero)

We have to consider all minimal (P,Q,R)-chains.
By rewriting [15] the rule new_mkVBalBranch3MkVBalBranch211(zzz537, zzz538, zzz539, zzz540, zzz541, zzz542, zzz543, zzz544, zzz545, zzz546, zzz547, bc) → new_mkVBalBranch3MkVBalBranch15(zzz537, zzz538, zzz539, zzz540, zzz541, zzz542, zzz543, zzz544, zzz545, zzz546, zzz547, new_primPlusNat2(Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat3(new_primPlusNat1(zzz539), zzz539)), zzz539))), Succ(zzz539)), bc) at position [11] we obtained the following new rules:

new_mkVBalBranch3MkVBalBranch211(zzz537, zzz538, zzz539, zzz540, zzz541, zzz542, zzz543, zzz544, zzz545, zzz546, zzz547, bc) → new_mkVBalBranch3MkVBalBranch15(zzz537, zzz538, zzz539, zzz540, zzz541, zzz542, zzz543, zzz544, zzz545, zzz546, zzz547, Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat2(Succ(new_primPlusNat3(new_primPlusNat1(zzz539), zzz539)), zzz539)), zzz539))), bc)



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

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

new_mkVBalBranch3MkVBalBranch211(zzz537, zzz538, zzz539, zzz540, zzz541, zzz542, zzz543, zzz544, zzz545, zzz546, zzz547, bc) → new_mkVBalBranch3MkVBalBranch15(zzz537, zzz538, zzz539, zzz540, zzz541, zzz542, zzz543, zzz544, zzz545, zzz546, zzz547, Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat2(Succ(new_primPlusNat3(new_primPlusNat1(zzz539), zzz539)), zzz539)), zzz539))), bc)
new_mkVBalBranch(zzz31, Branch(zzz520, zzz521, Neg(Succ(zzz52200)), zzz523, zzz524), Branch(zzz340, zzz341, zzz342, zzz343, zzz344), h) → new_mkVBalBranch3MkVBalBranch24(zzz340, zzz341, zzz342, zzz343, zzz344, zzz520, zzz521, zzz52200, zzz523, zzz524, zzz31, Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat3(new_primPlusNat1(zzz52200), zzz52200)), zzz52200))), h)
new_mkVBalBranch3MkVBalBranch11(zzz2033, zzz2034, zzz2035, zzz2036, zzz2037, zzz2038, zzz2039, zzz2040, zzz2041, zzz2042, zzz2043, Zero, Succ(zzz20450), bb) → new_mkVBalBranch(zzz2043, zzz2042, Branch(zzz2033, zzz2034, Pos(Succ(zzz2035)), zzz2036, zzz2037), bb)
new_mkVBalBranch3MkVBalBranch23(zzz929, zzz930, zzz931, zzz932, zzz933, zzz934, zzz935, zzz936, zzz937, zzz938, zzz939, ba) → new_mkVBalBranch3MkVBalBranch10(zzz929, zzz930, zzz931, zzz932, zzz933, zzz934, zzz935, zzz936, zzz937, zzz938, zzz939, new_primPlusNat2(Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat3(new_primPlusNat1(zzz931), zzz931)), zzz931))), Succ(zzz931)), ba)
new_mkVBalBranch3MkVBalBranch26(zzz1133, zzz1134, zzz1135, zzz1136, zzz1137, zzz1138, zzz1139, zzz1140, zzz1141, zzz1142, Succ(zzz11430), Succ(zzz11440), be) → new_mkVBalBranch3MkVBalBranch26(zzz1133, zzz1134, zzz1135, zzz1136, zzz1137, zzz1138, zzz1139, zzz1140, zzz1141, zzz1142, zzz11430, zzz11440, be)
new_mkVBalBranch3MkVBalBranch24(zzz340, zzz341, Pos(zzz3420), zzz343, zzz344, zzz520, zzz521, zzz52200, zzz523, zzz524, zzz31, Succ(zzz690), h) → new_mkVBalBranch(zzz31, Branch(zzz520, zzz521, Neg(Succ(zzz52200)), zzz523, zzz524), zzz343, h)
new_mkVBalBranch3MkVBalBranch12(zzz340, zzz341, zzz34200, zzz343, zzz344, zzz520, zzz521, zzz523, zzz524, zzz31, Succ(zzz1250), h) → new_mkVBalBranch(zzz31, zzz524, Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), h)
new_mkVBalBranch3MkVBalBranch20(zzz929, zzz930, zzz931, zzz932, zzz933, zzz934, zzz935, zzz936, zzz937, zzz938, zzz939, Zero, Succ(zzz9410), ba) → new_mkVBalBranch(zzz939, Branch(zzz934, zzz935, Pos(Succ(zzz936)), zzz937, zzz938), zzz932, ba)
new_mkVBalBranch3MkVBalBranch24(zzz340, zzz341, Neg(Succ(Succ(Zero))), zzz343, zzz344, zzz520, zzz521, Zero, zzz523, zzz524, zzz31, Succ(Succ(zzz6900)), h) → new_mkVBalBranch3MkVBalBranch26(zzz340, zzz341, Succ(Zero), zzz343, zzz344, zzz520, zzz521, zzz523, zzz524, zzz31, Zero, Succ(zzz6900), h)
new_mkVBalBranch3MkVBalBranch17(zzz340, zzz341, zzz34200, zzz343, zzz344, zzz520, zzz521, zzz52200, zzz523, zzz524, zzz31, h) → new_mkVBalBranch(zzz31, zzz524, Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), h)
new_mkVBalBranch3MkVBalBranch26(zzz1133, zzz1134, zzz1135, zzz1136, zzz1137, zzz1138, zzz1139, zzz1140, zzz1141, zzz1142, Zero, Zero, be) → new_mkVBalBranch3MkVBalBranch29(zzz1133, zzz1134, zzz1135, zzz1136, zzz1137, zzz1138, zzz1139, zzz1140, zzz1141, zzz1142, be)
new_mkVBalBranch3MkVBalBranch1(zzz340, zzz341, zzz34200, zzz343, zzz344, zzz520, zzz521, zzz52200, zzz523, zzz524, zzz31, Succ(zzz1430), h) → new_mkVBalBranch(zzz31, zzz524, Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), h)
new_mkVBalBranch3MkVBalBranch24(zzz340, zzz341, Neg(Succ(Zero)), zzz343, zzz344, zzz520, zzz521, zzz52200, zzz523, zzz524, zzz31, Succ(zzz690), h) → new_mkVBalBranch(zzz31, Branch(zzz520, zzz521, Neg(Succ(zzz52200)), zzz523, zzz524), zzz343, h)
new_mkVBalBranch3MkVBalBranch20(zzz929, zzz930, zzz931, zzz932, zzz933, zzz934, zzz935, zzz936, zzz937, zzz938, zzz939, Zero, Zero, ba) → new_mkVBalBranch3MkVBalBranch23(zzz929, zzz930, zzz931, zzz932, zzz933, zzz934, zzz935, zzz936, zzz937, zzz938, zzz939, ba)
new_mkVBalBranch3MkVBalBranch13(zzz340, zzz341, zzz34200, zzz343, zzz344, zzz520, zzz521, zzz523, zzz524, zzz31, Succ(zzz1290), h) → new_mkVBalBranch(zzz31, zzz524, Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), h)
new_mkVBalBranch3MkVBalBranch2(zzz340, zzz341, Pos(Succ(zzz34200)), zzz343, zzz344, zzz520, zzz521, zzz52200, zzz523, zzz524, zzz31, Succ(zzz680), h) → new_mkVBalBranch3MkVBalBranch20(zzz340, zzz341, zzz34200, zzz343, zzz344, zzz520, zzz521, zzz52200, zzz523, zzz524, zzz31, Succ(new_primPlusNat2(zzz680, zzz52200)), zzz34200, h)
new_mkVBalBranch(zzz31, Branch(zzz520, zzz521, Neg(Zero), zzz523, zzz524), Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), h) → new_mkVBalBranch3MkVBalBranch13(zzz340, zzz341, zzz34200, zzz343, zzz344, zzz520, zzz521, zzz523, zzz524, zzz31, new_primPlusNat2(Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat3(new_primPlusNat1(zzz34200), zzz34200)), zzz34200))), Succ(zzz34200)), h)
new_mkVBalBranch(zzz31, Branch(zzz520, zzz521, Neg(Zero), zzz523, zzz524), Branch(zzz340, zzz341, Pos(Succ(zzz34200)), zzz343, zzz344), h) → new_mkVBalBranch(zzz31, Branch(zzz520, zzz521, Neg(Zero), zzz523, zzz524), zzz343, h)
new_mkVBalBranch3MkVBalBranch24(zzz340, zzz341, Neg(Zero), zzz343, zzz344, zzz520, zzz521, zzz52200, zzz523, zzz524, zzz31, Succ(zzz690), h) → new_mkVBalBranch(zzz31, Branch(zzz520, zzz521, Neg(Succ(zzz52200)), zzz523, zzz524), zzz343, h)
new_mkVBalBranch3MkVBalBranch20(zzz929, zzz930, zzz931, zzz932, zzz933, zzz934, zzz935, zzz936, zzz937, zzz938, zzz939, Succ(zzz9400), Succ(zzz9410), ba) → new_mkVBalBranch3MkVBalBranch20(zzz929, zzz930, zzz931, zzz932, zzz933, zzz934, zzz935, zzz936, zzz937, zzz938, zzz939, zzz9400, zzz9410, ba)
new_mkVBalBranch3MkVBalBranch1(zzz340, zzz341, zzz34200, zzz343, zzz344, zzz520, zzz521, zzz52200, zzz523, zzz524, zzz31, Zero, h) → new_mkVBalBranch3MkVBalBranch17(zzz340, zzz341, zzz34200, zzz343, zzz344, zzz520, zzz521, zzz52200, zzz523, zzz524, zzz31, h)
new_mkVBalBranch3MkVBalBranch26(zzz1133, zzz1134, zzz1135, zzz1136, zzz1137, zzz1138, zzz1139, zzz1140, zzz1141, zzz1142, Succ(zzz11430), Zero, be) → new_mkVBalBranch3MkVBalBranch212(zzz1133, zzz1134, zzz1135, zzz1136, zzz1137, zzz1138, zzz1139, zzz1140, zzz1141, zzz1142, be)
new_mkVBalBranch3MkVBalBranch16(zzz1702, zzz1703, zzz1704, zzz1705, zzz1706, zzz1707, zzz1708, zzz1709, zzz1710, zzz1711, zzz1712, Succ(zzz17130), Succ(zzz17140), bd) → new_mkVBalBranch3MkVBalBranch16(zzz1702, zzz1703, zzz1704, zzz1705, zzz1706, zzz1707, zzz1708, zzz1709, zzz1710, zzz1711, zzz1712, zzz17130, zzz17140, bd)
new_mkVBalBranch3MkVBalBranch25(zzz537, zzz538, zzz539, zzz540, zzz541, zzz542, zzz543, zzz544, zzz545, zzz546, zzz547, Zero, Succ(zzz5490), bc) → new_mkVBalBranch(zzz547, Branch(zzz542, zzz543, Neg(Succ(Succ(zzz544))), zzz545, zzz546), zzz540, bc)
new_mkVBalBranch3MkVBalBranch11(zzz2033, zzz2034, zzz2035, zzz2036, zzz2037, zzz2038, zzz2039, zzz2040, zzz2041, zzz2042, zzz2043, Succ(zzz20440), Succ(zzz20450), bb) → new_mkVBalBranch3MkVBalBranch11(zzz2033, zzz2034, zzz2035, zzz2036, zzz2037, zzz2038, zzz2039, zzz2040, zzz2041, zzz2042, zzz2043, zzz20440, zzz20450, bb)
new_mkVBalBranch3MkVBalBranch25(zzz537, zzz538, zzz539, zzz540, zzz541, zzz542, zzz543, zzz544, zzz545, zzz546, zzz547, Succ(zzz5480), Zero, bc) → new_mkVBalBranch3MkVBalBranch15(zzz537, zzz538, zzz539, zzz540, zzz541, zzz542, zzz543, zzz544, zzz545, zzz546, zzz547, new_primPlusNat2(Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat3(new_primPlusNat1(zzz539), zzz539)), zzz539))), Succ(zzz539)), bc)
new_mkVBalBranch3MkVBalBranch25(zzz537, zzz538, zzz539, zzz540, zzz541, zzz542, zzz543, zzz544, zzz545, zzz546, zzz547, Succ(zzz5480), Succ(zzz5490), bc) → new_mkVBalBranch3MkVBalBranch25(zzz537, zzz538, zzz539, zzz540, zzz541, zzz542, zzz543, zzz544, zzz545, zzz546, zzz547, zzz5480, zzz5490, bc)
new_mkVBalBranch3MkVBalBranch29(zzz818, zzz819, zzz820, zzz821, zzz822, zzz823, zzz824, zzz825, zzz826, zzz827, bf) → new_mkVBalBranch3MkVBalBranch14(zzz818, zzz819, zzz820, zzz821, zzz822, zzz823, zzz824, zzz825, zzz826, zzz827, new_primPlusNat2(new_primPlusNat3(Succ(new_primPlusNat3(new_primPlusNat1(zzz820), zzz820)), Succ(zzz820)), Succ(zzz820)), bf)
new_mkVBalBranch(zzz31, Branch(zzz520, zzz521, Pos(Succ(zzz52200)), zzz523, zzz524), Branch(zzz340, zzz341, zzz342, zzz343, zzz344), h) → new_mkVBalBranch3MkVBalBranch2(zzz340, zzz341, zzz342, zzz343, zzz344, zzz520, zzz521, zzz52200, zzz523, zzz524, zzz31, Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat3(new_primPlusNat1(zzz52200), zzz52200)), zzz52200))), h)
new_mkVBalBranch3MkVBalBranch10(zzz929, zzz930, zzz931, zzz932, zzz933, zzz934, zzz935, zzz936, zzz937, zzz938, zzz939, Succ(zzz10020), ba) → new_mkVBalBranch3MkVBalBranch11(zzz929, zzz930, zzz931, zzz932, zzz933, zzz934, zzz935, zzz936, zzz937, zzz938, zzz939, Succ(zzz10020), Succ(zzz936), ba)
new_mkVBalBranch3MkVBalBranch14(zzz818, zzz819, zzz820, zzz821, zzz822, zzz823, zzz824, zzz825, zzz826, zzz827, Succ(zzz8960), bf) → new_mkVBalBranch3MkVBalBranch16(zzz818, zzz819, zzz820, zzz821, zzz822, zzz823, zzz824, Zero, zzz825, zzz826, zzz827, Succ(Zero), Succ(zzz8960), bf)
new_mkVBalBranch3MkVBalBranch24(zzz340, zzz341, Neg(Succ(Succ(Succ(zzz3420000)))), zzz343, zzz344, zzz520, zzz521, Succ(zzz522000), zzz523, zzz524, zzz31, Succ(Succ(zzz6900)), h) → new_mkVBalBranch3MkVBalBranch25(zzz340, zzz341, Succ(Succ(zzz3420000)), zzz343, zzz344, zzz520, zzz521, zzz522000, zzz523, zzz524, zzz31, Succ(zzz3420000), Succ(Succ(new_primPlusNat2(zzz6900, zzz522000))), h)
new_mkVBalBranch3MkVBalBranch26(zzz1133, zzz1134, zzz1135, zzz1136, zzz1137, zzz1138, zzz1139, zzz1140, zzz1141, zzz1142, Zero, Succ(zzz11440), be) → new_mkVBalBranch(zzz1142, Branch(zzz1138, zzz1139, Neg(Succ(Zero)), zzz1140, zzz1141), zzz1136, be)
new_mkVBalBranch3MkVBalBranch24(zzz340, zzz341, Neg(Succ(Succ(Zero))), zzz343, zzz344, zzz520, zzz521, Succ(zzz522000), zzz523, zzz524, zzz31, Succ(Succ(zzz6900)), h) → new_mkVBalBranch3MkVBalBranch25(zzz340, zzz341, Succ(Zero), zzz343, zzz344, zzz520, zzz521, zzz522000, zzz523, zzz524, zzz31, Zero, Succ(Succ(new_primPlusNat2(zzz6900, zzz522000))), h)
new_mkVBalBranch(zzz31, Branch(zzz520, zzz521, Pos(Zero), zzz523, zzz524), Branch(zzz340, zzz341, Pos(Succ(zzz34200)), zzz343, zzz344), h) → new_mkVBalBranch(zzz31, Branch(zzz520, zzz521, Pos(Zero), zzz523, zzz524), zzz343, h)
new_mkVBalBranch3MkVBalBranch20(zzz929, zzz930, zzz931, zzz932, zzz933, zzz934, zzz935, zzz936, zzz937, zzz938, zzz939, Succ(zzz9400), Zero, ba) → new_mkVBalBranch3MkVBalBranch10(zzz929, zzz930, zzz931, zzz932, zzz933, zzz934, zzz935, zzz936, zzz937, zzz938, zzz939, new_primPlusNat2(new_primPlusNat3(Succ(new_primPlusNat3(new_primPlusNat1(zzz931), zzz931)), Succ(zzz931)), Succ(zzz931)), ba)
new_mkVBalBranch(zzz31, Branch(zzz520, zzz521, Pos(Zero), zzz523, zzz524), Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), h) → new_mkVBalBranch3MkVBalBranch12(zzz340, zzz341, zzz34200, zzz343, zzz344, zzz520, zzz521, zzz523, zzz524, zzz31, new_primPlusNat2(Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat3(new_primPlusNat1(zzz34200), zzz34200)), zzz34200))), Succ(zzz34200)), h)
new_mkVBalBranch3MkVBalBranch2(zzz340, zzz341, Pos(Zero), zzz343, zzz344, zzz520, zzz521, zzz52200, zzz523, zzz524, zzz31, Succ(zzz680), h) → new_mkVBalBranch(zzz31, zzz524, Branch(zzz340, zzz341, Pos(Zero), zzz343, zzz344), h)
new_mkVBalBranch3MkVBalBranch2(zzz340, zzz341, Neg(Zero), zzz343, zzz344, zzz520, zzz521, zzz52200, zzz523, zzz524, zzz31, Succ(zzz680), h) → new_mkVBalBranch(zzz31, zzz524, Branch(zzz340, zzz341, Neg(Zero), zzz343, zzz344), h)
new_mkVBalBranch3MkVBalBranch2(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344, zzz520, zzz521, zzz52200, zzz523, zzz524, zzz31, Succ(zzz680), h) → new_mkVBalBranch3MkVBalBranch1(zzz340, zzz341, zzz34200, zzz343, zzz344, zzz520, zzz521, zzz52200, zzz523, zzz524, zzz31, new_primPlusNat2(Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat3(new_primPlusNat1(zzz34200), zzz34200)), zzz34200))), Succ(zzz34200)), h)
new_mkVBalBranch3MkVBalBranch16(zzz1702, zzz1703, zzz1704, zzz1705, zzz1706, zzz1707, zzz1708, zzz1709, zzz1710, zzz1711, zzz1712, Zero, Succ(zzz17140), bd) → new_mkVBalBranch(zzz1712, zzz1711, Branch(zzz1702, zzz1703, Neg(Succ(zzz1704)), zzz1705, zzz1706), bd)
new_mkVBalBranch3MkVBalBranch15(zzz537, zzz538, zzz539, zzz540, zzz541, zzz542, zzz543, zzz544, zzz545, zzz546, zzz547, Succ(zzz6990), bc) → new_mkVBalBranch3MkVBalBranch16(zzz537, zzz538, zzz539, zzz540, zzz541, zzz542, zzz543, Succ(zzz544), zzz545, zzz546, zzz547, Succ(Succ(zzz544)), Succ(zzz6990), bc)
new_mkVBalBranch3MkVBalBranch24(zzz340, zzz341, Neg(Succ(Succ(Succ(zzz3420000)))), zzz343, zzz344, zzz520, zzz521, Zero, zzz523, zzz524, zzz31, Succ(Succ(zzz6900)), h) → new_mkVBalBranch3MkVBalBranch26(zzz340, zzz341, Succ(Succ(zzz3420000)), zzz343, zzz344, zzz520, zzz521, zzz523, zzz524, zzz31, Succ(zzz3420000), Succ(zzz6900), h)
new_mkVBalBranch3MkVBalBranch10(zzz929, zzz930, zzz931, zzz932, zzz933, zzz934, zzz935, zzz936, zzz937, zzz938, zzz939, Zero, ba) → new_mkVBalBranch3MkVBalBranch11(zzz929, zzz930, zzz931, zzz932, zzz933, zzz934, zzz935, zzz936, zzz937, zzz938, zzz939, Zero, Succ(zzz936), ba)
new_mkVBalBranch3MkVBalBranch25(zzz537, zzz538, zzz539, zzz540, zzz541, zzz542, zzz543, zzz544, zzz545, zzz546, zzz547, Zero, Zero, bc) → new_mkVBalBranch3MkVBalBranch211(zzz537, zzz538, zzz539, zzz540, zzz541, zzz542, zzz543, zzz544, zzz545, zzz546, zzz547, bc)
new_mkVBalBranch3MkVBalBranch212(zzz818, zzz819, zzz820, zzz821, zzz822, zzz823, zzz824, zzz825, zzz826, zzz827, bf) → new_mkVBalBranch3MkVBalBranch14(zzz818, zzz819, zzz820, zzz821, zzz822, zzz823, zzz824, zzz825, zzz826, zzz827, new_primPlusNat2(Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat3(new_primPlusNat1(zzz820), zzz820)), zzz820))), Succ(zzz820)), bf)

The TRS R consists of the following rules:

new_primPlusNat1(Zero) → Zero
new_primPlusNat1(Succ(zzz62000)) → Succ(Succ(new_primPlusNat1(zzz62000)))
new_primPlusNat3(zzz90, Succ(zzz910)) → Succ(Succ(new_primPlusNat2(zzz90, zzz910)))
new_primPlusNat3(zzz90, Zero) → Succ(zzz90)
new_primPlusNat2(Succ(zzz900), Succ(zzz9100)) → Succ(Succ(new_primPlusNat2(zzz900, zzz9100)))
new_primPlusNat2(Zero, Succ(zzz9100)) → Succ(zzz9100)
new_primPlusNat2(Zero, Zero) → Zero
new_primPlusNat2(Succ(zzz900), Zero) → Succ(zzz900)

The set Q consists of the following terms:

new_primPlusNat2(Zero, Succ(x0))
new_primPlusNat3(x0, Succ(x1))
new_primPlusNat2(Succ(x0), Succ(x1))
new_primPlusNat3(x0, Zero)
new_primPlusNat1(Zero)
new_primPlusNat2(Zero, Zero)
new_primPlusNat1(Succ(x0))
new_primPlusNat2(Succ(x0), Zero)

We have to consider all minimal (P,Q,R)-chains.
By rewriting [15] the rule new_mkVBalBranch3MkVBalBranch25(zzz537, zzz538, zzz539, zzz540, zzz541, zzz542, zzz543, zzz544, zzz545, zzz546, zzz547, Succ(zzz5480), Zero, bc) → new_mkVBalBranch3MkVBalBranch15(zzz537, zzz538, zzz539, zzz540, zzz541, zzz542, zzz543, zzz544, zzz545, zzz546, zzz547, new_primPlusNat2(Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat3(new_primPlusNat1(zzz539), zzz539)), zzz539))), Succ(zzz539)), bc) at position [11] we obtained the following new rules:

new_mkVBalBranch3MkVBalBranch25(zzz537, zzz538, zzz539, zzz540, zzz541, zzz542, zzz543, zzz544, zzz545, zzz546, zzz547, Succ(zzz5480), Zero, bc) → new_mkVBalBranch3MkVBalBranch15(zzz537, zzz538, zzz539, zzz540, zzz541, zzz542, zzz543, zzz544, zzz545, zzz546, zzz547, Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat2(Succ(new_primPlusNat3(new_primPlusNat1(zzz539), zzz539)), zzz539)), zzz539))), bc)



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

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

new_mkVBalBranch3MkVBalBranch23(zzz929, zzz930, zzz931, zzz932, zzz933, zzz934, zzz935, zzz936, zzz937, zzz938, zzz939, ba) → new_mkVBalBranch3MkVBalBranch10(zzz929, zzz930, zzz931, zzz932, zzz933, zzz934, zzz935, zzz936, zzz937, zzz938, zzz939, new_primPlusNat2(Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat3(new_primPlusNat1(zzz931), zzz931)), zzz931))), Succ(zzz931)), ba)
new_mkVBalBranch3MkVBalBranch11(zzz2033, zzz2034, zzz2035, zzz2036, zzz2037, zzz2038, zzz2039, zzz2040, zzz2041, zzz2042, zzz2043, Zero, Succ(zzz20450), bb) → new_mkVBalBranch(zzz2043, zzz2042, Branch(zzz2033, zzz2034, Pos(Succ(zzz2035)), zzz2036, zzz2037), bb)
new_mkVBalBranch(zzz31, Branch(zzz520, zzz521, Neg(Succ(zzz52200)), zzz523, zzz524), Branch(zzz340, zzz341, zzz342, zzz343, zzz344), h) → new_mkVBalBranch3MkVBalBranch24(zzz340, zzz341, zzz342, zzz343, zzz344, zzz520, zzz521, zzz52200, zzz523, zzz524, zzz31, Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat3(new_primPlusNat1(zzz52200), zzz52200)), zzz52200))), h)
new_mkVBalBranch3MkVBalBranch211(zzz537, zzz538, zzz539, zzz540, zzz541, zzz542, zzz543, zzz544, zzz545, zzz546, zzz547, bc) → new_mkVBalBranch3MkVBalBranch15(zzz537, zzz538, zzz539, zzz540, zzz541, zzz542, zzz543, zzz544, zzz545, zzz546, zzz547, Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat2(Succ(new_primPlusNat3(new_primPlusNat1(zzz539), zzz539)), zzz539)), zzz539))), bc)
new_mkVBalBranch3MkVBalBranch26(zzz1133, zzz1134, zzz1135, zzz1136, zzz1137, zzz1138, zzz1139, zzz1140, zzz1141, zzz1142, Succ(zzz11430), Succ(zzz11440), be) → new_mkVBalBranch3MkVBalBranch26(zzz1133, zzz1134, zzz1135, zzz1136, zzz1137, zzz1138, zzz1139, zzz1140, zzz1141, zzz1142, zzz11430, zzz11440, be)
new_mkVBalBranch3MkVBalBranch24(zzz340, zzz341, Pos(zzz3420), zzz343, zzz344, zzz520, zzz521, zzz52200, zzz523, zzz524, zzz31, Succ(zzz690), h) → new_mkVBalBranch(zzz31, Branch(zzz520, zzz521, Neg(Succ(zzz52200)), zzz523, zzz524), zzz343, h)
new_mkVBalBranch3MkVBalBranch12(zzz340, zzz341, zzz34200, zzz343, zzz344, zzz520, zzz521, zzz523, zzz524, zzz31, Succ(zzz1250), h) → new_mkVBalBranch(zzz31, zzz524, Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), h)
new_mkVBalBranch3MkVBalBranch25(zzz537, zzz538, zzz539, zzz540, zzz541, zzz542, zzz543, zzz544, zzz545, zzz546, zzz547, Succ(zzz5480), Zero, bc) → new_mkVBalBranch3MkVBalBranch15(zzz537, zzz538, zzz539, zzz540, zzz541, zzz542, zzz543, zzz544, zzz545, zzz546, zzz547, Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat2(Succ(new_primPlusNat3(new_primPlusNat1(zzz539), zzz539)), zzz539)), zzz539))), bc)
new_mkVBalBranch3MkVBalBranch20(zzz929, zzz930, zzz931, zzz932, zzz933, zzz934, zzz935, zzz936, zzz937, zzz938, zzz939, Zero, Succ(zzz9410), ba) → new_mkVBalBranch(zzz939, Branch(zzz934, zzz935, Pos(Succ(zzz936)), zzz937, zzz938), zzz932, ba)
new_mkVBalBranch3MkVBalBranch24(zzz340, zzz341, Neg(Succ(Succ(Zero))), zzz343, zzz344, zzz520, zzz521, Zero, zzz523, zzz524, zzz31, Succ(Succ(zzz6900)), h) → new_mkVBalBranch3MkVBalBranch26(zzz340, zzz341, Succ(Zero), zzz343, zzz344, zzz520, zzz521, zzz523, zzz524, zzz31, Zero, Succ(zzz6900), h)
new_mkVBalBranch3MkVBalBranch17(zzz340, zzz341, zzz34200, zzz343, zzz344, zzz520, zzz521, zzz52200, zzz523, zzz524, zzz31, h) → new_mkVBalBranch(zzz31, zzz524, Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), h)
new_mkVBalBranch3MkVBalBranch1(zzz340, zzz341, zzz34200, zzz343, zzz344, zzz520, zzz521, zzz52200, zzz523, zzz524, zzz31, Succ(zzz1430), h) → new_mkVBalBranch(zzz31, zzz524, Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), h)
new_mkVBalBranch3MkVBalBranch26(zzz1133, zzz1134, zzz1135, zzz1136, zzz1137, zzz1138, zzz1139, zzz1140, zzz1141, zzz1142, Zero, Zero, be) → new_mkVBalBranch3MkVBalBranch29(zzz1133, zzz1134, zzz1135, zzz1136, zzz1137, zzz1138, zzz1139, zzz1140, zzz1141, zzz1142, be)
new_mkVBalBranch3MkVBalBranch20(zzz929, zzz930, zzz931, zzz932, zzz933, zzz934, zzz935, zzz936, zzz937, zzz938, zzz939, Zero, Zero, ba) → new_mkVBalBranch3MkVBalBranch23(zzz929, zzz930, zzz931, zzz932, zzz933, zzz934, zzz935, zzz936, zzz937, zzz938, zzz939, ba)
new_mkVBalBranch3MkVBalBranch24(zzz340, zzz341, Neg(Succ(Zero)), zzz343, zzz344, zzz520, zzz521, zzz52200, zzz523, zzz524, zzz31, Succ(zzz690), h) → new_mkVBalBranch(zzz31, Branch(zzz520, zzz521, Neg(Succ(zzz52200)), zzz523, zzz524), zzz343, h)
new_mkVBalBranch3MkVBalBranch13(zzz340, zzz341, zzz34200, zzz343, zzz344, zzz520, zzz521, zzz523, zzz524, zzz31, Succ(zzz1290), h) → new_mkVBalBranch(zzz31, zzz524, Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), h)
new_mkVBalBranch3MkVBalBranch2(zzz340, zzz341, Pos(Succ(zzz34200)), zzz343, zzz344, zzz520, zzz521, zzz52200, zzz523, zzz524, zzz31, Succ(zzz680), h) → new_mkVBalBranch3MkVBalBranch20(zzz340, zzz341, zzz34200, zzz343, zzz344, zzz520, zzz521, zzz52200, zzz523, zzz524, zzz31, Succ(new_primPlusNat2(zzz680, zzz52200)), zzz34200, h)
new_mkVBalBranch(zzz31, Branch(zzz520, zzz521, Neg(Zero), zzz523, zzz524), Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), h) → new_mkVBalBranch3MkVBalBranch13(zzz340, zzz341, zzz34200, zzz343, zzz344, zzz520, zzz521, zzz523, zzz524, zzz31, new_primPlusNat2(Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat3(new_primPlusNat1(zzz34200), zzz34200)), zzz34200))), Succ(zzz34200)), h)
new_mkVBalBranch3MkVBalBranch24(zzz340, zzz341, Neg(Zero), zzz343, zzz344, zzz520, zzz521, zzz52200, zzz523, zzz524, zzz31, Succ(zzz690), h) → new_mkVBalBranch(zzz31, Branch(zzz520, zzz521, Neg(Succ(zzz52200)), zzz523, zzz524), zzz343, h)
new_mkVBalBranch(zzz31, Branch(zzz520, zzz521, Neg(Zero), zzz523, zzz524), Branch(zzz340, zzz341, Pos(Succ(zzz34200)), zzz343, zzz344), h) → new_mkVBalBranch(zzz31, Branch(zzz520, zzz521, Neg(Zero), zzz523, zzz524), zzz343, h)
new_mkVBalBranch3MkVBalBranch20(zzz929, zzz930, zzz931, zzz932, zzz933, zzz934, zzz935, zzz936, zzz937, zzz938, zzz939, Succ(zzz9400), Succ(zzz9410), ba) → new_mkVBalBranch3MkVBalBranch20(zzz929, zzz930, zzz931, zzz932, zzz933, zzz934, zzz935, zzz936, zzz937, zzz938, zzz939, zzz9400, zzz9410, ba)
new_mkVBalBranch3MkVBalBranch26(zzz1133, zzz1134, zzz1135, zzz1136, zzz1137, zzz1138, zzz1139, zzz1140, zzz1141, zzz1142, Succ(zzz11430), Zero, be) → new_mkVBalBranch3MkVBalBranch212(zzz1133, zzz1134, zzz1135, zzz1136, zzz1137, zzz1138, zzz1139, zzz1140, zzz1141, zzz1142, be)
new_mkVBalBranch3MkVBalBranch1(zzz340, zzz341, zzz34200, zzz343, zzz344, zzz520, zzz521, zzz52200, zzz523, zzz524, zzz31, Zero, h) → new_mkVBalBranch3MkVBalBranch17(zzz340, zzz341, zzz34200, zzz343, zzz344, zzz520, zzz521, zzz52200, zzz523, zzz524, zzz31, h)
new_mkVBalBranch3MkVBalBranch16(zzz1702, zzz1703, zzz1704, zzz1705, zzz1706, zzz1707, zzz1708, zzz1709, zzz1710, zzz1711, zzz1712, Succ(zzz17130), Succ(zzz17140), bd) → new_mkVBalBranch3MkVBalBranch16(zzz1702, zzz1703, zzz1704, zzz1705, zzz1706, zzz1707, zzz1708, zzz1709, zzz1710, zzz1711, zzz1712, zzz17130, zzz17140, bd)
new_mkVBalBranch3MkVBalBranch25(zzz537, zzz538, zzz539, zzz540, zzz541, zzz542, zzz543, zzz544, zzz545, zzz546, zzz547, Zero, Succ(zzz5490), bc) → new_mkVBalBranch(zzz547, Branch(zzz542, zzz543, Neg(Succ(Succ(zzz544))), zzz545, zzz546), zzz540, bc)
new_mkVBalBranch3MkVBalBranch11(zzz2033, zzz2034, zzz2035, zzz2036, zzz2037, zzz2038, zzz2039, zzz2040, zzz2041, zzz2042, zzz2043, Succ(zzz20440), Succ(zzz20450), bb) → new_mkVBalBranch3MkVBalBranch11(zzz2033, zzz2034, zzz2035, zzz2036, zzz2037, zzz2038, zzz2039, zzz2040, zzz2041, zzz2042, zzz2043, zzz20440, zzz20450, bb)
new_mkVBalBranch3MkVBalBranch25(zzz537, zzz538, zzz539, zzz540, zzz541, zzz542, zzz543, zzz544, zzz545, zzz546, zzz547, Succ(zzz5480), Succ(zzz5490), bc) → new_mkVBalBranch3MkVBalBranch25(zzz537, zzz538, zzz539, zzz540, zzz541, zzz542, zzz543, zzz544, zzz545, zzz546, zzz547, zzz5480, zzz5490, bc)
new_mkVBalBranch3MkVBalBranch29(zzz818, zzz819, zzz820, zzz821, zzz822, zzz823, zzz824, zzz825, zzz826, zzz827, bf) → new_mkVBalBranch3MkVBalBranch14(zzz818, zzz819, zzz820, zzz821, zzz822, zzz823, zzz824, zzz825, zzz826, zzz827, new_primPlusNat2(new_primPlusNat3(Succ(new_primPlusNat3(new_primPlusNat1(zzz820), zzz820)), Succ(zzz820)), Succ(zzz820)), bf)
new_mkVBalBranch3MkVBalBranch10(zzz929, zzz930, zzz931, zzz932, zzz933, zzz934, zzz935, zzz936, zzz937, zzz938, zzz939, Succ(zzz10020), ba) → new_mkVBalBranch3MkVBalBranch11(zzz929, zzz930, zzz931, zzz932, zzz933, zzz934, zzz935, zzz936, zzz937, zzz938, zzz939, Succ(zzz10020), Succ(zzz936), ba)
new_mkVBalBranch(zzz31, Branch(zzz520, zzz521, Pos(Succ(zzz52200)), zzz523, zzz524), Branch(zzz340, zzz341, zzz342, zzz343, zzz344), h) → new_mkVBalBranch3MkVBalBranch2(zzz340, zzz341, zzz342, zzz343, zzz344, zzz520, zzz521, zzz52200, zzz523, zzz524, zzz31, Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat3(new_primPlusNat1(zzz52200), zzz52200)), zzz52200))), h)
new_mkVBalBranch3MkVBalBranch14(zzz818, zzz819, zzz820, zzz821, zzz822, zzz823, zzz824, zzz825, zzz826, zzz827, Succ(zzz8960), bf) → new_mkVBalBranch3MkVBalBranch16(zzz818, zzz819, zzz820, zzz821, zzz822, zzz823, zzz824, Zero, zzz825, zzz826, zzz827, Succ(Zero), Succ(zzz8960), bf)
new_mkVBalBranch3MkVBalBranch26(zzz1133, zzz1134, zzz1135, zzz1136, zzz1137, zzz1138, zzz1139, zzz1140, zzz1141, zzz1142, Zero, Succ(zzz11440), be) → new_mkVBalBranch(zzz1142, Branch(zzz1138, zzz1139, Neg(Succ(Zero)), zzz1140, zzz1141), zzz1136, be)
new_mkVBalBranch3MkVBalBranch24(zzz340, zzz341, Neg(Succ(Succ(Succ(zzz3420000)))), zzz343, zzz344, zzz520, zzz521, Succ(zzz522000), zzz523, zzz524, zzz31, Succ(Succ(zzz6900)), h) → new_mkVBalBranch3MkVBalBranch25(zzz340, zzz341, Succ(Succ(zzz3420000)), zzz343, zzz344, zzz520, zzz521, zzz522000, zzz523, zzz524, zzz31, Succ(zzz3420000), Succ(Succ(new_primPlusNat2(zzz6900, zzz522000))), h)
new_mkVBalBranch3MkVBalBranch24(zzz340, zzz341, Neg(Succ(Succ(Zero))), zzz343, zzz344, zzz520, zzz521, Succ(zzz522000), zzz523, zzz524, zzz31, Succ(Succ(zzz6900)), h) → new_mkVBalBranch3MkVBalBranch25(zzz340, zzz341, Succ(Zero), zzz343, zzz344, zzz520, zzz521, zzz522000, zzz523, zzz524, zzz31, Zero, Succ(Succ(new_primPlusNat2(zzz6900, zzz522000))), h)
new_mkVBalBranch3MkVBalBranch20(zzz929, zzz930, zzz931, zzz932, zzz933, zzz934, zzz935, zzz936, zzz937, zzz938, zzz939, Succ(zzz9400), Zero, ba) → new_mkVBalBranch3MkVBalBranch10(zzz929, zzz930, zzz931, zzz932, zzz933, zzz934, zzz935, zzz936, zzz937, zzz938, zzz939, new_primPlusNat2(new_primPlusNat3(Succ(new_primPlusNat3(new_primPlusNat1(zzz931), zzz931)), Succ(zzz931)), Succ(zzz931)), ba)
new_mkVBalBranch(zzz31, Branch(zzz520, zzz521, Pos(Zero), zzz523, zzz524), Branch(zzz340, zzz341, Pos(Succ(zzz34200)), zzz343, zzz344), h) → new_mkVBalBranch(zzz31, Branch(zzz520, zzz521, Pos(Zero), zzz523, zzz524), zzz343, h)
new_mkVBalBranch(zzz31, Branch(zzz520, zzz521, Pos(Zero), zzz523, zzz524), Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), h) → new_mkVBalBranch3MkVBalBranch12(zzz340, zzz341, zzz34200, zzz343, zzz344, zzz520, zzz521, zzz523, zzz524, zzz31, new_primPlusNat2(Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat3(new_primPlusNat1(zzz34200), zzz34200)), zzz34200))), Succ(zzz34200)), h)
new_mkVBalBranch3MkVBalBranch2(zzz340, zzz341, Pos(Zero), zzz343, zzz344, zzz520, zzz521, zzz52200, zzz523, zzz524, zzz31, Succ(zzz680), h) → new_mkVBalBranch(zzz31, zzz524, Branch(zzz340, zzz341, Pos(Zero), zzz343, zzz344), h)
new_mkVBalBranch3MkVBalBranch2(zzz340, zzz341, Neg(Zero), zzz343, zzz344, zzz520, zzz521, zzz52200, zzz523, zzz524, zzz31, Succ(zzz680), h) → new_mkVBalBranch(zzz31, zzz524, Branch(zzz340, zzz341, Neg(Zero), zzz343, zzz344), h)
new_mkVBalBranch3MkVBalBranch2(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344, zzz520, zzz521, zzz52200, zzz523, zzz524, zzz31, Succ(zzz680), h) → new_mkVBalBranch3MkVBalBranch1(zzz340, zzz341, zzz34200, zzz343, zzz344, zzz520, zzz521, zzz52200, zzz523, zzz524, zzz31, new_primPlusNat2(Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat3(new_primPlusNat1(zzz34200), zzz34200)), zzz34200))), Succ(zzz34200)), h)
new_mkVBalBranch3MkVBalBranch16(zzz1702, zzz1703, zzz1704, zzz1705, zzz1706, zzz1707, zzz1708, zzz1709, zzz1710, zzz1711, zzz1712, Zero, Succ(zzz17140), bd) → new_mkVBalBranch(zzz1712, zzz1711, Branch(zzz1702, zzz1703, Neg(Succ(zzz1704)), zzz1705, zzz1706), bd)
new_mkVBalBranch3MkVBalBranch10(zzz929, zzz930, zzz931, zzz932, zzz933, zzz934, zzz935, zzz936, zzz937, zzz938, zzz939, Zero, ba) → new_mkVBalBranch3MkVBalBranch11(zzz929, zzz930, zzz931, zzz932, zzz933, zzz934, zzz935, zzz936, zzz937, zzz938, zzz939, Zero, Succ(zzz936), ba)
new_mkVBalBranch3MkVBalBranch24(zzz340, zzz341, Neg(Succ(Succ(Succ(zzz3420000)))), zzz343, zzz344, zzz520, zzz521, Zero, zzz523, zzz524, zzz31, Succ(Succ(zzz6900)), h) → new_mkVBalBranch3MkVBalBranch26(zzz340, zzz341, Succ(Succ(zzz3420000)), zzz343, zzz344, zzz520, zzz521, zzz523, zzz524, zzz31, Succ(zzz3420000), Succ(zzz6900), h)
new_mkVBalBranch3MkVBalBranch15(zzz537, zzz538, zzz539, zzz540, zzz541, zzz542, zzz543, zzz544, zzz545, zzz546, zzz547, Succ(zzz6990), bc) → new_mkVBalBranch3MkVBalBranch16(zzz537, zzz538, zzz539, zzz540, zzz541, zzz542, zzz543, Succ(zzz544), zzz545, zzz546, zzz547, Succ(Succ(zzz544)), Succ(zzz6990), bc)
new_mkVBalBranch3MkVBalBranch25(zzz537, zzz538, zzz539, zzz540, zzz541, zzz542, zzz543, zzz544, zzz545, zzz546, zzz547, Zero, Zero, bc) → new_mkVBalBranch3MkVBalBranch211(zzz537, zzz538, zzz539, zzz540, zzz541, zzz542, zzz543, zzz544, zzz545, zzz546, zzz547, bc)
new_mkVBalBranch3MkVBalBranch212(zzz818, zzz819, zzz820, zzz821, zzz822, zzz823, zzz824, zzz825, zzz826, zzz827, bf) → new_mkVBalBranch3MkVBalBranch14(zzz818, zzz819, zzz820, zzz821, zzz822, zzz823, zzz824, zzz825, zzz826, zzz827, new_primPlusNat2(Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat3(new_primPlusNat1(zzz820), zzz820)), zzz820))), Succ(zzz820)), bf)

The TRS R consists of the following rules:

new_primPlusNat1(Zero) → Zero
new_primPlusNat1(Succ(zzz62000)) → Succ(Succ(new_primPlusNat1(zzz62000)))
new_primPlusNat3(zzz90, Succ(zzz910)) → Succ(Succ(new_primPlusNat2(zzz90, zzz910)))
new_primPlusNat3(zzz90, Zero) → Succ(zzz90)
new_primPlusNat2(Succ(zzz900), Succ(zzz9100)) → Succ(Succ(new_primPlusNat2(zzz900, zzz9100)))
new_primPlusNat2(Zero, Succ(zzz9100)) → Succ(zzz9100)
new_primPlusNat2(Zero, Zero) → Zero
new_primPlusNat2(Succ(zzz900), Zero) → Succ(zzz900)

The set Q consists of the following terms:

new_primPlusNat2(Zero, Succ(x0))
new_primPlusNat3(x0, Succ(x1))
new_primPlusNat2(Succ(x0), Succ(x1))
new_primPlusNat3(x0, Zero)
new_primPlusNat1(Zero)
new_primPlusNat2(Zero, Zero)
new_primPlusNat1(Succ(x0))
new_primPlusNat2(Succ(x0), Zero)

We have to consider all minimal (P,Q,R)-chains.
By rewriting [15] the rule new_mkVBalBranch3MkVBalBranch29(zzz818, zzz819, zzz820, zzz821, zzz822, zzz823, zzz824, zzz825, zzz826, zzz827, bf) → new_mkVBalBranch3MkVBalBranch14(zzz818, zzz819, zzz820, zzz821, zzz822, zzz823, zzz824, zzz825, zzz826, zzz827, new_primPlusNat2(new_primPlusNat3(Succ(new_primPlusNat3(new_primPlusNat1(zzz820), zzz820)), Succ(zzz820)), Succ(zzz820)), bf) at position [10,0] we obtained the following new rules:

new_mkVBalBranch3MkVBalBranch29(zzz818, zzz819, zzz820, zzz821, zzz822, zzz823, zzz824, zzz825, zzz826, zzz827, bf) → new_mkVBalBranch3MkVBalBranch14(zzz818, zzz819, zzz820, zzz821, zzz822, zzz823, zzz824, zzz825, zzz826, zzz827, new_primPlusNat2(Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat3(new_primPlusNat1(zzz820), zzz820)), zzz820))), Succ(zzz820)), bf)



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

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

new_mkVBalBranch3MkVBalBranch211(zzz537, zzz538, zzz539, zzz540, zzz541, zzz542, zzz543, zzz544, zzz545, zzz546, zzz547, bc) → new_mkVBalBranch3MkVBalBranch15(zzz537, zzz538, zzz539, zzz540, zzz541, zzz542, zzz543, zzz544, zzz545, zzz546, zzz547, Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat2(Succ(new_primPlusNat3(new_primPlusNat1(zzz539), zzz539)), zzz539)), zzz539))), bc)
new_mkVBalBranch(zzz31, Branch(zzz520, zzz521, Neg(Succ(zzz52200)), zzz523, zzz524), Branch(zzz340, zzz341, zzz342, zzz343, zzz344), h) → new_mkVBalBranch3MkVBalBranch24(zzz340, zzz341, zzz342, zzz343, zzz344, zzz520, zzz521, zzz52200, zzz523, zzz524, zzz31, Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat3(new_primPlusNat1(zzz52200), zzz52200)), zzz52200))), h)
new_mkVBalBranch3MkVBalBranch11(zzz2033, zzz2034, zzz2035, zzz2036, zzz2037, zzz2038, zzz2039, zzz2040, zzz2041, zzz2042, zzz2043, Zero, Succ(zzz20450), bb) → new_mkVBalBranch(zzz2043, zzz2042, Branch(zzz2033, zzz2034, Pos(Succ(zzz2035)), zzz2036, zzz2037), bb)
new_mkVBalBranch3MkVBalBranch23(zzz929, zzz930, zzz931, zzz932, zzz933, zzz934, zzz935, zzz936, zzz937, zzz938, zzz939, ba) → new_mkVBalBranch3MkVBalBranch10(zzz929, zzz930, zzz931, zzz932, zzz933, zzz934, zzz935, zzz936, zzz937, zzz938, zzz939, new_primPlusNat2(Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat3(new_primPlusNat1(zzz931), zzz931)), zzz931))), Succ(zzz931)), ba)
new_mkVBalBranch3MkVBalBranch26(zzz1133, zzz1134, zzz1135, zzz1136, zzz1137, zzz1138, zzz1139, zzz1140, zzz1141, zzz1142, Succ(zzz11430), Succ(zzz11440), be) → new_mkVBalBranch3MkVBalBranch26(zzz1133, zzz1134, zzz1135, zzz1136, zzz1137, zzz1138, zzz1139, zzz1140, zzz1141, zzz1142, zzz11430, zzz11440, be)
new_mkVBalBranch3MkVBalBranch24(zzz340, zzz341, Pos(zzz3420), zzz343, zzz344, zzz520, zzz521, zzz52200, zzz523, zzz524, zzz31, Succ(zzz690), h) → new_mkVBalBranch(zzz31, Branch(zzz520, zzz521, Neg(Succ(zzz52200)), zzz523, zzz524), zzz343, h)
new_mkVBalBranch3MkVBalBranch12(zzz340, zzz341, zzz34200, zzz343, zzz344, zzz520, zzz521, zzz523, zzz524, zzz31, Succ(zzz1250), h) → new_mkVBalBranch(zzz31, zzz524, Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), h)
new_mkVBalBranch3MkVBalBranch25(zzz537, zzz538, zzz539, zzz540, zzz541, zzz542, zzz543, zzz544, zzz545, zzz546, zzz547, Succ(zzz5480), Zero, bc) → new_mkVBalBranch3MkVBalBranch15(zzz537, zzz538, zzz539, zzz540, zzz541, zzz542, zzz543, zzz544, zzz545, zzz546, zzz547, Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat2(Succ(new_primPlusNat3(new_primPlusNat1(zzz539), zzz539)), zzz539)), zzz539))), bc)
new_mkVBalBranch3MkVBalBranch20(zzz929, zzz930, zzz931, zzz932, zzz933, zzz934, zzz935, zzz936, zzz937, zzz938, zzz939, Zero, Succ(zzz9410), ba) → new_mkVBalBranch(zzz939, Branch(zzz934, zzz935, Pos(Succ(zzz936)), zzz937, zzz938), zzz932, ba)
new_mkVBalBranch3MkVBalBranch24(zzz340, zzz341, Neg(Succ(Succ(Zero))), zzz343, zzz344, zzz520, zzz521, Zero, zzz523, zzz524, zzz31, Succ(Succ(zzz6900)), h) → new_mkVBalBranch3MkVBalBranch26(zzz340, zzz341, Succ(Zero), zzz343, zzz344, zzz520, zzz521, zzz523, zzz524, zzz31, Zero, Succ(zzz6900), h)
new_mkVBalBranch3MkVBalBranch17(zzz340, zzz341, zzz34200, zzz343, zzz344, zzz520, zzz521, zzz52200, zzz523, zzz524, zzz31, h) → new_mkVBalBranch(zzz31, zzz524, Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), h)
new_mkVBalBranch3MkVBalBranch26(zzz1133, zzz1134, zzz1135, zzz1136, zzz1137, zzz1138, zzz1139, zzz1140, zzz1141, zzz1142, Zero, Zero, be) → new_mkVBalBranch3MkVBalBranch29(zzz1133, zzz1134, zzz1135, zzz1136, zzz1137, zzz1138, zzz1139, zzz1140, zzz1141, zzz1142, be)
new_mkVBalBranch3MkVBalBranch1(zzz340, zzz341, zzz34200, zzz343, zzz344, zzz520, zzz521, zzz52200, zzz523, zzz524, zzz31, Succ(zzz1430), h) → new_mkVBalBranch(zzz31, zzz524, Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), h)
new_mkVBalBranch3MkVBalBranch24(zzz340, zzz341, Neg(Succ(Zero)), zzz343, zzz344, zzz520, zzz521, zzz52200, zzz523, zzz524, zzz31, Succ(zzz690), h) → new_mkVBalBranch(zzz31, Branch(zzz520, zzz521, Neg(Succ(zzz52200)), zzz523, zzz524), zzz343, h)
new_mkVBalBranch3MkVBalBranch20(zzz929, zzz930, zzz931, zzz932, zzz933, zzz934, zzz935, zzz936, zzz937, zzz938, zzz939, Zero, Zero, ba) → new_mkVBalBranch3MkVBalBranch23(zzz929, zzz930, zzz931, zzz932, zzz933, zzz934, zzz935, zzz936, zzz937, zzz938, zzz939, ba)
new_mkVBalBranch3MkVBalBranch13(zzz340, zzz341, zzz34200, zzz343, zzz344, zzz520, zzz521, zzz523, zzz524, zzz31, Succ(zzz1290), h) → new_mkVBalBranch(zzz31, zzz524, Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), h)
new_mkVBalBranch3MkVBalBranch2(zzz340, zzz341, Pos(Succ(zzz34200)), zzz343, zzz344, zzz520, zzz521, zzz52200, zzz523, zzz524, zzz31, Succ(zzz680), h) → new_mkVBalBranch3MkVBalBranch20(zzz340, zzz341, zzz34200, zzz343, zzz344, zzz520, zzz521, zzz52200, zzz523, zzz524, zzz31, Succ(new_primPlusNat2(zzz680, zzz52200)), zzz34200, h)
new_mkVBalBranch(zzz31, Branch(zzz520, zzz521, Neg(Zero), zzz523, zzz524), Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), h) → new_mkVBalBranch3MkVBalBranch13(zzz340, zzz341, zzz34200, zzz343, zzz344, zzz520, zzz521, zzz523, zzz524, zzz31, new_primPlusNat2(Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat3(new_primPlusNat1(zzz34200), zzz34200)), zzz34200))), Succ(zzz34200)), h)
new_mkVBalBranch(zzz31, Branch(zzz520, zzz521, Neg(Zero), zzz523, zzz524), Branch(zzz340, zzz341, Pos(Succ(zzz34200)), zzz343, zzz344), h) → new_mkVBalBranch(zzz31, Branch(zzz520, zzz521, Neg(Zero), zzz523, zzz524), zzz343, h)
new_mkVBalBranch3MkVBalBranch24(zzz340, zzz341, Neg(Zero), zzz343, zzz344, zzz520, zzz521, zzz52200, zzz523, zzz524, zzz31, Succ(zzz690), h) → new_mkVBalBranch(zzz31, Branch(zzz520, zzz521, Neg(Succ(zzz52200)), zzz523, zzz524), zzz343, h)
new_mkVBalBranch3MkVBalBranch20(zzz929, zzz930, zzz931, zzz932, zzz933, zzz934, zzz935, zzz936, zzz937, zzz938, zzz939, Succ(zzz9400), Succ(zzz9410), ba) → new_mkVBalBranch3MkVBalBranch20(zzz929, zzz930, zzz931, zzz932, zzz933, zzz934, zzz935, zzz936, zzz937, zzz938, zzz939, zzz9400, zzz9410, ba)
new_mkVBalBranch3MkVBalBranch1(zzz340, zzz341, zzz34200, zzz343, zzz344, zzz520, zzz521, zzz52200, zzz523, zzz524, zzz31, Zero, h) → new_mkVBalBranch3MkVBalBranch17(zzz340, zzz341, zzz34200, zzz343, zzz344, zzz520, zzz521, zzz52200, zzz523, zzz524, zzz31, h)
new_mkVBalBranch3MkVBalBranch26(zzz1133, zzz1134, zzz1135, zzz1136, zzz1137, zzz1138, zzz1139, zzz1140, zzz1141, zzz1142, Succ(zzz11430), Zero, be) → new_mkVBalBranch3MkVBalBranch212(zzz1133, zzz1134, zzz1135, zzz1136, zzz1137, zzz1138, zzz1139, zzz1140, zzz1141, zzz1142, be)
new_mkVBalBranch3MkVBalBranch16(zzz1702, zzz1703, zzz1704, zzz1705, zzz1706, zzz1707, zzz1708, zzz1709, zzz1710, zzz1711, zzz1712, Succ(zzz17130), Succ(zzz17140), bd) → new_mkVBalBranch3MkVBalBranch16(zzz1702, zzz1703, zzz1704, zzz1705, zzz1706, zzz1707, zzz1708, zzz1709, zzz1710, zzz1711, zzz1712, zzz17130, zzz17140, bd)
new_mkVBalBranch3MkVBalBranch25(zzz537, zzz538, zzz539, zzz540, zzz541, zzz542, zzz543, zzz544, zzz545, zzz546, zzz547, Zero, Succ(zzz5490), bc) → new_mkVBalBranch(zzz547, Branch(zzz542, zzz543, Neg(Succ(Succ(zzz544))), zzz545, zzz546), zzz540, bc)
new_mkVBalBranch3MkVBalBranch11(zzz2033, zzz2034, zzz2035, zzz2036, zzz2037, zzz2038, zzz2039, zzz2040, zzz2041, zzz2042, zzz2043, Succ(zzz20440), Succ(zzz20450), bb) → new_mkVBalBranch3MkVBalBranch11(zzz2033, zzz2034, zzz2035, zzz2036, zzz2037, zzz2038, zzz2039, zzz2040, zzz2041, zzz2042, zzz2043, zzz20440, zzz20450, bb)
new_mkVBalBranch3MkVBalBranch25(zzz537, zzz538, zzz539, zzz540, zzz541, zzz542, zzz543, zzz544, zzz545, zzz546, zzz547, Succ(zzz5480), Succ(zzz5490), bc) → new_mkVBalBranch3MkVBalBranch25(zzz537, zzz538, zzz539, zzz540, zzz541, zzz542, zzz543, zzz544, zzz545, zzz546, zzz547, zzz5480, zzz5490, bc)
new_mkVBalBranch3MkVBalBranch29(zzz818, zzz819, zzz820, zzz821, zzz822, zzz823, zzz824, zzz825, zzz826, zzz827, bf) → new_mkVBalBranch3MkVBalBranch14(zzz818, zzz819, zzz820, zzz821, zzz822, zzz823, zzz824, zzz825, zzz826, zzz827, new_primPlusNat2(Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat3(new_primPlusNat1(zzz820), zzz820)), zzz820))), Succ(zzz820)), bf)
new_mkVBalBranch(zzz31, Branch(zzz520, zzz521, Pos(Succ(zzz52200)), zzz523, zzz524), Branch(zzz340, zzz341, zzz342, zzz343, zzz344), h) → new_mkVBalBranch3MkVBalBranch2(zzz340, zzz341, zzz342, zzz343, zzz344, zzz520, zzz521, zzz52200, zzz523, zzz524, zzz31, Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat3(new_primPlusNat1(zzz52200), zzz52200)), zzz52200))), h)
new_mkVBalBranch3MkVBalBranch10(zzz929, zzz930, zzz931, zzz932, zzz933, zzz934, zzz935, zzz936, zzz937, zzz938, zzz939, Succ(zzz10020), ba) → new_mkVBalBranch3MkVBalBranch11(zzz929, zzz930, zzz931, zzz932, zzz933, zzz934, zzz935, zzz936, zzz937, zzz938, zzz939, Succ(zzz10020), Succ(zzz936), ba)
new_mkVBalBranch3MkVBalBranch14(zzz818, zzz819, zzz820, zzz821, zzz822, zzz823, zzz824, zzz825, zzz826, zzz827, Succ(zzz8960), bf) → new_mkVBalBranch3MkVBalBranch16(zzz818, zzz819, zzz820, zzz821, zzz822, zzz823, zzz824, Zero, zzz825, zzz826, zzz827, Succ(Zero), Succ(zzz8960), bf)
new_mkVBalBranch3MkVBalBranch24(zzz340, zzz341, Neg(Succ(Succ(Succ(zzz3420000)))), zzz343, zzz344, zzz520, zzz521, Succ(zzz522000), zzz523, zzz524, zzz31, Succ(Succ(zzz6900)), h) → new_mkVBalBranch3MkVBalBranch25(zzz340, zzz341, Succ(Succ(zzz3420000)), zzz343, zzz344, zzz520, zzz521, zzz522000, zzz523, zzz524, zzz31, Succ(zzz3420000), Succ(Succ(new_primPlusNat2(zzz6900, zzz522000))), h)
new_mkVBalBranch3MkVBalBranch26(zzz1133, zzz1134, zzz1135, zzz1136, zzz1137, zzz1138, zzz1139, zzz1140, zzz1141, zzz1142, Zero, Succ(zzz11440), be) → new_mkVBalBranch(zzz1142, Branch(zzz1138, zzz1139, Neg(Succ(Zero)), zzz1140, zzz1141), zzz1136, be)
new_mkVBalBranch3MkVBalBranch24(zzz340, zzz341, Neg(Succ(Succ(Zero))), zzz343, zzz344, zzz520, zzz521, Succ(zzz522000), zzz523, zzz524, zzz31, Succ(Succ(zzz6900)), h) → new_mkVBalBranch3MkVBalBranch25(zzz340, zzz341, Succ(Zero), zzz343, zzz344, zzz520, zzz521, zzz522000, zzz523, zzz524, zzz31, Zero, Succ(Succ(new_primPlusNat2(zzz6900, zzz522000))), h)
new_mkVBalBranch(zzz31, Branch(zzz520, zzz521, Pos(Zero), zzz523, zzz524), Branch(zzz340, zzz341, Pos(Succ(zzz34200)), zzz343, zzz344), h) → new_mkVBalBranch(zzz31, Branch(zzz520, zzz521, Pos(Zero), zzz523, zzz524), zzz343, h)
new_mkVBalBranch3MkVBalBranch20(zzz929, zzz930, zzz931, zzz932, zzz933, zzz934, zzz935, zzz936, zzz937, zzz938, zzz939, Succ(zzz9400), Zero, ba) → new_mkVBalBranch3MkVBalBranch10(zzz929, zzz930, zzz931, zzz932, zzz933, zzz934, zzz935, zzz936, zzz937, zzz938, zzz939, new_primPlusNat2(new_primPlusNat3(Succ(new_primPlusNat3(new_primPlusNat1(zzz931), zzz931)), Succ(zzz931)), Succ(zzz931)), ba)
new_mkVBalBranch(zzz31, Branch(zzz520, zzz521, Pos(Zero), zzz523, zzz524), Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), h) → new_mkVBalBranch3MkVBalBranch12(zzz340, zzz341, zzz34200, zzz343, zzz344, zzz520, zzz521, zzz523, zzz524, zzz31, new_primPlusNat2(Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat3(new_primPlusNat1(zzz34200), zzz34200)), zzz34200))), Succ(zzz34200)), h)
new_mkVBalBranch3MkVBalBranch2(zzz340, zzz341, Pos(Zero), zzz343, zzz344, zzz520, zzz521, zzz52200, zzz523, zzz524, zzz31, Succ(zzz680), h) → new_mkVBalBranch(zzz31, zzz524, Branch(zzz340, zzz341, Pos(Zero), zzz343, zzz344), h)
new_mkVBalBranch3MkVBalBranch2(zzz340, zzz341, Neg(Zero), zzz343, zzz344, zzz520, zzz521, zzz52200, zzz523, zzz524, zzz31, Succ(zzz680), h) → new_mkVBalBranch(zzz31, zzz524, Branch(zzz340, zzz341, Neg(Zero), zzz343, zzz344), h)
new_mkVBalBranch3MkVBalBranch2(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344, zzz520, zzz521, zzz52200, zzz523, zzz524, zzz31, Succ(zzz680), h) → new_mkVBalBranch3MkVBalBranch1(zzz340, zzz341, zzz34200, zzz343, zzz344, zzz520, zzz521, zzz52200, zzz523, zzz524, zzz31, new_primPlusNat2(Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat3(new_primPlusNat1(zzz34200), zzz34200)), zzz34200))), Succ(zzz34200)), h)
new_mkVBalBranch3MkVBalBranch16(zzz1702, zzz1703, zzz1704, zzz1705, zzz1706, zzz1707, zzz1708, zzz1709, zzz1710, zzz1711, zzz1712, Zero, Succ(zzz17140), bd) → new_mkVBalBranch(zzz1712, zzz1711, Branch(zzz1702, zzz1703, Neg(Succ(zzz1704)), zzz1705, zzz1706), bd)
new_mkVBalBranch3MkVBalBranch15(zzz537, zzz538, zzz539, zzz540, zzz541, zzz542, zzz543, zzz544, zzz545, zzz546, zzz547, Succ(zzz6990), bc) → new_mkVBalBranch3MkVBalBranch16(zzz537, zzz538, zzz539, zzz540, zzz541, zzz542, zzz543, Succ(zzz544), zzz545, zzz546, zzz547, Succ(Succ(zzz544)), Succ(zzz6990), bc)
new_mkVBalBranch3MkVBalBranch24(zzz340, zzz341, Neg(Succ(Succ(Succ(zzz3420000)))), zzz343, zzz344, zzz520, zzz521, Zero, zzz523, zzz524, zzz31, Succ(Succ(zzz6900)), h) → new_mkVBalBranch3MkVBalBranch26(zzz340, zzz341, Succ(Succ(zzz3420000)), zzz343, zzz344, zzz520, zzz521, zzz523, zzz524, zzz31, Succ(zzz3420000), Succ(zzz6900), h)
new_mkVBalBranch3MkVBalBranch10(zzz929, zzz930, zzz931, zzz932, zzz933, zzz934, zzz935, zzz936, zzz937, zzz938, zzz939, Zero, ba) → new_mkVBalBranch3MkVBalBranch11(zzz929, zzz930, zzz931, zzz932, zzz933, zzz934, zzz935, zzz936, zzz937, zzz938, zzz939, Zero, Succ(zzz936), ba)
new_mkVBalBranch3MkVBalBranch25(zzz537, zzz538, zzz539, zzz540, zzz541, zzz542, zzz543, zzz544, zzz545, zzz546, zzz547, Zero, Zero, bc) → new_mkVBalBranch3MkVBalBranch211(zzz537, zzz538, zzz539, zzz540, zzz541, zzz542, zzz543, zzz544, zzz545, zzz546, zzz547, bc)
new_mkVBalBranch3MkVBalBranch212(zzz818, zzz819, zzz820, zzz821, zzz822, zzz823, zzz824, zzz825, zzz826, zzz827, bf) → new_mkVBalBranch3MkVBalBranch14(zzz818, zzz819, zzz820, zzz821, zzz822, zzz823, zzz824, zzz825, zzz826, zzz827, new_primPlusNat2(Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat3(new_primPlusNat1(zzz820), zzz820)), zzz820))), Succ(zzz820)), bf)

The TRS R consists of the following rules:

new_primPlusNat1(Zero) → Zero
new_primPlusNat1(Succ(zzz62000)) → Succ(Succ(new_primPlusNat1(zzz62000)))
new_primPlusNat3(zzz90, Succ(zzz910)) → Succ(Succ(new_primPlusNat2(zzz90, zzz910)))
new_primPlusNat3(zzz90, Zero) → Succ(zzz90)
new_primPlusNat2(Succ(zzz900), Succ(zzz9100)) → Succ(Succ(new_primPlusNat2(zzz900, zzz9100)))
new_primPlusNat2(Zero, Succ(zzz9100)) → Succ(zzz9100)
new_primPlusNat2(Zero, Zero) → Zero
new_primPlusNat2(Succ(zzz900), Zero) → Succ(zzz900)

The set Q consists of the following terms:

new_primPlusNat2(Zero, Succ(x0))
new_primPlusNat3(x0, Succ(x1))
new_primPlusNat2(Succ(x0), Succ(x1))
new_primPlusNat3(x0, Zero)
new_primPlusNat1(Zero)
new_primPlusNat2(Zero, Zero)
new_primPlusNat1(Succ(x0))
new_primPlusNat2(Succ(x0), Zero)

We have to consider all minimal (P,Q,R)-chains.
By rewriting [15] the rule new_mkVBalBranch3MkVBalBranch20(zzz929, zzz930, zzz931, zzz932, zzz933, zzz934, zzz935, zzz936, zzz937, zzz938, zzz939, Succ(zzz9400), Zero, ba) → new_mkVBalBranch3MkVBalBranch10(zzz929, zzz930, zzz931, zzz932, zzz933, zzz934, zzz935, zzz936, zzz937, zzz938, zzz939, new_primPlusNat2(new_primPlusNat3(Succ(new_primPlusNat3(new_primPlusNat1(zzz931), zzz931)), Succ(zzz931)), Succ(zzz931)), ba) at position [11,0] we obtained the following new rules:

new_mkVBalBranch3MkVBalBranch20(zzz929, zzz930, zzz931, zzz932, zzz933, zzz934, zzz935, zzz936, zzz937, zzz938, zzz939, Succ(zzz9400), Zero, ba) → new_mkVBalBranch3MkVBalBranch10(zzz929, zzz930, zzz931, zzz932, zzz933, zzz934, zzz935, zzz936, zzz937, zzz938, zzz939, new_primPlusNat2(Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat3(new_primPlusNat1(zzz931), zzz931)), zzz931))), Succ(zzz931)), 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
                                    ↳ DependencyGraphProof
                                      ↳ QDP
                                        ↳ Rewriting
                                          ↳ QDP
                                            ↳ Rewriting
                                              ↳ QDP
                                                ↳ Rewriting
                                                  ↳ QDP
                                                    ↳ Rewriting
                                                      ↳ QDP
                                                        ↳ Rewriting
                                                          ↳ QDP
                                                            ↳ Rewriting
                                                              ↳ QDP
                                                                ↳ Rewriting
                                                                  ↳ QDP
                                                                    ↳ Rewriting
                                                                      ↳ QDP
                                                                        ↳ Rewriting
                                                                          ↳ QDP
                                                                            ↳ Rewriting
                                                                              ↳ QDP
                                                                                ↳ Rewriting
                                                                                  ↳ QDP
                                                                                    ↳ Rewriting
                                                                                      ↳ QDP
                                                                                        ↳ Rewriting
                                                                                          ↳ QDP
                                                                                            ↳ UsableRulesProof
                                                                                              ↳ QDP
                                                                                                ↳ QReductionProof
                                                                                                  ↳ QDP
                                                                                                    ↳ Rewriting
                                                                                                      ↳ QDP
                                                                                                        ↳ Rewriting
                                                                                                          ↳ QDP
                                                                                                            ↳ Rewriting
                                                                                                              ↳ QDP
                                                                                                                ↳ Rewriting
                                                                                                                  ↳ QDP
                                                                                                                    ↳ Rewriting
                                                                                                                      ↳ QDP
                                                                                                                        ↳ Rewriting
                                                                                                                          ↳ QDP
                                                                                                                            ↳ DependencyGraphProof
                                                                                                                              ↳ QDP
                                                                                                                                ↳ Rewriting
                                                                                                                                  ↳ QDP
                                                                                                                                    ↳ Rewriting
                                                                                                                                      ↳ QDP
                                                                                                                                        ↳ DependencyGraphProof
                                                                                                                                          ↳ QDP
                                                                                                                                            ↳ Rewriting
                                                                                                                                              ↳ QDP
                                                                                                                                                ↳ Rewriting
                                                                                                                                                  ↳ QDP
                                                                                                                                                    ↳ Rewriting
                                                                                                                                                      ↳ QDP
                                                                                                                                                        ↳ Rewriting
                                                                                                                                                          ↳ QDP
                                                                                                                                                            ↳ Rewriting
                                                                                                                                                              ↳ QDP
                                                                                                                                                                ↳ Rewriting
                                                                                                                                                                  ↳ QDP
                                                                                                                                                                    ↳ Rewriting
                                                                                                                                                                      ↳ QDP
                                                                                                                                                                        ↳ UsableRulesProof
                                                                                                                                                                          ↳ QDP
                                                                                                                                                                            ↳ QReductionProof
                                                                                                                                                                              ↳ QDP
                                                                                                                                                                                ↳ Rewriting
                                                                                                                                                                                  ↳ QDP
                                                                                                                                                                                    ↳ Rewriting
                                                                                                                                                                                      ↳ QDP
                                                                                                                                                                                        ↳ Rewriting
                                                                                                                                                                                          ↳ QDP
                                                                                                                                                                                            ↳ Rewriting
                                                                                                                                                                                              ↳ QDP
                                                                                                                                                                                                ↳ Rewriting
                                                                                                                                                                                                  ↳ QDP
                                                                                                                                                                                                    ↳ Rewriting
                                                                                                                                                                                                      ↳ QDP
                                                                                                                                                                                                        ↳ Rewriting
                                                                                                                                                                                                          ↳ QDP
                                                                                                                                                                                                            ↳ Rewriting
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP

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

new_mkVBalBranch3MkVBalBranch23(zzz929, zzz930, zzz931, zzz932, zzz933, zzz934, zzz935, zzz936, zzz937, zzz938, zzz939, ba) → new_mkVBalBranch3MkVBalBranch10(zzz929, zzz930, zzz931, zzz932, zzz933, zzz934, zzz935, zzz936, zzz937, zzz938, zzz939, new_primPlusNat2(Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat3(new_primPlusNat1(zzz931), zzz931)), zzz931))), Succ(zzz931)), ba)
new_mkVBalBranch3MkVBalBranch11(zzz2033, zzz2034, zzz2035, zzz2036, zzz2037, zzz2038, zzz2039, zzz2040, zzz2041, zzz2042, zzz2043, Zero, Succ(zzz20450), bb) → new_mkVBalBranch(zzz2043, zzz2042, Branch(zzz2033, zzz2034, Pos(Succ(zzz2035)), zzz2036, zzz2037), bb)
new_mkVBalBranch(zzz31, Branch(zzz520, zzz521, Neg(Succ(zzz52200)), zzz523, zzz524), Branch(zzz340, zzz341, zzz342, zzz343, zzz344), h) → new_mkVBalBranch3MkVBalBranch24(zzz340, zzz341, zzz342, zzz343, zzz344, zzz520, zzz521, zzz52200, zzz523, zzz524, zzz31, Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat3(new_primPlusNat1(zzz52200), zzz52200)), zzz52200))), h)
new_mkVBalBranch3MkVBalBranch211(zzz537, zzz538, zzz539, zzz540, zzz541, zzz542, zzz543, zzz544, zzz545, zzz546, zzz547, bc) → new_mkVBalBranch3MkVBalBranch15(zzz537, zzz538, zzz539, zzz540, zzz541, zzz542, zzz543, zzz544, zzz545, zzz546, zzz547, Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat2(Succ(new_primPlusNat3(new_primPlusNat1(zzz539), zzz539)), zzz539)), zzz539))), bc)
new_mkVBalBranch3MkVBalBranch26(zzz1133, zzz1134, zzz1135, zzz1136, zzz1137, zzz1138, zzz1139, zzz1140, zzz1141, zzz1142, Succ(zzz11430), Succ(zzz11440), be) → new_mkVBalBranch3MkVBalBranch26(zzz1133, zzz1134, zzz1135, zzz1136, zzz1137, zzz1138, zzz1139, zzz1140, zzz1141, zzz1142, zzz11430, zzz11440, be)
new_mkVBalBranch3MkVBalBranch24(zzz340, zzz341, Pos(zzz3420), zzz343, zzz344, zzz520, zzz521, zzz52200, zzz523, zzz524, zzz31, Succ(zzz690), h) → new_mkVBalBranch(zzz31, Branch(zzz520, zzz521, Neg(Succ(zzz52200)), zzz523, zzz524), zzz343, h)
new_mkVBalBranch3MkVBalBranch12(zzz340, zzz341, zzz34200, zzz343, zzz344, zzz520, zzz521, zzz523, zzz524, zzz31, Succ(zzz1250), h) → new_mkVBalBranch(zzz31, zzz524, Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), h)
new_mkVBalBranch3MkVBalBranch25(zzz537, zzz538, zzz539, zzz540, zzz541, zzz542, zzz543, zzz544, zzz545, zzz546, zzz547, Succ(zzz5480), Zero, bc) → new_mkVBalBranch3MkVBalBranch15(zzz537, zzz538, zzz539, zzz540, zzz541, zzz542, zzz543, zzz544, zzz545, zzz546, zzz547, Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat2(Succ(new_primPlusNat3(new_primPlusNat1(zzz539), zzz539)), zzz539)), zzz539))), bc)
new_mkVBalBranch3MkVBalBranch20(zzz929, zzz930, zzz931, zzz932, zzz933, zzz934, zzz935, zzz936, zzz937, zzz938, zzz939, Zero, Succ(zzz9410), ba) → new_mkVBalBranch(zzz939, Branch(zzz934, zzz935, Pos(Succ(zzz936)), zzz937, zzz938), zzz932, ba)
new_mkVBalBranch3MkVBalBranch24(zzz340, zzz341, Neg(Succ(Succ(Zero))), zzz343, zzz344, zzz520, zzz521, Zero, zzz523, zzz524, zzz31, Succ(Succ(zzz6900)), h) → new_mkVBalBranch3MkVBalBranch26(zzz340, zzz341, Succ(Zero), zzz343, zzz344, zzz520, zzz521, zzz523, zzz524, zzz31, Zero, Succ(zzz6900), h)
new_mkVBalBranch3MkVBalBranch17(zzz340, zzz341, zzz34200, zzz343, zzz344, zzz520, zzz521, zzz52200, zzz523, zzz524, zzz31, h) → new_mkVBalBranch(zzz31, zzz524, Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), h)
new_mkVBalBranch3MkVBalBranch1(zzz340, zzz341, zzz34200, zzz343, zzz344, zzz520, zzz521, zzz52200, zzz523, zzz524, zzz31, Succ(zzz1430), h) → new_mkVBalBranch(zzz31, zzz524, Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), h)
new_mkVBalBranch3MkVBalBranch26(zzz1133, zzz1134, zzz1135, zzz1136, zzz1137, zzz1138, zzz1139, zzz1140, zzz1141, zzz1142, Zero, Zero, be) → new_mkVBalBranch3MkVBalBranch29(zzz1133, zzz1134, zzz1135, zzz1136, zzz1137, zzz1138, zzz1139, zzz1140, zzz1141, zzz1142, be)
new_mkVBalBranch3MkVBalBranch20(zzz929, zzz930, zzz931, zzz932, zzz933, zzz934, zzz935, zzz936, zzz937, zzz938, zzz939, Zero, Zero, ba) → new_mkVBalBranch3MkVBalBranch23(zzz929, zzz930, zzz931, zzz932, zzz933, zzz934, zzz935, zzz936, zzz937, zzz938, zzz939, ba)
new_mkVBalBranch3MkVBalBranch24(zzz340, zzz341, Neg(Succ(Zero)), zzz343, zzz344, zzz520, zzz521, zzz52200, zzz523, zzz524, zzz31, Succ(zzz690), h) → new_mkVBalBranch(zzz31, Branch(zzz520, zzz521, Neg(Succ(zzz52200)), zzz523, zzz524), zzz343, h)
new_mkVBalBranch3MkVBalBranch13(zzz340, zzz341, zzz34200, zzz343, zzz344, zzz520, zzz521, zzz523, zzz524, zzz31, Succ(zzz1290), h) → new_mkVBalBranch(zzz31, zzz524, Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), h)
new_mkVBalBranch3MkVBalBranch2(zzz340, zzz341, Pos(Succ(zzz34200)), zzz343, zzz344, zzz520, zzz521, zzz52200, zzz523, zzz524, zzz31, Succ(zzz680), h) → new_mkVBalBranch3MkVBalBranch20(zzz340, zzz341, zzz34200, zzz343, zzz344, zzz520, zzz521, zzz52200, zzz523, zzz524, zzz31, Succ(new_primPlusNat2(zzz680, zzz52200)), zzz34200, h)
new_mkVBalBranch(zzz31, Branch(zzz520, zzz521, Neg(Zero), zzz523, zzz524), Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), h) → new_mkVBalBranch3MkVBalBranch13(zzz340, zzz341, zzz34200, zzz343, zzz344, zzz520, zzz521, zzz523, zzz524, zzz31, new_primPlusNat2(Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat3(new_primPlusNat1(zzz34200), zzz34200)), zzz34200))), Succ(zzz34200)), h)
new_mkVBalBranch3MkVBalBranch24(zzz340, zzz341, Neg(Zero), zzz343, zzz344, zzz520, zzz521, zzz52200, zzz523, zzz524, zzz31, Succ(zzz690), h) → new_mkVBalBranch(zzz31, Branch(zzz520, zzz521, Neg(Succ(zzz52200)), zzz523, zzz524), zzz343, h)
new_mkVBalBranch(zzz31, Branch(zzz520, zzz521, Neg(Zero), zzz523, zzz524), Branch(zzz340, zzz341, Pos(Succ(zzz34200)), zzz343, zzz344), h) → new_mkVBalBranch(zzz31, Branch(zzz520, zzz521, Neg(Zero), zzz523, zzz524), zzz343, h)
new_mkVBalBranch3MkVBalBranch20(zzz929, zzz930, zzz931, zzz932, zzz933, zzz934, zzz935, zzz936, zzz937, zzz938, zzz939, Succ(zzz9400), Succ(zzz9410), ba) → new_mkVBalBranch3MkVBalBranch20(zzz929, zzz930, zzz931, zzz932, zzz933, zzz934, zzz935, zzz936, zzz937, zzz938, zzz939, zzz9400, zzz9410, ba)
new_mkVBalBranch3MkVBalBranch26(zzz1133, zzz1134, zzz1135, zzz1136, zzz1137, zzz1138, zzz1139, zzz1140, zzz1141, zzz1142, Succ(zzz11430), Zero, be) → new_mkVBalBranch3MkVBalBranch212(zzz1133, zzz1134, zzz1135, zzz1136, zzz1137, zzz1138, zzz1139, zzz1140, zzz1141, zzz1142, be)
new_mkVBalBranch3MkVBalBranch1(zzz340, zzz341, zzz34200, zzz343, zzz344, zzz520, zzz521, zzz52200, zzz523, zzz524, zzz31, Zero, h) → new_mkVBalBranch3MkVBalBranch17(zzz340, zzz341, zzz34200, zzz343, zzz344, zzz520, zzz521, zzz52200, zzz523, zzz524, zzz31, h)
new_mkVBalBranch3MkVBalBranch16(zzz1702, zzz1703, zzz1704, zzz1705, zzz1706, zzz1707, zzz1708, zzz1709, zzz1710, zzz1711, zzz1712, Succ(zzz17130), Succ(zzz17140), bd) → new_mkVBalBranch3MkVBalBranch16(zzz1702, zzz1703, zzz1704, zzz1705, zzz1706, zzz1707, zzz1708, zzz1709, zzz1710, zzz1711, zzz1712, zzz17130, zzz17140, bd)
new_mkVBalBranch3MkVBalBranch25(zzz537, zzz538, zzz539, zzz540, zzz541, zzz542, zzz543, zzz544, zzz545, zzz546, zzz547, Zero, Succ(zzz5490), bc) → new_mkVBalBranch(zzz547, Branch(zzz542, zzz543, Neg(Succ(Succ(zzz544))), zzz545, zzz546), zzz540, bc)
new_mkVBalBranch3MkVBalBranch11(zzz2033, zzz2034, zzz2035, zzz2036, zzz2037, zzz2038, zzz2039, zzz2040, zzz2041, zzz2042, zzz2043, Succ(zzz20440), Succ(zzz20450), bb) → new_mkVBalBranch3MkVBalBranch11(zzz2033, zzz2034, zzz2035, zzz2036, zzz2037, zzz2038, zzz2039, zzz2040, zzz2041, zzz2042, zzz2043, zzz20440, zzz20450, bb)
new_mkVBalBranch3MkVBalBranch25(zzz537, zzz538, zzz539, zzz540, zzz541, zzz542, zzz543, zzz544, zzz545, zzz546, zzz547, Succ(zzz5480), Succ(zzz5490), bc) → new_mkVBalBranch3MkVBalBranch25(zzz537, zzz538, zzz539, zzz540, zzz541, zzz542, zzz543, zzz544, zzz545, zzz546, zzz547, zzz5480, zzz5490, bc)
new_mkVBalBranch3MkVBalBranch29(zzz818, zzz819, zzz820, zzz821, zzz822, zzz823, zzz824, zzz825, zzz826, zzz827, bf) → new_mkVBalBranch3MkVBalBranch14(zzz818, zzz819, zzz820, zzz821, zzz822, zzz823, zzz824, zzz825, zzz826, zzz827, new_primPlusNat2(Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat3(new_primPlusNat1(zzz820), zzz820)), zzz820))), Succ(zzz820)), bf)
new_mkVBalBranch3MkVBalBranch10(zzz929, zzz930, zzz931, zzz932, zzz933, zzz934, zzz935, zzz936, zzz937, zzz938, zzz939, Succ(zzz10020), ba) → new_mkVBalBranch3MkVBalBranch11(zzz929, zzz930, zzz931, zzz932, zzz933, zzz934, zzz935, zzz936, zzz937, zzz938, zzz939, Succ(zzz10020), Succ(zzz936), ba)
new_mkVBalBranch(zzz31, Branch(zzz520, zzz521, Pos(Succ(zzz52200)), zzz523, zzz524), Branch(zzz340, zzz341, zzz342, zzz343, zzz344), h) → new_mkVBalBranch3MkVBalBranch2(zzz340, zzz341, zzz342, zzz343, zzz344, zzz520, zzz521, zzz52200, zzz523, zzz524, zzz31, Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat3(new_primPlusNat1(zzz52200), zzz52200)), zzz52200))), h)
new_mkVBalBranch3MkVBalBranch14(zzz818, zzz819, zzz820, zzz821, zzz822, zzz823, zzz824, zzz825, zzz826, zzz827, Succ(zzz8960), bf) → new_mkVBalBranch3MkVBalBranch16(zzz818, zzz819, zzz820, zzz821, zzz822, zzz823, zzz824, Zero, zzz825, zzz826, zzz827, Succ(Zero), Succ(zzz8960), bf)
new_mkVBalBranch3MkVBalBranch26(zzz1133, zzz1134, zzz1135, zzz1136, zzz1137, zzz1138, zzz1139, zzz1140, zzz1141, zzz1142, Zero, Succ(zzz11440), be) → new_mkVBalBranch(zzz1142, Branch(zzz1138, zzz1139, Neg(Succ(Zero)), zzz1140, zzz1141), zzz1136, be)
new_mkVBalBranch3MkVBalBranch24(zzz340, zzz341, Neg(Succ(Succ(Succ(zzz3420000)))), zzz343, zzz344, zzz520, zzz521, Succ(zzz522000), zzz523, zzz524, zzz31, Succ(Succ(zzz6900)), h) → new_mkVBalBranch3MkVBalBranch25(zzz340, zzz341, Succ(Succ(zzz3420000)), zzz343, zzz344, zzz520, zzz521, zzz522000, zzz523, zzz524, zzz31, Succ(zzz3420000), Succ(Succ(new_primPlusNat2(zzz6900, zzz522000))), h)
new_mkVBalBranch3MkVBalBranch24(zzz340, zzz341, Neg(Succ(Succ(Zero))), zzz343, zzz344, zzz520, zzz521, Succ(zzz522000), zzz523, zzz524, zzz31, Succ(Succ(zzz6900)), h) → new_mkVBalBranch3MkVBalBranch25(zzz340, zzz341, Succ(Zero), zzz343, zzz344, zzz520, zzz521, zzz522000, zzz523, zzz524, zzz31, Zero, Succ(Succ(new_primPlusNat2(zzz6900, zzz522000))), h)
new_mkVBalBranch(zzz31, Branch(zzz520, zzz521, Pos(Zero), zzz523, zzz524), Branch(zzz340, zzz341, Pos(Succ(zzz34200)), zzz343, zzz344), h) → new_mkVBalBranch(zzz31, Branch(zzz520, zzz521, Pos(Zero), zzz523, zzz524), zzz343, h)
new_mkVBalBranch(zzz31, Branch(zzz520, zzz521, Pos(Zero), zzz523, zzz524), Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), h) → new_mkVBalBranch3MkVBalBranch12(zzz340, zzz341, zzz34200, zzz343, zzz344, zzz520, zzz521, zzz523, zzz524, zzz31, new_primPlusNat2(Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat3(new_primPlusNat1(zzz34200), zzz34200)), zzz34200))), Succ(zzz34200)), h)
new_mkVBalBranch3MkVBalBranch2(zzz340, zzz341, Pos(Zero), zzz343, zzz344, zzz520, zzz521, zzz52200, zzz523, zzz524, zzz31, Succ(zzz680), h) → new_mkVBalBranch(zzz31, zzz524, Branch(zzz340, zzz341, Pos(Zero), zzz343, zzz344), h)
new_mkVBalBranch3MkVBalBranch20(zzz929, zzz930, zzz931, zzz932, zzz933, zzz934, zzz935, zzz936, zzz937, zzz938, zzz939, Succ(zzz9400), Zero, ba) → new_mkVBalBranch3MkVBalBranch10(zzz929, zzz930, zzz931, zzz932, zzz933, zzz934, zzz935, zzz936, zzz937, zzz938, zzz939, new_primPlusNat2(Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat3(new_primPlusNat1(zzz931), zzz931)), zzz931))), Succ(zzz931)), ba)
new_mkVBalBranch3MkVBalBranch2(zzz340, zzz341, Neg(Zero), zzz343, zzz344, zzz520, zzz521, zzz52200, zzz523, zzz524, zzz31, Succ(zzz680), h) → new_mkVBalBranch(zzz31, zzz524, Branch(zzz340, zzz341, Neg(Zero), zzz343, zzz344), h)
new_mkVBalBranch3MkVBalBranch2(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344, zzz520, zzz521, zzz52200, zzz523, zzz524, zzz31, Succ(zzz680), h) → new_mkVBalBranch3MkVBalBranch1(zzz340, zzz341, zzz34200, zzz343, zzz344, zzz520, zzz521, zzz52200, zzz523, zzz524, zzz31, new_primPlusNat2(Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat3(new_primPlusNat1(zzz34200), zzz34200)), zzz34200))), Succ(zzz34200)), h)
new_mkVBalBranch3MkVBalBranch16(zzz1702, zzz1703, zzz1704, zzz1705, zzz1706, zzz1707, zzz1708, zzz1709, zzz1710, zzz1711, zzz1712, Zero, Succ(zzz17140), bd) → new_mkVBalBranch(zzz1712, zzz1711, Branch(zzz1702, zzz1703, Neg(Succ(zzz1704)), zzz1705, zzz1706), bd)
new_mkVBalBranch3MkVBalBranch10(zzz929, zzz930, zzz931, zzz932, zzz933, zzz934, zzz935, zzz936, zzz937, zzz938, zzz939, Zero, ba) → new_mkVBalBranch3MkVBalBranch11(zzz929, zzz930, zzz931, zzz932, zzz933, zzz934, zzz935, zzz936, zzz937, zzz938, zzz939, Zero, Succ(zzz936), ba)
new_mkVBalBranch3MkVBalBranch24(zzz340, zzz341, Neg(Succ(Succ(Succ(zzz3420000)))), zzz343, zzz344, zzz520, zzz521, Zero, zzz523, zzz524, zzz31, Succ(Succ(zzz6900)), h) → new_mkVBalBranch3MkVBalBranch26(zzz340, zzz341, Succ(Succ(zzz3420000)), zzz343, zzz344, zzz520, zzz521, zzz523, zzz524, zzz31, Succ(zzz3420000), Succ(zzz6900), h)
new_mkVBalBranch3MkVBalBranch15(zzz537, zzz538, zzz539, zzz540, zzz541, zzz542, zzz543, zzz544, zzz545, zzz546, zzz547, Succ(zzz6990), bc) → new_mkVBalBranch3MkVBalBranch16(zzz537, zzz538, zzz539, zzz540, zzz541, zzz542, zzz543, Succ(zzz544), zzz545, zzz546, zzz547, Succ(Succ(zzz544)), Succ(zzz6990), bc)
new_mkVBalBranch3MkVBalBranch25(zzz537, zzz538, zzz539, zzz540, zzz541, zzz542, zzz543, zzz544, zzz545, zzz546, zzz547, Zero, Zero, bc) → new_mkVBalBranch3MkVBalBranch211(zzz537, zzz538, zzz539, zzz540, zzz541, zzz542, zzz543, zzz544, zzz545, zzz546, zzz547, bc)
new_mkVBalBranch3MkVBalBranch212(zzz818, zzz819, zzz820, zzz821, zzz822, zzz823, zzz824, zzz825, zzz826, zzz827, bf) → new_mkVBalBranch3MkVBalBranch14(zzz818, zzz819, zzz820, zzz821, zzz822, zzz823, zzz824, zzz825, zzz826, zzz827, new_primPlusNat2(Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat3(new_primPlusNat1(zzz820), zzz820)), zzz820))), Succ(zzz820)), bf)

The TRS R consists of the following rules:

new_primPlusNat1(Zero) → Zero
new_primPlusNat1(Succ(zzz62000)) → Succ(Succ(new_primPlusNat1(zzz62000)))
new_primPlusNat3(zzz90, Succ(zzz910)) → Succ(Succ(new_primPlusNat2(zzz90, zzz910)))
new_primPlusNat3(zzz90, Zero) → Succ(zzz90)
new_primPlusNat2(Succ(zzz900), Succ(zzz9100)) → Succ(Succ(new_primPlusNat2(zzz900, zzz9100)))
new_primPlusNat2(Zero, Succ(zzz9100)) → Succ(zzz9100)
new_primPlusNat2(Zero, Zero) → Zero
new_primPlusNat2(Succ(zzz900), Zero) → Succ(zzz900)

The set Q consists of the following terms:

new_primPlusNat2(Zero, Succ(x0))
new_primPlusNat3(x0, Succ(x1))
new_primPlusNat2(Succ(x0), Succ(x1))
new_primPlusNat3(x0, Zero)
new_primPlusNat1(Zero)
new_primPlusNat2(Zero, Zero)
new_primPlusNat1(Succ(x0))
new_primPlusNat2(Succ(x0), Zero)

We have to consider all minimal (P,Q,R)-chains.
By rewriting [15] the rule new_mkVBalBranch(zzz31, Branch(zzz520, zzz521, Pos(Zero), zzz523, zzz524), Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), h) → new_mkVBalBranch3MkVBalBranch12(zzz340, zzz341, zzz34200, zzz343, zzz344, zzz520, zzz521, zzz523, zzz524, zzz31, new_primPlusNat2(Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat3(new_primPlusNat1(zzz34200), zzz34200)), zzz34200))), Succ(zzz34200)), h) at position [10] we obtained the following new rules:

new_mkVBalBranch(zzz31, Branch(zzz520, zzz521, Pos(Zero), zzz523, zzz524), Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), h) → new_mkVBalBranch3MkVBalBranch12(zzz340, zzz341, zzz34200, zzz343, zzz344, zzz520, zzz521, zzz523, zzz524, zzz31, Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat2(Succ(new_primPlusNat3(new_primPlusNat1(zzz34200), zzz34200)), 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
                                    ↳ DependencyGraphProof
                                      ↳ QDP
                                        ↳ Rewriting
                                          ↳ QDP
                                            ↳ Rewriting
                                              ↳ QDP
                                                ↳ Rewriting
                                                  ↳ QDP
                                                    ↳ Rewriting
                                                      ↳ QDP
                                                        ↳ Rewriting
                                                          ↳ QDP
                                                            ↳ Rewriting
                                                              ↳ QDP
                                                                ↳ Rewriting
                                                                  ↳ QDP
                                                                    ↳ Rewriting
                                                                      ↳ QDP
                                                                        ↳ Rewriting
                                                                          ↳ QDP
                                                                            ↳ Rewriting
                                                                              ↳ QDP
                                                                                ↳ Rewriting
                                                                                  ↳ QDP
                                                                                    ↳ Rewriting
                                                                                      ↳ QDP
                                                                                        ↳ Rewriting
                                                                                          ↳ QDP
                                                                                            ↳ UsableRulesProof
                                                                                              ↳ QDP
                                                                                                ↳ QReductionProof
                                                                                                  ↳ QDP
                                                                                                    ↳ Rewriting
                                                                                                      ↳ QDP
                                                                                                        ↳ Rewriting
                                                                                                          ↳ QDP
                                                                                                            ↳ Rewriting
                                                                                                              ↳ QDP
                                                                                                                ↳ Rewriting
                                                                                                                  ↳ QDP
                                                                                                                    ↳ Rewriting
                                                                                                                      ↳ QDP
                                                                                                                        ↳ Rewriting
                                                                                                                          ↳ QDP
                                                                                                                            ↳ DependencyGraphProof
                                                                                                                              ↳ QDP
                                                                                                                                ↳ Rewriting
                                                                                                                                  ↳ QDP
                                                                                                                                    ↳ Rewriting
                                                                                                                                      ↳ QDP
                                                                                                                                        ↳ DependencyGraphProof
                                                                                                                                          ↳ QDP
                                                                                                                                            ↳ Rewriting
                                                                                                                                              ↳ QDP
                                                                                                                                                ↳ Rewriting
                                                                                                                                                  ↳ QDP
                                                                                                                                                    ↳ Rewriting
                                                                                                                                                      ↳ QDP
                                                                                                                                                        ↳ Rewriting
                                                                                                                                                          ↳ QDP
                                                                                                                                                            ↳ Rewriting
                                                                                                                                                              ↳ QDP
                                                                                                                                                                ↳ Rewriting
                                                                                                                                                                  ↳ QDP
                                                                                                                                                                    ↳ Rewriting
                                                                                                                                                                      ↳ QDP
                                                                                                                                                                        ↳ UsableRulesProof
                                                                                                                                                                          ↳ QDP
                                                                                                                                                                            ↳ QReductionProof
                                                                                                                                                                              ↳ QDP
                                                                                                                                                                                ↳ Rewriting
                                                                                                                                                                                  ↳ QDP
                                                                                                                                                                                    ↳ Rewriting
                                                                                                                                                                                      ↳ QDP
                                                                                                                                                                                        ↳ Rewriting
                                                                                                                                                                                          ↳ QDP
                                                                                                                                                                                            ↳ Rewriting
                                                                                                                                                                                              ↳ QDP
                                                                                                                                                                                                ↳ Rewriting
                                                                                                                                                                                                  ↳ QDP
                                                                                                                                                                                                    ↳ Rewriting
                                                                                                                                                                                                      ↳ QDP
                                                                                                                                                                                                        ↳ Rewriting
                                                                                                                                                                                                          ↳ QDP
                                                                                                                                                                                                            ↳ Rewriting
                                                                                                                                                                                                              ↳ QDP
                                                                                                                                                                                                                ↳ Rewriting
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP

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

new_mkVBalBranch3MkVBalBranch211(zzz537, zzz538, zzz539, zzz540, zzz541, zzz542, zzz543, zzz544, zzz545, zzz546, zzz547, bc) → new_mkVBalBranch3MkVBalBranch15(zzz537, zzz538, zzz539, zzz540, zzz541, zzz542, zzz543, zzz544, zzz545, zzz546, zzz547, Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat2(Succ(new_primPlusNat3(new_primPlusNat1(zzz539), zzz539)), zzz539)), zzz539))), bc)
new_mkVBalBranch(zzz31, Branch(zzz520, zzz521, Neg(Succ(zzz52200)), zzz523, zzz524), Branch(zzz340, zzz341, zzz342, zzz343, zzz344), h) → new_mkVBalBranch3MkVBalBranch24(zzz340, zzz341, zzz342, zzz343, zzz344, zzz520, zzz521, zzz52200, zzz523, zzz524, zzz31, Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat3(new_primPlusNat1(zzz52200), zzz52200)), zzz52200))), h)
new_mkVBalBranch3MkVBalBranch11(zzz2033, zzz2034, zzz2035, zzz2036, zzz2037, zzz2038, zzz2039, zzz2040, zzz2041, zzz2042, zzz2043, Zero, Succ(zzz20450), bb) → new_mkVBalBranch(zzz2043, zzz2042, Branch(zzz2033, zzz2034, Pos(Succ(zzz2035)), zzz2036, zzz2037), bb)
new_mkVBalBranch3MkVBalBranch23(zzz929, zzz930, zzz931, zzz932, zzz933, zzz934, zzz935, zzz936, zzz937, zzz938, zzz939, ba) → new_mkVBalBranch3MkVBalBranch10(zzz929, zzz930, zzz931, zzz932, zzz933, zzz934, zzz935, zzz936, zzz937, zzz938, zzz939, new_primPlusNat2(Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat3(new_primPlusNat1(zzz931), zzz931)), zzz931))), Succ(zzz931)), ba)
new_mkVBalBranch3MkVBalBranch26(zzz1133, zzz1134, zzz1135, zzz1136, zzz1137, zzz1138, zzz1139, zzz1140, zzz1141, zzz1142, Succ(zzz11430), Succ(zzz11440), be) → new_mkVBalBranch3MkVBalBranch26(zzz1133, zzz1134, zzz1135, zzz1136, zzz1137, zzz1138, zzz1139, zzz1140, zzz1141, zzz1142, zzz11430, zzz11440, be)
new_mkVBalBranch3MkVBalBranch24(zzz340, zzz341, Pos(zzz3420), zzz343, zzz344, zzz520, zzz521, zzz52200, zzz523, zzz524, zzz31, Succ(zzz690), h) → new_mkVBalBranch(zzz31, Branch(zzz520, zzz521, Neg(Succ(zzz52200)), zzz523, zzz524), zzz343, h)
new_mkVBalBranch3MkVBalBranch12(zzz340, zzz341, zzz34200, zzz343, zzz344, zzz520, zzz521, zzz523, zzz524, zzz31, Succ(zzz1250), h) → new_mkVBalBranch(zzz31, zzz524, Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), h)
new_mkVBalBranch3MkVBalBranch25(zzz537, zzz538, zzz539, zzz540, zzz541, zzz542, zzz543, zzz544, zzz545, zzz546, zzz547, Succ(zzz5480), Zero, bc) → new_mkVBalBranch3MkVBalBranch15(zzz537, zzz538, zzz539, zzz540, zzz541, zzz542, zzz543, zzz544, zzz545, zzz546, zzz547, Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat2(Succ(new_primPlusNat3(new_primPlusNat1(zzz539), zzz539)), zzz539)), zzz539))), bc)
new_mkVBalBranch3MkVBalBranch20(zzz929, zzz930, zzz931, zzz932, zzz933, zzz934, zzz935, zzz936, zzz937, zzz938, zzz939, Zero, Succ(zzz9410), ba) → new_mkVBalBranch(zzz939, Branch(zzz934, zzz935, Pos(Succ(zzz936)), zzz937, zzz938), zzz932, ba)
new_mkVBalBranch3MkVBalBranch24(zzz340, zzz341, Neg(Succ(Succ(Zero))), zzz343, zzz344, zzz520, zzz521, Zero, zzz523, zzz524, zzz31, Succ(Succ(zzz6900)), h) → new_mkVBalBranch3MkVBalBranch26(zzz340, zzz341, Succ(Zero), zzz343, zzz344, zzz520, zzz521, zzz523, zzz524, zzz31, Zero, Succ(zzz6900), h)
new_mkVBalBranch3MkVBalBranch17(zzz340, zzz341, zzz34200, zzz343, zzz344, zzz520, zzz521, zzz52200, zzz523, zzz524, zzz31, h) → new_mkVBalBranch(zzz31, zzz524, Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), h)
new_mkVBalBranch3MkVBalBranch26(zzz1133, zzz1134, zzz1135, zzz1136, zzz1137, zzz1138, zzz1139, zzz1140, zzz1141, zzz1142, Zero, Zero, be) → new_mkVBalBranch3MkVBalBranch29(zzz1133, zzz1134, zzz1135, zzz1136, zzz1137, zzz1138, zzz1139, zzz1140, zzz1141, zzz1142, be)
new_mkVBalBranch3MkVBalBranch1(zzz340, zzz341, zzz34200, zzz343, zzz344, zzz520, zzz521, zzz52200, zzz523, zzz524, zzz31, Succ(zzz1430), h) → new_mkVBalBranch(zzz31, zzz524, Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), h)
new_mkVBalBranch3MkVBalBranch24(zzz340, zzz341, Neg(Succ(Zero)), zzz343, zzz344, zzz520, zzz521, zzz52200, zzz523, zzz524, zzz31, Succ(zzz690), h) → new_mkVBalBranch(zzz31, Branch(zzz520, zzz521, Neg(Succ(zzz52200)), zzz523, zzz524), zzz343, h)
new_mkVBalBranch3MkVBalBranch20(zzz929, zzz930, zzz931, zzz932, zzz933, zzz934, zzz935, zzz936, zzz937, zzz938, zzz939, Zero, Zero, ba) → new_mkVBalBranch3MkVBalBranch23(zzz929, zzz930, zzz931, zzz932, zzz933, zzz934, zzz935, zzz936, zzz937, zzz938, zzz939, ba)
new_mkVBalBranch3MkVBalBranch13(zzz340, zzz341, zzz34200, zzz343, zzz344, zzz520, zzz521, zzz523, zzz524, zzz31, Succ(zzz1290), h) → new_mkVBalBranch(zzz31, zzz524, Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), h)
new_mkVBalBranch3MkVBalBranch2(zzz340, zzz341, Pos(Succ(zzz34200)), zzz343, zzz344, zzz520, zzz521, zzz52200, zzz523, zzz524, zzz31, Succ(zzz680), h) → new_mkVBalBranch3MkVBalBranch20(zzz340, zzz341, zzz34200, zzz343, zzz344, zzz520, zzz521, zzz52200, zzz523, zzz524, zzz31, Succ(new_primPlusNat2(zzz680, zzz52200)), zzz34200, h)
new_mkVBalBranch(zzz31, Branch(zzz520, zzz521, Neg(Zero), zzz523, zzz524), Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), h) → new_mkVBalBranch3MkVBalBranch13(zzz340, zzz341, zzz34200, zzz343, zzz344, zzz520, zzz521, zzz523, zzz524, zzz31, new_primPlusNat2(Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat3(new_primPlusNat1(zzz34200), zzz34200)), zzz34200))), Succ(zzz34200)), h)
new_mkVBalBranch(zzz31, Branch(zzz520, zzz521, Neg(Zero), zzz523, zzz524), Branch(zzz340, zzz341, Pos(Succ(zzz34200)), zzz343, zzz344), h) → new_mkVBalBranch(zzz31, Branch(zzz520, zzz521, Neg(Zero), zzz523, zzz524), zzz343, h)
new_mkVBalBranch3MkVBalBranch24(zzz340, zzz341, Neg(Zero), zzz343, zzz344, zzz520, zzz521, zzz52200, zzz523, zzz524, zzz31, Succ(zzz690), h) → new_mkVBalBranch(zzz31, Branch(zzz520, zzz521, Neg(Succ(zzz52200)), zzz523, zzz524), zzz343, h)
new_mkVBalBranch3MkVBalBranch20(zzz929, zzz930, zzz931, zzz932, zzz933, zzz934, zzz935, zzz936, zzz937, zzz938, zzz939, Succ(zzz9400), Succ(zzz9410), ba) → new_mkVBalBranch3MkVBalBranch20(zzz929, zzz930, zzz931, zzz932, zzz933, zzz934, zzz935, zzz936, zzz937, zzz938, zzz939, zzz9400, zzz9410, ba)
new_mkVBalBranch3MkVBalBranch1(zzz340, zzz341, zzz34200, zzz343, zzz344, zzz520, zzz521, zzz52200, zzz523, zzz524, zzz31, Zero, h) → new_mkVBalBranch3MkVBalBranch17(zzz340, zzz341, zzz34200, zzz343, zzz344, zzz520, zzz521, zzz52200, zzz523, zzz524, zzz31, h)
new_mkVBalBranch3MkVBalBranch26(zzz1133, zzz1134, zzz1135, zzz1136, zzz1137, zzz1138, zzz1139, zzz1140, zzz1141, zzz1142, Succ(zzz11430), Zero, be) → new_mkVBalBranch3MkVBalBranch212(zzz1133, zzz1134, zzz1135, zzz1136, zzz1137, zzz1138, zzz1139, zzz1140, zzz1141, zzz1142, be)
new_mkVBalBranch3MkVBalBranch16(zzz1702, zzz1703, zzz1704, zzz1705, zzz1706, zzz1707, zzz1708, zzz1709, zzz1710, zzz1711, zzz1712, Succ(zzz17130), Succ(zzz17140), bd) → new_mkVBalBranch3MkVBalBranch16(zzz1702, zzz1703, zzz1704, zzz1705, zzz1706, zzz1707, zzz1708, zzz1709, zzz1710, zzz1711, zzz1712, zzz17130, zzz17140, bd)
new_mkVBalBranch3MkVBalBranch25(zzz537, zzz538, zzz539, zzz540, zzz541, zzz542, zzz543, zzz544, zzz545, zzz546, zzz547, Zero, Succ(zzz5490), bc) → new_mkVBalBranch(zzz547, Branch(zzz542, zzz543, Neg(Succ(Succ(zzz544))), zzz545, zzz546), zzz540, bc)
new_mkVBalBranch3MkVBalBranch11(zzz2033, zzz2034, zzz2035, zzz2036, zzz2037, zzz2038, zzz2039, zzz2040, zzz2041, zzz2042, zzz2043, Succ(zzz20440), Succ(zzz20450), bb) → new_mkVBalBranch3MkVBalBranch11(zzz2033, zzz2034, zzz2035, zzz2036, zzz2037, zzz2038, zzz2039, zzz2040, zzz2041, zzz2042, zzz2043, zzz20440, zzz20450, bb)
new_mkVBalBranch3MkVBalBranch25(zzz537, zzz538, zzz539, zzz540, zzz541, zzz542, zzz543, zzz544, zzz545, zzz546, zzz547, Succ(zzz5480), Succ(zzz5490), bc) → new_mkVBalBranch3MkVBalBranch25(zzz537, zzz538, zzz539, zzz540, zzz541, zzz542, zzz543, zzz544, zzz545, zzz546, zzz547, zzz5480, zzz5490, bc)
new_mkVBalBranch3MkVBalBranch29(zzz818, zzz819, zzz820, zzz821, zzz822, zzz823, zzz824, zzz825, zzz826, zzz827, bf) → new_mkVBalBranch3MkVBalBranch14(zzz818, zzz819, zzz820, zzz821, zzz822, zzz823, zzz824, zzz825, zzz826, zzz827, new_primPlusNat2(Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat3(new_primPlusNat1(zzz820), zzz820)), zzz820))), Succ(zzz820)), bf)
new_mkVBalBranch(zzz31, Branch(zzz520, zzz521, Pos(Succ(zzz52200)), zzz523, zzz524), Branch(zzz340, zzz341, zzz342, zzz343, zzz344), h) → new_mkVBalBranch3MkVBalBranch2(zzz340, zzz341, zzz342, zzz343, zzz344, zzz520, zzz521, zzz52200, zzz523, zzz524, zzz31, Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat3(new_primPlusNat1(zzz52200), zzz52200)), zzz52200))), h)
new_mkVBalBranch3MkVBalBranch10(zzz929, zzz930, zzz931, zzz932, zzz933, zzz934, zzz935, zzz936, zzz937, zzz938, zzz939, Succ(zzz10020), ba) → new_mkVBalBranch3MkVBalBranch11(zzz929, zzz930, zzz931, zzz932, zzz933, zzz934, zzz935, zzz936, zzz937, zzz938, zzz939, Succ(zzz10020), Succ(zzz936), ba)
new_mkVBalBranch3MkVBalBranch14(zzz818, zzz819, zzz820, zzz821, zzz822, zzz823, zzz824, zzz825, zzz826, zzz827, Succ(zzz8960), bf) → new_mkVBalBranch3MkVBalBranch16(zzz818, zzz819, zzz820, zzz821, zzz822, zzz823, zzz824, Zero, zzz825, zzz826, zzz827, Succ(Zero), Succ(zzz8960), bf)
new_mkVBalBranch(zzz31, Branch(zzz520, zzz521, Pos(Zero), zzz523, zzz524), Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), h) → new_mkVBalBranch3MkVBalBranch12(zzz340, zzz341, zzz34200, zzz343, zzz344, zzz520, zzz521, zzz523, zzz524, zzz31, Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat2(Succ(new_primPlusNat3(new_primPlusNat1(zzz34200), zzz34200)), zzz34200)), zzz34200))), h)
new_mkVBalBranch3MkVBalBranch24(zzz340, zzz341, Neg(Succ(Succ(Succ(zzz3420000)))), zzz343, zzz344, zzz520, zzz521, Succ(zzz522000), zzz523, zzz524, zzz31, Succ(Succ(zzz6900)), h) → new_mkVBalBranch3MkVBalBranch25(zzz340, zzz341, Succ(Succ(zzz3420000)), zzz343, zzz344, zzz520, zzz521, zzz522000, zzz523, zzz524, zzz31, Succ(zzz3420000), Succ(Succ(new_primPlusNat2(zzz6900, zzz522000))), h)
new_mkVBalBranch3MkVBalBranch26(zzz1133, zzz1134, zzz1135, zzz1136, zzz1137, zzz1138, zzz1139, zzz1140, zzz1141, zzz1142, Zero, Succ(zzz11440), be) → new_mkVBalBranch(zzz1142, Branch(zzz1138, zzz1139, Neg(Succ(Zero)), zzz1140, zzz1141), zzz1136, be)
new_mkVBalBranch3MkVBalBranch24(zzz340, zzz341, Neg(Succ(Succ(Zero))), zzz343, zzz344, zzz520, zzz521, Succ(zzz522000), zzz523, zzz524, zzz31, Succ(Succ(zzz6900)), h) → new_mkVBalBranch3MkVBalBranch25(zzz340, zzz341, Succ(Zero), zzz343, zzz344, zzz520, zzz521, zzz522000, zzz523, zzz524, zzz31, Zero, Succ(Succ(new_primPlusNat2(zzz6900, zzz522000))), h)
new_mkVBalBranch(zzz31, Branch(zzz520, zzz521, Pos(Zero), zzz523, zzz524), Branch(zzz340, zzz341, Pos(Succ(zzz34200)), zzz343, zzz344), h) → new_mkVBalBranch(zzz31, Branch(zzz520, zzz521, Pos(Zero), zzz523, zzz524), zzz343, h)
new_mkVBalBranch3MkVBalBranch2(zzz340, zzz341, Pos(Zero), zzz343, zzz344, zzz520, zzz521, zzz52200, zzz523, zzz524, zzz31, Succ(zzz680), h) → new_mkVBalBranch(zzz31, zzz524, Branch(zzz340, zzz341, Pos(Zero), zzz343, zzz344), h)
new_mkVBalBranch3MkVBalBranch20(zzz929, zzz930, zzz931, zzz932, zzz933, zzz934, zzz935, zzz936, zzz937, zzz938, zzz939, Succ(zzz9400), Zero, ba) → new_mkVBalBranch3MkVBalBranch10(zzz929, zzz930, zzz931, zzz932, zzz933, zzz934, zzz935, zzz936, zzz937, zzz938, zzz939, new_primPlusNat2(Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat3(new_primPlusNat1(zzz931), zzz931)), zzz931))), Succ(zzz931)), ba)
new_mkVBalBranch3MkVBalBranch2(zzz340, zzz341, Neg(Zero), zzz343, zzz344, zzz520, zzz521, zzz52200, zzz523, zzz524, zzz31, Succ(zzz680), h) → new_mkVBalBranch(zzz31, zzz524, Branch(zzz340, zzz341, Neg(Zero), zzz343, zzz344), h)
new_mkVBalBranch3MkVBalBranch2(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344, zzz520, zzz521, zzz52200, zzz523, zzz524, zzz31, Succ(zzz680), h) → new_mkVBalBranch3MkVBalBranch1(zzz340, zzz341, zzz34200, zzz343, zzz344, zzz520, zzz521, zzz52200, zzz523, zzz524, zzz31, new_primPlusNat2(Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat3(new_primPlusNat1(zzz34200), zzz34200)), zzz34200))), Succ(zzz34200)), h)
new_mkVBalBranch3MkVBalBranch16(zzz1702, zzz1703, zzz1704, zzz1705, zzz1706, zzz1707, zzz1708, zzz1709, zzz1710, zzz1711, zzz1712, Zero, Succ(zzz17140), bd) → new_mkVBalBranch(zzz1712, zzz1711, Branch(zzz1702, zzz1703, Neg(Succ(zzz1704)), zzz1705, zzz1706), bd)
new_mkVBalBranch3MkVBalBranch15(zzz537, zzz538, zzz539, zzz540, zzz541, zzz542, zzz543, zzz544, zzz545, zzz546, zzz547, Succ(zzz6990), bc) → new_mkVBalBranch3MkVBalBranch16(zzz537, zzz538, zzz539, zzz540, zzz541, zzz542, zzz543, Succ(zzz544), zzz545, zzz546, zzz547, Succ(Succ(zzz544)), Succ(zzz6990), bc)
new_mkVBalBranch3MkVBalBranch24(zzz340, zzz341, Neg(Succ(Succ(Succ(zzz3420000)))), zzz343, zzz344, zzz520, zzz521, Zero, zzz523, zzz524, zzz31, Succ(Succ(zzz6900)), h) → new_mkVBalBranch3MkVBalBranch26(zzz340, zzz341, Succ(Succ(zzz3420000)), zzz343, zzz344, zzz520, zzz521, zzz523, zzz524, zzz31, Succ(zzz3420000), Succ(zzz6900), h)
new_mkVBalBranch3MkVBalBranch10(zzz929, zzz930, zzz931, zzz932, zzz933, zzz934, zzz935, zzz936, zzz937, zzz938, zzz939, Zero, ba) → new_mkVBalBranch3MkVBalBranch11(zzz929, zzz930, zzz931, zzz932, zzz933, zzz934, zzz935, zzz936, zzz937, zzz938, zzz939, Zero, Succ(zzz936), ba)
new_mkVBalBranch3MkVBalBranch25(zzz537, zzz538, zzz539, zzz540, zzz541, zzz542, zzz543, zzz544, zzz545, zzz546, zzz547, Zero, Zero, bc) → new_mkVBalBranch3MkVBalBranch211(zzz537, zzz538, zzz539, zzz540, zzz541, zzz542, zzz543, zzz544, zzz545, zzz546, zzz547, bc)
new_mkVBalBranch3MkVBalBranch212(zzz818, zzz819, zzz820, zzz821, zzz822, zzz823, zzz824, zzz825, zzz826, zzz827, bf) → new_mkVBalBranch3MkVBalBranch14(zzz818, zzz819, zzz820, zzz821, zzz822, zzz823, zzz824, zzz825, zzz826, zzz827, new_primPlusNat2(Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat3(new_primPlusNat1(zzz820), zzz820)), zzz820))), Succ(zzz820)), bf)

The TRS R consists of the following rules:

new_primPlusNat1(Zero) → Zero
new_primPlusNat1(Succ(zzz62000)) → Succ(Succ(new_primPlusNat1(zzz62000)))
new_primPlusNat3(zzz90, Succ(zzz910)) → Succ(Succ(new_primPlusNat2(zzz90, zzz910)))
new_primPlusNat3(zzz90, Zero) → Succ(zzz90)
new_primPlusNat2(Succ(zzz900), Succ(zzz9100)) → Succ(Succ(new_primPlusNat2(zzz900, zzz9100)))
new_primPlusNat2(Zero, Succ(zzz9100)) → Succ(zzz9100)
new_primPlusNat2(Zero, Zero) → Zero
new_primPlusNat2(Succ(zzz900), Zero) → Succ(zzz900)

The set Q consists of the following terms:

new_primPlusNat2(Zero, Succ(x0))
new_primPlusNat3(x0, Succ(x1))
new_primPlusNat2(Succ(x0), Succ(x1))
new_primPlusNat3(x0, Zero)
new_primPlusNat1(Zero)
new_primPlusNat2(Zero, Zero)
new_primPlusNat1(Succ(x0))
new_primPlusNat2(Succ(x0), Zero)

We have to consider all minimal (P,Q,R)-chains.
By rewriting [15] the rule new_mkVBalBranch3MkVBalBranch2(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344, zzz520, zzz521, zzz52200, zzz523, zzz524, zzz31, Succ(zzz680), h) → new_mkVBalBranch3MkVBalBranch1(zzz340, zzz341, zzz34200, zzz343, zzz344, zzz520, zzz521, zzz52200, zzz523, zzz524, zzz31, new_primPlusNat2(Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat3(new_primPlusNat1(zzz34200), zzz34200)), zzz34200))), Succ(zzz34200)), h) at position [11] we obtained the following new rules:

new_mkVBalBranch3MkVBalBranch2(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344, zzz520, zzz521, zzz52200, zzz523, zzz524, zzz31, Succ(zzz680), h) → new_mkVBalBranch3MkVBalBranch1(zzz340, zzz341, zzz34200, zzz343, zzz344, zzz520, zzz521, zzz52200, zzz523, zzz524, zzz31, Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat2(Succ(new_primPlusNat3(new_primPlusNat1(zzz34200), zzz34200)), 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
                                    ↳ DependencyGraphProof
                                      ↳ QDP
                                        ↳ Rewriting
                                          ↳ QDP
                                            ↳ Rewriting
                                              ↳ QDP
                                                ↳ Rewriting
                                                  ↳ QDP
                                                    ↳ Rewriting
                                                      ↳ QDP
                                                        ↳ Rewriting
                                                          ↳ QDP
                                                            ↳ Rewriting
                                                              ↳ QDP
                                                                ↳ Rewriting
                                                                  ↳ QDP
                                                                    ↳ Rewriting
                                                                      ↳ QDP
                                                                        ↳ Rewriting
                                                                          ↳ QDP
                                                                            ↳ Rewriting
                                                                              ↳ QDP
                                                                                ↳ Rewriting
                                                                                  ↳ QDP
                                                                                    ↳ Rewriting
                                                                                      ↳ QDP
                                                                                        ↳ Rewriting
                                                                                          ↳ QDP
                                                                                            ↳ UsableRulesProof
                                                                                              ↳ QDP
                                                                                                ↳ QReductionProof
                                                                                                  ↳ QDP
                                                                                                    ↳ Rewriting
                                                                                                      ↳ QDP
                                                                                                        ↳ Rewriting
                                                                                                          ↳ QDP
                                                                                                            ↳ Rewriting
                                                                                                              ↳ QDP
                                                                                                                ↳ Rewriting
                                                                                                                  ↳ QDP
                                                                                                                    ↳ Rewriting
                                                                                                                      ↳ QDP
                                                                                                                        ↳ Rewriting
                                                                                                                          ↳ QDP
                                                                                                                            ↳ DependencyGraphProof
                                                                                                                              ↳ QDP
                                                                                                                                ↳ Rewriting
                                                                                                                                  ↳ QDP
                                                                                                                                    ↳ Rewriting
                                                                                                                                      ↳ QDP
                                                                                                                                        ↳ DependencyGraphProof
                                                                                                                                          ↳ QDP
                                                                                                                                            ↳ Rewriting
                                                                                                                                              ↳ QDP
                                                                                                                                                ↳ Rewriting
                                                                                                                                                  ↳ QDP
                                                                                                                                                    ↳ Rewriting
                                                                                                                                                      ↳ QDP
                                                                                                                                                        ↳ Rewriting
                                                                                                                                                          ↳ QDP
                                                                                                                                                            ↳ Rewriting
                                                                                                                                                              ↳ QDP
                                                                                                                                                                ↳ Rewriting
                                                                                                                                                                  ↳ QDP
                                                                                                                                                                    ↳ Rewriting
                                                                                                                                                                      ↳ QDP
                                                                                                                                                                        ↳ UsableRulesProof
                                                                                                                                                                          ↳ QDP
                                                                                                                                                                            ↳ QReductionProof
                                                                                                                                                                              ↳ QDP
                                                                                                                                                                                ↳ Rewriting
                                                                                                                                                                                  ↳ QDP
                                                                                                                                                                                    ↳ Rewriting
                                                                                                                                                                                      ↳ QDP
                                                                                                                                                                                        ↳ Rewriting
                                                                                                                                                                                          ↳ QDP
                                                                                                                                                                                            ↳ Rewriting
                                                                                                                                                                                              ↳ QDP
                                                                                                                                                                                                ↳ Rewriting
                                                                                                                                                                                                  ↳ QDP
                                                                                                                                                                                                    ↳ Rewriting
                                                                                                                                                                                                      ↳ QDP
                                                                                                                                                                                                        ↳ Rewriting
                                                                                                                                                                                                          ↳ QDP
                                                                                                                                                                                                            ↳ Rewriting
                                                                                                                                                                                                              ↳ QDP
                                                                                                                                                                                                                ↳ Rewriting
                                                                                                                                                                                                                  ↳ QDP
                                                                                                                                                                                                                    ↳ DependencyGraphProof
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP

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

new_mkVBalBranch3MkVBalBranch23(zzz929, zzz930, zzz931, zzz932, zzz933, zzz934, zzz935, zzz936, zzz937, zzz938, zzz939, ba) → new_mkVBalBranch3MkVBalBranch10(zzz929, zzz930, zzz931, zzz932, zzz933, zzz934, zzz935, zzz936, zzz937, zzz938, zzz939, new_primPlusNat2(Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat3(new_primPlusNat1(zzz931), zzz931)), zzz931))), Succ(zzz931)), ba)
new_mkVBalBranch3MkVBalBranch11(zzz2033, zzz2034, zzz2035, zzz2036, zzz2037, zzz2038, zzz2039, zzz2040, zzz2041, zzz2042, zzz2043, Zero, Succ(zzz20450), bb) → new_mkVBalBranch(zzz2043, zzz2042, Branch(zzz2033, zzz2034, Pos(Succ(zzz2035)), zzz2036, zzz2037), bb)
new_mkVBalBranch(zzz31, Branch(zzz520, zzz521, Neg(Succ(zzz52200)), zzz523, zzz524), Branch(zzz340, zzz341, zzz342, zzz343, zzz344), h) → new_mkVBalBranch3MkVBalBranch24(zzz340, zzz341, zzz342, zzz343, zzz344, zzz520, zzz521, zzz52200, zzz523, zzz524, zzz31, Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat3(new_primPlusNat1(zzz52200), zzz52200)), zzz52200))), h)
new_mkVBalBranch3MkVBalBranch211(zzz537, zzz538, zzz539, zzz540, zzz541, zzz542, zzz543, zzz544, zzz545, zzz546, zzz547, bc) → new_mkVBalBranch3MkVBalBranch15(zzz537, zzz538, zzz539, zzz540, zzz541, zzz542, zzz543, zzz544, zzz545, zzz546, zzz547, Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat2(Succ(new_primPlusNat3(new_primPlusNat1(zzz539), zzz539)), zzz539)), zzz539))), bc)
new_mkVBalBranch3MkVBalBranch26(zzz1133, zzz1134, zzz1135, zzz1136, zzz1137, zzz1138, zzz1139, zzz1140, zzz1141, zzz1142, Succ(zzz11430), Succ(zzz11440), be) → new_mkVBalBranch3MkVBalBranch26(zzz1133, zzz1134, zzz1135, zzz1136, zzz1137, zzz1138, zzz1139, zzz1140, zzz1141, zzz1142, zzz11430, zzz11440, be)
new_mkVBalBranch3MkVBalBranch24(zzz340, zzz341, Pos(zzz3420), zzz343, zzz344, zzz520, zzz521, zzz52200, zzz523, zzz524, zzz31, Succ(zzz690), h) → new_mkVBalBranch(zzz31, Branch(zzz520, zzz521, Neg(Succ(zzz52200)), zzz523, zzz524), zzz343, h)
new_mkVBalBranch3MkVBalBranch12(zzz340, zzz341, zzz34200, zzz343, zzz344, zzz520, zzz521, zzz523, zzz524, zzz31, Succ(zzz1250), h) → new_mkVBalBranch(zzz31, zzz524, Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), h)
new_mkVBalBranch3MkVBalBranch25(zzz537, zzz538, zzz539, zzz540, zzz541, zzz542, zzz543, zzz544, zzz545, zzz546, zzz547, Succ(zzz5480), Zero, bc) → new_mkVBalBranch3MkVBalBranch15(zzz537, zzz538, zzz539, zzz540, zzz541, zzz542, zzz543, zzz544, zzz545, zzz546, zzz547, Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat2(Succ(new_primPlusNat3(new_primPlusNat1(zzz539), zzz539)), zzz539)), zzz539))), bc)
new_mkVBalBranch3MkVBalBranch20(zzz929, zzz930, zzz931, zzz932, zzz933, zzz934, zzz935, zzz936, zzz937, zzz938, zzz939, Zero, Succ(zzz9410), ba) → new_mkVBalBranch(zzz939, Branch(zzz934, zzz935, Pos(Succ(zzz936)), zzz937, zzz938), zzz932, ba)
new_mkVBalBranch3MkVBalBranch24(zzz340, zzz341, Neg(Succ(Succ(Zero))), zzz343, zzz344, zzz520, zzz521, Zero, zzz523, zzz524, zzz31, Succ(Succ(zzz6900)), h) → new_mkVBalBranch3MkVBalBranch26(zzz340, zzz341, Succ(Zero), zzz343, zzz344, zzz520, zzz521, zzz523, zzz524, zzz31, Zero, Succ(zzz6900), h)
new_mkVBalBranch3MkVBalBranch17(zzz340, zzz341, zzz34200, zzz343, zzz344, zzz520, zzz521, zzz52200, zzz523, zzz524, zzz31, h) → new_mkVBalBranch(zzz31, zzz524, Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), h)
new_mkVBalBranch3MkVBalBranch1(zzz340, zzz341, zzz34200, zzz343, zzz344, zzz520, zzz521, zzz52200, zzz523, zzz524, zzz31, Succ(zzz1430), h) → new_mkVBalBranch(zzz31, zzz524, Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), h)
new_mkVBalBranch3MkVBalBranch26(zzz1133, zzz1134, zzz1135, zzz1136, zzz1137, zzz1138, zzz1139, zzz1140, zzz1141, zzz1142, Zero, Zero, be) → new_mkVBalBranch3MkVBalBranch29(zzz1133, zzz1134, zzz1135, zzz1136, zzz1137, zzz1138, zzz1139, zzz1140, zzz1141, zzz1142, be)
new_mkVBalBranch3MkVBalBranch20(zzz929, zzz930, zzz931, zzz932, zzz933, zzz934, zzz935, zzz936, zzz937, zzz938, zzz939, Zero, Zero, ba) → new_mkVBalBranch3MkVBalBranch23(zzz929, zzz930, zzz931, zzz932, zzz933, zzz934, zzz935, zzz936, zzz937, zzz938, zzz939, ba)
new_mkVBalBranch3MkVBalBranch24(zzz340, zzz341, Neg(Succ(Zero)), zzz343, zzz344, zzz520, zzz521, zzz52200, zzz523, zzz524, zzz31, Succ(zzz690), h) → new_mkVBalBranch(zzz31, Branch(zzz520, zzz521, Neg(Succ(zzz52200)), zzz523, zzz524), zzz343, h)
new_mkVBalBranch3MkVBalBranch13(zzz340, zzz341, zzz34200, zzz343, zzz344, zzz520, zzz521, zzz523, zzz524, zzz31, Succ(zzz1290), h) → new_mkVBalBranch(zzz31, zzz524, Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), h)
new_mkVBalBranch3MkVBalBranch2(zzz340, zzz341, Pos(Succ(zzz34200)), zzz343, zzz344, zzz520, zzz521, zzz52200, zzz523, zzz524, zzz31, Succ(zzz680), h) → new_mkVBalBranch3MkVBalBranch20(zzz340, zzz341, zzz34200, zzz343, zzz344, zzz520, zzz521, zzz52200, zzz523, zzz524, zzz31, Succ(new_primPlusNat2(zzz680, zzz52200)), zzz34200, h)
new_mkVBalBranch(zzz31, Branch(zzz520, zzz521, Neg(Zero), zzz523, zzz524), Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), h) → new_mkVBalBranch3MkVBalBranch13(zzz340, zzz341, zzz34200, zzz343, zzz344, zzz520, zzz521, zzz523, zzz524, zzz31, new_primPlusNat2(Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat3(new_primPlusNat1(zzz34200), zzz34200)), zzz34200))), Succ(zzz34200)), h)
new_mkVBalBranch3MkVBalBranch24(zzz340, zzz341, Neg(Zero), zzz343, zzz344, zzz520, zzz521, zzz52200, zzz523, zzz524, zzz31, Succ(zzz690), h) → new_mkVBalBranch(zzz31, Branch(zzz520, zzz521, Neg(Succ(zzz52200)), zzz523, zzz524), zzz343, h)
new_mkVBalBranch(zzz31, Branch(zzz520, zzz521, Neg(Zero), zzz523, zzz524), Branch(zzz340, zzz341, Pos(Succ(zzz34200)), zzz343, zzz344), h) → new_mkVBalBranch(zzz31, Branch(zzz520, zzz521, Neg(Zero), zzz523, zzz524), zzz343, h)
new_mkVBalBranch3MkVBalBranch20(zzz929, zzz930, zzz931, zzz932, zzz933, zzz934, zzz935, zzz936, zzz937, zzz938, zzz939, Succ(zzz9400), Succ(zzz9410), ba) → new_mkVBalBranch3MkVBalBranch20(zzz929, zzz930, zzz931, zzz932, zzz933, zzz934, zzz935, zzz936, zzz937, zzz938, zzz939, zzz9400, zzz9410, ba)
new_mkVBalBranch3MkVBalBranch26(zzz1133, zzz1134, zzz1135, zzz1136, zzz1137, zzz1138, zzz1139, zzz1140, zzz1141, zzz1142, Succ(zzz11430), Zero, be) → new_mkVBalBranch3MkVBalBranch212(zzz1133, zzz1134, zzz1135, zzz1136, zzz1137, zzz1138, zzz1139, zzz1140, zzz1141, zzz1142, be)
new_mkVBalBranch3MkVBalBranch1(zzz340, zzz341, zzz34200, zzz343, zzz344, zzz520, zzz521, zzz52200, zzz523, zzz524, zzz31, Zero, h) → new_mkVBalBranch3MkVBalBranch17(zzz340, zzz341, zzz34200, zzz343, zzz344, zzz520, zzz521, zzz52200, zzz523, zzz524, zzz31, h)
new_mkVBalBranch3MkVBalBranch16(zzz1702, zzz1703, zzz1704, zzz1705, zzz1706, zzz1707, zzz1708, zzz1709, zzz1710, zzz1711, zzz1712, Succ(zzz17130), Succ(zzz17140), bd) → new_mkVBalBranch3MkVBalBranch16(zzz1702, zzz1703, zzz1704, zzz1705, zzz1706, zzz1707, zzz1708, zzz1709, zzz1710, zzz1711, zzz1712, zzz17130, zzz17140, bd)
new_mkVBalBranch3MkVBalBranch25(zzz537, zzz538, zzz539, zzz540, zzz541, zzz542, zzz543, zzz544, zzz545, zzz546, zzz547, Zero, Succ(zzz5490), bc) → new_mkVBalBranch(zzz547, Branch(zzz542, zzz543, Neg(Succ(Succ(zzz544))), zzz545, zzz546), zzz540, bc)
new_mkVBalBranch3MkVBalBranch11(zzz2033, zzz2034, zzz2035, zzz2036, zzz2037, zzz2038, zzz2039, zzz2040, zzz2041, zzz2042, zzz2043, Succ(zzz20440), Succ(zzz20450), bb) → new_mkVBalBranch3MkVBalBranch11(zzz2033, zzz2034, zzz2035, zzz2036, zzz2037, zzz2038, zzz2039, zzz2040, zzz2041, zzz2042, zzz2043, zzz20440, zzz20450, bb)
new_mkVBalBranch3MkVBalBranch25(zzz537, zzz538, zzz539, zzz540, zzz541, zzz542, zzz543, zzz544, zzz545, zzz546, zzz547, Succ(zzz5480), Succ(zzz5490), bc) → new_mkVBalBranch3MkVBalBranch25(zzz537, zzz538, zzz539, zzz540, zzz541, zzz542, zzz543, zzz544, zzz545, zzz546, zzz547, zzz5480, zzz5490, bc)
new_mkVBalBranch3MkVBalBranch29(zzz818, zzz819, zzz820, zzz821, zzz822, zzz823, zzz824, zzz825, zzz826, zzz827, bf) → new_mkVBalBranch3MkVBalBranch14(zzz818, zzz819, zzz820, zzz821, zzz822, zzz823, zzz824, zzz825, zzz826, zzz827, new_primPlusNat2(Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat3(new_primPlusNat1(zzz820), zzz820)), zzz820))), Succ(zzz820)), bf)
new_mkVBalBranch3MkVBalBranch10(zzz929, zzz930, zzz931, zzz932, zzz933, zzz934, zzz935, zzz936, zzz937, zzz938, zzz939, Succ(zzz10020), ba) → new_mkVBalBranch3MkVBalBranch11(zzz929, zzz930, zzz931, zzz932, zzz933, zzz934, zzz935, zzz936, zzz937, zzz938, zzz939, Succ(zzz10020), Succ(zzz936), ba)
new_mkVBalBranch(zzz31, Branch(zzz520, zzz521, Pos(Succ(zzz52200)), zzz523, zzz524), Branch(zzz340, zzz341, zzz342, zzz343, zzz344), h) → new_mkVBalBranch3MkVBalBranch2(zzz340, zzz341, zzz342, zzz343, zzz344, zzz520, zzz521, zzz52200, zzz523, zzz524, zzz31, Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat3(new_primPlusNat1(zzz52200), zzz52200)), zzz52200))), h)
new_mkVBalBranch3MkVBalBranch14(zzz818, zzz819, zzz820, zzz821, zzz822, zzz823, zzz824, zzz825, zzz826, zzz827, Succ(zzz8960), bf) → new_mkVBalBranch3MkVBalBranch16(zzz818, zzz819, zzz820, zzz821, zzz822, zzz823, zzz824, Zero, zzz825, zzz826, zzz827, Succ(Zero), Succ(zzz8960), bf)
new_mkVBalBranch3MkVBalBranch26(zzz1133, zzz1134, zzz1135, zzz1136, zzz1137, zzz1138, zzz1139, zzz1140, zzz1141, zzz1142, Zero, Succ(zzz11440), be) → new_mkVBalBranch(zzz1142, Branch(zzz1138, zzz1139, Neg(Succ(Zero)), zzz1140, zzz1141), zzz1136, be)
new_mkVBalBranch3MkVBalBranch24(zzz340, zzz341, Neg(Succ(Succ(Succ(zzz3420000)))), zzz343, zzz344, zzz520, zzz521, Succ(zzz522000), zzz523, zzz524, zzz31, Succ(Succ(zzz6900)), h) → new_mkVBalBranch3MkVBalBranch25(zzz340, zzz341, Succ(Succ(zzz3420000)), zzz343, zzz344, zzz520, zzz521, zzz522000, zzz523, zzz524, zzz31, Succ(zzz3420000), Succ(Succ(new_primPlusNat2(zzz6900, zzz522000))), h)
new_mkVBalBranch(zzz31, Branch(zzz520, zzz521, Pos(Zero), zzz523, zzz524), Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), h) → new_mkVBalBranch3MkVBalBranch12(zzz340, zzz341, zzz34200, zzz343, zzz344, zzz520, zzz521, zzz523, zzz524, zzz31, Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat2(Succ(new_primPlusNat3(new_primPlusNat1(zzz34200), zzz34200)), zzz34200)), zzz34200))), h)
new_mkVBalBranch3MkVBalBranch24(zzz340, zzz341, Neg(Succ(Succ(Zero))), zzz343, zzz344, zzz520, zzz521, Succ(zzz522000), zzz523, zzz524, zzz31, Succ(Succ(zzz6900)), h) → new_mkVBalBranch3MkVBalBranch25(zzz340, zzz341, Succ(Zero), zzz343, zzz344, zzz520, zzz521, zzz522000, zzz523, zzz524, zzz31, Zero, Succ(Succ(new_primPlusNat2(zzz6900, zzz522000))), h)
new_mkVBalBranch(zzz31, Branch(zzz520, zzz521, Pos(Zero), zzz523, zzz524), Branch(zzz340, zzz341, Pos(Succ(zzz34200)), zzz343, zzz344), h) → new_mkVBalBranch(zzz31, Branch(zzz520, zzz521, Pos(Zero), zzz523, zzz524), zzz343, h)
new_mkVBalBranch3MkVBalBranch2(zzz340, zzz341, Pos(Zero), zzz343, zzz344, zzz520, zzz521, zzz52200, zzz523, zzz524, zzz31, Succ(zzz680), h) → new_mkVBalBranch(zzz31, zzz524, Branch(zzz340, zzz341, Pos(Zero), zzz343, zzz344), h)
new_mkVBalBranch3MkVBalBranch20(zzz929, zzz930, zzz931, zzz932, zzz933, zzz934, zzz935, zzz936, zzz937, zzz938, zzz939, Succ(zzz9400), Zero, ba) → new_mkVBalBranch3MkVBalBranch10(zzz929, zzz930, zzz931, zzz932, zzz933, zzz934, zzz935, zzz936, zzz937, zzz938, zzz939, new_primPlusNat2(Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat3(new_primPlusNat1(zzz931), zzz931)), zzz931))), Succ(zzz931)), ba)
new_mkVBalBranch3MkVBalBranch2(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344, zzz520, zzz521, zzz52200, zzz523, zzz524, zzz31, Succ(zzz680), h) → new_mkVBalBranch3MkVBalBranch1(zzz340, zzz341, zzz34200, zzz343, zzz344, zzz520, zzz521, zzz52200, zzz523, zzz524, zzz31, Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat2(Succ(new_primPlusNat3(new_primPlusNat1(zzz34200), zzz34200)), zzz34200)), zzz34200))), h)
new_mkVBalBranch3MkVBalBranch2(zzz340, zzz341, Neg(Zero), zzz343, zzz344, zzz520, zzz521, zzz52200, zzz523, zzz524, zzz31, Succ(zzz680), h) → new_mkVBalBranch(zzz31, zzz524, Branch(zzz340, zzz341, Neg(Zero), zzz343, zzz344), h)
new_mkVBalBranch3MkVBalBranch16(zzz1702, zzz1703, zzz1704, zzz1705, zzz1706, zzz1707, zzz1708, zzz1709, zzz1710, zzz1711, zzz1712, Zero, Succ(zzz17140), bd) → new_mkVBalBranch(zzz1712, zzz1711, Branch(zzz1702, zzz1703, Neg(Succ(zzz1704)), zzz1705, zzz1706), bd)
new_mkVBalBranch3MkVBalBranch10(zzz929, zzz930, zzz931, zzz932, zzz933, zzz934, zzz935, zzz936, zzz937, zzz938, zzz939, Zero, ba) → new_mkVBalBranch3MkVBalBranch11(zzz929, zzz930, zzz931, zzz932, zzz933, zzz934, zzz935, zzz936, zzz937, zzz938, zzz939, Zero, Succ(zzz936), ba)
new_mkVBalBranch3MkVBalBranch24(zzz340, zzz341, Neg(Succ(Succ(Succ(zzz3420000)))), zzz343, zzz344, zzz520, zzz521, Zero, zzz523, zzz524, zzz31, Succ(Succ(zzz6900)), h) → new_mkVBalBranch3MkVBalBranch26(zzz340, zzz341, Succ(Succ(zzz3420000)), zzz343, zzz344, zzz520, zzz521, zzz523, zzz524, zzz31, Succ(zzz3420000), Succ(zzz6900), h)
new_mkVBalBranch3MkVBalBranch15(zzz537, zzz538, zzz539, zzz540, zzz541, zzz542, zzz543, zzz544, zzz545, zzz546, zzz547, Succ(zzz6990), bc) → new_mkVBalBranch3MkVBalBranch16(zzz537, zzz538, zzz539, zzz540, zzz541, zzz542, zzz543, Succ(zzz544), zzz545, zzz546, zzz547, Succ(Succ(zzz544)), Succ(zzz6990), bc)
new_mkVBalBranch3MkVBalBranch25(zzz537, zzz538, zzz539, zzz540, zzz541, zzz542, zzz543, zzz544, zzz545, zzz546, zzz547, Zero, Zero, bc) → new_mkVBalBranch3MkVBalBranch211(zzz537, zzz538, zzz539, zzz540, zzz541, zzz542, zzz543, zzz544, zzz545, zzz546, zzz547, bc)
new_mkVBalBranch3MkVBalBranch212(zzz818, zzz819, zzz820, zzz821, zzz822, zzz823, zzz824, zzz825, zzz826, zzz827, bf) → new_mkVBalBranch3MkVBalBranch14(zzz818, zzz819, zzz820, zzz821, zzz822, zzz823, zzz824, zzz825, zzz826, zzz827, new_primPlusNat2(Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat3(new_primPlusNat1(zzz820), zzz820)), zzz820))), Succ(zzz820)), bf)

The TRS R consists of the following rules:

new_primPlusNat1(Zero) → Zero
new_primPlusNat1(Succ(zzz62000)) → Succ(Succ(new_primPlusNat1(zzz62000)))
new_primPlusNat3(zzz90, Succ(zzz910)) → Succ(Succ(new_primPlusNat2(zzz90, zzz910)))
new_primPlusNat3(zzz90, Zero) → Succ(zzz90)
new_primPlusNat2(Succ(zzz900), Succ(zzz9100)) → Succ(Succ(new_primPlusNat2(zzz900, zzz9100)))
new_primPlusNat2(Zero, Succ(zzz9100)) → Succ(zzz9100)
new_primPlusNat2(Zero, Zero) → Zero
new_primPlusNat2(Succ(zzz900), Zero) → Succ(zzz900)

The set Q consists of the following terms:

new_primPlusNat2(Zero, Succ(x0))
new_primPlusNat3(x0, Succ(x1))
new_primPlusNat2(Succ(x0), Succ(x1))
new_primPlusNat3(x0, Zero)
new_primPlusNat1(Zero)
new_primPlusNat2(Zero, Zero)
new_primPlusNat1(Succ(x0))
new_primPlusNat2(Succ(x0), Zero)

We have to consider all minimal (P,Q,R)-chains.
The approximation of the Dependency Graph [15,17,22] contains 1 SCC with 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
                                    ↳ DependencyGraphProof
                                      ↳ QDP
                                        ↳ Rewriting
                                          ↳ QDP
                                            ↳ Rewriting
                                              ↳ QDP
                                                ↳ Rewriting
                                                  ↳ QDP
                                                    ↳ Rewriting
                                                      ↳ QDP
                                                        ↳ Rewriting
                                                          ↳ QDP
                                                            ↳ Rewriting
                                                              ↳ QDP
                                                                ↳ Rewriting
                                                                  ↳ QDP
                                                                    ↳ Rewriting
                                                                      ↳ QDP
                                                                        ↳ Rewriting
                                                                          ↳ QDP
                                                                            ↳ Rewriting
                                                                              ↳ QDP
                                                                                ↳ Rewriting
                                                                                  ↳ QDP
                                                                                    ↳ Rewriting
                                                                                      ↳ QDP
                                                                                        ↳ Rewriting
                                                                                          ↳ QDP
                                                                                            ↳ UsableRulesProof
                                                                                              ↳ QDP
                                                                                                ↳ QReductionProof
                                                                                                  ↳ QDP
                                                                                                    ↳ Rewriting
                                                                                                      ↳ QDP
                                                                                                        ↳ Rewriting
                                                                                                          ↳ QDP
                                                                                                            ↳ Rewriting
                                                                                                              ↳ QDP
                                                                                                                ↳ Rewriting
                                                                                                                  ↳ QDP
                                                                                                                    ↳ Rewriting
                                                                                                                      ↳ QDP
                                                                                                                        ↳ Rewriting
                                                                                                                          ↳ QDP
                                                                                                                            ↳ DependencyGraphProof
                                                                                                                              ↳ QDP
                                                                                                                                ↳ Rewriting
                                                                                                                                  ↳ QDP
                                                                                                                                    ↳ Rewriting
                                                                                                                                      ↳ QDP
                                                                                                                                        ↳ DependencyGraphProof
                                                                                                                                          ↳ QDP
                                                                                                                                            ↳ Rewriting
                                                                                                                                              ↳ QDP
                                                                                                                                                ↳ Rewriting
                                                                                                                                                  ↳ QDP
                                                                                                                                                    ↳ Rewriting
                                                                                                                                                      ↳ QDP
                                                                                                                                                        ↳ Rewriting
                                                                                                                                                          ↳ QDP
                                                                                                                                                            ↳ Rewriting
                                                                                                                                                              ↳ QDP
                                                                                                                                                                ↳ Rewriting
                                                                                                                                                                  ↳ QDP
                                                                                                                                                                    ↳ Rewriting
                                                                                                                                                                      ↳ QDP
                                                                                                                                                                        ↳ UsableRulesProof
                                                                                                                                                                          ↳ QDP
                                                                                                                                                                            ↳ QReductionProof
                                                                                                                                                                              ↳ QDP
                                                                                                                                                                                ↳ Rewriting
                                                                                                                                                                                  ↳ QDP
                                                                                                                                                                                    ↳ Rewriting
                                                                                                                                                                                      ↳ QDP
                                                                                                                                                                                        ↳ Rewriting
                                                                                                                                                                                          ↳ QDP
                                                                                                                                                                                            ↳ Rewriting
                                                                                                                                                                                              ↳ QDP
                                                                                                                                                                                                ↳ Rewriting
                                                                                                                                                                                                  ↳ QDP
                                                                                                                                                                                                    ↳ Rewriting
                                                                                                                                                                                                      ↳ QDP
                                                                                                                                                                                                        ↳ Rewriting
                                                                                                                                                                                                          ↳ QDP
                                                                                                                                                                                                            ↳ Rewriting
                                                                                                                                                                                                              ↳ QDP
                                                                                                                                                                                                                ↳ Rewriting
                                                                                                                                                                                                                  ↳ QDP
                                                                                                                                                                                                                    ↳ DependencyGraphProof
                                                                                                                                                                                                                      ↳ QDP
                                                                                                                                                                                                                        ↳ Rewriting
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP

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

new_mkVBalBranch3MkVBalBranch11(zzz2033, zzz2034, zzz2035, zzz2036, zzz2037, zzz2038, zzz2039, zzz2040, zzz2041, zzz2042, zzz2043, Zero, Succ(zzz20450), bb) → new_mkVBalBranch(zzz2043, zzz2042, Branch(zzz2033, zzz2034, Pos(Succ(zzz2035)), zzz2036, zzz2037), bb)
new_mkVBalBranch3MkVBalBranch23(zzz929, zzz930, zzz931, zzz932, zzz933, zzz934, zzz935, zzz936, zzz937, zzz938, zzz939, ba) → new_mkVBalBranch3MkVBalBranch10(zzz929, zzz930, zzz931, zzz932, zzz933, zzz934, zzz935, zzz936, zzz937, zzz938, zzz939, new_primPlusNat2(Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat3(new_primPlusNat1(zzz931), zzz931)), zzz931))), Succ(zzz931)), ba)
new_mkVBalBranch3MkVBalBranch211(zzz537, zzz538, zzz539, zzz540, zzz541, zzz542, zzz543, zzz544, zzz545, zzz546, zzz547, bc) → new_mkVBalBranch3MkVBalBranch15(zzz537, zzz538, zzz539, zzz540, zzz541, zzz542, zzz543, zzz544, zzz545, zzz546, zzz547, Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat2(Succ(new_primPlusNat3(new_primPlusNat1(zzz539), zzz539)), zzz539)), zzz539))), bc)
new_mkVBalBranch(zzz31, Branch(zzz520, zzz521, Neg(Succ(zzz52200)), zzz523, zzz524), Branch(zzz340, zzz341, zzz342, zzz343, zzz344), h) → new_mkVBalBranch3MkVBalBranch24(zzz340, zzz341, zzz342, zzz343, zzz344, zzz520, zzz521, zzz52200, zzz523, zzz524, zzz31, Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat3(new_primPlusNat1(zzz52200), zzz52200)), zzz52200))), h)
new_mkVBalBranch3MkVBalBranch26(zzz1133, zzz1134, zzz1135, zzz1136, zzz1137, zzz1138, zzz1139, zzz1140, zzz1141, zzz1142, Succ(zzz11430), Succ(zzz11440), be) → new_mkVBalBranch3MkVBalBranch26(zzz1133, zzz1134, zzz1135, zzz1136, zzz1137, zzz1138, zzz1139, zzz1140, zzz1141, zzz1142, zzz11430, zzz11440, be)
new_mkVBalBranch3MkVBalBranch24(zzz340, zzz341, Pos(zzz3420), zzz343, zzz344, zzz520, zzz521, zzz52200, zzz523, zzz524, zzz31, Succ(zzz690), h) → new_mkVBalBranch(zzz31, Branch(zzz520, zzz521, Neg(Succ(zzz52200)), zzz523, zzz524), zzz343, h)
new_mkVBalBranch3MkVBalBranch12(zzz340, zzz341, zzz34200, zzz343, zzz344, zzz520, zzz521, zzz523, zzz524, zzz31, Succ(zzz1250), h) → new_mkVBalBranch(zzz31, zzz524, Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), h)
new_mkVBalBranch3MkVBalBranch25(zzz537, zzz538, zzz539, zzz540, zzz541, zzz542, zzz543, zzz544, zzz545, zzz546, zzz547, Succ(zzz5480), Zero, bc) → new_mkVBalBranch3MkVBalBranch15(zzz537, zzz538, zzz539, zzz540, zzz541, zzz542, zzz543, zzz544, zzz545, zzz546, zzz547, Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat2(Succ(new_primPlusNat3(new_primPlusNat1(zzz539), zzz539)), zzz539)), zzz539))), bc)
new_mkVBalBranch3MkVBalBranch20(zzz929, zzz930, zzz931, zzz932, zzz933, zzz934, zzz935, zzz936, zzz937, zzz938, zzz939, Zero, Succ(zzz9410), ba) → new_mkVBalBranch(zzz939, Branch(zzz934, zzz935, Pos(Succ(zzz936)), zzz937, zzz938), zzz932, ba)
new_mkVBalBranch3MkVBalBranch24(zzz340, zzz341, Neg(Succ(Succ(Zero))), zzz343, zzz344, zzz520, zzz521, Zero, zzz523, zzz524, zzz31, Succ(Succ(zzz6900)), h) → new_mkVBalBranch3MkVBalBranch26(zzz340, zzz341, Succ(Zero), zzz343, zzz344, zzz520, zzz521, zzz523, zzz524, zzz31, Zero, Succ(zzz6900), h)
new_mkVBalBranch3MkVBalBranch1(zzz340, zzz341, zzz34200, zzz343, zzz344, zzz520, zzz521, zzz52200, zzz523, zzz524, zzz31, Succ(zzz1430), h) → new_mkVBalBranch(zzz31, zzz524, Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), h)
new_mkVBalBranch3MkVBalBranch26(zzz1133, zzz1134, zzz1135, zzz1136, zzz1137, zzz1138, zzz1139, zzz1140, zzz1141, zzz1142, Zero, Zero, be) → new_mkVBalBranch3MkVBalBranch29(zzz1133, zzz1134, zzz1135, zzz1136, zzz1137, zzz1138, zzz1139, zzz1140, zzz1141, zzz1142, be)
new_mkVBalBranch3MkVBalBranch20(zzz929, zzz930, zzz931, zzz932, zzz933, zzz934, zzz935, zzz936, zzz937, zzz938, zzz939, Zero, Zero, ba) → new_mkVBalBranch3MkVBalBranch23(zzz929, zzz930, zzz931, zzz932, zzz933, zzz934, zzz935, zzz936, zzz937, zzz938, zzz939, ba)
new_mkVBalBranch3MkVBalBranch24(zzz340, zzz341, Neg(Succ(Zero)), zzz343, zzz344, zzz520, zzz521, zzz52200, zzz523, zzz524, zzz31, Succ(zzz690), h) → new_mkVBalBranch(zzz31, Branch(zzz520, zzz521, Neg(Succ(zzz52200)), zzz523, zzz524), zzz343, h)
new_mkVBalBranch3MkVBalBranch13(zzz340, zzz341, zzz34200, zzz343, zzz344, zzz520, zzz521, zzz523, zzz524, zzz31, Succ(zzz1290), h) → new_mkVBalBranch(zzz31, zzz524, Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), h)
new_mkVBalBranch3MkVBalBranch2(zzz340, zzz341, Pos(Succ(zzz34200)), zzz343, zzz344, zzz520, zzz521, zzz52200, zzz523, zzz524, zzz31, Succ(zzz680), h) → new_mkVBalBranch3MkVBalBranch20(zzz340, zzz341, zzz34200, zzz343, zzz344, zzz520, zzz521, zzz52200, zzz523, zzz524, zzz31, Succ(new_primPlusNat2(zzz680, zzz52200)), zzz34200, h)
new_mkVBalBranch(zzz31, Branch(zzz520, zzz521, Neg(Zero), zzz523, zzz524), Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), h) → new_mkVBalBranch3MkVBalBranch13(zzz340, zzz341, zzz34200, zzz343, zzz344, zzz520, zzz521, zzz523, zzz524, zzz31, new_primPlusNat2(Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat3(new_primPlusNat1(zzz34200), zzz34200)), zzz34200))), Succ(zzz34200)), h)
new_mkVBalBranch(zzz31, Branch(zzz520, zzz521, Neg(Zero), zzz523, zzz524), Branch(zzz340, zzz341, Pos(Succ(zzz34200)), zzz343, zzz344), h) → new_mkVBalBranch(zzz31, Branch(zzz520, zzz521, Neg(Zero), zzz523, zzz524), zzz343, h)
new_mkVBalBranch3MkVBalBranch24(zzz340, zzz341, Neg(Zero), zzz343, zzz344, zzz520, zzz521, zzz52200, zzz523, zzz524, zzz31, Succ(zzz690), h) → new_mkVBalBranch(zzz31, Branch(zzz520, zzz521, Neg(Succ(zzz52200)), zzz523, zzz524), zzz343, h)
new_mkVBalBranch3MkVBalBranch20(zzz929, zzz930, zzz931, zzz932, zzz933, zzz934, zzz935, zzz936, zzz937, zzz938, zzz939, Succ(zzz9400), Succ(zzz9410), ba) → new_mkVBalBranch3MkVBalBranch20(zzz929, zzz930, zzz931, zzz932, zzz933, zzz934, zzz935, zzz936, zzz937, zzz938, zzz939, zzz9400, zzz9410, ba)
new_mkVBalBranch3MkVBalBranch26(zzz1133, zzz1134, zzz1135, zzz1136, zzz1137, zzz1138, zzz1139, zzz1140, zzz1141, zzz1142, Succ(zzz11430), Zero, be) → new_mkVBalBranch3MkVBalBranch212(zzz1133, zzz1134, zzz1135, zzz1136, zzz1137, zzz1138, zzz1139, zzz1140, zzz1141, zzz1142, be)
new_mkVBalBranch3MkVBalBranch16(zzz1702, zzz1703, zzz1704, zzz1705, zzz1706, zzz1707, zzz1708, zzz1709, zzz1710, zzz1711, zzz1712, Succ(zzz17130), Succ(zzz17140), bd) → new_mkVBalBranch3MkVBalBranch16(zzz1702, zzz1703, zzz1704, zzz1705, zzz1706, zzz1707, zzz1708, zzz1709, zzz1710, zzz1711, zzz1712, zzz17130, zzz17140, bd)
new_mkVBalBranch3MkVBalBranch25(zzz537, zzz538, zzz539, zzz540, zzz541, zzz542, zzz543, zzz544, zzz545, zzz546, zzz547, Zero, Succ(zzz5490), bc) → new_mkVBalBranch(zzz547, Branch(zzz542, zzz543, Neg(Succ(Succ(zzz544))), zzz545, zzz546), zzz540, bc)
new_mkVBalBranch3MkVBalBranch11(zzz2033, zzz2034, zzz2035, zzz2036, zzz2037, zzz2038, zzz2039, zzz2040, zzz2041, zzz2042, zzz2043, Succ(zzz20440), Succ(zzz20450), bb) → new_mkVBalBranch3MkVBalBranch11(zzz2033, zzz2034, zzz2035, zzz2036, zzz2037, zzz2038, zzz2039, zzz2040, zzz2041, zzz2042, zzz2043, zzz20440, zzz20450, bb)
new_mkVBalBranch3MkVBalBranch25(zzz537, zzz538, zzz539, zzz540, zzz541, zzz542, zzz543, zzz544, zzz545, zzz546, zzz547, Succ(zzz5480), Succ(zzz5490), bc) → new_mkVBalBranch3MkVBalBranch25(zzz537, zzz538, zzz539, zzz540, zzz541, zzz542, zzz543, zzz544, zzz545, zzz546, zzz547, zzz5480, zzz5490, bc)
new_mkVBalBranch3MkVBalBranch29(zzz818, zzz819, zzz820, zzz821, zzz822, zzz823, zzz824, zzz825, zzz826, zzz827, bf) → new_mkVBalBranch3MkVBalBranch14(zzz818, zzz819, zzz820, zzz821, zzz822, zzz823, zzz824, zzz825, zzz826, zzz827, new_primPlusNat2(Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat3(new_primPlusNat1(zzz820), zzz820)), zzz820))), Succ(zzz820)), bf)
new_mkVBalBranch3MkVBalBranch10(zzz929, zzz930, zzz931, zzz932, zzz933, zzz934, zzz935, zzz936, zzz937, zzz938, zzz939, Succ(zzz10020), ba) → new_mkVBalBranch3MkVBalBranch11(zzz929, zzz930, zzz931, zzz932, zzz933, zzz934, zzz935, zzz936, zzz937, zzz938, zzz939, Succ(zzz10020), Succ(zzz936), ba)
new_mkVBalBranch(zzz31, Branch(zzz520, zzz521, Pos(Succ(zzz52200)), zzz523, zzz524), Branch(zzz340, zzz341, zzz342, zzz343, zzz344), h) → new_mkVBalBranch3MkVBalBranch2(zzz340, zzz341, zzz342, zzz343, zzz344, zzz520, zzz521, zzz52200, zzz523, zzz524, zzz31, Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat3(new_primPlusNat1(zzz52200), zzz52200)), zzz52200))), h)
new_mkVBalBranch3MkVBalBranch14(zzz818, zzz819, zzz820, zzz821, zzz822, zzz823, zzz824, zzz825, zzz826, zzz827, Succ(zzz8960), bf) → new_mkVBalBranch3MkVBalBranch16(zzz818, zzz819, zzz820, zzz821, zzz822, zzz823, zzz824, Zero, zzz825, zzz826, zzz827, Succ(Zero), Succ(zzz8960), bf)
new_mkVBalBranch(zzz31, Branch(zzz520, zzz521, Pos(Zero), zzz523, zzz524), Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), h) → new_mkVBalBranch3MkVBalBranch12(zzz340, zzz341, zzz34200, zzz343, zzz344, zzz520, zzz521, zzz523, zzz524, zzz31, Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat2(Succ(new_primPlusNat3(new_primPlusNat1(zzz34200), zzz34200)), zzz34200)), zzz34200))), h)
new_mkVBalBranch3MkVBalBranch26(zzz1133, zzz1134, zzz1135, zzz1136, zzz1137, zzz1138, zzz1139, zzz1140, zzz1141, zzz1142, Zero, Succ(zzz11440), be) → new_mkVBalBranch(zzz1142, Branch(zzz1138, zzz1139, Neg(Succ(Zero)), zzz1140, zzz1141), zzz1136, be)
new_mkVBalBranch3MkVBalBranch24(zzz340, zzz341, Neg(Succ(Succ(Succ(zzz3420000)))), zzz343, zzz344, zzz520, zzz521, Succ(zzz522000), zzz523, zzz524, zzz31, Succ(Succ(zzz6900)), h) → new_mkVBalBranch3MkVBalBranch25(zzz340, zzz341, Succ(Succ(zzz3420000)), zzz343, zzz344, zzz520, zzz521, zzz522000, zzz523, zzz524, zzz31, Succ(zzz3420000), Succ(Succ(new_primPlusNat2(zzz6900, zzz522000))), h)
new_mkVBalBranch3MkVBalBranch24(zzz340, zzz341, Neg(Succ(Succ(Zero))), zzz343, zzz344, zzz520, zzz521, Succ(zzz522000), zzz523, zzz524, zzz31, Succ(Succ(zzz6900)), h) → new_mkVBalBranch3MkVBalBranch25(zzz340, zzz341, Succ(Zero), zzz343, zzz344, zzz520, zzz521, zzz522000, zzz523, zzz524, zzz31, Zero, Succ(Succ(new_primPlusNat2(zzz6900, zzz522000))), h)
new_mkVBalBranch(zzz31, Branch(zzz520, zzz521, Pos(Zero), zzz523, zzz524), Branch(zzz340, zzz341, Pos(Succ(zzz34200)), zzz343, zzz344), h) → new_mkVBalBranch(zzz31, Branch(zzz520, zzz521, Pos(Zero), zzz523, zzz524), zzz343, h)
new_mkVBalBranch3MkVBalBranch2(zzz340, zzz341, Pos(Zero), zzz343, zzz344, zzz520, zzz521, zzz52200, zzz523, zzz524, zzz31, Succ(zzz680), h) → new_mkVBalBranch(zzz31, zzz524, Branch(zzz340, zzz341, Pos(Zero), zzz343, zzz344), h)
new_mkVBalBranch3MkVBalBranch20(zzz929, zzz930, zzz931, zzz932, zzz933, zzz934, zzz935, zzz936, zzz937, zzz938, zzz939, Succ(zzz9400), Zero, ba) → new_mkVBalBranch3MkVBalBranch10(zzz929, zzz930, zzz931, zzz932, zzz933, zzz934, zzz935, zzz936, zzz937, zzz938, zzz939, new_primPlusNat2(Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat3(new_primPlusNat1(zzz931), zzz931)), zzz931))), Succ(zzz931)), ba)
new_mkVBalBranch3MkVBalBranch2(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344, zzz520, zzz521, zzz52200, zzz523, zzz524, zzz31, Succ(zzz680), h) → new_mkVBalBranch3MkVBalBranch1(zzz340, zzz341, zzz34200, zzz343, zzz344, zzz520, zzz521, zzz52200, zzz523, zzz524, zzz31, Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat2(Succ(new_primPlusNat3(new_primPlusNat1(zzz34200), zzz34200)), zzz34200)), zzz34200))), h)
new_mkVBalBranch3MkVBalBranch2(zzz340, zzz341, Neg(Zero), zzz343, zzz344, zzz520, zzz521, zzz52200, zzz523, zzz524, zzz31, Succ(zzz680), h) → new_mkVBalBranch(zzz31, zzz524, Branch(zzz340, zzz341, Neg(Zero), zzz343, zzz344), h)
new_mkVBalBranch3MkVBalBranch16(zzz1702, zzz1703, zzz1704, zzz1705, zzz1706, zzz1707, zzz1708, zzz1709, zzz1710, zzz1711, zzz1712, Zero, Succ(zzz17140), bd) → new_mkVBalBranch(zzz1712, zzz1711, Branch(zzz1702, zzz1703, Neg(Succ(zzz1704)), zzz1705, zzz1706), bd)
new_mkVBalBranch3MkVBalBranch10(zzz929, zzz930, zzz931, zzz932, zzz933, zzz934, zzz935, zzz936, zzz937, zzz938, zzz939, Zero, ba) → new_mkVBalBranch3MkVBalBranch11(zzz929, zzz930, zzz931, zzz932, zzz933, zzz934, zzz935, zzz936, zzz937, zzz938, zzz939, Zero, Succ(zzz936), ba)
new_mkVBalBranch3MkVBalBranch15(zzz537, zzz538, zzz539, zzz540, zzz541, zzz542, zzz543, zzz544, zzz545, zzz546, zzz547, Succ(zzz6990), bc) → new_mkVBalBranch3MkVBalBranch16(zzz537, zzz538, zzz539, zzz540, zzz541, zzz542, zzz543, Succ(zzz544), zzz545, zzz546, zzz547, Succ(Succ(zzz544)), Succ(zzz6990), bc)
new_mkVBalBranch3MkVBalBranch24(zzz340, zzz341, Neg(Succ(Succ(Succ(zzz3420000)))), zzz343, zzz344, zzz520, zzz521, Zero, zzz523, zzz524, zzz31, Succ(Succ(zzz6900)), h) → new_mkVBalBranch3MkVBalBranch26(zzz340, zzz341, Succ(Succ(zzz3420000)), zzz343, zzz344, zzz520, zzz521, zzz523, zzz524, zzz31, Succ(zzz3420000), Succ(zzz6900), h)
new_mkVBalBranch3MkVBalBranch25(zzz537, zzz538, zzz539, zzz540, zzz541, zzz542, zzz543, zzz544, zzz545, zzz546, zzz547, Zero, Zero, bc) → new_mkVBalBranch3MkVBalBranch211(zzz537, zzz538, zzz539, zzz540, zzz541, zzz542, zzz543, zzz544, zzz545, zzz546, zzz547, bc)
new_mkVBalBranch3MkVBalBranch212(zzz818, zzz819, zzz820, zzz821, zzz822, zzz823, zzz824, zzz825, zzz826, zzz827, bf) → new_mkVBalBranch3MkVBalBranch14(zzz818, zzz819, zzz820, zzz821, zzz822, zzz823, zzz824, zzz825, zzz826, zzz827, new_primPlusNat2(Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat3(new_primPlusNat1(zzz820), zzz820)), zzz820))), Succ(zzz820)), bf)

The TRS R consists of the following rules:

new_primPlusNat1(Zero) → Zero
new_primPlusNat1(Succ(zzz62000)) → Succ(Succ(new_primPlusNat1(zzz62000)))
new_primPlusNat3(zzz90, Succ(zzz910)) → Succ(Succ(new_primPlusNat2(zzz90, zzz910)))
new_primPlusNat3(zzz90, Zero) → Succ(zzz90)
new_primPlusNat2(Succ(zzz900), Succ(zzz9100)) → Succ(Succ(new_primPlusNat2(zzz900, zzz9100)))
new_primPlusNat2(Zero, Succ(zzz9100)) → Succ(zzz9100)
new_primPlusNat2(Zero, Zero) → Zero
new_primPlusNat2(Succ(zzz900), Zero) → Succ(zzz900)

The set Q consists of the following terms:

new_primPlusNat2(Zero, Succ(x0))
new_primPlusNat3(x0, Succ(x1))
new_primPlusNat2(Succ(x0), Succ(x1))
new_primPlusNat3(x0, Zero)
new_primPlusNat1(Zero)
new_primPlusNat2(Zero, Zero)
new_primPlusNat1(Succ(x0))
new_primPlusNat2(Succ(x0), Zero)

We have to consider all minimal (P,Q,R)-chains.
By rewriting [15] the rule new_mkVBalBranch3MkVBalBranch29(zzz818, zzz819, zzz820, zzz821, zzz822, zzz823, zzz824, zzz825, zzz826, zzz827, bf) → new_mkVBalBranch3MkVBalBranch14(zzz818, zzz819, zzz820, zzz821, zzz822, zzz823, zzz824, zzz825, zzz826, zzz827, new_primPlusNat2(Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat3(new_primPlusNat1(zzz820), zzz820)), zzz820))), Succ(zzz820)), bf) at position [10] we obtained the following new rules:

new_mkVBalBranch3MkVBalBranch29(zzz818, zzz819, zzz820, zzz821, zzz822, zzz823, zzz824, zzz825, zzz826, zzz827, bf) → new_mkVBalBranch3MkVBalBranch14(zzz818, zzz819, zzz820, zzz821, zzz822, zzz823, zzz824, zzz825, zzz826, zzz827, Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat2(Succ(new_primPlusNat3(new_primPlusNat1(zzz820), zzz820)), zzz820)), zzz820))), bf)



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

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

new_mkVBalBranch(zzz31, Branch(zzz520, zzz521, Neg(Succ(zzz52200)), zzz523, zzz524), Branch(zzz340, zzz341, zzz342, zzz343, zzz344), h) → new_mkVBalBranch3MkVBalBranch24(zzz340, zzz341, zzz342, zzz343, zzz344, zzz520, zzz521, zzz52200, zzz523, zzz524, zzz31, Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat3(new_primPlusNat1(zzz52200), zzz52200)), zzz52200))), h)
new_mkVBalBranch3MkVBalBranch211(zzz537, zzz538, zzz539, zzz540, zzz541, zzz542, zzz543, zzz544, zzz545, zzz546, zzz547, bc) → new_mkVBalBranch3MkVBalBranch15(zzz537, zzz538, zzz539, zzz540, zzz541, zzz542, zzz543, zzz544, zzz545, zzz546, zzz547, Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat2(Succ(new_primPlusNat3(new_primPlusNat1(zzz539), zzz539)), zzz539)), zzz539))), bc)
new_mkVBalBranch3MkVBalBranch23(zzz929, zzz930, zzz931, zzz932, zzz933, zzz934, zzz935, zzz936, zzz937, zzz938, zzz939, ba) → new_mkVBalBranch3MkVBalBranch10(zzz929, zzz930, zzz931, zzz932, zzz933, zzz934, zzz935, zzz936, zzz937, zzz938, zzz939, new_primPlusNat2(Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat3(new_primPlusNat1(zzz931), zzz931)), zzz931))), Succ(zzz931)), ba)
new_mkVBalBranch3MkVBalBranch11(zzz2033, zzz2034, zzz2035, zzz2036, zzz2037, zzz2038, zzz2039, zzz2040, zzz2041, zzz2042, zzz2043, Zero, Succ(zzz20450), bb) → new_mkVBalBranch(zzz2043, zzz2042, Branch(zzz2033, zzz2034, Pos(Succ(zzz2035)), zzz2036, zzz2037), bb)
new_mkVBalBranch3MkVBalBranch26(zzz1133, zzz1134, zzz1135, zzz1136, zzz1137, zzz1138, zzz1139, zzz1140, zzz1141, zzz1142, Succ(zzz11430), Succ(zzz11440), be) → new_mkVBalBranch3MkVBalBranch26(zzz1133, zzz1134, zzz1135, zzz1136, zzz1137, zzz1138, zzz1139, zzz1140, zzz1141, zzz1142, zzz11430, zzz11440, be)
new_mkVBalBranch3MkVBalBranch24(zzz340, zzz341, Pos(zzz3420), zzz343, zzz344, zzz520, zzz521, zzz52200, zzz523, zzz524, zzz31, Succ(zzz690), h) → new_mkVBalBranch(zzz31, Branch(zzz520, zzz521, Neg(Succ(zzz52200)), zzz523, zzz524), zzz343, h)
new_mkVBalBranch3MkVBalBranch12(zzz340, zzz341, zzz34200, zzz343, zzz344, zzz520, zzz521, zzz523, zzz524, zzz31, Succ(zzz1250), h) → new_mkVBalBranch(zzz31, zzz524, Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), h)
new_mkVBalBranch3MkVBalBranch25(zzz537, zzz538, zzz539, zzz540, zzz541, zzz542, zzz543, zzz544, zzz545, zzz546, zzz547, Succ(zzz5480), Zero, bc) → new_mkVBalBranch3MkVBalBranch15(zzz537, zzz538, zzz539, zzz540, zzz541, zzz542, zzz543, zzz544, zzz545, zzz546, zzz547, Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat2(Succ(new_primPlusNat3(new_primPlusNat1(zzz539), zzz539)), zzz539)), zzz539))), bc)
new_mkVBalBranch3MkVBalBranch20(zzz929, zzz930, zzz931, zzz932, zzz933, zzz934, zzz935, zzz936, zzz937, zzz938, zzz939, Zero, Succ(zzz9410), ba) → new_mkVBalBranch(zzz939, Branch(zzz934, zzz935, Pos(Succ(zzz936)), zzz937, zzz938), zzz932, ba)
new_mkVBalBranch3MkVBalBranch24(zzz340, zzz341, Neg(Succ(Succ(Zero))), zzz343, zzz344, zzz520, zzz521, Zero, zzz523, zzz524, zzz31, Succ(Succ(zzz6900)), h) → new_mkVBalBranch3MkVBalBranch26(zzz340, zzz341, Succ(Zero), zzz343, zzz344, zzz520, zzz521, zzz523, zzz524, zzz31, Zero, Succ(zzz6900), h)
new_mkVBalBranch3MkVBalBranch26(zzz1133, zzz1134, zzz1135, zzz1136, zzz1137, zzz1138, zzz1139, zzz1140, zzz1141, zzz1142, Zero, Zero, be) → new_mkVBalBranch3MkVBalBranch29(zzz1133, zzz1134, zzz1135, zzz1136, zzz1137, zzz1138, zzz1139, zzz1140, zzz1141, zzz1142, be)
new_mkVBalBranch3MkVBalBranch1(zzz340, zzz341, zzz34200, zzz343, zzz344, zzz520, zzz521, zzz52200, zzz523, zzz524, zzz31, Succ(zzz1430), h) → new_mkVBalBranch(zzz31, zzz524, Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), h)
new_mkVBalBranch3MkVBalBranch24(zzz340, zzz341, Neg(Succ(Zero)), zzz343, zzz344, zzz520, zzz521, zzz52200, zzz523, zzz524, zzz31, Succ(zzz690), h) → new_mkVBalBranch(zzz31, Branch(zzz520, zzz521, Neg(Succ(zzz52200)), zzz523, zzz524), zzz343, h)
new_mkVBalBranch3MkVBalBranch20(zzz929, zzz930, zzz931, zzz932, zzz933, zzz934, zzz935, zzz936, zzz937, zzz938, zzz939, Zero, Zero, ba) → new_mkVBalBranch3MkVBalBranch23(zzz929, zzz930, zzz931, zzz932, zzz933, zzz934, zzz935, zzz936, zzz937, zzz938, zzz939, ba)
new_mkVBalBranch3MkVBalBranch13(zzz340, zzz341, zzz34200, zzz343, zzz344, zzz520, zzz521, zzz523, zzz524, zzz31, Succ(zzz1290), h) → new_mkVBalBranch(zzz31, zzz524, Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), h)
new_mkVBalBranch3MkVBalBranch2(zzz340, zzz341, Pos(Succ(zzz34200)), zzz343, zzz344, zzz520, zzz521, zzz52200, zzz523, zzz524, zzz31, Succ(zzz680), h) → new_mkVBalBranch3MkVBalBranch20(zzz340, zzz341, zzz34200, zzz343, zzz344, zzz520, zzz521, zzz52200, zzz523, zzz524, zzz31, Succ(new_primPlusNat2(zzz680, zzz52200)), zzz34200, h)
new_mkVBalBranch(zzz31, Branch(zzz520, zzz521, Neg(Zero), zzz523, zzz524), Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), h) → new_mkVBalBranch3MkVBalBranch13(zzz340, zzz341, zzz34200, zzz343, zzz344, zzz520, zzz521, zzz523, zzz524, zzz31, new_primPlusNat2(Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat3(new_primPlusNat1(zzz34200), zzz34200)), zzz34200))), Succ(zzz34200)), h)
new_mkVBalBranch3MkVBalBranch24(zzz340, zzz341, Neg(Zero), zzz343, zzz344, zzz520, zzz521, zzz52200, zzz523, zzz524, zzz31, Succ(zzz690), h) → new_mkVBalBranch(zzz31, Branch(zzz520, zzz521, Neg(Succ(zzz52200)), zzz523, zzz524), zzz343, h)
new_mkVBalBranch(zzz31, Branch(zzz520, zzz521, Neg(Zero), zzz523, zzz524), Branch(zzz340, zzz341, Pos(Succ(zzz34200)), zzz343, zzz344), h) → new_mkVBalBranch(zzz31, Branch(zzz520, zzz521, Neg(Zero), zzz523, zzz524), zzz343, h)
new_mkVBalBranch3MkVBalBranch20(zzz929, zzz930, zzz931, zzz932, zzz933, zzz934, zzz935, zzz936, zzz937, zzz938, zzz939, Succ(zzz9400), Succ(zzz9410), ba) → new_mkVBalBranch3MkVBalBranch20(zzz929, zzz930, zzz931, zzz932, zzz933, zzz934, zzz935, zzz936, zzz937, zzz938, zzz939, zzz9400, zzz9410, ba)
new_mkVBalBranch3MkVBalBranch29(zzz818, zzz819, zzz820, zzz821, zzz822, zzz823, zzz824, zzz825, zzz826, zzz827, bf) → new_mkVBalBranch3MkVBalBranch14(zzz818, zzz819, zzz820, zzz821, zzz822, zzz823, zzz824, zzz825, zzz826, zzz827, Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat2(Succ(new_primPlusNat3(new_primPlusNat1(zzz820), zzz820)), zzz820)), zzz820))), bf)
new_mkVBalBranch3MkVBalBranch26(zzz1133, zzz1134, zzz1135, zzz1136, zzz1137, zzz1138, zzz1139, zzz1140, zzz1141, zzz1142, Succ(zzz11430), Zero, be) → new_mkVBalBranch3MkVBalBranch212(zzz1133, zzz1134, zzz1135, zzz1136, zzz1137, zzz1138, zzz1139, zzz1140, zzz1141, zzz1142, be)
new_mkVBalBranch3MkVBalBranch16(zzz1702, zzz1703, zzz1704, zzz1705, zzz1706, zzz1707, zzz1708, zzz1709, zzz1710, zzz1711, zzz1712, Succ(zzz17130), Succ(zzz17140), bd) → new_mkVBalBranch3MkVBalBranch16(zzz1702, zzz1703, zzz1704, zzz1705, zzz1706, zzz1707, zzz1708, zzz1709, zzz1710, zzz1711, zzz1712, zzz17130, zzz17140, bd)
new_mkVBalBranch3MkVBalBranch25(zzz537, zzz538, zzz539, zzz540, zzz541, zzz542, zzz543, zzz544, zzz545, zzz546, zzz547, Zero, Succ(zzz5490), bc) → new_mkVBalBranch(zzz547, Branch(zzz542, zzz543, Neg(Succ(Succ(zzz544))), zzz545, zzz546), zzz540, bc)
new_mkVBalBranch3MkVBalBranch11(zzz2033, zzz2034, zzz2035, zzz2036, zzz2037, zzz2038, zzz2039, zzz2040, zzz2041, zzz2042, zzz2043, Succ(zzz20440), Succ(zzz20450), bb) → new_mkVBalBranch3MkVBalBranch11(zzz2033, zzz2034, zzz2035, zzz2036, zzz2037, zzz2038, zzz2039, zzz2040, zzz2041, zzz2042, zzz2043, zzz20440, zzz20450, bb)
new_mkVBalBranch3MkVBalBranch25(zzz537, zzz538, zzz539, zzz540, zzz541, zzz542, zzz543, zzz544, zzz545, zzz546, zzz547, Succ(zzz5480), Succ(zzz5490), bc) → new_mkVBalBranch3MkVBalBranch25(zzz537, zzz538, zzz539, zzz540, zzz541, zzz542, zzz543, zzz544, zzz545, zzz546, zzz547, zzz5480, zzz5490, bc)
new_mkVBalBranch(zzz31, Branch(zzz520, zzz521, Pos(Succ(zzz52200)), zzz523, zzz524), Branch(zzz340, zzz341, zzz342, zzz343, zzz344), h) → new_mkVBalBranch3MkVBalBranch2(zzz340, zzz341, zzz342, zzz343, zzz344, zzz520, zzz521, zzz52200, zzz523, zzz524, zzz31, Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat3(new_primPlusNat1(zzz52200), zzz52200)), zzz52200))), h)
new_mkVBalBranch3MkVBalBranch10(zzz929, zzz930, zzz931, zzz932, zzz933, zzz934, zzz935, zzz936, zzz937, zzz938, zzz939, Succ(zzz10020), ba) → new_mkVBalBranch3MkVBalBranch11(zzz929, zzz930, zzz931, zzz932, zzz933, zzz934, zzz935, zzz936, zzz937, zzz938, zzz939, Succ(zzz10020), Succ(zzz936), ba)
new_mkVBalBranch3MkVBalBranch14(zzz818, zzz819, zzz820, zzz821, zzz822, zzz823, zzz824, zzz825, zzz826, zzz827, Succ(zzz8960), bf) → new_mkVBalBranch3MkVBalBranch16(zzz818, zzz819, zzz820, zzz821, zzz822, zzz823, zzz824, Zero, zzz825, zzz826, zzz827, Succ(Zero), Succ(zzz8960), bf)
new_mkVBalBranch3MkVBalBranch24(zzz340, zzz341, Neg(Succ(Succ(Succ(zzz3420000)))), zzz343, zzz344, zzz520, zzz521, Succ(zzz522000), zzz523, zzz524, zzz31, Succ(Succ(zzz6900)), h) → new_mkVBalBranch3MkVBalBranch25(zzz340, zzz341, Succ(Succ(zzz3420000)), zzz343, zzz344, zzz520, zzz521, zzz522000, zzz523, zzz524, zzz31, Succ(zzz3420000), Succ(Succ(new_primPlusNat2(zzz6900, zzz522000))), h)
new_mkVBalBranch3MkVBalBranch26(zzz1133, zzz1134, zzz1135, zzz1136, zzz1137, zzz1138, zzz1139, zzz1140, zzz1141, zzz1142, Zero, Succ(zzz11440), be) → new_mkVBalBranch(zzz1142, Branch(zzz1138, zzz1139, Neg(Succ(Zero)), zzz1140, zzz1141), zzz1136, be)
new_mkVBalBranch(zzz31, Branch(zzz520, zzz521, Pos(Zero), zzz523, zzz524), Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), h) → new_mkVBalBranch3MkVBalBranch12(zzz340, zzz341, zzz34200, zzz343, zzz344, zzz520, zzz521, zzz523, zzz524, zzz31, Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat2(Succ(new_primPlusNat3(new_primPlusNat1(zzz34200), zzz34200)), zzz34200)), zzz34200))), h)
new_mkVBalBranch3MkVBalBranch24(zzz340, zzz341, Neg(Succ(Succ(Zero))), zzz343, zzz344, zzz520, zzz521, Succ(zzz522000), zzz523, zzz524, zzz31, Succ(Succ(zzz6900)), h) → new_mkVBalBranch3MkVBalBranch25(zzz340, zzz341, Succ(Zero), zzz343, zzz344, zzz520, zzz521, zzz522000, zzz523, zzz524, zzz31, Zero, Succ(Succ(new_primPlusNat2(zzz6900, zzz522000))), h)
new_mkVBalBranch(zzz31, Branch(zzz520, zzz521, Pos(Zero), zzz523, zzz524), Branch(zzz340, zzz341, Pos(Succ(zzz34200)), zzz343, zzz344), h) → new_mkVBalBranch(zzz31, Branch(zzz520, zzz521, Pos(Zero), zzz523, zzz524), zzz343, h)
new_mkVBalBranch3MkVBalBranch2(zzz340, zzz341, Pos(Zero), zzz343, zzz344, zzz520, zzz521, zzz52200, zzz523, zzz524, zzz31, Succ(zzz680), h) → new_mkVBalBranch(zzz31, zzz524, Branch(zzz340, zzz341, Pos(Zero), zzz343, zzz344), h)
new_mkVBalBranch3MkVBalBranch20(zzz929, zzz930, zzz931, zzz932, zzz933, zzz934, zzz935, zzz936, zzz937, zzz938, zzz939, Succ(zzz9400), Zero, ba) → new_mkVBalBranch3MkVBalBranch10(zzz929, zzz930, zzz931, zzz932, zzz933, zzz934, zzz935, zzz936, zzz937, zzz938, zzz939, new_primPlusNat2(Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat3(new_primPlusNat1(zzz931), zzz931)), zzz931))), Succ(zzz931)), ba)
new_mkVBalBranch3MkVBalBranch2(zzz340, zzz341, Neg(Zero), zzz343, zzz344, zzz520, zzz521, zzz52200, zzz523, zzz524, zzz31, Succ(zzz680), h) → new_mkVBalBranch(zzz31, zzz524, Branch(zzz340, zzz341, Neg(Zero), zzz343, zzz344), h)
new_mkVBalBranch3MkVBalBranch2(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344, zzz520, zzz521, zzz52200, zzz523, zzz524, zzz31, Succ(zzz680), h) → new_mkVBalBranch3MkVBalBranch1(zzz340, zzz341, zzz34200, zzz343, zzz344, zzz520, zzz521, zzz52200, zzz523, zzz524, zzz31, Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat2(Succ(new_primPlusNat3(new_primPlusNat1(zzz34200), zzz34200)), zzz34200)), zzz34200))), h)
new_mkVBalBranch3MkVBalBranch16(zzz1702, zzz1703, zzz1704, zzz1705, zzz1706, zzz1707, zzz1708, zzz1709, zzz1710, zzz1711, zzz1712, Zero, Succ(zzz17140), bd) → new_mkVBalBranch(zzz1712, zzz1711, Branch(zzz1702, zzz1703, Neg(Succ(zzz1704)), zzz1705, zzz1706), bd)
new_mkVBalBranch3MkVBalBranch24(zzz340, zzz341, Neg(Succ(Succ(Succ(zzz3420000)))), zzz343, zzz344, zzz520, zzz521, Zero, zzz523, zzz524, zzz31, Succ(Succ(zzz6900)), h) → new_mkVBalBranch3MkVBalBranch26(zzz340, zzz341, Succ(Succ(zzz3420000)), zzz343, zzz344, zzz520, zzz521, zzz523, zzz524, zzz31, Succ(zzz3420000), Succ(zzz6900), h)
new_mkVBalBranch3MkVBalBranch15(zzz537, zzz538, zzz539, zzz540, zzz541, zzz542, zzz543, zzz544, zzz545, zzz546, zzz547, Succ(zzz6990), bc) → new_mkVBalBranch3MkVBalBranch16(zzz537, zzz538, zzz539, zzz540, zzz541, zzz542, zzz543, Succ(zzz544), zzz545, zzz546, zzz547, Succ(Succ(zzz544)), Succ(zzz6990), bc)
new_mkVBalBranch3MkVBalBranch10(zzz929, zzz930, zzz931, zzz932, zzz933, zzz934, zzz935, zzz936, zzz937, zzz938, zzz939, Zero, ba) → new_mkVBalBranch3MkVBalBranch11(zzz929, zzz930, zzz931, zzz932, zzz933, zzz934, zzz935, zzz936, zzz937, zzz938, zzz939, Zero, Succ(zzz936), ba)
new_mkVBalBranch3MkVBalBranch25(zzz537, zzz538, zzz539, zzz540, zzz541, zzz542, zzz543, zzz544, zzz545, zzz546, zzz547, Zero, Zero, bc) → new_mkVBalBranch3MkVBalBranch211(zzz537, zzz538, zzz539, zzz540, zzz541, zzz542, zzz543, zzz544, zzz545, zzz546, zzz547, bc)
new_mkVBalBranch3MkVBalBranch212(zzz818, zzz819, zzz820, zzz821, zzz822, zzz823, zzz824, zzz825, zzz826, zzz827, bf) → new_mkVBalBranch3MkVBalBranch14(zzz818, zzz819, zzz820, zzz821, zzz822, zzz823, zzz824, zzz825, zzz826, zzz827, new_primPlusNat2(Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat3(new_primPlusNat1(zzz820), zzz820)), zzz820))), Succ(zzz820)), bf)

The TRS R consists of the following rules:

new_primPlusNat1(Zero) → Zero
new_primPlusNat1(Succ(zzz62000)) → Succ(Succ(new_primPlusNat1(zzz62000)))
new_primPlusNat3(zzz90, Succ(zzz910)) → Succ(Succ(new_primPlusNat2(zzz90, zzz910)))
new_primPlusNat3(zzz90, Zero) → Succ(zzz90)
new_primPlusNat2(Succ(zzz900), Succ(zzz9100)) → Succ(Succ(new_primPlusNat2(zzz900, zzz9100)))
new_primPlusNat2(Zero, Succ(zzz9100)) → Succ(zzz9100)
new_primPlusNat2(Zero, Zero) → Zero
new_primPlusNat2(Succ(zzz900), Zero) → Succ(zzz900)

The set Q consists of the following terms:

new_primPlusNat2(Zero, Succ(x0))
new_primPlusNat3(x0, Succ(x1))
new_primPlusNat2(Succ(x0), Succ(x1))
new_primPlusNat3(x0, Zero)
new_primPlusNat1(Zero)
new_primPlusNat2(Zero, Zero)
new_primPlusNat1(Succ(x0))
new_primPlusNat2(Succ(x0), Zero)

We have to consider all minimal (P,Q,R)-chains.
By rewriting [15] the rule new_mkVBalBranch(zzz31, Branch(zzz520, zzz521, Neg(Zero), zzz523, zzz524), Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), h) → new_mkVBalBranch3MkVBalBranch13(zzz340, zzz341, zzz34200, zzz343, zzz344, zzz520, zzz521, zzz523, zzz524, zzz31, new_primPlusNat2(Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat3(new_primPlusNat1(zzz34200), zzz34200)), zzz34200))), Succ(zzz34200)), h) at position [10] we obtained the following new rules:

new_mkVBalBranch(zzz31, Branch(zzz520, zzz521, Neg(Zero), zzz523, zzz524), Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), h) → new_mkVBalBranch3MkVBalBranch13(zzz340, zzz341, zzz34200, zzz343, zzz344, zzz520, zzz521, zzz523, zzz524, zzz31, Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat2(Succ(new_primPlusNat3(new_primPlusNat1(zzz34200), zzz34200)), 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
                                    ↳ DependencyGraphProof
                                      ↳ QDP
                                        ↳ Rewriting
                                          ↳ QDP
                                            ↳ Rewriting
                                              ↳ QDP
                                                ↳ Rewriting
                                                  ↳ QDP
                                                    ↳ Rewriting
                                                      ↳ QDP
                                                        ↳ Rewriting
                                                          ↳ QDP
                                                            ↳ Rewriting
                                                              ↳ QDP
                                                                ↳ Rewriting
                                                                  ↳ QDP
                                                                    ↳ Rewriting
                                                                      ↳ QDP
                                                                        ↳ Rewriting
                                                                          ↳ QDP
                                                                            ↳ Rewriting
                                                                              ↳ QDP
                                                                                ↳ Rewriting
                                                                                  ↳ QDP
                                                                                    ↳ Rewriting
                                                                                      ↳ QDP
                                                                                        ↳ Rewriting
                                                                                          ↳ QDP
                                                                                            ↳ UsableRulesProof
                                                                                              ↳ QDP
                                                                                                ↳ QReductionProof
                                                                                                  ↳ QDP
                                                                                                    ↳ Rewriting
                                                                                                      ↳ QDP
                                                                                                        ↳ Rewriting
                                                                                                          ↳ QDP
                                                                                                            ↳ Rewriting
                                                                                                              ↳ QDP
                                                                                                                ↳ Rewriting
                                                                                                                  ↳ QDP
                                                                                                                    ↳ Rewriting
                                                                                                                      ↳ QDP
                                                                                                                        ↳ Rewriting
                                                                                                                          ↳ QDP
                                                                                                                            ↳ DependencyGraphProof
                                                                                                                              ↳ QDP
                                                                                                                                ↳ Rewriting
                                                                                                                                  ↳ QDP
                                                                                                                                    ↳ Rewriting
                                                                                                                                      ↳ QDP
                                                                                                                                        ↳ DependencyGraphProof
                                                                                                                                          ↳ QDP
                                                                                                                                            ↳ Rewriting
                                                                                                                                              ↳ QDP
                                                                                                                                                ↳ Rewriting
                                                                                                                                                  ↳ QDP
                                                                                                                                                    ↳ Rewriting
                                                                                                                                                      ↳ QDP
                                                                                                                                                        ↳ Rewriting
                                                                                                                                                          ↳ QDP
                                                                                                                                                            ↳ Rewriting
                                                                                                                                                              ↳ QDP
                                                                                                                                                                ↳ Rewriting
                                                                                                                                                                  ↳ QDP
                                                                                                                                                                    ↳ Rewriting
                                                                                                                                                                      ↳ QDP
                                                                                                                                                                        ↳ UsableRulesProof
                                                                                                                                                                          ↳ QDP
                                                                                                                                                                            ↳ QReductionProof
                                                                                                                                                                              ↳ QDP
                                                                                                                                                                                ↳ Rewriting
                                                                                                                                                                                  ↳ QDP
                                                                                                                                                                                    ↳ Rewriting
                                                                                                                                                                                      ↳ QDP
                                                                                                                                                                                        ↳ Rewriting
                                                                                                                                                                                          ↳ QDP
                                                                                                                                                                                            ↳ Rewriting
                                                                                                                                                                                              ↳ QDP
                                                                                                                                                                                                ↳ Rewriting
                                                                                                                                                                                                  ↳ QDP
                                                                                                                                                                                                    ↳ Rewriting
                                                                                                                                                                                                      ↳ QDP
                                                                                                                                                                                                        ↳ Rewriting
                                                                                                                                                                                                          ↳ QDP
                                                                                                                                                                                                            ↳ Rewriting
                                                                                                                                                                                                              ↳ QDP
                                                                                                                                                                                                                ↳ Rewriting
                                                                                                                                                                                                                  ↳ QDP
                                                                                                                                                                                                                    ↳ DependencyGraphProof
                                                                                                                                                                                                                      ↳ QDP
                                                                                                                                                                                                                        ↳ Rewriting
                                                                                                                                                                                                                          ↳ QDP
                                                                                                                                                                                                                            ↳ Rewriting
                                                                                                                                                                                                                              ↳ QDP
                                                                                                                                                                                                                                ↳ Rewriting
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP

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

new_mkVBalBranch3MkVBalBranch11(zzz2033, zzz2034, zzz2035, zzz2036, zzz2037, zzz2038, zzz2039, zzz2040, zzz2041, zzz2042, zzz2043, Zero, Succ(zzz20450), bb) → new_mkVBalBranch(zzz2043, zzz2042, Branch(zzz2033, zzz2034, Pos(Succ(zzz2035)), zzz2036, zzz2037), bb)
new_mkVBalBranch3MkVBalBranch23(zzz929, zzz930, zzz931, zzz932, zzz933, zzz934, zzz935, zzz936, zzz937, zzz938, zzz939, ba) → new_mkVBalBranch3MkVBalBranch10(zzz929, zzz930, zzz931, zzz932, zzz933, zzz934, zzz935, zzz936, zzz937, zzz938, zzz939, new_primPlusNat2(Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat3(new_primPlusNat1(zzz931), zzz931)), zzz931))), Succ(zzz931)), ba)
new_mkVBalBranch3MkVBalBranch211(zzz537, zzz538, zzz539, zzz540, zzz541, zzz542, zzz543, zzz544, zzz545, zzz546, zzz547, bc) → new_mkVBalBranch3MkVBalBranch15(zzz537, zzz538, zzz539, zzz540, zzz541, zzz542, zzz543, zzz544, zzz545, zzz546, zzz547, Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat2(Succ(new_primPlusNat3(new_primPlusNat1(zzz539), zzz539)), zzz539)), zzz539))), bc)
new_mkVBalBranch(zzz31, Branch(zzz520, zzz521, Neg(Succ(zzz52200)), zzz523, zzz524), Branch(zzz340, zzz341, zzz342, zzz343, zzz344), h) → new_mkVBalBranch3MkVBalBranch24(zzz340, zzz341, zzz342, zzz343, zzz344, zzz520, zzz521, zzz52200, zzz523, zzz524, zzz31, Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat3(new_primPlusNat1(zzz52200), zzz52200)), zzz52200))), h)
new_mkVBalBranch3MkVBalBranch26(zzz1133, zzz1134, zzz1135, zzz1136, zzz1137, zzz1138, zzz1139, zzz1140, zzz1141, zzz1142, Succ(zzz11430), Succ(zzz11440), be) → new_mkVBalBranch3MkVBalBranch26(zzz1133, zzz1134, zzz1135, zzz1136, zzz1137, zzz1138, zzz1139, zzz1140, zzz1141, zzz1142, zzz11430, zzz11440, be)
new_mkVBalBranch3MkVBalBranch24(zzz340, zzz341, Pos(zzz3420), zzz343, zzz344, zzz520, zzz521, zzz52200, zzz523, zzz524, zzz31, Succ(zzz690), h) → new_mkVBalBranch(zzz31, Branch(zzz520, zzz521, Neg(Succ(zzz52200)), zzz523, zzz524), zzz343, h)
new_mkVBalBranch3MkVBalBranch12(zzz340, zzz341, zzz34200, zzz343, zzz344, zzz520, zzz521, zzz523, zzz524, zzz31, Succ(zzz1250), h) → new_mkVBalBranch(zzz31, zzz524, Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), h)
new_mkVBalBranch3MkVBalBranch25(zzz537, zzz538, zzz539, zzz540, zzz541, zzz542, zzz543, zzz544, zzz545, zzz546, zzz547, Succ(zzz5480), Zero, bc) → new_mkVBalBranch3MkVBalBranch15(zzz537, zzz538, zzz539, zzz540, zzz541, zzz542, zzz543, zzz544, zzz545, zzz546, zzz547, Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat2(Succ(new_primPlusNat3(new_primPlusNat1(zzz539), zzz539)), zzz539)), zzz539))), bc)
new_mkVBalBranch3MkVBalBranch20(zzz929, zzz930, zzz931, zzz932, zzz933, zzz934, zzz935, zzz936, zzz937, zzz938, zzz939, Zero, Succ(zzz9410), ba) → new_mkVBalBranch(zzz939, Branch(zzz934, zzz935, Pos(Succ(zzz936)), zzz937, zzz938), zzz932, ba)
new_mkVBalBranch3MkVBalBranch24(zzz340, zzz341, Neg(Succ(Succ(Zero))), zzz343, zzz344, zzz520, zzz521, Zero, zzz523, zzz524, zzz31, Succ(Succ(zzz6900)), h) → new_mkVBalBranch3MkVBalBranch26(zzz340, zzz341, Succ(Zero), zzz343, zzz344, zzz520, zzz521, zzz523, zzz524, zzz31, Zero, Succ(zzz6900), h)
new_mkVBalBranch3MkVBalBranch1(zzz340, zzz341, zzz34200, zzz343, zzz344, zzz520, zzz521, zzz52200, zzz523, zzz524, zzz31, Succ(zzz1430), h) → new_mkVBalBranch(zzz31, zzz524, Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), h)
new_mkVBalBranch3MkVBalBranch26(zzz1133, zzz1134, zzz1135, zzz1136, zzz1137, zzz1138, zzz1139, zzz1140, zzz1141, zzz1142, Zero, Zero, be) → new_mkVBalBranch3MkVBalBranch29(zzz1133, zzz1134, zzz1135, zzz1136, zzz1137, zzz1138, zzz1139, zzz1140, zzz1141, zzz1142, be)
new_mkVBalBranch(zzz31, Branch(zzz520, zzz521, Neg(Zero), zzz523, zzz524), Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), h) → new_mkVBalBranch3MkVBalBranch13(zzz340, zzz341, zzz34200, zzz343, zzz344, zzz520, zzz521, zzz523, zzz524, zzz31, Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat2(Succ(new_primPlusNat3(new_primPlusNat1(zzz34200), zzz34200)), zzz34200)), zzz34200))), h)
new_mkVBalBranch3MkVBalBranch20(zzz929, zzz930, zzz931, zzz932, zzz933, zzz934, zzz935, zzz936, zzz937, zzz938, zzz939, Zero, Zero, ba) → new_mkVBalBranch3MkVBalBranch23(zzz929, zzz930, zzz931, zzz932, zzz933, zzz934, zzz935, zzz936, zzz937, zzz938, zzz939, ba)
new_mkVBalBranch3MkVBalBranch24(zzz340, zzz341, Neg(Succ(Zero)), zzz343, zzz344, zzz520, zzz521, zzz52200, zzz523, zzz524, zzz31, Succ(zzz690), h) → new_mkVBalBranch(zzz31, Branch(zzz520, zzz521, Neg(Succ(zzz52200)), zzz523, zzz524), zzz343, h)
new_mkVBalBranch3MkVBalBranch13(zzz340, zzz341, zzz34200, zzz343, zzz344, zzz520, zzz521, zzz523, zzz524, zzz31, Succ(zzz1290), h) → new_mkVBalBranch(zzz31, zzz524, Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), h)
new_mkVBalBranch3MkVBalBranch2(zzz340, zzz341, Pos(Succ(zzz34200)), zzz343, zzz344, zzz520, zzz521, zzz52200, zzz523, zzz524, zzz31, Succ(zzz680), h) → new_mkVBalBranch3MkVBalBranch20(zzz340, zzz341, zzz34200, zzz343, zzz344, zzz520, zzz521, zzz52200, zzz523, zzz524, zzz31, Succ(new_primPlusNat2(zzz680, zzz52200)), zzz34200, h)
new_mkVBalBranch(zzz31, Branch(zzz520, zzz521, Neg(Zero), zzz523, zzz524), Branch(zzz340, zzz341, Pos(Succ(zzz34200)), zzz343, zzz344), h) → new_mkVBalBranch(zzz31, Branch(zzz520, zzz521, Neg(Zero), zzz523, zzz524), zzz343, h)
new_mkVBalBranch3MkVBalBranch24(zzz340, zzz341, Neg(Zero), zzz343, zzz344, zzz520, zzz521, zzz52200, zzz523, zzz524, zzz31, Succ(zzz690), h) → new_mkVBalBranch(zzz31, Branch(zzz520, zzz521, Neg(Succ(zzz52200)), zzz523, zzz524), zzz343, h)
new_mkVBalBranch3MkVBalBranch20(zzz929, zzz930, zzz931, zzz932, zzz933, zzz934, zzz935, zzz936, zzz937, zzz938, zzz939, Succ(zzz9400), Succ(zzz9410), ba) → new_mkVBalBranch3MkVBalBranch20(zzz929, zzz930, zzz931, zzz932, zzz933, zzz934, zzz935, zzz936, zzz937, zzz938, zzz939, zzz9400, zzz9410, ba)
new_mkVBalBranch3MkVBalBranch26(zzz1133, zzz1134, zzz1135, zzz1136, zzz1137, zzz1138, zzz1139, zzz1140, zzz1141, zzz1142, Succ(zzz11430), Zero, be) → new_mkVBalBranch3MkVBalBranch212(zzz1133, zzz1134, zzz1135, zzz1136, zzz1137, zzz1138, zzz1139, zzz1140, zzz1141, zzz1142, be)
new_mkVBalBranch3MkVBalBranch29(zzz818, zzz819, zzz820, zzz821, zzz822, zzz823, zzz824, zzz825, zzz826, zzz827, bf) → new_mkVBalBranch3MkVBalBranch14(zzz818, zzz819, zzz820, zzz821, zzz822, zzz823, zzz824, zzz825, zzz826, zzz827, Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat2(Succ(new_primPlusNat3(new_primPlusNat1(zzz820), zzz820)), zzz820)), zzz820))), bf)
new_mkVBalBranch3MkVBalBranch16(zzz1702, zzz1703, zzz1704, zzz1705, zzz1706, zzz1707, zzz1708, zzz1709, zzz1710, zzz1711, zzz1712, Succ(zzz17130), Succ(zzz17140), bd) → new_mkVBalBranch3MkVBalBranch16(zzz1702, zzz1703, zzz1704, zzz1705, zzz1706, zzz1707, zzz1708, zzz1709, zzz1710, zzz1711, zzz1712, zzz17130, zzz17140, bd)
new_mkVBalBranch3MkVBalBranch25(zzz537, zzz538, zzz539, zzz540, zzz541, zzz542, zzz543, zzz544, zzz545, zzz546, zzz547, Zero, Succ(zzz5490), bc) → new_mkVBalBranch(zzz547, Branch(zzz542, zzz543, Neg(Succ(Succ(zzz544))), zzz545, zzz546), zzz540, bc)
new_mkVBalBranch3MkVBalBranch11(zzz2033, zzz2034, zzz2035, zzz2036, zzz2037, zzz2038, zzz2039, zzz2040, zzz2041, zzz2042, zzz2043, Succ(zzz20440), Succ(zzz20450), bb) → new_mkVBalBranch3MkVBalBranch11(zzz2033, zzz2034, zzz2035, zzz2036, zzz2037, zzz2038, zzz2039, zzz2040, zzz2041, zzz2042, zzz2043, zzz20440, zzz20450, bb)
new_mkVBalBranch3MkVBalBranch25(zzz537, zzz538, zzz539, zzz540, zzz541, zzz542, zzz543, zzz544, zzz545, zzz546, zzz547, Succ(zzz5480), Succ(zzz5490), bc) → new_mkVBalBranch3MkVBalBranch25(zzz537, zzz538, zzz539, zzz540, zzz541, zzz542, zzz543, zzz544, zzz545, zzz546, zzz547, zzz5480, zzz5490, bc)
new_mkVBalBranch3MkVBalBranch10(zzz929, zzz930, zzz931, zzz932, zzz933, zzz934, zzz935, zzz936, zzz937, zzz938, zzz939, Succ(zzz10020), ba) → new_mkVBalBranch3MkVBalBranch11(zzz929, zzz930, zzz931, zzz932, zzz933, zzz934, zzz935, zzz936, zzz937, zzz938, zzz939, Succ(zzz10020), Succ(zzz936), ba)
new_mkVBalBranch(zzz31, Branch(zzz520, zzz521, Pos(Succ(zzz52200)), zzz523, zzz524), Branch(zzz340, zzz341, zzz342, zzz343, zzz344), h) → new_mkVBalBranch3MkVBalBranch2(zzz340, zzz341, zzz342, zzz343, zzz344, zzz520, zzz521, zzz52200, zzz523, zzz524, zzz31, Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat3(new_primPlusNat1(zzz52200), zzz52200)), zzz52200))), h)
new_mkVBalBranch3MkVBalBranch14(zzz818, zzz819, zzz820, zzz821, zzz822, zzz823, zzz824, zzz825, zzz826, zzz827, Succ(zzz8960), bf) → new_mkVBalBranch3MkVBalBranch16(zzz818, zzz819, zzz820, zzz821, zzz822, zzz823, zzz824, Zero, zzz825, zzz826, zzz827, Succ(Zero), Succ(zzz8960), bf)
new_mkVBalBranch(zzz31, Branch(zzz520, zzz521, Pos(Zero), zzz523, zzz524), Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), h) → new_mkVBalBranch3MkVBalBranch12(zzz340, zzz341, zzz34200, zzz343, zzz344, zzz520, zzz521, zzz523, zzz524, zzz31, Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat2(Succ(new_primPlusNat3(new_primPlusNat1(zzz34200), zzz34200)), zzz34200)), zzz34200))), h)
new_mkVBalBranch3MkVBalBranch26(zzz1133, zzz1134, zzz1135, zzz1136, zzz1137, zzz1138, zzz1139, zzz1140, zzz1141, zzz1142, Zero, Succ(zzz11440), be) → new_mkVBalBranch(zzz1142, Branch(zzz1138, zzz1139, Neg(Succ(Zero)), zzz1140, zzz1141), zzz1136, be)
new_mkVBalBranch3MkVBalBranch24(zzz340, zzz341, Neg(Succ(Succ(Succ(zzz3420000)))), zzz343, zzz344, zzz520, zzz521, Succ(zzz522000), zzz523, zzz524, zzz31, Succ(Succ(zzz6900)), h) → new_mkVBalBranch3MkVBalBranch25(zzz340, zzz341, Succ(Succ(zzz3420000)), zzz343, zzz344, zzz520, zzz521, zzz522000, zzz523, zzz524, zzz31, Succ(zzz3420000), Succ(Succ(new_primPlusNat2(zzz6900, zzz522000))), h)
new_mkVBalBranch3MkVBalBranch24(zzz340, zzz341, Neg(Succ(Succ(Zero))), zzz343, zzz344, zzz520, zzz521, Succ(zzz522000), zzz523, zzz524, zzz31, Succ(Succ(zzz6900)), h) → new_mkVBalBranch3MkVBalBranch25(zzz340, zzz341, Succ(Zero), zzz343, zzz344, zzz520, zzz521, zzz522000, zzz523, zzz524, zzz31, Zero, Succ(Succ(new_primPlusNat2(zzz6900, zzz522000))), h)
new_mkVBalBranch(zzz31, Branch(zzz520, zzz521, Pos(Zero), zzz523, zzz524), Branch(zzz340, zzz341, Pos(Succ(zzz34200)), zzz343, zzz344), h) → new_mkVBalBranch(zzz31, Branch(zzz520, zzz521, Pos(Zero), zzz523, zzz524), zzz343, h)
new_mkVBalBranch3MkVBalBranch2(zzz340, zzz341, Pos(Zero), zzz343, zzz344, zzz520, zzz521, zzz52200, zzz523, zzz524, zzz31, Succ(zzz680), h) → new_mkVBalBranch(zzz31, zzz524, Branch(zzz340, zzz341, Pos(Zero), zzz343, zzz344), h)
new_mkVBalBranch3MkVBalBranch20(zzz929, zzz930, zzz931, zzz932, zzz933, zzz934, zzz935, zzz936, zzz937, zzz938, zzz939, Succ(zzz9400), Zero, ba) → new_mkVBalBranch3MkVBalBranch10(zzz929, zzz930, zzz931, zzz932, zzz933, zzz934, zzz935, zzz936, zzz937, zzz938, zzz939, new_primPlusNat2(Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat3(new_primPlusNat1(zzz931), zzz931)), zzz931))), Succ(zzz931)), ba)
new_mkVBalBranch3MkVBalBranch2(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344, zzz520, zzz521, zzz52200, zzz523, zzz524, zzz31, Succ(zzz680), h) → new_mkVBalBranch3MkVBalBranch1(zzz340, zzz341, zzz34200, zzz343, zzz344, zzz520, zzz521, zzz52200, zzz523, zzz524, zzz31, Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat2(Succ(new_primPlusNat3(new_primPlusNat1(zzz34200), zzz34200)), zzz34200)), zzz34200))), h)
new_mkVBalBranch3MkVBalBranch2(zzz340, zzz341, Neg(Zero), zzz343, zzz344, zzz520, zzz521, zzz52200, zzz523, zzz524, zzz31, Succ(zzz680), h) → new_mkVBalBranch(zzz31, zzz524, Branch(zzz340, zzz341, Neg(Zero), zzz343, zzz344), h)
new_mkVBalBranch3MkVBalBranch16(zzz1702, zzz1703, zzz1704, zzz1705, zzz1706, zzz1707, zzz1708, zzz1709, zzz1710, zzz1711, zzz1712, Zero, Succ(zzz17140), bd) → new_mkVBalBranch(zzz1712, zzz1711, Branch(zzz1702, zzz1703, Neg(Succ(zzz1704)), zzz1705, zzz1706), bd)
new_mkVBalBranch3MkVBalBranch10(zzz929, zzz930, zzz931, zzz932, zzz933, zzz934, zzz935, zzz936, zzz937, zzz938, zzz939, Zero, ba) → new_mkVBalBranch3MkVBalBranch11(zzz929, zzz930, zzz931, zzz932, zzz933, zzz934, zzz935, zzz936, zzz937, zzz938, zzz939, Zero, Succ(zzz936), ba)
new_mkVBalBranch3MkVBalBranch15(zzz537, zzz538, zzz539, zzz540, zzz541, zzz542, zzz543, zzz544, zzz545, zzz546, zzz547, Succ(zzz6990), bc) → new_mkVBalBranch3MkVBalBranch16(zzz537, zzz538, zzz539, zzz540, zzz541, zzz542, zzz543, Succ(zzz544), zzz545, zzz546, zzz547, Succ(Succ(zzz544)), Succ(zzz6990), bc)
new_mkVBalBranch3MkVBalBranch24(zzz340, zzz341, Neg(Succ(Succ(Succ(zzz3420000)))), zzz343, zzz344, zzz520, zzz521, Zero, zzz523, zzz524, zzz31, Succ(Succ(zzz6900)), h) → new_mkVBalBranch3MkVBalBranch26(zzz340, zzz341, Succ(Succ(zzz3420000)), zzz343, zzz344, zzz520, zzz521, zzz523, zzz524, zzz31, Succ(zzz3420000), Succ(zzz6900), h)
new_mkVBalBranch3MkVBalBranch25(zzz537, zzz538, zzz539, zzz540, zzz541, zzz542, zzz543, zzz544, zzz545, zzz546, zzz547, Zero, Zero, bc) → new_mkVBalBranch3MkVBalBranch211(zzz537, zzz538, zzz539, zzz540, zzz541, zzz542, zzz543, zzz544, zzz545, zzz546, zzz547, bc)
new_mkVBalBranch3MkVBalBranch212(zzz818, zzz819, zzz820, zzz821, zzz822, zzz823, zzz824, zzz825, zzz826, zzz827, bf) → new_mkVBalBranch3MkVBalBranch14(zzz818, zzz819, zzz820, zzz821, zzz822, zzz823, zzz824, zzz825, zzz826, zzz827, new_primPlusNat2(Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat3(new_primPlusNat1(zzz820), zzz820)), zzz820))), Succ(zzz820)), bf)

The TRS R consists of the following rules:

new_primPlusNat1(Zero) → Zero
new_primPlusNat1(Succ(zzz62000)) → Succ(Succ(new_primPlusNat1(zzz62000)))
new_primPlusNat3(zzz90, Succ(zzz910)) → Succ(Succ(new_primPlusNat2(zzz90, zzz910)))
new_primPlusNat3(zzz90, Zero) → Succ(zzz90)
new_primPlusNat2(Succ(zzz900), Succ(zzz9100)) → Succ(Succ(new_primPlusNat2(zzz900, zzz9100)))
new_primPlusNat2(Zero, Succ(zzz9100)) → Succ(zzz9100)
new_primPlusNat2(Zero, Zero) → Zero
new_primPlusNat2(Succ(zzz900), Zero) → Succ(zzz900)

The set Q consists of the following terms:

new_primPlusNat2(Zero, Succ(x0))
new_primPlusNat3(x0, Succ(x1))
new_primPlusNat2(Succ(x0), Succ(x1))
new_primPlusNat3(x0, Zero)
new_primPlusNat1(Zero)
new_primPlusNat2(Zero, Zero)
new_primPlusNat1(Succ(x0))
new_primPlusNat2(Succ(x0), Zero)

We have to consider all minimal (P,Q,R)-chains.
By rewriting [15] the rule new_mkVBalBranch3MkVBalBranch212(zzz818, zzz819, zzz820, zzz821, zzz822, zzz823, zzz824, zzz825, zzz826, zzz827, bf) → new_mkVBalBranch3MkVBalBranch14(zzz818, zzz819, zzz820, zzz821, zzz822, zzz823, zzz824, zzz825, zzz826, zzz827, new_primPlusNat2(Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat3(new_primPlusNat1(zzz820), zzz820)), zzz820))), Succ(zzz820)), bf) at position [10] we obtained the following new rules:

new_mkVBalBranch3MkVBalBranch212(zzz818, zzz819, zzz820, zzz821, zzz822, zzz823, zzz824, zzz825, zzz826, zzz827, bf) → new_mkVBalBranch3MkVBalBranch14(zzz818, zzz819, zzz820, zzz821, zzz822, zzz823, zzz824, zzz825, zzz826, zzz827, Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat2(Succ(new_primPlusNat3(new_primPlusNat1(zzz820), zzz820)), zzz820)), zzz820))), bf)



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

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

new_mkVBalBranch(zzz31, Branch(zzz520, zzz521, Neg(Succ(zzz52200)), zzz523, zzz524), Branch(zzz340, zzz341, zzz342, zzz343, zzz344), h) → new_mkVBalBranch3MkVBalBranch24(zzz340, zzz341, zzz342, zzz343, zzz344, zzz520, zzz521, zzz52200, zzz523, zzz524, zzz31, Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat3(new_primPlusNat1(zzz52200), zzz52200)), zzz52200))), h)
new_mkVBalBranch3MkVBalBranch211(zzz537, zzz538, zzz539, zzz540, zzz541, zzz542, zzz543, zzz544, zzz545, zzz546, zzz547, bc) → new_mkVBalBranch3MkVBalBranch15(zzz537, zzz538, zzz539, zzz540, zzz541, zzz542, zzz543, zzz544, zzz545, zzz546, zzz547, Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat2(Succ(new_primPlusNat3(new_primPlusNat1(zzz539), zzz539)), zzz539)), zzz539))), bc)
new_mkVBalBranch3MkVBalBranch23(zzz929, zzz930, zzz931, zzz932, zzz933, zzz934, zzz935, zzz936, zzz937, zzz938, zzz939, ba) → new_mkVBalBranch3MkVBalBranch10(zzz929, zzz930, zzz931, zzz932, zzz933, zzz934, zzz935, zzz936, zzz937, zzz938, zzz939, new_primPlusNat2(Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat3(new_primPlusNat1(zzz931), zzz931)), zzz931))), Succ(zzz931)), ba)
new_mkVBalBranch3MkVBalBranch11(zzz2033, zzz2034, zzz2035, zzz2036, zzz2037, zzz2038, zzz2039, zzz2040, zzz2041, zzz2042, zzz2043, Zero, Succ(zzz20450), bb) → new_mkVBalBranch(zzz2043, zzz2042, Branch(zzz2033, zzz2034, Pos(Succ(zzz2035)), zzz2036, zzz2037), bb)
new_mkVBalBranch3MkVBalBranch26(zzz1133, zzz1134, zzz1135, zzz1136, zzz1137, zzz1138, zzz1139, zzz1140, zzz1141, zzz1142, Succ(zzz11430), Succ(zzz11440), be) → new_mkVBalBranch3MkVBalBranch26(zzz1133, zzz1134, zzz1135, zzz1136, zzz1137, zzz1138, zzz1139, zzz1140, zzz1141, zzz1142, zzz11430, zzz11440, be)
new_mkVBalBranch3MkVBalBranch24(zzz340, zzz341, Pos(zzz3420), zzz343, zzz344, zzz520, zzz521, zzz52200, zzz523, zzz524, zzz31, Succ(zzz690), h) → new_mkVBalBranch(zzz31, Branch(zzz520, zzz521, Neg(Succ(zzz52200)), zzz523, zzz524), zzz343, h)
new_mkVBalBranch3MkVBalBranch12(zzz340, zzz341, zzz34200, zzz343, zzz344, zzz520, zzz521, zzz523, zzz524, zzz31, Succ(zzz1250), h) → new_mkVBalBranch(zzz31, zzz524, Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), h)
new_mkVBalBranch3MkVBalBranch25(zzz537, zzz538, zzz539, zzz540, zzz541, zzz542, zzz543, zzz544, zzz545, zzz546, zzz547, Succ(zzz5480), Zero, bc) → new_mkVBalBranch3MkVBalBranch15(zzz537, zzz538, zzz539, zzz540, zzz541, zzz542, zzz543, zzz544, zzz545, zzz546, zzz547, Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat2(Succ(new_primPlusNat3(new_primPlusNat1(zzz539), zzz539)), zzz539)), zzz539))), bc)
new_mkVBalBranch3MkVBalBranch20(zzz929, zzz930, zzz931, zzz932, zzz933, zzz934, zzz935, zzz936, zzz937, zzz938, zzz939, Zero, Succ(zzz9410), ba) → new_mkVBalBranch(zzz939, Branch(zzz934, zzz935, Pos(Succ(zzz936)), zzz937, zzz938), zzz932, ba)
new_mkVBalBranch3MkVBalBranch24(zzz340, zzz341, Neg(Succ(Succ(Zero))), zzz343, zzz344, zzz520, zzz521, Zero, zzz523, zzz524, zzz31, Succ(Succ(zzz6900)), h) → new_mkVBalBranch3MkVBalBranch26(zzz340, zzz341, Succ(Zero), zzz343, zzz344, zzz520, zzz521, zzz523, zzz524, zzz31, Zero, Succ(zzz6900), h)
new_mkVBalBranch3MkVBalBranch26(zzz1133, zzz1134, zzz1135, zzz1136, zzz1137, zzz1138, zzz1139, zzz1140, zzz1141, zzz1142, Zero, Zero, be) → new_mkVBalBranch3MkVBalBranch29(zzz1133, zzz1134, zzz1135, zzz1136, zzz1137, zzz1138, zzz1139, zzz1140, zzz1141, zzz1142, be)
new_mkVBalBranch3MkVBalBranch1(zzz340, zzz341, zzz34200, zzz343, zzz344, zzz520, zzz521, zzz52200, zzz523, zzz524, zzz31, Succ(zzz1430), h) → new_mkVBalBranch(zzz31, zzz524, Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), h)
new_mkVBalBranch3MkVBalBranch24(zzz340, zzz341, Neg(Succ(Zero)), zzz343, zzz344, zzz520, zzz521, zzz52200, zzz523, zzz524, zzz31, Succ(zzz690), h) → new_mkVBalBranch(zzz31, Branch(zzz520, zzz521, Neg(Succ(zzz52200)), zzz523, zzz524), zzz343, h)
new_mkVBalBranch3MkVBalBranch20(zzz929, zzz930, zzz931, zzz932, zzz933, zzz934, zzz935, zzz936, zzz937, zzz938, zzz939, Zero, Zero, ba) → new_mkVBalBranch3MkVBalBranch23(zzz929, zzz930, zzz931, zzz932, zzz933, zzz934, zzz935, zzz936, zzz937, zzz938, zzz939, ba)
new_mkVBalBranch(zzz31, Branch(zzz520, zzz521, Neg(Zero), zzz523, zzz524), Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), h) → new_mkVBalBranch3MkVBalBranch13(zzz340, zzz341, zzz34200, zzz343, zzz344, zzz520, zzz521, zzz523, zzz524, zzz31, Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat2(Succ(new_primPlusNat3(new_primPlusNat1(zzz34200), zzz34200)), zzz34200)), zzz34200))), h)
new_mkVBalBranch3MkVBalBranch13(zzz340, zzz341, zzz34200, zzz343, zzz344, zzz520, zzz521, zzz523, zzz524, zzz31, Succ(zzz1290), h) → new_mkVBalBranch(zzz31, zzz524, Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), h)
new_mkVBalBranch3MkVBalBranch2(zzz340, zzz341, Pos(Succ(zzz34200)), zzz343, zzz344, zzz520, zzz521, zzz52200, zzz523, zzz524, zzz31, Succ(zzz680), h) → new_mkVBalBranch3MkVBalBranch20(zzz340, zzz341, zzz34200, zzz343, zzz344, zzz520, zzz521, zzz52200, zzz523, zzz524, zzz31, Succ(new_primPlusNat2(zzz680, zzz52200)), zzz34200, h)
new_mkVBalBranch3MkVBalBranch24(zzz340, zzz341, Neg(Zero), zzz343, zzz344, zzz520, zzz521, zzz52200, zzz523, zzz524, zzz31, Succ(zzz690), h) → new_mkVBalBranch(zzz31, Branch(zzz520, zzz521, Neg(Succ(zzz52200)), zzz523, zzz524), zzz343, h)
new_mkVBalBranch(zzz31, Branch(zzz520, zzz521, Neg(Zero), zzz523, zzz524), Branch(zzz340, zzz341, Pos(Succ(zzz34200)), zzz343, zzz344), h) → new_mkVBalBranch(zzz31, Branch(zzz520, zzz521, Neg(Zero), zzz523, zzz524), zzz343, h)
new_mkVBalBranch3MkVBalBranch20(zzz929, zzz930, zzz931, zzz932, zzz933, zzz934, zzz935, zzz936, zzz937, zzz938, zzz939, Succ(zzz9400), Succ(zzz9410), ba) → new_mkVBalBranch3MkVBalBranch20(zzz929, zzz930, zzz931, zzz932, zzz933, zzz934, zzz935, zzz936, zzz937, zzz938, zzz939, zzz9400, zzz9410, ba)
new_mkVBalBranch3MkVBalBranch29(zzz818, zzz819, zzz820, zzz821, zzz822, zzz823, zzz824, zzz825, zzz826, zzz827, bf) → new_mkVBalBranch3MkVBalBranch14(zzz818, zzz819, zzz820, zzz821, zzz822, zzz823, zzz824, zzz825, zzz826, zzz827, Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat2(Succ(new_primPlusNat3(new_primPlusNat1(zzz820), zzz820)), zzz820)), zzz820))), bf)
new_mkVBalBranch3MkVBalBranch26(zzz1133, zzz1134, zzz1135, zzz1136, zzz1137, zzz1138, zzz1139, zzz1140, zzz1141, zzz1142, Succ(zzz11430), Zero, be) → new_mkVBalBranch3MkVBalBranch212(zzz1133, zzz1134, zzz1135, zzz1136, zzz1137, zzz1138, zzz1139, zzz1140, zzz1141, zzz1142, be)
new_mkVBalBranch3MkVBalBranch16(zzz1702, zzz1703, zzz1704, zzz1705, zzz1706, zzz1707, zzz1708, zzz1709, zzz1710, zzz1711, zzz1712, Succ(zzz17130), Succ(zzz17140), bd) → new_mkVBalBranch3MkVBalBranch16(zzz1702, zzz1703, zzz1704, zzz1705, zzz1706, zzz1707, zzz1708, zzz1709, zzz1710, zzz1711, zzz1712, zzz17130, zzz17140, bd)
new_mkVBalBranch3MkVBalBranch25(zzz537, zzz538, zzz539, zzz540, zzz541, zzz542, zzz543, zzz544, zzz545, zzz546, zzz547, Zero, Succ(zzz5490), bc) → new_mkVBalBranch(zzz547, Branch(zzz542, zzz543, Neg(Succ(Succ(zzz544))), zzz545, zzz546), zzz540, bc)
new_mkVBalBranch3MkVBalBranch11(zzz2033, zzz2034, zzz2035, zzz2036, zzz2037, zzz2038, zzz2039, zzz2040, zzz2041, zzz2042, zzz2043, Succ(zzz20440), Succ(zzz20450), bb) → new_mkVBalBranch3MkVBalBranch11(zzz2033, zzz2034, zzz2035, zzz2036, zzz2037, zzz2038, zzz2039, zzz2040, zzz2041, zzz2042, zzz2043, zzz20440, zzz20450, bb)
new_mkVBalBranch3MkVBalBranch25(zzz537, zzz538, zzz539, zzz540, zzz541, zzz542, zzz543, zzz544, zzz545, zzz546, zzz547, Succ(zzz5480), Succ(zzz5490), bc) → new_mkVBalBranch3MkVBalBranch25(zzz537, zzz538, zzz539, zzz540, zzz541, zzz542, zzz543, zzz544, zzz545, zzz546, zzz547, zzz5480, zzz5490, bc)
new_mkVBalBranch(zzz31, Branch(zzz520, zzz521, Pos(Succ(zzz52200)), zzz523, zzz524), Branch(zzz340, zzz341, zzz342, zzz343, zzz344), h) → new_mkVBalBranch3MkVBalBranch2(zzz340, zzz341, zzz342, zzz343, zzz344, zzz520, zzz521, zzz52200, zzz523, zzz524, zzz31, Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat3(new_primPlusNat1(zzz52200), zzz52200)), zzz52200))), h)
new_mkVBalBranch3MkVBalBranch10(zzz929, zzz930, zzz931, zzz932, zzz933, zzz934, zzz935, zzz936, zzz937, zzz938, zzz939, Succ(zzz10020), ba) → new_mkVBalBranch3MkVBalBranch11(zzz929, zzz930, zzz931, zzz932, zzz933, zzz934, zzz935, zzz936, zzz937, zzz938, zzz939, Succ(zzz10020), Succ(zzz936), ba)
new_mkVBalBranch3MkVBalBranch14(zzz818, zzz819, zzz820, zzz821, zzz822, zzz823, zzz824, zzz825, zzz826, zzz827, Succ(zzz8960), bf) → new_mkVBalBranch3MkVBalBranch16(zzz818, zzz819, zzz820, zzz821, zzz822, zzz823, zzz824, Zero, zzz825, zzz826, zzz827, Succ(Zero), Succ(zzz8960), bf)
new_mkVBalBranch3MkVBalBranch24(zzz340, zzz341, Neg(Succ(Succ(Succ(zzz3420000)))), zzz343, zzz344, zzz520, zzz521, Succ(zzz522000), zzz523, zzz524, zzz31, Succ(Succ(zzz6900)), h) → new_mkVBalBranch3MkVBalBranch25(zzz340, zzz341, Succ(Succ(zzz3420000)), zzz343, zzz344, zzz520, zzz521, zzz522000, zzz523, zzz524, zzz31, Succ(zzz3420000), Succ(Succ(new_primPlusNat2(zzz6900, zzz522000))), h)
new_mkVBalBranch3MkVBalBranch26(zzz1133, zzz1134, zzz1135, zzz1136, zzz1137, zzz1138, zzz1139, zzz1140, zzz1141, zzz1142, Zero, Succ(zzz11440), be) → new_mkVBalBranch(zzz1142, Branch(zzz1138, zzz1139, Neg(Succ(Zero)), zzz1140, zzz1141), zzz1136, be)
new_mkVBalBranch(zzz31, Branch(zzz520, zzz521, Pos(Zero), zzz523, zzz524), Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), h) → new_mkVBalBranch3MkVBalBranch12(zzz340, zzz341, zzz34200, zzz343, zzz344, zzz520, zzz521, zzz523, zzz524, zzz31, Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat2(Succ(new_primPlusNat3(new_primPlusNat1(zzz34200), zzz34200)), zzz34200)), zzz34200))), h)
new_mkVBalBranch3MkVBalBranch212(zzz818, zzz819, zzz820, zzz821, zzz822, zzz823, zzz824, zzz825, zzz826, zzz827, bf) → new_mkVBalBranch3MkVBalBranch14(zzz818, zzz819, zzz820, zzz821, zzz822, zzz823, zzz824, zzz825, zzz826, zzz827, Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat2(Succ(new_primPlusNat3(new_primPlusNat1(zzz820), zzz820)), zzz820)), zzz820))), bf)
new_mkVBalBranch3MkVBalBranch24(zzz340, zzz341, Neg(Succ(Succ(Zero))), zzz343, zzz344, zzz520, zzz521, Succ(zzz522000), zzz523, zzz524, zzz31, Succ(Succ(zzz6900)), h) → new_mkVBalBranch3MkVBalBranch25(zzz340, zzz341, Succ(Zero), zzz343, zzz344, zzz520, zzz521, zzz522000, zzz523, zzz524, zzz31, Zero, Succ(Succ(new_primPlusNat2(zzz6900, zzz522000))), h)
new_mkVBalBranch(zzz31, Branch(zzz520, zzz521, Pos(Zero), zzz523, zzz524), Branch(zzz340, zzz341, Pos(Succ(zzz34200)), zzz343, zzz344), h) → new_mkVBalBranch(zzz31, Branch(zzz520, zzz521, Pos(Zero), zzz523, zzz524), zzz343, h)
new_mkVBalBranch3MkVBalBranch2(zzz340, zzz341, Pos(Zero), zzz343, zzz344, zzz520, zzz521, zzz52200, zzz523, zzz524, zzz31, Succ(zzz680), h) → new_mkVBalBranch(zzz31, zzz524, Branch(zzz340, zzz341, Pos(Zero), zzz343, zzz344), h)
new_mkVBalBranch3MkVBalBranch20(zzz929, zzz930, zzz931, zzz932, zzz933, zzz934, zzz935, zzz936, zzz937, zzz938, zzz939, Succ(zzz9400), Zero, ba) → new_mkVBalBranch3MkVBalBranch10(zzz929, zzz930, zzz931, zzz932, zzz933, zzz934, zzz935, zzz936, zzz937, zzz938, zzz939, new_primPlusNat2(Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat3(new_primPlusNat1(zzz931), zzz931)), zzz931))), Succ(zzz931)), ba)
new_mkVBalBranch3MkVBalBranch2(zzz340, zzz341, Neg(Zero), zzz343, zzz344, zzz520, zzz521, zzz52200, zzz523, zzz524, zzz31, Succ(zzz680), h) → new_mkVBalBranch(zzz31, zzz524, Branch(zzz340, zzz341, Neg(Zero), zzz343, zzz344), h)
new_mkVBalBranch3MkVBalBranch2(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344, zzz520, zzz521, zzz52200, zzz523, zzz524, zzz31, Succ(zzz680), h) → new_mkVBalBranch3MkVBalBranch1(zzz340, zzz341, zzz34200, zzz343, zzz344, zzz520, zzz521, zzz52200, zzz523, zzz524, zzz31, Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat2(Succ(new_primPlusNat3(new_primPlusNat1(zzz34200), zzz34200)), zzz34200)), zzz34200))), h)
new_mkVBalBranch3MkVBalBranch16(zzz1702, zzz1703, zzz1704, zzz1705, zzz1706, zzz1707, zzz1708, zzz1709, zzz1710, zzz1711, zzz1712, Zero, Succ(zzz17140), bd) → new_mkVBalBranch(zzz1712, zzz1711, Branch(zzz1702, zzz1703, Neg(Succ(zzz1704)), zzz1705, zzz1706), bd)
new_mkVBalBranch3MkVBalBranch24(zzz340, zzz341, Neg(Succ(Succ(Succ(zzz3420000)))), zzz343, zzz344, zzz520, zzz521, Zero, zzz523, zzz524, zzz31, Succ(Succ(zzz6900)), h) → new_mkVBalBranch3MkVBalBranch26(zzz340, zzz341, Succ(Succ(zzz3420000)), zzz343, zzz344, zzz520, zzz521, zzz523, zzz524, zzz31, Succ(zzz3420000), Succ(zzz6900), h)
new_mkVBalBranch3MkVBalBranch15(zzz537, zzz538, zzz539, zzz540, zzz541, zzz542, zzz543, zzz544, zzz545, zzz546, zzz547, Succ(zzz6990), bc) → new_mkVBalBranch3MkVBalBranch16(zzz537, zzz538, zzz539, zzz540, zzz541, zzz542, zzz543, Succ(zzz544), zzz545, zzz546, zzz547, Succ(Succ(zzz544)), Succ(zzz6990), bc)
new_mkVBalBranch3MkVBalBranch10(zzz929, zzz930, zzz931, zzz932, zzz933, zzz934, zzz935, zzz936, zzz937, zzz938, zzz939, Zero, ba) → new_mkVBalBranch3MkVBalBranch11(zzz929, zzz930, zzz931, zzz932, zzz933, zzz934, zzz935, zzz936, zzz937, zzz938, zzz939, Zero, Succ(zzz936), ba)
new_mkVBalBranch3MkVBalBranch25(zzz537, zzz538, zzz539, zzz540, zzz541, zzz542, zzz543, zzz544, zzz545, zzz546, zzz547, Zero, Zero, bc) → new_mkVBalBranch3MkVBalBranch211(zzz537, zzz538, zzz539, zzz540, zzz541, zzz542, zzz543, zzz544, zzz545, zzz546, zzz547, bc)

The TRS R consists of the following rules:

new_primPlusNat1(Zero) → Zero
new_primPlusNat1(Succ(zzz62000)) → Succ(Succ(new_primPlusNat1(zzz62000)))
new_primPlusNat3(zzz90, Succ(zzz910)) → Succ(Succ(new_primPlusNat2(zzz90, zzz910)))
new_primPlusNat3(zzz90, Zero) → Succ(zzz90)
new_primPlusNat2(Succ(zzz900), Succ(zzz9100)) → Succ(Succ(new_primPlusNat2(zzz900, zzz9100)))
new_primPlusNat2(Zero, Succ(zzz9100)) → Succ(zzz9100)
new_primPlusNat2(Zero, Zero) → Zero
new_primPlusNat2(Succ(zzz900), Zero) → Succ(zzz900)

The set Q consists of the following terms:

new_primPlusNat2(Zero, Succ(x0))
new_primPlusNat3(x0, Succ(x1))
new_primPlusNat2(Succ(x0), Succ(x1))
new_primPlusNat3(x0, Zero)
new_primPlusNat1(Zero)
new_primPlusNat2(Zero, Zero)
new_primPlusNat1(Succ(x0))
new_primPlusNat2(Succ(x0), Zero)

We have to consider all minimal (P,Q,R)-chains.
By rewriting [15] the rule new_mkVBalBranch3MkVBalBranch23(zzz929, zzz930, zzz931, zzz932, zzz933, zzz934, zzz935, zzz936, zzz937, zzz938, zzz939, ba) → new_mkVBalBranch3MkVBalBranch10(zzz929, zzz930, zzz931, zzz932, zzz933, zzz934, zzz935, zzz936, zzz937, zzz938, zzz939, new_primPlusNat2(Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat3(new_primPlusNat1(zzz931), zzz931)), zzz931))), Succ(zzz931)), ba) at position [11] we obtained the following new rules:

new_mkVBalBranch3MkVBalBranch23(zzz929, zzz930, zzz931, zzz932, zzz933, zzz934, zzz935, zzz936, zzz937, zzz938, zzz939, ba) → new_mkVBalBranch3MkVBalBranch10(zzz929, zzz930, zzz931, zzz932, zzz933, zzz934, zzz935, zzz936, zzz937, zzz938, zzz939, Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat2(Succ(new_primPlusNat3(new_primPlusNat1(zzz931), zzz931)), zzz931)), zzz931))), 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
                                    ↳ DependencyGraphProof
                                      ↳ QDP
                                        ↳ Rewriting
                                          ↳ QDP
                                            ↳ Rewriting
                                              ↳ QDP
                                                ↳ Rewriting
                                                  ↳ QDP
                                                    ↳ Rewriting
                                                      ↳ QDP
                                                        ↳ Rewriting
                                                          ↳ QDP
                                                            ↳ Rewriting
                                                              ↳ QDP
                                                                ↳ Rewriting
                                                                  ↳ QDP
                                                                    ↳ Rewriting
                                                                      ↳ QDP
                                                                        ↳ Rewriting
                                                                          ↳ QDP
                                                                            ↳ Rewriting
                                                                              ↳ QDP
                                                                                ↳ Rewriting
                                                                                  ↳ QDP
                                                                                    ↳ Rewriting
                                                                                      ↳ QDP
                                                                                        ↳ Rewriting
                                                                                          ↳ QDP
                                                                                            ↳ UsableRulesProof
                                                                                              ↳ QDP
                                                                                                ↳ QReductionProof
                                                                                                  ↳ QDP
                                                                                                    ↳ Rewriting
                                                                                                      ↳ QDP
                                                                                                        ↳ Rewriting
                                                                                                          ↳ QDP
                                                                                                            ↳ Rewriting
                                                                                                              ↳ QDP
                                                                                                                ↳ Rewriting
                                                                                                                  ↳ QDP
                                                                                                                    ↳ Rewriting
                                                                                                                      ↳ QDP
                                                                                                                        ↳ Rewriting
                                                                                                                          ↳ QDP
                                                                                                                            ↳ DependencyGraphProof
                                                                                                                              ↳ QDP
                                                                                                                                ↳ Rewriting
                                                                                                                                  ↳ QDP
                                                                                                                                    ↳ Rewriting
                                                                                                                                      ↳ QDP
                                                                                                                                        ↳ DependencyGraphProof
                                                                                                                                          ↳ QDP
                                                                                                                                            ↳ Rewriting
                                                                                                                                              ↳ QDP
                                                                                                                                                ↳ Rewriting
                                                                                                                                                  ↳ QDP
                                                                                                                                                    ↳ Rewriting
                                                                                                                                                      ↳ QDP
                                                                                                                                                        ↳ Rewriting
                                                                                                                                                          ↳ QDP
                                                                                                                                                            ↳ Rewriting
                                                                                                                                                              ↳ QDP
                                                                                                                                                                ↳ Rewriting
                                                                                                                                                                  ↳ QDP
                                                                                                                                                                    ↳ Rewriting
                                                                                                                                                                      ↳ QDP
                                                                                                                                                                        ↳ UsableRulesProof
                                                                                                                                                                          ↳ QDP
                                                                                                                                                                            ↳ QReductionProof
                                                                                                                                                                              ↳ QDP
                                                                                                                                                                                ↳ Rewriting
                                                                                                                                                                                  ↳ QDP
                                                                                                                                                                                    ↳ Rewriting
                                                                                                                                                                                      ↳ QDP
                                                                                                                                                                                        ↳ Rewriting
                                                                                                                                                                                          ↳ QDP
                                                                                                                                                                                            ↳ Rewriting
                                                                                                                                                                                              ↳ QDP
                                                                                                                                                                                                ↳ Rewriting
                                                                                                                                                                                                  ↳ QDP
                                                                                                                                                                                                    ↳ Rewriting
                                                                                                                                                                                                      ↳ QDP
                                                                                                                                                                                                        ↳ Rewriting
                                                                                                                                                                                                          ↳ QDP
                                                                                                                                                                                                            ↳ Rewriting
                                                                                                                                                                                                              ↳ QDP
                                                                                                                                                                                                                ↳ Rewriting
                                                                                                                                                                                                                  ↳ QDP
                                                                                                                                                                                                                    ↳ DependencyGraphProof
                                                                                                                                                                                                                      ↳ QDP
                                                                                                                                                                                                                        ↳ Rewriting
                                                                                                                                                                                                                          ↳ QDP
                                                                                                                                                                                                                            ↳ Rewriting
                                                                                                                                                                                                                              ↳ QDP
                                                                                                                                                                                                                                ↳ Rewriting
                                                                                                                                                                                                                                  ↳ QDP
                                                                                                                                                                                                                                    ↳ Rewriting
                                                                                                                                                                                                                                      ↳ QDP
                                                                                                                                                                                                                                        ↳ Rewriting
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP

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

new_mkVBalBranch3MkVBalBranch11(zzz2033, zzz2034, zzz2035, zzz2036, zzz2037, zzz2038, zzz2039, zzz2040, zzz2041, zzz2042, zzz2043, Zero, Succ(zzz20450), bb) → new_mkVBalBranch(zzz2043, zzz2042, Branch(zzz2033, zzz2034, Pos(Succ(zzz2035)), zzz2036, zzz2037), bb)
new_mkVBalBranch3MkVBalBranch211(zzz537, zzz538, zzz539, zzz540, zzz541, zzz542, zzz543, zzz544, zzz545, zzz546, zzz547, bc) → new_mkVBalBranch3MkVBalBranch15(zzz537, zzz538, zzz539, zzz540, zzz541, zzz542, zzz543, zzz544, zzz545, zzz546, zzz547, Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat2(Succ(new_primPlusNat3(new_primPlusNat1(zzz539), zzz539)), zzz539)), zzz539))), bc)
new_mkVBalBranch(zzz31, Branch(zzz520, zzz521, Neg(Succ(zzz52200)), zzz523, zzz524), Branch(zzz340, zzz341, zzz342, zzz343, zzz344), h) → new_mkVBalBranch3MkVBalBranch24(zzz340, zzz341, zzz342, zzz343, zzz344, zzz520, zzz521, zzz52200, zzz523, zzz524, zzz31, Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat3(new_primPlusNat1(zzz52200), zzz52200)), zzz52200))), h)
new_mkVBalBranch3MkVBalBranch23(zzz929, zzz930, zzz931, zzz932, zzz933, zzz934, zzz935, zzz936, zzz937, zzz938, zzz939, ba) → new_mkVBalBranch3MkVBalBranch10(zzz929, zzz930, zzz931, zzz932, zzz933, zzz934, zzz935, zzz936, zzz937, zzz938, zzz939, Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat2(Succ(new_primPlusNat3(new_primPlusNat1(zzz931), zzz931)), zzz931)), zzz931))), ba)
new_mkVBalBranch3MkVBalBranch26(zzz1133, zzz1134, zzz1135, zzz1136, zzz1137, zzz1138, zzz1139, zzz1140, zzz1141, zzz1142, Succ(zzz11430), Succ(zzz11440), be) → new_mkVBalBranch3MkVBalBranch26(zzz1133, zzz1134, zzz1135, zzz1136, zzz1137, zzz1138, zzz1139, zzz1140, zzz1141, zzz1142, zzz11430, zzz11440, be)
new_mkVBalBranch3MkVBalBranch24(zzz340, zzz341, Pos(zzz3420), zzz343, zzz344, zzz520, zzz521, zzz52200, zzz523, zzz524, zzz31, Succ(zzz690), h) → new_mkVBalBranch(zzz31, Branch(zzz520, zzz521, Neg(Succ(zzz52200)), zzz523, zzz524), zzz343, h)
new_mkVBalBranch3MkVBalBranch12(zzz340, zzz341, zzz34200, zzz343, zzz344, zzz520, zzz521, zzz523, zzz524, zzz31, Succ(zzz1250), h) → new_mkVBalBranch(zzz31, zzz524, Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), h)
new_mkVBalBranch3MkVBalBranch25(zzz537, zzz538, zzz539, zzz540, zzz541, zzz542, zzz543, zzz544, zzz545, zzz546, zzz547, Succ(zzz5480), Zero, bc) → new_mkVBalBranch3MkVBalBranch15(zzz537, zzz538, zzz539, zzz540, zzz541, zzz542, zzz543, zzz544, zzz545, zzz546, zzz547, Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat2(Succ(new_primPlusNat3(new_primPlusNat1(zzz539), zzz539)), zzz539)), zzz539))), bc)
new_mkVBalBranch3MkVBalBranch20(zzz929, zzz930, zzz931, zzz932, zzz933, zzz934, zzz935, zzz936, zzz937, zzz938, zzz939, Zero, Succ(zzz9410), ba) → new_mkVBalBranch(zzz939, Branch(zzz934, zzz935, Pos(Succ(zzz936)), zzz937, zzz938), zzz932, ba)
new_mkVBalBranch3MkVBalBranch24(zzz340, zzz341, Neg(Succ(Succ(Zero))), zzz343, zzz344, zzz520, zzz521, Zero, zzz523, zzz524, zzz31, Succ(Succ(zzz6900)), h) → new_mkVBalBranch3MkVBalBranch26(zzz340, zzz341, Succ(Zero), zzz343, zzz344, zzz520, zzz521, zzz523, zzz524, zzz31, Zero, Succ(zzz6900), h)
new_mkVBalBranch3MkVBalBranch1(zzz340, zzz341, zzz34200, zzz343, zzz344, zzz520, zzz521, zzz52200, zzz523, zzz524, zzz31, Succ(zzz1430), h) → new_mkVBalBranch(zzz31, zzz524, Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), h)
new_mkVBalBranch3MkVBalBranch26(zzz1133, zzz1134, zzz1135, zzz1136, zzz1137, zzz1138, zzz1139, zzz1140, zzz1141, zzz1142, Zero, Zero, be) → new_mkVBalBranch3MkVBalBranch29(zzz1133, zzz1134, zzz1135, zzz1136, zzz1137, zzz1138, zzz1139, zzz1140, zzz1141, zzz1142, be)
new_mkVBalBranch(zzz31, Branch(zzz520, zzz521, Neg(Zero), zzz523, zzz524), Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), h) → new_mkVBalBranch3MkVBalBranch13(zzz340, zzz341, zzz34200, zzz343, zzz344, zzz520, zzz521, zzz523, zzz524, zzz31, Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat2(Succ(new_primPlusNat3(new_primPlusNat1(zzz34200), zzz34200)), zzz34200)), zzz34200))), h)
new_mkVBalBranch3MkVBalBranch20(zzz929, zzz930, zzz931, zzz932, zzz933, zzz934, zzz935, zzz936, zzz937, zzz938, zzz939, Zero, Zero, ba) → new_mkVBalBranch3MkVBalBranch23(zzz929, zzz930, zzz931, zzz932, zzz933, zzz934, zzz935, zzz936, zzz937, zzz938, zzz939, ba)
new_mkVBalBranch3MkVBalBranch24(zzz340, zzz341, Neg(Succ(Zero)), zzz343, zzz344, zzz520, zzz521, zzz52200, zzz523, zzz524, zzz31, Succ(zzz690), h) → new_mkVBalBranch(zzz31, Branch(zzz520, zzz521, Neg(Succ(zzz52200)), zzz523, zzz524), zzz343, h)
new_mkVBalBranch3MkVBalBranch13(zzz340, zzz341, zzz34200, zzz343, zzz344, zzz520, zzz521, zzz523, zzz524, zzz31, Succ(zzz1290), h) → new_mkVBalBranch(zzz31, zzz524, Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), h)
new_mkVBalBranch3MkVBalBranch2(zzz340, zzz341, Pos(Succ(zzz34200)), zzz343, zzz344, zzz520, zzz521, zzz52200, zzz523, zzz524, zzz31, Succ(zzz680), h) → new_mkVBalBranch3MkVBalBranch20(zzz340, zzz341, zzz34200, zzz343, zzz344, zzz520, zzz521, zzz52200, zzz523, zzz524, zzz31, Succ(new_primPlusNat2(zzz680, zzz52200)), zzz34200, h)
new_mkVBalBranch(zzz31, Branch(zzz520, zzz521, Neg(Zero), zzz523, zzz524), Branch(zzz340, zzz341, Pos(Succ(zzz34200)), zzz343, zzz344), h) → new_mkVBalBranch(zzz31, Branch(zzz520, zzz521, Neg(Zero), zzz523, zzz524), zzz343, h)
new_mkVBalBranch3MkVBalBranch24(zzz340, zzz341, Neg(Zero), zzz343, zzz344, zzz520, zzz521, zzz52200, zzz523, zzz524, zzz31, Succ(zzz690), h) → new_mkVBalBranch(zzz31, Branch(zzz520, zzz521, Neg(Succ(zzz52200)), zzz523, zzz524), zzz343, h)
new_mkVBalBranch3MkVBalBranch20(zzz929, zzz930, zzz931, zzz932, zzz933, zzz934, zzz935, zzz936, zzz937, zzz938, zzz939, Succ(zzz9400), Succ(zzz9410), ba) → new_mkVBalBranch3MkVBalBranch20(zzz929, zzz930, zzz931, zzz932, zzz933, zzz934, zzz935, zzz936, zzz937, zzz938, zzz939, zzz9400, zzz9410, ba)
new_mkVBalBranch3MkVBalBranch26(zzz1133, zzz1134, zzz1135, zzz1136, zzz1137, zzz1138, zzz1139, zzz1140, zzz1141, zzz1142, Succ(zzz11430), Zero, be) → new_mkVBalBranch3MkVBalBranch212(zzz1133, zzz1134, zzz1135, zzz1136, zzz1137, zzz1138, zzz1139, zzz1140, zzz1141, zzz1142, be)
new_mkVBalBranch3MkVBalBranch29(zzz818, zzz819, zzz820, zzz821, zzz822, zzz823, zzz824, zzz825, zzz826, zzz827, bf) → new_mkVBalBranch3MkVBalBranch14(zzz818, zzz819, zzz820, zzz821, zzz822, zzz823, zzz824, zzz825, zzz826, zzz827, Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat2(Succ(new_primPlusNat3(new_primPlusNat1(zzz820), zzz820)), zzz820)), zzz820))), bf)
new_mkVBalBranch3MkVBalBranch16(zzz1702, zzz1703, zzz1704, zzz1705, zzz1706, zzz1707, zzz1708, zzz1709, zzz1710, zzz1711, zzz1712, Succ(zzz17130), Succ(zzz17140), bd) → new_mkVBalBranch3MkVBalBranch16(zzz1702, zzz1703, zzz1704, zzz1705, zzz1706, zzz1707, zzz1708, zzz1709, zzz1710, zzz1711, zzz1712, zzz17130, zzz17140, bd)
new_mkVBalBranch3MkVBalBranch25(zzz537, zzz538, zzz539, zzz540, zzz541, zzz542, zzz543, zzz544, zzz545, zzz546, zzz547, Zero, Succ(zzz5490), bc) → new_mkVBalBranch(zzz547, Branch(zzz542, zzz543, Neg(Succ(Succ(zzz544))), zzz545, zzz546), zzz540, bc)
new_mkVBalBranch3MkVBalBranch11(zzz2033, zzz2034, zzz2035, zzz2036, zzz2037, zzz2038, zzz2039, zzz2040, zzz2041, zzz2042, zzz2043, Succ(zzz20440), Succ(zzz20450), bb) → new_mkVBalBranch3MkVBalBranch11(zzz2033, zzz2034, zzz2035, zzz2036, zzz2037, zzz2038, zzz2039, zzz2040, zzz2041, zzz2042, zzz2043, zzz20440, zzz20450, bb)
new_mkVBalBranch3MkVBalBranch25(zzz537, zzz538, zzz539, zzz540, zzz541, zzz542, zzz543, zzz544, zzz545, zzz546, zzz547, Succ(zzz5480), Succ(zzz5490), bc) → new_mkVBalBranch3MkVBalBranch25(zzz537, zzz538, zzz539, zzz540, zzz541, zzz542, zzz543, zzz544, zzz545, zzz546, zzz547, zzz5480, zzz5490, bc)
new_mkVBalBranch3MkVBalBranch10(zzz929, zzz930, zzz931, zzz932, zzz933, zzz934, zzz935, zzz936, zzz937, zzz938, zzz939, Succ(zzz10020), ba) → new_mkVBalBranch3MkVBalBranch11(zzz929, zzz930, zzz931, zzz932, zzz933, zzz934, zzz935, zzz936, zzz937, zzz938, zzz939, Succ(zzz10020), Succ(zzz936), ba)
new_mkVBalBranch(zzz31, Branch(zzz520, zzz521, Pos(Succ(zzz52200)), zzz523, zzz524), Branch(zzz340, zzz341, zzz342, zzz343, zzz344), h) → new_mkVBalBranch3MkVBalBranch2(zzz340, zzz341, zzz342, zzz343, zzz344, zzz520, zzz521, zzz52200, zzz523, zzz524, zzz31, Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat3(new_primPlusNat1(zzz52200), zzz52200)), zzz52200))), h)
new_mkVBalBranch3MkVBalBranch14(zzz818, zzz819, zzz820, zzz821, zzz822, zzz823, zzz824, zzz825, zzz826, zzz827, Succ(zzz8960), bf) → new_mkVBalBranch3MkVBalBranch16(zzz818, zzz819, zzz820, zzz821, zzz822, zzz823, zzz824, Zero, zzz825, zzz826, zzz827, Succ(Zero), Succ(zzz8960), bf)
new_mkVBalBranch(zzz31, Branch(zzz520, zzz521, Pos(Zero), zzz523, zzz524), Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), h) → new_mkVBalBranch3MkVBalBranch12(zzz340, zzz341, zzz34200, zzz343, zzz344, zzz520, zzz521, zzz523, zzz524, zzz31, Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat2(Succ(new_primPlusNat3(new_primPlusNat1(zzz34200), zzz34200)), zzz34200)), zzz34200))), h)
new_mkVBalBranch3MkVBalBranch26(zzz1133, zzz1134, zzz1135, zzz1136, zzz1137, zzz1138, zzz1139, zzz1140, zzz1141, zzz1142, Zero, Succ(zzz11440), be) → new_mkVBalBranch(zzz1142, Branch(zzz1138, zzz1139, Neg(Succ(Zero)), zzz1140, zzz1141), zzz1136, be)
new_mkVBalBranch3MkVBalBranch24(zzz340, zzz341, Neg(Succ(Succ(Succ(zzz3420000)))), zzz343, zzz344, zzz520, zzz521, Succ(zzz522000), zzz523, zzz524, zzz31, Succ(Succ(zzz6900)), h) → new_mkVBalBranch3MkVBalBranch25(zzz340, zzz341, Succ(Succ(zzz3420000)), zzz343, zzz344, zzz520, zzz521, zzz522000, zzz523, zzz524, zzz31, Succ(zzz3420000), Succ(Succ(new_primPlusNat2(zzz6900, zzz522000))), h)
new_mkVBalBranch3MkVBalBranch212(zzz818, zzz819, zzz820, zzz821, zzz822, zzz823, zzz824, zzz825, zzz826, zzz827, bf) → new_mkVBalBranch3MkVBalBranch14(zzz818, zzz819, zzz820, zzz821, zzz822, zzz823, zzz824, zzz825, zzz826, zzz827, Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat2(Succ(new_primPlusNat3(new_primPlusNat1(zzz820), zzz820)), zzz820)), zzz820))), bf)
new_mkVBalBranch3MkVBalBranch24(zzz340, zzz341, Neg(Succ(Succ(Zero))), zzz343, zzz344, zzz520, zzz521, Succ(zzz522000), zzz523, zzz524, zzz31, Succ(Succ(zzz6900)), h) → new_mkVBalBranch3MkVBalBranch25(zzz340, zzz341, Succ(Zero), zzz343, zzz344, zzz520, zzz521, zzz522000, zzz523, zzz524, zzz31, Zero, Succ(Succ(new_primPlusNat2(zzz6900, zzz522000))), h)
new_mkVBalBranch(zzz31, Branch(zzz520, zzz521, Pos(Zero), zzz523, zzz524), Branch(zzz340, zzz341, Pos(Succ(zzz34200)), zzz343, zzz344), h) → new_mkVBalBranch(zzz31, Branch(zzz520, zzz521, Pos(Zero), zzz523, zzz524), zzz343, h)
new_mkVBalBranch3MkVBalBranch2(zzz340, zzz341, Pos(Zero), zzz343, zzz344, zzz520, zzz521, zzz52200, zzz523, zzz524, zzz31, Succ(zzz680), h) → new_mkVBalBranch(zzz31, zzz524, Branch(zzz340, zzz341, Pos(Zero), zzz343, zzz344), h)
new_mkVBalBranch3MkVBalBranch20(zzz929, zzz930, zzz931, zzz932, zzz933, zzz934, zzz935, zzz936, zzz937, zzz938, zzz939, Succ(zzz9400), Zero, ba) → new_mkVBalBranch3MkVBalBranch10(zzz929, zzz930, zzz931, zzz932, zzz933, zzz934, zzz935, zzz936, zzz937, zzz938, zzz939, new_primPlusNat2(Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat3(new_primPlusNat1(zzz931), zzz931)), zzz931))), Succ(zzz931)), ba)
new_mkVBalBranch3MkVBalBranch2(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344, zzz520, zzz521, zzz52200, zzz523, zzz524, zzz31, Succ(zzz680), h) → new_mkVBalBranch3MkVBalBranch1(zzz340, zzz341, zzz34200, zzz343, zzz344, zzz520, zzz521, zzz52200, zzz523, zzz524, zzz31, Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat2(Succ(new_primPlusNat3(new_primPlusNat1(zzz34200), zzz34200)), zzz34200)), zzz34200))), h)
new_mkVBalBranch3MkVBalBranch2(zzz340, zzz341, Neg(Zero), zzz343, zzz344, zzz520, zzz521, zzz52200, zzz523, zzz524, zzz31, Succ(zzz680), h) → new_mkVBalBranch(zzz31, zzz524, Branch(zzz340, zzz341, Neg(Zero), zzz343, zzz344), h)
new_mkVBalBranch3MkVBalBranch16(zzz1702, zzz1703, zzz1704, zzz1705, zzz1706, zzz1707, zzz1708, zzz1709, zzz1710, zzz1711, zzz1712, Zero, Succ(zzz17140), bd) → new_mkVBalBranch(zzz1712, zzz1711, Branch(zzz1702, zzz1703, Neg(Succ(zzz1704)), zzz1705, zzz1706), bd)
new_mkVBalBranch3MkVBalBranch10(zzz929, zzz930, zzz931, zzz932, zzz933, zzz934, zzz935, zzz936, zzz937, zzz938, zzz939, Zero, ba) → new_mkVBalBranch3MkVBalBranch11(zzz929, zzz930, zzz931, zzz932, zzz933, zzz934, zzz935, zzz936, zzz937, zzz938, zzz939, Zero, Succ(zzz936), ba)
new_mkVBalBranch3MkVBalBranch15(zzz537, zzz538, zzz539, zzz540, zzz541, zzz542, zzz543, zzz544, zzz545, zzz546, zzz547, Succ(zzz6990), bc) → new_mkVBalBranch3MkVBalBranch16(zzz537, zzz538, zzz539, zzz540, zzz541, zzz542, zzz543, Succ(zzz544), zzz545, zzz546, zzz547, Succ(Succ(zzz544)), Succ(zzz6990), bc)
new_mkVBalBranch3MkVBalBranch24(zzz340, zzz341, Neg(Succ(Succ(Succ(zzz3420000)))), zzz343, zzz344, zzz520, zzz521, Zero, zzz523, zzz524, zzz31, Succ(Succ(zzz6900)), h) → new_mkVBalBranch3MkVBalBranch26(zzz340, zzz341, Succ(Succ(zzz3420000)), zzz343, zzz344, zzz520, zzz521, zzz523, zzz524, zzz31, Succ(zzz3420000), Succ(zzz6900), h)
new_mkVBalBranch3MkVBalBranch25(zzz537, zzz538, zzz539, zzz540, zzz541, zzz542, zzz543, zzz544, zzz545, zzz546, zzz547, Zero, Zero, bc) → new_mkVBalBranch3MkVBalBranch211(zzz537, zzz538, zzz539, zzz540, zzz541, zzz542, zzz543, zzz544, zzz545, zzz546, zzz547, bc)

The TRS R consists of the following rules:

new_primPlusNat1(Zero) → Zero
new_primPlusNat1(Succ(zzz62000)) → Succ(Succ(new_primPlusNat1(zzz62000)))
new_primPlusNat3(zzz90, Succ(zzz910)) → Succ(Succ(new_primPlusNat2(zzz90, zzz910)))
new_primPlusNat3(zzz90, Zero) → Succ(zzz90)
new_primPlusNat2(Succ(zzz900), Succ(zzz9100)) → Succ(Succ(new_primPlusNat2(zzz900, zzz9100)))
new_primPlusNat2(Zero, Succ(zzz9100)) → Succ(zzz9100)
new_primPlusNat2(Zero, Zero) → Zero
new_primPlusNat2(Succ(zzz900), Zero) → Succ(zzz900)

The set Q consists of the following terms:

new_primPlusNat2(Zero, Succ(x0))
new_primPlusNat3(x0, Succ(x1))
new_primPlusNat2(Succ(x0), Succ(x1))
new_primPlusNat3(x0, Zero)
new_primPlusNat1(Zero)
new_primPlusNat2(Zero, Zero)
new_primPlusNat1(Succ(x0))
new_primPlusNat2(Succ(x0), Zero)

We have to consider all minimal (P,Q,R)-chains.
By rewriting [15] the rule new_mkVBalBranch3MkVBalBranch20(zzz929, zzz930, zzz931, zzz932, zzz933, zzz934, zzz935, zzz936, zzz937, zzz938, zzz939, Succ(zzz9400), Zero, ba) → new_mkVBalBranch3MkVBalBranch10(zzz929, zzz930, zzz931, zzz932, zzz933, zzz934, zzz935, zzz936, zzz937, zzz938, zzz939, new_primPlusNat2(Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat3(new_primPlusNat1(zzz931), zzz931)), zzz931))), Succ(zzz931)), ba) at position [11] we obtained the following new rules:

new_mkVBalBranch3MkVBalBranch20(zzz929, zzz930, zzz931, zzz932, zzz933, zzz934, zzz935, zzz936, zzz937, zzz938, zzz939, Succ(zzz9400), Zero, ba) → new_mkVBalBranch3MkVBalBranch10(zzz929, zzz930, zzz931, zzz932, zzz933, zzz934, zzz935, zzz936, zzz937, zzz938, zzz939, Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat2(Succ(new_primPlusNat3(new_primPlusNat1(zzz931), zzz931)), zzz931)), zzz931))), 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
                                    ↳ DependencyGraphProof
                                      ↳ QDP
                                        ↳ Rewriting
                                          ↳ QDP
                                            ↳ Rewriting
                                              ↳ QDP
                                                ↳ Rewriting
                                                  ↳ QDP
                                                    ↳ Rewriting
                                                      ↳ QDP
                                                        ↳ Rewriting
                                                          ↳ QDP
                                                            ↳ Rewriting
                                                              ↳ QDP
                                                                ↳ Rewriting
                                                                  ↳ QDP
                                                                    ↳ Rewriting
                                                                      ↳ QDP
                                                                        ↳ Rewriting
                                                                          ↳ QDP
                                                                            ↳ Rewriting
                                                                              ↳ QDP
                                                                                ↳ Rewriting
                                                                                  ↳ QDP
                                                                                    ↳ Rewriting
                                                                                      ↳ QDP
                                                                                        ↳ Rewriting
                                                                                          ↳ QDP
                                                                                            ↳ UsableRulesProof
                                                                                              ↳ QDP
                                                                                                ↳ QReductionProof
                                                                                                  ↳ QDP
                                                                                                    ↳ Rewriting
                                                                                                      ↳ QDP
                                                                                                        ↳ Rewriting
                                                                                                          ↳ QDP
                                                                                                            ↳ Rewriting
                                                                                                              ↳ QDP
                                                                                                                ↳ Rewriting
                                                                                                                  ↳ QDP
                                                                                                                    ↳ Rewriting
                                                                                                                      ↳ QDP
                                                                                                                        ↳ Rewriting
                                                                                                                          ↳ QDP
                                                                                                                            ↳ DependencyGraphProof
                                                                                                                              ↳ QDP
                                                                                                                                ↳ Rewriting
                                                                                                                                  ↳ QDP
                                                                                                                                    ↳ Rewriting
                                                                                                                                      ↳ QDP
                                                                                                                                        ↳ DependencyGraphProof
                                                                                                                                          ↳ QDP
                                                                                                                                            ↳ Rewriting
                                                                                                                                              ↳ QDP
                                                                                                                                                ↳ Rewriting
                                                                                                                                                  ↳ QDP
                                                                                                                                                    ↳ Rewriting
                                                                                                                                                      ↳ QDP
                                                                                                                                                        ↳ Rewriting
                                                                                                                                                          ↳ QDP
                                                                                                                                                            ↳ Rewriting
                                                                                                                                                              ↳ QDP
                                                                                                                                                                ↳ Rewriting
                                                                                                                                                                  ↳ QDP
                                                                                                                                                                    ↳ Rewriting
                                                                                                                                                                      ↳ QDP
                                                                                                                                                                        ↳ UsableRulesProof
                                                                                                                                                                          ↳ QDP
                                                                                                                                                                            ↳ QReductionProof
                                                                                                                                                                              ↳ QDP
                                                                                                                                                                                ↳ Rewriting
                                                                                                                                                                                  ↳ QDP
                                                                                                                                                                                    ↳ Rewriting
                                                                                                                                                                                      ↳ QDP
                                                                                                                                                                                        ↳ Rewriting
                                                                                                                                                                                          ↳ QDP
                                                                                                                                                                                            ↳ Rewriting
                                                                                                                                                                                              ↳ QDP
                                                                                                                                                                                                ↳ Rewriting
                                                                                                                                                                                                  ↳ QDP
                                                                                                                                                                                                    ↳ Rewriting
                                                                                                                                                                                                      ↳ QDP
                                                                                                                                                                                                        ↳ Rewriting
                                                                                                                                                                                                          ↳ QDP
                                                                                                                                                                                                            ↳ Rewriting
                                                                                                                                                                                                              ↳ QDP
                                                                                                                                                                                                                ↳ Rewriting
                                                                                                                                                                                                                  ↳ QDP
                                                                                                                                                                                                                    ↳ DependencyGraphProof
                                                                                                                                                                                                                      ↳ QDP
                                                                                                                                                                                                                        ↳ Rewriting
                                                                                                                                                                                                                          ↳ QDP
                                                                                                                                                                                                                            ↳ Rewriting
                                                                                                                                                                                                                              ↳ QDP
                                                                                                                                                                                                                                ↳ Rewriting
                                                                                                                                                                                                                                  ↳ QDP
                                                                                                                                                                                                                                    ↳ Rewriting
                                                                                                                                                                                                                                      ↳ QDP
                                                                                                                                                                                                                                        ↳ Rewriting
                                                                                                                                                                                                                                          ↳ QDP
                                                                                                                                                                                                                                            ↳ DependencyGraphProof
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP

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

new_mkVBalBranch(zzz31, Branch(zzz520, zzz521, Neg(Succ(zzz52200)), zzz523, zzz524), Branch(zzz340, zzz341, zzz342, zzz343, zzz344), h) → new_mkVBalBranch3MkVBalBranch24(zzz340, zzz341, zzz342, zzz343, zzz344, zzz520, zzz521, zzz52200, zzz523, zzz524, zzz31, Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat3(new_primPlusNat1(zzz52200), zzz52200)), zzz52200))), h)
new_mkVBalBranch3MkVBalBranch211(zzz537, zzz538, zzz539, zzz540, zzz541, zzz542, zzz543, zzz544, zzz545, zzz546, zzz547, bc) → new_mkVBalBranch3MkVBalBranch15(zzz537, zzz538, zzz539, zzz540, zzz541, zzz542, zzz543, zzz544, zzz545, zzz546, zzz547, Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat2(Succ(new_primPlusNat3(new_primPlusNat1(zzz539), zzz539)), zzz539)), zzz539))), bc)
new_mkVBalBranch3MkVBalBranch11(zzz2033, zzz2034, zzz2035, zzz2036, zzz2037, zzz2038, zzz2039, zzz2040, zzz2041, zzz2042, zzz2043, Zero, Succ(zzz20450), bb) → new_mkVBalBranch(zzz2043, zzz2042, Branch(zzz2033, zzz2034, Pos(Succ(zzz2035)), zzz2036, zzz2037), bb)
new_mkVBalBranch3MkVBalBranch26(zzz1133, zzz1134, zzz1135, zzz1136, zzz1137, zzz1138, zzz1139, zzz1140, zzz1141, zzz1142, Succ(zzz11430), Succ(zzz11440), be) → new_mkVBalBranch3MkVBalBranch26(zzz1133, zzz1134, zzz1135, zzz1136, zzz1137, zzz1138, zzz1139, zzz1140, zzz1141, zzz1142, zzz11430, zzz11440, be)
new_mkVBalBranch3MkVBalBranch23(zzz929, zzz930, zzz931, zzz932, zzz933, zzz934, zzz935, zzz936, zzz937, zzz938, zzz939, ba) → new_mkVBalBranch3MkVBalBranch10(zzz929, zzz930, zzz931, zzz932, zzz933, zzz934, zzz935, zzz936, zzz937, zzz938, zzz939, Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat2(Succ(new_primPlusNat3(new_primPlusNat1(zzz931), zzz931)), zzz931)), zzz931))), ba)
new_mkVBalBranch3MkVBalBranch24(zzz340, zzz341, Pos(zzz3420), zzz343, zzz344, zzz520, zzz521, zzz52200, zzz523, zzz524, zzz31, Succ(zzz690), h) → new_mkVBalBranch(zzz31, Branch(zzz520, zzz521, Neg(Succ(zzz52200)), zzz523, zzz524), zzz343, h)
new_mkVBalBranch3MkVBalBranch12(zzz340, zzz341, zzz34200, zzz343, zzz344, zzz520, zzz521, zzz523, zzz524, zzz31, Succ(zzz1250), h) → new_mkVBalBranch(zzz31, zzz524, Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), h)
new_mkVBalBranch3MkVBalBranch25(zzz537, zzz538, zzz539, zzz540, zzz541, zzz542, zzz543, zzz544, zzz545, zzz546, zzz547, Succ(zzz5480), Zero, bc) → new_mkVBalBranch3MkVBalBranch15(zzz537, zzz538, zzz539, zzz540, zzz541, zzz542, zzz543, zzz544, zzz545, zzz546, zzz547, Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat2(Succ(new_primPlusNat3(new_primPlusNat1(zzz539), zzz539)), zzz539)), zzz539))), bc)
new_mkVBalBranch3MkVBalBranch20(zzz929, zzz930, zzz931, zzz932, zzz933, zzz934, zzz935, zzz936, zzz937, zzz938, zzz939, Zero, Succ(zzz9410), ba) → new_mkVBalBranch(zzz939, Branch(zzz934, zzz935, Pos(Succ(zzz936)), zzz937, zzz938), zzz932, ba)
new_mkVBalBranch3MkVBalBranch24(zzz340, zzz341, Neg(Succ(Succ(Zero))), zzz343, zzz344, zzz520, zzz521, Zero, zzz523, zzz524, zzz31, Succ(Succ(zzz6900)), h) → new_mkVBalBranch3MkVBalBranch26(zzz340, zzz341, Succ(Zero), zzz343, zzz344, zzz520, zzz521, zzz523, zzz524, zzz31, Zero, Succ(zzz6900), h)
new_mkVBalBranch3MkVBalBranch26(zzz1133, zzz1134, zzz1135, zzz1136, zzz1137, zzz1138, zzz1139, zzz1140, zzz1141, zzz1142, Zero, Zero, be) → new_mkVBalBranch3MkVBalBranch29(zzz1133, zzz1134, zzz1135, zzz1136, zzz1137, zzz1138, zzz1139, zzz1140, zzz1141, zzz1142, be)
new_mkVBalBranch3MkVBalBranch1(zzz340, zzz341, zzz34200, zzz343, zzz344, zzz520, zzz521, zzz52200, zzz523, zzz524, zzz31, Succ(zzz1430), h) → new_mkVBalBranch(zzz31, zzz524, Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), h)
new_mkVBalBranch3MkVBalBranch24(zzz340, zzz341, Neg(Succ(Zero)), zzz343, zzz344, zzz520, zzz521, zzz52200, zzz523, zzz524, zzz31, Succ(zzz690), h) → new_mkVBalBranch(zzz31, Branch(zzz520, zzz521, Neg(Succ(zzz52200)), zzz523, zzz524), zzz343, h)
new_mkVBalBranch3MkVBalBranch20(zzz929, zzz930, zzz931, zzz932, zzz933, zzz934, zzz935, zzz936, zzz937, zzz938, zzz939, Zero, Zero, ba) → new_mkVBalBranch3MkVBalBranch23(zzz929, zzz930, zzz931, zzz932, zzz933, zzz934, zzz935, zzz936, zzz937, zzz938, zzz939, ba)
new_mkVBalBranch(zzz31, Branch(zzz520, zzz521, Neg(Zero), zzz523, zzz524), Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), h) → new_mkVBalBranch3MkVBalBranch13(zzz340, zzz341, zzz34200, zzz343, zzz344, zzz520, zzz521, zzz523, zzz524, zzz31, Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat2(Succ(new_primPlusNat3(new_primPlusNat1(zzz34200), zzz34200)), zzz34200)), zzz34200))), h)
new_mkVBalBranch3MkVBalBranch13(zzz340, zzz341, zzz34200, zzz343, zzz344, zzz520, zzz521, zzz523, zzz524, zzz31, Succ(zzz1290), h) → new_mkVBalBranch(zzz31, zzz524, Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), h)
new_mkVBalBranch3MkVBalBranch2(zzz340, zzz341, Pos(Succ(zzz34200)), zzz343, zzz344, zzz520, zzz521, zzz52200, zzz523, zzz524, zzz31, Succ(zzz680), h) → new_mkVBalBranch3MkVBalBranch20(zzz340, zzz341, zzz34200, zzz343, zzz344, zzz520, zzz521, zzz52200, zzz523, zzz524, zzz31, Succ(new_primPlusNat2(zzz680, zzz52200)), zzz34200, h)
new_mkVBalBranch3MkVBalBranch24(zzz340, zzz341, Neg(Zero), zzz343, zzz344, zzz520, zzz521, zzz52200, zzz523, zzz524, zzz31, Succ(zzz690), h) → new_mkVBalBranch(zzz31, Branch(zzz520, zzz521, Neg(Succ(zzz52200)), zzz523, zzz524), zzz343, h)
new_mkVBalBranch(zzz31, Branch(zzz520, zzz521, Neg(Zero), zzz523, zzz524), Branch(zzz340, zzz341, Pos(Succ(zzz34200)), zzz343, zzz344), h) → new_mkVBalBranch(zzz31, Branch(zzz520, zzz521, Neg(Zero), zzz523, zzz524), zzz343, h)
new_mkVBalBranch3MkVBalBranch20(zzz929, zzz930, zzz931, zzz932, zzz933, zzz934, zzz935, zzz936, zzz937, zzz938, zzz939, Succ(zzz9400), Succ(zzz9410), ba) → new_mkVBalBranch3MkVBalBranch20(zzz929, zzz930, zzz931, zzz932, zzz933, zzz934, zzz935, zzz936, zzz937, zzz938, zzz939, zzz9400, zzz9410, ba)
new_mkVBalBranch3MkVBalBranch29(zzz818, zzz819, zzz820, zzz821, zzz822, zzz823, zzz824, zzz825, zzz826, zzz827, bf) → new_mkVBalBranch3MkVBalBranch14(zzz818, zzz819, zzz820, zzz821, zzz822, zzz823, zzz824, zzz825, zzz826, zzz827, Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat2(Succ(new_primPlusNat3(new_primPlusNat1(zzz820), zzz820)), zzz820)), zzz820))), bf)
new_mkVBalBranch3MkVBalBranch26(zzz1133, zzz1134, zzz1135, zzz1136, zzz1137, zzz1138, zzz1139, zzz1140, zzz1141, zzz1142, Succ(zzz11430), Zero, be) → new_mkVBalBranch3MkVBalBranch212(zzz1133, zzz1134, zzz1135, zzz1136, zzz1137, zzz1138, zzz1139, zzz1140, zzz1141, zzz1142, be)
new_mkVBalBranch3MkVBalBranch16(zzz1702, zzz1703, zzz1704, zzz1705, zzz1706, zzz1707, zzz1708, zzz1709, zzz1710, zzz1711, zzz1712, Succ(zzz17130), Succ(zzz17140), bd) → new_mkVBalBranch3MkVBalBranch16(zzz1702, zzz1703, zzz1704, zzz1705, zzz1706, zzz1707, zzz1708, zzz1709, zzz1710, zzz1711, zzz1712, zzz17130, zzz17140, bd)
new_mkVBalBranch3MkVBalBranch25(zzz537, zzz538, zzz539, zzz540, zzz541, zzz542, zzz543, zzz544, zzz545, zzz546, zzz547, Zero, Succ(zzz5490), bc) → new_mkVBalBranch(zzz547, Branch(zzz542, zzz543, Neg(Succ(Succ(zzz544))), zzz545, zzz546), zzz540, bc)
new_mkVBalBranch3MkVBalBranch11(zzz2033, zzz2034, zzz2035, zzz2036, zzz2037, zzz2038, zzz2039, zzz2040, zzz2041, zzz2042, zzz2043, Succ(zzz20440), Succ(zzz20450), bb) → new_mkVBalBranch3MkVBalBranch11(zzz2033, zzz2034, zzz2035, zzz2036, zzz2037, zzz2038, zzz2039, zzz2040, zzz2041, zzz2042, zzz2043, zzz20440, zzz20450, bb)
new_mkVBalBranch3MkVBalBranch25(zzz537, zzz538, zzz539, zzz540, zzz541, zzz542, zzz543, zzz544, zzz545, zzz546, zzz547, Succ(zzz5480), Succ(zzz5490), bc) → new_mkVBalBranch3MkVBalBranch25(zzz537, zzz538, zzz539, zzz540, zzz541, zzz542, zzz543, zzz544, zzz545, zzz546, zzz547, zzz5480, zzz5490, bc)
new_mkVBalBranch(zzz31, Branch(zzz520, zzz521, Pos(Succ(zzz52200)), zzz523, zzz524), Branch(zzz340, zzz341, zzz342, zzz343, zzz344), h) → new_mkVBalBranch3MkVBalBranch2(zzz340, zzz341, zzz342, zzz343, zzz344, zzz520, zzz521, zzz52200, zzz523, zzz524, zzz31, Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat3(new_primPlusNat1(zzz52200), zzz52200)), zzz52200))), h)
new_mkVBalBranch3MkVBalBranch10(zzz929, zzz930, zzz931, zzz932, zzz933, zzz934, zzz935, zzz936, zzz937, zzz938, zzz939, Succ(zzz10020), ba) → new_mkVBalBranch3MkVBalBranch11(zzz929, zzz930, zzz931, zzz932, zzz933, zzz934, zzz935, zzz936, zzz937, zzz938, zzz939, Succ(zzz10020), Succ(zzz936), ba)
new_mkVBalBranch3MkVBalBranch14(zzz818, zzz819, zzz820, zzz821, zzz822, zzz823, zzz824, zzz825, zzz826, zzz827, Succ(zzz8960), bf) → new_mkVBalBranch3MkVBalBranch16(zzz818, zzz819, zzz820, zzz821, zzz822, zzz823, zzz824, Zero, zzz825, zzz826, zzz827, Succ(Zero), Succ(zzz8960), bf)
new_mkVBalBranch3MkVBalBranch24(zzz340, zzz341, Neg(Succ(Succ(Succ(zzz3420000)))), zzz343, zzz344, zzz520, zzz521, Succ(zzz522000), zzz523, zzz524, zzz31, Succ(Succ(zzz6900)), h) → new_mkVBalBranch3MkVBalBranch25(zzz340, zzz341, Succ(Succ(zzz3420000)), zzz343, zzz344, zzz520, zzz521, zzz522000, zzz523, zzz524, zzz31, Succ(zzz3420000), Succ(Succ(new_primPlusNat2(zzz6900, zzz522000))), h)
new_mkVBalBranch3MkVBalBranch26(zzz1133, zzz1134, zzz1135, zzz1136, zzz1137, zzz1138, zzz1139, zzz1140, zzz1141, zzz1142, Zero, Succ(zzz11440), be) → new_mkVBalBranch(zzz1142, Branch(zzz1138, zzz1139, Neg(Succ(Zero)), zzz1140, zzz1141), zzz1136, be)
new_mkVBalBranch(zzz31, Branch(zzz520, zzz521, Pos(Zero), zzz523, zzz524), Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), h) → new_mkVBalBranch3MkVBalBranch12(zzz340, zzz341, zzz34200, zzz343, zzz344, zzz520, zzz521, zzz523, zzz524, zzz31, Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat2(Succ(new_primPlusNat3(new_primPlusNat1(zzz34200), zzz34200)), zzz34200)), zzz34200))), h)
new_mkVBalBranch3MkVBalBranch212(zzz818, zzz819, zzz820, zzz821, zzz822, zzz823, zzz824, zzz825, zzz826, zzz827, bf) → new_mkVBalBranch3MkVBalBranch14(zzz818, zzz819, zzz820, zzz821, zzz822, zzz823, zzz824, zzz825, zzz826, zzz827, Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat2(Succ(new_primPlusNat3(new_primPlusNat1(zzz820), zzz820)), zzz820)), zzz820))), bf)
new_mkVBalBranch3MkVBalBranch24(zzz340, zzz341, Neg(Succ(Succ(Zero))), zzz343, zzz344, zzz520, zzz521, Succ(zzz522000), zzz523, zzz524, zzz31, Succ(Succ(zzz6900)), h) → new_mkVBalBranch3MkVBalBranch25(zzz340, zzz341, Succ(Zero), zzz343, zzz344, zzz520, zzz521, zzz522000, zzz523, zzz524, zzz31, Zero, Succ(Succ(new_primPlusNat2(zzz6900, zzz522000))), h)
new_mkVBalBranch(zzz31, Branch(zzz520, zzz521, Pos(Zero), zzz523, zzz524), Branch(zzz340, zzz341, Pos(Succ(zzz34200)), zzz343, zzz344), h) → new_mkVBalBranch(zzz31, Branch(zzz520, zzz521, Pos(Zero), zzz523, zzz524), zzz343, h)
new_mkVBalBranch3MkVBalBranch20(zzz929, zzz930, zzz931, zzz932, zzz933, zzz934, zzz935, zzz936, zzz937, zzz938, zzz939, Succ(zzz9400), Zero, ba) → new_mkVBalBranch3MkVBalBranch10(zzz929, zzz930, zzz931, zzz932, zzz933, zzz934, zzz935, zzz936, zzz937, zzz938, zzz939, Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat2(Succ(new_primPlusNat3(new_primPlusNat1(zzz931), zzz931)), zzz931)), zzz931))), ba)
new_mkVBalBranch3MkVBalBranch2(zzz340, zzz341, Pos(Zero), zzz343, zzz344, zzz520, zzz521, zzz52200, zzz523, zzz524, zzz31, Succ(zzz680), h) → new_mkVBalBranch(zzz31, zzz524, Branch(zzz340, zzz341, Pos(Zero), zzz343, zzz344), h)
new_mkVBalBranch3MkVBalBranch2(zzz340, zzz341, Neg(Zero), zzz343, zzz344, zzz520, zzz521, zzz52200, zzz523, zzz524, zzz31, Succ(zzz680), h) → new_mkVBalBranch(zzz31, zzz524, Branch(zzz340, zzz341, Neg(Zero), zzz343, zzz344), h)
new_mkVBalBranch3MkVBalBranch2(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344, zzz520, zzz521, zzz52200, zzz523, zzz524, zzz31, Succ(zzz680), h) → new_mkVBalBranch3MkVBalBranch1(zzz340, zzz341, zzz34200, zzz343, zzz344, zzz520, zzz521, zzz52200, zzz523, zzz524, zzz31, Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat2(Succ(new_primPlusNat3(new_primPlusNat1(zzz34200), zzz34200)), zzz34200)), zzz34200))), h)
new_mkVBalBranch3MkVBalBranch16(zzz1702, zzz1703, zzz1704, zzz1705, zzz1706, zzz1707, zzz1708, zzz1709, zzz1710, zzz1711, zzz1712, Zero, Succ(zzz17140), bd) → new_mkVBalBranch(zzz1712, zzz1711, Branch(zzz1702, zzz1703, Neg(Succ(zzz1704)), zzz1705, zzz1706), bd)
new_mkVBalBranch3MkVBalBranch24(zzz340, zzz341, Neg(Succ(Succ(Succ(zzz3420000)))), zzz343, zzz344, zzz520, zzz521, Zero, zzz523, zzz524, zzz31, Succ(Succ(zzz6900)), h) → new_mkVBalBranch3MkVBalBranch26(zzz340, zzz341, Succ(Succ(zzz3420000)), zzz343, zzz344, zzz520, zzz521, zzz523, zzz524, zzz31, Succ(zzz3420000), Succ(zzz6900), h)
new_mkVBalBranch3MkVBalBranch15(zzz537, zzz538, zzz539, zzz540, zzz541, zzz542, zzz543, zzz544, zzz545, zzz546, zzz547, Succ(zzz6990), bc) → new_mkVBalBranch3MkVBalBranch16(zzz537, zzz538, zzz539, zzz540, zzz541, zzz542, zzz543, Succ(zzz544), zzz545, zzz546, zzz547, Succ(Succ(zzz544)), Succ(zzz6990), bc)
new_mkVBalBranch3MkVBalBranch10(zzz929, zzz930, zzz931, zzz932, zzz933, zzz934, zzz935, zzz936, zzz937, zzz938, zzz939, Zero, ba) → new_mkVBalBranch3MkVBalBranch11(zzz929, zzz930, zzz931, zzz932, zzz933, zzz934, zzz935, zzz936, zzz937, zzz938, zzz939, Zero, Succ(zzz936), ba)
new_mkVBalBranch3MkVBalBranch25(zzz537, zzz538, zzz539, zzz540, zzz541, zzz542, zzz543, zzz544, zzz545, zzz546, zzz547, Zero, Zero, bc) → new_mkVBalBranch3MkVBalBranch211(zzz537, zzz538, zzz539, zzz540, zzz541, zzz542, zzz543, zzz544, zzz545, zzz546, zzz547, bc)

The TRS R consists of the following rules:

new_primPlusNat1(Zero) → Zero
new_primPlusNat1(Succ(zzz62000)) → Succ(Succ(new_primPlusNat1(zzz62000)))
new_primPlusNat3(zzz90, Succ(zzz910)) → Succ(Succ(new_primPlusNat2(zzz90, zzz910)))
new_primPlusNat3(zzz90, Zero) → Succ(zzz90)
new_primPlusNat2(Succ(zzz900), Succ(zzz9100)) → Succ(Succ(new_primPlusNat2(zzz900, zzz9100)))
new_primPlusNat2(Zero, Succ(zzz9100)) → Succ(zzz9100)
new_primPlusNat2(Zero, Zero) → Zero
new_primPlusNat2(Succ(zzz900), Zero) → Succ(zzz900)

The set Q consists of the following terms:

new_primPlusNat2(Zero, Succ(x0))
new_primPlusNat3(x0, Succ(x1))
new_primPlusNat2(Succ(x0), Succ(x1))
new_primPlusNat3(x0, Zero)
new_primPlusNat1(Zero)
new_primPlusNat2(Zero, Zero)
new_primPlusNat1(Succ(x0))
new_primPlusNat2(Succ(x0), Zero)

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

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

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

new_mkVBalBranch3MkVBalBranch11(zzz2033, zzz2034, zzz2035, zzz2036, zzz2037, zzz2038, zzz2039, zzz2040, zzz2041, zzz2042, zzz2043, Zero, Succ(zzz20450), bb) → new_mkVBalBranch(zzz2043, zzz2042, Branch(zzz2033, zzz2034, Pos(Succ(zzz2035)), zzz2036, zzz2037), bb)
new_mkVBalBranch3MkVBalBranch211(zzz537, zzz538, zzz539, zzz540, zzz541, zzz542, zzz543, zzz544, zzz545, zzz546, zzz547, bc) → new_mkVBalBranch3MkVBalBranch15(zzz537, zzz538, zzz539, zzz540, zzz541, zzz542, zzz543, zzz544, zzz545, zzz546, zzz547, Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat2(Succ(new_primPlusNat3(new_primPlusNat1(zzz539), zzz539)), zzz539)), zzz539))), bc)
new_mkVBalBranch(zzz31, Branch(zzz520, zzz521, Neg(Succ(zzz52200)), zzz523, zzz524), Branch(zzz340, zzz341, zzz342, zzz343, zzz344), h) → new_mkVBalBranch3MkVBalBranch24(zzz340, zzz341, zzz342, zzz343, zzz344, zzz520, zzz521, zzz52200, zzz523, zzz524, zzz31, Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat3(new_primPlusNat1(zzz52200), zzz52200)), zzz52200))), h)
new_mkVBalBranch3MkVBalBranch23(zzz929, zzz930, zzz931, zzz932, zzz933, zzz934, zzz935, zzz936, zzz937, zzz938, zzz939, ba) → new_mkVBalBranch3MkVBalBranch10(zzz929, zzz930, zzz931, zzz932, zzz933, zzz934, zzz935, zzz936, zzz937, zzz938, zzz939, Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat2(Succ(new_primPlusNat3(new_primPlusNat1(zzz931), zzz931)), zzz931)), zzz931))), ba)
new_mkVBalBranch3MkVBalBranch26(zzz1133, zzz1134, zzz1135, zzz1136, zzz1137, zzz1138, zzz1139, zzz1140, zzz1141, zzz1142, Succ(zzz11430), Succ(zzz11440), be) → new_mkVBalBranch3MkVBalBranch26(zzz1133, zzz1134, zzz1135, zzz1136, zzz1137, zzz1138, zzz1139, zzz1140, zzz1141, zzz1142, zzz11430, zzz11440, be)
new_mkVBalBranch3MkVBalBranch24(zzz340, zzz341, Pos(zzz3420), zzz343, zzz344, zzz520, zzz521, zzz52200, zzz523, zzz524, zzz31, Succ(zzz690), h) → new_mkVBalBranch(zzz31, Branch(zzz520, zzz521, Neg(Succ(zzz52200)), zzz523, zzz524), zzz343, h)
new_mkVBalBranch3MkVBalBranch12(zzz340, zzz341, zzz34200, zzz343, zzz344, zzz520, zzz521, zzz523, zzz524, zzz31, Succ(zzz1250), h) → new_mkVBalBranch(zzz31, zzz524, Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), h)
new_mkVBalBranch3MkVBalBranch25(zzz537, zzz538, zzz539, zzz540, zzz541, zzz542, zzz543, zzz544, zzz545, zzz546, zzz547, Succ(zzz5480), Zero, bc) → new_mkVBalBranch3MkVBalBranch15(zzz537, zzz538, zzz539, zzz540, zzz541, zzz542, zzz543, zzz544, zzz545, zzz546, zzz547, Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat2(Succ(new_primPlusNat3(new_primPlusNat1(zzz539), zzz539)), zzz539)), zzz539))), bc)
new_mkVBalBranch3MkVBalBranch20(zzz929, zzz930, zzz931, zzz932, zzz933, zzz934, zzz935, zzz936, zzz937, zzz938, zzz939, Zero, Succ(zzz9410), ba) → new_mkVBalBranch(zzz939, Branch(zzz934, zzz935, Pos(Succ(zzz936)), zzz937, zzz938), zzz932, ba)
new_mkVBalBranch3MkVBalBranch24(zzz340, zzz341, Neg(Succ(Succ(Zero))), zzz343, zzz344, zzz520, zzz521, Zero, zzz523, zzz524, zzz31, Succ(Succ(zzz6900)), h) → new_mkVBalBranch3MkVBalBranch26(zzz340, zzz341, Succ(Zero), zzz343, zzz344, zzz520, zzz521, zzz523, zzz524, zzz31, Zero, Succ(zzz6900), h)
new_mkVBalBranch3MkVBalBranch1(zzz340, zzz341, zzz34200, zzz343, zzz344, zzz520, zzz521, zzz52200, zzz523, zzz524, zzz31, Succ(zzz1430), h) → new_mkVBalBranch(zzz31, zzz524, Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), h)
new_mkVBalBranch3MkVBalBranch26(zzz1133, zzz1134, zzz1135, zzz1136, zzz1137, zzz1138, zzz1139, zzz1140, zzz1141, zzz1142, Zero, Zero, be) → new_mkVBalBranch3MkVBalBranch29(zzz1133, zzz1134, zzz1135, zzz1136, zzz1137, zzz1138, zzz1139, zzz1140, zzz1141, zzz1142, be)
new_mkVBalBranch3MkVBalBranch20(zzz929, zzz930, zzz931, zzz932, zzz933, zzz934, zzz935, zzz936, zzz937, zzz938, zzz939, Zero, Zero, ba) → new_mkVBalBranch3MkVBalBranch23(zzz929, zzz930, zzz931, zzz932, zzz933, zzz934, zzz935, zzz936, zzz937, zzz938, zzz939, ba)
new_mkVBalBranch(zzz31, Branch(zzz520, zzz521, Neg(Zero), zzz523, zzz524), Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), h) → new_mkVBalBranch3MkVBalBranch13(zzz340, zzz341, zzz34200, zzz343, zzz344, zzz520, zzz521, zzz523, zzz524, zzz31, Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat2(Succ(new_primPlusNat3(new_primPlusNat1(zzz34200), zzz34200)), zzz34200)), zzz34200))), h)
new_mkVBalBranch3MkVBalBranch24(zzz340, zzz341, Neg(Succ(Zero)), zzz343, zzz344, zzz520, zzz521, zzz52200, zzz523, zzz524, zzz31, Succ(zzz690), h) → new_mkVBalBranch(zzz31, Branch(zzz520, zzz521, Neg(Succ(zzz52200)), zzz523, zzz524), zzz343, h)
new_mkVBalBranch3MkVBalBranch13(zzz340, zzz341, zzz34200, zzz343, zzz344, zzz520, zzz521, zzz523, zzz524, zzz31, Succ(zzz1290), h) → new_mkVBalBranch(zzz31, zzz524, Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), h)
new_mkVBalBranch3MkVBalBranch2(zzz340, zzz341, Pos(Succ(zzz34200)), zzz343, zzz344, zzz520, zzz521, zzz52200, zzz523, zzz524, zzz31, Succ(zzz680), h) → new_mkVBalBranch3MkVBalBranch20(zzz340, zzz341, zzz34200, zzz343, zzz344, zzz520, zzz521, zzz52200, zzz523, zzz524, zzz31, Succ(new_primPlusNat2(zzz680, zzz52200)), zzz34200, h)
new_mkVBalBranch(zzz31, Branch(zzz520, zzz521, Neg(Zero), zzz523, zzz524), Branch(zzz340, zzz341, Pos(Succ(zzz34200)), zzz343, zzz344), h) → new_mkVBalBranch(zzz31, Branch(zzz520, zzz521, Neg(Zero), zzz523, zzz524), zzz343, h)
new_mkVBalBranch3MkVBalBranch24(zzz340, zzz341, Neg(Zero), zzz343, zzz344, zzz520, zzz521, zzz52200, zzz523, zzz524, zzz31, Succ(zzz690), h) → new_mkVBalBranch(zzz31, Branch(zzz520, zzz521, Neg(Succ(zzz52200)), zzz523, zzz524), zzz343, h)
new_mkVBalBranch3MkVBalBranch20(zzz929, zzz930, zzz931, zzz932, zzz933, zzz934, zzz935, zzz936, zzz937, zzz938, zzz939, Succ(zzz9400), Succ(zzz9410), ba) → new_mkVBalBranch3MkVBalBranch20(zzz929, zzz930, zzz931, zzz932, zzz933, zzz934, zzz935, zzz936, zzz937, zzz938, zzz939, zzz9400, zzz9410, ba)
new_mkVBalBranch3MkVBalBranch29(zzz818, zzz819, zzz820, zzz821, zzz822, zzz823, zzz824, zzz825, zzz826, zzz827, bf) → new_mkVBalBranch3MkVBalBranch14(zzz818, zzz819, zzz820, zzz821, zzz822, zzz823, zzz824, zzz825, zzz826, zzz827, Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat2(Succ(new_primPlusNat3(new_primPlusNat1(zzz820), zzz820)), zzz820)), zzz820))), bf)
new_mkVBalBranch3MkVBalBranch26(zzz1133, zzz1134, zzz1135, zzz1136, zzz1137, zzz1138, zzz1139, zzz1140, zzz1141, zzz1142, Succ(zzz11430), Zero, be) → new_mkVBalBranch3MkVBalBranch212(zzz1133, zzz1134, zzz1135, zzz1136, zzz1137, zzz1138, zzz1139, zzz1140, zzz1141, zzz1142, be)
new_mkVBalBranch3MkVBalBranch16(zzz1702, zzz1703, zzz1704, zzz1705, zzz1706, zzz1707, zzz1708, zzz1709, zzz1710, zzz1711, zzz1712, Succ(zzz17130), Succ(zzz17140), bd) → new_mkVBalBranch3MkVBalBranch16(zzz1702, zzz1703, zzz1704, zzz1705, zzz1706, zzz1707, zzz1708, zzz1709, zzz1710, zzz1711, zzz1712, zzz17130, zzz17140, bd)
new_mkVBalBranch3MkVBalBranch25(zzz537, zzz538, zzz539, zzz540, zzz541, zzz542, zzz543, zzz544, zzz545, zzz546, zzz547, Zero, Succ(zzz5490), bc) → new_mkVBalBranch(zzz547, Branch(zzz542, zzz543, Neg(Succ(Succ(zzz544))), zzz545, zzz546), zzz540, bc)
new_mkVBalBranch3MkVBalBranch11(zzz2033, zzz2034, zzz2035, zzz2036, zzz2037, zzz2038, zzz2039, zzz2040, zzz2041, zzz2042, zzz2043, Succ(zzz20440), Succ(zzz20450), bb) → new_mkVBalBranch3MkVBalBranch11(zzz2033, zzz2034, zzz2035, zzz2036, zzz2037, zzz2038, zzz2039, zzz2040, zzz2041, zzz2042, zzz2043, zzz20440, zzz20450, bb)
new_mkVBalBranch3MkVBalBranch25(zzz537, zzz538, zzz539, zzz540, zzz541, zzz542, zzz543, zzz544, zzz545, zzz546, zzz547, Succ(zzz5480), Succ(zzz5490), bc) → new_mkVBalBranch3MkVBalBranch25(zzz537, zzz538, zzz539, zzz540, zzz541, zzz542, zzz543, zzz544, zzz545, zzz546, zzz547, zzz5480, zzz5490, bc)
new_mkVBalBranch3MkVBalBranch10(zzz929, zzz930, zzz931, zzz932, zzz933, zzz934, zzz935, zzz936, zzz937, zzz938, zzz939, Succ(zzz10020), ba) → new_mkVBalBranch3MkVBalBranch11(zzz929, zzz930, zzz931, zzz932, zzz933, zzz934, zzz935, zzz936, zzz937, zzz938, zzz939, Succ(zzz10020), Succ(zzz936), ba)
new_mkVBalBranch(zzz31, Branch(zzz520, zzz521, Pos(Succ(zzz52200)), zzz523, zzz524), Branch(zzz340, zzz341, zzz342, zzz343, zzz344), h) → new_mkVBalBranch3MkVBalBranch2(zzz340, zzz341, zzz342, zzz343, zzz344, zzz520, zzz521, zzz52200, zzz523, zzz524, zzz31, Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat3(new_primPlusNat1(zzz52200), zzz52200)), zzz52200))), h)
new_mkVBalBranch3MkVBalBranch14(zzz818, zzz819, zzz820, zzz821, zzz822, zzz823, zzz824, zzz825, zzz826, zzz827, Succ(zzz8960), bf) → new_mkVBalBranch3MkVBalBranch16(zzz818, zzz819, zzz820, zzz821, zzz822, zzz823, zzz824, Zero, zzz825, zzz826, zzz827, Succ(Zero), Succ(zzz8960), bf)
new_mkVBalBranch(zzz31, Branch(zzz520, zzz521, Pos(Zero), zzz523, zzz524), Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), h) → new_mkVBalBranch3MkVBalBranch12(zzz340, zzz341, zzz34200, zzz343, zzz344, zzz520, zzz521, zzz523, zzz524, zzz31, Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat2(Succ(new_primPlusNat3(new_primPlusNat1(zzz34200), zzz34200)), zzz34200)), zzz34200))), h)
new_mkVBalBranch3MkVBalBranch26(zzz1133, zzz1134, zzz1135, zzz1136, zzz1137, zzz1138, zzz1139, zzz1140, zzz1141, zzz1142, Zero, Succ(zzz11440), be) → new_mkVBalBranch(zzz1142, Branch(zzz1138, zzz1139, Neg(Succ(Zero)), zzz1140, zzz1141), zzz1136, be)
new_mkVBalBranch3MkVBalBranch24(zzz340, zzz341, Neg(Succ(Succ(Succ(zzz3420000)))), zzz343, zzz344, zzz520, zzz521, Succ(zzz522000), zzz523, zzz524, zzz31, Succ(Succ(zzz6900)), h) → new_mkVBalBranch3MkVBalBranch25(zzz340, zzz341, Succ(Succ(zzz3420000)), zzz343, zzz344, zzz520, zzz521, zzz522000, zzz523, zzz524, zzz31, Succ(zzz3420000), Succ(Succ(new_primPlusNat2(zzz6900, zzz522000))), h)
new_mkVBalBranch3MkVBalBranch212(zzz818, zzz819, zzz820, zzz821, zzz822, zzz823, zzz824, zzz825, zzz826, zzz827, bf) → new_mkVBalBranch3MkVBalBranch14(zzz818, zzz819, zzz820, zzz821, zzz822, zzz823, zzz824, zzz825, zzz826, zzz827, Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat2(Succ(new_primPlusNat3(new_primPlusNat1(zzz820), zzz820)), zzz820)), zzz820))), bf)
new_mkVBalBranch3MkVBalBranch24(zzz340, zzz341, Neg(Succ(Succ(Zero))), zzz343, zzz344, zzz520, zzz521, Succ(zzz522000), zzz523, zzz524, zzz31, Succ(Succ(zzz6900)), h) → new_mkVBalBranch3MkVBalBranch25(zzz340, zzz341, Succ(Zero), zzz343, zzz344, zzz520, zzz521, zzz522000, zzz523, zzz524, zzz31, Zero, Succ(Succ(new_primPlusNat2(zzz6900, zzz522000))), h)
new_mkVBalBranch(zzz31, Branch(zzz520, zzz521, Pos(Zero), zzz523, zzz524), Branch(zzz340, zzz341, Pos(Succ(zzz34200)), zzz343, zzz344), h) → new_mkVBalBranch(zzz31, Branch(zzz520, zzz521, Pos(Zero), zzz523, zzz524), zzz343, h)
new_mkVBalBranch3MkVBalBranch20(zzz929, zzz930, zzz931, zzz932, zzz933, zzz934, zzz935, zzz936, zzz937, zzz938, zzz939, Succ(zzz9400), Zero, ba) → new_mkVBalBranch3MkVBalBranch10(zzz929, zzz930, zzz931, zzz932, zzz933, zzz934, zzz935, zzz936, zzz937, zzz938, zzz939, Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat2(Succ(new_primPlusNat3(new_primPlusNat1(zzz931), zzz931)), zzz931)), zzz931))), ba)
new_mkVBalBranch3MkVBalBranch2(zzz340, zzz341, Pos(Zero), zzz343, zzz344, zzz520, zzz521, zzz52200, zzz523, zzz524, zzz31, Succ(zzz680), h) → new_mkVBalBranch(zzz31, zzz524, Branch(zzz340, zzz341, Pos(Zero), zzz343, zzz344), h)
new_mkVBalBranch3MkVBalBranch2(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344, zzz520, zzz521, zzz52200, zzz523, zzz524, zzz31, Succ(zzz680), h) → new_mkVBalBranch3MkVBalBranch1(zzz340, zzz341, zzz34200, zzz343, zzz344, zzz520, zzz521, zzz52200, zzz523, zzz524, zzz31, Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat2(Succ(new_primPlusNat3(new_primPlusNat1(zzz34200), zzz34200)), zzz34200)), zzz34200))), h)
new_mkVBalBranch3MkVBalBranch2(zzz340, zzz341, Neg(Zero), zzz343, zzz344, zzz520, zzz521, zzz52200, zzz523, zzz524, zzz31, Succ(zzz680), h) → new_mkVBalBranch(zzz31, zzz524, Branch(zzz340, zzz341, Neg(Zero), zzz343, zzz344), h)
new_mkVBalBranch3MkVBalBranch16(zzz1702, zzz1703, zzz1704, zzz1705, zzz1706, zzz1707, zzz1708, zzz1709, zzz1710, zzz1711, zzz1712, Zero, Succ(zzz17140), bd) → new_mkVBalBranch(zzz1712, zzz1711, Branch(zzz1702, zzz1703, Neg(Succ(zzz1704)), zzz1705, zzz1706), bd)
new_mkVBalBranch3MkVBalBranch15(zzz537, zzz538, zzz539, zzz540, zzz541, zzz542, zzz543, zzz544, zzz545, zzz546, zzz547, Succ(zzz6990), bc) → new_mkVBalBranch3MkVBalBranch16(zzz537, zzz538, zzz539, zzz540, zzz541, zzz542, zzz543, Succ(zzz544), zzz545, zzz546, zzz547, Succ(Succ(zzz544)), Succ(zzz6990), bc)
new_mkVBalBranch3MkVBalBranch24(zzz340, zzz341, Neg(Succ(Succ(Succ(zzz3420000)))), zzz343, zzz344, zzz520, zzz521, Zero, zzz523, zzz524, zzz31, Succ(Succ(zzz6900)), h) → new_mkVBalBranch3MkVBalBranch26(zzz340, zzz341, Succ(Succ(zzz3420000)), zzz343, zzz344, zzz520, zzz521, zzz523, zzz524, zzz31, Succ(zzz3420000), Succ(zzz6900), h)
new_mkVBalBranch3MkVBalBranch25(zzz537, zzz538, zzz539, zzz540, zzz541, zzz542, zzz543, zzz544, zzz545, zzz546, zzz547, Zero, Zero, bc) → new_mkVBalBranch3MkVBalBranch211(zzz537, zzz538, zzz539, zzz540, zzz541, zzz542, zzz543, zzz544, zzz545, zzz546, zzz547, bc)

The TRS R consists of the following rules:

new_primPlusNat1(Zero) → Zero
new_primPlusNat1(Succ(zzz62000)) → Succ(Succ(new_primPlusNat1(zzz62000)))
new_primPlusNat3(zzz90, Succ(zzz910)) → Succ(Succ(new_primPlusNat2(zzz90, zzz910)))
new_primPlusNat3(zzz90, Zero) → Succ(zzz90)
new_primPlusNat2(Succ(zzz900), Succ(zzz9100)) → Succ(Succ(new_primPlusNat2(zzz900, zzz9100)))
new_primPlusNat2(Zero, Succ(zzz9100)) → Succ(zzz9100)
new_primPlusNat2(Zero, Zero) → Zero
new_primPlusNat2(Succ(zzz900), Zero) → Succ(zzz900)

The set Q consists of the following terms:

new_primPlusNat2(Zero, Succ(x0))
new_primPlusNat3(x0, Succ(x1))
new_primPlusNat2(Succ(x0), Succ(x1))
new_primPlusNat3(x0, Zero)
new_primPlusNat1(Zero)
new_primPlusNat2(Zero, Zero)
new_primPlusNat1(Succ(x0))
new_primPlusNat2(Succ(x0), Zero)

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


The following pairs can be oriented strictly and are deleted.


new_mkVBalBranch3MkVBalBranch24(zzz340, zzz341, Pos(zzz3420), zzz343, zzz344, zzz520, zzz521, zzz52200, zzz523, zzz524, zzz31, Succ(zzz690), h) → new_mkVBalBranch(zzz31, Branch(zzz520, zzz521, Neg(Succ(zzz52200)), zzz523, zzz524), zzz343, h)
new_mkVBalBranch3MkVBalBranch12(zzz340, zzz341, zzz34200, zzz343, zzz344, zzz520, zzz521, zzz523, zzz524, zzz31, Succ(zzz1250), h) → new_mkVBalBranch(zzz31, zzz524, Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), h)
new_mkVBalBranch3MkVBalBranch24(zzz340, zzz341, Neg(Succ(Succ(Zero))), zzz343, zzz344, zzz520, zzz521, Zero, zzz523, zzz524, zzz31, Succ(Succ(zzz6900)), h) → new_mkVBalBranch3MkVBalBranch26(zzz340, zzz341, Succ(Zero), zzz343, zzz344, zzz520, zzz521, zzz523, zzz524, zzz31, Zero, Succ(zzz6900), h)
new_mkVBalBranch3MkVBalBranch24(zzz340, zzz341, Neg(Succ(Zero)), zzz343, zzz344, zzz520, zzz521, zzz52200, zzz523, zzz524, zzz31, Succ(zzz690), h) → new_mkVBalBranch(zzz31, Branch(zzz520, zzz521, Neg(Succ(zzz52200)), zzz523, zzz524), zzz343, h)
new_mkVBalBranch3MkVBalBranch13(zzz340, zzz341, zzz34200, zzz343, zzz344, zzz520, zzz521, zzz523, zzz524, zzz31, Succ(zzz1290), h) → new_mkVBalBranch(zzz31, zzz524, Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), h)
new_mkVBalBranch(zzz31, Branch(zzz520, zzz521, Neg(Zero), zzz523, zzz524), Branch(zzz340, zzz341, Pos(Succ(zzz34200)), zzz343, zzz344), h) → new_mkVBalBranch(zzz31, Branch(zzz520, zzz521, Neg(Zero), zzz523, zzz524), zzz343, h)
new_mkVBalBranch3MkVBalBranch24(zzz340, zzz341, Neg(Zero), zzz343, zzz344, zzz520, zzz521, zzz52200, zzz523, zzz524, zzz31, Succ(zzz690), h) → new_mkVBalBranch(zzz31, Branch(zzz520, zzz521, Neg(Succ(zzz52200)), zzz523, zzz524), zzz343, h)
new_mkVBalBranch(zzz31, Branch(zzz520, zzz521, Pos(Succ(zzz52200)), zzz523, zzz524), Branch(zzz340, zzz341, zzz342, zzz343, zzz344), h) → new_mkVBalBranch3MkVBalBranch2(zzz340, zzz341, zzz342, zzz343, zzz344, zzz520, zzz521, zzz52200, zzz523, zzz524, zzz31, Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat3(new_primPlusNat1(zzz52200), zzz52200)), zzz52200))), h)
new_mkVBalBranch(zzz31, Branch(zzz520, zzz521, Pos(Zero), zzz523, zzz524), Branch(zzz340, zzz341, Pos(Succ(zzz34200)), zzz343, zzz344), h) → new_mkVBalBranch(zzz31, Branch(zzz520, zzz521, Pos(Zero), zzz523, zzz524), zzz343, h)
new_mkVBalBranch3MkVBalBranch24(zzz340, zzz341, Neg(Succ(Succ(Succ(zzz3420000)))), zzz343, zzz344, zzz520, zzz521, Zero, zzz523, zzz524, zzz31, Succ(Succ(zzz6900)), h) → new_mkVBalBranch3MkVBalBranch26(zzz340, zzz341, Succ(Succ(zzz3420000)), zzz343, zzz344, zzz520, zzz521, zzz523, zzz524, zzz31, Succ(zzz3420000), Succ(zzz6900), h)
The remaining pairs can at least be oriented weakly.

new_mkVBalBranch3MkVBalBranch11(zzz2033, zzz2034, zzz2035, zzz2036, zzz2037, zzz2038, zzz2039, zzz2040, zzz2041, zzz2042, zzz2043, Zero, Succ(zzz20450), bb) → new_mkVBalBranch(zzz2043, zzz2042, Branch(zzz2033, zzz2034, Pos(Succ(zzz2035)), zzz2036, zzz2037), bb)
new_mkVBalBranch3MkVBalBranch211(zzz537, zzz538, zzz539, zzz540, zzz541, zzz542, zzz543, zzz544, zzz545, zzz546, zzz547, bc) → new_mkVBalBranch3MkVBalBranch15(zzz537, zzz538, zzz539, zzz540, zzz541, zzz542, zzz543, zzz544, zzz545, zzz546, zzz547, Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat2(Succ(new_primPlusNat3(new_primPlusNat1(zzz539), zzz539)), zzz539)), zzz539))), bc)
new_mkVBalBranch(zzz31, Branch(zzz520, zzz521, Neg(Succ(zzz52200)), zzz523, zzz524), Branch(zzz340, zzz341, zzz342, zzz343, zzz344), h) → new_mkVBalBranch3MkVBalBranch24(zzz340, zzz341, zzz342, zzz343, zzz344, zzz520, zzz521, zzz52200, zzz523, zzz524, zzz31, Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat3(new_primPlusNat1(zzz52200), zzz52200)), zzz52200))), h)
new_mkVBalBranch3MkVBalBranch23(zzz929, zzz930, zzz931, zzz932, zzz933, zzz934, zzz935, zzz936, zzz937, zzz938, zzz939, ba) → new_mkVBalBranch3MkVBalBranch10(zzz929, zzz930, zzz931, zzz932, zzz933, zzz934, zzz935, zzz936, zzz937, zzz938, zzz939, Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat2(Succ(new_primPlusNat3(new_primPlusNat1(zzz931), zzz931)), zzz931)), zzz931))), ba)
new_mkVBalBranch3MkVBalBranch26(zzz1133, zzz1134, zzz1135, zzz1136, zzz1137, zzz1138, zzz1139, zzz1140, zzz1141, zzz1142, Succ(zzz11430), Succ(zzz11440), be) → new_mkVBalBranch3MkVBalBranch26(zzz1133, zzz1134, zzz1135, zzz1136, zzz1137, zzz1138, zzz1139, zzz1140, zzz1141, zzz1142, zzz11430, zzz11440, be)
new_mkVBalBranch3MkVBalBranch25(zzz537, zzz538, zzz539, zzz540, zzz541, zzz542, zzz543, zzz544, zzz545, zzz546, zzz547, Succ(zzz5480), Zero, bc) → new_mkVBalBranch3MkVBalBranch15(zzz537, zzz538, zzz539, zzz540, zzz541, zzz542, zzz543, zzz544, zzz545, zzz546, zzz547, Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat2(Succ(new_primPlusNat3(new_primPlusNat1(zzz539), zzz539)), zzz539)), zzz539))), bc)
new_mkVBalBranch3MkVBalBranch20(zzz929, zzz930, zzz931, zzz932, zzz933, zzz934, zzz935, zzz936, zzz937, zzz938, zzz939, Zero, Succ(zzz9410), ba) → new_mkVBalBranch(zzz939, Branch(zzz934, zzz935, Pos(Succ(zzz936)), zzz937, zzz938), zzz932, ba)
new_mkVBalBranch3MkVBalBranch1(zzz340, zzz341, zzz34200, zzz343, zzz344, zzz520, zzz521, zzz52200, zzz523, zzz524, zzz31, Succ(zzz1430), h) → new_mkVBalBranch(zzz31, zzz524, Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), h)
new_mkVBalBranch3MkVBalBranch26(zzz1133, zzz1134, zzz1135, zzz1136, zzz1137, zzz1138, zzz1139, zzz1140, zzz1141, zzz1142, Zero, Zero, be) → new_mkVBalBranch3MkVBalBranch29(zzz1133, zzz1134, zzz1135, zzz1136, zzz1137, zzz1138, zzz1139, zzz1140, zzz1141, zzz1142, be)
new_mkVBalBranch3MkVBalBranch20(zzz929, zzz930, zzz931, zzz932, zzz933, zzz934, zzz935, zzz936, zzz937, zzz938, zzz939, Zero, Zero, ba) → new_mkVBalBranch3MkVBalBranch23(zzz929, zzz930, zzz931, zzz932, zzz933, zzz934, zzz935, zzz936, zzz937, zzz938, zzz939, ba)
new_mkVBalBranch(zzz31, Branch(zzz520, zzz521, Neg(Zero), zzz523, zzz524), Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), h) → new_mkVBalBranch3MkVBalBranch13(zzz340, zzz341, zzz34200, zzz343, zzz344, zzz520, zzz521, zzz523, zzz524, zzz31, Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat2(Succ(new_primPlusNat3(new_primPlusNat1(zzz34200), zzz34200)), zzz34200)), zzz34200))), h)
new_mkVBalBranch3MkVBalBranch2(zzz340, zzz341, Pos(Succ(zzz34200)), zzz343, zzz344, zzz520, zzz521, zzz52200, zzz523, zzz524, zzz31, Succ(zzz680), h) → new_mkVBalBranch3MkVBalBranch20(zzz340, zzz341, zzz34200, zzz343, zzz344, zzz520, zzz521, zzz52200, zzz523, zzz524, zzz31, Succ(new_primPlusNat2(zzz680, zzz52200)), zzz34200, h)
new_mkVBalBranch3MkVBalBranch20(zzz929, zzz930, zzz931, zzz932, zzz933, zzz934, zzz935, zzz936, zzz937, zzz938, zzz939, Succ(zzz9400), Succ(zzz9410), ba) → new_mkVBalBranch3MkVBalBranch20(zzz929, zzz930, zzz931, zzz932, zzz933, zzz934, zzz935, zzz936, zzz937, zzz938, zzz939, zzz9400, zzz9410, ba)
new_mkVBalBranch3MkVBalBranch29(zzz818, zzz819, zzz820, zzz821, zzz822, zzz823, zzz824, zzz825, zzz826, zzz827, bf) → new_mkVBalBranch3MkVBalBranch14(zzz818, zzz819, zzz820, zzz821, zzz822, zzz823, zzz824, zzz825, zzz826, zzz827, Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat2(Succ(new_primPlusNat3(new_primPlusNat1(zzz820), zzz820)), zzz820)), zzz820))), bf)
new_mkVBalBranch3MkVBalBranch26(zzz1133, zzz1134, zzz1135, zzz1136, zzz1137, zzz1138, zzz1139, zzz1140, zzz1141, zzz1142, Succ(zzz11430), Zero, be) → new_mkVBalBranch3MkVBalBranch212(zzz1133, zzz1134, zzz1135, zzz1136, zzz1137, zzz1138, zzz1139, zzz1140, zzz1141, zzz1142, be)
new_mkVBalBranch3MkVBalBranch16(zzz1702, zzz1703, zzz1704, zzz1705, zzz1706, zzz1707, zzz1708, zzz1709, zzz1710, zzz1711, zzz1712, Succ(zzz17130), Succ(zzz17140), bd) → new_mkVBalBranch3MkVBalBranch16(zzz1702, zzz1703, zzz1704, zzz1705, zzz1706, zzz1707, zzz1708, zzz1709, zzz1710, zzz1711, zzz1712, zzz17130, zzz17140, bd)
new_mkVBalBranch3MkVBalBranch25(zzz537, zzz538, zzz539, zzz540, zzz541, zzz542, zzz543, zzz544, zzz545, zzz546, zzz547, Zero, Succ(zzz5490), bc) → new_mkVBalBranch(zzz547, Branch(zzz542, zzz543, Neg(Succ(Succ(zzz544))), zzz545, zzz546), zzz540, bc)
new_mkVBalBranch3MkVBalBranch11(zzz2033, zzz2034, zzz2035, zzz2036, zzz2037, zzz2038, zzz2039, zzz2040, zzz2041, zzz2042, zzz2043, Succ(zzz20440), Succ(zzz20450), bb) → new_mkVBalBranch3MkVBalBranch11(zzz2033, zzz2034, zzz2035, zzz2036, zzz2037, zzz2038, zzz2039, zzz2040, zzz2041, zzz2042, zzz2043, zzz20440, zzz20450, bb)
new_mkVBalBranch3MkVBalBranch25(zzz537, zzz538, zzz539, zzz540, zzz541, zzz542, zzz543, zzz544, zzz545, zzz546, zzz547, Succ(zzz5480), Succ(zzz5490), bc) → new_mkVBalBranch3MkVBalBranch25(zzz537, zzz538, zzz539, zzz540, zzz541, zzz542, zzz543, zzz544, zzz545, zzz546, zzz547, zzz5480, zzz5490, bc)
new_mkVBalBranch3MkVBalBranch10(zzz929, zzz930, zzz931, zzz932, zzz933, zzz934, zzz935, zzz936, zzz937, zzz938, zzz939, Succ(zzz10020), ba) → new_mkVBalBranch3MkVBalBranch11(zzz929, zzz930, zzz931, zzz932, zzz933, zzz934, zzz935, zzz936, zzz937, zzz938, zzz939, Succ(zzz10020), Succ(zzz936), ba)
new_mkVBalBranch3MkVBalBranch14(zzz818, zzz819, zzz820, zzz821, zzz822, zzz823, zzz824, zzz825, zzz826, zzz827, Succ(zzz8960), bf) → new_mkVBalBranch3MkVBalBranch16(zzz818, zzz819, zzz820, zzz821, zzz822, zzz823, zzz824, Zero, zzz825, zzz826, zzz827, Succ(Zero), Succ(zzz8960), bf)
new_mkVBalBranch(zzz31, Branch(zzz520, zzz521, Pos(Zero), zzz523, zzz524), Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), h) → new_mkVBalBranch3MkVBalBranch12(zzz340, zzz341, zzz34200, zzz343, zzz344, zzz520, zzz521, zzz523, zzz524, zzz31, Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat2(Succ(new_primPlusNat3(new_primPlusNat1(zzz34200), zzz34200)), zzz34200)), zzz34200))), h)
new_mkVBalBranch3MkVBalBranch26(zzz1133, zzz1134, zzz1135, zzz1136, zzz1137, zzz1138, zzz1139, zzz1140, zzz1141, zzz1142, Zero, Succ(zzz11440), be) → new_mkVBalBranch(zzz1142, Branch(zzz1138, zzz1139, Neg(Succ(Zero)), zzz1140, zzz1141), zzz1136, be)
new_mkVBalBranch3MkVBalBranch24(zzz340, zzz341, Neg(Succ(Succ(Succ(zzz3420000)))), zzz343, zzz344, zzz520, zzz521, Succ(zzz522000), zzz523, zzz524, zzz31, Succ(Succ(zzz6900)), h) → new_mkVBalBranch3MkVBalBranch25(zzz340, zzz341, Succ(Succ(zzz3420000)), zzz343, zzz344, zzz520, zzz521, zzz522000, zzz523, zzz524, zzz31, Succ(zzz3420000), Succ(Succ(new_primPlusNat2(zzz6900, zzz522000))), h)
new_mkVBalBranch3MkVBalBranch212(zzz818, zzz819, zzz820, zzz821, zzz822, zzz823, zzz824, zzz825, zzz826, zzz827, bf) → new_mkVBalBranch3MkVBalBranch14(zzz818, zzz819, zzz820, zzz821, zzz822, zzz823, zzz824, zzz825, zzz826, zzz827, Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat2(Succ(new_primPlusNat3(new_primPlusNat1(zzz820), zzz820)), zzz820)), zzz820))), bf)
new_mkVBalBranch3MkVBalBranch24(zzz340, zzz341, Neg(Succ(Succ(Zero))), zzz343, zzz344, zzz520, zzz521, Succ(zzz522000), zzz523, zzz524, zzz31, Succ(Succ(zzz6900)), h) → new_mkVBalBranch3MkVBalBranch25(zzz340, zzz341, Succ(Zero), zzz343, zzz344, zzz520, zzz521, zzz522000, zzz523, zzz524, zzz31, Zero, Succ(Succ(new_primPlusNat2(zzz6900, zzz522000))), h)
new_mkVBalBranch3MkVBalBranch20(zzz929, zzz930, zzz931, zzz932, zzz933, zzz934, zzz935, zzz936, zzz937, zzz938, zzz939, Succ(zzz9400), Zero, ba) → new_mkVBalBranch3MkVBalBranch10(zzz929, zzz930, zzz931, zzz932, zzz933, zzz934, zzz935, zzz936, zzz937, zzz938, zzz939, Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat2(Succ(new_primPlusNat3(new_primPlusNat1(zzz931), zzz931)), zzz931)), zzz931))), ba)
new_mkVBalBranch3MkVBalBranch2(zzz340, zzz341, Pos(Zero), zzz343, zzz344, zzz520, zzz521, zzz52200, zzz523, zzz524, zzz31, Succ(zzz680), h) → new_mkVBalBranch(zzz31, zzz524, Branch(zzz340, zzz341, Pos(Zero), zzz343, zzz344), h)
new_mkVBalBranch3MkVBalBranch2(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344, zzz520, zzz521, zzz52200, zzz523, zzz524, zzz31, Succ(zzz680), h) → new_mkVBalBranch3MkVBalBranch1(zzz340, zzz341, zzz34200, zzz343, zzz344, zzz520, zzz521, zzz52200, zzz523, zzz524, zzz31, Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat2(Succ(new_primPlusNat3(new_primPlusNat1(zzz34200), zzz34200)), zzz34200)), zzz34200))), h)
new_mkVBalBranch3MkVBalBranch2(zzz340, zzz341, Neg(Zero), zzz343, zzz344, zzz520, zzz521, zzz52200, zzz523, zzz524, zzz31, Succ(zzz680), h) → new_mkVBalBranch(zzz31, zzz524, Branch(zzz340, zzz341, Neg(Zero), zzz343, zzz344), h)
new_mkVBalBranch3MkVBalBranch16(zzz1702, zzz1703, zzz1704, zzz1705, zzz1706, zzz1707, zzz1708, zzz1709, zzz1710, zzz1711, zzz1712, Zero, Succ(zzz17140), bd) → new_mkVBalBranch(zzz1712, zzz1711, Branch(zzz1702, zzz1703, Neg(Succ(zzz1704)), zzz1705, zzz1706), bd)
new_mkVBalBranch3MkVBalBranch15(zzz537, zzz538, zzz539, zzz540, zzz541, zzz542, zzz543, zzz544, zzz545, zzz546, zzz547, Succ(zzz6990), bc) → new_mkVBalBranch3MkVBalBranch16(zzz537, zzz538, zzz539, zzz540, zzz541, zzz542, zzz543, Succ(zzz544), zzz545, zzz546, zzz547, Succ(Succ(zzz544)), Succ(zzz6990), bc)
new_mkVBalBranch3MkVBalBranch25(zzz537, zzz538, zzz539, zzz540, zzz541, zzz542, zzz543, zzz544, zzz545, zzz546, zzz547, Zero, Zero, bc) → new_mkVBalBranch3MkVBalBranch211(zzz537, zzz538, zzz539, zzz540, zzz541, zzz542, zzz543, zzz544, zzz545, zzz546, zzz547, bc)
Used ordering: Polynomial interpretation [25]:

POL(Branch(x1, x2, x3, x4, x5)) = 1 + x1 + x4 + x5   
POL(Neg(x1)) = 0   
POL(Pos(x1)) = 0   
POL(Succ(x1)) = 1   
POL(Zero) = 0   
POL(new_mkVBalBranch(x1, x2, x3, x4)) = x2 + x3   
POL(new_mkVBalBranch3MkVBalBranch1(x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12, x13)) = 1 + x1 + x10 + x4 + x5   
POL(new_mkVBalBranch3MkVBalBranch10(x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12, x13)) = 1 + x1 + x10 + x4 + x5 + x9   
POL(new_mkVBalBranch3MkVBalBranch11(x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12, x13, x14)) = 1 + x1 + x10 + x4 + x5   
POL(new_mkVBalBranch3MkVBalBranch12(x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12)) = 1 + x1 + x11 + x4 + x5 + x6 + x8 + x9   
POL(new_mkVBalBranch3MkVBalBranch13(x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12)) = 1 + x1 + x11 + x4 + x5 + x9   
POL(new_mkVBalBranch3MkVBalBranch14(x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12)) = 1 + x1 + x4 + x5 + x9   
POL(new_mkVBalBranch3MkVBalBranch15(x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12, x13)) = 1 + x1 + x10 + x4 + x5 + x9   
POL(new_mkVBalBranch3MkVBalBranch16(x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12, x13, x14)) = 1 + x1 + x10 + x4 + x5   
POL(new_mkVBalBranch3MkVBalBranch2(x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12, x13)) = x1 + x10 + x12 + x4 + x5 + x6 + x9   
POL(new_mkVBalBranch3MkVBalBranch20(x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12, x13, x14)) = 1 + x1 + x10 + x4 + x5 + x6 + x9   
POL(new_mkVBalBranch3MkVBalBranch211(x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12)) = 1 + x1 + x10 + x3 + x4 + x5 + x9   
POL(new_mkVBalBranch3MkVBalBranch212(x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11)) = 1 + x1 + x4 + x5 + x6 + x9   
POL(new_mkVBalBranch3MkVBalBranch23(x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12)) = 1 + x1 + x10 + x4 + x5 + x6 + x9   
POL(new_mkVBalBranch3MkVBalBranch24(x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12, x13)) = 1 + x1 + x10 + x12 + x4 + x5 + x6 + x9   
POL(new_mkVBalBranch3MkVBalBranch25(x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12, x13, x14)) = 1 + x1 + x10 + x3 + x4 + x5 + x6 + x9   
POL(new_mkVBalBranch3MkVBalBranch26(x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12, x13)) = 1 + x1 + x4 + x5 + x6 + x8 + x9   
POL(new_mkVBalBranch3MkVBalBranch29(x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11)) = 1 + x1 + x4 + x5 + x6 + x9   
POL(new_primPlusNat1(x1)) = 1   
POL(new_primPlusNat2(x1, x2)) = 0   
POL(new_primPlusNat3(x1, x2)) = 1   

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

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

new_mkVBalBranch(zzz31, Branch(zzz520, zzz521, Neg(Succ(zzz52200)), zzz523, zzz524), Branch(zzz340, zzz341, zzz342, zzz343, zzz344), h) → new_mkVBalBranch3MkVBalBranch24(zzz340, zzz341, zzz342, zzz343, zzz344, zzz520, zzz521, zzz52200, zzz523, zzz524, zzz31, Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat3(new_primPlusNat1(zzz52200), zzz52200)), zzz52200))), h)
new_mkVBalBranch3MkVBalBranch211(zzz537, zzz538, zzz539, zzz540, zzz541, zzz542, zzz543, zzz544, zzz545, zzz546, zzz547, bc) → new_mkVBalBranch3MkVBalBranch15(zzz537, zzz538, zzz539, zzz540, zzz541, zzz542, zzz543, zzz544, zzz545, zzz546, zzz547, Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat2(Succ(new_primPlusNat3(new_primPlusNat1(zzz539), zzz539)), zzz539)), zzz539))), bc)
new_mkVBalBranch3MkVBalBranch11(zzz2033, zzz2034, zzz2035, zzz2036, zzz2037, zzz2038, zzz2039, zzz2040, zzz2041, zzz2042, zzz2043, Zero, Succ(zzz20450), bb) → new_mkVBalBranch(zzz2043, zzz2042, Branch(zzz2033, zzz2034, Pos(Succ(zzz2035)), zzz2036, zzz2037), bb)
new_mkVBalBranch3MkVBalBranch26(zzz1133, zzz1134, zzz1135, zzz1136, zzz1137, zzz1138, zzz1139, zzz1140, zzz1141, zzz1142, Succ(zzz11430), Succ(zzz11440), be) → new_mkVBalBranch3MkVBalBranch26(zzz1133, zzz1134, zzz1135, zzz1136, zzz1137, zzz1138, zzz1139, zzz1140, zzz1141, zzz1142, zzz11430, zzz11440, be)
new_mkVBalBranch3MkVBalBranch23(zzz929, zzz930, zzz931, zzz932, zzz933, zzz934, zzz935, zzz936, zzz937, zzz938, zzz939, ba) → new_mkVBalBranch3MkVBalBranch10(zzz929, zzz930, zzz931, zzz932, zzz933, zzz934, zzz935, zzz936, zzz937, zzz938, zzz939, Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat2(Succ(new_primPlusNat3(new_primPlusNat1(zzz931), zzz931)), zzz931)), zzz931))), ba)
new_mkVBalBranch3MkVBalBranch25(zzz537, zzz538, zzz539, zzz540, zzz541, zzz542, zzz543, zzz544, zzz545, zzz546, zzz547, Succ(zzz5480), Zero, bc) → new_mkVBalBranch3MkVBalBranch15(zzz537, zzz538, zzz539, zzz540, zzz541, zzz542, zzz543, zzz544, zzz545, zzz546, zzz547, Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat2(Succ(new_primPlusNat3(new_primPlusNat1(zzz539), zzz539)), zzz539)), zzz539))), bc)
new_mkVBalBranch3MkVBalBranch20(zzz929, zzz930, zzz931, zzz932, zzz933, zzz934, zzz935, zzz936, zzz937, zzz938, zzz939, Zero, Succ(zzz9410), ba) → new_mkVBalBranch(zzz939, Branch(zzz934, zzz935, Pos(Succ(zzz936)), zzz937, zzz938), zzz932, ba)
new_mkVBalBranch3MkVBalBranch26(zzz1133, zzz1134, zzz1135, zzz1136, zzz1137, zzz1138, zzz1139, zzz1140, zzz1141, zzz1142, Zero, Zero, be) → new_mkVBalBranch3MkVBalBranch29(zzz1133, zzz1134, zzz1135, zzz1136, zzz1137, zzz1138, zzz1139, zzz1140, zzz1141, zzz1142, be)
new_mkVBalBranch3MkVBalBranch1(zzz340, zzz341, zzz34200, zzz343, zzz344, zzz520, zzz521, zzz52200, zzz523, zzz524, zzz31, Succ(zzz1430), h) → new_mkVBalBranch(zzz31, zzz524, Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), h)
new_mkVBalBranch(zzz31, Branch(zzz520, zzz521, Neg(Zero), zzz523, zzz524), Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), h) → new_mkVBalBranch3MkVBalBranch13(zzz340, zzz341, zzz34200, zzz343, zzz344, zzz520, zzz521, zzz523, zzz524, zzz31, Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat2(Succ(new_primPlusNat3(new_primPlusNat1(zzz34200), zzz34200)), zzz34200)), zzz34200))), h)
new_mkVBalBranch3MkVBalBranch20(zzz929, zzz930, zzz931, zzz932, zzz933, zzz934, zzz935, zzz936, zzz937, zzz938, zzz939, Zero, Zero, ba) → new_mkVBalBranch3MkVBalBranch23(zzz929, zzz930, zzz931, zzz932, zzz933, zzz934, zzz935, zzz936, zzz937, zzz938, zzz939, ba)
new_mkVBalBranch3MkVBalBranch2(zzz340, zzz341, Pos(Succ(zzz34200)), zzz343, zzz344, zzz520, zzz521, zzz52200, zzz523, zzz524, zzz31, Succ(zzz680), h) → new_mkVBalBranch3MkVBalBranch20(zzz340, zzz341, zzz34200, zzz343, zzz344, zzz520, zzz521, zzz52200, zzz523, zzz524, zzz31, Succ(new_primPlusNat2(zzz680, zzz52200)), zzz34200, h)
new_mkVBalBranch3MkVBalBranch20(zzz929, zzz930, zzz931, zzz932, zzz933, zzz934, zzz935, zzz936, zzz937, zzz938, zzz939, Succ(zzz9400), Succ(zzz9410), ba) → new_mkVBalBranch3MkVBalBranch20(zzz929, zzz930, zzz931, zzz932, zzz933, zzz934, zzz935, zzz936, zzz937, zzz938, zzz939, zzz9400, zzz9410, ba)
new_mkVBalBranch3MkVBalBranch29(zzz818, zzz819, zzz820, zzz821, zzz822, zzz823, zzz824, zzz825, zzz826, zzz827, bf) → new_mkVBalBranch3MkVBalBranch14(zzz818, zzz819, zzz820, zzz821, zzz822, zzz823, zzz824, zzz825, zzz826, zzz827, Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat2(Succ(new_primPlusNat3(new_primPlusNat1(zzz820), zzz820)), zzz820)), zzz820))), bf)
new_mkVBalBranch3MkVBalBranch26(zzz1133, zzz1134, zzz1135, zzz1136, zzz1137, zzz1138, zzz1139, zzz1140, zzz1141, zzz1142, Succ(zzz11430), Zero, be) → new_mkVBalBranch3MkVBalBranch212(zzz1133, zzz1134, zzz1135, zzz1136, zzz1137, zzz1138, zzz1139, zzz1140, zzz1141, zzz1142, be)
new_mkVBalBranch3MkVBalBranch16(zzz1702, zzz1703, zzz1704, zzz1705, zzz1706, zzz1707, zzz1708, zzz1709, zzz1710, zzz1711, zzz1712, Succ(zzz17130), Succ(zzz17140), bd) → new_mkVBalBranch3MkVBalBranch16(zzz1702, zzz1703, zzz1704, zzz1705, zzz1706, zzz1707, zzz1708, zzz1709, zzz1710, zzz1711, zzz1712, zzz17130, zzz17140, bd)
new_mkVBalBranch3MkVBalBranch25(zzz537, zzz538, zzz539, zzz540, zzz541, zzz542, zzz543, zzz544, zzz545, zzz546, zzz547, Zero, Succ(zzz5490), bc) → new_mkVBalBranch(zzz547, Branch(zzz542, zzz543, Neg(Succ(Succ(zzz544))), zzz545, zzz546), zzz540, bc)
new_mkVBalBranch3MkVBalBranch11(zzz2033, zzz2034, zzz2035, zzz2036, zzz2037, zzz2038, zzz2039, zzz2040, zzz2041, zzz2042, zzz2043, Succ(zzz20440), Succ(zzz20450), bb) → new_mkVBalBranch3MkVBalBranch11(zzz2033, zzz2034, zzz2035, zzz2036, zzz2037, zzz2038, zzz2039, zzz2040, zzz2041, zzz2042, zzz2043, zzz20440, zzz20450, bb)
new_mkVBalBranch3MkVBalBranch25(zzz537, zzz538, zzz539, zzz540, zzz541, zzz542, zzz543, zzz544, zzz545, zzz546, zzz547, Succ(zzz5480), Succ(zzz5490), bc) → new_mkVBalBranch3MkVBalBranch25(zzz537, zzz538, zzz539, zzz540, zzz541, zzz542, zzz543, zzz544, zzz545, zzz546, zzz547, zzz5480, zzz5490, bc)
new_mkVBalBranch3MkVBalBranch10(zzz929, zzz930, zzz931, zzz932, zzz933, zzz934, zzz935, zzz936, zzz937, zzz938, zzz939, Succ(zzz10020), ba) → new_mkVBalBranch3MkVBalBranch11(zzz929, zzz930, zzz931, zzz932, zzz933, zzz934, zzz935, zzz936, zzz937, zzz938, zzz939, Succ(zzz10020), Succ(zzz936), ba)
new_mkVBalBranch3MkVBalBranch14(zzz818, zzz819, zzz820, zzz821, zzz822, zzz823, zzz824, zzz825, zzz826, zzz827, Succ(zzz8960), bf) → new_mkVBalBranch3MkVBalBranch16(zzz818, zzz819, zzz820, zzz821, zzz822, zzz823, zzz824, Zero, zzz825, zzz826, zzz827, Succ(Zero), Succ(zzz8960), bf)
new_mkVBalBranch(zzz31, Branch(zzz520, zzz521, Pos(Zero), zzz523, zzz524), Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), h) → new_mkVBalBranch3MkVBalBranch12(zzz340, zzz341, zzz34200, zzz343, zzz344, zzz520, zzz521, zzz523, zzz524, zzz31, Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat2(Succ(new_primPlusNat3(new_primPlusNat1(zzz34200), zzz34200)), zzz34200)), zzz34200))), h)
new_mkVBalBranch3MkVBalBranch26(zzz1133, zzz1134, zzz1135, zzz1136, zzz1137, zzz1138, zzz1139, zzz1140, zzz1141, zzz1142, Zero, Succ(zzz11440), be) → new_mkVBalBranch(zzz1142, Branch(zzz1138, zzz1139, Neg(Succ(Zero)), zzz1140, zzz1141), zzz1136, be)
new_mkVBalBranch3MkVBalBranch24(zzz340, zzz341, Neg(Succ(Succ(Succ(zzz3420000)))), zzz343, zzz344, zzz520, zzz521, Succ(zzz522000), zzz523, zzz524, zzz31, Succ(Succ(zzz6900)), h) → new_mkVBalBranch3MkVBalBranch25(zzz340, zzz341, Succ(Succ(zzz3420000)), zzz343, zzz344, zzz520, zzz521, zzz522000, zzz523, zzz524, zzz31, Succ(zzz3420000), Succ(Succ(new_primPlusNat2(zzz6900, zzz522000))), h)
new_mkVBalBranch3MkVBalBranch212(zzz818, zzz819, zzz820, zzz821, zzz822, zzz823, zzz824, zzz825, zzz826, zzz827, bf) → new_mkVBalBranch3MkVBalBranch14(zzz818, zzz819, zzz820, zzz821, zzz822, zzz823, zzz824, zzz825, zzz826, zzz827, Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat2(Succ(new_primPlusNat3(new_primPlusNat1(zzz820), zzz820)), zzz820)), zzz820))), bf)
new_mkVBalBranch3MkVBalBranch24(zzz340, zzz341, Neg(Succ(Succ(Zero))), zzz343, zzz344, zzz520, zzz521, Succ(zzz522000), zzz523, zzz524, zzz31, Succ(Succ(zzz6900)), h) → new_mkVBalBranch3MkVBalBranch25(zzz340, zzz341, Succ(Zero), zzz343, zzz344, zzz520, zzz521, zzz522000, zzz523, zzz524, zzz31, Zero, Succ(Succ(new_primPlusNat2(zzz6900, zzz522000))), h)
new_mkVBalBranch3MkVBalBranch20(zzz929, zzz930, zzz931, zzz932, zzz933, zzz934, zzz935, zzz936, zzz937, zzz938, zzz939, Succ(zzz9400), Zero, ba) → new_mkVBalBranch3MkVBalBranch10(zzz929, zzz930, zzz931, zzz932, zzz933, zzz934, zzz935, zzz936, zzz937, zzz938, zzz939, Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat2(Succ(new_primPlusNat3(new_primPlusNat1(zzz931), zzz931)), zzz931)), zzz931))), ba)
new_mkVBalBranch3MkVBalBranch2(zzz340, zzz341, Pos(Zero), zzz343, zzz344, zzz520, zzz521, zzz52200, zzz523, zzz524, zzz31, Succ(zzz680), h) → new_mkVBalBranch(zzz31, zzz524, Branch(zzz340, zzz341, Pos(Zero), zzz343, zzz344), h)
new_mkVBalBranch3MkVBalBranch2(zzz340, zzz341, Neg(Zero), zzz343, zzz344, zzz520, zzz521, zzz52200, zzz523, zzz524, zzz31, Succ(zzz680), h) → new_mkVBalBranch(zzz31, zzz524, Branch(zzz340, zzz341, Neg(Zero), zzz343, zzz344), h)
new_mkVBalBranch3MkVBalBranch2(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344, zzz520, zzz521, zzz52200, zzz523, zzz524, zzz31, Succ(zzz680), h) → new_mkVBalBranch3MkVBalBranch1(zzz340, zzz341, zzz34200, zzz343, zzz344, zzz520, zzz521, zzz52200, zzz523, zzz524, zzz31, Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat2(Succ(new_primPlusNat3(new_primPlusNat1(zzz34200), zzz34200)), zzz34200)), zzz34200))), h)
new_mkVBalBranch3MkVBalBranch16(zzz1702, zzz1703, zzz1704, zzz1705, zzz1706, zzz1707, zzz1708, zzz1709, zzz1710, zzz1711, zzz1712, Zero, Succ(zzz17140), bd) → new_mkVBalBranch(zzz1712, zzz1711, Branch(zzz1702, zzz1703, Neg(Succ(zzz1704)), zzz1705, zzz1706), bd)
new_mkVBalBranch3MkVBalBranch15(zzz537, zzz538, zzz539, zzz540, zzz541, zzz542, zzz543, zzz544, zzz545, zzz546, zzz547, Succ(zzz6990), bc) → new_mkVBalBranch3MkVBalBranch16(zzz537, zzz538, zzz539, zzz540, zzz541, zzz542, zzz543, Succ(zzz544), zzz545, zzz546, zzz547, Succ(Succ(zzz544)), Succ(zzz6990), bc)
new_mkVBalBranch3MkVBalBranch25(zzz537, zzz538, zzz539, zzz540, zzz541, zzz542, zzz543, zzz544, zzz545, zzz546, zzz547, Zero, Zero, bc) → new_mkVBalBranch3MkVBalBranch211(zzz537, zzz538, zzz539, zzz540, zzz541, zzz542, zzz543, zzz544, zzz545, zzz546, zzz547, bc)

The TRS R consists of the following rules:

new_primPlusNat1(Zero) → Zero
new_primPlusNat1(Succ(zzz62000)) → Succ(Succ(new_primPlusNat1(zzz62000)))
new_primPlusNat3(zzz90, Succ(zzz910)) → Succ(Succ(new_primPlusNat2(zzz90, zzz910)))
new_primPlusNat3(zzz90, Zero) → Succ(zzz90)
new_primPlusNat2(Succ(zzz900), Succ(zzz9100)) → Succ(Succ(new_primPlusNat2(zzz900, zzz9100)))
new_primPlusNat2(Zero, Succ(zzz9100)) → Succ(zzz9100)
new_primPlusNat2(Zero, Zero) → Zero
new_primPlusNat2(Succ(zzz900), Zero) → Succ(zzz900)

The set Q consists of the following terms:

new_primPlusNat2(Zero, Succ(x0))
new_primPlusNat3(x0, Succ(x1))
new_primPlusNat2(Succ(x0), Succ(x1))
new_primPlusNat3(x0, Zero)
new_primPlusNat1(Zero)
new_primPlusNat2(Zero, Zero)
new_primPlusNat1(Succ(x0))
new_primPlusNat2(Succ(x0), Zero)

We have to consider all minimal (P,Q,R)-chains.
The approximation of the Dependency Graph [15,17,22] contains 4 SCCs with 19 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
                                    ↳ DependencyGraphProof
                                      ↳ QDP
                                        ↳ Rewriting
                                          ↳ QDP
                                            ↳ Rewriting
                                              ↳ QDP
                                                ↳ Rewriting
                                                  ↳ QDP
                                                    ↳ Rewriting
                                                      ↳ QDP
                                                        ↳ Rewriting
                                                          ↳ QDP
                                                            ↳ Rewriting
                                                              ↳ QDP
                                                                ↳ Rewriting
                                                                  ↳ QDP
                                                                    ↳ Rewriting
                                                                      ↳ QDP
                                                                        ↳ Rewriting
                                                                          ↳ QDP
                                                                            ↳ Rewriting
                                                                              ↳ QDP
                                                                                ↳ Rewriting
                                                                                  ↳ QDP
                                                                                    ↳ Rewriting
                                                                                      ↳ QDP
                                                                                        ↳ Rewriting
                                                                                          ↳ QDP
                                                                                            ↳ UsableRulesProof
                                                                                              ↳ QDP
                                                                                                ↳ QReductionProof
                                                                                                  ↳ QDP
                                                                                                    ↳ Rewriting
                                                                                                      ↳ QDP
                                                                                                        ↳ Rewriting
                                                                                                          ↳ QDP
                                                                                                            ↳ Rewriting
                                                                                                              ↳ QDP
                                                                                                                ↳ Rewriting
                                                                                                                  ↳ QDP
                                                                                                                    ↳ Rewriting
                                                                                                                      ↳ QDP
                                                                                                                        ↳ Rewriting
                                                                                                                          ↳ QDP
                                                                                                                            ↳ DependencyGraphProof
                                                                                                                              ↳ QDP
                                                                                                                                ↳ Rewriting
                                                                                                                                  ↳ QDP
                                                                                                                                    ↳ Rewriting
                                                                                                                                      ↳ QDP
                                                                                                                                        ↳ DependencyGraphProof
                                                                                                                                          ↳ QDP
                                                                                                                                            ↳ Rewriting
                                                                                                                                              ↳ QDP
                                                                                                                                                ↳ Rewriting
                                                                                                                                                  ↳ QDP
                                                                                                                                                    ↳ Rewriting
                                                                                                                                                      ↳ QDP
                                                                                                                                                        ↳ Rewriting
                                                                                                                                                          ↳ QDP
                                                                                                                                                            ↳ Rewriting
                                                                                                                                                              ↳ QDP
                                                                                                                                                                ↳ Rewriting
                                                                                                                                                                  ↳ QDP
                                                                                                                                                                    ↳ Rewriting
                                                                                                                                                                      ↳ QDP
                                                                                                                                                                        ↳ UsableRulesProof
                                                                                                                                                                          ↳ QDP
                                                                                                                                                                            ↳ QReductionProof
                                                                                                                                                                              ↳ QDP
                                                                                                                                                                                ↳ Rewriting
                                                                                                                                                                                  ↳ QDP
                                                                                                                                                                                    ↳ Rewriting
                                                                                                                                                                                      ↳ QDP
                                                                                                                                                                                        ↳ Rewriting
                                                                                                                                                                                          ↳ QDP
                                                                                                                                                                                            ↳ Rewriting
                                                                                                                                                                                              ↳ QDP
                                                                                                                                                                                                ↳ Rewriting
                                                                                                                                                                                                  ↳ QDP
                                                                                                                                                                                                    ↳ Rewriting
                                                                                                                                                                                                      ↳ QDP
                                                                                                                                                                                                        ↳ Rewriting
                                                                                                                                                                                                          ↳ QDP
                                                                                                                                                                                                            ↳ Rewriting
                                                                                                                                                                                                              ↳ QDP
                                                                                                                                                                                                                ↳ Rewriting
                                                                                                                                                                                                                  ↳ QDP
                                                                                                                                                                                                                    ↳ DependencyGraphProof
                                                                                                                                                                                                                      ↳ QDP
                                                                                                                                                                                                                        ↳ Rewriting
                                                                                                                                                                                                                          ↳ QDP
                                                                                                                                                                                                                            ↳ Rewriting
                                                                                                                                                                                                                              ↳ QDP
                                                                                                                                                                                                                                ↳ Rewriting
                                                                                                                                                                                                                                  ↳ QDP
                                                                                                                                                                                                                                    ↳ Rewriting
                                                                                                                                                                                                                                      ↳ QDP
                                                                                                                                                                                                                                        ↳ Rewriting
                                                                                                                                                                                                                                          ↳ QDP
                                                                                                                                                                                                                                            ↳ DependencyGraphProof
                                                                                                                                                                                                                                              ↳ QDP
                                                                                                                                                                                                                                                ↳ QDPOrderProof
                                                                                                                                                                                                                                                  ↳ QDP
                                                                                                                                                                                                                                                    ↳ DependencyGraphProof
                                                                                                                                                                                                                                                      ↳ AND
                                                                                                                                                                                                                                                        ↳ QDP
                                                                                                                                                                                                                                                          ↳ QDPOrderProof
                                                                                                                                                                                                                                                        ↳ 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_mkVBalBranch3MkVBalBranch25(zzz537, zzz538, zzz539, zzz540, zzz541, zzz542, zzz543, zzz544, zzz545, zzz546, zzz547, Succ(zzz5480), Succ(zzz5490), bc) → new_mkVBalBranch3MkVBalBranch25(zzz537, zzz538, zzz539, zzz540, zzz541, zzz542, zzz543, zzz544, zzz545, zzz546, zzz547, zzz5480, zzz5490, bc)
new_mkVBalBranch3MkVBalBranch211(zzz537, zzz538, zzz539, zzz540, zzz541, zzz542, zzz543, zzz544, zzz545, zzz546, zzz547, bc) → new_mkVBalBranch3MkVBalBranch15(zzz537, zzz538, zzz539, zzz540, zzz541, zzz542, zzz543, zzz544, zzz545, zzz546, zzz547, Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat2(Succ(new_primPlusNat3(new_primPlusNat1(zzz539), zzz539)), zzz539)), zzz539))), bc)
new_mkVBalBranch(zzz31, Branch(zzz520, zzz521, Neg(Succ(zzz52200)), zzz523, zzz524), Branch(zzz340, zzz341, zzz342, zzz343, zzz344), h) → new_mkVBalBranch3MkVBalBranch24(zzz340, zzz341, zzz342, zzz343, zzz344, zzz520, zzz521, zzz52200, zzz523, zzz524, zzz31, Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat3(new_primPlusNat1(zzz52200), zzz52200)), zzz52200))), h)
new_mkVBalBranch3MkVBalBranch25(zzz537, zzz538, zzz539, zzz540, zzz541, zzz542, zzz543, zzz544, zzz545, zzz546, zzz547, Succ(zzz5480), Zero, bc) → new_mkVBalBranch3MkVBalBranch15(zzz537, zzz538, zzz539, zzz540, zzz541, zzz542, zzz543, zzz544, zzz545, zzz546, zzz547, Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat2(Succ(new_primPlusNat3(new_primPlusNat1(zzz539), zzz539)), zzz539)), zzz539))), bc)
new_mkVBalBranch3MkVBalBranch24(zzz340, zzz341, Neg(Succ(Succ(Succ(zzz3420000)))), zzz343, zzz344, zzz520, zzz521, Succ(zzz522000), zzz523, zzz524, zzz31, Succ(Succ(zzz6900)), h) → new_mkVBalBranch3MkVBalBranch25(zzz340, zzz341, Succ(Succ(zzz3420000)), zzz343, zzz344, zzz520, zzz521, zzz522000, zzz523, zzz524, zzz31, Succ(zzz3420000), Succ(Succ(new_primPlusNat2(zzz6900, zzz522000))), h)
new_mkVBalBranch3MkVBalBranch16(zzz1702, zzz1703, zzz1704, zzz1705, zzz1706, zzz1707, zzz1708, zzz1709, zzz1710, zzz1711, zzz1712, Succ(zzz17130), Succ(zzz17140), bd) → new_mkVBalBranch3MkVBalBranch16(zzz1702, zzz1703, zzz1704, zzz1705, zzz1706, zzz1707, zzz1708, zzz1709, zzz1710, zzz1711, zzz1712, zzz17130, zzz17140, bd)
new_mkVBalBranch3MkVBalBranch16(zzz1702, zzz1703, zzz1704, zzz1705, zzz1706, zzz1707, zzz1708, zzz1709, zzz1710, zzz1711, zzz1712, Zero, Succ(zzz17140), bd) → new_mkVBalBranch(zzz1712, zzz1711, Branch(zzz1702, zzz1703, Neg(Succ(zzz1704)), zzz1705, zzz1706), bd)
new_mkVBalBranch3MkVBalBranch25(zzz537, zzz538, zzz539, zzz540, zzz541, zzz542, zzz543, zzz544, zzz545, zzz546, zzz547, Zero, Succ(zzz5490), bc) → new_mkVBalBranch(zzz547, Branch(zzz542, zzz543, Neg(Succ(Succ(zzz544))), zzz545, zzz546), zzz540, bc)
new_mkVBalBranch3MkVBalBranch15(zzz537, zzz538, zzz539, zzz540, zzz541, zzz542, zzz543, zzz544, zzz545, zzz546, zzz547, Succ(zzz6990), bc) → new_mkVBalBranch3MkVBalBranch16(zzz537, zzz538, zzz539, zzz540, zzz541, zzz542, zzz543, Succ(zzz544), zzz545, zzz546, zzz547, Succ(Succ(zzz544)), Succ(zzz6990), bc)
new_mkVBalBranch3MkVBalBranch24(zzz340, zzz341, Neg(Succ(Succ(Zero))), zzz343, zzz344, zzz520, zzz521, Succ(zzz522000), zzz523, zzz524, zzz31, Succ(Succ(zzz6900)), h) → new_mkVBalBranch3MkVBalBranch25(zzz340, zzz341, Succ(Zero), zzz343, zzz344, zzz520, zzz521, zzz522000, zzz523, zzz524, zzz31, Zero, Succ(Succ(new_primPlusNat2(zzz6900, zzz522000))), h)
new_mkVBalBranch3MkVBalBranch25(zzz537, zzz538, zzz539, zzz540, zzz541, zzz542, zzz543, zzz544, zzz545, zzz546, zzz547, Zero, Zero, bc) → new_mkVBalBranch3MkVBalBranch211(zzz537, zzz538, zzz539, zzz540, zzz541, zzz542, zzz543, zzz544, zzz545, zzz546, zzz547, bc)

The TRS R consists of the following rules:

new_primPlusNat1(Zero) → Zero
new_primPlusNat1(Succ(zzz62000)) → Succ(Succ(new_primPlusNat1(zzz62000)))
new_primPlusNat3(zzz90, Succ(zzz910)) → Succ(Succ(new_primPlusNat2(zzz90, zzz910)))
new_primPlusNat3(zzz90, Zero) → Succ(zzz90)
new_primPlusNat2(Succ(zzz900), Succ(zzz9100)) → Succ(Succ(new_primPlusNat2(zzz900, zzz9100)))
new_primPlusNat2(Zero, Succ(zzz9100)) → Succ(zzz9100)
new_primPlusNat2(Zero, Zero) → Zero
new_primPlusNat2(Succ(zzz900), Zero) → Succ(zzz900)

The set Q consists of the following terms:

new_primPlusNat2(Zero, Succ(x0))
new_primPlusNat3(x0, Succ(x1))
new_primPlusNat2(Succ(x0), Succ(x1))
new_primPlusNat3(x0, Zero)
new_primPlusNat1(Zero)
new_primPlusNat2(Zero, Zero)
new_primPlusNat1(Succ(x0))
new_primPlusNat2(Succ(x0), Zero)

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


The following pairs can be oriented strictly and are deleted.


new_mkVBalBranch3MkVBalBranch25(zzz537, zzz538, zzz539, zzz540, zzz541, zzz542, zzz543, zzz544, zzz545, zzz546, zzz547, Zero, Succ(zzz5490), bc) → new_mkVBalBranch(zzz547, Branch(zzz542, zzz543, Neg(Succ(Succ(zzz544))), zzz545, zzz546), zzz540, bc)
The remaining pairs can at least be oriented weakly.

new_mkVBalBranch3MkVBalBranch25(zzz537, zzz538, zzz539, zzz540, zzz541, zzz542, zzz543, zzz544, zzz545, zzz546, zzz547, Succ(zzz5480), Succ(zzz5490), bc) → new_mkVBalBranch3MkVBalBranch25(zzz537, zzz538, zzz539, zzz540, zzz541, zzz542, zzz543, zzz544, zzz545, zzz546, zzz547, zzz5480, zzz5490, bc)
new_mkVBalBranch3MkVBalBranch211(zzz537, zzz538, zzz539, zzz540, zzz541, zzz542, zzz543, zzz544, zzz545, zzz546, zzz547, bc) → new_mkVBalBranch3MkVBalBranch15(zzz537, zzz538, zzz539, zzz540, zzz541, zzz542, zzz543, zzz544, zzz545, zzz546, zzz547, Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat2(Succ(new_primPlusNat3(new_primPlusNat1(zzz539), zzz539)), zzz539)), zzz539))), bc)
new_mkVBalBranch(zzz31, Branch(zzz520, zzz521, Neg(Succ(zzz52200)), zzz523, zzz524), Branch(zzz340, zzz341, zzz342, zzz343, zzz344), h) → new_mkVBalBranch3MkVBalBranch24(zzz340, zzz341, zzz342, zzz343, zzz344, zzz520, zzz521, zzz52200, zzz523, zzz524, zzz31, Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat3(new_primPlusNat1(zzz52200), zzz52200)), zzz52200))), h)
new_mkVBalBranch3MkVBalBranch25(zzz537, zzz538, zzz539, zzz540, zzz541, zzz542, zzz543, zzz544, zzz545, zzz546, zzz547, Succ(zzz5480), Zero, bc) → new_mkVBalBranch3MkVBalBranch15(zzz537, zzz538, zzz539, zzz540, zzz541, zzz542, zzz543, zzz544, zzz545, zzz546, zzz547, Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat2(Succ(new_primPlusNat3(new_primPlusNat1(zzz539), zzz539)), zzz539)), zzz539))), bc)
new_mkVBalBranch3MkVBalBranch24(zzz340, zzz341, Neg(Succ(Succ(Succ(zzz3420000)))), zzz343, zzz344, zzz520, zzz521, Succ(zzz522000), zzz523, zzz524, zzz31, Succ(Succ(zzz6900)), h) → new_mkVBalBranch3MkVBalBranch25(zzz340, zzz341, Succ(Succ(zzz3420000)), zzz343, zzz344, zzz520, zzz521, zzz522000, zzz523, zzz524, zzz31, Succ(zzz3420000), Succ(Succ(new_primPlusNat2(zzz6900, zzz522000))), h)
new_mkVBalBranch3MkVBalBranch16(zzz1702, zzz1703, zzz1704, zzz1705, zzz1706, zzz1707, zzz1708, zzz1709, zzz1710, zzz1711, zzz1712, Succ(zzz17130), Succ(zzz17140), bd) → new_mkVBalBranch3MkVBalBranch16(zzz1702, zzz1703, zzz1704, zzz1705, zzz1706, zzz1707, zzz1708, zzz1709, zzz1710, zzz1711, zzz1712, zzz17130, zzz17140, bd)
new_mkVBalBranch3MkVBalBranch16(zzz1702, zzz1703, zzz1704, zzz1705, zzz1706, zzz1707, zzz1708, zzz1709, zzz1710, zzz1711, zzz1712, Zero, Succ(zzz17140), bd) → new_mkVBalBranch(zzz1712, zzz1711, Branch(zzz1702, zzz1703, Neg(Succ(zzz1704)), zzz1705, zzz1706), bd)
new_mkVBalBranch3MkVBalBranch15(zzz537, zzz538, zzz539, zzz540, zzz541, zzz542, zzz543, zzz544, zzz545, zzz546, zzz547, Succ(zzz6990), bc) → new_mkVBalBranch3MkVBalBranch16(zzz537, zzz538, zzz539, zzz540, zzz541, zzz542, zzz543, Succ(zzz544), zzz545, zzz546, zzz547, Succ(Succ(zzz544)), Succ(zzz6990), bc)
new_mkVBalBranch3MkVBalBranch24(zzz340, zzz341, Neg(Succ(Succ(Zero))), zzz343, zzz344, zzz520, zzz521, Succ(zzz522000), zzz523, zzz524, zzz31, Succ(Succ(zzz6900)), h) → new_mkVBalBranch3MkVBalBranch25(zzz340, zzz341, Succ(Zero), zzz343, zzz344, zzz520, zzz521, zzz522000, zzz523, zzz524, zzz31, Zero, Succ(Succ(new_primPlusNat2(zzz6900, zzz522000))), h)
new_mkVBalBranch3MkVBalBranch25(zzz537, zzz538, zzz539, zzz540, zzz541, zzz542, zzz543, zzz544, zzz545, zzz546, zzz547, Zero, Zero, bc) → new_mkVBalBranch3MkVBalBranch211(zzz537, zzz538, zzz539, zzz540, zzz541, zzz542, zzz543, zzz544, zzz545, zzz546, zzz547, bc)
Used ordering: Polynomial interpretation [25]:

POL(Branch(x1, x2, x3, x4, x5)) = x2 + x3 + x4   
POL(Neg(x1)) = 1   
POL(Succ(x1)) = 0   
POL(Zero) = 0   
POL(new_mkVBalBranch(x1, x2, x3, x4)) = x3   
POL(new_mkVBalBranch3MkVBalBranch15(x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12, x13)) = 1 + x2 + x4   
POL(new_mkVBalBranch3MkVBalBranch16(x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12, x13, x14)) = 1 + x2 + x4   
POL(new_mkVBalBranch3MkVBalBranch211(x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12)) = 1 + x2 + x4   
POL(new_mkVBalBranch3MkVBalBranch24(x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12, x13)) = x2 + x3 + x4   
POL(new_mkVBalBranch3MkVBalBranch25(x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12, x13, x14)) = 1 + x2 + x4   
POL(new_primPlusNat1(x1)) = 1   
POL(new_primPlusNat2(x1, x2)) = 0   
POL(new_primPlusNat3(x1, x2)) = 0   

The following usable rules [17] were oriented: none



↳ HASKELL
  ↳ LR
    ↳ HASKELL
      ↳ CR
        ↳ HASKELL
          ↳ IFR
            ↳ HASKELL
              ↳ BR
                ↳ HASKELL
                  ↳ COR
                    ↳ HASKELL
                      ↳ LetRed
                        ↳ HASKELL
                          ↳ NumRed
                            ↳ HASKELL
                              ↳ Narrow
                                ↳ AND
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                    ↳ DependencyGraphProof
                                      ↳ QDP
                                        ↳ Rewriting
                                          ↳ QDP
                                            ↳ Rewriting
                                              ↳ QDP
                                                ↳ Rewriting
                                                  ↳ QDP
                                                    ↳ Rewriting
                                                      ↳ QDP
                                                        ↳ Rewriting
                                                          ↳ QDP
                                                            ↳ Rewriting
                                                              ↳ QDP
                                                                ↳ Rewriting
                                                                  ↳ QDP
                                                                    ↳ Rewriting
                                                                      ↳ QDP
                                                                        ↳ Rewriting
                                                                          ↳ QDP
                                                                            ↳ Rewriting
                                                                              ↳ QDP
                                                                                ↳ Rewriting
                                                                                  ↳ QDP
                                                                                    ↳ Rewriting
                                                                                      ↳ QDP
                                                                                        ↳ Rewriting
                                                                                          ↳ QDP
                                                                                            ↳ UsableRulesProof
                                                                                              ↳ QDP
                                                                                                ↳ QReductionProof
                                                                                                  ↳ QDP
                                                                                                    ↳ Rewriting
                                                                                                      ↳ QDP
                                                                                                        ↳ Rewriting
                                                                                                          ↳ QDP
                                                                                                            ↳ Rewriting
                                                                                                              ↳ QDP
                                                                                                                ↳ Rewriting
                                                                                                                  ↳ QDP
                                                                                                                    ↳ Rewriting
                                                                                                                      ↳ QDP
                                                                                                                        ↳ Rewriting
                                                                                                                          ↳ QDP
                                                                                                                            ↳ DependencyGraphProof
                                                                                                                              ↳ QDP
                                                                                                                                ↳ Rewriting
                                                                                                                                  ↳ QDP
                                                                                                                                    ↳ Rewriting
                                                                                                                                      ↳ QDP
                                                                                                                                        ↳ DependencyGraphProof
                                                                                                                                          ↳ QDP
                                                                                                                                            ↳ Rewriting
                                                                                                                                              ↳ QDP
                                                                                                                                                ↳ Rewriting
                                                                                                                                                  ↳ QDP
                                                                                                                                                    ↳ Rewriting
                                                                                                                                                      ↳ QDP
                                                                                                                                                        ↳ Rewriting
                                                                                                                                                          ↳ QDP
                                                                                                                                                            ↳ Rewriting
                                                                                                                                                              ↳ QDP
                                                                                                                                                                ↳ Rewriting
                                                                                                                                                                  ↳ QDP
                                                                                                                                                                    ↳ Rewriting
                                                                                                                                                                      ↳ QDP
                                                                                                                                                                        ↳ UsableRulesProof
                                                                                                                                                                          ↳ QDP
                                                                                                                                                                            ↳ QReductionProof
                                                                                                                                                                              ↳ QDP
                                                                                                                                                                                ↳ Rewriting
                                                                                                                                                                                  ↳ QDP
                                                                                                                                                                                    ↳ Rewriting
                                                                                                                                                                                      ↳ QDP
                                                                                                                                                                                        ↳ Rewriting
                                                                                                                                                                                          ↳ QDP
                                                                                                                                                                                            ↳ Rewriting
                                                                                                                                                                                              ↳ QDP
                                                                                                                                                                                                ↳ Rewriting
                                                                                                                                                                                                  ↳ QDP
                                                                                                                                                                                                    ↳ Rewriting
                                                                                                                                                                                                      ↳ QDP
                                                                                                                                                                                                        ↳ Rewriting
                                                                                                                                                                                                          ↳ QDP
                                                                                                                                                                                                            ↳ Rewriting
                                                                                                                                                                                                              ↳ QDP
                                                                                                                                                                                                                ↳ Rewriting
                                                                                                                                                                                                                  ↳ QDP
                                                                                                                                                                                                                    ↳ DependencyGraphProof
                                                                                                                                                                                                                      ↳ QDP
                                                                                                                                                                                                                        ↳ Rewriting
                                                                                                                                                                                                                          ↳ QDP
                                                                                                                                                                                                                            ↳ Rewriting
                                                                                                                                                                                                                              ↳ QDP
                                                                                                                                                                                                                                ↳ Rewriting
                                                                                                                                                                                                                                  ↳ QDP
                                                                                                                                                                                                                                    ↳ Rewriting
                                                                                                                                                                                                                                      ↳ QDP
                                                                                                                                                                                                                                        ↳ Rewriting
                                                                                                                                                                                                                                          ↳ QDP
                                                                                                                                                                                                                                            ↳ DependencyGraphProof
                                                                                                                                                                                                                                              ↳ QDP
                                                                                                                                                                                                                                                ↳ QDPOrderProof
                                                                                                                                                                                                                                                  ↳ QDP
                                                                                                                                                                                                                                                    ↳ DependencyGraphProof
                                                                                                                                                                                                                                                      ↳ AND
                                                                                                                                                                                                                                                        ↳ QDP
                                                                                                                                                                                                                                                          ↳ QDPOrderProof
                                                                                                                                                                                                                                                            ↳ QDP
                                                                                                                                                                                                                                                              ↳ DependencyGraphProof
                                                                                                                                                                                                                                                        ↳ 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_mkVBalBranch3MkVBalBranch25(zzz537, zzz538, zzz539, zzz540, zzz541, zzz542, zzz543, zzz544, zzz545, zzz546, zzz547, Succ(zzz5480), Succ(zzz5490), bc) → new_mkVBalBranch3MkVBalBranch25(zzz537, zzz538, zzz539, zzz540, zzz541, zzz542, zzz543, zzz544, zzz545, zzz546, zzz547, zzz5480, zzz5490, bc)
new_mkVBalBranch(zzz31, Branch(zzz520, zzz521, Neg(Succ(zzz52200)), zzz523, zzz524), Branch(zzz340, zzz341, zzz342, zzz343, zzz344), h) → new_mkVBalBranch3MkVBalBranch24(zzz340, zzz341, zzz342, zzz343, zzz344, zzz520, zzz521, zzz52200, zzz523, zzz524, zzz31, Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat3(new_primPlusNat1(zzz52200), zzz52200)), zzz52200))), h)
new_mkVBalBranch3MkVBalBranch211(zzz537, zzz538, zzz539, zzz540, zzz541, zzz542, zzz543, zzz544, zzz545, zzz546, zzz547, bc) → new_mkVBalBranch3MkVBalBranch15(zzz537, zzz538, zzz539, zzz540, zzz541, zzz542, zzz543, zzz544, zzz545, zzz546, zzz547, Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat2(Succ(new_primPlusNat3(new_primPlusNat1(zzz539), zzz539)), zzz539)), zzz539))), bc)
new_mkVBalBranch3MkVBalBranch25(zzz537, zzz538, zzz539, zzz540, zzz541, zzz542, zzz543, zzz544, zzz545, zzz546, zzz547, Succ(zzz5480), Zero, bc) → new_mkVBalBranch3MkVBalBranch15(zzz537, zzz538, zzz539, zzz540, zzz541, zzz542, zzz543, zzz544, zzz545, zzz546, zzz547, Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat2(Succ(new_primPlusNat3(new_primPlusNat1(zzz539), zzz539)), zzz539)), zzz539))), bc)
new_mkVBalBranch3MkVBalBranch24(zzz340, zzz341, Neg(Succ(Succ(Succ(zzz3420000)))), zzz343, zzz344, zzz520, zzz521, Succ(zzz522000), zzz523, zzz524, zzz31, Succ(Succ(zzz6900)), h) → new_mkVBalBranch3MkVBalBranch25(zzz340, zzz341, Succ(Succ(zzz3420000)), zzz343, zzz344, zzz520, zzz521, zzz522000, zzz523, zzz524, zzz31, Succ(zzz3420000), Succ(Succ(new_primPlusNat2(zzz6900, zzz522000))), h)
new_mkVBalBranch3MkVBalBranch16(zzz1702, zzz1703, zzz1704, zzz1705, zzz1706, zzz1707, zzz1708, zzz1709, zzz1710, zzz1711, zzz1712, Succ(zzz17130), Succ(zzz17140), bd) → new_mkVBalBranch3MkVBalBranch16(zzz1702, zzz1703, zzz1704, zzz1705, zzz1706, zzz1707, zzz1708, zzz1709, zzz1710, zzz1711, zzz1712, zzz17130, zzz17140, bd)
new_mkVBalBranch3MkVBalBranch16(zzz1702, zzz1703, zzz1704, zzz1705, zzz1706, zzz1707, zzz1708, zzz1709, zzz1710, zzz1711, zzz1712, Zero, Succ(zzz17140), bd) → new_mkVBalBranch(zzz1712, zzz1711, Branch(zzz1702, zzz1703, Neg(Succ(zzz1704)), zzz1705, zzz1706), bd)
new_mkVBalBranch3MkVBalBranch15(zzz537, zzz538, zzz539, zzz540, zzz541, zzz542, zzz543, zzz544, zzz545, zzz546, zzz547, Succ(zzz6990), bc) → new_mkVBalBranch3MkVBalBranch16(zzz537, zzz538, zzz539, zzz540, zzz541, zzz542, zzz543, Succ(zzz544), zzz545, zzz546, zzz547, Succ(Succ(zzz544)), Succ(zzz6990), bc)
new_mkVBalBranch3MkVBalBranch25(zzz537, zzz538, zzz539, zzz540, zzz541, zzz542, zzz543, zzz544, zzz545, zzz546, zzz547, Zero, Zero, bc) → new_mkVBalBranch3MkVBalBranch211(zzz537, zzz538, zzz539, zzz540, zzz541, zzz542, zzz543, zzz544, zzz545, zzz546, zzz547, bc)
new_mkVBalBranch3MkVBalBranch24(zzz340, zzz341, Neg(Succ(Succ(Zero))), zzz343, zzz344, zzz520, zzz521, Succ(zzz522000), zzz523, zzz524, zzz31, Succ(Succ(zzz6900)), h) → new_mkVBalBranch3MkVBalBranch25(zzz340, zzz341, Succ(Zero), zzz343, zzz344, zzz520, zzz521, zzz522000, zzz523, zzz524, zzz31, Zero, Succ(Succ(new_primPlusNat2(zzz6900, zzz522000))), h)

The TRS R consists of the following rules:

new_primPlusNat1(Zero) → Zero
new_primPlusNat1(Succ(zzz62000)) → Succ(Succ(new_primPlusNat1(zzz62000)))
new_primPlusNat3(zzz90, Succ(zzz910)) → Succ(Succ(new_primPlusNat2(zzz90, zzz910)))
new_primPlusNat3(zzz90, Zero) → Succ(zzz90)
new_primPlusNat2(Succ(zzz900), Succ(zzz9100)) → Succ(Succ(new_primPlusNat2(zzz900, zzz9100)))
new_primPlusNat2(Zero, Succ(zzz9100)) → Succ(zzz9100)
new_primPlusNat2(Zero, Zero) → Zero
new_primPlusNat2(Succ(zzz900), Zero) → Succ(zzz900)

The set Q consists of the following terms:

new_primPlusNat2(Zero, Succ(x0))
new_primPlusNat3(x0, Succ(x1))
new_primPlusNat2(Succ(x0), Succ(x1))
new_primPlusNat3(x0, Zero)
new_primPlusNat1(Zero)
new_primPlusNat2(Zero, Zero)
new_primPlusNat1(Succ(x0))
new_primPlusNat2(Succ(x0), Zero)

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

↳ HASKELL
  ↳ LR
    ↳ HASKELL
      ↳ CR
        ↳ HASKELL
          ↳ IFR
            ↳ HASKELL
              ↳ BR
                ↳ HASKELL
                  ↳ COR
                    ↳ HASKELL
                      ↳ LetRed
                        ↳ HASKELL
                          ↳ NumRed
                            ↳ HASKELL
                              ↳ Narrow
                                ↳ AND
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                    ↳ DependencyGraphProof
                                      ↳ QDP
                                        ↳ Rewriting
                                          ↳ QDP
                                            ↳ Rewriting
                                              ↳ QDP
                                                ↳ Rewriting
                                                  ↳ QDP
                                                    ↳ Rewriting
                                                      ↳ QDP
                                                        ↳ Rewriting
                                                          ↳ QDP
                                                            ↳ Rewriting
                                                              ↳ QDP
                                                                ↳ Rewriting
                                                                  ↳ QDP
                                                                    ↳ Rewriting
                                                                      ↳ QDP
                                                                        ↳ Rewriting
                                                                          ↳ QDP
                                                                            ↳ Rewriting
                                                                              ↳ QDP
                                                                                ↳ Rewriting
                                                                                  ↳ QDP
                                                                                    ↳ Rewriting
                                                                                      ↳ QDP
                                                                                        ↳ Rewriting
                                                                                          ↳ QDP
                                                                                            ↳ UsableRulesProof
                                                                                              ↳ QDP
                                                                                                ↳ QReductionProof
                                                                                                  ↳ QDP
                                                                                                    ↳ Rewriting
                                                                                                      ↳ QDP
                                                                                                        ↳ Rewriting
                                                                                                          ↳ QDP
                                                                                                            ↳ Rewriting
                                                                                                              ↳ QDP
                                                                                                                ↳ Rewriting
                                                                                                                  ↳ QDP
                                                                                                                    ↳ Rewriting
                                                                                                                      ↳ QDP
                                                                                                                        ↳ Rewriting
                                                                                                                          ↳ QDP
                                                                                                                            ↳ DependencyGraphProof
                                                                                                                              ↳ QDP
                                                                                                                                ↳ Rewriting
                                                                                                                                  ↳ QDP
                                                                                                                                    ↳ Rewriting
                                                                                                                                      ↳ QDP
                                                                                                                                        ↳ DependencyGraphProof
                                                                                                                                          ↳ QDP
                                                                                                                                            ↳ Rewriting
                                                                                                                                              ↳ QDP
                                                                                                                                                ↳ Rewriting
                                                                                                                                                  ↳ QDP
                                                                                                                                                    ↳ Rewriting
                                                                                                                                                      ↳ QDP
                                                                                                                                                        ↳ Rewriting
                                                                                                                                                          ↳ QDP
                                                                                                                                                            ↳ Rewriting
                                                                                                                                                              ↳ QDP
                                                                                                                                                                ↳ Rewriting
                                                                                                                                                                  ↳ QDP
                                                                                                                                                                    ↳ Rewriting
                                                                                                                                                                      ↳ QDP
                                                                                                                                                                        ↳ UsableRulesProof
                                                                                                                                                                          ↳ QDP
                                                                                                                                                                            ↳ QReductionProof
                                                                                                                                                                              ↳ QDP
                                                                                                                                                                                ↳ Rewriting
                                                                                                                                                                                  ↳ QDP
                                                                                                                                                                                    ↳ Rewriting
                                                                                                                                                                                      ↳ QDP
                                                                                                                                                                                        ↳ Rewriting
                                                                                                                                                                                          ↳ QDP
                                                                                                                                                                                            ↳ Rewriting
                                                                                                                                                                                              ↳ QDP
                                                                                                                                                                                                ↳ Rewriting
                                                                                                                                                                                                  ↳ QDP
                                                                                                                                                                                                    ↳ Rewriting
                                                                                                                                                                                                      ↳ QDP
                                                                                                                                                                                                        ↳ Rewriting
                                                                                                                                                                                                          ↳ QDP
                                                                                                                                                                                                            ↳ Rewriting
                                                                                                                                                                                                              ↳ QDP
                                                                                                                                                                                                                ↳ Rewriting
                                                                                                                                                                                                                  ↳ QDP
                                                                                                                                                                                                                    ↳ DependencyGraphProof
                                                                                                                                                                                                                      ↳ QDP
                                                                                                                                                                                                                        ↳ Rewriting
                                                                                                                                                                                                                          ↳ QDP
                                                                                                                                                                                                                            ↳ Rewriting
                                                                                                                                                                                                                              ↳ QDP
                                                                                                                                                                                                                                ↳ Rewriting
                                                                                                                                                                                                                                  ↳ QDP
                                                                                                                                                                                                                                    ↳ Rewriting
                                                                                                                                                                                                                                      ↳ QDP
                                                                                                                                                                                                                                        ↳ Rewriting
                                                                                                                                                                                                                                          ↳ QDP
                                                                                                                                                                                                                                            ↳ DependencyGraphProof
                                                                                                                                                                                                                                              ↳ QDP
                                                                                                                                                                                                                                                ↳ QDPOrderProof
                                                                                                                                                                                                                                                  ↳ QDP
                                                                                                                                                                                                                                                    ↳ DependencyGraphProof
                                                                                                                                                                                                                                                      ↳ AND
                                                                                                                                                                                                                                                        ↳ QDP
                                                                                                                                                                                                                                                          ↳ QDPOrderProof
                                                                                                                                                                                                                                                            ↳ QDP
                                                                                                                                                                                                                                                              ↳ DependencyGraphProof
                                                                                                                                                                                                                                                                ↳ 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_mkVBalBranch3MkVBalBranch25(zzz537, zzz538, zzz539, zzz540, zzz541, zzz542, zzz543, zzz544, zzz545, zzz546, zzz547, Succ(zzz5480), Succ(zzz5490), bc) → new_mkVBalBranch3MkVBalBranch25(zzz537, zzz538, zzz539, zzz540, zzz541, zzz542, zzz543, zzz544, zzz545, zzz546, zzz547, zzz5480, zzz5490, bc)
new_mkVBalBranch(zzz31, Branch(zzz520, zzz521, Neg(Succ(zzz52200)), zzz523, zzz524), Branch(zzz340, zzz341, zzz342, zzz343, zzz344), h) → new_mkVBalBranch3MkVBalBranch24(zzz340, zzz341, zzz342, zzz343, zzz344, zzz520, zzz521, zzz52200, zzz523, zzz524, zzz31, Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat3(new_primPlusNat1(zzz52200), zzz52200)), zzz52200))), h)
new_mkVBalBranch3MkVBalBranch211(zzz537, zzz538, zzz539, zzz540, zzz541, zzz542, zzz543, zzz544, zzz545, zzz546, zzz547, bc) → new_mkVBalBranch3MkVBalBranch15(zzz537, zzz538, zzz539, zzz540, zzz541, zzz542, zzz543, zzz544, zzz545, zzz546, zzz547, Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat2(Succ(new_primPlusNat3(new_primPlusNat1(zzz539), zzz539)), zzz539)), zzz539))), bc)
new_mkVBalBranch3MkVBalBranch25(zzz537, zzz538, zzz539, zzz540, zzz541, zzz542, zzz543, zzz544, zzz545, zzz546, zzz547, Succ(zzz5480), Zero, bc) → new_mkVBalBranch3MkVBalBranch15(zzz537, zzz538, zzz539, zzz540, zzz541, zzz542, zzz543, zzz544, zzz545, zzz546, zzz547, Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat2(Succ(new_primPlusNat3(new_primPlusNat1(zzz539), zzz539)), zzz539)), zzz539))), bc)
new_mkVBalBranch3MkVBalBranch24(zzz340, zzz341, Neg(Succ(Succ(Succ(zzz3420000)))), zzz343, zzz344, zzz520, zzz521, Succ(zzz522000), zzz523, zzz524, zzz31, Succ(Succ(zzz6900)), h) → new_mkVBalBranch3MkVBalBranch25(zzz340, zzz341, Succ(Succ(zzz3420000)), zzz343, zzz344, zzz520, zzz521, zzz522000, zzz523, zzz524, zzz31, Succ(zzz3420000), Succ(Succ(new_primPlusNat2(zzz6900, zzz522000))), h)
new_mkVBalBranch3MkVBalBranch16(zzz1702, zzz1703, zzz1704, zzz1705, zzz1706, zzz1707, zzz1708, zzz1709, zzz1710, zzz1711, zzz1712, Succ(zzz17130), Succ(zzz17140), bd) → new_mkVBalBranch3MkVBalBranch16(zzz1702, zzz1703, zzz1704, zzz1705, zzz1706, zzz1707, zzz1708, zzz1709, zzz1710, zzz1711, zzz1712, zzz17130, zzz17140, bd)
new_mkVBalBranch3MkVBalBranch16(zzz1702, zzz1703, zzz1704, zzz1705, zzz1706, zzz1707, zzz1708, zzz1709, zzz1710, zzz1711, zzz1712, Zero, Succ(zzz17140), bd) → new_mkVBalBranch(zzz1712, zzz1711, Branch(zzz1702, zzz1703, Neg(Succ(zzz1704)), zzz1705, zzz1706), bd)
new_mkVBalBranch3MkVBalBranch15(zzz537, zzz538, zzz539, zzz540, zzz541, zzz542, zzz543, zzz544, zzz545, zzz546, zzz547, Succ(zzz6990), bc) → new_mkVBalBranch3MkVBalBranch16(zzz537, zzz538, zzz539, zzz540, zzz541, zzz542, zzz543, Succ(zzz544), zzz545, zzz546, zzz547, Succ(Succ(zzz544)), Succ(zzz6990), bc)
new_mkVBalBranch3MkVBalBranch25(zzz537, zzz538, zzz539, zzz540, zzz541, zzz542, zzz543, zzz544, zzz545, zzz546, zzz547, Zero, Zero, bc) → new_mkVBalBranch3MkVBalBranch211(zzz537, zzz538, zzz539, zzz540, zzz541, zzz542, zzz543, zzz544, zzz545, zzz546, zzz547, bc)

The TRS R consists of the following rules:

new_primPlusNat1(Zero) → Zero
new_primPlusNat1(Succ(zzz62000)) → Succ(Succ(new_primPlusNat1(zzz62000)))
new_primPlusNat3(zzz90, Succ(zzz910)) → Succ(Succ(new_primPlusNat2(zzz90, zzz910)))
new_primPlusNat3(zzz90, Zero) → Succ(zzz90)
new_primPlusNat2(Succ(zzz900), Succ(zzz9100)) → Succ(Succ(new_primPlusNat2(zzz900, zzz9100)))
new_primPlusNat2(Zero, Succ(zzz9100)) → Succ(zzz9100)
new_primPlusNat2(Zero, Zero) → Zero
new_primPlusNat2(Succ(zzz900), Zero) → Succ(zzz900)

The set Q consists of the following terms:

new_primPlusNat2(Zero, Succ(x0))
new_primPlusNat3(x0, Succ(x1))
new_primPlusNat2(Succ(x0), Succ(x1))
new_primPlusNat3(x0, Zero)
new_primPlusNat1(Zero)
new_primPlusNat2(Zero, Zero)
new_primPlusNat1(Succ(x0))
new_primPlusNat2(Succ(x0), Zero)

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

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



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

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

new_mkVBalBranch3MkVBalBranch26(zzz1133, zzz1134, zzz1135, zzz1136, zzz1137, zzz1138, zzz1139, zzz1140, zzz1141, zzz1142, Succ(zzz11430), Succ(zzz11440), be) → new_mkVBalBranch3MkVBalBranch26(zzz1133, zzz1134, zzz1135, zzz1136, zzz1137, zzz1138, zzz1139, zzz1140, zzz1141, zzz1142, zzz11430, zzz11440, be)

The TRS R consists of the following rules:

new_primPlusNat1(Zero) → Zero
new_primPlusNat1(Succ(zzz62000)) → Succ(Succ(new_primPlusNat1(zzz62000)))
new_primPlusNat3(zzz90, Succ(zzz910)) → Succ(Succ(new_primPlusNat2(zzz90, zzz910)))
new_primPlusNat3(zzz90, Zero) → Succ(zzz90)
new_primPlusNat2(Succ(zzz900), Succ(zzz9100)) → Succ(Succ(new_primPlusNat2(zzz900, zzz9100)))
new_primPlusNat2(Zero, Succ(zzz9100)) → Succ(zzz9100)
new_primPlusNat2(Zero, Zero) → Zero
new_primPlusNat2(Succ(zzz900), Zero) → Succ(zzz900)

The set Q consists of the following terms:

new_primPlusNat2(Zero, Succ(x0))
new_primPlusNat3(x0, Succ(x1))
new_primPlusNat2(Succ(x0), Succ(x1))
new_primPlusNat3(x0, Zero)
new_primPlusNat1(Zero)
new_primPlusNat2(Zero, Zero)
new_primPlusNat1(Succ(x0))
new_primPlusNat2(Succ(x0), Zero)

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

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

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

new_mkVBalBranch3MkVBalBranch26(zzz1133, zzz1134, zzz1135, zzz1136, zzz1137, zzz1138, zzz1139, zzz1140, zzz1141, zzz1142, Succ(zzz11430), Succ(zzz11440), be) → new_mkVBalBranch3MkVBalBranch26(zzz1133, zzz1134, zzz1135, zzz1136, zzz1137, zzz1138, zzz1139, zzz1140, zzz1141, zzz1142, zzz11430, zzz11440, be)

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

new_primPlusNat2(Zero, Succ(x0))
new_primPlusNat3(x0, Succ(x1))
new_primPlusNat2(Succ(x0), Succ(x1))
new_primPlusNat3(x0, Zero)
new_primPlusNat1(Zero)
new_primPlusNat2(Zero, Zero)
new_primPlusNat1(Succ(x0))
new_primPlusNat2(Succ(x0), Zero)

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

new_primPlusNat2(Zero, Succ(x0))
new_primPlusNat3(x0, Succ(x1))
new_primPlusNat2(Succ(x0), Succ(x1))
new_primPlusNat3(x0, Zero)
new_primPlusNat1(Zero)
new_primPlusNat2(Zero, Zero)
new_primPlusNat1(Succ(x0))
new_primPlusNat2(Succ(x0), 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
                                    ↳ DependencyGraphProof
                                      ↳ QDP
                                        ↳ Rewriting
                                          ↳ QDP
                                            ↳ Rewriting
                                              ↳ QDP
                                                ↳ Rewriting
                                                  ↳ QDP
                                                    ↳ Rewriting
                                                      ↳ QDP
                                                        ↳ Rewriting
                                                          ↳ QDP
                                                            ↳ Rewriting
                                                              ↳ QDP
                                                                ↳ Rewriting
                                                                  ↳ QDP
                                                                    ↳ Rewriting
                                                                      ↳ QDP
                                                                        ↳ Rewriting
                                                                          ↳ QDP
                                                                            ↳ Rewriting
                                                                              ↳ QDP
                                                                                ↳ Rewriting
                                                                                  ↳ QDP
                                                                                    ↳ Rewriting
                                                                                      ↳ QDP
                                                                                        ↳ Rewriting
                                                                                          ↳ QDP
                                                                                            ↳ UsableRulesProof
                                                                                              ↳ QDP
                                                                                                ↳ QReductionProof
                                                                                                  ↳ QDP
                                                                                                    ↳ Rewriting
                                                                                                      ↳ QDP
                                                                                                        ↳ Rewriting
                                                                                                          ↳ QDP
                                                                                                            ↳ Rewriting
                                                                                                              ↳ QDP
                                                                                                                ↳ Rewriting
                                                                                                                  ↳ QDP
                                                                                                                    ↳ Rewriting
                                                                                                                      ↳ QDP
                                                                                                                        ↳ Rewriting
                                                                                                                          ↳ QDP
                                                                                                                            ↳ DependencyGraphProof
                                                                                                                              ↳ QDP
                                                                                                                                ↳ Rewriting
                                                                                                                                  ↳ QDP
                                                                                                                                    ↳ Rewriting
                                                                                                                                      ↳ QDP
                                                                                                                                        ↳ DependencyGraphProof
                                                                                                                                          ↳ QDP
                                                                                                                                            ↳ Rewriting
                                                                                                                                              ↳ QDP
                                                                                                                                                ↳ Rewriting
                                                                                                                                                  ↳ QDP
                                                                                                                                                    ↳ Rewriting
                                                                                                                                                      ↳ QDP
                                                                                                                                                        ↳ Rewriting
                                                                                                                                                          ↳ QDP
                                                                                                                                                            ↳ Rewriting
                                                                                                                                                              ↳ QDP
                                                                                                                                                                ↳ Rewriting
                                                                                                                                                                  ↳ QDP
                                                                                                                                                                    ↳ Rewriting
                                                                                                                                                                      ↳ QDP
                                                                                                                                                                        ↳ UsableRulesProof
                                                                                                                                                                          ↳ QDP
                                                                                                                                                                            ↳ QReductionProof
                                                                                                                                                                              ↳ QDP
                                                                                                                                                                                ↳ Rewriting
                                                                                                                                                                                  ↳ QDP
                                                                                                                                                                                    ↳ Rewriting
                                                                                                                                                                                      ↳ QDP
                                                                                                                                                                                        ↳ Rewriting
                                                                                                                                                                                          ↳ QDP
                                                                                                                                                                                            ↳ Rewriting
                                                                                                                                                                                              ↳ QDP
                                                                                                                                                                                                ↳ Rewriting
                                                                                                                                                                                                  ↳ QDP
                                                                                                                                                                                                    ↳ Rewriting
                                                                                                                                                                                                      ↳ QDP
                                                                                                                                                                                                        ↳ Rewriting
                                                                                                                                                                                                          ↳ QDP
                                                                                                                                                                                                            ↳ Rewriting
                                                                                                                                                                                                              ↳ QDP
                                                                                                                                                                                                                ↳ Rewriting
                                                                                                                                                                                                                  ↳ QDP
                                                                                                                                                                                                                    ↳ DependencyGraphProof
                                                                                                                                                                                                                      ↳ QDP
                                                                                                                                                                                                                        ↳ Rewriting
                                                                                                                                                                                                                          ↳ QDP
                                                                                                                                                                                                                            ↳ Rewriting
                                                                                                                                                                                                                              ↳ QDP
                                                                                                                                                                                                                                ↳ Rewriting
                                                                                                                                                                                                                                  ↳ QDP
                                                                                                                                                                                                                                    ↳ Rewriting
                                                                                                                                                                                                                                      ↳ QDP
                                                                                                                                                                                                                                        ↳ Rewriting
                                                                                                                                                                                                                                          ↳ QDP
                                                                                                                                                                                                                                            ↳ DependencyGraphProof
                                                                                                                                                                                                                                              ↳ QDP
                                                                                                                                                                                                                                                ↳ QDPOrderProof
                                                                                                                                                                                                                                                  ↳ QDP
                                                                                                                                                                                                                                                    ↳ DependencyGraphProof
                                                                                                                                                                                                                                                      ↳ AND
                                                                                                                                                                                                                                                        ↳ QDP
                                                                                                                                                                                                                                                        ↳ QDP
                                                                                                                                                                                                                                                          ↳ UsableRulesProof
                                                                                                                                                                                                                                                            ↳ QDP
                                                                                                                                                                                                                                                              ↳ QReductionProof
                                                                                                                                                                                                                                                                ↳ 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_mkVBalBranch3MkVBalBranch26(zzz1133, zzz1134, zzz1135, zzz1136, zzz1137, zzz1138, zzz1139, zzz1140, zzz1141, zzz1142, Succ(zzz11430), Succ(zzz11440), be) → new_mkVBalBranch3MkVBalBranch26(zzz1133, zzz1134, zzz1135, zzz1136, zzz1137, zzz1138, zzz1139, zzz1140, zzz1141, zzz1142, zzz11430, zzz11440, be)

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

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

new_mkVBalBranch3MkVBalBranch11(zzz2033, zzz2034, zzz2035, zzz2036, zzz2037, zzz2038, zzz2039, zzz2040, zzz2041, zzz2042, zzz2043, Succ(zzz20440), Succ(zzz20450), bb) → new_mkVBalBranch3MkVBalBranch11(zzz2033, zzz2034, zzz2035, zzz2036, zzz2037, zzz2038, zzz2039, zzz2040, zzz2041, zzz2042, zzz2043, zzz20440, zzz20450, bb)

The TRS R consists of the following rules:

new_primPlusNat1(Zero) → Zero
new_primPlusNat1(Succ(zzz62000)) → Succ(Succ(new_primPlusNat1(zzz62000)))
new_primPlusNat3(zzz90, Succ(zzz910)) → Succ(Succ(new_primPlusNat2(zzz90, zzz910)))
new_primPlusNat3(zzz90, Zero) → Succ(zzz90)
new_primPlusNat2(Succ(zzz900), Succ(zzz9100)) → Succ(Succ(new_primPlusNat2(zzz900, zzz9100)))
new_primPlusNat2(Zero, Succ(zzz9100)) → Succ(zzz9100)
new_primPlusNat2(Zero, Zero) → Zero
new_primPlusNat2(Succ(zzz900), Zero) → Succ(zzz900)

The set Q consists of the following terms:

new_primPlusNat2(Zero, Succ(x0))
new_primPlusNat3(x0, Succ(x1))
new_primPlusNat2(Succ(x0), Succ(x1))
new_primPlusNat3(x0, Zero)
new_primPlusNat1(Zero)
new_primPlusNat2(Zero, Zero)
new_primPlusNat1(Succ(x0))
new_primPlusNat2(Succ(x0), Zero)

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

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

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

new_mkVBalBranch3MkVBalBranch11(zzz2033, zzz2034, zzz2035, zzz2036, zzz2037, zzz2038, zzz2039, zzz2040, zzz2041, zzz2042, zzz2043, Succ(zzz20440), Succ(zzz20450), bb) → new_mkVBalBranch3MkVBalBranch11(zzz2033, zzz2034, zzz2035, zzz2036, zzz2037, zzz2038, zzz2039, zzz2040, zzz2041, zzz2042, zzz2043, zzz20440, zzz20450, bb)

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

new_primPlusNat2(Zero, Succ(x0))
new_primPlusNat3(x0, Succ(x1))
new_primPlusNat2(Succ(x0), Succ(x1))
new_primPlusNat3(x0, Zero)
new_primPlusNat1(Zero)
new_primPlusNat2(Zero, Zero)
new_primPlusNat1(Succ(x0))
new_primPlusNat2(Succ(x0), Zero)

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

new_primPlusNat2(Zero, Succ(x0))
new_primPlusNat3(x0, Succ(x1))
new_primPlusNat2(Succ(x0), Succ(x1))
new_primPlusNat3(x0, Zero)
new_primPlusNat1(Zero)
new_primPlusNat2(Zero, Zero)
new_primPlusNat1(Succ(x0))
new_primPlusNat2(Succ(x0), 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
                                    ↳ DependencyGraphProof
                                      ↳ QDP
                                        ↳ Rewriting
                                          ↳ QDP
                                            ↳ Rewriting
                                              ↳ QDP
                                                ↳ Rewriting
                                                  ↳ QDP
                                                    ↳ Rewriting
                                                      ↳ QDP
                                                        ↳ Rewriting
                                                          ↳ QDP
                                                            ↳ Rewriting
                                                              ↳ QDP
                                                                ↳ Rewriting
                                                                  ↳ QDP
                                                                    ↳ Rewriting
                                                                      ↳ QDP
                                                                        ↳ Rewriting
                                                                          ↳ QDP
                                                                            ↳ Rewriting
                                                                              ↳ QDP
                                                                                ↳ Rewriting
                                                                                  ↳ QDP
                                                                                    ↳ Rewriting
                                                                                      ↳ QDP
                                                                                        ↳ Rewriting
                                                                                          ↳ QDP
                                                                                            ↳ UsableRulesProof
                                                                                              ↳ QDP
                                                                                                ↳ QReductionProof
                                                                                                  ↳ QDP
                                                                                                    ↳ Rewriting
                                                                                                      ↳ QDP
                                                                                                        ↳ Rewriting
                                                                                                          ↳ QDP
                                                                                                            ↳ Rewriting
                                                                                                              ↳ QDP
                                                                                                                ↳ Rewriting
                                                                                                                  ↳ QDP
                                                                                                                    ↳ Rewriting
                                                                                                                      ↳ QDP
                                                                                                                        ↳ Rewriting
                                                                                                                          ↳ QDP
                                                                                                                            ↳ DependencyGraphProof
                                                                                                                              ↳ QDP
                                                                                                                                ↳ Rewriting
                                                                                                                                  ↳ QDP
                                                                                                                                    ↳ Rewriting
                                                                                                                                      ↳ QDP
                                                                                                                                        ↳ DependencyGraphProof
                                                                                                                                          ↳ QDP
                                                                                                                                            ↳ Rewriting
                                                                                                                                              ↳ QDP
                                                                                                                                                ↳ Rewriting
                                                                                                                                                  ↳ QDP
                                                                                                                                                    ↳ Rewriting
                                                                                                                                                      ↳ QDP
                                                                                                                                                        ↳ Rewriting
                                                                                                                                                          ↳ QDP
                                                                                                                                                            ↳ Rewriting
                                                                                                                                                              ↳ QDP
                                                                                                                                                                ↳ Rewriting
                                                                                                                                                                  ↳ QDP
                                                                                                                                                                    ↳ Rewriting
                                                                                                                                                                      ↳ QDP
                                                                                                                                                                        ↳ UsableRulesProof
                                                                                                                                                                          ↳ QDP
                                                                                                                                                                            ↳ QReductionProof
                                                                                                                                                                              ↳ QDP
                                                                                                                                                                                ↳ Rewriting
                                                                                                                                                                                  ↳ QDP
                                                                                                                                                                                    ↳ Rewriting
                                                                                                                                                                                      ↳ QDP
                                                                                                                                                                                        ↳ Rewriting
                                                                                                                                                                                          ↳ QDP
                                                                                                                                                                                            ↳ Rewriting
                                                                                                                                                                                              ↳ QDP
                                                                                                                                                                                                ↳ Rewriting
                                                                                                                                                                                                  ↳ QDP
                                                                                                                                                                                                    ↳ Rewriting
                                                                                                                                                                                                      ↳ QDP
                                                                                                                                                                                                        ↳ Rewriting
                                                                                                                                                                                                          ↳ QDP
                                                                                                                                                                                                            ↳ Rewriting
                                                                                                                                                                                                              ↳ QDP
                                                                                                                                                                                                                ↳ Rewriting
                                                                                                                                                                                                                  ↳ QDP
                                                                                                                                                                                                                    ↳ DependencyGraphProof
                                                                                                                                                                                                                      ↳ QDP
                                                                                                                                                                                                                        ↳ Rewriting
                                                                                                                                                                                                                          ↳ QDP
                                                                                                                                                                                                                            ↳ Rewriting
                                                                                                                                                                                                                              ↳ QDP
                                                                                                                                                                                                                                ↳ Rewriting
                                                                                                                                                                                                                                  ↳ QDP
                                                                                                                                                                                                                                    ↳ Rewriting
                                                                                                                                                                                                                                      ↳ QDP
                                                                                                                                                                                                                                        ↳ Rewriting
                                                                                                                                                                                                                                          ↳ QDP
                                                                                                                                                                                                                                            ↳ DependencyGraphProof
                                                                                                                                                                                                                                              ↳ QDP
                                                                                                                                                                                                                                                ↳ QDPOrderProof
                                                                                                                                                                                                                                                  ↳ QDP
                                                                                                                                                                                                                                                    ↳ DependencyGraphProof
                                                                                                                                                                                                                                                      ↳ AND
                                                                                                                                                                                                                                                        ↳ QDP
                                                                                                                                                                                                                                                        ↳ QDP
                                                                                                                                                                                                                                                        ↳ QDP
                                                                                                                                                                                                                                                          ↳ UsableRulesProof
                                                                                                                                                                                                                                                            ↳ QDP
                                                                                                                                                                                                                                                              ↳ QReductionProof
                                                                                                                                                                                                                                                                ↳ 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_mkVBalBranch3MkVBalBranch11(zzz2033, zzz2034, zzz2035, zzz2036, zzz2037, zzz2038, zzz2039, zzz2040, zzz2041, zzz2042, zzz2043, Succ(zzz20440), Succ(zzz20450), bb) → new_mkVBalBranch3MkVBalBranch11(zzz2033, zzz2034, zzz2035, zzz2036, zzz2037, zzz2038, zzz2039, zzz2040, zzz2041, zzz2042, zzz2043, zzz20440, zzz20450, 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
                                    ↳ DependencyGraphProof
                                      ↳ QDP
                                        ↳ Rewriting
                                          ↳ QDP
                                            ↳ Rewriting
                                              ↳ QDP
                                                ↳ Rewriting
                                                  ↳ QDP
                                                    ↳ Rewriting
                                                      ↳ QDP
                                                        ↳ Rewriting
                                                          ↳ QDP
                                                            ↳ Rewriting
                                                              ↳ QDP
                                                                ↳ Rewriting
                                                                  ↳ QDP
                                                                    ↳ Rewriting
                                                                      ↳ QDP
                                                                        ↳ Rewriting
                                                                          ↳ QDP
                                                                            ↳ Rewriting
                                                                              ↳ QDP
                                                                                ↳ Rewriting
                                                                                  ↳ QDP
                                                                                    ↳ Rewriting
                                                                                      ↳ QDP
                                                                                        ↳ Rewriting
                                                                                          ↳ QDP
                                                                                            ↳ UsableRulesProof
                                                                                              ↳ QDP
                                                                                                ↳ QReductionProof
                                                                                                  ↳ QDP
                                                                                                    ↳ Rewriting
                                                                                                      ↳ QDP
                                                                                                        ↳ Rewriting
                                                                                                          ↳ QDP
                                                                                                            ↳ Rewriting
                                                                                                              ↳ QDP
                                                                                                                ↳ Rewriting
                                                                                                                  ↳ QDP
                                                                                                                    ↳ Rewriting
                                                                                                                      ↳ QDP
                                                                                                                        ↳ Rewriting
                                                                                                                          ↳ QDP
                                                                                                                            ↳ DependencyGraphProof
                                                                                                                              ↳ QDP
                                                                                                                                ↳ Rewriting
                                                                                                                                  ↳ QDP
                                                                                                                                    ↳ Rewriting
                                                                                                                                      ↳ QDP
                                                                                                                                        ↳ DependencyGraphProof
                                                                                                                                          ↳ QDP
                                                                                                                                            ↳ Rewriting
                                                                                                                                              ↳ QDP
                                                                                                                                                ↳ Rewriting
                                                                                                                                                  ↳ QDP
                                                                                                                                                    ↳ Rewriting
                                                                                                                                                      ↳ QDP
                                                                                                                                                        ↳ Rewriting
                                                                                                                                                          ↳ QDP
                                                                                                                                                            ↳ Rewriting
                                                                                                                                                              ↳ QDP
                                                                                                                                                                ↳ Rewriting
                                                                                                                                                                  ↳ QDP
                                                                                                                                                                    ↳ Rewriting
                                                                                                                                                                      ↳ QDP
                                                                                                                                                                        ↳ UsableRulesProof
                                                                                                                                                                          ↳ QDP
                                                                                                                                                                            ↳ QReductionProof
                                                                                                                                                                              ↳ QDP
                                                                                                                                                                                ↳ Rewriting
                                                                                                                                                                                  ↳ QDP
                                                                                                                                                                                    ↳ Rewriting
                                                                                                                                                                                      ↳ QDP
                                                                                                                                                                                        ↳ Rewriting
                                                                                                                                                                                          ↳ QDP
                                                                                                                                                                                            ↳ Rewriting
                                                                                                                                                                                              ↳ QDP
                                                                                                                                                                                                ↳ Rewriting
                                                                                                                                                                                                  ↳ QDP
                                                                                                                                                                                                    ↳ Rewriting
                                                                                                                                                                                                      ↳ QDP
                                                                                                                                                                                                        ↳ Rewriting
                                                                                                                                                                                                          ↳ QDP
                                                                                                                                                                                                            ↳ Rewriting
                                                                                                                                                                                                              ↳ QDP
                                                                                                                                                                                                                ↳ Rewriting
                                                                                                                                                                                                                  ↳ QDP
                                                                                                                                                                                                                    ↳ DependencyGraphProof
                                                                                                                                                                                                                      ↳ QDP
                                                                                                                                                                                                                        ↳ Rewriting
                                                                                                                                                                                                                          ↳ QDP
                                                                                                                                                                                                                            ↳ Rewriting
                                                                                                                                                                                                                              ↳ QDP
                                                                                                                                                                                                                                ↳ Rewriting
                                                                                                                                                                                                                                  ↳ QDP
                                                                                                                                                                                                                                    ↳ Rewriting
                                                                                                                                                                                                                                      ↳ QDP
                                                                                                                                                                                                                                        ↳ Rewriting
                                                                                                                                                                                                                                          ↳ QDP
                                                                                                                                                                                                                                            ↳ DependencyGraphProof
                                                                                                                                                                                                                                              ↳ QDP
                                                                                                                                                                                                                                                ↳ QDPOrderProof
                                                                                                                                                                                                                                                  ↳ QDP
                                                                                                                                                                                                                                                    ↳ DependencyGraphProof
                                                                                                                                                                                                                                                      ↳ AND
                                                                                                                                                                                                                                                        ↳ QDP
                                                                                                                                                                                                                                                        ↳ QDP
                                                                                                                                                                                                                                                        ↳ QDP
                                                                                                                                                                                                                                                        ↳ QDP
                                                                                                                                                                                                                                                          ↳ UsableRulesProof
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP

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

new_mkVBalBranch3MkVBalBranch20(zzz929, zzz930, zzz931, zzz932, zzz933, zzz934, zzz935, zzz936, zzz937, zzz938, zzz939, Succ(zzz9400), Succ(zzz9410), ba) → new_mkVBalBranch3MkVBalBranch20(zzz929, zzz930, zzz931, zzz932, zzz933, zzz934, zzz935, zzz936, zzz937, zzz938, zzz939, zzz9400, zzz9410, ba)

The TRS R consists of the following rules:

new_primPlusNat1(Zero) → Zero
new_primPlusNat1(Succ(zzz62000)) → Succ(Succ(new_primPlusNat1(zzz62000)))
new_primPlusNat3(zzz90, Succ(zzz910)) → Succ(Succ(new_primPlusNat2(zzz90, zzz910)))
new_primPlusNat3(zzz90, Zero) → Succ(zzz90)
new_primPlusNat2(Succ(zzz900), Succ(zzz9100)) → Succ(Succ(new_primPlusNat2(zzz900, zzz9100)))
new_primPlusNat2(Zero, Succ(zzz9100)) → Succ(zzz9100)
new_primPlusNat2(Zero, Zero) → Zero
new_primPlusNat2(Succ(zzz900), Zero) → Succ(zzz900)

The set Q consists of the following terms:

new_primPlusNat2(Zero, Succ(x0))
new_primPlusNat3(x0, Succ(x1))
new_primPlusNat2(Succ(x0), Succ(x1))
new_primPlusNat3(x0, Zero)
new_primPlusNat1(Zero)
new_primPlusNat2(Zero, Zero)
new_primPlusNat1(Succ(x0))
new_primPlusNat2(Succ(x0), Zero)

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

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

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

new_mkVBalBranch3MkVBalBranch20(zzz929, zzz930, zzz931, zzz932, zzz933, zzz934, zzz935, zzz936, zzz937, zzz938, zzz939, Succ(zzz9400), Succ(zzz9410), ba) → new_mkVBalBranch3MkVBalBranch20(zzz929, zzz930, zzz931, zzz932, zzz933, zzz934, zzz935, zzz936, zzz937, zzz938, zzz939, zzz9400, zzz9410, ba)

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

new_primPlusNat2(Zero, Succ(x0))
new_primPlusNat3(x0, Succ(x1))
new_primPlusNat2(Succ(x0), Succ(x1))
new_primPlusNat3(x0, Zero)
new_primPlusNat1(Zero)
new_primPlusNat2(Zero, Zero)
new_primPlusNat1(Succ(x0))
new_primPlusNat2(Succ(x0), Zero)

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

new_primPlusNat2(Zero, Succ(x0))
new_primPlusNat3(x0, Succ(x1))
new_primPlusNat2(Succ(x0), Succ(x1))
new_primPlusNat3(x0, Zero)
new_primPlusNat1(Zero)
new_primPlusNat2(Zero, Zero)
new_primPlusNat1(Succ(x0))
new_primPlusNat2(Succ(x0), 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
                                    ↳ DependencyGraphProof
                                      ↳ QDP
                                        ↳ Rewriting
                                          ↳ QDP
                                            ↳ Rewriting
                                              ↳ QDP
                                                ↳ Rewriting
                                                  ↳ QDP
                                                    ↳ Rewriting
                                                      ↳ QDP
                                                        ↳ Rewriting
                                                          ↳ QDP
                                                            ↳ Rewriting
                                                              ↳ QDP
                                                                ↳ Rewriting
                                                                  ↳ QDP
                                                                    ↳ Rewriting
                                                                      ↳ QDP
                                                                        ↳ Rewriting
                                                                          ↳ QDP
                                                                            ↳ Rewriting
                                                                              ↳ QDP
                                                                                ↳ Rewriting
                                                                                  ↳ QDP
                                                                                    ↳ Rewriting
                                                                                      ↳ QDP
                                                                                        ↳ Rewriting
                                                                                          ↳ QDP
                                                                                            ↳ UsableRulesProof
                                                                                              ↳ QDP
                                                                                                ↳ QReductionProof
                                                                                                  ↳ QDP
                                                                                                    ↳ Rewriting
                                                                                                      ↳ QDP
                                                                                                        ↳ Rewriting
                                                                                                          ↳ QDP
                                                                                                            ↳ Rewriting
                                                                                                              ↳ QDP
                                                                                                                ↳ Rewriting
                                                                                                                  ↳ QDP
                                                                                                                    ↳ Rewriting
                                                                                                                      ↳ QDP
                                                                                                                        ↳ Rewriting
                                                                                                                          ↳ QDP
                                                                                                                            ↳ DependencyGraphProof
                                                                                                                              ↳ QDP
                                                                                                                                ↳ Rewriting
                                                                                                                                  ↳ QDP
                                                                                                                                    ↳ Rewriting
                                                                                                                                      ↳ QDP
                                                                                                                                        ↳ DependencyGraphProof
                                                                                                                                          ↳ QDP
                                                                                                                                            ↳ Rewriting
                                                                                                                                              ↳ QDP
                                                                                                                                                ↳ Rewriting
                                                                                                                                                  ↳ QDP
                                                                                                                                                    ↳ Rewriting
                                                                                                                                                      ↳ QDP
                                                                                                                                                        ↳ Rewriting
                                                                                                                                                          ↳ QDP
                                                                                                                                                            ↳ Rewriting
                                                                                                                                                              ↳ QDP
                                                                                                                                                                ↳ Rewriting
                                                                                                                                                                  ↳ QDP
                                                                                                                                                                    ↳ Rewriting
                                                                                                                                                                      ↳ QDP
                                                                                                                                                                        ↳ UsableRulesProof
                                                                                                                                                                          ↳ QDP
                                                                                                                                                                            ↳ QReductionProof
                                                                                                                                                                              ↳ QDP
                                                                                                                                                                                ↳ Rewriting
                                                                                                                                                                                  ↳ QDP
                                                                                                                                                                                    ↳ Rewriting
                                                                                                                                                                                      ↳ QDP
                                                                                                                                                                                        ↳ Rewriting
                                                                                                                                                                                          ↳ QDP
                                                                                                                                                                                            ↳ Rewriting
                                                                                                                                                                                              ↳ QDP
                                                                                                                                                                                                ↳ Rewriting
                                                                                                                                                                                                  ↳ QDP
                                                                                                                                                                                                    ↳ Rewriting
                                                                                                                                                                                                      ↳ QDP
                                                                                                                                                                                                        ↳ Rewriting
                                                                                                                                                                                                          ↳ QDP
                                                                                                                                                                                                            ↳ Rewriting
                                                                                                                                                                                                              ↳ QDP
                                                                                                                                                                                                                ↳ Rewriting
                                                                                                                                                                                                                  ↳ QDP
                                                                                                                                                                                                                    ↳ DependencyGraphProof
                                                                                                                                                                                                                      ↳ QDP
                                                                                                                                                                                                                        ↳ Rewriting
                                                                                                                                                                                                                          ↳ QDP
                                                                                                                                                                                                                            ↳ Rewriting
                                                                                                                                                                                                                              ↳ QDP
                                                                                                                                                                                                                                ↳ Rewriting
                                                                                                                                                                                                                                  ↳ QDP
                                                                                                                                                                                                                                    ↳ Rewriting
                                                                                                                                                                                                                                      ↳ QDP
                                                                                                                                                                                                                                        ↳ Rewriting
                                                                                                                                                                                                                                          ↳ QDP
                                                                                                                                                                                                                                            ↳ DependencyGraphProof
                                                                                                                                                                                                                                              ↳ QDP
                                                                                                                                                                                                                                                ↳ QDPOrderProof
                                                                                                                                                                                                                                                  ↳ QDP
                                                                                                                                                                                                                                                    ↳ DependencyGraphProof
                                                                                                                                                                                                                                                      ↳ AND
                                                                                                                                                                                                                                                        ↳ QDP
                                                                                                                                                                                                                                                        ↳ QDP
                                                                                                                                                                                                                                                        ↳ QDP
                                                                                                                                                                                                                                                        ↳ QDP
                                                                                                                                                                                                                                                          ↳ UsableRulesProof
                                                                                                                                                                                                                                                            ↳ QDP
                                                                                                                                                                                                                                                              ↳ QReductionProof
                                                                                                                                                                                                                                                                ↳ QDP
                                                                                                                                                                                                                                                                  ↳ QDPSizeChangeProof
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP

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

new_mkVBalBranch3MkVBalBranch20(zzz929, zzz930, zzz931, zzz932, zzz933, zzz934, zzz935, zzz936, zzz937, zzz938, zzz939, Succ(zzz9400), Succ(zzz9410), ba) → new_mkVBalBranch3MkVBalBranch20(zzz929, zzz930, zzz931, zzz932, zzz933, zzz934, zzz935, zzz936, zzz937, zzz938, zzz939, zzz9400, zzz9410, 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
                                    ↳ DependencyGraphProof
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP

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

new_splitGT20(zzz76, zzz77, zzz78, zzz79, ba) → new_splitGT0(zzz78, ba)
new_splitGT0(Branch(GT, zzz8861, zzz8862, zzz8863, zzz8864), h) → new_splitGT20(zzz8861, zzz8862, zzz8863, zzz8864, h)
new_splitGT21(zzz76, zzz77, zzz78, zzz79, ba) → new_splitGT0(zzz78, ba)
new_splitGT2(zzz883, zzz884, zzz885, Branch(LT, zzz8861, zzz8862, zzz8863, zzz8864), h) → new_splitGT2(zzz8861, zzz8862, zzz8863, zzz8864, h)
new_splitGT2(zzz883, zzz884, zzz885, Branch(GT, zzz8861, zzz8862, zzz8863, zzz8864), h) → new_splitGT20(zzz8861, zzz8862, zzz8863, zzz8864, h)
new_splitGT0(Branch(LT, zzz8861, zzz8862, zzz8863, zzz8864), h) → new_splitGT2(zzz8861, zzz8862, zzz8863, zzz8864, h)

R is empty.
Q is empty.
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
                                        ↳ QDPSizeChangeProof
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP

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

new_splitGT20(zzz76, zzz77, zzz78, zzz79, ba) → new_splitGT0(zzz78, ba)
new_splitGT0(Branch(GT, zzz8861, zzz8862, zzz8863, zzz8864), h) → new_splitGT20(zzz8861, zzz8862, zzz8863, zzz8864, h)
new_splitGT2(zzz883, zzz884, zzz885, Branch(LT, zzz8861, zzz8862, zzz8863, zzz8864), h) → new_splitGT2(zzz8861, zzz8862, zzz8863, zzz8864, h)
new_splitGT2(zzz883, zzz884, zzz885, Branch(GT, zzz8861, zzz8862, zzz8863, zzz8864), h) → new_splitGT20(zzz8861, zzz8862, zzz8863, zzz8864, h)
new_splitGT0(Branch(LT, zzz8861, zzz8862, zzz8863, zzz8864), h) → new_splitGT2(zzz8861, zzz8862, zzz8863, zzz8864, 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
                                    ↳ QDPSizeChangeProof
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP

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

new_splitLT2(zzz854, zzz855, Branch(EQ, zzz8561, zzz8562, zzz8563, zzz8564), zzz857, h) → new_splitLT2(zzz8561, zzz8562, zzz8563, zzz8564, h)
new_splitLT20(zzz869, zzz870, zzz871, zzz872, ba) → new_splitLT(zzz871, ba)
new_splitLT(Branch(EQ, zzz8561, zzz8562, zzz8563, zzz8564), h) → new_splitLT2(zzz8561, zzz8562, zzz8563, zzz8564, h)
new_splitLT2(zzz854, zzz855, Branch(GT, zzz8561, zzz8562, zzz8563, zzz8564), zzz857, h) → new_splitLT20(zzz8561, zzz8562, zzz8563, zzz8564, h)
new_splitLT(Branch(GT, zzz8561, zzz8562, zzz8563, zzz8564), h) → new_splitLT20(zzz8561, zzz8562, zzz8563, zzz8564, 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
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP

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

new_addToFM_C0(Branch(GT, zzz341, zzz342, zzz343, zzz344), zzz31, h) → new_addToFM_C0(zzz343, zzz31, h)
new_addToFM_C0(Branch(LT, zzz341, zzz342, zzz343, zzz344), zzz31, h) → new_addToFM_C0(zzz344, zzz31, 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
                                    ↳ DependencyGraphProof
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP

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

new_mkVBalBranch3MkVBalBranch225(zzz498, zzz499, zzz500, zzz501, zzz502, zzz503, zzz504, zzz505, zzz506, zzz507, Zero, Zero, bg) → new_mkVBalBranch3MkVBalBranch230(zzz498, zzz499, zzz500, zzz501, zzz502, zzz503, zzz504, zzz505, zzz506, zzz507, bg)
new_mkVBalBranch3MkVBalBranch215(zzz340, zzz341, Neg(zzz3420), zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, Zero, h) → new_mkVBalBranch3MkVBalBranch221(zzz340, zzz341, zzz3420, zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, h)
new_mkVBalBranch3MkVBalBranch18(zzz340, zzz341, zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, Succ(zzz1480), h) → new_mkVBalBranch3MkVBalBranch115(zzz340, zzz341, Zero, zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, Succ(zzz1480), Succ(zzz51200), h)
new_mkVBalBranch3MkVBalBranch231(zzz340, zzz341, zzz342000, zzz343, zzz344, zzz510, zzz511, zzz513, zzz514, zzz31, h) → new_mkVBalBranch3MkVBalBranch118(zzz340, zzz341, Succ(zzz342000), zzz343, zzz344, zzz510, zzz511, zzz513, zzz514, zzz31, new_primMulNat1(Succ(zzz342000)), h)
new_mkVBalBranch3MkVBalBranch215(zzz340, zzz341, Pos(Succ(Succ(zzz342000))), zzz343, zzz344, zzz510, zzz511, Succ(zzz512000), zzz513, zzz514, zzz31, Succ(Succ(zzz6600)), h) → new_mkVBalBranch3MkVBalBranch216(zzz340, zzz341, Succ(zzz342000), zzz343, zzz344, zzz510, zzz511, zzz512000, zzz513, zzz514, zzz31, Succ(Succ(new_primPlusNat2(zzz6600, zzz512000))), zzz342000, h)
new_mkVBalBranch0(zzz31, Branch(zzz510, zzz511, Neg(Zero), zzz513, zzz514), Branch(zzz340, zzz341, Pos(Succ(zzz34200)), zzz343, zzz344), h) → new_mkVBalBranch0(zzz31, Branch(zzz510, zzz511, Neg(Zero), zzz513, zzz514), zzz343, h)
new_mkVBalBranch3MkVBalBranch223(zzz340, zzz341, Neg(Succ(Succ(Succ(zzz3420000)))), zzz343, zzz344, zzz510, zzz511, Zero, zzz513, zzz514, zzz31, Succ(Succ(zzz6700)), h) → new_mkVBalBranch3MkVBalBranch225(zzz340, zzz341, Succ(Succ(zzz3420000)), zzz343, zzz344, zzz510, zzz511, zzz513, zzz514, zzz31, Succ(zzz3420000), Succ(zzz6700), h)
new_mkVBalBranch3MkVBalBranch220(zzz340, zzz341, zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, h) → new_mkVBalBranch0(zzz31, zzz514, Branch(zzz340, zzz341, Pos(Zero), zzz343, zzz344), h)
new_mkVBalBranch3MkVBalBranch120(zzz2050, zzz2051, zzz2052, zzz2053, zzz2054, zzz2055, zzz2056, zzz2057, zzz2058, zzz2059, zzz2060, Zero, Succ(zzz20620), be) → new_mkVBalBranch0(zzz2060, zzz2059, Branch(zzz2050, zzz2051, Neg(Succ(zzz2052)), zzz2053, zzz2054), be)
new_mkVBalBranch3MkVBalBranch121(zzz473, zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, zzz481, zzz482, Succ(zzz7390), bh) → new_mkVBalBranch3MkVBalBranch115(zzz473, zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, Zero, zzz480, zzz481, zzz482, Succ(zzz7390), Succ(Zero), bh)
new_mkVBalBranch3MkVBalBranch228(zzz340, zzz341, zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, h) → new_mkVBalBranch0(zzz31, Branch(zzz510, zzz511, Neg(Succ(zzz51200)), zzz513, zzz514), zzz343, h)
new_mkVBalBranch0(zzz31, Branch(zzz510, zzz511, Pos(Zero), zzz513, zzz514), Branch(zzz340, zzz341, Pos(Succ(zzz34200)), zzz343, zzz344), h) → new_mkVBalBranch0(zzz31, Branch(zzz510, zzz511, Pos(Zero), zzz513, zzz514), zzz343, h)
new_mkVBalBranch3MkVBalBranch223(zzz340, zzz341, Neg(Succ(Succ(Zero))), zzz343, zzz344, zzz510, zzz511, Succ(zzz512000), zzz513, zzz514, zzz31, Succ(Succ(zzz6700)), h) → new_mkVBalBranch3MkVBalBranch224(zzz340, zzz341, Succ(Zero), zzz343, zzz344, zzz510, zzz511, zzz512000, zzz513, zzz514, zzz31, Zero, Succ(Succ(new_primPlusNat2(zzz6700, zzz512000))), h)
new_mkVBalBranch3MkVBalBranch215(zzz340, zzz341, Pos(Succ(Zero)), zzz343, zzz344, zzz510, zzz511, Zero, zzz513, zzz514, zzz31, Zero, h) → new_mkVBalBranch3MkVBalBranch219(zzz340, zzz341, zzz343, zzz344, zzz510, zzz511, Zero, zzz513, zzz514, zzz31, h)
new_mkVBalBranch3MkVBalBranch223(zzz340, zzz341, Neg(Succ(Succ(Zero))), zzz343, zzz344, zzz510, zzz511, Zero, zzz513, zzz514, zzz31, Succ(Zero), h) → new_mkVBalBranch3MkVBalBranch225(zzz340, zzz341, Succ(Zero), zzz343, zzz344, zzz510, zzz511, zzz513, zzz514, zzz31, Zero, Zero, h)
new_mkVBalBranch3MkVBalBranch224(zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, zzz1125, zzz1126, zzz1127, zzz1128, zzz1129, Succ(zzz11300), Succ(zzz11310), bd) → new_mkVBalBranch3MkVBalBranch224(zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, zzz1125, zzz1126, zzz1127, zzz1128, zzz1129, zzz11300, zzz11310, bd)
new_mkVBalBranch3MkVBalBranch119(zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, zzz1125, zzz1126, zzz1127, zzz1128, zzz1129, Zero, bd) → new_mkVBalBranch3MkVBalBranch120(zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, zzz1125, Succ(zzz1126), zzz1127, zzz1128, zzz1129, Succ(Succ(zzz1126)), Zero, bd)
new_mkVBalBranch3MkVBalBranch118(zzz498, zzz499, zzz500, zzz501, zzz502, zzz503, zzz504, zzz505, zzz506, zzz507, Zero, bg) → new_mkVBalBranch3MkVBalBranch120(zzz498, zzz499, zzz500, zzz501, zzz502, zzz503, zzz504, Zero, zzz505, zzz506, zzz507, Succ(Zero), Zero, bg)
new_mkVBalBranch3MkVBalBranch217(zzz473, zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, zzz481, zzz482, Zero, Succ(zzz4840), bh) → new_mkVBalBranch0(zzz482, Branch(zzz478, zzz479, Pos(Succ(Zero)), zzz480, zzz481), zzz476, bh)
new_mkVBalBranch3MkVBalBranch215(zzz340, zzz341, Pos(Succ(Succ(zzz342000))), zzz343, zzz344, zzz510, zzz511, Succ(zzz512000), zzz513, zzz514, zzz31, Zero, h) → new_mkVBalBranch3MkVBalBranch216(zzz340, zzz341, Succ(zzz342000), zzz343, zzz344, zzz510, zzz511, zzz512000, zzz513, zzz514, zzz31, zzz512000, zzz342000, h)
new_mkVBalBranch0(zzz31, Branch(zzz510, zzz511, Pos(Succ(zzz51200)), zzz513, zzz514), Branch(zzz340, zzz341, zzz342, zzz343, zzz344), h) → new_mkVBalBranch3MkVBalBranch215(zzz340, zzz341, zzz342, zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, new_primMulNat0(zzz51200), h)
new_mkVBalBranch0(zzz31, Branch(zzz510, zzz511, Neg(Succ(zzz51200)), zzz513, zzz514), Branch(zzz340, zzz341, zzz342, zzz343, zzz344), h) → new_mkVBalBranch3MkVBalBranch223(zzz340, zzz341, zzz342, zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, new_primMulNat0(zzz51200), h)
new_mkVBalBranch3MkVBalBranch114(zzz461, zzz462, zzz463, zzz464, zzz465, zzz466, zzz467, zzz468, zzz469, zzz470, zzz471, bb) → new_mkVBalBranch3MkVBalBranch110(zzz461, zzz462, zzz463, zzz464, zzz465, zzz466, zzz467, zzz468, zzz469, zzz470, zzz471, new_primMulNat1(zzz463), bb)
new_mkVBalBranch3MkVBalBranch110(zzz461, zzz462, zzz463, zzz464, zzz465, zzz466, zzz467, zzz468, zzz469, zzz470, zzz471, Succ(zzz5800), bb) → new_mkVBalBranch3MkVBalBranch115(zzz461, zzz462, zzz463, zzz464, zzz465, zzz466, zzz467, Succ(zzz468), zzz469, zzz470, zzz471, Succ(zzz5800), Succ(Succ(zzz468)), bb)
new_mkVBalBranch3MkVBalBranch227(zzz486, zzz487, zzz488, zzz489, zzz490, zzz491, zzz492, zzz493, zzz494, zzz495, zzz496, bf) → new_mkVBalBranch0(zzz496, Branch(zzz491, zzz492, Neg(Succ(Succ(zzz493))), zzz494, zzz495), zzz489, bf)
new_mkVBalBranch3MkVBalBranch215(zzz340, zzz341, Pos(Zero), zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, Succ(zzz660), h) → new_mkVBalBranch0(zzz31, zzz514, Branch(zzz340, zzz341, Pos(Zero), zzz343, zzz344), h)
new_mkVBalBranch3MkVBalBranch223(zzz340, zzz341, Neg(Zero), zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, Succ(zzz670), h) → new_mkVBalBranch0(zzz31, Branch(zzz510, zzz511, Neg(Succ(zzz51200)), zzz513, zzz514), zzz343, h)
new_mkVBalBranch3MkVBalBranch216(zzz1105, zzz1106, zzz1107, zzz1108, zzz1109, zzz1110, zzz1111, zzz1112, zzz1113, zzz1114, zzz1115, Zero, Succ(zzz11170), ba) → new_mkVBalBranch0(zzz1115, Branch(zzz1110, zzz1111, Pos(Succ(Succ(zzz1112))), zzz1113, zzz1114), zzz1108, ba)
new_mkVBalBranch3MkVBalBranch217(zzz473, zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, zzz481, zzz482, Succ(zzz4830), Zero, bh) → new_mkVBalBranch3MkVBalBranch121(zzz473, zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, zzz481, zzz482, new_primMulNat1(zzz475), bh)
new_mkVBalBranch3MkVBalBranch222(zzz461, zzz462, zzz463, zzz464, zzz465, zzz466, zzz467, zzz468, zzz469, zzz470, zzz471, bb) → new_mkVBalBranch3MkVBalBranch110(zzz461, zzz462, zzz463, zzz464, zzz465, zzz466, zzz467, zzz468, zzz469, zzz470, zzz471, new_primMulNat1(zzz463), bb)
new_mkVBalBranch3MkVBalBranch115(zzz1986, zzz1987, zzz1988, zzz1989, zzz1990, zzz1991, zzz1992, zzz1993, zzz1994, zzz1995, zzz1996, Zero, Succ(zzz19980), bc) → new_mkVBalBranch0(zzz1996, zzz1995, Branch(zzz1986, zzz1987, Pos(Succ(zzz1988)), zzz1989, zzz1990), bc)
new_mkVBalBranch3MkVBalBranch234(zzz340, zzz341, zzz342000, zzz343, zzz344, zzz510, zzz511, zzz513, zzz514, zzz31, h) → new_mkVBalBranch0(zzz31, Branch(zzz510, zzz511, Pos(Succ(Zero)), zzz513, zzz514), zzz343, h)
new_mkVBalBranch3MkVBalBranch221(zzz340, zzz341, Succ(zzz34200), zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, h) → new_mkVBalBranch3MkVBalBranch19(zzz340, zzz341, zzz34200, zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, new_primPlusNat2(new_primMulNat0(zzz34200), Succ(zzz34200)), h)
new_mkVBalBranch3MkVBalBranch232(zzz340, zzz341, zzz342000, zzz343, zzz344, zzz510, zzz511, zzz513, zzz514, zzz31, h) → new_mkVBalBranch3MkVBalBranch118(zzz340, zzz341, Succ(zzz342000), zzz343, zzz344, zzz510, zzz511, zzz513, zzz514, zzz31, new_primMulNat1(Succ(zzz342000)), h)
new_mkVBalBranch3MkVBalBranch223(zzz340, zzz341, Neg(Zero), zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, Zero, h) → new_mkVBalBranch3MkVBalBranch228(zzz340, zzz341, zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, h)
new_mkVBalBranch3MkVBalBranch122(zzz340, zzz341, zzz34200, zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, h) → new_mkVBalBranch0(zzz31, zzz514, Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), h)
new_mkVBalBranch3MkVBalBranch113(zzz461, zzz462, zzz463, zzz464, zzz465, zzz466, zzz467, zzz468, zzz469, zzz470, zzz471, bb) → new_mkVBalBranch3MkVBalBranch110(zzz461, zzz462, zzz463, zzz464, zzz465, zzz466, zzz467, zzz468, zzz469, zzz470, zzz471, new_primMulNat1(zzz463), bb)
new_mkVBalBranch3MkVBalBranch217(zzz473, zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, zzz481, zzz482, Succ(zzz4830), Succ(zzz4840), bh) → new_mkVBalBranch3MkVBalBranch217(zzz473, zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, zzz481, zzz482, zzz4830, zzz4840, bh)
new_mkVBalBranch3MkVBalBranch116(zzz340, zzz341, zzz34200, zzz343, zzz344, zzz510, zzz511, zzz513, zzz514, zzz31, Succ(zzz1200), h) → new_mkVBalBranch0(zzz31, zzz514, Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), h)
new_mkVBalBranch3MkVBalBranch110(zzz461, zzz462, zzz463, zzz464, zzz465, zzz466, zzz467, zzz468, zzz469, zzz470, zzz471, Zero, bb) → new_mkVBalBranch3MkVBalBranch115(zzz461, zzz462, zzz463, zzz464, zzz465, zzz466, zzz467, Succ(zzz468), zzz469, zzz470, zzz471, Zero, Succ(Succ(zzz468)), bb)
new_mkVBalBranch3MkVBalBranch225(zzz498, zzz499, zzz500, zzz501, zzz502, zzz503, zzz504, zzz505, zzz506, zzz507, Zero, Succ(zzz5090), bg) → new_mkVBalBranch0(zzz507, Branch(zzz503, zzz504, Neg(Succ(Zero)), zzz505, zzz506), zzz501, bg)
new_mkVBalBranch3MkVBalBranch223(zzz340, zzz341, Neg(Succ(Succ(Succ(zzz3420000)))), zzz343, zzz344, zzz510, zzz511, Zero, zzz513, zzz514, zzz31, Succ(Zero), h) → new_mkVBalBranch3MkVBalBranch225(zzz340, zzz341, Succ(Succ(zzz3420000)), zzz343, zzz344, zzz510, zzz511, zzz513, zzz514, zzz31, Succ(zzz3420000), Zero, h)
new_mkVBalBranch3MkVBalBranch121(zzz473, zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, zzz481, zzz482, Zero, bh) → new_mkVBalBranch3MkVBalBranch115(zzz473, zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, Zero, zzz480, zzz481, zzz482, Zero, Succ(Zero), bh)
new_mkVBalBranch3MkVBalBranch215(zzz340, zzz341, Pos(Succ(Zero)), zzz343, zzz344, zzz510, zzz511, Succ(zzz512000), zzz513, zzz514, zzz31, Zero, h) → new_mkVBalBranch3MkVBalBranch218(zzz340, zzz341, Zero, zzz343, zzz344, zzz510, zzz511, zzz512000, zzz513, zzz514, zzz31, h)
new_mkVBalBranch3MkVBalBranch223(zzz340, zzz341, Neg(Succ(Zero)), zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, Succ(zzz670), h) → new_mkVBalBranch0(zzz31, Branch(zzz510, zzz511, Neg(Succ(zzz51200)), zzz513, zzz514), zzz343, h)
new_mkVBalBranch3MkVBalBranch218(zzz461, zzz462, zzz463, zzz464, zzz465, zzz466, zzz467, zzz468, zzz469, zzz470, zzz471, bb) → new_mkVBalBranch3MkVBalBranch110(zzz461, zzz462, zzz463, zzz464, zzz465, zzz466, zzz467, zzz468, zzz469, zzz470, zzz471, new_primMulNat1(zzz463), bb)
new_mkVBalBranch3MkVBalBranch223(zzz340, zzz341, Neg(Succ(Zero)), zzz343, zzz344, zzz510, zzz511, Succ(zzz512000), zzz513, zzz514, zzz31, Zero, h) → new_mkVBalBranch3MkVBalBranch227(zzz340, zzz341, Zero, zzz343, zzz344, zzz510, zzz511, zzz512000, zzz513, zzz514, zzz31, h)
new_mkVBalBranch3MkVBalBranch215(zzz340, zzz341, Pos(Succ(Zero)), zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, Succ(zzz660), h) → new_mkVBalBranch3MkVBalBranch18(zzz340, zzz341, zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, new_primMulNat1(Zero), h)
new_mkVBalBranch3MkVBalBranch229(zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, zzz1125, zzz1126, zzz1127, zzz1128, zzz1129, bd) → new_mkVBalBranch3MkVBalBranch119(zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, zzz1125, zzz1126, zzz1127, zzz1128, zzz1129, new_primMulNat1(zzz1121), bd)
new_mkVBalBranch3MkVBalBranch223(zzz340, zzz341, Neg(Succ(Succ(zzz342000))), zzz343, zzz344, zzz510, zzz511, Succ(zzz512000), zzz513, zzz514, zzz31, Zero, h) → new_mkVBalBranch3MkVBalBranch224(zzz340, zzz341, Succ(zzz342000), zzz343, zzz344, zzz510, zzz511, zzz512000, zzz513, zzz514, zzz31, zzz342000, zzz512000, h)
new_mkVBalBranch3MkVBalBranch215(zzz340, zzz341, Pos(Succ(Succ(zzz342000))), zzz343, zzz344, zzz510, zzz511, Zero, zzz513, zzz514, zzz31, Succ(Succ(zzz6600)), h) → new_mkVBalBranch3MkVBalBranch217(zzz340, zzz341, Succ(zzz342000), zzz343, zzz344, zzz510, zzz511, zzz513, zzz514, zzz31, Succ(zzz6600), zzz342000, h)
new_mkVBalBranch3MkVBalBranch226(zzz340, zzz341, zzz3420, zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, h) → new_mkVBalBranch0(zzz31, Branch(zzz510, zzz511, Neg(Succ(zzz51200)), zzz513, zzz514), zzz343, h)
new_mkVBalBranch3MkVBalBranch117(zzz340, zzz341, zzz34200, zzz343, zzz344, zzz510, zzz511, zzz513, zzz514, zzz31, Succ(zzz1240), h) → new_mkVBalBranch0(zzz31, zzz514, Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), h)
new_mkVBalBranch3MkVBalBranch120(zzz2050, zzz2051, zzz2052, zzz2053, zzz2054, zzz2055, zzz2056, zzz2057, zzz2058, zzz2059, zzz2060, Succ(zzz20610), Succ(zzz20620), be) → new_mkVBalBranch3MkVBalBranch120(zzz2050, zzz2051, zzz2052, zzz2053, zzz2054, zzz2055, zzz2056, zzz2057, zzz2058, zzz2059, zzz2060, zzz20610, zzz20620, be)
new_mkVBalBranch3MkVBalBranch217(zzz473, zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, zzz481, zzz482, Zero, Zero, bh) → new_mkVBalBranch3MkVBalBranch233(zzz473, zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, zzz481, zzz482, bh)
new_mkVBalBranch3MkVBalBranch223(zzz340, zzz341, Neg(Succ(Succ(zzz342000))), zzz343, zzz344, zzz510, zzz511, Zero, zzz513, zzz514, zzz31, Zero, h) → new_mkVBalBranch3MkVBalBranch118(zzz340, zzz341, Succ(zzz342000), zzz343, zzz344, zzz510, zzz511, zzz513, zzz514, zzz31, new_primMulNat1(Succ(zzz342000)), h)
new_mkVBalBranch3MkVBalBranch223(zzz340, zzz341, Pos(zzz3420), zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, Succ(zzz670), h) → new_mkVBalBranch0(zzz31, Branch(zzz510, zzz511, Neg(Succ(zzz51200)), zzz513, zzz514), zzz343, h)
new_mkVBalBranch3MkVBalBranch216(zzz1105, zzz1106, zzz1107, zzz1108, zzz1109, zzz1110, zzz1111, zzz1112, zzz1113, zzz1114, zzz1115, Succ(zzz11160), Succ(zzz11170), ba) → new_mkVBalBranch3MkVBalBranch216(zzz1105, zzz1106, zzz1107, zzz1108, zzz1109, zzz1110, zzz1111, zzz1112, zzz1113, zzz1114, zzz1115, zzz11160, zzz11170, ba)
new_mkVBalBranch3MkVBalBranch223(zzz340, zzz341, Neg(Succ(Succ(Succ(zzz3420000)))), zzz343, zzz344, zzz510, zzz511, Succ(zzz512000), zzz513, zzz514, zzz31, Succ(Zero), h) → new_mkVBalBranch3MkVBalBranch224(zzz340, zzz341, Succ(Succ(zzz3420000)), zzz343, zzz344, zzz510, zzz511, zzz512000, zzz513, zzz514, zzz31, Succ(zzz3420000), Succ(zzz512000), h)
new_mkVBalBranch3MkVBalBranch19(zzz340, zzz341, zzz34200, zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, Zero, h) → new_mkVBalBranch3MkVBalBranch122(zzz340, zzz341, zzz34200, zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, h)
new_mkVBalBranch0(zzz31, Branch(zzz510, zzz511, Neg(Zero), zzz513, zzz514), Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), h) → new_mkVBalBranch3MkVBalBranch117(zzz340, zzz341, zzz34200, zzz343, zzz344, zzz510, zzz511, zzz513, zzz514, zzz31, new_primMulNat1(zzz34200), h)
new_mkVBalBranch3MkVBalBranch230(zzz498, zzz499, zzz500, zzz501, zzz502, zzz503, zzz504, zzz505, zzz506, zzz507, bg) → new_mkVBalBranch3MkVBalBranch118(zzz498, zzz499, zzz500, zzz501, zzz502, zzz503, zzz504, zzz505, zzz506, zzz507, new_primMulNat1(zzz500), bg)
new_mkVBalBranch3MkVBalBranch215(zzz340, zzz341, Pos(Succ(Succ(zzz342000))), zzz343, zzz344, zzz510, zzz511, Zero, zzz513, zzz514, zzz31, Zero, h) → new_mkVBalBranch0(zzz31, Branch(zzz510, zzz511, Pos(Succ(Zero)), zzz513, zzz514), zzz343, h)
new_mkVBalBranch3MkVBalBranch225(zzz498, zzz499, zzz500, zzz501, zzz502, zzz503, zzz504, zzz505, zzz506, zzz507, Succ(zzz5080), Zero, bg) → new_mkVBalBranch3MkVBalBranch118(zzz498, zzz499, zzz500, zzz501, zzz502, zzz503, zzz504, zzz505, zzz506, zzz507, new_primMulNat1(zzz500), bg)
new_mkVBalBranch3MkVBalBranch225(zzz498, zzz499, zzz500, zzz501, zzz502, zzz503, zzz504, zzz505, zzz506, zzz507, Succ(zzz5080), Succ(zzz5090), bg) → new_mkVBalBranch3MkVBalBranch225(zzz498, zzz499, zzz500, zzz501, zzz502, zzz503, zzz504, zzz505, zzz506, zzz507, zzz5080, zzz5090, bg)
new_mkVBalBranch3MkVBalBranch19(zzz340, zzz341, zzz34200, zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, Succ(zzz1410), h) → new_mkVBalBranch0(zzz31, zzz514, Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), h)
new_mkVBalBranch3MkVBalBranch112(zzz461, zzz462, zzz463, zzz464, zzz465, zzz466, zzz467, zzz468, zzz469, zzz470, zzz471, bb) → new_mkVBalBranch3MkVBalBranch110(zzz461, zzz462, zzz463, zzz464, zzz465, zzz466, zzz467, zzz468, zzz469, zzz470, zzz471, new_primMulNat1(zzz463), bb)
new_mkVBalBranch3MkVBalBranch223(zzz340, zzz341, Pos(zzz3420), zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, Zero, h) → new_mkVBalBranch3MkVBalBranch226(zzz340, zzz341, zzz3420, zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, h)
new_mkVBalBranch3MkVBalBranch223(zzz340, zzz341, Neg(Succ(Succ(Zero))), zzz343, zzz344, zzz510, zzz511, Succ(zzz512000), zzz513, zzz514, zzz31, Succ(Zero), h) → new_mkVBalBranch3MkVBalBranch224(zzz340, zzz341, Succ(Zero), zzz343, zzz344, zzz510, zzz511, zzz512000, zzz513, zzz514, zzz31, Zero, Succ(zzz512000), h)
new_mkVBalBranch3MkVBalBranch224(zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, zzz1125, zzz1126, zzz1127, zzz1128, zzz1129, Zero, Succ(zzz11310), bd) → new_mkVBalBranch3MkVBalBranch227(zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, zzz1125, zzz1126, zzz1127, zzz1128, zzz1129, bd)
new_mkVBalBranch3MkVBalBranch224(zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, zzz1125, zzz1126, zzz1127, zzz1128, zzz1129, Zero, Zero, bd) → new_mkVBalBranch3MkVBalBranch229(zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, zzz1125, zzz1126, zzz1127, zzz1128, zzz1129, bd)
new_mkVBalBranch3MkVBalBranch224(zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, zzz1125, zzz1126, zzz1127, zzz1128, zzz1129, Succ(zzz11300), Zero, bd) → new_mkVBalBranch3MkVBalBranch119(zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, zzz1125, zzz1126, zzz1127, zzz1128, zzz1129, new_primMulNat1(zzz1121), bd)
new_mkVBalBranch3MkVBalBranch223(zzz340, zzz341, Neg(Succ(Succ(Zero))), zzz343, zzz344, zzz510, zzz511, Zero, zzz513, zzz514, zzz31, Succ(Succ(zzz6700)), h) → new_mkVBalBranch3MkVBalBranch225(zzz340, zzz341, Succ(Zero), zzz343, zzz344, zzz510, zzz511, zzz513, zzz514, zzz31, Zero, Succ(zzz6700), h)
new_mkVBalBranch3MkVBalBranch223(zzz340, zzz341, Neg(Succ(Succ(Succ(zzz3420000)))), zzz343, zzz344, zzz510, zzz511, Succ(zzz512000), zzz513, zzz514, zzz31, Succ(Succ(zzz6700)), h) → new_mkVBalBranch3MkVBalBranch224(zzz340, zzz341, Succ(Succ(zzz3420000)), zzz343, zzz344, zzz510, zzz511, zzz512000, zzz513, zzz514, zzz31, Succ(zzz3420000), Succ(Succ(new_primPlusNat2(zzz6700, zzz512000))), h)
new_mkVBalBranch3MkVBalBranch115(zzz1986, zzz1987, zzz1988, zzz1989, zzz1990, zzz1991, zzz1992, zzz1993, zzz1994, zzz1995, zzz1996, Succ(zzz19970), Succ(zzz19980), bc) → new_mkVBalBranch3MkVBalBranch115(zzz1986, zzz1987, zzz1988, zzz1989, zzz1990, zzz1991, zzz1992, zzz1993, zzz1994, zzz1995, zzz1996, zzz19970, zzz19980, bc)
new_mkVBalBranch3MkVBalBranch215(zzz340, zzz341, Pos(Zero), zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, Zero, h) → new_mkVBalBranch3MkVBalBranch220(zzz340, zzz341, zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, h)
new_mkVBalBranch3MkVBalBranch215(zzz340, zzz341, Neg(Zero), zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, Succ(zzz660), h) → new_mkVBalBranch0(zzz31, zzz514, Branch(zzz340, zzz341, Neg(Zero), zzz343, zzz344), h)
new_mkVBalBranch3MkVBalBranch118(zzz498, zzz499, zzz500, zzz501, zzz502, zzz503, zzz504, zzz505, zzz506, zzz507, Succ(zzz8040), bg) → new_mkVBalBranch3MkVBalBranch120(zzz498, zzz499, zzz500, zzz501, zzz502, zzz503, zzz504, Zero, zzz505, zzz506, zzz507, Succ(Zero), Succ(zzz8040), bg)
new_mkVBalBranch3MkVBalBranch216(zzz1105, zzz1106, zzz1107, zzz1108, zzz1109, zzz1110, zzz1111, zzz1112, zzz1113, zzz1114, zzz1115, Succ(zzz11160), Zero, ba) → new_mkVBalBranch3MkVBalBranch218(zzz1105, zzz1106, zzz1107, zzz1108, zzz1109, zzz1110, zzz1111, zzz1112, zzz1113, zzz1114, zzz1115, ba)
new_mkVBalBranch3MkVBalBranch215(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, Succ(zzz660), h) → new_mkVBalBranch3MkVBalBranch19(zzz340, zzz341, zzz34200, zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, new_primPlusNat2(new_primMulNat0(zzz34200), Succ(zzz34200)), h)
new_mkVBalBranch3MkVBalBranch215(zzz340, zzz341, Pos(Succ(Succ(zzz342000))), zzz343, zzz344, zzz510, zzz511, Succ(zzz512000), zzz513, zzz514, zzz31, Succ(Zero), h) → new_mkVBalBranch3MkVBalBranch216(zzz340, zzz341, Succ(zzz342000), zzz343, zzz344, zzz510, zzz511, zzz512000, zzz513, zzz514, zzz31, Succ(zzz512000), zzz342000, h)
new_mkVBalBranch3MkVBalBranch219(zzz340, zzz341, zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, h) → new_mkVBalBranch3MkVBalBranch18(zzz340, zzz341, zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, new_primMulNat1(Zero), h)
new_mkVBalBranch3MkVBalBranch221(zzz340, zzz341, Zero, zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, h) → new_mkVBalBranch0(zzz31, zzz514, Branch(zzz340, zzz341, Neg(Zero), zzz343, zzz344), h)
new_mkVBalBranch3MkVBalBranch216(zzz1105, zzz1106, zzz1107, zzz1108, zzz1109, zzz1110, zzz1111, zzz1112, zzz1113, zzz1114, zzz1115, Zero, Zero, ba) → new_mkVBalBranch3MkVBalBranch222(zzz1105, zzz1106, zzz1107, zzz1108, zzz1109, zzz1110, zzz1111, zzz1112, zzz1113, zzz1114, zzz1115, ba)
new_mkVBalBranch3MkVBalBranch233(zzz473, zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, zzz481, zzz482, bh) → new_mkVBalBranch3MkVBalBranch121(zzz473, zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, zzz481, zzz482, new_primMulNat1(zzz475), bh)
new_mkVBalBranch3MkVBalBranch215(zzz340, zzz341, Pos(Succ(Succ(zzz342000))), zzz343, zzz344, zzz510, zzz511, Zero, zzz513, zzz514, zzz31, Succ(Zero), h) → new_mkVBalBranch3MkVBalBranch217(zzz340, zzz341, Succ(zzz342000), zzz343, zzz344, zzz510, zzz511, zzz513, zzz514, zzz31, Zero, zzz342000, h)
new_mkVBalBranch3MkVBalBranch111(zzz461, zzz462, zzz463, zzz464, zzz465, zzz466, zzz467, zzz468, zzz469, zzz470, zzz471, bb) → new_mkVBalBranch3MkVBalBranch110(zzz461, zzz462, zzz463, zzz464, zzz465, zzz466, zzz467, zzz468, zzz469, zzz470, zzz471, new_primMulNat1(zzz463), bb)
new_mkVBalBranch0(zzz31, Branch(zzz510, zzz511, Pos(Zero), zzz513, zzz514), Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), h) → new_mkVBalBranch3MkVBalBranch116(zzz340, zzz341, zzz34200, zzz343, zzz344, zzz510, zzz511, zzz513, zzz514, zzz31, new_primMulNat1(zzz34200), h)
new_mkVBalBranch3MkVBalBranch119(zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, zzz1125, zzz1126, zzz1127, zzz1128, zzz1129, Succ(zzz12130), bd) → new_mkVBalBranch3MkVBalBranch120(zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, zzz1125, Succ(zzz1126), zzz1127, zzz1128, zzz1129, Succ(Succ(zzz1126)), Succ(zzz12130), bd)
new_mkVBalBranch3MkVBalBranch18(zzz340, zzz341, zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, Zero, h) → new_mkVBalBranch3MkVBalBranch115(zzz340, zzz341, Zero, zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, Zero, Succ(zzz51200), h)
new_mkVBalBranch3MkVBalBranch223(zzz340, zzz341, Neg(Succ(Zero)), zzz343, zzz344, zzz510, zzz511, Zero, zzz513, zzz514, zzz31, Zero, h) → new_mkVBalBranch3MkVBalBranch118(zzz340, zzz341, Zero, zzz343, zzz344, zzz510, zzz511, zzz513, zzz514, zzz31, new_primMulNat1(Zero), h)

The TRS R consists of the following rules:

new_primPlusNat1(Zero) → Zero
new_primMulNat0(zzz6200) → new_primPlusNat3(Succ(new_primPlusNat3(new_primPlusNat1(zzz6200), zzz6200)), Succ(zzz6200))
new_primPlusNat2(Succ(zzz900), Succ(zzz9100)) → Succ(Succ(new_primPlusNat2(zzz900, zzz9100)))
new_primPlusNat3(zzz90, Succ(zzz910)) → Succ(Succ(new_primPlusNat2(zzz90, zzz910)))
new_primPlusNat3(zzz90, Zero) → Succ(zzz90)
new_primMulNat1(zzz34200) → new_primPlusNat2(new_primMulNat0(zzz34200), Succ(zzz34200))
new_primPlusNat2(Zero, Zero) → Zero
new_primPlusNat1(Succ(zzz62000)) → Succ(Succ(new_primPlusNat1(zzz62000)))
new_primPlusNat2(Succ(zzz900), Zero) → Succ(zzz900)
new_primPlusNat2(Zero, Succ(zzz9100)) → Succ(zzz9100)

The set Q consists of the following terms:

new_primPlusNat2(Zero, Succ(x0))
new_primMulNat1(x0)
new_primMulNat0(x0)
new_primPlusNat3(x0, Succ(x1))
new_primPlusNat2(Succ(x0), Succ(x1))
new_primPlusNat3(x0, Zero)
new_primPlusNat1(Zero)
new_primPlusNat2(Zero, Zero)
new_primPlusNat1(Succ(x0))
new_primPlusNat2(Succ(x0), Zero)

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

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

new_mkVBalBranch3MkVBalBranch215(zzz340, zzz341, Neg(zzz3420), zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, Zero, h) → new_mkVBalBranch3MkVBalBranch221(zzz340, zzz341, zzz3420, zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, h)
new_mkVBalBranch3MkVBalBranch225(zzz498, zzz499, zzz500, zzz501, zzz502, zzz503, zzz504, zzz505, zzz506, zzz507, Zero, Zero, bg) → new_mkVBalBranch3MkVBalBranch230(zzz498, zzz499, zzz500, zzz501, zzz502, zzz503, zzz504, zzz505, zzz506, zzz507, bg)
new_mkVBalBranch3MkVBalBranch18(zzz340, zzz341, zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, Succ(zzz1480), h) → new_mkVBalBranch3MkVBalBranch115(zzz340, zzz341, Zero, zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, Succ(zzz1480), Succ(zzz51200), h)
new_mkVBalBranch0(zzz31, Branch(zzz510, zzz511, Neg(Zero), zzz513, zzz514), Branch(zzz340, zzz341, Pos(Succ(zzz34200)), zzz343, zzz344), h) → new_mkVBalBranch0(zzz31, Branch(zzz510, zzz511, Neg(Zero), zzz513, zzz514), zzz343, h)
new_mkVBalBranch3MkVBalBranch215(zzz340, zzz341, Pos(Succ(Succ(zzz342000))), zzz343, zzz344, zzz510, zzz511, Succ(zzz512000), zzz513, zzz514, zzz31, Succ(Succ(zzz6600)), h) → new_mkVBalBranch3MkVBalBranch216(zzz340, zzz341, Succ(zzz342000), zzz343, zzz344, zzz510, zzz511, zzz512000, zzz513, zzz514, zzz31, Succ(Succ(new_primPlusNat2(zzz6600, zzz512000))), zzz342000, h)
new_mkVBalBranch3MkVBalBranch223(zzz340, zzz341, Neg(Succ(Succ(Succ(zzz3420000)))), zzz343, zzz344, zzz510, zzz511, Zero, zzz513, zzz514, zzz31, Succ(Succ(zzz6700)), h) → new_mkVBalBranch3MkVBalBranch225(zzz340, zzz341, Succ(Succ(zzz3420000)), zzz343, zzz344, zzz510, zzz511, zzz513, zzz514, zzz31, Succ(zzz3420000), Succ(zzz6700), h)
new_mkVBalBranch3MkVBalBranch220(zzz340, zzz341, zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, h) → new_mkVBalBranch0(zzz31, zzz514, Branch(zzz340, zzz341, Pos(Zero), zzz343, zzz344), h)
new_mkVBalBranch3MkVBalBranch120(zzz2050, zzz2051, zzz2052, zzz2053, zzz2054, zzz2055, zzz2056, zzz2057, zzz2058, zzz2059, zzz2060, Zero, Succ(zzz20620), be) → new_mkVBalBranch0(zzz2060, zzz2059, Branch(zzz2050, zzz2051, Neg(Succ(zzz2052)), zzz2053, zzz2054), be)
new_mkVBalBranch3MkVBalBranch121(zzz473, zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, zzz481, zzz482, Succ(zzz7390), bh) → new_mkVBalBranch3MkVBalBranch115(zzz473, zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, Zero, zzz480, zzz481, zzz482, Succ(zzz7390), Succ(Zero), bh)
new_mkVBalBranch0(zzz31, Branch(zzz510, zzz511, Pos(Zero), zzz513, zzz514), Branch(zzz340, zzz341, Pos(Succ(zzz34200)), zzz343, zzz344), h) → new_mkVBalBranch0(zzz31, Branch(zzz510, zzz511, Pos(Zero), zzz513, zzz514), zzz343, h)
new_mkVBalBranch3MkVBalBranch228(zzz340, zzz341, zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, h) → new_mkVBalBranch0(zzz31, Branch(zzz510, zzz511, Neg(Succ(zzz51200)), zzz513, zzz514), zzz343, h)
new_mkVBalBranch3MkVBalBranch215(zzz340, zzz341, Pos(Succ(Zero)), zzz343, zzz344, zzz510, zzz511, Zero, zzz513, zzz514, zzz31, Zero, h) → new_mkVBalBranch3MkVBalBranch219(zzz340, zzz341, zzz343, zzz344, zzz510, zzz511, Zero, zzz513, zzz514, zzz31, h)
new_mkVBalBranch3MkVBalBranch223(zzz340, zzz341, Neg(Succ(Succ(Zero))), zzz343, zzz344, zzz510, zzz511, Succ(zzz512000), zzz513, zzz514, zzz31, Succ(Succ(zzz6700)), h) → new_mkVBalBranch3MkVBalBranch224(zzz340, zzz341, Succ(Zero), zzz343, zzz344, zzz510, zzz511, zzz512000, zzz513, zzz514, zzz31, Zero, Succ(Succ(new_primPlusNat2(zzz6700, zzz512000))), h)
new_mkVBalBranch3MkVBalBranch223(zzz340, zzz341, Neg(Succ(Succ(Zero))), zzz343, zzz344, zzz510, zzz511, Zero, zzz513, zzz514, zzz31, Succ(Zero), h) → new_mkVBalBranch3MkVBalBranch225(zzz340, zzz341, Succ(Zero), zzz343, zzz344, zzz510, zzz511, zzz513, zzz514, zzz31, Zero, Zero, h)
new_mkVBalBranch3MkVBalBranch224(zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, zzz1125, zzz1126, zzz1127, zzz1128, zzz1129, Succ(zzz11300), Succ(zzz11310), bd) → new_mkVBalBranch3MkVBalBranch224(zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, zzz1125, zzz1126, zzz1127, zzz1128, zzz1129, zzz11300, zzz11310, bd)
new_mkVBalBranch3MkVBalBranch217(zzz473, zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, zzz481, zzz482, Zero, Succ(zzz4840), bh) → new_mkVBalBranch0(zzz482, Branch(zzz478, zzz479, Pos(Succ(Zero)), zzz480, zzz481), zzz476, bh)
new_mkVBalBranch3MkVBalBranch215(zzz340, zzz341, Pos(Succ(Succ(zzz342000))), zzz343, zzz344, zzz510, zzz511, Succ(zzz512000), zzz513, zzz514, zzz31, Zero, h) → new_mkVBalBranch3MkVBalBranch216(zzz340, zzz341, Succ(zzz342000), zzz343, zzz344, zzz510, zzz511, zzz512000, zzz513, zzz514, zzz31, zzz512000, zzz342000, h)
new_mkVBalBranch0(zzz31, Branch(zzz510, zzz511, Pos(Succ(zzz51200)), zzz513, zzz514), Branch(zzz340, zzz341, zzz342, zzz343, zzz344), h) → new_mkVBalBranch3MkVBalBranch215(zzz340, zzz341, zzz342, zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, new_primMulNat0(zzz51200), h)
new_mkVBalBranch0(zzz31, Branch(zzz510, zzz511, Neg(Succ(zzz51200)), zzz513, zzz514), Branch(zzz340, zzz341, zzz342, zzz343, zzz344), h) → new_mkVBalBranch3MkVBalBranch223(zzz340, zzz341, zzz342, zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, new_primMulNat0(zzz51200), h)
new_mkVBalBranch3MkVBalBranch110(zzz461, zzz462, zzz463, zzz464, zzz465, zzz466, zzz467, zzz468, zzz469, zzz470, zzz471, Succ(zzz5800), bb) → new_mkVBalBranch3MkVBalBranch115(zzz461, zzz462, zzz463, zzz464, zzz465, zzz466, zzz467, Succ(zzz468), zzz469, zzz470, zzz471, Succ(zzz5800), Succ(Succ(zzz468)), bb)
new_mkVBalBranch3MkVBalBranch227(zzz486, zzz487, zzz488, zzz489, zzz490, zzz491, zzz492, zzz493, zzz494, zzz495, zzz496, bf) → new_mkVBalBranch0(zzz496, Branch(zzz491, zzz492, Neg(Succ(Succ(zzz493))), zzz494, zzz495), zzz489, bf)
new_mkVBalBranch3MkVBalBranch215(zzz340, zzz341, Pos(Zero), zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, Succ(zzz660), h) → new_mkVBalBranch0(zzz31, zzz514, Branch(zzz340, zzz341, Pos(Zero), zzz343, zzz344), h)
new_mkVBalBranch3MkVBalBranch223(zzz340, zzz341, Neg(Zero), zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, Succ(zzz670), h) → new_mkVBalBranch0(zzz31, Branch(zzz510, zzz511, Neg(Succ(zzz51200)), zzz513, zzz514), zzz343, h)
new_mkVBalBranch3MkVBalBranch216(zzz1105, zzz1106, zzz1107, zzz1108, zzz1109, zzz1110, zzz1111, zzz1112, zzz1113, zzz1114, zzz1115, Zero, Succ(zzz11170), ba) → new_mkVBalBranch0(zzz1115, Branch(zzz1110, zzz1111, Pos(Succ(Succ(zzz1112))), zzz1113, zzz1114), zzz1108, ba)
new_mkVBalBranch3MkVBalBranch217(zzz473, zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, zzz481, zzz482, Succ(zzz4830), Zero, bh) → new_mkVBalBranch3MkVBalBranch121(zzz473, zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, zzz481, zzz482, new_primMulNat1(zzz475), bh)
new_mkVBalBranch3MkVBalBranch222(zzz461, zzz462, zzz463, zzz464, zzz465, zzz466, zzz467, zzz468, zzz469, zzz470, zzz471, bb) → new_mkVBalBranch3MkVBalBranch110(zzz461, zzz462, zzz463, zzz464, zzz465, zzz466, zzz467, zzz468, zzz469, zzz470, zzz471, new_primMulNat1(zzz463), bb)
new_mkVBalBranch3MkVBalBranch115(zzz1986, zzz1987, zzz1988, zzz1989, zzz1990, zzz1991, zzz1992, zzz1993, zzz1994, zzz1995, zzz1996, Zero, Succ(zzz19980), bc) → new_mkVBalBranch0(zzz1996, zzz1995, Branch(zzz1986, zzz1987, Pos(Succ(zzz1988)), zzz1989, zzz1990), bc)
new_mkVBalBranch3MkVBalBranch221(zzz340, zzz341, Succ(zzz34200), zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, h) → new_mkVBalBranch3MkVBalBranch19(zzz340, zzz341, zzz34200, zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, new_primPlusNat2(new_primMulNat0(zzz34200), Succ(zzz34200)), h)
new_mkVBalBranch3MkVBalBranch223(zzz340, zzz341, Neg(Zero), zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, Zero, h) → new_mkVBalBranch3MkVBalBranch228(zzz340, zzz341, zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, h)
new_mkVBalBranch3MkVBalBranch122(zzz340, zzz341, zzz34200, zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, h) → new_mkVBalBranch0(zzz31, zzz514, Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), h)
new_mkVBalBranch3MkVBalBranch217(zzz473, zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, zzz481, zzz482, Succ(zzz4830), Succ(zzz4840), bh) → new_mkVBalBranch3MkVBalBranch217(zzz473, zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, zzz481, zzz482, zzz4830, zzz4840, bh)
new_mkVBalBranch3MkVBalBranch116(zzz340, zzz341, zzz34200, zzz343, zzz344, zzz510, zzz511, zzz513, zzz514, zzz31, Succ(zzz1200), h) → new_mkVBalBranch0(zzz31, zzz514, Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), h)
new_mkVBalBranch3MkVBalBranch110(zzz461, zzz462, zzz463, zzz464, zzz465, zzz466, zzz467, zzz468, zzz469, zzz470, zzz471, Zero, bb) → new_mkVBalBranch3MkVBalBranch115(zzz461, zzz462, zzz463, zzz464, zzz465, zzz466, zzz467, Succ(zzz468), zzz469, zzz470, zzz471, Zero, Succ(Succ(zzz468)), bb)
new_mkVBalBranch3MkVBalBranch225(zzz498, zzz499, zzz500, zzz501, zzz502, zzz503, zzz504, zzz505, zzz506, zzz507, Zero, Succ(zzz5090), bg) → new_mkVBalBranch0(zzz507, Branch(zzz503, zzz504, Neg(Succ(Zero)), zzz505, zzz506), zzz501, bg)
new_mkVBalBranch3MkVBalBranch223(zzz340, zzz341, Neg(Succ(Succ(Succ(zzz3420000)))), zzz343, zzz344, zzz510, zzz511, Zero, zzz513, zzz514, zzz31, Succ(Zero), h) → new_mkVBalBranch3MkVBalBranch225(zzz340, zzz341, Succ(Succ(zzz3420000)), zzz343, zzz344, zzz510, zzz511, zzz513, zzz514, zzz31, Succ(zzz3420000), Zero, h)
new_mkVBalBranch3MkVBalBranch121(zzz473, zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, zzz481, zzz482, Zero, bh) → new_mkVBalBranch3MkVBalBranch115(zzz473, zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, Zero, zzz480, zzz481, zzz482, Zero, Succ(Zero), bh)
new_mkVBalBranch3MkVBalBranch215(zzz340, zzz341, Pos(Succ(Zero)), zzz343, zzz344, zzz510, zzz511, Succ(zzz512000), zzz513, zzz514, zzz31, Zero, h) → new_mkVBalBranch3MkVBalBranch218(zzz340, zzz341, Zero, zzz343, zzz344, zzz510, zzz511, zzz512000, zzz513, zzz514, zzz31, h)
new_mkVBalBranch3MkVBalBranch223(zzz340, zzz341, Neg(Succ(Zero)), zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, Succ(zzz670), h) → new_mkVBalBranch0(zzz31, Branch(zzz510, zzz511, Neg(Succ(zzz51200)), zzz513, zzz514), zzz343, h)
new_mkVBalBranch3MkVBalBranch218(zzz461, zzz462, zzz463, zzz464, zzz465, zzz466, zzz467, zzz468, zzz469, zzz470, zzz471, bb) → new_mkVBalBranch3MkVBalBranch110(zzz461, zzz462, zzz463, zzz464, zzz465, zzz466, zzz467, zzz468, zzz469, zzz470, zzz471, new_primMulNat1(zzz463), bb)
new_mkVBalBranch3MkVBalBranch223(zzz340, zzz341, Neg(Succ(Zero)), zzz343, zzz344, zzz510, zzz511, Succ(zzz512000), zzz513, zzz514, zzz31, Zero, h) → new_mkVBalBranch3MkVBalBranch227(zzz340, zzz341, Zero, zzz343, zzz344, zzz510, zzz511, zzz512000, zzz513, zzz514, zzz31, h)
new_mkVBalBranch3MkVBalBranch215(zzz340, zzz341, Pos(Succ(Zero)), zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, Succ(zzz660), h) → new_mkVBalBranch3MkVBalBranch18(zzz340, zzz341, zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, new_primMulNat1(Zero), h)
new_mkVBalBranch3MkVBalBranch229(zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, zzz1125, zzz1126, zzz1127, zzz1128, zzz1129, bd) → new_mkVBalBranch3MkVBalBranch119(zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, zzz1125, zzz1126, zzz1127, zzz1128, zzz1129, new_primMulNat1(zzz1121), bd)
new_mkVBalBranch3MkVBalBranch215(zzz340, zzz341, Pos(Succ(Succ(zzz342000))), zzz343, zzz344, zzz510, zzz511, Zero, zzz513, zzz514, zzz31, Succ(Succ(zzz6600)), h) → new_mkVBalBranch3MkVBalBranch217(zzz340, zzz341, Succ(zzz342000), zzz343, zzz344, zzz510, zzz511, zzz513, zzz514, zzz31, Succ(zzz6600), zzz342000, h)
new_mkVBalBranch3MkVBalBranch223(zzz340, zzz341, Neg(Succ(Succ(zzz342000))), zzz343, zzz344, zzz510, zzz511, Succ(zzz512000), zzz513, zzz514, zzz31, Zero, h) → new_mkVBalBranch3MkVBalBranch224(zzz340, zzz341, Succ(zzz342000), zzz343, zzz344, zzz510, zzz511, zzz512000, zzz513, zzz514, zzz31, zzz342000, zzz512000, h)
new_mkVBalBranch3MkVBalBranch226(zzz340, zzz341, zzz3420, zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, h) → new_mkVBalBranch0(zzz31, Branch(zzz510, zzz511, Neg(Succ(zzz51200)), zzz513, zzz514), zzz343, h)
new_mkVBalBranch3MkVBalBranch117(zzz340, zzz341, zzz34200, zzz343, zzz344, zzz510, zzz511, zzz513, zzz514, zzz31, Succ(zzz1240), h) → new_mkVBalBranch0(zzz31, zzz514, Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), h)
new_mkVBalBranch3MkVBalBranch217(zzz473, zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, zzz481, zzz482, Zero, Zero, bh) → new_mkVBalBranch3MkVBalBranch233(zzz473, zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, zzz481, zzz482, bh)
new_mkVBalBranch3MkVBalBranch120(zzz2050, zzz2051, zzz2052, zzz2053, zzz2054, zzz2055, zzz2056, zzz2057, zzz2058, zzz2059, zzz2060, Succ(zzz20610), Succ(zzz20620), be) → new_mkVBalBranch3MkVBalBranch120(zzz2050, zzz2051, zzz2052, zzz2053, zzz2054, zzz2055, zzz2056, zzz2057, zzz2058, zzz2059, zzz2060, zzz20610, zzz20620, be)
new_mkVBalBranch3MkVBalBranch223(zzz340, zzz341, Neg(Succ(Succ(zzz342000))), zzz343, zzz344, zzz510, zzz511, Zero, zzz513, zzz514, zzz31, Zero, h) → new_mkVBalBranch3MkVBalBranch118(zzz340, zzz341, Succ(zzz342000), zzz343, zzz344, zzz510, zzz511, zzz513, zzz514, zzz31, new_primMulNat1(Succ(zzz342000)), h)
new_mkVBalBranch3MkVBalBranch223(zzz340, zzz341, Pos(zzz3420), zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, Succ(zzz670), h) → new_mkVBalBranch0(zzz31, Branch(zzz510, zzz511, Neg(Succ(zzz51200)), zzz513, zzz514), zzz343, h)
new_mkVBalBranch3MkVBalBranch216(zzz1105, zzz1106, zzz1107, zzz1108, zzz1109, zzz1110, zzz1111, zzz1112, zzz1113, zzz1114, zzz1115, Succ(zzz11160), Succ(zzz11170), ba) → new_mkVBalBranch3MkVBalBranch216(zzz1105, zzz1106, zzz1107, zzz1108, zzz1109, zzz1110, zzz1111, zzz1112, zzz1113, zzz1114, zzz1115, zzz11160, zzz11170, ba)
new_mkVBalBranch3MkVBalBranch19(zzz340, zzz341, zzz34200, zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, Zero, h) → new_mkVBalBranch3MkVBalBranch122(zzz340, zzz341, zzz34200, zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, h)
new_mkVBalBranch3MkVBalBranch223(zzz340, zzz341, Neg(Succ(Succ(Succ(zzz3420000)))), zzz343, zzz344, zzz510, zzz511, Succ(zzz512000), zzz513, zzz514, zzz31, Succ(Zero), h) → new_mkVBalBranch3MkVBalBranch224(zzz340, zzz341, Succ(Succ(zzz3420000)), zzz343, zzz344, zzz510, zzz511, zzz512000, zzz513, zzz514, zzz31, Succ(zzz3420000), Succ(zzz512000), h)
new_mkVBalBranch3MkVBalBranch230(zzz498, zzz499, zzz500, zzz501, zzz502, zzz503, zzz504, zzz505, zzz506, zzz507, bg) → new_mkVBalBranch3MkVBalBranch118(zzz498, zzz499, zzz500, zzz501, zzz502, zzz503, zzz504, zzz505, zzz506, zzz507, new_primMulNat1(zzz500), bg)
new_mkVBalBranch0(zzz31, Branch(zzz510, zzz511, Neg(Zero), zzz513, zzz514), Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), h) → new_mkVBalBranch3MkVBalBranch117(zzz340, zzz341, zzz34200, zzz343, zzz344, zzz510, zzz511, zzz513, zzz514, zzz31, new_primMulNat1(zzz34200), h)
new_mkVBalBranch3MkVBalBranch215(zzz340, zzz341, Pos(Succ(Succ(zzz342000))), zzz343, zzz344, zzz510, zzz511, Zero, zzz513, zzz514, zzz31, Zero, h) → new_mkVBalBranch0(zzz31, Branch(zzz510, zzz511, Pos(Succ(Zero)), zzz513, zzz514), zzz343, h)
new_mkVBalBranch3MkVBalBranch225(zzz498, zzz499, zzz500, zzz501, zzz502, zzz503, zzz504, zzz505, zzz506, zzz507, Succ(zzz5080), Zero, bg) → new_mkVBalBranch3MkVBalBranch118(zzz498, zzz499, zzz500, zzz501, zzz502, zzz503, zzz504, zzz505, zzz506, zzz507, new_primMulNat1(zzz500), bg)
new_mkVBalBranch3MkVBalBranch225(zzz498, zzz499, zzz500, zzz501, zzz502, zzz503, zzz504, zzz505, zzz506, zzz507, Succ(zzz5080), Succ(zzz5090), bg) → new_mkVBalBranch3MkVBalBranch225(zzz498, zzz499, zzz500, zzz501, zzz502, zzz503, zzz504, zzz505, zzz506, zzz507, zzz5080, zzz5090, bg)
new_mkVBalBranch3MkVBalBranch19(zzz340, zzz341, zzz34200, zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, Succ(zzz1410), h) → new_mkVBalBranch0(zzz31, zzz514, Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), h)
new_mkVBalBranch3MkVBalBranch224(zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, zzz1125, zzz1126, zzz1127, zzz1128, zzz1129, Zero, Succ(zzz11310), bd) → new_mkVBalBranch3MkVBalBranch227(zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, zzz1125, zzz1126, zzz1127, zzz1128, zzz1129, bd)
new_mkVBalBranch3MkVBalBranch224(zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, zzz1125, zzz1126, zzz1127, zzz1128, zzz1129, Zero, Zero, bd) → new_mkVBalBranch3MkVBalBranch229(zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, zzz1125, zzz1126, zzz1127, zzz1128, zzz1129, bd)
new_mkVBalBranch3MkVBalBranch223(zzz340, zzz341, Neg(Succ(Succ(Zero))), zzz343, zzz344, zzz510, zzz511, Succ(zzz512000), zzz513, zzz514, zzz31, Succ(Zero), h) → new_mkVBalBranch3MkVBalBranch224(zzz340, zzz341, Succ(Zero), zzz343, zzz344, zzz510, zzz511, zzz512000, zzz513, zzz514, zzz31, Zero, Succ(zzz512000), h)
new_mkVBalBranch3MkVBalBranch223(zzz340, zzz341, Pos(zzz3420), zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, Zero, h) → new_mkVBalBranch3MkVBalBranch226(zzz340, zzz341, zzz3420, zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, h)
new_mkVBalBranch3MkVBalBranch224(zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, zzz1125, zzz1126, zzz1127, zzz1128, zzz1129, Succ(zzz11300), Zero, bd) → new_mkVBalBranch3MkVBalBranch119(zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, zzz1125, zzz1126, zzz1127, zzz1128, zzz1129, new_primMulNat1(zzz1121), bd)
new_mkVBalBranch3MkVBalBranch223(zzz340, zzz341, Neg(Succ(Succ(Succ(zzz3420000)))), zzz343, zzz344, zzz510, zzz511, Succ(zzz512000), zzz513, zzz514, zzz31, Succ(Succ(zzz6700)), h) → new_mkVBalBranch3MkVBalBranch224(zzz340, zzz341, Succ(Succ(zzz3420000)), zzz343, zzz344, zzz510, zzz511, zzz512000, zzz513, zzz514, zzz31, Succ(zzz3420000), Succ(Succ(new_primPlusNat2(zzz6700, zzz512000))), h)
new_mkVBalBranch3MkVBalBranch223(zzz340, zzz341, Neg(Succ(Succ(Zero))), zzz343, zzz344, zzz510, zzz511, Zero, zzz513, zzz514, zzz31, Succ(Succ(zzz6700)), h) → new_mkVBalBranch3MkVBalBranch225(zzz340, zzz341, Succ(Zero), zzz343, zzz344, zzz510, zzz511, zzz513, zzz514, zzz31, Zero, Succ(zzz6700), h)
new_mkVBalBranch3MkVBalBranch215(zzz340, zzz341, Pos(Zero), zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, Zero, h) → new_mkVBalBranch3MkVBalBranch220(zzz340, zzz341, zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, h)
new_mkVBalBranch3MkVBalBranch115(zzz1986, zzz1987, zzz1988, zzz1989, zzz1990, zzz1991, zzz1992, zzz1993, zzz1994, zzz1995, zzz1996, Succ(zzz19970), Succ(zzz19980), bc) → new_mkVBalBranch3MkVBalBranch115(zzz1986, zzz1987, zzz1988, zzz1989, zzz1990, zzz1991, zzz1992, zzz1993, zzz1994, zzz1995, zzz1996, zzz19970, zzz19980, bc)
new_mkVBalBranch3MkVBalBranch215(zzz340, zzz341, Neg(Zero), zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, Succ(zzz660), h) → new_mkVBalBranch0(zzz31, zzz514, Branch(zzz340, zzz341, Neg(Zero), zzz343, zzz344), h)
new_mkVBalBranch3MkVBalBranch118(zzz498, zzz499, zzz500, zzz501, zzz502, zzz503, zzz504, zzz505, zzz506, zzz507, Succ(zzz8040), bg) → new_mkVBalBranch3MkVBalBranch120(zzz498, zzz499, zzz500, zzz501, zzz502, zzz503, zzz504, Zero, zzz505, zzz506, zzz507, Succ(Zero), Succ(zzz8040), bg)
new_mkVBalBranch3MkVBalBranch216(zzz1105, zzz1106, zzz1107, zzz1108, zzz1109, zzz1110, zzz1111, zzz1112, zzz1113, zzz1114, zzz1115, Succ(zzz11160), Zero, ba) → new_mkVBalBranch3MkVBalBranch218(zzz1105, zzz1106, zzz1107, zzz1108, zzz1109, zzz1110, zzz1111, zzz1112, zzz1113, zzz1114, zzz1115, ba)
new_mkVBalBranch3MkVBalBranch215(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, Succ(zzz660), h) → new_mkVBalBranch3MkVBalBranch19(zzz340, zzz341, zzz34200, zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, new_primPlusNat2(new_primMulNat0(zzz34200), Succ(zzz34200)), h)
new_mkVBalBranch3MkVBalBranch215(zzz340, zzz341, Pos(Succ(Succ(zzz342000))), zzz343, zzz344, zzz510, zzz511, Succ(zzz512000), zzz513, zzz514, zzz31, Succ(Zero), h) → new_mkVBalBranch3MkVBalBranch216(zzz340, zzz341, Succ(zzz342000), zzz343, zzz344, zzz510, zzz511, zzz512000, zzz513, zzz514, zzz31, Succ(zzz512000), zzz342000, h)
new_mkVBalBranch3MkVBalBranch219(zzz340, zzz341, zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, h) → new_mkVBalBranch3MkVBalBranch18(zzz340, zzz341, zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, new_primMulNat1(Zero), h)
new_mkVBalBranch3MkVBalBranch221(zzz340, zzz341, Zero, zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, h) → new_mkVBalBranch0(zzz31, zzz514, Branch(zzz340, zzz341, Neg(Zero), zzz343, zzz344), h)
new_mkVBalBranch3MkVBalBranch216(zzz1105, zzz1106, zzz1107, zzz1108, zzz1109, zzz1110, zzz1111, zzz1112, zzz1113, zzz1114, zzz1115, Zero, Zero, ba) → new_mkVBalBranch3MkVBalBranch222(zzz1105, zzz1106, zzz1107, zzz1108, zzz1109, zzz1110, zzz1111, zzz1112, zzz1113, zzz1114, zzz1115, ba)
new_mkVBalBranch3MkVBalBranch233(zzz473, zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, zzz481, zzz482, bh) → new_mkVBalBranch3MkVBalBranch121(zzz473, zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, zzz481, zzz482, new_primMulNat1(zzz475), bh)
new_mkVBalBranch3MkVBalBranch215(zzz340, zzz341, Pos(Succ(Succ(zzz342000))), zzz343, zzz344, zzz510, zzz511, Zero, zzz513, zzz514, zzz31, Succ(Zero), h) → new_mkVBalBranch3MkVBalBranch217(zzz340, zzz341, Succ(zzz342000), zzz343, zzz344, zzz510, zzz511, zzz513, zzz514, zzz31, Zero, zzz342000, h)
new_mkVBalBranch0(zzz31, Branch(zzz510, zzz511, Pos(Zero), zzz513, zzz514), Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), h) → new_mkVBalBranch3MkVBalBranch116(zzz340, zzz341, zzz34200, zzz343, zzz344, zzz510, zzz511, zzz513, zzz514, zzz31, new_primMulNat1(zzz34200), h)
new_mkVBalBranch3MkVBalBranch18(zzz340, zzz341, zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, Zero, h) → new_mkVBalBranch3MkVBalBranch115(zzz340, zzz341, Zero, zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, Zero, Succ(zzz51200), h)
new_mkVBalBranch3MkVBalBranch119(zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, zzz1125, zzz1126, zzz1127, zzz1128, zzz1129, Succ(zzz12130), bd) → new_mkVBalBranch3MkVBalBranch120(zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, zzz1125, Succ(zzz1126), zzz1127, zzz1128, zzz1129, Succ(Succ(zzz1126)), Succ(zzz12130), bd)
new_mkVBalBranch3MkVBalBranch223(zzz340, zzz341, Neg(Succ(Zero)), zzz343, zzz344, zzz510, zzz511, Zero, zzz513, zzz514, zzz31, Zero, h) → new_mkVBalBranch3MkVBalBranch118(zzz340, zzz341, Zero, zzz343, zzz344, zzz510, zzz511, zzz513, zzz514, zzz31, new_primMulNat1(Zero), h)

The TRS R consists of the following rules:

new_primPlusNat1(Zero) → Zero
new_primMulNat0(zzz6200) → new_primPlusNat3(Succ(new_primPlusNat3(new_primPlusNat1(zzz6200), zzz6200)), Succ(zzz6200))
new_primPlusNat2(Succ(zzz900), Succ(zzz9100)) → Succ(Succ(new_primPlusNat2(zzz900, zzz9100)))
new_primPlusNat3(zzz90, Succ(zzz910)) → Succ(Succ(new_primPlusNat2(zzz90, zzz910)))
new_primPlusNat3(zzz90, Zero) → Succ(zzz90)
new_primMulNat1(zzz34200) → new_primPlusNat2(new_primMulNat0(zzz34200), Succ(zzz34200))
new_primPlusNat2(Zero, Zero) → Zero
new_primPlusNat1(Succ(zzz62000)) → Succ(Succ(new_primPlusNat1(zzz62000)))
new_primPlusNat2(Succ(zzz900), Zero) → Succ(zzz900)
new_primPlusNat2(Zero, Succ(zzz9100)) → Succ(zzz9100)

The set Q consists of the following terms:

new_primPlusNat2(Zero, Succ(x0))
new_primMulNat1(x0)
new_primMulNat0(x0)
new_primPlusNat3(x0, Succ(x1))
new_primPlusNat2(Succ(x0), Succ(x1))
new_primPlusNat3(x0, Zero)
new_primPlusNat1(Zero)
new_primPlusNat2(Zero, Zero)
new_primPlusNat1(Succ(x0))
new_primPlusNat2(Succ(x0), Zero)

We have to consider all minimal (P,Q,R)-chains.
By rewriting [15] the rule new_mkVBalBranch3MkVBalBranch230(zzz498, zzz499, zzz500, zzz501, zzz502, zzz503, zzz504, zzz505, zzz506, zzz507, bg) → new_mkVBalBranch3MkVBalBranch118(zzz498, zzz499, zzz500, zzz501, zzz502, zzz503, zzz504, zzz505, zzz506, zzz507, new_primMulNat1(zzz500), bg) at position [10] we obtained the following new rules:

new_mkVBalBranch3MkVBalBranch230(zzz498, zzz499, zzz500, zzz501, zzz502, zzz503, zzz504, zzz505, zzz506, zzz507, bg) → new_mkVBalBranch3MkVBalBranch118(zzz498, zzz499, zzz500, zzz501, zzz502, zzz503, zzz504, zzz505, zzz506, zzz507, new_primPlusNat2(new_primMulNat0(zzz500), Succ(zzz500)), bg)



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

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

new_mkVBalBranch3MkVBalBranch225(zzz498, zzz499, zzz500, zzz501, zzz502, zzz503, zzz504, zzz505, zzz506, zzz507, Zero, Zero, bg) → new_mkVBalBranch3MkVBalBranch230(zzz498, zzz499, zzz500, zzz501, zzz502, zzz503, zzz504, zzz505, zzz506, zzz507, bg)
new_mkVBalBranch3MkVBalBranch215(zzz340, zzz341, Neg(zzz3420), zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, Zero, h) → new_mkVBalBranch3MkVBalBranch221(zzz340, zzz341, zzz3420, zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, h)
new_mkVBalBranch3MkVBalBranch18(zzz340, zzz341, zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, Succ(zzz1480), h) → new_mkVBalBranch3MkVBalBranch115(zzz340, zzz341, Zero, zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, Succ(zzz1480), Succ(zzz51200), h)
new_mkVBalBranch3MkVBalBranch215(zzz340, zzz341, Pos(Succ(Succ(zzz342000))), zzz343, zzz344, zzz510, zzz511, Succ(zzz512000), zzz513, zzz514, zzz31, Succ(Succ(zzz6600)), h) → new_mkVBalBranch3MkVBalBranch216(zzz340, zzz341, Succ(zzz342000), zzz343, zzz344, zzz510, zzz511, zzz512000, zzz513, zzz514, zzz31, Succ(Succ(new_primPlusNat2(zzz6600, zzz512000))), zzz342000, h)
new_mkVBalBranch0(zzz31, Branch(zzz510, zzz511, Neg(Zero), zzz513, zzz514), Branch(zzz340, zzz341, Pos(Succ(zzz34200)), zzz343, zzz344), h) → new_mkVBalBranch0(zzz31, Branch(zzz510, zzz511, Neg(Zero), zzz513, zzz514), zzz343, h)
new_mkVBalBranch3MkVBalBranch223(zzz340, zzz341, Neg(Succ(Succ(Succ(zzz3420000)))), zzz343, zzz344, zzz510, zzz511, Zero, zzz513, zzz514, zzz31, Succ(Succ(zzz6700)), h) → new_mkVBalBranch3MkVBalBranch225(zzz340, zzz341, Succ(Succ(zzz3420000)), zzz343, zzz344, zzz510, zzz511, zzz513, zzz514, zzz31, Succ(zzz3420000), Succ(zzz6700), h)
new_mkVBalBranch3MkVBalBranch120(zzz2050, zzz2051, zzz2052, zzz2053, zzz2054, zzz2055, zzz2056, zzz2057, zzz2058, zzz2059, zzz2060, Zero, Succ(zzz20620), be) → new_mkVBalBranch0(zzz2060, zzz2059, Branch(zzz2050, zzz2051, Neg(Succ(zzz2052)), zzz2053, zzz2054), be)
new_mkVBalBranch3MkVBalBranch220(zzz340, zzz341, zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, h) → new_mkVBalBranch0(zzz31, zzz514, Branch(zzz340, zzz341, Pos(Zero), zzz343, zzz344), h)
new_mkVBalBranch3MkVBalBranch228(zzz340, zzz341, zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, h) → new_mkVBalBranch0(zzz31, Branch(zzz510, zzz511, Neg(Succ(zzz51200)), zzz513, zzz514), zzz343, h)
new_mkVBalBranch0(zzz31, Branch(zzz510, zzz511, Pos(Zero), zzz513, zzz514), Branch(zzz340, zzz341, Pos(Succ(zzz34200)), zzz343, zzz344), h) → new_mkVBalBranch0(zzz31, Branch(zzz510, zzz511, Pos(Zero), zzz513, zzz514), zzz343, h)
new_mkVBalBranch3MkVBalBranch121(zzz473, zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, zzz481, zzz482, Succ(zzz7390), bh) → new_mkVBalBranch3MkVBalBranch115(zzz473, zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, Zero, zzz480, zzz481, zzz482, Succ(zzz7390), Succ(Zero), bh)
new_mkVBalBranch3MkVBalBranch223(zzz340, zzz341, Neg(Succ(Succ(Zero))), zzz343, zzz344, zzz510, zzz511, Succ(zzz512000), zzz513, zzz514, zzz31, Succ(Succ(zzz6700)), h) → new_mkVBalBranch3MkVBalBranch224(zzz340, zzz341, Succ(Zero), zzz343, zzz344, zzz510, zzz511, zzz512000, zzz513, zzz514, zzz31, Zero, Succ(Succ(new_primPlusNat2(zzz6700, zzz512000))), h)
new_mkVBalBranch3MkVBalBranch215(zzz340, zzz341, Pos(Succ(Zero)), zzz343, zzz344, zzz510, zzz511, Zero, zzz513, zzz514, zzz31, Zero, h) → new_mkVBalBranch3MkVBalBranch219(zzz340, zzz341, zzz343, zzz344, zzz510, zzz511, Zero, zzz513, zzz514, zzz31, h)
new_mkVBalBranch3MkVBalBranch223(zzz340, zzz341, Neg(Succ(Succ(Zero))), zzz343, zzz344, zzz510, zzz511, Zero, zzz513, zzz514, zzz31, Succ(Zero), h) → new_mkVBalBranch3MkVBalBranch225(zzz340, zzz341, Succ(Zero), zzz343, zzz344, zzz510, zzz511, zzz513, zzz514, zzz31, Zero, Zero, h)
new_mkVBalBranch3MkVBalBranch224(zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, zzz1125, zzz1126, zzz1127, zzz1128, zzz1129, Succ(zzz11300), Succ(zzz11310), bd) → new_mkVBalBranch3MkVBalBranch224(zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, zzz1125, zzz1126, zzz1127, zzz1128, zzz1129, zzz11300, zzz11310, bd)
new_mkVBalBranch3MkVBalBranch217(zzz473, zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, zzz481, zzz482, Zero, Succ(zzz4840), bh) → new_mkVBalBranch0(zzz482, Branch(zzz478, zzz479, Pos(Succ(Zero)), zzz480, zzz481), zzz476, bh)
new_mkVBalBranch3MkVBalBranch215(zzz340, zzz341, Pos(Succ(Succ(zzz342000))), zzz343, zzz344, zzz510, zzz511, Succ(zzz512000), zzz513, zzz514, zzz31, Zero, h) → new_mkVBalBranch3MkVBalBranch216(zzz340, zzz341, Succ(zzz342000), zzz343, zzz344, zzz510, zzz511, zzz512000, zzz513, zzz514, zzz31, zzz512000, zzz342000, h)
new_mkVBalBranch0(zzz31, Branch(zzz510, zzz511, Pos(Succ(zzz51200)), zzz513, zzz514), Branch(zzz340, zzz341, zzz342, zzz343, zzz344), h) → new_mkVBalBranch3MkVBalBranch215(zzz340, zzz341, zzz342, zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, new_primMulNat0(zzz51200), h)
new_mkVBalBranch0(zzz31, Branch(zzz510, zzz511, Neg(Succ(zzz51200)), zzz513, zzz514), Branch(zzz340, zzz341, zzz342, zzz343, zzz344), h) → new_mkVBalBranch3MkVBalBranch223(zzz340, zzz341, zzz342, zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, new_primMulNat0(zzz51200), h)
new_mkVBalBranch3MkVBalBranch110(zzz461, zzz462, zzz463, zzz464, zzz465, zzz466, zzz467, zzz468, zzz469, zzz470, zzz471, Succ(zzz5800), bb) → new_mkVBalBranch3MkVBalBranch115(zzz461, zzz462, zzz463, zzz464, zzz465, zzz466, zzz467, Succ(zzz468), zzz469, zzz470, zzz471, Succ(zzz5800), Succ(Succ(zzz468)), bb)
new_mkVBalBranch3MkVBalBranch227(zzz486, zzz487, zzz488, zzz489, zzz490, zzz491, zzz492, zzz493, zzz494, zzz495, zzz496, bf) → new_mkVBalBranch0(zzz496, Branch(zzz491, zzz492, Neg(Succ(Succ(zzz493))), zzz494, zzz495), zzz489, bf)
new_mkVBalBranch3MkVBalBranch215(zzz340, zzz341, Pos(Zero), zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, Succ(zzz660), h) → new_mkVBalBranch0(zzz31, zzz514, Branch(zzz340, zzz341, Pos(Zero), zzz343, zzz344), h)
new_mkVBalBranch3MkVBalBranch223(zzz340, zzz341, Neg(Zero), zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, Succ(zzz670), h) → new_mkVBalBranch0(zzz31, Branch(zzz510, zzz511, Neg(Succ(zzz51200)), zzz513, zzz514), zzz343, h)
new_mkVBalBranch3MkVBalBranch216(zzz1105, zzz1106, zzz1107, zzz1108, zzz1109, zzz1110, zzz1111, zzz1112, zzz1113, zzz1114, zzz1115, Zero, Succ(zzz11170), ba) → new_mkVBalBranch0(zzz1115, Branch(zzz1110, zzz1111, Pos(Succ(Succ(zzz1112))), zzz1113, zzz1114), zzz1108, ba)
new_mkVBalBranch3MkVBalBranch222(zzz461, zzz462, zzz463, zzz464, zzz465, zzz466, zzz467, zzz468, zzz469, zzz470, zzz471, bb) → new_mkVBalBranch3MkVBalBranch110(zzz461, zzz462, zzz463, zzz464, zzz465, zzz466, zzz467, zzz468, zzz469, zzz470, zzz471, new_primMulNat1(zzz463), bb)
new_mkVBalBranch3MkVBalBranch217(zzz473, zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, zzz481, zzz482, Succ(zzz4830), Zero, bh) → new_mkVBalBranch3MkVBalBranch121(zzz473, zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, zzz481, zzz482, new_primMulNat1(zzz475), bh)
new_mkVBalBranch3MkVBalBranch115(zzz1986, zzz1987, zzz1988, zzz1989, zzz1990, zzz1991, zzz1992, zzz1993, zzz1994, zzz1995, zzz1996, Zero, Succ(zzz19980), bc) → new_mkVBalBranch0(zzz1996, zzz1995, Branch(zzz1986, zzz1987, Pos(Succ(zzz1988)), zzz1989, zzz1990), bc)
new_mkVBalBranch3MkVBalBranch221(zzz340, zzz341, Succ(zzz34200), zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, h) → new_mkVBalBranch3MkVBalBranch19(zzz340, zzz341, zzz34200, zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, new_primPlusNat2(new_primMulNat0(zzz34200), Succ(zzz34200)), h)
new_mkVBalBranch3MkVBalBranch223(zzz340, zzz341, Neg(Zero), zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, Zero, h) → new_mkVBalBranch3MkVBalBranch228(zzz340, zzz341, zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, h)
new_mkVBalBranch3MkVBalBranch122(zzz340, zzz341, zzz34200, zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, h) → new_mkVBalBranch0(zzz31, zzz514, Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), h)
new_mkVBalBranch3MkVBalBranch217(zzz473, zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, zzz481, zzz482, Succ(zzz4830), Succ(zzz4840), bh) → new_mkVBalBranch3MkVBalBranch217(zzz473, zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, zzz481, zzz482, zzz4830, zzz4840, bh)
new_mkVBalBranch3MkVBalBranch116(zzz340, zzz341, zzz34200, zzz343, zzz344, zzz510, zzz511, zzz513, zzz514, zzz31, Succ(zzz1200), h) → new_mkVBalBranch0(zzz31, zzz514, Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), h)
new_mkVBalBranch3MkVBalBranch110(zzz461, zzz462, zzz463, zzz464, zzz465, zzz466, zzz467, zzz468, zzz469, zzz470, zzz471, Zero, bb) → new_mkVBalBranch3MkVBalBranch115(zzz461, zzz462, zzz463, zzz464, zzz465, zzz466, zzz467, Succ(zzz468), zzz469, zzz470, zzz471, Zero, Succ(Succ(zzz468)), bb)
new_mkVBalBranch3MkVBalBranch225(zzz498, zzz499, zzz500, zzz501, zzz502, zzz503, zzz504, zzz505, zzz506, zzz507, Zero, Succ(zzz5090), bg) → new_mkVBalBranch0(zzz507, Branch(zzz503, zzz504, Neg(Succ(Zero)), zzz505, zzz506), zzz501, bg)
new_mkVBalBranch3MkVBalBranch223(zzz340, zzz341, Neg(Succ(Succ(Succ(zzz3420000)))), zzz343, zzz344, zzz510, zzz511, Zero, zzz513, zzz514, zzz31, Succ(Zero), h) → new_mkVBalBranch3MkVBalBranch225(zzz340, zzz341, Succ(Succ(zzz3420000)), zzz343, zzz344, zzz510, zzz511, zzz513, zzz514, zzz31, Succ(zzz3420000), Zero, h)
new_mkVBalBranch3MkVBalBranch121(zzz473, zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, zzz481, zzz482, Zero, bh) → new_mkVBalBranch3MkVBalBranch115(zzz473, zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, Zero, zzz480, zzz481, zzz482, Zero, Succ(Zero), bh)
new_mkVBalBranch3MkVBalBranch215(zzz340, zzz341, Pos(Succ(Zero)), zzz343, zzz344, zzz510, zzz511, Succ(zzz512000), zzz513, zzz514, zzz31, Zero, h) → new_mkVBalBranch3MkVBalBranch218(zzz340, zzz341, Zero, zzz343, zzz344, zzz510, zzz511, zzz512000, zzz513, zzz514, zzz31, h)
new_mkVBalBranch3MkVBalBranch223(zzz340, zzz341, Neg(Succ(Zero)), zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, Succ(zzz670), h) → new_mkVBalBranch0(zzz31, Branch(zzz510, zzz511, Neg(Succ(zzz51200)), zzz513, zzz514), zzz343, h)
new_mkVBalBranch3MkVBalBranch218(zzz461, zzz462, zzz463, zzz464, zzz465, zzz466, zzz467, zzz468, zzz469, zzz470, zzz471, bb) → new_mkVBalBranch3MkVBalBranch110(zzz461, zzz462, zzz463, zzz464, zzz465, zzz466, zzz467, zzz468, zzz469, zzz470, zzz471, new_primMulNat1(zzz463), bb)
new_mkVBalBranch3MkVBalBranch223(zzz340, zzz341, Neg(Succ(Zero)), zzz343, zzz344, zzz510, zzz511, Succ(zzz512000), zzz513, zzz514, zzz31, Zero, h) → new_mkVBalBranch3MkVBalBranch227(zzz340, zzz341, Zero, zzz343, zzz344, zzz510, zzz511, zzz512000, zzz513, zzz514, zzz31, h)
new_mkVBalBranch3MkVBalBranch215(zzz340, zzz341, Pos(Succ(Zero)), zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, Succ(zzz660), h) → new_mkVBalBranch3MkVBalBranch18(zzz340, zzz341, zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, new_primMulNat1(Zero), h)
new_mkVBalBranch3MkVBalBranch229(zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, zzz1125, zzz1126, zzz1127, zzz1128, zzz1129, bd) → new_mkVBalBranch3MkVBalBranch119(zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, zzz1125, zzz1126, zzz1127, zzz1128, zzz1129, new_primMulNat1(zzz1121), bd)
new_mkVBalBranch3MkVBalBranch226(zzz340, zzz341, zzz3420, zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, h) → new_mkVBalBranch0(zzz31, Branch(zzz510, zzz511, Neg(Succ(zzz51200)), zzz513, zzz514), zzz343, h)
new_mkVBalBranch3MkVBalBranch223(zzz340, zzz341, Neg(Succ(Succ(zzz342000))), zzz343, zzz344, zzz510, zzz511, Succ(zzz512000), zzz513, zzz514, zzz31, Zero, h) → new_mkVBalBranch3MkVBalBranch224(zzz340, zzz341, Succ(zzz342000), zzz343, zzz344, zzz510, zzz511, zzz512000, zzz513, zzz514, zzz31, zzz342000, zzz512000, h)
new_mkVBalBranch3MkVBalBranch215(zzz340, zzz341, Pos(Succ(Succ(zzz342000))), zzz343, zzz344, zzz510, zzz511, Zero, zzz513, zzz514, zzz31, Succ(Succ(zzz6600)), h) → new_mkVBalBranch3MkVBalBranch217(zzz340, zzz341, Succ(zzz342000), zzz343, zzz344, zzz510, zzz511, zzz513, zzz514, zzz31, Succ(zzz6600), zzz342000, h)
new_mkVBalBranch3MkVBalBranch117(zzz340, zzz341, zzz34200, zzz343, zzz344, zzz510, zzz511, zzz513, zzz514, zzz31, Succ(zzz1240), h) → new_mkVBalBranch0(zzz31, zzz514, Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), h)
new_mkVBalBranch3MkVBalBranch120(zzz2050, zzz2051, zzz2052, zzz2053, zzz2054, zzz2055, zzz2056, zzz2057, zzz2058, zzz2059, zzz2060, Succ(zzz20610), Succ(zzz20620), be) → new_mkVBalBranch3MkVBalBranch120(zzz2050, zzz2051, zzz2052, zzz2053, zzz2054, zzz2055, zzz2056, zzz2057, zzz2058, zzz2059, zzz2060, zzz20610, zzz20620, be)
new_mkVBalBranch3MkVBalBranch217(zzz473, zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, zzz481, zzz482, Zero, Zero, bh) → new_mkVBalBranch3MkVBalBranch233(zzz473, zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, zzz481, zzz482, bh)
new_mkVBalBranch3MkVBalBranch223(zzz340, zzz341, Neg(Succ(Succ(zzz342000))), zzz343, zzz344, zzz510, zzz511, Zero, zzz513, zzz514, zzz31, Zero, h) → new_mkVBalBranch3MkVBalBranch118(zzz340, zzz341, Succ(zzz342000), zzz343, zzz344, zzz510, zzz511, zzz513, zzz514, zzz31, new_primMulNat1(Succ(zzz342000)), h)
new_mkVBalBranch3MkVBalBranch216(zzz1105, zzz1106, zzz1107, zzz1108, zzz1109, zzz1110, zzz1111, zzz1112, zzz1113, zzz1114, zzz1115, Succ(zzz11160), Succ(zzz11170), ba) → new_mkVBalBranch3MkVBalBranch216(zzz1105, zzz1106, zzz1107, zzz1108, zzz1109, zzz1110, zzz1111, zzz1112, zzz1113, zzz1114, zzz1115, zzz11160, zzz11170, ba)
new_mkVBalBranch3MkVBalBranch223(zzz340, zzz341, Pos(zzz3420), zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, Succ(zzz670), h) → new_mkVBalBranch0(zzz31, Branch(zzz510, zzz511, Neg(Succ(zzz51200)), zzz513, zzz514), zzz343, h)
new_mkVBalBranch3MkVBalBranch223(zzz340, zzz341, Neg(Succ(Succ(Succ(zzz3420000)))), zzz343, zzz344, zzz510, zzz511, Succ(zzz512000), zzz513, zzz514, zzz31, Succ(Zero), h) → new_mkVBalBranch3MkVBalBranch224(zzz340, zzz341, Succ(Succ(zzz3420000)), zzz343, zzz344, zzz510, zzz511, zzz512000, zzz513, zzz514, zzz31, Succ(zzz3420000), Succ(zzz512000), h)
new_mkVBalBranch3MkVBalBranch19(zzz340, zzz341, zzz34200, zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, Zero, h) → new_mkVBalBranch3MkVBalBranch122(zzz340, zzz341, zzz34200, zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, h)
new_mkVBalBranch0(zzz31, Branch(zzz510, zzz511, Neg(Zero), zzz513, zzz514), Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), h) → new_mkVBalBranch3MkVBalBranch117(zzz340, zzz341, zzz34200, zzz343, zzz344, zzz510, zzz511, zzz513, zzz514, zzz31, new_primMulNat1(zzz34200), h)
new_mkVBalBranch3MkVBalBranch225(zzz498, zzz499, zzz500, zzz501, zzz502, zzz503, zzz504, zzz505, zzz506, zzz507, Succ(zzz5080), Zero, bg) → new_mkVBalBranch3MkVBalBranch118(zzz498, zzz499, zzz500, zzz501, zzz502, zzz503, zzz504, zzz505, zzz506, zzz507, new_primMulNat1(zzz500), bg)
new_mkVBalBranch3MkVBalBranch215(zzz340, zzz341, Pos(Succ(Succ(zzz342000))), zzz343, zzz344, zzz510, zzz511, Zero, zzz513, zzz514, zzz31, Zero, h) → new_mkVBalBranch0(zzz31, Branch(zzz510, zzz511, Pos(Succ(Zero)), zzz513, zzz514), zzz343, h)
new_mkVBalBranch3MkVBalBranch225(zzz498, zzz499, zzz500, zzz501, zzz502, zzz503, zzz504, zzz505, zzz506, zzz507, Succ(zzz5080), Succ(zzz5090), bg) → new_mkVBalBranch3MkVBalBranch225(zzz498, zzz499, zzz500, zzz501, zzz502, zzz503, zzz504, zzz505, zzz506, zzz507, zzz5080, zzz5090, bg)
new_mkVBalBranch3MkVBalBranch19(zzz340, zzz341, zzz34200, zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, Succ(zzz1410), h) → new_mkVBalBranch0(zzz31, zzz514, Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), h)
new_mkVBalBranch3MkVBalBranch223(zzz340, zzz341, Pos(zzz3420), zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, Zero, h) → new_mkVBalBranch3MkVBalBranch226(zzz340, zzz341, zzz3420, zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, h)
new_mkVBalBranch3MkVBalBranch223(zzz340, zzz341, Neg(Succ(Succ(Zero))), zzz343, zzz344, zzz510, zzz511, Succ(zzz512000), zzz513, zzz514, zzz31, Succ(Zero), h) → new_mkVBalBranch3MkVBalBranch224(zzz340, zzz341, Succ(Zero), zzz343, zzz344, zzz510, zzz511, zzz512000, zzz513, zzz514, zzz31, Zero, Succ(zzz512000), h)
new_mkVBalBranch3MkVBalBranch224(zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, zzz1125, zzz1126, zzz1127, zzz1128, zzz1129, Zero, Zero, bd) → new_mkVBalBranch3MkVBalBranch229(zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, zzz1125, zzz1126, zzz1127, zzz1128, zzz1129, bd)
new_mkVBalBranch3MkVBalBranch224(zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, zzz1125, zzz1126, zzz1127, zzz1128, zzz1129, Zero, Succ(zzz11310), bd) → new_mkVBalBranch3MkVBalBranch227(zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, zzz1125, zzz1126, zzz1127, zzz1128, zzz1129, bd)
new_mkVBalBranch3MkVBalBranch224(zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, zzz1125, zzz1126, zzz1127, zzz1128, zzz1129, Succ(zzz11300), Zero, bd) → new_mkVBalBranch3MkVBalBranch119(zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, zzz1125, zzz1126, zzz1127, zzz1128, zzz1129, new_primMulNat1(zzz1121), bd)
new_mkVBalBranch3MkVBalBranch230(zzz498, zzz499, zzz500, zzz501, zzz502, zzz503, zzz504, zzz505, zzz506, zzz507, bg) → new_mkVBalBranch3MkVBalBranch118(zzz498, zzz499, zzz500, zzz501, zzz502, zzz503, zzz504, zzz505, zzz506, zzz507, new_primPlusNat2(new_primMulNat0(zzz500), Succ(zzz500)), bg)
new_mkVBalBranch3MkVBalBranch223(zzz340, zzz341, Neg(Succ(Succ(Zero))), zzz343, zzz344, zzz510, zzz511, Zero, zzz513, zzz514, zzz31, Succ(Succ(zzz6700)), h) → new_mkVBalBranch3MkVBalBranch225(zzz340, zzz341, Succ(Zero), zzz343, zzz344, zzz510, zzz511, zzz513, zzz514, zzz31, Zero, Succ(zzz6700), h)
new_mkVBalBranch3MkVBalBranch223(zzz340, zzz341, Neg(Succ(Succ(Succ(zzz3420000)))), zzz343, zzz344, zzz510, zzz511, Succ(zzz512000), zzz513, zzz514, zzz31, Succ(Succ(zzz6700)), h) → new_mkVBalBranch3MkVBalBranch224(zzz340, zzz341, Succ(Succ(zzz3420000)), zzz343, zzz344, zzz510, zzz511, zzz512000, zzz513, zzz514, zzz31, Succ(zzz3420000), Succ(Succ(new_primPlusNat2(zzz6700, zzz512000))), h)
new_mkVBalBranch3MkVBalBranch115(zzz1986, zzz1987, zzz1988, zzz1989, zzz1990, zzz1991, zzz1992, zzz1993, zzz1994, zzz1995, zzz1996, Succ(zzz19970), Succ(zzz19980), bc) → new_mkVBalBranch3MkVBalBranch115(zzz1986, zzz1987, zzz1988, zzz1989, zzz1990, zzz1991, zzz1992, zzz1993, zzz1994, zzz1995, zzz1996, zzz19970, zzz19980, bc)
new_mkVBalBranch3MkVBalBranch215(zzz340, zzz341, Pos(Zero), zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, Zero, h) → new_mkVBalBranch3MkVBalBranch220(zzz340, zzz341, zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, h)
new_mkVBalBranch3MkVBalBranch215(zzz340, zzz341, Neg(Zero), zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, Succ(zzz660), h) → new_mkVBalBranch0(zzz31, zzz514, Branch(zzz340, zzz341, Neg(Zero), zzz343, zzz344), h)
new_mkVBalBranch3MkVBalBranch118(zzz498, zzz499, zzz500, zzz501, zzz502, zzz503, zzz504, zzz505, zzz506, zzz507, Succ(zzz8040), bg) → new_mkVBalBranch3MkVBalBranch120(zzz498, zzz499, zzz500, zzz501, zzz502, zzz503, zzz504, Zero, zzz505, zzz506, zzz507, Succ(Zero), Succ(zzz8040), bg)
new_mkVBalBranch3MkVBalBranch216(zzz1105, zzz1106, zzz1107, zzz1108, zzz1109, zzz1110, zzz1111, zzz1112, zzz1113, zzz1114, zzz1115, Succ(zzz11160), Zero, ba) → new_mkVBalBranch3MkVBalBranch218(zzz1105, zzz1106, zzz1107, zzz1108, zzz1109, zzz1110, zzz1111, zzz1112, zzz1113, zzz1114, zzz1115, ba)
new_mkVBalBranch3MkVBalBranch221(zzz340, zzz341, Zero, zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, h) → new_mkVBalBranch0(zzz31, zzz514, Branch(zzz340, zzz341, Neg(Zero), zzz343, zzz344), h)
new_mkVBalBranch3MkVBalBranch219(zzz340, zzz341, zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, h) → new_mkVBalBranch3MkVBalBranch18(zzz340, zzz341, zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, new_primMulNat1(Zero), h)
new_mkVBalBranch3MkVBalBranch215(zzz340, zzz341, Pos(Succ(Succ(zzz342000))), zzz343, zzz344, zzz510, zzz511, Succ(zzz512000), zzz513, zzz514, zzz31, Succ(Zero), h) → new_mkVBalBranch3MkVBalBranch216(zzz340, zzz341, Succ(zzz342000), zzz343, zzz344, zzz510, zzz511, zzz512000, zzz513, zzz514, zzz31, Succ(zzz512000), zzz342000, h)
new_mkVBalBranch3MkVBalBranch215(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, Succ(zzz660), h) → new_mkVBalBranch3MkVBalBranch19(zzz340, zzz341, zzz34200, zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, new_primPlusNat2(new_primMulNat0(zzz34200), Succ(zzz34200)), h)
new_mkVBalBranch3MkVBalBranch216(zzz1105, zzz1106, zzz1107, zzz1108, zzz1109, zzz1110, zzz1111, zzz1112, zzz1113, zzz1114, zzz1115, Zero, Zero, ba) → new_mkVBalBranch3MkVBalBranch222(zzz1105, zzz1106, zzz1107, zzz1108, zzz1109, zzz1110, zzz1111, zzz1112, zzz1113, zzz1114, zzz1115, ba)
new_mkVBalBranch3MkVBalBranch233(zzz473, zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, zzz481, zzz482, bh) → new_mkVBalBranch3MkVBalBranch121(zzz473, zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, zzz481, zzz482, new_primMulNat1(zzz475), bh)
new_mkVBalBranch3MkVBalBranch215(zzz340, zzz341, Pos(Succ(Succ(zzz342000))), zzz343, zzz344, zzz510, zzz511, Zero, zzz513, zzz514, zzz31, Succ(Zero), h) → new_mkVBalBranch3MkVBalBranch217(zzz340, zzz341, Succ(zzz342000), zzz343, zzz344, zzz510, zzz511, zzz513, zzz514, zzz31, Zero, zzz342000, h)
new_mkVBalBranch0(zzz31, Branch(zzz510, zzz511, Pos(Zero), zzz513, zzz514), Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), h) → new_mkVBalBranch3MkVBalBranch116(zzz340, zzz341, zzz34200, zzz343, zzz344, zzz510, zzz511, zzz513, zzz514, zzz31, new_primMulNat1(zzz34200), h)
new_mkVBalBranch3MkVBalBranch119(zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, zzz1125, zzz1126, zzz1127, zzz1128, zzz1129, Succ(zzz12130), bd) → new_mkVBalBranch3MkVBalBranch120(zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, zzz1125, Succ(zzz1126), zzz1127, zzz1128, zzz1129, Succ(Succ(zzz1126)), Succ(zzz12130), bd)
new_mkVBalBranch3MkVBalBranch18(zzz340, zzz341, zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, Zero, h) → new_mkVBalBranch3MkVBalBranch115(zzz340, zzz341, Zero, zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, Zero, Succ(zzz51200), h)
new_mkVBalBranch3MkVBalBranch223(zzz340, zzz341, Neg(Succ(Zero)), zzz343, zzz344, zzz510, zzz511, Zero, zzz513, zzz514, zzz31, Zero, h) → new_mkVBalBranch3MkVBalBranch118(zzz340, zzz341, Zero, zzz343, zzz344, zzz510, zzz511, zzz513, zzz514, zzz31, new_primMulNat1(Zero), h)

The TRS R consists of the following rules:

new_primPlusNat1(Zero) → Zero
new_primMulNat0(zzz6200) → new_primPlusNat3(Succ(new_primPlusNat3(new_primPlusNat1(zzz6200), zzz6200)), Succ(zzz6200))
new_primPlusNat2(Succ(zzz900), Succ(zzz9100)) → Succ(Succ(new_primPlusNat2(zzz900, zzz9100)))
new_primPlusNat3(zzz90, Succ(zzz910)) → Succ(Succ(new_primPlusNat2(zzz90, zzz910)))
new_primPlusNat3(zzz90, Zero) → Succ(zzz90)
new_primMulNat1(zzz34200) → new_primPlusNat2(new_primMulNat0(zzz34200), Succ(zzz34200))
new_primPlusNat2(Zero, Zero) → Zero
new_primPlusNat1(Succ(zzz62000)) → Succ(Succ(new_primPlusNat1(zzz62000)))
new_primPlusNat2(Succ(zzz900), Zero) → Succ(zzz900)
new_primPlusNat2(Zero, Succ(zzz9100)) → Succ(zzz9100)

The set Q consists of the following terms:

new_primPlusNat2(Zero, Succ(x0))
new_primMulNat1(x0)
new_primMulNat0(x0)
new_primPlusNat3(x0, Succ(x1))
new_primPlusNat2(Succ(x0), Succ(x1))
new_primPlusNat3(x0, Zero)
new_primPlusNat1(Zero)
new_primPlusNat2(Zero, Zero)
new_primPlusNat1(Succ(x0))
new_primPlusNat2(Succ(x0), Zero)

We have to consider all minimal (P,Q,R)-chains.
By rewriting [15] the rule new_mkVBalBranch0(zzz31, Branch(zzz510, zzz511, Pos(Succ(zzz51200)), zzz513, zzz514), Branch(zzz340, zzz341, zzz342, zzz343, zzz344), h) → new_mkVBalBranch3MkVBalBranch215(zzz340, zzz341, zzz342, zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, new_primMulNat0(zzz51200), h) at position [11] we obtained the following new rules:

new_mkVBalBranch0(zzz31, Branch(zzz510, zzz511, Pos(Succ(zzz51200)), zzz513, zzz514), Branch(zzz340, zzz341, zzz342, zzz343, zzz344), h) → new_mkVBalBranch3MkVBalBranch215(zzz340, zzz341, zzz342, zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, new_primPlusNat3(Succ(new_primPlusNat3(new_primPlusNat1(zzz51200), zzz51200)), Succ(zzz51200)), 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
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                    ↳ DependencyGraphProof
                                      ↳ QDP
                                        ↳ Rewriting
                                          ↳ QDP
                                            ↳ Rewriting
                                              ↳ QDP
                                                ↳ Rewriting
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP

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

new_mkVBalBranch3MkVBalBranch215(zzz340, zzz341, Neg(zzz3420), zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, Zero, h) → new_mkVBalBranch3MkVBalBranch221(zzz340, zzz341, zzz3420, zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, h)
new_mkVBalBranch3MkVBalBranch225(zzz498, zzz499, zzz500, zzz501, zzz502, zzz503, zzz504, zzz505, zzz506, zzz507, Zero, Zero, bg) → new_mkVBalBranch3MkVBalBranch230(zzz498, zzz499, zzz500, zzz501, zzz502, zzz503, zzz504, zzz505, zzz506, zzz507, bg)
new_mkVBalBranch3MkVBalBranch18(zzz340, zzz341, zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, Succ(zzz1480), h) → new_mkVBalBranch3MkVBalBranch115(zzz340, zzz341, Zero, zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, Succ(zzz1480), Succ(zzz51200), h)
new_mkVBalBranch0(zzz31, Branch(zzz510, zzz511, Neg(Zero), zzz513, zzz514), Branch(zzz340, zzz341, Pos(Succ(zzz34200)), zzz343, zzz344), h) → new_mkVBalBranch0(zzz31, Branch(zzz510, zzz511, Neg(Zero), zzz513, zzz514), zzz343, h)
new_mkVBalBranch3MkVBalBranch215(zzz340, zzz341, Pos(Succ(Succ(zzz342000))), zzz343, zzz344, zzz510, zzz511, Succ(zzz512000), zzz513, zzz514, zzz31, Succ(Succ(zzz6600)), h) → new_mkVBalBranch3MkVBalBranch216(zzz340, zzz341, Succ(zzz342000), zzz343, zzz344, zzz510, zzz511, zzz512000, zzz513, zzz514, zzz31, Succ(Succ(new_primPlusNat2(zzz6600, zzz512000))), zzz342000, h)
new_mkVBalBranch3MkVBalBranch223(zzz340, zzz341, Neg(Succ(Succ(Succ(zzz3420000)))), zzz343, zzz344, zzz510, zzz511, Zero, zzz513, zzz514, zzz31, Succ(Succ(zzz6700)), h) → new_mkVBalBranch3MkVBalBranch225(zzz340, zzz341, Succ(Succ(zzz3420000)), zzz343, zzz344, zzz510, zzz511, zzz513, zzz514, zzz31, Succ(zzz3420000), Succ(zzz6700), h)
new_mkVBalBranch3MkVBalBranch220(zzz340, zzz341, zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, h) → new_mkVBalBranch0(zzz31, zzz514, Branch(zzz340, zzz341, Pos(Zero), zzz343, zzz344), h)
new_mkVBalBranch3MkVBalBranch120(zzz2050, zzz2051, zzz2052, zzz2053, zzz2054, zzz2055, zzz2056, zzz2057, zzz2058, zzz2059, zzz2060, Zero, Succ(zzz20620), be) → new_mkVBalBranch0(zzz2060, zzz2059, Branch(zzz2050, zzz2051, Neg(Succ(zzz2052)), zzz2053, zzz2054), be)
new_mkVBalBranch3MkVBalBranch121(zzz473, zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, zzz481, zzz482, Succ(zzz7390), bh) → new_mkVBalBranch3MkVBalBranch115(zzz473, zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, Zero, zzz480, zzz481, zzz482, Succ(zzz7390), Succ(Zero), bh)
new_mkVBalBranch0(zzz31, Branch(zzz510, zzz511, Pos(Zero), zzz513, zzz514), Branch(zzz340, zzz341, Pos(Succ(zzz34200)), zzz343, zzz344), h) → new_mkVBalBranch0(zzz31, Branch(zzz510, zzz511, Pos(Zero), zzz513, zzz514), zzz343, h)
new_mkVBalBranch3MkVBalBranch228(zzz340, zzz341, zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, h) → new_mkVBalBranch0(zzz31, Branch(zzz510, zzz511, Neg(Succ(zzz51200)), zzz513, zzz514), zzz343, h)
new_mkVBalBranch3MkVBalBranch215(zzz340, zzz341, Pos(Succ(Zero)), zzz343, zzz344, zzz510, zzz511, Zero, zzz513, zzz514, zzz31, Zero, h) → new_mkVBalBranch3MkVBalBranch219(zzz340, zzz341, zzz343, zzz344, zzz510, zzz511, Zero, zzz513, zzz514, zzz31, h)
new_mkVBalBranch3MkVBalBranch223(zzz340, zzz341, Neg(Succ(Succ(Zero))), zzz343, zzz344, zzz510, zzz511, Succ(zzz512000), zzz513, zzz514, zzz31, Succ(Succ(zzz6700)), h) → new_mkVBalBranch3MkVBalBranch224(zzz340, zzz341, Succ(Zero), zzz343, zzz344, zzz510, zzz511, zzz512000, zzz513, zzz514, zzz31, Zero, Succ(Succ(new_primPlusNat2(zzz6700, zzz512000))), h)
new_mkVBalBranch3MkVBalBranch223(zzz340, zzz341, Neg(Succ(Succ(Zero))), zzz343, zzz344, zzz510, zzz511, Zero, zzz513, zzz514, zzz31, Succ(Zero), h) → new_mkVBalBranch3MkVBalBranch225(zzz340, zzz341, Succ(Zero), zzz343, zzz344, zzz510, zzz511, zzz513, zzz514, zzz31, Zero, Zero, h)
new_mkVBalBranch3MkVBalBranch224(zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, zzz1125, zzz1126, zzz1127, zzz1128, zzz1129, Succ(zzz11300), Succ(zzz11310), bd) → new_mkVBalBranch3MkVBalBranch224(zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, zzz1125, zzz1126, zzz1127, zzz1128, zzz1129, zzz11300, zzz11310, bd)
new_mkVBalBranch0(zzz31, Branch(zzz510, zzz511, Pos(Succ(zzz51200)), zzz513, zzz514), Branch(zzz340, zzz341, zzz342, zzz343, zzz344), h) → new_mkVBalBranch3MkVBalBranch215(zzz340, zzz341, zzz342, zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, new_primPlusNat3(Succ(new_primPlusNat3(new_primPlusNat1(zzz51200), zzz51200)), Succ(zzz51200)), h)
new_mkVBalBranch3MkVBalBranch217(zzz473, zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, zzz481, zzz482, Zero, Succ(zzz4840), bh) → new_mkVBalBranch0(zzz482, Branch(zzz478, zzz479, Pos(Succ(Zero)), zzz480, zzz481), zzz476, bh)
new_mkVBalBranch3MkVBalBranch215(zzz340, zzz341, Pos(Succ(Succ(zzz342000))), zzz343, zzz344, zzz510, zzz511, Succ(zzz512000), zzz513, zzz514, zzz31, Zero, h) → new_mkVBalBranch3MkVBalBranch216(zzz340, zzz341, Succ(zzz342000), zzz343, zzz344, zzz510, zzz511, zzz512000, zzz513, zzz514, zzz31, zzz512000, zzz342000, h)
new_mkVBalBranch0(zzz31, Branch(zzz510, zzz511, Neg(Succ(zzz51200)), zzz513, zzz514), Branch(zzz340, zzz341, zzz342, zzz343, zzz344), h) → new_mkVBalBranch3MkVBalBranch223(zzz340, zzz341, zzz342, zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, new_primMulNat0(zzz51200), h)
new_mkVBalBranch3MkVBalBranch110(zzz461, zzz462, zzz463, zzz464, zzz465, zzz466, zzz467, zzz468, zzz469, zzz470, zzz471, Succ(zzz5800), bb) → new_mkVBalBranch3MkVBalBranch115(zzz461, zzz462, zzz463, zzz464, zzz465, zzz466, zzz467, Succ(zzz468), zzz469, zzz470, zzz471, Succ(zzz5800), Succ(Succ(zzz468)), bb)
new_mkVBalBranch3MkVBalBranch227(zzz486, zzz487, zzz488, zzz489, zzz490, zzz491, zzz492, zzz493, zzz494, zzz495, zzz496, bf) → new_mkVBalBranch0(zzz496, Branch(zzz491, zzz492, Neg(Succ(Succ(zzz493))), zzz494, zzz495), zzz489, bf)
new_mkVBalBranch3MkVBalBranch215(zzz340, zzz341, Pos(Zero), zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, Succ(zzz660), h) → new_mkVBalBranch0(zzz31, zzz514, Branch(zzz340, zzz341, Pos(Zero), zzz343, zzz344), h)
new_mkVBalBranch3MkVBalBranch223(zzz340, zzz341, Neg(Zero), zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, Succ(zzz670), h) → new_mkVBalBranch0(zzz31, Branch(zzz510, zzz511, Neg(Succ(zzz51200)), zzz513, zzz514), zzz343, h)
new_mkVBalBranch3MkVBalBranch216(zzz1105, zzz1106, zzz1107, zzz1108, zzz1109, zzz1110, zzz1111, zzz1112, zzz1113, zzz1114, zzz1115, Zero, Succ(zzz11170), ba) → new_mkVBalBranch0(zzz1115, Branch(zzz1110, zzz1111, Pos(Succ(Succ(zzz1112))), zzz1113, zzz1114), zzz1108, ba)
new_mkVBalBranch3MkVBalBranch217(zzz473, zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, zzz481, zzz482, Succ(zzz4830), Zero, bh) → new_mkVBalBranch3MkVBalBranch121(zzz473, zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, zzz481, zzz482, new_primMulNat1(zzz475), bh)
new_mkVBalBranch3MkVBalBranch222(zzz461, zzz462, zzz463, zzz464, zzz465, zzz466, zzz467, zzz468, zzz469, zzz470, zzz471, bb) → new_mkVBalBranch3MkVBalBranch110(zzz461, zzz462, zzz463, zzz464, zzz465, zzz466, zzz467, zzz468, zzz469, zzz470, zzz471, new_primMulNat1(zzz463), bb)
new_mkVBalBranch3MkVBalBranch115(zzz1986, zzz1987, zzz1988, zzz1989, zzz1990, zzz1991, zzz1992, zzz1993, zzz1994, zzz1995, zzz1996, Zero, Succ(zzz19980), bc) → new_mkVBalBranch0(zzz1996, zzz1995, Branch(zzz1986, zzz1987, Pos(Succ(zzz1988)), zzz1989, zzz1990), bc)
new_mkVBalBranch3MkVBalBranch221(zzz340, zzz341, Succ(zzz34200), zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, h) → new_mkVBalBranch3MkVBalBranch19(zzz340, zzz341, zzz34200, zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, new_primPlusNat2(new_primMulNat0(zzz34200), Succ(zzz34200)), h)
new_mkVBalBranch3MkVBalBranch223(zzz340, zzz341, Neg(Zero), zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, Zero, h) → new_mkVBalBranch3MkVBalBranch228(zzz340, zzz341, zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, h)
new_mkVBalBranch3MkVBalBranch122(zzz340, zzz341, zzz34200, zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, h) → new_mkVBalBranch0(zzz31, zzz514, Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), h)
new_mkVBalBranch3MkVBalBranch217(zzz473, zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, zzz481, zzz482, Succ(zzz4830), Succ(zzz4840), bh) → new_mkVBalBranch3MkVBalBranch217(zzz473, zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, zzz481, zzz482, zzz4830, zzz4840, bh)
new_mkVBalBranch3MkVBalBranch116(zzz340, zzz341, zzz34200, zzz343, zzz344, zzz510, zzz511, zzz513, zzz514, zzz31, Succ(zzz1200), h) → new_mkVBalBranch0(zzz31, zzz514, Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), h)
new_mkVBalBranch3MkVBalBranch110(zzz461, zzz462, zzz463, zzz464, zzz465, zzz466, zzz467, zzz468, zzz469, zzz470, zzz471, Zero, bb) → new_mkVBalBranch3MkVBalBranch115(zzz461, zzz462, zzz463, zzz464, zzz465, zzz466, zzz467, Succ(zzz468), zzz469, zzz470, zzz471, Zero, Succ(Succ(zzz468)), bb)
new_mkVBalBranch3MkVBalBranch225(zzz498, zzz499, zzz500, zzz501, zzz502, zzz503, zzz504, zzz505, zzz506, zzz507, Zero, Succ(zzz5090), bg) → new_mkVBalBranch0(zzz507, Branch(zzz503, zzz504, Neg(Succ(Zero)), zzz505, zzz506), zzz501, bg)
new_mkVBalBranch3MkVBalBranch223(zzz340, zzz341, Neg(Succ(Succ(Succ(zzz3420000)))), zzz343, zzz344, zzz510, zzz511, Zero, zzz513, zzz514, zzz31, Succ(Zero), h) → new_mkVBalBranch3MkVBalBranch225(zzz340, zzz341, Succ(Succ(zzz3420000)), zzz343, zzz344, zzz510, zzz511, zzz513, zzz514, zzz31, Succ(zzz3420000), Zero, h)
new_mkVBalBranch3MkVBalBranch121(zzz473, zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, zzz481, zzz482, Zero, bh) → new_mkVBalBranch3MkVBalBranch115(zzz473, zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, Zero, zzz480, zzz481, zzz482, Zero, Succ(Zero), bh)
new_mkVBalBranch3MkVBalBranch215(zzz340, zzz341, Pos(Succ(Zero)), zzz343, zzz344, zzz510, zzz511, Succ(zzz512000), zzz513, zzz514, zzz31, Zero, h) → new_mkVBalBranch3MkVBalBranch218(zzz340, zzz341, Zero, zzz343, zzz344, zzz510, zzz511, zzz512000, zzz513, zzz514, zzz31, h)
new_mkVBalBranch3MkVBalBranch223(zzz340, zzz341, Neg(Succ(Zero)), zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, Succ(zzz670), h) → new_mkVBalBranch0(zzz31, Branch(zzz510, zzz511, Neg(Succ(zzz51200)), zzz513, zzz514), zzz343, h)
new_mkVBalBranch3MkVBalBranch218(zzz461, zzz462, zzz463, zzz464, zzz465, zzz466, zzz467, zzz468, zzz469, zzz470, zzz471, bb) → new_mkVBalBranch3MkVBalBranch110(zzz461, zzz462, zzz463, zzz464, zzz465, zzz466, zzz467, zzz468, zzz469, zzz470, zzz471, new_primMulNat1(zzz463), bb)
new_mkVBalBranch3MkVBalBranch223(zzz340, zzz341, Neg(Succ(Zero)), zzz343, zzz344, zzz510, zzz511, Succ(zzz512000), zzz513, zzz514, zzz31, Zero, h) → new_mkVBalBranch3MkVBalBranch227(zzz340, zzz341, Zero, zzz343, zzz344, zzz510, zzz511, zzz512000, zzz513, zzz514, zzz31, h)
new_mkVBalBranch3MkVBalBranch215(zzz340, zzz341, Pos(Succ(Zero)), zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, Succ(zzz660), h) → new_mkVBalBranch3MkVBalBranch18(zzz340, zzz341, zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, new_primMulNat1(Zero), h)
new_mkVBalBranch3MkVBalBranch229(zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, zzz1125, zzz1126, zzz1127, zzz1128, zzz1129, bd) → new_mkVBalBranch3MkVBalBranch119(zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, zzz1125, zzz1126, zzz1127, zzz1128, zzz1129, new_primMulNat1(zzz1121), bd)
new_mkVBalBranch3MkVBalBranch215(zzz340, zzz341, Pos(Succ(Succ(zzz342000))), zzz343, zzz344, zzz510, zzz511, Zero, zzz513, zzz514, zzz31, Succ(Succ(zzz6600)), h) → new_mkVBalBranch3MkVBalBranch217(zzz340, zzz341, Succ(zzz342000), zzz343, zzz344, zzz510, zzz511, zzz513, zzz514, zzz31, Succ(zzz6600), zzz342000, h)
new_mkVBalBranch3MkVBalBranch223(zzz340, zzz341, Neg(Succ(Succ(zzz342000))), zzz343, zzz344, zzz510, zzz511, Succ(zzz512000), zzz513, zzz514, zzz31, Zero, h) → new_mkVBalBranch3MkVBalBranch224(zzz340, zzz341, Succ(zzz342000), zzz343, zzz344, zzz510, zzz511, zzz512000, zzz513, zzz514, zzz31, zzz342000, zzz512000, h)
new_mkVBalBranch3MkVBalBranch226(zzz340, zzz341, zzz3420, zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, h) → new_mkVBalBranch0(zzz31, Branch(zzz510, zzz511, Neg(Succ(zzz51200)), zzz513, zzz514), zzz343, h)
new_mkVBalBranch3MkVBalBranch117(zzz340, zzz341, zzz34200, zzz343, zzz344, zzz510, zzz511, zzz513, zzz514, zzz31, Succ(zzz1240), h) → new_mkVBalBranch0(zzz31, zzz514, Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), h)
new_mkVBalBranch3MkVBalBranch217(zzz473, zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, zzz481, zzz482, Zero, Zero, bh) → new_mkVBalBranch3MkVBalBranch233(zzz473, zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, zzz481, zzz482, bh)
new_mkVBalBranch3MkVBalBranch120(zzz2050, zzz2051, zzz2052, zzz2053, zzz2054, zzz2055, zzz2056, zzz2057, zzz2058, zzz2059, zzz2060, Succ(zzz20610), Succ(zzz20620), be) → new_mkVBalBranch3MkVBalBranch120(zzz2050, zzz2051, zzz2052, zzz2053, zzz2054, zzz2055, zzz2056, zzz2057, zzz2058, zzz2059, zzz2060, zzz20610, zzz20620, be)
new_mkVBalBranch3MkVBalBranch223(zzz340, zzz341, Neg(Succ(Succ(zzz342000))), zzz343, zzz344, zzz510, zzz511, Zero, zzz513, zzz514, zzz31, Zero, h) → new_mkVBalBranch3MkVBalBranch118(zzz340, zzz341, Succ(zzz342000), zzz343, zzz344, zzz510, zzz511, zzz513, zzz514, zzz31, new_primMulNat1(Succ(zzz342000)), h)
new_mkVBalBranch3MkVBalBranch223(zzz340, zzz341, Pos(zzz3420), zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, Succ(zzz670), h) → new_mkVBalBranch0(zzz31, Branch(zzz510, zzz511, Neg(Succ(zzz51200)), zzz513, zzz514), zzz343, h)
new_mkVBalBranch3MkVBalBranch216(zzz1105, zzz1106, zzz1107, zzz1108, zzz1109, zzz1110, zzz1111, zzz1112, zzz1113, zzz1114, zzz1115, Succ(zzz11160), Succ(zzz11170), ba) → new_mkVBalBranch3MkVBalBranch216(zzz1105, zzz1106, zzz1107, zzz1108, zzz1109, zzz1110, zzz1111, zzz1112, zzz1113, zzz1114, zzz1115, zzz11160, zzz11170, ba)
new_mkVBalBranch3MkVBalBranch19(zzz340, zzz341, zzz34200, zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, Zero, h) → new_mkVBalBranch3MkVBalBranch122(zzz340, zzz341, zzz34200, zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, h)
new_mkVBalBranch3MkVBalBranch223(zzz340, zzz341, Neg(Succ(Succ(Succ(zzz3420000)))), zzz343, zzz344, zzz510, zzz511, Succ(zzz512000), zzz513, zzz514, zzz31, Succ(Zero), h) → new_mkVBalBranch3MkVBalBranch224(zzz340, zzz341, Succ(Succ(zzz3420000)), zzz343, zzz344, zzz510, zzz511, zzz512000, zzz513, zzz514, zzz31, Succ(zzz3420000), Succ(zzz512000), h)
new_mkVBalBranch0(zzz31, Branch(zzz510, zzz511, Neg(Zero), zzz513, zzz514), Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), h) → new_mkVBalBranch3MkVBalBranch117(zzz340, zzz341, zzz34200, zzz343, zzz344, zzz510, zzz511, zzz513, zzz514, zzz31, new_primMulNat1(zzz34200), h)
new_mkVBalBranch3MkVBalBranch215(zzz340, zzz341, Pos(Succ(Succ(zzz342000))), zzz343, zzz344, zzz510, zzz511, Zero, zzz513, zzz514, zzz31, Zero, h) → new_mkVBalBranch0(zzz31, Branch(zzz510, zzz511, Pos(Succ(Zero)), zzz513, zzz514), zzz343, h)
new_mkVBalBranch3MkVBalBranch225(zzz498, zzz499, zzz500, zzz501, zzz502, zzz503, zzz504, zzz505, zzz506, zzz507, Succ(zzz5080), Zero, bg) → new_mkVBalBranch3MkVBalBranch118(zzz498, zzz499, zzz500, zzz501, zzz502, zzz503, zzz504, zzz505, zzz506, zzz507, new_primMulNat1(zzz500), bg)
new_mkVBalBranch3MkVBalBranch225(zzz498, zzz499, zzz500, zzz501, zzz502, zzz503, zzz504, zzz505, zzz506, zzz507, Succ(zzz5080), Succ(zzz5090), bg) → new_mkVBalBranch3MkVBalBranch225(zzz498, zzz499, zzz500, zzz501, zzz502, zzz503, zzz504, zzz505, zzz506, zzz507, zzz5080, zzz5090, bg)
new_mkVBalBranch3MkVBalBranch19(zzz340, zzz341, zzz34200, zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, Succ(zzz1410), h) → new_mkVBalBranch0(zzz31, zzz514, Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), h)
new_mkVBalBranch3MkVBalBranch224(zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, zzz1125, zzz1126, zzz1127, zzz1128, zzz1129, Zero, Succ(zzz11310), bd) → new_mkVBalBranch3MkVBalBranch227(zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, zzz1125, zzz1126, zzz1127, zzz1128, zzz1129, bd)
new_mkVBalBranch3MkVBalBranch224(zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, zzz1125, zzz1126, zzz1127, zzz1128, zzz1129, Zero, Zero, bd) → new_mkVBalBranch3MkVBalBranch229(zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, zzz1125, zzz1126, zzz1127, zzz1128, zzz1129, bd)
new_mkVBalBranch3MkVBalBranch223(zzz340, zzz341, Neg(Succ(Succ(Zero))), zzz343, zzz344, zzz510, zzz511, Succ(zzz512000), zzz513, zzz514, zzz31, Succ(Zero), h) → new_mkVBalBranch3MkVBalBranch224(zzz340, zzz341, Succ(Zero), zzz343, zzz344, zzz510, zzz511, zzz512000, zzz513, zzz514, zzz31, Zero, Succ(zzz512000), h)
new_mkVBalBranch3MkVBalBranch223(zzz340, zzz341, Pos(zzz3420), zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, Zero, h) → new_mkVBalBranch3MkVBalBranch226(zzz340, zzz341, zzz3420, zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, h)
new_mkVBalBranch3MkVBalBranch224(zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, zzz1125, zzz1126, zzz1127, zzz1128, zzz1129, Succ(zzz11300), Zero, bd) → new_mkVBalBranch3MkVBalBranch119(zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, zzz1125, zzz1126, zzz1127, zzz1128, zzz1129, new_primMulNat1(zzz1121), bd)
new_mkVBalBranch3MkVBalBranch230(zzz498, zzz499, zzz500, zzz501, zzz502, zzz503, zzz504, zzz505, zzz506, zzz507, bg) → new_mkVBalBranch3MkVBalBranch118(zzz498, zzz499, zzz500, zzz501, zzz502, zzz503, zzz504, zzz505, zzz506, zzz507, new_primPlusNat2(new_primMulNat0(zzz500), Succ(zzz500)), bg)
new_mkVBalBranch3MkVBalBranch223(zzz340, zzz341, Neg(Succ(Succ(Succ(zzz3420000)))), zzz343, zzz344, zzz510, zzz511, Succ(zzz512000), zzz513, zzz514, zzz31, Succ(Succ(zzz6700)), h) → new_mkVBalBranch3MkVBalBranch224(zzz340, zzz341, Succ(Succ(zzz3420000)), zzz343, zzz344, zzz510, zzz511, zzz512000, zzz513, zzz514, zzz31, Succ(zzz3420000), Succ(Succ(new_primPlusNat2(zzz6700, zzz512000))), h)
new_mkVBalBranch3MkVBalBranch223(zzz340, zzz341, Neg(Succ(Succ(Zero))), zzz343, zzz344, zzz510, zzz511, Zero, zzz513, zzz514, zzz31, Succ(Succ(zzz6700)), h) → new_mkVBalBranch3MkVBalBranch225(zzz340, zzz341, Succ(Zero), zzz343, zzz344, zzz510, zzz511, zzz513, zzz514, zzz31, Zero, Succ(zzz6700), h)
new_mkVBalBranch3MkVBalBranch215(zzz340, zzz341, Pos(Zero), zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, Zero, h) → new_mkVBalBranch3MkVBalBranch220(zzz340, zzz341, zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, h)
new_mkVBalBranch3MkVBalBranch115(zzz1986, zzz1987, zzz1988, zzz1989, zzz1990, zzz1991, zzz1992, zzz1993, zzz1994, zzz1995, zzz1996, Succ(zzz19970), Succ(zzz19980), bc) → new_mkVBalBranch3MkVBalBranch115(zzz1986, zzz1987, zzz1988, zzz1989, zzz1990, zzz1991, zzz1992, zzz1993, zzz1994, zzz1995, zzz1996, zzz19970, zzz19980, bc)
new_mkVBalBranch3MkVBalBranch215(zzz340, zzz341, Neg(Zero), zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, Succ(zzz660), h) → new_mkVBalBranch0(zzz31, zzz514, Branch(zzz340, zzz341, Neg(Zero), zzz343, zzz344), h)
new_mkVBalBranch3MkVBalBranch118(zzz498, zzz499, zzz500, zzz501, zzz502, zzz503, zzz504, zzz505, zzz506, zzz507, Succ(zzz8040), bg) → new_mkVBalBranch3MkVBalBranch120(zzz498, zzz499, zzz500, zzz501, zzz502, zzz503, zzz504, Zero, zzz505, zzz506, zzz507, Succ(Zero), Succ(zzz8040), bg)
new_mkVBalBranch3MkVBalBranch216(zzz1105, zzz1106, zzz1107, zzz1108, zzz1109, zzz1110, zzz1111, zzz1112, zzz1113, zzz1114, zzz1115, Succ(zzz11160), Zero, ba) → new_mkVBalBranch3MkVBalBranch218(zzz1105, zzz1106, zzz1107, zzz1108, zzz1109, zzz1110, zzz1111, zzz1112, zzz1113, zzz1114, zzz1115, ba)
new_mkVBalBranch3MkVBalBranch215(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, Succ(zzz660), h) → new_mkVBalBranch3MkVBalBranch19(zzz340, zzz341, zzz34200, zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, new_primPlusNat2(new_primMulNat0(zzz34200), Succ(zzz34200)), h)
new_mkVBalBranch3MkVBalBranch215(zzz340, zzz341, Pos(Succ(Succ(zzz342000))), zzz343, zzz344, zzz510, zzz511, Succ(zzz512000), zzz513, zzz514, zzz31, Succ(Zero), h) → new_mkVBalBranch3MkVBalBranch216(zzz340, zzz341, Succ(zzz342000), zzz343, zzz344, zzz510, zzz511, zzz512000, zzz513, zzz514, zzz31, Succ(zzz512000), zzz342000, h)
new_mkVBalBranch3MkVBalBranch219(zzz340, zzz341, zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, h) → new_mkVBalBranch3MkVBalBranch18(zzz340, zzz341, zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, new_primMulNat1(Zero), h)
new_mkVBalBranch3MkVBalBranch221(zzz340, zzz341, Zero, zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, h) → new_mkVBalBranch0(zzz31, zzz514, Branch(zzz340, zzz341, Neg(Zero), zzz343, zzz344), h)
new_mkVBalBranch3MkVBalBranch216(zzz1105, zzz1106, zzz1107, zzz1108, zzz1109, zzz1110, zzz1111, zzz1112, zzz1113, zzz1114, zzz1115, Zero, Zero, ba) → new_mkVBalBranch3MkVBalBranch222(zzz1105, zzz1106, zzz1107, zzz1108, zzz1109, zzz1110, zzz1111, zzz1112, zzz1113, zzz1114, zzz1115, ba)
new_mkVBalBranch3MkVBalBranch233(zzz473, zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, zzz481, zzz482, bh) → new_mkVBalBranch3MkVBalBranch121(zzz473, zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, zzz481, zzz482, new_primMulNat1(zzz475), bh)
new_mkVBalBranch3MkVBalBranch215(zzz340, zzz341, Pos(Succ(Succ(zzz342000))), zzz343, zzz344, zzz510, zzz511, Zero, zzz513, zzz514, zzz31, Succ(Zero), h) → new_mkVBalBranch3MkVBalBranch217(zzz340, zzz341, Succ(zzz342000), zzz343, zzz344, zzz510, zzz511, zzz513, zzz514, zzz31, Zero, zzz342000, h)
new_mkVBalBranch0(zzz31, Branch(zzz510, zzz511, Pos(Zero), zzz513, zzz514), Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), h) → new_mkVBalBranch3MkVBalBranch116(zzz340, zzz341, zzz34200, zzz343, zzz344, zzz510, zzz511, zzz513, zzz514, zzz31, new_primMulNat1(zzz34200), h)
new_mkVBalBranch3MkVBalBranch18(zzz340, zzz341, zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, Zero, h) → new_mkVBalBranch3MkVBalBranch115(zzz340, zzz341, Zero, zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, Zero, Succ(zzz51200), h)
new_mkVBalBranch3MkVBalBranch119(zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, zzz1125, zzz1126, zzz1127, zzz1128, zzz1129, Succ(zzz12130), bd) → new_mkVBalBranch3MkVBalBranch120(zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, zzz1125, Succ(zzz1126), zzz1127, zzz1128, zzz1129, Succ(Succ(zzz1126)), Succ(zzz12130), bd)
new_mkVBalBranch3MkVBalBranch223(zzz340, zzz341, Neg(Succ(Zero)), zzz343, zzz344, zzz510, zzz511, Zero, zzz513, zzz514, zzz31, Zero, h) → new_mkVBalBranch3MkVBalBranch118(zzz340, zzz341, Zero, zzz343, zzz344, zzz510, zzz511, zzz513, zzz514, zzz31, new_primMulNat1(Zero), h)

The TRS R consists of the following rules:

new_primPlusNat1(Zero) → Zero
new_primMulNat0(zzz6200) → new_primPlusNat3(Succ(new_primPlusNat3(new_primPlusNat1(zzz6200), zzz6200)), Succ(zzz6200))
new_primPlusNat2(Succ(zzz900), Succ(zzz9100)) → Succ(Succ(new_primPlusNat2(zzz900, zzz9100)))
new_primPlusNat3(zzz90, Succ(zzz910)) → Succ(Succ(new_primPlusNat2(zzz90, zzz910)))
new_primPlusNat3(zzz90, Zero) → Succ(zzz90)
new_primMulNat1(zzz34200) → new_primPlusNat2(new_primMulNat0(zzz34200), Succ(zzz34200))
new_primPlusNat2(Zero, Zero) → Zero
new_primPlusNat1(Succ(zzz62000)) → Succ(Succ(new_primPlusNat1(zzz62000)))
new_primPlusNat2(Succ(zzz900), Zero) → Succ(zzz900)
new_primPlusNat2(Zero, Succ(zzz9100)) → Succ(zzz9100)

The set Q consists of the following terms:

new_primPlusNat2(Zero, Succ(x0))
new_primMulNat1(x0)
new_primMulNat0(x0)
new_primPlusNat3(x0, Succ(x1))
new_primPlusNat2(Succ(x0), Succ(x1))
new_primPlusNat3(x0, Zero)
new_primPlusNat1(Zero)
new_primPlusNat2(Zero, Zero)
new_primPlusNat1(Succ(x0))
new_primPlusNat2(Succ(x0), Zero)

We have to consider all minimal (P,Q,R)-chains.
By rewriting [15] the rule new_mkVBalBranch3MkVBalBranch221(zzz340, zzz341, Succ(zzz34200), zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, h) → new_mkVBalBranch3MkVBalBranch19(zzz340, zzz341, zzz34200, zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, new_primPlusNat2(new_primMulNat0(zzz34200), Succ(zzz34200)), h) at position [11,0] we obtained the following new rules:

new_mkVBalBranch3MkVBalBranch221(zzz340, zzz341, Succ(zzz34200), zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, h) → new_mkVBalBranch3MkVBalBranch19(zzz340, zzz341, zzz34200, zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, new_primPlusNat2(new_primPlusNat3(Succ(new_primPlusNat3(new_primPlusNat1(zzz34200), zzz34200)), Succ(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
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                    ↳ DependencyGraphProof
                                      ↳ QDP
                                        ↳ Rewriting
                                          ↳ QDP
                                            ↳ Rewriting
                                              ↳ QDP
                                                ↳ Rewriting
                                                  ↳ QDP
                                                    ↳ Rewriting
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP

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

new_mkVBalBranch3MkVBalBranch225(zzz498, zzz499, zzz500, zzz501, zzz502, zzz503, zzz504, zzz505, zzz506, zzz507, Zero, Zero, bg) → new_mkVBalBranch3MkVBalBranch230(zzz498, zzz499, zzz500, zzz501, zzz502, zzz503, zzz504, zzz505, zzz506, zzz507, bg)
new_mkVBalBranch3MkVBalBranch215(zzz340, zzz341, Neg(zzz3420), zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, Zero, h) → new_mkVBalBranch3MkVBalBranch221(zzz340, zzz341, zzz3420, zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, h)
new_mkVBalBranch3MkVBalBranch18(zzz340, zzz341, zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, Succ(zzz1480), h) → new_mkVBalBranch3MkVBalBranch115(zzz340, zzz341, Zero, zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, Succ(zzz1480), Succ(zzz51200), h)
new_mkVBalBranch3MkVBalBranch215(zzz340, zzz341, Pos(Succ(Succ(zzz342000))), zzz343, zzz344, zzz510, zzz511, Succ(zzz512000), zzz513, zzz514, zzz31, Succ(Succ(zzz6600)), h) → new_mkVBalBranch3MkVBalBranch216(zzz340, zzz341, Succ(zzz342000), zzz343, zzz344, zzz510, zzz511, zzz512000, zzz513, zzz514, zzz31, Succ(Succ(new_primPlusNat2(zzz6600, zzz512000))), zzz342000, h)
new_mkVBalBranch0(zzz31, Branch(zzz510, zzz511, Neg(Zero), zzz513, zzz514), Branch(zzz340, zzz341, Pos(Succ(zzz34200)), zzz343, zzz344), h) → new_mkVBalBranch0(zzz31, Branch(zzz510, zzz511, Neg(Zero), zzz513, zzz514), zzz343, h)
new_mkVBalBranch3MkVBalBranch223(zzz340, zzz341, Neg(Succ(Succ(Succ(zzz3420000)))), zzz343, zzz344, zzz510, zzz511, Zero, zzz513, zzz514, zzz31, Succ(Succ(zzz6700)), h) → new_mkVBalBranch3MkVBalBranch225(zzz340, zzz341, Succ(Succ(zzz3420000)), zzz343, zzz344, zzz510, zzz511, zzz513, zzz514, zzz31, Succ(zzz3420000), Succ(zzz6700), h)
new_mkVBalBranch3MkVBalBranch120(zzz2050, zzz2051, zzz2052, zzz2053, zzz2054, zzz2055, zzz2056, zzz2057, zzz2058, zzz2059, zzz2060, Zero, Succ(zzz20620), be) → new_mkVBalBranch0(zzz2060, zzz2059, Branch(zzz2050, zzz2051, Neg(Succ(zzz2052)), zzz2053, zzz2054), be)
new_mkVBalBranch3MkVBalBranch220(zzz340, zzz341, zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, h) → new_mkVBalBranch0(zzz31, zzz514, Branch(zzz340, zzz341, Pos(Zero), zzz343, zzz344), h)
new_mkVBalBranch3MkVBalBranch228(zzz340, zzz341, zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, h) → new_mkVBalBranch0(zzz31, Branch(zzz510, zzz511, Neg(Succ(zzz51200)), zzz513, zzz514), zzz343, h)
new_mkVBalBranch0(zzz31, Branch(zzz510, zzz511, Pos(Zero), zzz513, zzz514), Branch(zzz340, zzz341, Pos(Succ(zzz34200)), zzz343, zzz344), h) → new_mkVBalBranch0(zzz31, Branch(zzz510, zzz511, Pos(Zero), zzz513, zzz514), zzz343, h)
new_mkVBalBranch3MkVBalBranch121(zzz473, zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, zzz481, zzz482, Succ(zzz7390), bh) → new_mkVBalBranch3MkVBalBranch115(zzz473, zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, Zero, zzz480, zzz481, zzz482, Succ(zzz7390), Succ(Zero), bh)
new_mkVBalBranch3MkVBalBranch223(zzz340, zzz341, Neg(Succ(Succ(Zero))), zzz343, zzz344, zzz510, zzz511, Succ(zzz512000), zzz513, zzz514, zzz31, Succ(Succ(zzz6700)), h) → new_mkVBalBranch3MkVBalBranch224(zzz340, zzz341, Succ(Zero), zzz343, zzz344, zzz510, zzz511, zzz512000, zzz513, zzz514, zzz31, Zero, Succ(Succ(new_primPlusNat2(zzz6700, zzz512000))), h)
new_mkVBalBranch3MkVBalBranch215(zzz340, zzz341, Pos(Succ(Zero)), zzz343, zzz344, zzz510, zzz511, Zero, zzz513, zzz514, zzz31, Zero, h) → new_mkVBalBranch3MkVBalBranch219(zzz340, zzz341, zzz343, zzz344, zzz510, zzz511, Zero, zzz513, zzz514, zzz31, h)
new_mkVBalBranch3MkVBalBranch223(zzz340, zzz341, Neg(Succ(Succ(Zero))), zzz343, zzz344, zzz510, zzz511, Zero, zzz513, zzz514, zzz31, Succ(Zero), h) → new_mkVBalBranch3MkVBalBranch225(zzz340, zzz341, Succ(Zero), zzz343, zzz344, zzz510, zzz511, zzz513, zzz514, zzz31, Zero, Zero, h)
new_mkVBalBranch3MkVBalBranch224(zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, zzz1125, zzz1126, zzz1127, zzz1128, zzz1129, Succ(zzz11300), Succ(zzz11310), bd) → new_mkVBalBranch3MkVBalBranch224(zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, zzz1125, zzz1126, zzz1127, zzz1128, zzz1129, zzz11300, zzz11310, bd)
new_mkVBalBranch3MkVBalBranch217(zzz473, zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, zzz481, zzz482, Zero, Succ(zzz4840), bh) → new_mkVBalBranch0(zzz482, Branch(zzz478, zzz479, Pos(Succ(Zero)), zzz480, zzz481), zzz476, bh)
new_mkVBalBranch0(zzz31, Branch(zzz510, zzz511, Pos(Succ(zzz51200)), zzz513, zzz514), Branch(zzz340, zzz341, zzz342, zzz343, zzz344), h) → new_mkVBalBranch3MkVBalBranch215(zzz340, zzz341, zzz342, zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, new_primPlusNat3(Succ(new_primPlusNat3(new_primPlusNat1(zzz51200), zzz51200)), Succ(zzz51200)), h)
new_mkVBalBranch3MkVBalBranch215(zzz340, zzz341, Pos(Succ(Succ(zzz342000))), zzz343, zzz344, zzz510, zzz511, Succ(zzz512000), zzz513, zzz514, zzz31, Zero, h) → new_mkVBalBranch3MkVBalBranch216(zzz340, zzz341, Succ(zzz342000), zzz343, zzz344, zzz510, zzz511, zzz512000, zzz513, zzz514, zzz31, zzz512000, zzz342000, h)
new_mkVBalBranch0(zzz31, Branch(zzz510, zzz511, Neg(Succ(zzz51200)), zzz513, zzz514), Branch(zzz340, zzz341, zzz342, zzz343, zzz344), h) → new_mkVBalBranch3MkVBalBranch223(zzz340, zzz341, zzz342, zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, new_primMulNat0(zzz51200), h)
new_mkVBalBranch3MkVBalBranch110(zzz461, zzz462, zzz463, zzz464, zzz465, zzz466, zzz467, zzz468, zzz469, zzz470, zzz471, Succ(zzz5800), bb) → new_mkVBalBranch3MkVBalBranch115(zzz461, zzz462, zzz463, zzz464, zzz465, zzz466, zzz467, Succ(zzz468), zzz469, zzz470, zzz471, Succ(zzz5800), Succ(Succ(zzz468)), bb)
new_mkVBalBranch3MkVBalBranch227(zzz486, zzz487, zzz488, zzz489, zzz490, zzz491, zzz492, zzz493, zzz494, zzz495, zzz496, bf) → new_mkVBalBranch0(zzz496, Branch(zzz491, zzz492, Neg(Succ(Succ(zzz493))), zzz494, zzz495), zzz489, bf)
new_mkVBalBranch3MkVBalBranch215(zzz340, zzz341, Pos(Zero), zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, Succ(zzz660), h) → new_mkVBalBranch0(zzz31, zzz514, Branch(zzz340, zzz341, Pos(Zero), zzz343, zzz344), h)
new_mkVBalBranch3MkVBalBranch223(zzz340, zzz341, Neg(Zero), zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, Succ(zzz670), h) → new_mkVBalBranch0(zzz31, Branch(zzz510, zzz511, Neg(Succ(zzz51200)), zzz513, zzz514), zzz343, h)
new_mkVBalBranch3MkVBalBranch216(zzz1105, zzz1106, zzz1107, zzz1108, zzz1109, zzz1110, zzz1111, zzz1112, zzz1113, zzz1114, zzz1115, Zero, Succ(zzz11170), ba) → new_mkVBalBranch0(zzz1115, Branch(zzz1110, zzz1111, Pos(Succ(Succ(zzz1112))), zzz1113, zzz1114), zzz1108, ba)
new_mkVBalBranch3MkVBalBranch222(zzz461, zzz462, zzz463, zzz464, zzz465, zzz466, zzz467, zzz468, zzz469, zzz470, zzz471, bb) → new_mkVBalBranch3MkVBalBranch110(zzz461, zzz462, zzz463, zzz464, zzz465, zzz466, zzz467, zzz468, zzz469, zzz470, zzz471, new_primMulNat1(zzz463), bb)
new_mkVBalBranch3MkVBalBranch217(zzz473, zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, zzz481, zzz482, Succ(zzz4830), Zero, bh) → new_mkVBalBranch3MkVBalBranch121(zzz473, zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, zzz481, zzz482, new_primMulNat1(zzz475), bh)
new_mkVBalBranch3MkVBalBranch115(zzz1986, zzz1987, zzz1988, zzz1989, zzz1990, zzz1991, zzz1992, zzz1993, zzz1994, zzz1995, zzz1996, Zero, Succ(zzz19980), bc) → new_mkVBalBranch0(zzz1996, zzz1995, Branch(zzz1986, zzz1987, Pos(Succ(zzz1988)), zzz1989, zzz1990), bc)
new_mkVBalBranch3MkVBalBranch223(zzz340, zzz341, Neg(Zero), zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, Zero, h) → new_mkVBalBranch3MkVBalBranch228(zzz340, zzz341, zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, h)
new_mkVBalBranch3MkVBalBranch122(zzz340, zzz341, zzz34200, zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, h) → new_mkVBalBranch0(zzz31, zzz514, Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), h)
new_mkVBalBranch3MkVBalBranch217(zzz473, zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, zzz481, zzz482, Succ(zzz4830), Succ(zzz4840), bh) → new_mkVBalBranch3MkVBalBranch217(zzz473, zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, zzz481, zzz482, zzz4830, zzz4840, bh)
new_mkVBalBranch3MkVBalBranch116(zzz340, zzz341, zzz34200, zzz343, zzz344, zzz510, zzz511, zzz513, zzz514, zzz31, Succ(zzz1200), h) → new_mkVBalBranch0(zzz31, zzz514, Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), h)
new_mkVBalBranch3MkVBalBranch110(zzz461, zzz462, zzz463, zzz464, zzz465, zzz466, zzz467, zzz468, zzz469, zzz470, zzz471, Zero, bb) → new_mkVBalBranch3MkVBalBranch115(zzz461, zzz462, zzz463, zzz464, zzz465, zzz466, zzz467, Succ(zzz468), zzz469, zzz470, zzz471, Zero, Succ(Succ(zzz468)), bb)
new_mkVBalBranch3MkVBalBranch225(zzz498, zzz499, zzz500, zzz501, zzz502, zzz503, zzz504, zzz505, zzz506, zzz507, Zero, Succ(zzz5090), bg) → new_mkVBalBranch0(zzz507, Branch(zzz503, zzz504, Neg(Succ(Zero)), zzz505, zzz506), zzz501, bg)
new_mkVBalBranch3MkVBalBranch223(zzz340, zzz341, Neg(Succ(Succ(Succ(zzz3420000)))), zzz343, zzz344, zzz510, zzz511, Zero, zzz513, zzz514, zzz31, Succ(Zero), h) → new_mkVBalBranch3MkVBalBranch225(zzz340, zzz341, Succ(Succ(zzz3420000)), zzz343, zzz344, zzz510, zzz511, zzz513, zzz514, zzz31, Succ(zzz3420000), Zero, h)
new_mkVBalBranch3MkVBalBranch121(zzz473, zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, zzz481, zzz482, Zero, bh) → new_mkVBalBranch3MkVBalBranch115(zzz473, zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, Zero, zzz480, zzz481, zzz482, Zero, Succ(Zero), bh)
new_mkVBalBranch3MkVBalBranch215(zzz340, zzz341, Pos(Succ(Zero)), zzz343, zzz344, zzz510, zzz511, Succ(zzz512000), zzz513, zzz514, zzz31, Zero, h) → new_mkVBalBranch3MkVBalBranch218(zzz340, zzz341, Zero, zzz343, zzz344, zzz510, zzz511, zzz512000, zzz513, zzz514, zzz31, h)
new_mkVBalBranch3MkVBalBranch223(zzz340, zzz341, Neg(Succ(Zero)), zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, Succ(zzz670), h) → new_mkVBalBranch0(zzz31, Branch(zzz510, zzz511, Neg(Succ(zzz51200)), zzz513, zzz514), zzz343, h)
new_mkVBalBranch3MkVBalBranch218(zzz461, zzz462, zzz463, zzz464, zzz465, zzz466, zzz467, zzz468, zzz469, zzz470, zzz471, bb) → new_mkVBalBranch3MkVBalBranch110(zzz461, zzz462, zzz463, zzz464, zzz465, zzz466, zzz467, zzz468, zzz469, zzz470, zzz471, new_primMulNat1(zzz463), bb)
new_mkVBalBranch3MkVBalBranch223(zzz340, zzz341, Neg(Succ(Zero)), zzz343, zzz344, zzz510, zzz511, Succ(zzz512000), zzz513, zzz514, zzz31, Zero, h) → new_mkVBalBranch3MkVBalBranch227(zzz340, zzz341, Zero, zzz343, zzz344, zzz510, zzz511, zzz512000, zzz513, zzz514, zzz31, h)
new_mkVBalBranch3MkVBalBranch215(zzz340, zzz341, Pos(Succ(Zero)), zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, Succ(zzz660), h) → new_mkVBalBranch3MkVBalBranch18(zzz340, zzz341, zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, new_primMulNat1(Zero), h)
new_mkVBalBranch3MkVBalBranch229(zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, zzz1125, zzz1126, zzz1127, zzz1128, zzz1129, bd) → new_mkVBalBranch3MkVBalBranch119(zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, zzz1125, zzz1126, zzz1127, zzz1128, zzz1129, new_primMulNat1(zzz1121), bd)
new_mkVBalBranch3MkVBalBranch226(zzz340, zzz341, zzz3420, zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, h) → new_mkVBalBranch0(zzz31, Branch(zzz510, zzz511, Neg(Succ(zzz51200)), zzz513, zzz514), zzz343, h)
new_mkVBalBranch3MkVBalBranch223(zzz340, zzz341, Neg(Succ(Succ(zzz342000))), zzz343, zzz344, zzz510, zzz511, Succ(zzz512000), zzz513, zzz514, zzz31, Zero, h) → new_mkVBalBranch3MkVBalBranch224(zzz340, zzz341, Succ(zzz342000), zzz343, zzz344, zzz510, zzz511, zzz512000, zzz513, zzz514, zzz31, zzz342000, zzz512000, h)
new_mkVBalBranch3MkVBalBranch215(zzz340, zzz341, Pos(Succ(Succ(zzz342000))), zzz343, zzz344, zzz510, zzz511, Zero, zzz513, zzz514, zzz31, Succ(Succ(zzz6600)), h) → new_mkVBalBranch3MkVBalBranch217(zzz340, zzz341, Succ(zzz342000), zzz343, zzz344, zzz510, zzz511, zzz513, zzz514, zzz31, Succ(zzz6600), zzz342000, h)
new_mkVBalBranch3MkVBalBranch117(zzz340, zzz341, zzz34200, zzz343, zzz344, zzz510, zzz511, zzz513, zzz514, zzz31, Succ(zzz1240), h) → new_mkVBalBranch0(zzz31, zzz514, Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), h)
new_mkVBalBranch3MkVBalBranch221(zzz340, zzz341, Succ(zzz34200), zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, h) → new_mkVBalBranch3MkVBalBranch19(zzz340, zzz341, zzz34200, zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, new_primPlusNat2(new_primPlusNat3(Succ(new_primPlusNat3(new_primPlusNat1(zzz34200), zzz34200)), Succ(zzz34200)), Succ(zzz34200)), h)
new_mkVBalBranch3MkVBalBranch120(zzz2050, zzz2051, zzz2052, zzz2053, zzz2054, zzz2055, zzz2056, zzz2057, zzz2058, zzz2059, zzz2060, Succ(zzz20610), Succ(zzz20620), be) → new_mkVBalBranch3MkVBalBranch120(zzz2050, zzz2051, zzz2052, zzz2053, zzz2054, zzz2055, zzz2056, zzz2057, zzz2058, zzz2059, zzz2060, zzz20610, zzz20620, be)
new_mkVBalBranch3MkVBalBranch217(zzz473, zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, zzz481, zzz482, Zero, Zero, bh) → new_mkVBalBranch3MkVBalBranch233(zzz473, zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, zzz481, zzz482, bh)
new_mkVBalBranch3MkVBalBranch223(zzz340, zzz341, Neg(Succ(Succ(zzz342000))), zzz343, zzz344, zzz510, zzz511, Zero, zzz513, zzz514, zzz31, Zero, h) → new_mkVBalBranch3MkVBalBranch118(zzz340, zzz341, Succ(zzz342000), zzz343, zzz344, zzz510, zzz511, zzz513, zzz514, zzz31, new_primMulNat1(Succ(zzz342000)), h)
new_mkVBalBranch3MkVBalBranch216(zzz1105, zzz1106, zzz1107, zzz1108, zzz1109, zzz1110, zzz1111, zzz1112, zzz1113, zzz1114, zzz1115, Succ(zzz11160), Succ(zzz11170), ba) → new_mkVBalBranch3MkVBalBranch216(zzz1105, zzz1106, zzz1107, zzz1108, zzz1109, zzz1110, zzz1111, zzz1112, zzz1113, zzz1114, zzz1115, zzz11160, zzz11170, ba)
new_mkVBalBranch3MkVBalBranch223(zzz340, zzz341, Pos(zzz3420), zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, Succ(zzz670), h) → new_mkVBalBranch0(zzz31, Branch(zzz510, zzz511, Neg(Succ(zzz51200)), zzz513, zzz514), zzz343, h)
new_mkVBalBranch3MkVBalBranch223(zzz340, zzz341, Neg(Succ(Succ(Succ(zzz3420000)))), zzz343, zzz344, zzz510, zzz511, Succ(zzz512000), zzz513, zzz514, zzz31, Succ(Zero), h) → new_mkVBalBranch3MkVBalBranch224(zzz340, zzz341, Succ(Succ(zzz3420000)), zzz343, zzz344, zzz510, zzz511, zzz512000, zzz513, zzz514, zzz31, Succ(zzz3420000), Succ(zzz512000), h)
new_mkVBalBranch3MkVBalBranch19(zzz340, zzz341, zzz34200, zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, Zero, h) → new_mkVBalBranch3MkVBalBranch122(zzz340, zzz341, zzz34200, zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, h)
new_mkVBalBranch0(zzz31, Branch(zzz510, zzz511, Neg(Zero), zzz513, zzz514), Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), h) → new_mkVBalBranch3MkVBalBranch117(zzz340, zzz341, zzz34200, zzz343, zzz344, zzz510, zzz511, zzz513, zzz514, zzz31, new_primMulNat1(zzz34200), h)
new_mkVBalBranch3MkVBalBranch225(zzz498, zzz499, zzz500, zzz501, zzz502, zzz503, zzz504, zzz505, zzz506, zzz507, Succ(zzz5080), Zero, bg) → new_mkVBalBranch3MkVBalBranch118(zzz498, zzz499, zzz500, zzz501, zzz502, zzz503, zzz504, zzz505, zzz506, zzz507, new_primMulNat1(zzz500), bg)
new_mkVBalBranch3MkVBalBranch215(zzz340, zzz341, Pos(Succ(Succ(zzz342000))), zzz343, zzz344, zzz510, zzz511, Zero, zzz513, zzz514, zzz31, Zero, h) → new_mkVBalBranch0(zzz31, Branch(zzz510, zzz511, Pos(Succ(Zero)), zzz513, zzz514), zzz343, h)
new_mkVBalBranch3MkVBalBranch225(zzz498, zzz499, zzz500, zzz501, zzz502, zzz503, zzz504, zzz505, zzz506, zzz507, Succ(zzz5080), Succ(zzz5090), bg) → new_mkVBalBranch3MkVBalBranch225(zzz498, zzz499, zzz500, zzz501, zzz502, zzz503, zzz504, zzz505, zzz506, zzz507, zzz5080, zzz5090, bg)
new_mkVBalBranch3MkVBalBranch19(zzz340, zzz341, zzz34200, zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, Succ(zzz1410), h) → new_mkVBalBranch0(zzz31, zzz514, Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), h)
new_mkVBalBranch3MkVBalBranch223(zzz340, zzz341, Pos(zzz3420), zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, Zero, h) → new_mkVBalBranch3MkVBalBranch226(zzz340, zzz341, zzz3420, zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, h)
new_mkVBalBranch3MkVBalBranch223(zzz340, zzz341, Neg(Succ(Succ(Zero))), zzz343, zzz344, zzz510, zzz511, Succ(zzz512000), zzz513, zzz514, zzz31, Succ(Zero), h) → new_mkVBalBranch3MkVBalBranch224(zzz340, zzz341, Succ(Zero), zzz343, zzz344, zzz510, zzz511, zzz512000, zzz513, zzz514, zzz31, Zero, Succ(zzz512000), h)
new_mkVBalBranch3MkVBalBranch224(zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, zzz1125, zzz1126, zzz1127, zzz1128, zzz1129, Zero, Zero, bd) → new_mkVBalBranch3MkVBalBranch229(zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, zzz1125, zzz1126, zzz1127, zzz1128, zzz1129, bd)
new_mkVBalBranch3MkVBalBranch224(zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, zzz1125, zzz1126, zzz1127, zzz1128, zzz1129, Zero, Succ(zzz11310), bd) → new_mkVBalBranch3MkVBalBranch227(zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, zzz1125, zzz1126, zzz1127, zzz1128, zzz1129, bd)
new_mkVBalBranch3MkVBalBranch224(zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, zzz1125, zzz1126, zzz1127, zzz1128, zzz1129, Succ(zzz11300), Zero, bd) → new_mkVBalBranch3MkVBalBranch119(zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, zzz1125, zzz1126, zzz1127, zzz1128, zzz1129, new_primMulNat1(zzz1121), bd)
new_mkVBalBranch3MkVBalBranch230(zzz498, zzz499, zzz500, zzz501, zzz502, zzz503, zzz504, zzz505, zzz506, zzz507, bg) → new_mkVBalBranch3MkVBalBranch118(zzz498, zzz499, zzz500, zzz501, zzz502, zzz503, zzz504, zzz505, zzz506, zzz507, new_primPlusNat2(new_primMulNat0(zzz500), Succ(zzz500)), bg)
new_mkVBalBranch3MkVBalBranch223(zzz340, zzz341, Neg(Succ(Succ(Zero))), zzz343, zzz344, zzz510, zzz511, Zero, zzz513, zzz514, zzz31, Succ(Succ(zzz6700)), h) → new_mkVBalBranch3MkVBalBranch225(zzz340, zzz341, Succ(Zero), zzz343, zzz344, zzz510, zzz511, zzz513, zzz514, zzz31, Zero, Succ(zzz6700), h)
new_mkVBalBranch3MkVBalBranch223(zzz340, zzz341, Neg(Succ(Succ(Succ(zzz3420000)))), zzz343, zzz344, zzz510, zzz511, Succ(zzz512000), zzz513, zzz514, zzz31, Succ(Succ(zzz6700)), h) → new_mkVBalBranch3MkVBalBranch224(zzz340, zzz341, Succ(Succ(zzz3420000)), zzz343, zzz344, zzz510, zzz511, zzz512000, zzz513, zzz514, zzz31, Succ(zzz3420000), Succ(Succ(new_primPlusNat2(zzz6700, zzz512000))), h)
new_mkVBalBranch3MkVBalBranch115(zzz1986, zzz1987, zzz1988, zzz1989, zzz1990, zzz1991, zzz1992, zzz1993, zzz1994, zzz1995, zzz1996, Succ(zzz19970), Succ(zzz19980), bc) → new_mkVBalBranch3MkVBalBranch115(zzz1986, zzz1987, zzz1988, zzz1989, zzz1990, zzz1991, zzz1992, zzz1993, zzz1994, zzz1995, zzz1996, zzz19970, zzz19980, bc)
new_mkVBalBranch3MkVBalBranch215(zzz340, zzz341, Pos(Zero), zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, Zero, h) → new_mkVBalBranch3MkVBalBranch220(zzz340, zzz341, zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, h)
new_mkVBalBranch3MkVBalBranch215(zzz340, zzz341, Neg(Zero), zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, Succ(zzz660), h) → new_mkVBalBranch0(zzz31, zzz514, Branch(zzz340, zzz341, Neg(Zero), zzz343, zzz344), h)
new_mkVBalBranch3MkVBalBranch118(zzz498, zzz499, zzz500, zzz501, zzz502, zzz503, zzz504, zzz505, zzz506, zzz507, Succ(zzz8040), bg) → new_mkVBalBranch3MkVBalBranch120(zzz498, zzz499, zzz500, zzz501, zzz502, zzz503, zzz504, Zero, zzz505, zzz506, zzz507, Succ(Zero), Succ(zzz8040), bg)
new_mkVBalBranch3MkVBalBranch216(zzz1105, zzz1106, zzz1107, zzz1108, zzz1109, zzz1110, zzz1111, zzz1112, zzz1113, zzz1114, zzz1115, Succ(zzz11160), Zero, ba) → new_mkVBalBranch3MkVBalBranch218(zzz1105, zzz1106, zzz1107, zzz1108, zzz1109, zzz1110, zzz1111, zzz1112, zzz1113, zzz1114, zzz1115, ba)
new_mkVBalBranch3MkVBalBranch221(zzz340, zzz341, Zero, zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, h) → new_mkVBalBranch0(zzz31, zzz514, Branch(zzz340, zzz341, Neg(Zero), zzz343, zzz344), h)
new_mkVBalBranch3MkVBalBranch219(zzz340, zzz341, zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, h) → new_mkVBalBranch3MkVBalBranch18(zzz340, zzz341, zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, new_primMulNat1(Zero), h)
new_mkVBalBranch3MkVBalBranch215(zzz340, zzz341, Pos(Succ(Succ(zzz342000))), zzz343, zzz344, zzz510, zzz511, Succ(zzz512000), zzz513, zzz514, zzz31, Succ(Zero), h) → new_mkVBalBranch3MkVBalBranch216(zzz340, zzz341, Succ(zzz342000), zzz343, zzz344, zzz510, zzz511, zzz512000, zzz513, zzz514, zzz31, Succ(zzz512000), zzz342000, h)
new_mkVBalBranch3MkVBalBranch215(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, Succ(zzz660), h) → new_mkVBalBranch3MkVBalBranch19(zzz340, zzz341, zzz34200, zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, new_primPlusNat2(new_primMulNat0(zzz34200), Succ(zzz34200)), h)
new_mkVBalBranch3MkVBalBranch216(zzz1105, zzz1106, zzz1107, zzz1108, zzz1109, zzz1110, zzz1111, zzz1112, zzz1113, zzz1114, zzz1115, Zero, Zero, ba) → new_mkVBalBranch3MkVBalBranch222(zzz1105, zzz1106, zzz1107, zzz1108, zzz1109, zzz1110, zzz1111, zzz1112, zzz1113, zzz1114, zzz1115, ba)
new_mkVBalBranch3MkVBalBranch233(zzz473, zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, zzz481, zzz482, bh) → new_mkVBalBranch3MkVBalBranch121(zzz473, zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, zzz481, zzz482, new_primMulNat1(zzz475), bh)
new_mkVBalBranch3MkVBalBranch215(zzz340, zzz341, Pos(Succ(Succ(zzz342000))), zzz343, zzz344, zzz510, zzz511, Zero, zzz513, zzz514, zzz31, Succ(Zero), h) → new_mkVBalBranch3MkVBalBranch217(zzz340, zzz341, Succ(zzz342000), zzz343, zzz344, zzz510, zzz511, zzz513, zzz514, zzz31, Zero, zzz342000, h)
new_mkVBalBranch0(zzz31, Branch(zzz510, zzz511, Pos(Zero), zzz513, zzz514), Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), h) → new_mkVBalBranch3MkVBalBranch116(zzz340, zzz341, zzz34200, zzz343, zzz344, zzz510, zzz511, zzz513, zzz514, zzz31, new_primMulNat1(zzz34200), h)
new_mkVBalBranch3MkVBalBranch119(zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, zzz1125, zzz1126, zzz1127, zzz1128, zzz1129, Succ(zzz12130), bd) → new_mkVBalBranch3MkVBalBranch120(zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, zzz1125, Succ(zzz1126), zzz1127, zzz1128, zzz1129, Succ(Succ(zzz1126)), Succ(zzz12130), bd)
new_mkVBalBranch3MkVBalBranch18(zzz340, zzz341, zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, Zero, h) → new_mkVBalBranch3MkVBalBranch115(zzz340, zzz341, Zero, zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, Zero, Succ(zzz51200), h)
new_mkVBalBranch3MkVBalBranch223(zzz340, zzz341, Neg(Succ(Zero)), zzz343, zzz344, zzz510, zzz511, Zero, zzz513, zzz514, zzz31, Zero, h) → new_mkVBalBranch3MkVBalBranch118(zzz340, zzz341, Zero, zzz343, zzz344, zzz510, zzz511, zzz513, zzz514, zzz31, new_primMulNat1(Zero), h)

The TRS R consists of the following rules:

new_primPlusNat1(Zero) → Zero
new_primMulNat0(zzz6200) → new_primPlusNat3(Succ(new_primPlusNat3(new_primPlusNat1(zzz6200), zzz6200)), Succ(zzz6200))
new_primPlusNat2(Succ(zzz900), Succ(zzz9100)) → Succ(Succ(new_primPlusNat2(zzz900, zzz9100)))
new_primPlusNat3(zzz90, Succ(zzz910)) → Succ(Succ(new_primPlusNat2(zzz90, zzz910)))
new_primPlusNat3(zzz90, Zero) → Succ(zzz90)
new_primMulNat1(zzz34200) → new_primPlusNat2(new_primMulNat0(zzz34200), Succ(zzz34200))
new_primPlusNat2(Zero, Zero) → Zero
new_primPlusNat1(Succ(zzz62000)) → Succ(Succ(new_primPlusNat1(zzz62000)))
new_primPlusNat2(Succ(zzz900), Zero) → Succ(zzz900)
new_primPlusNat2(Zero, Succ(zzz9100)) → Succ(zzz9100)

The set Q consists of the following terms:

new_primPlusNat2(Zero, Succ(x0))
new_primMulNat1(x0)
new_primMulNat0(x0)
new_primPlusNat3(x0, Succ(x1))
new_primPlusNat2(Succ(x0), Succ(x1))
new_primPlusNat3(x0, Zero)
new_primPlusNat1(Zero)
new_primPlusNat2(Zero, Zero)
new_primPlusNat1(Succ(x0))
new_primPlusNat2(Succ(x0), Zero)

We have to consider all minimal (P,Q,R)-chains.
By rewriting [15] the rule new_mkVBalBranch0(zzz31, Branch(zzz510, zzz511, Neg(Succ(zzz51200)), zzz513, zzz514), Branch(zzz340, zzz341, zzz342, zzz343, zzz344), h) → new_mkVBalBranch3MkVBalBranch223(zzz340, zzz341, zzz342, zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, new_primMulNat0(zzz51200), h) at position [11] we obtained the following new rules:

new_mkVBalBranch0(zzz31, Branch(zzz510, zzz511, Neg(Succ(zzz51200)), zzz513, zzz514), Branch(zzz340, zzz341, zzz342, zzz343, zzz344), h) → new_mkVBalBranch3MkVBalBranch223(zzz340, zzz341, zzz342, zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, new_primPlusNat3(Succ(new_primPlusNat3(new_primPlusNat1(zzz51200), zzz51200)), Succ(zzz51200)), 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
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                    ↳ DependencyGraphProof
                                      ↳ QDP
                                        ↳ Rewriting
                                          ↳ QDP
                                            ↳ Rewriting
                                              ↳ QDP
                                                ↳ Rewriting
                                                  ↳ QDP
                                                    ↳ Rewriting
                                                      ↳ QDP
                                                        ↳ Rewriting
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP

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

new_mkVBalBranch3MkVBalBranch215(zzz340, zzz341, Neg(zzz3420), zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, Zero, h) → new_mkVBalBranch3MkVBalBranch221(zzz340, zzz341, zzz3420, zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, h)
new_mkVBalBranch3MkVBalBranch225(zzz498, zzz499, zzz500, zzz501, zzz502, zzz503, zzz504, zzz505, zzz506, zzz507, Zero, Zero, bg) → new_mkVBalBranch3MkVBalBranch230(zzz498, zzz499, zzz500, zzz501, zzz502, zzz503, zzz504, zzz505, zzz506, zzz507, bg)
new_mkVBalBranch3MkVBalBranch18(zzz340, zzz341, zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, Succ(zzz1480), h) → new_mkVBalBranch3MkVBalBranch115(zzz340, zzz341, Zero, zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, Succ(zzz1480), Succ(zzz51200), h)
new_mkVBalBranch0(zzz31, Branch(zzz510, zzz511, Neg(Zero), zzz513, zzz514), Branch(zzz340, zzz341, Pos(Succ(zzz34200)), zzz343, zzz344), h) → new_mkVBalBranch0(zzz31, Branch(zzz510, zzz511, Neg(Zero), zzz513, zzz514), zzz343, h)
new_mkVBalBranch3MkVBalBranch215(zzz340, zzz341, Pos(Succ(Succ(zzz342000))), zzz343, zzz344, zzz510, zzz511, Succ(zzz512000), zzz513, zzz514, zzz31, Succ(Succ(zzz6600)), h) → new_mkVBalBranch3MkVBalBranch216(zzz340, zzz341, Succ(zzz342000), zzz343, zzz344, zzz510, zzz511, zzz512000, zzz513, zzz514, zzz31, Succ(Succ(new_primPlusNat2(zzz6600, zzz512000))), zzz342000, h)
new_mkVBalBranch3MkVBalBranch223(zzz340, zzz341, Neg(Succ(Succ(Succ(zzz3420000)))), zzz343, zzz344, zzz510, zzz511, Zero, zzz513, zzz514, zzz31, Succ(Succ(zzz6700)), h) → new_mkVBalBranch3MkVBalBranch225(zzz340, zzz341, Succ(Succ(zzz3420000)), zzz343, zzz344, zzz510, zzz511, zzz513, zzz514, zzz31, Succ(zzz3420000), Succ(zzz6700), h)
new_mkVBalBranch3MkVBalBranch220(zzz340, zzz341, zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, h) → new_mkVBalBranch0(zzz31, zzz514, Branch(zzz340, zzz341, Pos(Zero), zzz343, zzz344), h)
new_mkVBalBranch3MkVBalBranch120(zzz2050, zzz2051, zzz2052, zzz2053, zzz2054, zzz2055, zzz2056, zzz2057, zzz2058, zzz2059, zzz2060, Zero, Succ(zzz20620), be) → new_mkVBalBranch0(zzz2060, zzz2059, Branch(zzz2050, zzz2051, Neg(Succ(zzz2052)), zzz2053, zzz2054), be)
new_mkVBalBranch3MkVBalBranch121(zzz473, zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, zzz481, zzz482, Succ(zzz7390), bh) → new_mkVBalBranch3MkVBalBranch115(zzz473, zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, Zero, zzz480, zzz481, zzz482, Succ(zzz7390), Succ(Zero), bh)
new_mkVBalBranch0(zzz31, Branch(zzz510, zzz511, Pos(Zero), zzz513, zzz514), Branch(zzz340, zzz341, Pos(Succ(zzz34200)), zzz343, zzz344), h) → new_mkVBalBranch0(zzz31, Branch(zzz510, zzz511, Pos(Zero), zzz513, zzz514), zzz343, h)
new_mkVBalBranch3MkVBalBranch228(zzz340, zzz341, zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, h) → new_mkVBalBranch0(zzz31, Branch(zzz510, zzz511, Neg(Succ(zzz51200)), zzz513, zzz514), zzz343, h)
new_mkVBalBranch3MkVBalBranch215(zzz340, zzz341, Pos(Succ(Zero)), zzz343, zzz344, zzz510, zzz511, Zero, zzz513, zzz514, zzz31, Zero, h) → new_mkVBalBranch3MkVBalBranch219(zzz340, zzz341, zzz343, zzz344, zzz510, zzz511, Zero, zzz513, zzz514, zzz31, h)
new_mkVBalBranch3MkVBalBranch223(zzz340, zzz341, Neg(Succ(Succ(Zero))), zzz343, zzz344, zzz510, zzz511, Succ(zzz512000), zzz513, zzz514, zzz31, Succ(Succ(zzz6700)), h) → new_mkVBalBranch3MkVBalBranch224(zzz340, zzz341, Succ(Zero), zzz343, zzz344, zzz510, zzz511, zzz512000, zzz513, zzz514, zzz31, Zero, Succ(Succ(new_primPlusNat2(zzz6700, zzz512000))), h)
new_mkVBalBranch3MkVBalBranch223(zzz340, zzz341, Neg(Succ(Succ(Zero))), zzz343, zzz344, zzz510, zzz511, Zero, zzz513, zzz514, zzz31, Succ(Zero), h) → new_mkVBalBranch3MkVBalBranch225(zzz340, zzz341, Succ(Zero), zzz343, zzz344, zzz510, zzz511, zzz513, zzz514, zzz31, Zero, Zero, h)
new_mkVBalBranch3MkVBalBranch224(zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, zzz1125, zzz1126, zzz1127, zzz1128, zzz1129, Succ(zzz11300), Succ(zzz11310), bd) → new_mkVBalBranch3MkVBalBranch224(zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, zzz1125, zzz1126, zzz1127, zzz1128, zzz1129, zzz11300, zzz11310, bd)
new_mkVBalBranch0(zzz31, Branch(zzz510, zzz511, Pos(Succ(zzz51200)), zzz513, zzz514), Branch(zzz340, zzz341, zzz342, zzz343, zzz344), h) → new_mkVBalBranch3MkVBalBranch215(zzz340, zzz341, zzz342, zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, new_primPlusNat3(Succ(new_primPlusNat3(new_primPlusNat1(zzz51200), zzz51200)), Succ(zzz51200)), h)
new_mkVBalBranch3MkVBalBranch217(zzz473, zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, zzz481, zzz482, Zero, Succ(zzz4840), bh) → new_mkVBalBranch0(zzz482, Branch(zzz478, zzz479, Pos(Succ(Zero)), zzz480, zzz481), zzz476, bh)
new_mkVBalBranch3MkVBalBranch215(zzz340, zzz341, Pos(Succ(Succ(zzz342000))), zzz343, zzz344, zzz510, zzz511, Succ(zzz512000), zzz513, zzz514, zzz31, Zero, h) → new_mkVBalBranch3MkVBalBranch216(zzz340, zzz341, Succ(zzz342000), zzz343, zzz344, zzz510, zzz511, zzz512000, zzz513, zzz514, zzz31, zzz512000, zzz342000, h)
new_mkVBalBranch3MkVBalBranch110(zzz461, zzz462, zzz463, zzz464, zzz465, zzz466, zzz467, zzz468, zzz469, zzz470, zzz471, Succ(zzz5800), bb) → new_mkVBalBranch3MkVBalBranch115(zzz461, zzz462, zzz463, zzz464, zzz465, zzz466, zzz467, Succ(zzz468), zzz469, zzz470, zzz471, Succ(zzz5800), Succ(Succ(zzz468)), bb)
new_mkVBalBranch3MkVBalBranch227(zzz486, zzz487, zzz488, zzz489, zzz490, zzz491, zzz492, zzz493, zzz494, zzz495, zzz496, bf) → new_mkVBalBranch0(zzz496, Branch(zzz491, zzz492, Neg(Succ(Succ(zzz493))), zzz494, zzz495), zzz489, bf)
new_mkVBalBranch3MkVBalBranch215(zzz340, zzz341, Pos(Zero), zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, Succ(zzz660), h) → new_mkVBalBranch0(zzz31, zzz514, Branch(zzz340, zzz341, Pos(Zero), zzz343, zzz344), h)
new_mkVBalBranch3MkVBalBranch223(zzz340, zzz341, Neg(Zero), zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, Succ(zzz670), h) → new_mkVBalBranch0(zzz31, Branch(zzz510, zzz511, Neg(Succ(zzz51200)), zzz513, zzz514), zzz343, h)
new_mkVBalBranch3MkVBalBranch216(zzz1105, zzz1106, zzz1107, zzz1108, zzz1109, zzz1110, zzz1111, zzz1112, zzz1113, zzz1114, zzz1115, Zero, Succ(zzz11170), ba) → new_mkVBalBranch0(zzz1115, Branch(zzz1110, zzz1111, Pos(Succ(Succ(zzz1112))), zzz1113, zzz1114), zzz1108, ba)
new_mkVBalBranch3MkVBalBranch217(zzz473, zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, zzz481, zzz482, Succ(zzz4830), Zero, bh) → new_mkVBalBranch3MkVBalBranch121(zzz473, zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, zzz481, zzz482, new_primMulNat1(zzz475), bh)
new_mkVBalBranch3MkVBalBranch222(zzz461, zzz462, zzz463, zzz464, zzz465, zzz466, zzz467, zzz468, zzz469, zzz470, zzz471, bb) → new_mkVBalBranch3MkVBalBranch110(zzz461, zzz462, zzz463, zzz464, zzz465, zzz466, zzz467, zzz468, zzz469, zzz470, zzz471, new_primMulNat1(zzz463), bb)
new_mkVBalBranch3MkVBalBranch115(zzz1986, zzz1987, zzz1988, zzz1989, zzz1990, zzz1991, zzz1992, zzz1993, zzz1994, zzz1995, zzz1996, Zero, Succ(zzz19980), bc) → new_mkVBalBranch0(zzz1996, zzz1995, Branch(zzz1986, zzz1987, Pos(Succ(zzz1988)), zzz1989, zzz1990), bc)
new_mkVBalBranch3MkVBalBranch223(zzz340, zzz341, Neg(Zero), zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, Zero, h) → new_mkVBalBranch3MkVBalBranch228(zzz340, zzz341, zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, h)
new_mkVBalBranch3MkVBalBranch122(zzz340, zzz341, zzz34200, zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, h) → new_mkVBalBranch0(zzz31, zzz514, Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), h)
new_mkVBalBranch3MkVBalBranch217(zzz473, zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, zzz481, zzz482, Succ(zzz4830), Succ(zzz4840), bh) → new_mkVBalBranch3MkVBalBranch217(zzz473, zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, zzz481, zzz482, zzz4830, zzz4840, bh)
new_mkVBalBranch3MkVBalBranch116(zzz340, zzz341, zzz34200, zzz343, zzz344, zzz510, zzz511, zzz513, zzz514, zzz31, Succ(zzz1200), h) → new_mkVBalBranch0(zzz31, zzz514, Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), h)
new_mkVBalBranch3MkVBalBranch110(zzz461, zzz462, zzz463, zzz464, zzz465, zzz466, zzz467, zzz468, zzz469, zzz470, zzz471, Zero, bb) → new_mkVBalBranch3MkVBalBranch115(zzz461, zzz462, zzz463, zzz464, zzz465, zzz466, zzz467, Succ(zzz468), zzz469, zzz470, zzz471, Zero, Succ(Succ(zzz468)), bb)
new_mkVBalBranch3MkVBalBranch225(zzz498, zzz499, zzz500, zzz501, zzz502, zzz503, zzz504, zzz505, zzz506, zzz507, Zero, Succ(zzz5090), bg) → new_mkVBalBranch0(zzz507, Branch(zzz503, zzz504, Neg(Succ(Zero)), zzz505, zzz506), zzz501, bg)
new_mkVBalBranch3MkVBalBranch223(zzz340, zzz341, Neg(Succ(Succ(Succ(zzz3420000)))), zzz343, zzz344, zzz510, zzz511, Zero, zzz513, zzz514, zzz31, Succ(Zero), h) → new_mkVBalBranch3MkVBalBranch225(zzz340, zzz341, Succ(Succ(zzz3420000)), zzz343, zzz344, zzz510, zzz511, zzz513, zzz514, zzz31, Succ(zzz3420000), Zero, h)
new_mkVBalBranch3MkVBalBranch121(zzz473, zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, zzz481, zzz482, Zero, bh) → new_mkVBalBranch3MkVBalBranch115(zzz473, zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, Zero, zzz480, zzz481, zzz482, Zero, Succ(Zero), bh)
new_mkVBalBranch3MkVBalBranch215(zzz340, zzz341, Pos(Succ(Zero)), zzz343, zzz344, zzz510, zzz511, Succ(zzz512000), zzz513, zzz514, zzz31, Zero, h) → new_mkVBalBranch3MkVBalBranch218(zzz340, zzz341, Zero, zzz343, zzz344, zzz510, zzz511, zzz512000, zzz513, zzz514, zzz31, h)
new_mkVBalBranch3MkVBalBranch223(zzz340, zzz341, Neg(Succ(Zero)), zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, Succ(zzz670), h) → new_mkVBalBranch0(zzz31, Branch(zzz510, zzz511, Neg(Succ(zzz51200)), zzz513, zzz514), zzz343, h)
new_mkVBalBranch3MkVBalBranch218(zzz461, zzz462, zzz463, zzz464, zzz465, zzz466, zzz467, zzz468, zzz469, zzz470, zzz471, bb) → new_mkVBalBranch3MkVBalBranch110(zzz461, zzz462, zzz463, zzz464, zzz465, zzz466, zzz467, zzz468, zzz469, zzz470, zzz471, new_primMulNat1(zzz463), bb)
new_mkVBalBranch3MkVBalBranch223(zzz340, zzz341, Neg(Succ(Zero)), zzz343, zzz344, zzz510, zzz511, Succ(zzz512000), zzz513, zzz514, zzz31, Zero, h) → new_mkVBalBranch3MkVBalBranch227(zzz340, zzz341, Zero, zzz343, zzz344, zzz510, zzz511, zzz512000, zzz513, zzz514, zzz31, h)
new_mkVBalBranch3MkVBalBranch215(zzz340, zzz341, Pos(Succ(Zero)), zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, Succ(zzz660), h) → new_mkVBalBranch3MkVBalBranch18(zzz340, zzz341, zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, new_primMulNat1(Zero), h)
new_mkVBalBranch3MkVBalBranch229(zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, zzz1125, zzz1126, zzz1127, zzz1128, zzz1129, bd) → new_mkVBalBranch3MkVBalBranch119(zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, zzz1125, zzz1126, zzz1127, zzz1128, zzz1129, new_primMulNat1(zzz1121), bd)
new_mkVBalBranch3MkVBalBranch215(zzz340, zzz341, Pos(Succ(Succ(zzz342000))), zzz343, zzz344, zzz510, zzz511, Zero, zzz513, zzz514, zzz31, Succ(Succ(zzz6600)), h) → new_mkVBalBranch3MkVBalBranch217(zzz340, zzz341, Succ(zzz342000), zzz343, zzz344, zzz510, zzz511, zzz513, zzz514, zzz31, Succ(zzz6600), zzz342000, h)
new_mkVBalBranch3MkVBalBranch223(zzz340, zzz341, Neg(Succ(Succ(zzz342000))), zzz343, zzz344, zzz510, zzz511, Succ(zzz512000), zzz513, zzz514, zzz31, Zero, h) → new_mkVBalBranch3MkVBalBranch224(zzz340, zzz341, Succ(zzz342000), zzz343, zzz344, zzz510, zzz511, zzz512000, zzz513, zzz514, zzz31, zzz342000, zzz512000, h)
new_mkVBalBranch3MkVBalBranch226(zzz340, zzz341, zzz3420, zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, h) → new_mkVBalBranch0(zzz31, Branch(zzz510, zzz511, Neg(Succ(zzz51200)), zzz513, zzz514), zzz343, h)
new_mkVBalBranch3MkVBalBranch117(zzz340, zzz341, zzz34200, zzz343, zzz344, zzz510, zzz511, zzz513, zzz514, zzz31, Succ(zzz1240), h) → new_mkVBalBranch0(zzz31, zzz514, Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), h)
new_mkVBalBranch0(zzz31, Branch(zzz510, zzz511, Neg(Succ(zzz51200)), zzz513, zzz514), Branch(zzz340, zzz341, zzz342, zzz343, zzz344), h) → new_mkVBalBranch3MkVBalBranch223(zzz340, zzz341, zzz342, zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, new_primPlusNat3(Succ(new_primPlusNat3(new_primPlusNat1(zzz51200), zzz51200)), Succ(zzz51200)), h)
new_mkVBalBranch3MkVBalBranch217(zzz473, zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, zzz481, zzz482, Zero, Zero, bh) → new_mkVBalBranch3MkVBalBranch233(zzz473, zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, zzz481, zzz482, bh)
new_mkVBalBranch3MkVBalBranch120(zzz2050, zzz2051, zzz2052, zzz2053, zzz2054, zzz2055, zzz2056, zzz2057, zzz2058, zzz2059, zzz2060, Succ(zzz20610), Succ(zzz20620), be) → new_mkVBalBranch3MkVBalBranch120(zzz2050, zzz2051, zzz2052, zzz2053, zzz2054, zzz2055, zzz2056, zzz2057, zzz2058, zzz2059, zzz2060, zzz20610, zzz20620, be)
new_mkVBalBranch3MkVBalBranch221(zzz340, zzz341, Succ(zzz34200), zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, h) → new_mkVBalBranch3MkVBalBranch19(zzz340, zzz341, zzz34200, zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, new_primPlusNat2(new_primPlusNat3(Succ(new_primPlusNat3(new_primPlusNat1(zzz34200), zzz34200)), Succ(zzz34200)), Succ(zzz34200)), h)
new_mkVBalBranch3MkVBalBranch223(zzz340, zzz341, Neg(Succ(Succ(zzz342000))), zzz343, zzz344, zzz510, zzz511, Zero, zzz513, zzz514, zzz31, Zero, h) → new_mkVBalBranch3MkVBalBranch118(zzz340, zzz341, Succ(zzz342000), zzz343, zzz344, zzz510, zzz511, zzz513, zzz514, zzz31, new_primMulNat1(Succ(zzz342000)), h)
new_mkVBalBranch3MkVBalBranch223(zzz340, zzz341, Pos(zzz3420), zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, Succ(zzz670), h) → new_mkVBalBranch0(zzz31, Branch(zzz510, zzz511, Neg(Succ(zzz51200)), zzz513, zzz514), zzz343, h)
new_mkVBalBranch3MkVBalBranch216(zzz1105, zzz1106, zzz1107, zzz1108, zzz1109, zzz1110, zzz1111, zzz1112, zzz1113, zzz1114, zzz1115, Succ(zzz11160), Succ(zzz11170), ba) → new_mkVBalBranch3MkVBalBranch216(zzz1105, zzz1106, zzz1107, zzz1108, zzz1109, zzz1110, zzz1111, zzz1112, zzz1113, zzz1114, zzz1115, zzz11160, zzz11170, ba)
new_mkVBalBranch3MkVBalBranch19(zzz340, zzz341, zzz34200, zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, Zero, h) → new_mkVBalBranch3MkVBalBranch122(zzz340, zzz341, zzz34200, zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, h)
new_mkVBalBranch3MkVBalBranch223(zzz340, zzz341, Neg(Succ(Succ(Succ(zzz3420000)))), zzz343, zzz344, zzz510, zzz511, Succ(zzz512000), zzz513, zzz514, zzz31, Succ(Zero), h) → new_mkVBalBranch3MkVBalBranch224(zzz340, zzz341, Succ(Succ(zzz3420000)), zzz343, zzz344, zzz510, zzz511, zzz512000, zzz513, zzz514, zzz31, Succ(zzz3420000), Succ(zzz512000), h)
new_mkVBalBranch0(zzz31, Branch(zzz510, zzz511, Neg(Zero), zzz513, zzz514), Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), h) → new_mkVBalBranch3MkVBalBranch117(zzz340, zzz341, zzz34200, zzz343, zzz344, zzz510, zzz511, zzz513, zzz514, zzz31, new_primMulNat1(zzz34200), h)
new_mkVBalBranch3MkVBalBranch215(zzz340, zzz341, Pos(Succ(Succ(zzz342000))), zzz343, zzz344, zzz510, zzz511, Zero, zzz513, zzz514, zzz31, Zero, h) → new_mkVBalBranch0(zzz31, Branch(zzz510, zzz511, Pos(Succ(Zero)), zzz513, zzz514), zzz343, h)
new_mkVBalBranch3MkVBalBranch225(zzz498, zzz499, zzz500, zzz501, zzz502, zzz503, zzz504, zzz505, zzz506, zzz507, Succ(zzz5080), Zero, bg) → new_mkVBalBranch3MkVBalBranch118(zzz498, zzz499, zzz500, zzz501, zzz502, zzz503, zzz504, zzz505, zzz506, zzz507, new_primMulNat1(zzz500), bg)
new_mkVBalBranch3MkVBalBranch225(zzz498, zzz499, zzz500, zzz501, zzz502, zzz503, zzz504, zzz505, zzz506, zzz507, Succ(zzz5080), Succ(zzz5090), bg) → new_mkVBalBranch3MkVBalBranch225(zzz498, zzz499, zzz500, zzz501, zzz502, zzz503, zzz504, zzz505, zzz506, zzz507, zzz5080, zzz5090, bg)
new_mkVBalBranch3MkVBalBranch19(zzz340, zzz341, zzz34200, zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, Succ(zzz1410), h) → new_mkVBalBranch0(zzz31, zzz514, Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), h)
new_mkVBalBranch3MkVBalBranch224(zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, zzz1125, zzz1126, zzz1127, zzz1128, zzz1129, Zero, Succ(zzz11310), bd) → new_mkVBalBranch3MkVBalBranch227(zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, zzz1125, zzz1126, zzz1127, zzz1128, zzz1129, bd)
new_mkVBalBranch3MkVBalBranch224(zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, zzz1125, zzz1126, zzz1127, zzz1128, zzz1129, Zero, Zero, bd) → new_mkVBalBranch3MkVBalBranch229(zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, zzz1125, zzz1126, zzz1127, zzz1128, zzz1129, bd)
new_mkVBalBranch3MkVBalBranch223(zzz340, zzz341, Neg(Succ(Succ(Zero))), zzz343, zzz344, zzz510, zzz511, Succ(zzz512000), zzz513, zzz514, zzz31, Succ(Zero), h) → new_mkVBalBranch3MkVBalBranch224(zzz340, zzz341, Succ(Zero), zzz343, zzz344, zzz510, zzz511, zzz512000, zzz513, zzz514, zzz31, Zero, Succ(zzz512000), h)
new_mkVBalBranch3MkVBalBranch223(zzz340, zzz341, Pos(zzz3420), zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, Zero, h) → new_mkVBalBranch3MkVBalBranch226(zzz340, zzz341, zzz3420, zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, h)
new_mkVBalBranch3MkVBalBranch224(zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, zzz1125, zzz1126, zzz1127, zzz1128, zzz1129, Succ(zzz11300), Zero, bd) → new_mkVBalBranch3MkVBalBranch119(zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, zzz1125, zzz1126, zzz1127, zzz1128, zzz1129, new_primMulNat1(zzz1121), bd)
new_mkVBalBranch3MkVBalBranch230(zzz498, zzz499, zzz500, zzz501, zzz502, zzz503, zzz504, zzz505, zzz506, zzz507, bg) → new_mkVBalBranch3MkVBalBranch118(zzz498, zzz499, zzz500, zzz501, zzz502, zzz503, zzz504, zzz505, zzz506, zzz507, new_primPlusNat2(new_primMulNat0(zzz500), Succ(zzz500)), bg)
new_mkVBalBranch3MkVBalBranch223(zzz340, zzz341, Neg(Succ(Succ(Succ(zzz3420000)))), zzz343, zzz344, zzz510, zzz511, Succ(zzz512000), zzz513, zzz514, zzz31, Succ(Succ(zzz6700)), h) → new_mkVBalBranch3MkVBalBranch224(zzz340, zzz341, Succ(Succ(zzz3420000)), zzz343, zzz344, zzz510, zzz511, zzz512000, zzz513, zzz514, zzz31, Succ(zzz3420000), Succ(Succ(new_primPlusNat2(zzz6700, zzz512000))), h)
new_mkVBalBranch3MkVBalBranch223(zzz340, zzz341, Neg(Succ(Succ(Zero))), zzz343, zzz344, zzz510, zzz511, Zero, zzz513, zzz514, zzz31, Succ(Succ(zzz6700)), h) → new_mkVBalBranch3MkVBalBranch225(zzz340, zzz341, Succ(Zero), zzz343, zzz344, zzz510, zzz511, zzz513, zzz514, zzz31, Zero, Succ(zzz6700), h)
new_mkVBalBranch3MkVBalBranch215(zzz340, zzz341, Pos(Zero), zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, Zero, h) → new_mkVBalBranch3MkVBalBranch220(zzz340, zzz341, zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, h)
new_mkVBalBranch3MkVBalBranch115(zzz1986, zzz1987, zzz1988, zzz1989, zzz1990, zzz1991, zzz1992, zzz1993, zzz1994, zzz1995, zzz1996, Succ(zzz19970), Succ(zzz19980), bc) → new_mkVBalBranch3MkVBalBranch115(zzz1986, zzz1987, zzz1988, zzz1989, zzz1990, zzz1991, zzz1992, zzz1993, zzz1994, zzz1995, zzz1996, zzz19970, zzz19980, bc)
new_mkVBalBranch3MkVBalBranch215(zzz340, zzz341, Neg(Zero), zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, Succ(zzz660), h) → new_mkVBalBranch0(zzz31, zzz514, Branch(zzz340, zzz341, Neg(Zero), zzz343, zzz344), h)
new_mkVBalBranch3MkVBalBranch118(zzz498, zzz499, zzz500, zzz501, zzz502, zzz503, zzz504, zzz505, zzz506, zzz507, Succ(zzz8040), bg) → new_mkVBalBranch3MkVBalBranch120(zzz498, zzz499, zzz500, zzz501, zzz502, zzz503, zzz504, Zero, zzz505, zzz506, zzz507, Succ(Zero), Succ(zzz8040), bg)
new_mkVBalBranch3MkVBalBranch216(zzz1105, zzz1106, zzz1107, zzz1108, zzz1109, zzz1110, zzz1111, zzz1112, zzz1113, zzz1114, zzz1115, Succ(zzz11160), Zero, ba) → new_mkVBalBranch3MkVBalBranch218(zzz1105, zzz1106, zzz1107, zzz1108, zzz1109, zzz1110, zzz1111, zzz1112, zzz1113, zzz1114, zzz1115, ba)
new_mkVBalBranch3MkVBalBranch215(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, Succ(zzz660), h) → new_mkVBalBranch3MkVBalBranch19(zzz340, zzz341, zzz34200, zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, new_primPlusNat2(new_primMulNat0(zzz34200), Succ(zzz34200)), h)
new_mkVBalBranch3MkVBalBranch215(zzz340, zzz341, Pos(Succ(Succ(zzz342000))), zzz343, zzz344, zzz510, zzz511, Succ(zzz512000), zzz513, zzz514, zzz31, Succ(Zero), h) → new_mkVBalBranch3MkVBalBranch216(zzz340, zzz341, Succ(zzz342000), zzz343, zzz344, zzz510, zzz511, zzz512000, zzz513, zzz514, zzz31, Succ(zzz512000), zzz342000, h)
new_mkVBalBranch3MkVBalBranch219(zzz340, zzz341, zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, h) → new_mkVBalBranch3MkVBalBranch18(zzz340, zzz341, zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, new_primMulNat1(Zero), h)
new_mkVBalBranch3MkVBalBranch221(zzz340, zzz341, Zero, zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, h) → new_mkVBalBranch0(zzz31, zzz514, Branch(zzz340, zzz341, Neg(Zero), zzz343, zzz344), h)
new_mkVBalBranch3MkVBalBranch216(zzz1105, zzz1106, zzz1107, zzz1108, zzz1109, zzz1110, zzz1111, zzz1112, zzz1113, zzz1114, zzz1115, Zero, Zero, ba) → new_mkVBalBranch3MkVBalBranch222(zzz1105, zzz1106, zzz1107, zzz1108, zzz1109, zzz1110, zzz1111, zzz1112, zzz1113, zzz1114, zzz1115, ba)
new_mkVBalBranch3MkVBalBranch233(zzz473, zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, zzz481, zzz482, bh) → new_mkVBalBranch3MkVBalBranch121(zzz473, zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, zzz481, zzz482, new_primMulNat1(zzz475), bh)
new_mkVBalBranch3MkVBalBranch215(zzz340, zzz341, Pos(Succ(Succ(zzz342000))), zzz343, zzz344, zzz510, zzz511, Zero, zzz513, zzz514, zzz31, Succ(Zero), h) → new_mkVBalBranch3MkVBalBranch217(zzz340, zzz341, Succ(zzz342000), zzz343, zzz344, zzz510, zzz511, zzz513, zzz514, zzz31, Zero, zzz342000, h)
new_mkVBalBranch0(zzz31, Branch(zzz510, zzz511, Pos(Zero), zzz513, zzz514), Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), h) → new_mkVBalBranch3MkVBalBranch116(zzz340, zzz341, zzz34200, zzz343, zzz344, zzz510, zzz511, zzz513, zzz514, zzz31, new_primMulNat1(zzz34200), h)
new_mkVBalBranch3MkVBalBranch18(zzz340, zzz341, zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, Zero, h) → new_mkVBalBranch3MkVBalBranch115(zzz340, zzz341, Zero, zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, Zero, Succ(zzz51200), h)
new_mkVBalBranch3MkVBalBranch119(zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, zzz1125, zzz1126, zzz1127, zzz1128, zzz1129, Succ(zzz12130), bd) → new_mkVBalBranch3MkVBalBranch120(zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, zzz1125, Succ(zzz1126), zzz1127, zzz1128, zzz1129, Succ(Succ(zzz1126)), Succ(zzz12130), bd)
new_mkVBalBranch3MkVBalBranch223(zzz340, zzz341, Neg(Succ(Zero)), zzz343, zzz344, zzz510, zzz511, Zero, zzz513, zzz514, zzz31, Zero, h) → new_mkVBalBranch3MkVBalBranch118(zzz340, zzz341, Zero, zzz343, zzz344, zzz510, zzz511, zzz513, zzz514, zzz31, new_primMulNat1(Zero), h)

The TRS R consists of the following rules:

new_primPlusNat1(Zero) → Zero
new_primMulNat0(zzz6200) → new_primPlusNat3(Succ(new_primPlusNat3(new_primPlusNat1(zzz6200), zzz6200)), Succ(zzz6200))
new_primPlusNat2(Succ(zzz900), Succ(zzz9100)) → Succ(Succ(new_primPlusNat2(zzz900, zzz9100)))
new_primPlusNat3(zzz90, Succ(zzz910)) → Succ(Succ(new_primPlusNat2(zzz90, zzz910)))
new_primPlusNat3(zzz90, Zero) → Succ(zzz90)
new_primMulNat1(zzz34200) → new_primPlusNat2(new_primMulNat0(zzz34200), Succ(zzz34200))
new_primPlusNat2(Zero, Zero) → Zero
new_primPlusNat1(Succ(zzz62000)) → Succ(Succ(new_primPlusNat1(zzz62000)))
new_primPlusNat2(Succ(zzz900), Zero) → Succ(zzz900)
new_primPlusNat2(Zero, Succ(zzz9100)) → Succ(zzz9100)

The set Q consists of the following terms:

new_primPlusNat2(Zero, Succ(x0))
new_primMulNat1(x0)
new_primMulNat0(x0)
new_primPlusNat3(x0, Succ(x1))
new_primPlusNat2(Succ(x0), Succ(x1))
new_primPlusNat3(x0, Zero)
new_primPlusNat1(Zero)
new_primPlusNat2(Zero, Zero)
new_primPlusNat1(Succ(x0))
new_primPlusNat2(Succ(x0), Zero)

We have to consider all minimal (P,Q,R)-chains.
By rewriting [15] the rule new_mkVBalBranch3MkVBalBranch225(zzz498, zzz499, zzz500, zzz501, zzz502, zzz503, zzz504, zzz505, zzz506, zzz507, Succ(zzz5080), Zero, bg) → new_mkVBalBranch3MkVBalBranch118(zzz498, zzz499, zzz500, zzz501, zzz502, zzz503, zzz504, zzz505, zzz506, zzz507, new_primMulNat1(zzz500), bg) at position [10] we obtained the following new rules:

new_mkVBalBranch3MkVBalBranch225(zzz498, zzz499, zzz500, zzz501, zzz502, zzz503, zzz504, zzz505, zzz506, zzz507, Succ(zzz5080), Zero, bg) → new_mkVBalBranch3MkVBalBranch118(zzz498, zzz499, zzz500, zzz501, zzz502, zzz503, zzz504, zzz505, zzz506, zzz507, new_primPlusNat2(new_primMulNat0(zzz500), Succ(zzz500)), bg)



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

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

new_mkVBalBranch3MkVBalBranch225(zzz498, zzz499, zzz500, zzz501, zzz502, zzz503, zzz504, zzz505, zzz506, zzz507, Zero, Zero, bg) → new_mkVBalBranch3MkVBalBranch230(zzz498, zzz499, zzz500, zzz501, zzz502, zzz503, zzz504, zzz505, zzz506, zzz507, bg)
new_mkVBalBranch3MkVBalBranch215(zzz340, zzz341, Neg(zzz3420), zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, Zero, h) → new_mkVBalBranch3MkVBalBranch221(zzz340, zzz341, zzz3420, zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, h)
new_mkVBalBranch3MkVBalBranch18(zzz340, zzz341, zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, Succ(zzz1480), h) → new_mkVBalBranch3MkVBalBranch115(zzz340, zzz341, Zero, zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, Succ(zzz1480), Succ(zzz51200), h)
new_mkVBalBranch3MkVBalBranch215(zzz340, zzz341, Pos(Succ(Succ(zzz342000))), zzz343, zzz344, zzz510, zzz511, Succ(zzz512000), zzz513, zzz514, zzz31, Succ(Succ(zzz6600)), h) → new_mkVBalBranch3MkVBalBranch216(zzz340, zzz341, Succ(zzz342000), zzz343, zzz344, zzz510, zzz511, zzz512000, zzz513, zzz514, zzz31, Succ(Succ(new_primPlusNat2(zzz6600, zzz512000))), zzz342000, h)
new_mkVBalBranch0(zzz31, Branch(zzz510, zzz511, Neg(Zero), zzz513, zzz514), Branch(zzz340, zzz341, Pos(Succ(zzz34200)), zzz343, zzz344), h) → new_mkVBalBranch0(zzz31, Branch(zzz510, zzz511, Neg(Zero), zzz513, zzz514), zzz343, h)
new_mkVBalBranch3MkVBalBranch223(zzz340, zzz341, Neg(Succ(Succ(Succ(zzz3420000)))), zzz343, zzz344, zzz510, zzz511, Zero, zzz513, zzz514, zzz31, Succ(Succ(zzz6700)), h) → new_mkVBalBranch3MkVBalBranch225(zzz340, zzz341, Succ(Succ(zzz3420000)), zzz343, zzz344, zzz510, zzz511, zzz513, zzz514, zzz31, Succ(zzz3420000), Succ(zzz6700), h)
new_mkVBalBranch3MkVBalBranch120(zzz2050, zzz2051, zzz2052, zzz2053, zzz2054, zzz2055, zzz2056, zzz2057, zzz2058, zzz2059, zzz2060, Zero, Succ(zzz20620), be) → new_mkVBalBranch0(zzz2060, zzz2059, Branch(zzz2050, zzz2051, Neg(Succ(zzz2052)), zzz2053, zzz2054), be)
new_mkVBalBranch3MkVBalBranch220(zzz340, zzz341, zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, h) → new_mkVBalBranch0(zzz31, zzz514, Branch(zzz340, zzz341, Pos(Zero), zzz343, zzz344), h)
new_mkVBalBranch3MkVBalBranch228(zzz340, zzz341, zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, h) → new_mkVBalBranch0(zzz31, Branch(zzz510, zzz511, Neg(Succ(zzz51200)), zzz513, zzz514), zzz343, h)
new_mkVBalBranch0(zzz31, Branch(zzz510, zzz511, Pos(Zero), zzz513, zzz514), Branch(zzz340, zzz341, Pos(Succ(zzz34200)), zzz343, zzz344), h) → new_mkVBalBranch0(zzz31, Branch(zzz510, zzz511, Pos(Zero), zzz513, zzz514), zzz343, h)
new_mkVBalBranch3MkVBalBranch121(zzz473, zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, zzz481, zzz482, Succ(zzz7390), bh) → new_mkVBalBranch3MkVBalBranch115(zzz473, zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, Zero, zzz480, zzz481, zzz482, Succ(zzz7390), Succ(Zero), bh)
new_mkVBalBranch3MkVBalBranch223(zzz340, zzz341, Neg(Succ(Succ(Zero))), zzz343, zzz344, zzz510, zzz511, Succ(zzz512000), zzz513, zzz514, zzz31, Succ(Succ(zzz6700)), h) → new_mkVBalBranch3MkVBalBranch224(zzz340, zzz341, Succ(Zero), zzz343, zzz344, zzz510, zzz511, zzz512000, zzz513, zzz514, zzz31, Zero, Succ(Succ(new_primPlusNat2(zzz6700, zzz512000))), h)
new_mkVBalBranch3MkVBalBranch215(zzz340, zzz341, Pos(Succ(Zero)), zzz343, zzz344, zzz510, zzz511, Zero, zzz513, zzz514, zzz31, Zero, h) → new_mkVBalBranch3MkVBalBranch219(zzz340, zzz341, zzz343, zzz344, zzz510, zzz511, Zero, zzz513, zzz514, zzz31, h)
new_mkVBalBranch3MkVBalBranch223(zzz340, zzz341, Neg(Succ(Succ(Zero))), zzz343, zzz344, zzz510, zzz511, Zero, zzz513, zzz514, zzz31, Succ(Zero), h) → new_mkVBalBranch3MkVBalBranch225(zzz340, zzz341, Succ(Zero), zzz343, zzz344, zzz510, zzz511, zzz513, zzz514, zzz31, Zero, Zero, h)
new_mkVBalBranch3MkVBalBranch224(zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, zzz1125, zzz1126, zzz1127, zzz1128, zzz1129, Succ(zzz11300), Succ(zzz11310), bd) → new_mkVBalBranch3MkVBalBranch224(zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, zzz1125, zzz1126, zzz1127, zzz1128, zzz1129, zzz11300, zzz11310, bd)
new_mkVBalBranch3MkVBalBranch217(zzz473, zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, zzz481, zzz482, Zero, Succ(zzz4840), bh) → new_mkVBalBranch0(zzz482, Branch(zzz478, zzz479, Pos(Succ(Zero)), zzz480, zzz481), zzz476, bh)
new_mkVBalBranch0(zzz31, Branch(zzz510, zzz511, Pos(Succ(zzz51200)), zzz513, zzz514), Branch(zzz340, zzz341, zzz342, zzz343, zzz344), h) → new_mkVBalBranch3MkVBalBranch215(zzz340, zzz341, zzz342, zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, new_primPlusNat3(Succ(new_primPlusNat3(new_primPlusNat1(zzz51200), zzz51200)), Succ(zzz51200)), h)
new_mkVBalBranch3MkVBalBranch215(zzz340, zzz341, Pos(Succ(Succ(zzz342000))), zzz343, zzz344, zzz510, zzz511, Succ(zzz512000), zzz513, zzz514, zzz31, Zero, h) → new_mkVBalBranch3MkVBalBranch216(zzz340, zzz341, Succ(zzz342000), zzz343, zzz344, zzz510, zzz511, zzz512000, zzz513, zzz514, zzz31, zzz512000, zzz342000, h)
new_mkVBalBranch3MkVBalBranch110(zzz461, zzz462, zzz463, zzz464, zzz465, zzz466, zzz467, zzz468, zzz469, zzz470, zzz471, Succ(zzz5800), bb) → new_mkVBalBranch3MkVBalBranch115(zzz461, zzz462, zzz463, zzz464, zzz465, zzz466, zzz467, Succ(zzz468), zzz469, zzz470, zzz471, Succ(zzz5800), Succ(Succ(zzz468)), bb)
new_mkVBalBranch3MkVBalBranch227(zzz486, zzz487, zzz488, zzz489, zzz490, zzz491, zzz492, zzz493, zzz494, zzz495, zzz496, bf) → new_mkVBalBranch0(zzz496, Branch(zzz491, zzz492, Neg(Succ(Succ(zzz493))), zzz494, zzz495), zzz489, bf)
new_mkVBalBranch3MkVBalBranch215(zzz340, zzz341, Pos(Zero), zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, Succ(zzz660), h) → new_mkVBalBranch0(zzz31, zzz514, Branch(zzz340, zzz341, Pos(Zero), zzz343, zzz344), h)
new_mkVBalBranch3MkVBalBranch223(zzz340, zzz341, Neg(Zero), zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, Succ(zzz670), h) → new_mkVBalBranch0(zzz31, Branch(zzz510, zzz511, Neg(Succ(zzz51200)), zzz513, zzz514), zzz343, h)
new_mkVBalBranch3MkVBalBranch216(zzz1105, zzz1106, zzz1107, zzz1108, zzz1109, zzz1110, zzz1111, zzz1112, zzz1113, zzz1114, zzz1115, Zero, Succ(zzz11170), ba) → new_mkVBalBranch0(zzz1115, Branch(zzz1110, zzz1111, Pos(Succ(Succ(zzz1112))), zzz1113, zzz1114), zzz1108, ba)
new_mkVBalBranch3MkVBalBranch222(zzz461, zzz462, zzz463, zzz464, zzz465, zzz466, zzz467, zzz468, zzz469, zzz470, zzz471, bb) → new_mkVBalBranch3MkVBalBranch110(zzz461, zzz462, zzz463, zzz464, zzz465, zzz466, zzz467, zzz468, zzz469, zzz470, zzz471, new_primMulNat1(zzz463), bb)
new_mkVBalBranch3MkVBalBranch217(zzz473, zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, zzz481, zzz482, Succ(zzz4830), Zero, bh) → new_mkVBalBranch3MkVBalBranch121(zzz473, zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, zzz481, zzz482, new_primMulNat1(zzz475), bh)
new_mkVBalBranch3MkVBalBranch115(zzz1986, zzz1987, zzz1988, zzz1989, zzz1990, zzz1991, zzz1992, zzz1993, zzz1994, zzz1995, zzz1996, Zero, Succ(zzz19980), bc) → new_mkVBalBranch0(zzz1996, zzz1995, Branch(zzz1986, zzz1987, Pos(Succ(zzz1988)), zzz1989, zzz1990), bc)
new_mkVBalBranch3MkVBalBranch223(zzz340, zzz341, Neg(Zero), zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, Zero, h) → new_mkVBalBranch3MkVBalBranch228(zzz340, zzz341, zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, h)
new_mkVBalBranch3MkVBalBranch122(zzz340, zzz341, zzz34200, zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, h) → new_mkVBalBranch0(zzz31, zzz514, Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), h)
new_mkVBalBranch3MkVBalBranch217(zzz473, zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, zzz481, zzz482, Succ(zzz4830), Succ(zzz4840), bh) → new_mkVBalBranch3MkVBalBranch217(zzz473, zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, zzz481, zzz482, zzz4830, zzz4840, bh)
new_mkVBalBranch3MkVBalBranch116(zzz340, zzz341, zzz34200, zzz343, zzz344, zzz510, zzz511, zzz513, zzz514, zzz31, Succ(zzz1200), h) → new_mkVBalBranch0(zzz31, zzz514, Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), h)
new_mkVBalBranch3MkVBalBranch110(zzz461, zzz462, zzz463, zzz464, zzz465, zzz466, zzz467, zzz468, zzz469, zzz470, zzz471, Zero, bb) → new_mkVBalBranch3MkVBalBranch115(zzz461, zzz462, zzz463, zzz464, zzz465, zzz466, zzz467, Succ(zzz468), zzz469, zzz470, zzz471, Zero, Succ(Succ(zzz468)), bb)
new_mkVBalBranch3MkVBalBranch225(zzz498, zzz499, zzz500, zzz501, zzz502, zzz503, zzz504, zzz505, zzz506, zzz507, Zero, Succ(zzz5090), bg) → new_mkVBalBranch0(zzz507, Branch(zzz503, zzz504, Neg(Succ(Zero)), zzz505, zzz506), zzz501, bg)
new_mkVBalBranch3MkVBalBranch223(zzz340, zzz341, Neg(Succ(Succ(Succ(zzz3420000)))), zzz343, zzz344, zzz510, zzz511, Zero, zzz513, zzz514, zzz31, Succ(Zero), h) → new_mkVBalBranch3MkVBalBranch225(zzz340, zzz341, Succ(Succ(zzz3420000)), zzz343, zzz344, zzz510, zzz511, zzz513, zzz514, zzz31, Succ(zzz3420000), Zero, h)
new_mkVBalBranch3MkVBalBranch121(zzz473, zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, zzz481, zzz482, Zero, bh) → new_mkVBalBranch3MkVBalBranch115(zzz473, zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, Zero, zzz480, zzz481, zzz482, Zero, Succ(Zero), bh)
new_mkVBalBranch3MkVBalBranch215(zzz340, zzz341, Pos(Succ(Zero)), zzz343, zzz344, zzz510, zzz511, Succ(zzz512000), zzz513, zzz514, zzz31, Zero, h) → new_mkVBalBranch3MkVBalBranch218(zzz340, zzz341, Zero, zzz343, zzz344, zzz510, zzz511, zzz512000, zzz513, zzz514, zzz31, h)
new_mkVBalBranch3MkVBalBranch225(zzz498, zzz499, zzz500, zzz501, zzz502, zzz503, zzz504, zzz505, zzz506, zzz507, Succ(zzz5080), Zero, bg) → new_mkVBalBranch3MkVBalBranch118(zzz498, zzz499, zzz500, zzz501, zzz502, zzz503, zzz504, zzz505, zzz506, zzz507, new_primPlusNat2(new_primMulNat0(zzz500), Succ(zzz500)), bg)
new_mkVBalBranch3MkVBalBranch223(zzz340, zzz341, Neg(Succ(Zero)), zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, Succ(zzz670), h) → new_mkVBalBranch0(zzz31, Branch(zzz510, zzz511, Neg(Succ(zzz51200)), zzz513, zzz514), zzz343, h)
new_mkVBalBranch3MkVBalBranch218(zzz461, zzz462, zzz463, zzz464, zzz465, zzz466, zzz467, zzz468, zzz469, zzz470, zzz471, bb) → new_mkVBalBranch3MkVBalBranch110(zzz461, zzz462, zzz463, zzz464, zzz465, zzz466, zzz467, zzz468, zzz469, zzz470, zzz471, new_primMulNat1(zzz463), bb)
new_mkVBalBranch3MkVBalBranch223(zzz340, zzz341, Neg(Succ(Zero)), zzz343, zzz344, zzz510, zzz511, Succ(zzz512000), zzz513, zzz514, zzz31, Zero, h) → new_mkVBalBranch3MkVBalBranch227(zzz340, zzz341, Zero, zzz343, zzz344, zzz510, zzz511, zzz512000, zzz513, zzz514, zzz31, h)
new_mkVBalBranch3MkVBalBranch215(zzz340, zzz341, Pos(Succ(Zero)), zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, Succ(zzz660), h) → new_mkVBalBranch3MkVBalBranch18(zzz340, zzz341, zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, new_primMulNat1(Zero), h)
new_mkVBalBranch3MkVBalBranch229(zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, zzz1125, zzz1126, zzz1127, zzz1128, zzz1129, bd) → new_mkVBalBranch3MkVBalBranch119(zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, zzz1125, zzz1126, zzz1127, zzz1128, zzz1129, new_primMulNat1(zzz1121), bd)
new_mkVBalBranch3MkVBalBranch226(zzz340, zzz341, zzz3420, zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, h) → new_mkVBalBranch0(zzz31, Branch(zzz510, zzz511, Neg(Succ(zzz51200)), zzz513, zzz514), zzz343, h)
new_mkVBalBranch3MkVBalBranch223(zzz340, zzz341, Neg(Succ(Succ(zzz342000))), zzz343, zzz344, zzz510, zzz511, Succ(zzz512000), zzz513, zzz514, zzz31, Zero, h) → new_mkVBalBranch3MkVBalBranch224(zzz340, zzz341, Succ(zzz342000), zzz343, zzz344, zzz510, zzz511, zzz512000, zzz513, zzz514, zzz31, zzz342000, zzz512000, h)
new_mkVBalBranch3MkVBalBranch215(zzz340, zzz341, Pos(Succ(Succ(zzz342000))), zzz343, zzz344, zzz510, zzz511, Zero, zzz513, zzz514, zzz31, Succ(Succ(zzz6600)), h) → new_mkVBalBranch3MkVBalBranch217(zzz340, zzz341, Succ(zzz342000), zzz343, zzz344, zzz510, zzz511, zzz513, zzz514, zzz31, Succ(zzz6600), zzz342000, h)
new_mkVBalBranch3MkVBalBranch117(zzz340, zzz341, zzz34200, zzz343, zzz344, zzz510, zzz511, zzz513, zzz514, zzz31, Succ(zzz1240), h) → new_mkVBalBranch0(zzz31, zzz514, Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), h)
new_mkVBalBranch3MkVBalBranch221(zzz340, zzz341, Succ(zzz34200), zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, h) → new_mkVBalBranch3MkVBalBranch19(zzz340, zzz341, zzz34200, zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, new_primPlusNat2(new_primPlusNat3(Succ(new_primPlusNat3(new_primPlusNat1(zzz34200), zzz34200)), Succ(zzz34200)), Succ(zzz34200)), h)
new_mkVBalBranch3MkVBalBranch120(zzz2050, zzz2051, zzz2052, zzz2053, zzz2054, zzz2055, zzz2056, zzz2057, zzz2058, zzz2059, zzz2060, Succ(zzz20610), Succ(zzz20620), be) → new_mkVBalBranch3MkVBalBranch120(zzz2050, zzz2051, zzz2052, zzz2053, zzz2054, zzz2055, zzz2056, zzz2057, zzz2058, zzz2059, zzz2060, zzz20610, zzz20620, be)
new_mkVBalBranch3MkVBalBranch217(zzz473, zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, zzz481, zzz482, Zero, Zero, bh) → new_mkVBalBranch3MkVBalBranch233(zzz473, zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, zzz481, zzz482, bh)
new_mkVBalBranch0(zzz31, Branch(zzz510, zzz511, Neg(Succ(zzz51200)), zzz513, zzz514), Branch(zzz340, zzz341, zzz342, zzz343, zzz344), h) → new_mkVBalBranch3MkVBalBranch223(zzz340, zzz341, zzz342, zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, new_primPlusNat3(Succ(new_primPlusNat3(new_primPlusNat1(zzz51200), zzz51200)), Succ(zzz51200)), h)
new_mkVBalBranch3MkVBalBranch223(zzz340, zzz341, Neg(Succ(Succ(zzz342000))), zzz343, zzz344, zzz510, zzz511, Zero, zzz513, zzz514, zzz31, Zero, h) → new_mkVBalBranch3MkVBalBranch118(zzz340, zzz341, Succ(zzz342000), zzz343, zzz344, zzz510, zzz511, zzz513, zzz514, zzz31, new_primMulNat1(Succ(zzz342000)), h)
new_mkVBalBranch3MkVBalBranch216(zzz1105, zzz1106, zzz1107, zzz1108, zzz1109, zzz1110, zzz1111, zzz1112, zzz1113, zzz1114, zzz1115, Succ(zzz11160), Succ(zzz11170), ba) → new_mkVBalBranch3MkVBalBranch216(zzz1105, zzz1106, zzz1107, zzz1108, zzz1109, zzz1110, zzz1111, zzz1112, zzz1113, zzz1114, zzz1115, zzz11160, zzz11170, ba)
new_mkVBalBranch3MkVBalBranch223(zzz340, zzz341, Pos(zzz3420), zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, Succ(zzz670), h) → new_mkVBalBranch0(zzz31, Branch(zzz510, zzz511, Neg(Succ(zzz51200)), zzz513, zzz514), zzz343, h)
new_mkVBalBranch3MkVBalBranch223(zzz340, zzz341, Neg(Succ(Succ(Succ(zzz3420000)))), zzz343, zzz344, zzz510, zzz511, Succ(zzz512000), zzz513, zzz514, zzz31, Succ(Zero), h) → new_mkVBalBranch3MkVBalBranch224(zzz340, zzz341, Succ(Succ(zzz3420000)), zzz343, zzz344, zzz510, zzz511, zzz512000, zzz513, zzz514, zzz31, Succ(zzz3420000), Succ(zzz512000), h)
new_mkVBalBranch3MkVBalBranch19(zzz340, zzz341, zzz34200, zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, Zero, h) → new_mkVBalBranch3MkVBalBranch122(zzz340, zzz341, zzz34200, zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, h)
new_mkVBalBranch0(zzz31, Branch(zzz510, zzz511, Neg(Zero), zzz513, zzz514), Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), h) → new_mkVBalBranch3MkVBalBranch117(zzz340, zzz341, zzz34200, zzz343, zzz344, zzz510, zzz511, zzz513, zzz514, zzz31, new_primMulNat1(zzz34200), h)
new_mkVBalBranch3MkVBalBranch215(zzz340, zzz341, Pos(Succ(Succ(zzz342000))), zzz343, zzz344, zzz510, zzz511, Zero, zzz513, zzz514, zzz31, Zero, h) → new_mkVBalBranch0(zzz31, Branch(zzz510, zzz511, Pos(Succ(Zero)), zzz513, zzz514), zzz343, h)
new_mkVBalBranch3MkVBalBranch225(zzz498, zzz499, zzz500, zzz501, zzz502, zzz503, zzz504, zzz505, zzz506, zzz507, Succ(zzz5080), Succ(zzz5090), bg) → new_mkVBalBranch3MkVBalBranch225(zzz498, zzz499, zzz500, zzz501, zzz502, zzz503, zzz504, zzz505, zzz506, zzz507, zzz5080, zzz5090, bg)
new_mkVBalBranch3MkVBalBranch19(zzz340, zzz341, zzz34200, zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, Succ(zzz1410), h) → new_mkVBalBranch0(zzz31, zzz514, Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), h)
new_mkVBalBranch3MkVBalBranch223(zzz340, zzz341, Pos(zzz3420), zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, Zero, h) → new_mkVBalBranch3MkVBalBranch226(zzz340, zzz341, zzz3420, zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, h)
new_mkVBalBranch3MkVBalBranch223(zzz340, zzz341, Neg(Succ(Succ(Zero))), zzz343, zzz344, zzz510, zzz511, Succ(zzz512000), zzz513, zzz514, zzz31, Succ(Zero), h) → new_mkVBalBranch3MkVBalBranch224(zzz340, zzz341, Succ(Zero), zzz343, zzz344, zzz510, zzz511, zzz512000, zzz513, zzz514, zzz31, Zero, Succ(zzz512000), h)
new_mkVBalBranch3MkVBalBranch224(zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, zzz1125, zzz1126, zzz1127, zzz1128, zzz1129, Zero, Zero, bd) → new_mkVBalBranch3MkVBalBranch229(zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, zzz1125, zzz1126, zzz1127, zzz1128, zzz1129, bd)
new_mkVBalBranch3MkVBalBranch224(zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, zzz1125, zzz1126, zzz1127, zzz1128, zzz1129, Zero, Succ(zzz11310), bd) → new_mkVBalBranch3MkVBalBranch227(zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, zzz1125, zzz1126, zzz1127, zzz1128, zzz1129, bd)
new_mkVBalBranch3MkVBalBranch224(zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, zzz1125, zzz1126, zzz1127, zzz1128, zzz1129, Succ(zzz11300), Zero, bd) → new_mkVBalBranch3MkVBalBranch119(zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, zzz1125, zzz1126, zzz1127, zzz1128, zzz1129, new_primMulNat1(zzz1121), bd)
new_mkVBalBranch3MkVBalBranch230(zzz498, zzz499, zzz500, zzz501, zzz502, zzz503, zzz504, zzz505, zzz506, zzz507, bg) → new_mkVBalBranch3MkVBalBranch118(zzz498, zzz499, zzz500, zzz501, zzz502, zzz503, zzz504, zzz505, zzz506, zzz507, new_primPlusNat2(new_primMulNat0(zzz500), Succ(zzz500)), bg)
new_mkVBalBranch3MkVBalBranch223(zzz340, zzz341, Neg(Succ(Succ(Zero))), zzz343, zzz344, zzz510, zzz511, Zero, zzz513, zzz514, zzz31, Succ(Succ(zzz6700)), h) → new_mkVBalBranch3MkVBalBranch225(zzz340, zzz341, Succ(Zero), zzz343, zzz344, zzz510, zzz511, zzz513, zzz514, zzz31, Zero, Succ(zzz6700), h)
new_mkVBalBranch3MkVBalBranch223(zzz340, zzz341, Neg(Succ(Succ(Succ(zzz3420000)))), zzz343, zzz344, zzz510, zzz511, Succ(zzz512000), zzz513, zzz514, zzz31, Succ(Succ(zzz6700)), h) → new_mkVBalBranch3MkVBalBranch224(zzz340, zzz341, Succ(Succ(zzz3420000)), zzz343, zzz344, zzz510, zzz511, zzz512000, zzz513, zzz514, zzz31, Succ(zzz3420000), Succ(Succ(new_primPlusNat2(zzz6700, zzz512000))), h)
new_mkVBalBranch3MkVBalBranch115(zzz1986, zzz1987, zzz1988, zzz1989, zzz1990, zzz1991, zzz1992, zzz1993, zzz1994, zzz1995, zzz1996, Succ(zzz19970), Succ(zzz19980), bc) → new_mkVBalBranch3MkVBalBranch115(zzz1986, zzz1987, zzz1988, zzz1989, zzz1990, zzz1991, zzz1992, zzz1993, zzz1994, zzz1995, zzz1996, zzz19970, zzz19980, bc)
new_mkVBalBranch3MkVBalBranch215(zzz340, zzz341, Pos(Zero), zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, Zero, h) → new_mkVBalBranch3MkVBalBranch220(zzz340, zzz341, zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, h)
new_mkVBalBranch3MkVBalBranch215(zzz340, zzz341, Neg(Zero), zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, Succ(zzz660), h) → new_mkVBalBranch0(zzz31, zzz514, Branch(zzz340, zzz341, Neg(Zero), zzz343, zzz344), h)
new_mkVBalBranch3MkVBalBranch118(zzz498, zzz499, zzz500, zzz501, zzz502, zzz503, zzz504, zzz505, zzz506, zzz507, Succ(zzz8040), bg) → new_mkVBalBranch3MkVBalBranch120(zzz498, zzz499, zzz500, zzz501, zzz502, zzz503, zzz504, Zero, zzz505, zzz506, zzz507, Succ(Zero), Succ(zzz8040), bg)
new_mkVBalBranch3MkVBalBranch216(zzz1105, zzz1106, zzz1107, zzz1108, zzz1109, zzz1110, zzz1111, zzz1112, zzz1113, zzz1114, zzz1115, Succ(zzz11160), Zero, ba) → new_mkVBalBranch3MkVBalBranch218(zzz1105, zzz1106, zzz1107, zzz1108, zzz1109, zzz1110, zzz1111, zzz1112, zzz1113, zzz1114, zzz1115, ba)
new_mkVBalBranch3MkVBalBranch221(zzz340, zzz341, Zero, zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, h) → new_mkVBalBranch0(zzz31, zzz514, Branch(zzz340, zzz341, Neg(Zero), zzz343, zzz344), h)
new_mkVBalBranch3MkVBalBranch219(zzz340, zzz341, zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, h) → new_mkVBalBranch3MkVBalBranch18(zzz340, zzz341, zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, new_primMulNat1(Zero), h)
new_mkVBalBranch3MkVBalBranch215(zzz340, zzz341, Pos(Succ(Succ(zzz342000))), zzz343, zzz344, zzz510, zzz511, Succ(zzz512000), zzz513, zzz514, zzz31, Succ(Zero), h) → new_mkVBalBranch3MkVBalBranch216(zzz340, zzz341, Succ(zzz342000), zzz343, zzz344, zzz510, zzz511, zzz512000, zzz513, zzz514, zzz31, Succ(zzz512000), zzz342000, h)
new_mkVBalBranch3MkVBalBranch215(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, Succ(zzz660), h) → new_mkVBalBranch3MkVBalBranch19(zzz340, zzz341, zzz34200, zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, new_primPlusNat2(new_primMulNat0(zzz34200), Succ(zzz34200)), h)
new_mkVBalBranch3MkVBalBranch216(zzz1105, zzz1106, zzz1107, zzz1108, zzz1109, zzz1110, zzz1111, zzz1112, zzz1113, zzz1114, zzz1115, Zero, Zero, ba) → new_mkVBalBranch3MkVBalBranch222(zzz1105, zzz1106, zzz1107, zzz1108, zzz1109, zzz1110, zzz1111, zzz1112, zzz1113, zzz1114, zzz1115, ba)
new_mkVBalBranch3MkVBalBranch233(zzz473, zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, zzz481, zzz482, bh) → new_mkVBalBranch3MkVBalBranch121(zzz473, zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, zzz481, zzz482, new_primMulNat1(zzz475), bh)
new_mkVBalBranch3MkVBalBranch215(zzz340, zzz341, Pos(Succ(Succ(zzz342000))), zzz343, zzz344, zzz510, zzz511, Zero, zzz513, zzz514, zzz31, Succ(Zero), h) → new_mkVBalBranch3MkVBalBranch217(zzz340, zzz341, Succ(zzz342000), zzz343, zzz344, zzz510, zzz511, zzz513, zzz514, zzz31, Zero, zzz342000, h)
new_mkVBalBranch0(zzz31, Branch(zzz510, zzz511, Pos(Zero), zzz513, zzz514), Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), h) → new_mkVBalBranch3MkVBalBranch116(zzz340, zzz341, zzz34200, zzz343, zzz344, zzz510, zzz511, zzz513, zzz514, zzz31, new_primMulNat1(zzz34200), h)
new_mkVBalBranch3MkVBalBranch119(zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, zzz1125, zzz1126, zzz1127, zzz1128, zzz1129, Succ(zzz12130), bd) → new_mkVBalBranch3MkVBalBranch120(zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, zzz1125, Succ(zzz1126), zzz1127, zzz1128, zzz1129, Succ(Succ(zzz1126)), Succ(zzz12130), bd)
new_mkVBalBranch3MkVBalBranch18(zzz340, zzz341, zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, Zero, h) → new_mkVBalBranch3MkVBalBranch115(zzz340, zzz341, Zero, zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, Zero, Succ(zzz51200), h)
new_mkVBalBranch3MkVBalBranch223(zzz340, zzz341, Neg(Succ(Zero)), zzz343, zzz344, zzz510, zzz511, Zero, zzz513, zzz514, zzz31, Zero, h) → new_mkVBalBranch3MkVBalBranch118(zzz340, zzz341, Zero, zzz343, zzz344, zzz510, zzz511, zzz513, zzz514, zzz31, new_primMulNat1(Zero), h)

The TRS R consists of the following rules:

new_primPlusNat1(Zero) → Zero
new_primMulNat0(zzz6200) → new_primPlusNat3(Succ(new_primPlusNat3(new_primPlusNat1(zzz6200), zzz6200)), Succ(zzz6200))
new_primPlusNat2(Succ(zzz900), Succ(zzz9100)) → Succ(Succ(new_primPlusNat2(zzz900, zzz9100)))
new_primPlusNat3(zzz90, Succ(zzz910)) → Succ(Succ(new_primPlusNat2(zzz90, zzz910)))
new_primPlusNat3(zzz90, Zero) → Succ(zzz90)
new_primMulNat1(zzz34200) → new_primPlusNat2(new_primMulNat0(zzz34200), Succ(zzz34200))
new_primPlusNat2(Zero, Zero) → Zero
new_primPlusNat1(Succ(zzz62000)) → Succ(Succ(new_primPlusNat1(zzz62000)))
new_primPlusNat2(Succ(zzz900), Zero) → Succ(zzz900)
new_primPlusNat2(Zero, Succ(zzz9100)) → Succ(zzz9100)

The set Q consists of the following terms:

new_primPlusNat2(Zero, Succ(x0))
new_primMulNat1(x0)
new_primMulNat0(x0)
new_primPlusNat3(x0, Succ(x1))
new_primPlusNat2(Succ(x0), Succ(x1))
new_primPlusNat3(x0, Zero)
new_primPlusNat1(Zero)
new_primPlusNat2(Zero, Zero)
new_primPlusNat1(Succ(x0))
new_primPlusNat2(Succ(x0), Zero)

We have to consider all minimal (P,Q,R)-chains.
By rewriting [15] the rule new_mkVBalBranch3MkVBalBranch229(zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, zzz1125, zzz1126, zzz1127, zzz1128, zzz1129, bd) → new_mkVBalBranch3MkVBalBranch119(zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, zzz1125, zzz1126, zzz1127, zzz1128, zzz1129, new_primMulNat1(zzz1121), bd) at position [11] we obtained the following new rules:

new_mkVBalBranch3MkVBalBranch229(zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, zzz1125, zzz1126, zzz1127, zzz1128, zzz1129, bd) → new_mkVBalBranch3MkVBalBranch119(zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, zzz1125, zzz1126, zzz1127, zzz1128, zzz1129, new_primPlusNat2(new_primMulNat0(zzz1121), Succ(zzz1121)), bd)



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

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

new_mkVBalBranch3MkVBalBranch215(zzz340, zzz341, Neg(zzz3420), zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, Zero, h) → new_mkVBalBranch3MkVBalBranch221(zzz340, zzz341, zzz3420, zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, h)
new_mkVBalBranch3MkVBalBranch225(zzz498, zzz499, zzz500, zzz501, zzz502, zzz503, zzz504, zzz505, zzz506, zzz507, Zero, Zero, bg) → new_mkVBalBranch3MkVBalBranch230(zzz498, zzz499, zzz500, zzz501, zzz502, zzz503, zzz504, zzz505, zzz506, zzz507, bg)
new_mkVBalBranch3MkVBalBranch18(zzz340, zzz341, zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, Succ(zzz1480), h) → new_mkVBalBranch3MkVBalBranch115(zzz340, zzz341, Zero, zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, Succ(zzz1480), Succ(zzz51200), h)
new_mkVBalBranch0(zzz31, Branch(zzz510, zzz511, Neg(Zero), zzz513, zzz514), Branch(zzz340, zzz341, Pos(Succ(zzz34200)), zzz343, zzz344), h) → new_mkVBalBranch0(zzz31, Branch(zzz510, zzz511, Neg(Zero), zzz513, zzz514), zzz343, h)
new_mkVBalBranch3MkVBalBranch215(zzz340, zzz341, Pos(Succ(Succ(zzz342000))), zzz343, zzz344, zzz510, zzz511, Succ(zzz512000), zzz513, zzz514, zzz31, Succ(Succ(zzz6600)), h) → new_mkVBalBranch3MkVBalBranch216(zzz340, zzz341, Succ(zzz342000), zzz343, zzz344, zzz510, zzz511, zzz512000, zzz513, zzz514, zzz31, Succ(Succ(new_primPlusNat2(zzz6600, zzz512000))), zzz342000, h)
new_mkVBalBranch3MkVBalBranch223(zzz340, zzz341, Neg(Succ(Succ(Succ(zzz3420000)))), zzz343, zzz344, zzz510, zzz511, Zero, zzz513, zzz514, zzz31, Succ(Succ(zzz6700)), h) → new_mkVBalBranch3MkVBalBranch225(zzz340, zzz341, Succ(Succ(zzz3420000)), zzz343, zzz344, zzz510, zzz511, zzz513, zzz514, zzz31, Succ(zzz3420000), Succ(zzz6700), h)
new_mkVBalBranch3MkVBalBranch220(zzz340, zzz341, zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, h) → new_mkVBalBranch0(zzz31, zzz514, Branch(zzz340, zzz341, Pos(Zero), zzz343, zzz344), h)
new_mkVBalBranch3MkVBalBranch120(zzz2050, zzz2051, zzz2052, zzz2053, zzz2054, zzz2055, zzz2056, zzz2057, zzz2058, zzz2059, zzz2060, Zero, Succ(zzz20620), be) → new_mkVBalBranch0(zzz2060, zzz2059, Branch(zzz2050, zzz2051, Neg(Succ(zzz2052)), zzz2053, zzz2054), be)
new_mkVBalBranch3MkVBalBranch121(zzz473, zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, zzz481, zzz482, Succ(zzz7390), bh) → new_mkVBalBranch3MkVBalBranch115(zzz473, zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, Zero, zzz480, zzz481, zzz482, Succ(zzz7390), Succ(Zero), bh)
new_mkVBalBranch0(zzz31, Branch(zzz510, zzz511, Pos(Zero), zzz513, zzz514), Branch(zzz340, zzz341, Pos(Succ(zzz34200)), zzz343, zzz344), h) → new_mkVBalBranch0(zzz31, Branch(zzz510, zzz511, Pos(Zero), zzz513, zzz514), zzz343, h)
new_mkVBalBranch3MkVBalBranch228(zzz340, zzz341, zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, h) → new_mkVBalBranch0(zzz31, Branch(zzz510, zzz511, Neg(Succ(zzz51200)), zzz513, zzz514), zzz343, h)
new_mkVBalBranch3MkVBalBranch215(zzz340, zzz341, Pos(Succ(Zero)), zzz343, zzz344, zzz510, zzz511, Zero, zzz513, zzz514, zzz31, Zero, h) → new_mkVBalBranch3MkVBalBranch219(zzz340, zzz341, zzz343, zzz344, zzz510, zzz511, Zero, zzz513, zzz514, zzz31, h)
new_mkVBalBranch3MkVBalBranch223(zzz340, zzz341, Neg(Succ(Succ(Zero))), zzz343, zzz344, zzz510, zzz511, Succ(zzz512000), zzz513, zzz514, zzz31, Succ(Succ(zzz6700)), h) → new_mkVBalBranch3MkVBalBranch224(zzz340, zzz341, Succ(Zero), zzz343, zzz344, zzz510, zzz511, zzz512000, zzz513, zzz514, zzz31, Zero, Succ(Succ(new_primPlusNat2(zzz6700, zzz512000))), h)
new_mkVBalBranch3MkVBalBranch223(zzz340, zzz341, Neg(Succ(Succ(Zero))), zzz343, zzz344, zzz510, zzz511, Zero, zzz513, zzz514, zzz31, Succ(Zero), h) → new_mkVBalBranch3MkVBalBranch225(zzz340, zzz341, Succ(Zero), zzz343, zzz344, zzz510, zzz511, zzz513, zzz514, zzz31, Zero, Zero, h)
new_mkVBalBranch3MkVBalBranch224(zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, zzz1125, zzz1126, zzz1127, zzz1128, zzz1129, Succ(zzz11300), Succ(zzz11310), bd) → new_mkVBalBranch3MkVBalBranch224(zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, zzz1125, zzz1126, zzz1127, zzz1128, zzz1129, zzz11300, zzz11310, bd)
new_mkVBalBranch0(zzz31, Branch(zzz510, zzz511, Pos(Succ(zzz51200)), zzz513, zzz514), Branch(zzz340, zzz341, zzz342, zzz343, zzz344), h) → new_mkVBalBranch3MkVBalBranch215(zzz340, zzz341, zzz342, zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, new_primPlusNat3(Succ(new_primPlusNat3(new_primPlusNat1(zzz51200), zzz51200)), Succ(zzz51200)), h)
new_mkVBalBranch3MkVBalBranch217(zzz473, zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, zzz481, zzz482, Zero, Succ(zzz4840), bh) → new_mkVBalBranch0(zzz482, Branch(zzz478, zzz479, Pos(Succ(Zero)), zzz480, zzz481), zzz476, bh)
new_mkVBalBranch3MkVBalBranch215(zzz340, zzz341, Pos(Succ(Succ(zzz342000))), zzz343, zzz344, zzz510, zzz511, Succ(zzz512000), zzz513, zzz514, zzz31, Zero, h) → new_mkVBalBranch3MkVBalBranch216(zzz340, zzz341, Succ(zzz342000), zzz343, zzz344, zzz510, zzz511, zzz512000, zzz513, zzz514, zzz31, zzz512000, zzz342000, h)
new_mkVBalBranch3MkVBalBranch110(zzz461, zzz462, zzz463, zzz464, zzz465, zzz466, zzz467, zzz468, zzz469, zzz470, zzz471, Succ(zzz5800), bb) → new_mkVBalBranch3MkVBalBranch115(zzz461, zzz462, zzz463, zzz464, zzz465, zzz466, zzz467, Succ(zzz468), zzz469, zzz470, zzz471, Succ(zzz5800), Succ(Succ(zzz468)), bb)
new_mkVBalBranch3MkVBalBranch227(zzz486, zzz487, zzz488, zzz489, zzz490, zzz491, zzz492, zzz493, zzz494, zzz495, zzz496, bf) → new_mkVBalBranch0(zzz496, Branch(zzz491, zzz492, Neg(Succ(Succ(zzz493))), zzz494, zzz495), zzz489, bf)
new_mkVBalBranch3MkVBalBranch215(zzz340, zzz341, Pos(Zero), zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, Succ(zzz660), h) → new_mkVBalBranch0(zzz31, zzz514, Branch(zzz340, zzz341, Pos(Zero), zzz343, zzz344), h)
new_mkVBalBranch3MkVBalBranch223(zzz340, zzz341, Neg(Zero), zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, Succ(zzz670), h) → new_mkVBalBranch0(zzz31, Branch(zzz510, zzz511, Neg(Succ(zzz51200)), zzz513, zzz514), zzz343, h)
new_mkVBalBranch3MkVBalBranch216(zzz1105, zzz1106, zzz1107, zzz1108, zzz1109, zzz1110, zzz1111, zzz1112, zzz1113, zzz1114, zzz1115, Zero, Succ(zzz11170), ba) → new_mkVBalBranch0(zzz1115, Branch(zzz1110, zzz1111, Pos(Succ(Succ(zzz1112))), zzz1113, zzz1114), zzz1108, ba)
new_mkVBalBranch3MkVBalBranch217(zzz473, zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, zzz481, zzz482, Succ(zzz4830), Zero, bh) → new_mkVBalBranch3MkVBalBranch121(zzz473, zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, zzz481, zzz482, new_primMulNat1(zzz475), bh)
new_mkVBalBranch3MkVBalBranch222(zzz461, zzz462, zzz463, zzz464, zzz465, zzz466, zzz467, zzz468, zzz469, zzz470, zzz471, bb) → new_mkVBalBranch3MkVBalBranch110(zzz461, zzz462, zzz463, zzz464, zzz465, zzz466, zzz467, zzz468, zzz469, zzz470, zzz471, new_primMulNat1(zzz463), bb)
new_mkVBalBranch3MkVBalBranch115(zzz1986, zzz1987, zzz1988, zzz1989, zzz1990, zzz1991, zzz1992, zzz1993, zzz1994, zzz1995, zzz1996, Zero, Succ(zzz19980), bc) → new_mkVBalBranch0(zzz1996, zzz1995, Branch(zzz1986, zzz1987, Pos(Succ(zzz1988)), zzz1989, zzz1990), bc)
new_mkVBalBranch3MkVBalBranch223(zzz340, zzz341, Neg(Zero), zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, Zero, h) → new_mkVBalBranch3MkVBalBranch228(zzz340, zzz341, zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, h)
new_mkVBalBranch3MkVBalBranch122(zzz340, zzz341, zzz34200, zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, h) → new_mkVBalBranch0(zzz31, zzz514, Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), h)
new_mkVBalBranch3MkVBalBranch217(zzz473, zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, zzz481, zzz482, Succ(zzz4830), Succ(zzz4840), bh) → new_mkVBalBranch3MkVBalBranch217(zzz473, zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, zzz481, zzz482, zzz4830, zzz4840, bh)
new_mkVBalBranch3MkVBalBranch116(zzz340, zzz341, zzz34200, zzz343, zzz344, zzz510, zzz511, zzz513, zzz514, zzz31, Succ(zzz1200), h) → new_mkVBalBranch0(zzz31, zzz514, Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), h)
new_mkVBalBranch3MkVBalBranch110(zzz461, zzz462, zzz463, zzz464, zzz465, zzz466, zzz467, zzz468, zzz469, zzz470, zzz471, Zero, bb) → new_mkVBalBranch3MkVBalBranch115(zzz461, zzz462, zzz463, zzz464, zzz465, zzz466, zzz467, Succ(zzz468), zzz469, zzz470, zzz471, Zero, Succ(Succ(zzz468)), bb)
new_mkVBalBranch3MkVBalBranch225(zzz498, zzz499, zzz500, zzz501, zzz502, zzz503, zzz504, zzz505, zzz506, zzz507, Zero, Succ(zzz5090), bg) → new_mkVBalBranch0(zzz507, Branch(zzz503, zzz504, Neg(Succ(Zero)), zzz505, zzz506), zzz501, bg)
new_mkVBalBranch3MkVBalBranch223(zzz340, zzz341, Neg(Succ(Succ(Succ(zzz3420000)))), zzz343, zzz344, zzz510, zzz511, Zero, zzz513, zzz514, zzz31, Succ(Zero), h) → new_mkVBalBranch3MkVBalBranch225(zzz340, zzz341, Succ(Succ(zzz3420000)), zzz343, zzz344, zzz510, zzz511, zzz513, zzz514, zzz31, Succ(zzz3420000), Zero, h)
new_mkVBalBranch3MkVBalBranch121(zzz473, zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, zzz481, zzz482, Zero, bh) → new_mkVBalBranch3MkVBalBranch115(zzz473, zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, Zero, zzz480, zzz481, zzz482, Zero, Succ(Zero), bh)
new_mkVBalBranch3MkVBalBranch215(zzz340, zzz341, Pos(Succ(Zero)), zzz343, zzz344, zzz510, zzz511, Succ(zzz512000), zzz513, zzz514, zzz31, Zero, h) → new_mkVBalBranch3MkVBalBranch218(zzz340, zzz341, Zero, zzz343, zzz344, zzz510, zzz511, zzz512000, zzz513, zzz514, zzz31, h)
new_mkVBalBranch3MkVBalBranch223(zzz340, zzz341, Neg(Succ(Zero)), zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, Succ(zzz670), h) → new_mkVBalBranch0(zzz31, Branch(zzz510, zzz511, Neg(Succ(zzz51200)), zzz513, zzz514), zzz343, h)
new_mkVBalBranch3MkVBalBranch225(zzz498, zzz499, zzz500, zzz501, zzz502, zzz503, zzz504, zzz505, zzz506, zzz507, Succ(zzz5080), Zero, bg) → new_mkVBalBranch3MkVBalBranch118(zzz498, zzz499, zzz500, zzz501, zzz502, zzz503, zzz504, zzz505, zzz506, zzz507, new_primPlusNat2(new_primMulNat0(zzz500), Succ(zzz500)), bg)
new_mkVBalBranch3MkVBalBranch229(zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, zzz1125, zzz1126, zzz1127, zzz1128, zzz1129, bd) → new_mkVBalBranch3MkVBalBranch119(zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, zzz1125, zzz1126, zzz1127, zzz1128, zzz1129, new_primPlusNat2(new_primMulNat0(zzz1121), Succ(zzz1121)), bd)
new_mkVBalBranch3MkVBalBranch218(zzz461, zzz462, zzz463, zzz464, zzz465, zzz466, zzz467, zzz468, zzz469, zzz470, zzz471, bb) → new_mkVBalBranch3MkVBalBranch110(zzz461, zzz462, zzz463, zzz464, zzz465, zzz466, zzz467, zzz468, zzz469, zzz470, zzz471, new_primMulNat1(zzz463), bb)
new_mkVBalBranch3MkVBalBranch223(zzz340, zzz341, Neg(Succ(Zero)), zzz343, zzz344, zzz510, zzz511, Succ(zzz512000), zzz513, zzz514, zzz31, Zero, h) → new_mkVBalBranch3MkVBalBranch227(zzz340, zzz341, Zero, zzz343, zzz344, zzz510, zzz511, zzz512000, zzz513, zzz514, zzz31, h)
new_mkVBalBranch3MkVBalBranch215(zzz340, zzz341, Pos(Succ(Zero)), zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, Succ(zzz660), h) → new_mkVBalBranch3MkVBalBranch18(zzz340, zzz341, zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, new_primMulNat1(Zero), h)
new_mkVBalBranch3MkVBalBranch215(zzz340, zzz341, Pos(Succ(Succ(zzz342000))), zzz343, zzz344, zzz510, zzz511, Zero, zzz513, zzz514, zzz31, Succ(Succ(zzz6600)), h) → new_mkVBalBranch3MkVBalBranch217(zzz340, zzz341, Succ(zzz342000), zzz343, zzz344, zzz510, zzz511, zzz513, zzz514, zzz31, Succ(zzz6600), zzz342000, h)
new_mkVBalBranch3MkVBalBranch223(zzz340, zzz341, Neg(Succ(Succ(zzz342000))), zzz343, zzz344, zzz510, zzz511, Succ(zzz512000), zzz513, zzz514, zzz31, Zero, h) → new_mkVBalBranch3MkVBalBranch224(zzz340, zzz341, Succ(zzz342000), zzz343, zzz344, zzz510, zzz511, zzz512000, zzz513, zzz514, zzz31, zzz342000, zzz512000, h)
new_mkVBalBranch3MkVBalBranch226(zzz340, zzz341, zzz3420, zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, h) → new_mkVBalBranch0(zzz31, Branch(zzz510, zzz511, Neg(Succ(zzz51200)), zzz513, zzz514), zzz343, h)
new_mkVBalBranch3MkVBalBranch117(zzz340, zzz341, zzz34200, zzz343, zzz344, zzz510, zzz511, zzz513, zzz514, zzz31, Succ(zzz1240), h) → new_mkVBalBranch0(zzz31, zzz514, Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), h)
new_mkVBalBranch0(zzz31, Branch(zzz510, zzz511, Neg(Succ(zzz51200)), zzz513, zzz514), Branch(zzz340, zzz341, zzz342, zzz343, zzz344), h) → new_mkVBalBranch3MkVBalBranch223(zzz340, zzz341, zzz342, zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, new_primPlusNat3(Succ(new_primPlusNat3(new_primPlusNat1(zzz51200), zzz51200)), Succ(zzz51200)), h)
new_mkVBalBranch3MkVBalBranch217(zzz473, zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, zzz481, zzz482, Zero, Zero, bh) → new_mkVBalBranch3MkVBalBranch233(zzz473, zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, zzz481, zzz482, bh)
new_mkVBalBranch3MkVBalBranch120(zzz2050, zzz2051, zzz2052, zzz2053, zzz2054, zzz2055, zzz2056, zzz2057, zzz2058, zzz2059, zzz2060, Succ(zzz20610), Succ(zzz20620), be) → new_mkVBalBranch3MkVBalBranch120(zzz2050, zzz2051, zzz2052, zzz2053, zzz2054, zzz2055, zzz2056, zzz2057, zzz2058, zzz2059, zzz2060, zzz20610, zzz20620, be)
new_mkVBalBranch3MkVBalBranch221(zzz340, zzz341, Succ(zzz34200), zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, h) → new_mkVBalBranch3MkVBalBranch19(zzz340, zzz341, zzz34200, zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, new_primPlusNat2(new_primPlusNat3(Succ(new_primPlusNat3(new_primPlusNat1(zzz34200), zzz34200)), Succ(zzz34200)), Succ(zzz34200)), h)
new_mkVBalBranch3MkVBalBranch223(zzz340, zzz341, Neg(Succ(Succ(zzz342000))), zzz343, zzz344, zzz510, zzz511, Zero, zzz513, zzz514, zzz31, Zero, h) → new_mkVBalBranch3MkVBalBranch118(zzz340, zzz341, Succ(zzz342000), zzz343, zzz344, zzz510, zzz511, zzz513, zzz514, zzz31, new_primMulNat1(Succ(zzz342000)), h)
new_mkVBalBranch3MkVBalBranch223(zzz340, zzz341, Pos(zzz3420), zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, Succ(zzz670), h) → new_mkVBalBranch0(zzz31, Branch(zzz510, zzz511, Neg(Succ(zzz51200)), zzz513, zzz514), zzz343, h)
new_mkVBalBranch3MkVBalBranch216(zzz1105, zzz1106, zzz1107, zzz1108, zzz1109, zzz1110, zzz1111, zzz1112, zzz1113, zzz1114, zzz1115, Succ(zzz11160), Succ(zzz11170), ba) → new_mkVBalBranch3MkVBalBranch216(zzz1105, zzz1106, zzz1107, zzz1108, zzz1109, zzz1110, zzz1111, zzz1112, zzz1113, zzz1114, zzz1115, zzz11160, zzz11170, ba)
new_mkVBalBranch3MkVBalBranch19(zzz340, zzz341, zzz34200, zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, Zero, h) → new_mkVBalBranch3MkVBalBranch122(zzz340, zzz341, zzz34200, zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, h)
new_mkVBalBranch3MkVBalBranch223(zzz340, zzz341, Neg(Succ(Succ(Succ(zzz3420000)))), zzz343, zzz344, zzz510, zzz511, Succ(zzz512000), zzz513, zzz514, zzz31, Succ(Zero), h) → new_mkVBalBranch3MkVBalBranch224(zzz340, zzz341, Succ(Succ(zzz3420000)), zzz343, zzz344, zzz510, zzz511, zzz512000, zzz513, zzz514, zzz31, Succ(zzz3420000), Succ(zzz512000), h)
new_mkVBalBranch0(zzz31, Branch(zzz510, zzz511, Neg(Zero), zzz513, zzz514), Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), h) → new_mkVBalBranch3MkVBalBranch117(zzz340, zzz341, zzz34200, zzz343, zzz344, zzz510, zzz511, zzz513, zzz514, zzz31, new_primMulNat1(zzz34200), h)
new_mkVBalBranch3MkVBalBranch215(zzz340, zzz341, Pos(Succ(Succ(zzz342000))), zzz343, zzz344, zzz510, zzz511, Zero, zzz513, zzz514, zzz31, Zero, h) → new_mkVBalBranch0(zzz31, Branch(zzz510, zzz511, Pos(Succ(Zero)), zzz513, zzz514), zzz343, h)
new_mkVBalBranch3MkVBalBranch225(zzz498, zzz499, zzz500, zzz501, zzz502, zzz503, zzz504, zzz505, zzz506, zzz507, Succ(zzz5080), Succ(zzz5090), bg) → new_mkVBalBranch3MkVBalBranch225(zzz498, zzz499, zzz500, zzz501, zzz502, zzz503, zzz504, zzz505, zzz506, zzz507, zzz5080, zzz5090, bg)
new_mkVBalBranch3MkVBalBranch19(zzz340, zzz341, zzz34200, zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, Succ(zzz1410), h) → new_mkVBalBranch0(zzz31, zzz514, Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), h)
new_mkVBalBranch3MkVBalBranch224(zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, zzz1125, zzz1126, zzz1127, zzz1128, zzz1129, Zero, Succ(zzz11310), bd) → new_mkVBalBranch3MkVBalBranch227(zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, zzz1125, zzz1126, zzz1127, zzz1128, zzz1129, bd)
new_mkVBalBranch3MkVBalBranch224(zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, zzz1125, zzz1126, zzz1127, zzz1128, zzz1129, Zero, Zero, bd) → new_mkVBalBranch3MkVBalBranch229(zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, zzz1125, zzz1126, zzz1127, zzz1128, zzz1129, bd)
new_mkVBalBranch3MkVBalBranch223(zzz340, zzz341, Neg(Succ(Succ(Zero))), zzz343, zzz344, zzz510, zzz511, Succ(zzz512000), zzz513, zzz514, zzz31, Succ(Zero), h) → new_mkVBalBranch3MkVBalBranch224(zzz340, zzz341, Succ(Zero), zzz343, zzz344, zzz510, zzz511, zzz512000, zzz513, zzz514, zzz31, Zero, Succ(zzz512000), h)
new_mkVBalBranch3MkVBalBranch223(zzz340, zzz341, Pos(zzz3420), zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, Zero, h) → new_mkVBalBranch3MkVBalBranch226(zzz340, zzz341, zzz3420, zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, h)
new_mkVBalBranch3MkVBalBranch224(zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, zzz1125, zzz1126, zzz1127, zzz1128, zzz1129, Succ(zzz11300), Zero, bd) → new_mkVBalBranch3MkVBalBranch119(zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, zzz1125, zzz1126, zzz1127, zzz1128, zzz1129, new_primMulNat1(zzz1121), bd)
new_mkVBalBranch3MkVBalBranch230(zzz498, zzz499, zzz500, zzz501, zzz502, zzz503, zzz504, zzz505, zzz506, zzz507, bg) → new_mkVBalBranch3MkVBalBranch118(zzz498, zzz499, zzz500, zzz501, zzz502, zzz503, zzz504, zzz505, zzz506, zzz507, new_primPlusNat2(new_primMulNat0(zzz500), Succ(zzz500)), bg)
new_mkVBalBranch3MkVBalBranch223(zzz340, zzz341, Neg(Succ(Succ(Succ(zzz3420000)))), zzz343, zzz344, zzz510, zzz511, Succ(zzz512000), zzz513, zzz514, zzz31, Succ(Succ(zzz6700)), h) → new_mkVBalBranch3MkVBalBranch224(zzz340, zzz341, Succ(Succ(zzz3420000)), zzz343, zzz344, zzz510, zzz511, zzz512000, zzz513, zzz514, zzz31, Succ(zzz3420000), Succ(Succ(new_primPlusNat2(zzz6700, zzz512000))), h)
new_mkVBalBranch3MkVBalBranch223(zzz340, zzz341, Neg(Succ(Succ(Zero))), zzz343, zzz344, zzz510, zzz511, Zero, zzz513, zzz514, zzz31, Succ(Succ(zzz6700)), h) → new_mkVBalBranch3MkVBalBranch225(zzz340, zzz341, Succ(Zero), zzz343, zzz344, zzz510, zzz511, zzz513, zzz514, zzz31, Zero, Succ(zzz6700), h)
new_mkVBalBranch3MkVBalBranch215(zzz340, zzz341, Pos(Zero), zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, Zero, h) → new_mkVBalBranch3MkVBalBranch220(zzz340, zzz341, zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, h)
new_mkVBalBranch3MkVBalBranch115(zzz1986, zzz1987, zzz1988, zzz1989, zzz1990, zzz1991, zzz1992, zzz1993, zzz1994, zzz1995, zzz1996, Succ(zzz19970), Succ(zzz19980), bc) → new_mkVBalBranch3MkVBalBranch115(zzz1986, zzz1987, zzz1988, zzz1989, zzz1990, zzz1991, zzz1992, zzz1993, zzz1994, zzz1995, zzz1996, zzz19970, zzz19980, bc)
new_mkVBalBranch3MkVBalBranch215(zzz340, zzz341, Neg(Zero), zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, Succ(zzz660), h) → new_mkVBalBranch0(zzz31, zzz514, Branch(zzz340, zzz341, Neg(Zero), zzz343, zzz344), h)
new_mkVBalBranch3MkVBalBranch118(zzz498, zzz499, zzz500, zzz501, zzz502, zzz503, zzz504, zzz505, zzz506, zzz507, Succ(zzz8040), bg) → new_mkVBalBranch3MkVBalBranch120(zzz498, zzz499, zzz500, zzz501, zzz502, zzz503, zzz504, Zero, zzz505, zzz506, zzz507, Succ(Zero), Succ(zzz8040), bg)
new_mkVBalBranch3MkVBalBranch216(zzz1105, zzz1106, zzz1107, zzz1108, zzz1109, zzz1110, zzz1111, zzz1112, zzz1113, zzz1114, zzz1115, Succ(zzz11160), Zero, ba) → new_mkVBalBranch3MkVBalBranch218(zzz1105, zzz1106, zzz1107, zzz1108, zzz1109, zzz1110, zzz1111, zzz1112, zzz1113, zzz1114, zzz1115, ba)
new_mkVBalBranch3MkVBalBranch215(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, Succ(zzz660), h) → new_mkVBalBranch3MkVBalBranch19(zzz340, zzz341, zzz34200, zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, new_primPlusNat2(new_primMulNat0(zzz34200), Succ(zzz34200)), h)
new_mkVBalBranch3MkVBalBranch215(zzz340, zzz341, Pos(Succ(Succ(zzz342000))), zzz343, zzz344, zzz510, zzz511, Succ(zzz512000), zzz513, zzz514, zzz31, Succ(Zero), h) → new_mkVBalBranch3MkVBalBranch216(zzz340, zzz341, Succ(zzz342000), zzz343, zzz344, zzz510, zzz511, zzz512000, zzz513, zzz514, zzz31, Succ(zzz512000), zzz342000, h)
new_mkVBalBranch3MkVBalBranch219(zzz340, zzz341, zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, h) → new_mkVBalBranch3MkVBalBranch18(zzz340, zzz341, zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, new_primMulNat1(Zero), h)
new_mkVBalBranch3MkVBalBranch221(zzz340, zzz341, Zero, zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, h) → new_mkVBalBranch0(zzz31, zzz514, Branch(zzz340, zzz341, Neg(Zero), zzz343, zzz344), h)
new_mkVBalBranch3MkVBalBranch216(zzz1105, zzz1106, zzz1107, zzz1108, zzz1109, zzz1110, zzz1111, zzz1112, zzz1113, zzz1114, zzz1115, Zero, Zero, ba) → new_mkVBalBranch3MkVBalBranch222(zzz1105, zzz1106, zzz1107, zzz1108, zzz1109, zzz1110, zzz1111, zzz1112, zzz1113, zzz1114, zzz1115, ba)
new_mkVBalBranch3MkVBalBranch233(zzz473, zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, zzz481, zzz482, bh) → new_mkVBalBranch3MkVBalBranch121(zzz473, zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, zzz481, zzz482, new_primMulNat1(zzz475), bh)
new_mkVBalBranch3MkVBalBranch215(zzz340, zzz341, Pos(Succ(Succ(zzz342000))), zzz343, zzz344, zzz510, zzz511, Zero, zzz513, zzz514, zzz31, Succ(Zero), h) → new_mkVBalBranch3MkVBalBranch217(zzz340, zzz341, Succ(zzz342000), zzz343, zzz344, zzz510, zzz511, zzz513, zzz514, zzz31, Zero, zzz342000, h)
new_mkVBalBranch0(zzz31, Branch(zzz510, zzz511, Pos(Zero), zzz513, zzz514), Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), h) → new_mkVBalBranch3MkVBalBranch116(zzz340, zzz341, zzz34200, zzz343, zzz344, zzz510, zzz511, zzz513, zzz514, zzz31, new_primMulNat1(zzz34200), h)
new_mkVBalBranch3MkVBalBranch18(zzz340, zzz341, zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, Zero, h) → new_mkVBalBranch3MkVBalBranch115(zzz340, zzz341, Zero, zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, Zero, Succ(zzz51200), h)
new_mkVBalBranch3MkVBalBranch119(zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, zzz1125, zzz1126, zzz1127, zzz1128, zzz1129, Succ(zzz12130), bd) → new_mkVBalBranch3MkVBalBranch120(zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, zzz1125, Succ(zzz1126), zzz1127, zzz1128, zzz1129, Succ(Succ(zzz1126)), Succ(zzz12130), bd)
new_mkVBalBranch3MkVBalBranch223(zzz340, zzz341, Neg(Succ(Zero)), zzz343, zzz344, zzz510, zzz511, Zero, zzz513, zzz514, zzz31, Zero, h) → new_mkVBalBranch3MkVBalBranch118(zzz340, zzz341, Zero, zzz343, zzz344, zzz510, zzz511, zzz513, zzz514, zzz31, new_primMulNat1(Zero), h)

The TRS R consists of the following rules:

new_primPlusNat1(Zero) → Zero
new_primMulNat0(zzz6200) → new_primPlusNat3(Succ(new_primPlusNat3(new_primPlusNat1(zzz6200), zzz6200)), Succ(zzz6200))
new_primPlusNat2(Succ(zzz900), Succ(zzz9100)) → Succ(Succ(new_primPlusNat2(zzz900, zzz9100)))
new_primPlusNat3(zzz90, Succ(zzz910)) → Succ(Succ(new_primPlusNat2(zzz90, zzz910)))
new_primPlusNat3(zzz90, Zero) → Succ(zzz90)
new_primMulNat1(zzz34200) → new_primPlusNat2(new_primMulNat0(zzz34200), Succ(zzz34200))
new_primPlusNat2(Zero, Zero) → Zero
new_primPlusNat1(Succ(zzz62000)) → Succ(Succ(new_primPlusNat1(zzz62000)))
new_primPlusNat2(Succ(zzz900), Zero) → Succ(zzz900)
new_primPlusNat2(Zero, Succ(zzz9100)) → Succ(zzz9100)

The set Q consists of the following terms:

new_primPlusNat2(Zero, Succ(x0))
new_primMulNat1(x0)
new_primMulNat0(x0)
new_primPlusNat3(x0, Succ(x1))
new_primPlusNat2(Succ(x0), Succ(x1))
new_primPlusNat3(x0, Zero)
new_primPlusNat1(Zero)
new_primPlusNat2(Zero, Zero)
new_primPlusNat1(Succ(x0))
new_primPlusNat2(Succ(x0), Zero)

We have to consider all minimal (P,Q,R)-chains.
By rewriting [15] the rule new_mkVBalBranch3MkVBalBranch224(zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, zzz1125, zzz1126, zzz1127, zzz1128, zzz1129, Succ(zzz11300), Zero, bd) → new_mkVBalBranch3MkVBalBranch119(zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, zzz1125, zzz1126, zzz1127, zzz1128, zzz1129, new_primMulNat1(zzz1121), bd) at position [11] we obtained the following new rules:

new_mkVBalBranch3MkVBalBranch224(zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, zzz1125, zzz1126, zzz1127, zzz1128, zzz1129, Succ(zzz11300), Zero, bd) → new_mkVBalBranch3MkVBalBranch119(zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, zzz1125, zzz1126, zzz1127, zzz1128, zzz1129, new_primPlusNat2(new_primMulNat0(zzz1121), Succ(zzz1121)), bd)



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

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

new_mkVBalBranch3MkVBalBranch225(zzz498, zzz499, zzz500, zzz501, zzz502, zzz503, zzz504, zzz505, zzz506, zzz507, Zero, Zero, bg) → new_mkVBalBranch3MkVBalBranch230(zzz498, zzz499, zzz500, zzz501, zzz502, zzz503, zzz504, zzz505, zzz506, zzz507, bg)
new_mkVBalBranch3MkVBalBranch215(zzz340, zzz341, Neg(zzz3420), zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, Zero, h) → new_mkVBalBranch3MkVBalBranch221(zzz340, zzz341, zzz3420, zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, h)
new_mkVBalBranch3MkVBalBranch18(zzz340, zzz341, zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, Succ(zzz1480), h) → new_mkVBalBranch3MkVBalBranch115(zzz340, zzz341, Zero, zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, Succ(zzz1480), Succ(zzz51200), h)
new_mkVBalBranch3MkVBalBranch215(zzz340, zzz341, Pos(Succ(Succ(zzz342000))), zzz343, zzz344, zzz510, zzz511, Succ(zzz512000), zzz513, zzz514, zzz31, Succ(Succ(zzz6600)), h) → new_mkVBalBranch3MkVBalBranch216(zzz340, zzz341, Succ(zzz342000), zzz343, zzz344, zzz510, zzz511, zzz512000, zzz513, zzz514, zzz31, Succ(Succ(new_primPlusNat2(zzz6600, zzz512000))), zzz342000, h)
new_mkVBalBranch0(zzz31, Branch(zzz510, zzz511, Neg(Zero), zzz513, zzz514), Branch(zzz340, zzz341, Pos(Succ(zzz34200)), zzz343, zzz344), h) → new_mkVBalBranch0(zzz31, Branch(zzz510, zzz511, Neg(Zero), zzz513, zzz514), zzz343, h)
new_mkVBalBranch3MkVBalBranch223(zzz340, zzz341, Neg(Succ(Succ(Succ(zzz3420000)))), zzz343, zzz344, zzz510, zzz511, Zero, zzz513, zzz514, zzz31, Succ(Succ(zzz6700)), h) → new_mkVBalBranch3MkVBalBranch225(zzz340, zzz341, Succ(Succ(zzz3420000)), zzz343, zzz344, zzz510, zzz511, zzz513, zzz514, zzz31, Succ(zzz3420000), Succ(zzz6700), h)
new_mkVBalBranch3MkVBalBranch120(zzz2050, zzz2051, zzz2052, zzz2053, zzz2054, zzz2055, zzz2056, zzz2057, zzz2058, zzz2059, zzz2060, Zero, Succ(zzz20620), be) → new_mkVBalBranch0(zzz2060, zzz2059, Branch(zzz2050, zzz2051, Neg(Succ(zzz2052)), zzz2053, zzz2054), be)
new_mkVBalBranch3MkVBalBranch220(zzz340, zzz341, zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, h) → new_mkVBalBranch0(zzz31, zzz514, Branch(zzz340, zzz341, Pos(Zero), zzz343, zzz344), h)
new_mkVBalBranch3MkVBalBranch228(zzz340, zzz341, zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, h) → new_mkVBalBranch0(zzz31, Branch(zzz510, zzz511, Neg(Succ(zzz51200)), zzz513, zzz514), zzz343, h)
new_mkVBalBranch0(zzz31, Branch(zzz510, zzz511, Pos(Zero), zzz513, zzz514), Branch(zzz340, zzz341, Pos(Succ(zzz34200)), zzz343, zzz344), h) → new_mkVBalBranch0(zzz31, Branch(zzz510, zzz511, Pos(Zero), zzz513, zzz514), zzz343, h)
new_mkVBalBranch3MkVBalBranch121(zzz473, zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, zzz481, zzz482, Succ(zzz7390), bh) → new_mkVBalBranch3MkVBalBranch115(zzz473, zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, Zero, zzz480, zzz481, zzz482, Succ(zzz7390), Succ(Zero), bh)
new_mkVBalBranch3MkVBalBranch223(zzz340, zzz341, Neg(Succ(Succ(Zero))), zzz343, zzz344, zzz510, zzz511, Succ(zzz512000), zzz513, zzz514, zzz31, Succ(Succ(zzz6700)), h) → new_mkVBalBranch3MkVBalBranch224(zzz340, zzz341, Succ(Zero), zzz343, zzz344, zzz510, zzz511, zzz512000, zzz513, zzz514, zzz31, Zero, Succ(Succ(new_primPlusNat2(zzz6700, zzz512000))), h)
new_mkVBalBranch3MkVBalBranch215(zzz340, zzz341, Pos(Succ(Zero)), zzz343, zzz344, zzz510, zzz511, Zero, zzz513, zzz514, zzz31, Zero, h) → new_mkVBalBranch3MkVBalBranch219(zzz340, zzz341, zzz343, zzz344, zzz510, zzz511, Zero, zzz513, zzz514, zzz31, h)
new_mkVBalBranch3MkVBalBranch223(zzz340, zzz341, Neg(Succ(Succ(Zero))), zzz343, zzz344, zzz510, zzz511, Zero, zzz513, zzz514, zzz31, Succ(Zero), h) → new_mkVBalBranch3MkVBalBranch225(zzz340, zzz341, Succ(Zero), zzz343, zzz344, zzz510, zzz511, zzz513, zzz514, zzz31, Zero, Zero, h)
new_mkVBalBranch3MkVBalBranch224(zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, zzz1125, zzz1126, zzz1127, zzz1128, zzz1129, Succ(zzz11300), Succ(zzz11310), bd) → new_mkVBalBranch3MkVBalBranch224(zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, zzz1125, zzz1126, zzz1127, zzz1128, zzz1129, zzz11300, zzz11310, bd)
new_mkVBalBranch3MkVBalBranch217(zzz473, zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, zzz481, zzz482, Zero, Succ(zzz4840), bh) → new_mkVBalBranch0(zzz482, Branch(zzz478, zzz479, Pos(Succ(Zero)), zzz480, zzz481), zzz476, bh)
new_mkVBalBranch0(zzz31, Branch(zzz510, zzz511, Pos(Succ(zzz51200)), zzz513, zzz514), Branch(zzz340, zzz341, zzz342, zzz343, zzz344), h) → new_mkVBalBranch3MkVBalBranch215(zzz340, zzz341, zzz342, zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, new_primPlusNat3(Succ(new_primPlusNat3(new_primPlusNat1(zzz51200), zzz51200)), Succ(zzz51200)), h)
new_mkVBalBranch3MkVBalBranch215(zzz340, zzz341, Pos(Succ(Succ(zzz342000))), zzz343, zzz344, zzz510, zzz511, Succ(zzz512000), zzz513, zzz514, zzz31, Zero, h) → new_mkVBalBranch3MkVBalBranch216(zzz340, zzz341, Succ(zzz342000), zzz343, zzz344, zzz510, zzz511, zzz512000, zzz513, zzz514, zzz31, zzz512000, zzz342000, h)
new_mkVBalBranch3MkVBalBranch110(zzz461, zzz462, zzz463, zzz464, zzz465, zzz466, zzz467, zzz468, zzz469, zzz470, zzz471, Succ(zzz5800), bb) → new_mkVBalBranch3MkVBalBranch115(zzz461, zzz462, zzz463, zzz464, zzz465, zzz466, zzz467, Succ(zzz468), zzz469, zzz470, zzz471, Succ(zzz5800), Succ(Succ(zzz468)), bb)
new_mkVBalBranch3MkVBalBranch227(zzz486, zzz487, zzz488, zzz489, zzz490, zzz491, zzz492, zzz493, zzz494, zzz495, zzz496, bf) → new_mkVBalBranch0(zzz496, Branch(zzz491, zzz492, Neg(Succ(Succ(zzz493))), zzz494, zzz495), zzz489, bf)
new_mkVBalBranch3MkVBalBranch215(zzz340, zzz341, Pos(Zero), zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, Succ(zzz660), h) → new_mkVBalBranch0(zzz31, zzz514, Branch(zzz340, zzz341, Pos(Zero), zzz343, zzz344), h)
new_mkVBalBranch3MkVBalBranch223(zzz340, zzz341, Neg(Zero), zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, Succ(zzz670), h) → new_mkVBalBranch0(zzz31, Branch(zzz510, zzz511, Neg(Succ(zzz51200)), zzz513, zzz514), zzz343, h)
new_mkVBalBranch3MkVBalBranch216(zzz1105, zzz1106, zzz1107, zzz1108, zzz1109, zzz1110, zzz1111, zzz1112, zzz1113, zzz1114, zzz1115, Zero, Succ(zzz11170), ba) → new_mkVBalBranch0(zzz1115, Branch(zzz1110, zzz1111, Pos(Succ(Succ(zzz1112))), zzz1113, zzz1114), zzz1108, ba)
new_mkVBalBranch3MkVBalBranch222(zzz461, zzz462, zzz463, zzz464, zzz465, zzz466, zzz467, zzz468, zzz469, zzz470, zzz471, bb) → new_mkVBalBranch3MkVBalBranch110(zzz461, zzz462, zzz463, zzz464, zzz465, zzz466, zzz467, zzz468, zzz469, zzz470, zzz471, new_primMulNat1(zzz463), bb)
new_mkVBalBranch3MkVBalBranch217(zzz473, zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, zzz481, zzz482, Succ(zzz4830), Zero, bh) → new_mkVBalBranch3MkVBalBranch121(zzz473, zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, zzz481, zzz482, new_primMulNat1(zzz475), bh)
new_mkVBalBranch3MkVBalBranch115(zzz1986, zzz1987, zzz1988, zzz1989, zzz1990, zzz1991, zzz1992, zzz1993, zzz1994, zzz1995, zzz1996, Zero, Succ(zzz19980), bc) → new_mkVBalBranch0(zzz1996, zzz1995, Branch(zzz1986, zzz1987, Pos(Succ(zzz1988)), zzz1989, zzz1990), bc)
new_mkVBalBranch3MkVBalBranch223(zzz340, zzz341, Neg(Zero), zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, Zero, h) → new_mkVBalBranch3MkVBalBranch228(zzz340, zzz341, zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, h)
new_mkVBalBranch3MkVBalBranch122(zzz340, zzz341, zzz34200, zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, h) → new_mkVBalBranch0(zzz31, zzz514, Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), h)
new_mkVBalBranch3MkVBalBranch217(zzz473, zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, zzz481, zzz482, Succ(zzz4830), Succ(zzz4840), bh) → new_mkVBalBranch3MkVBalBranch217(zzz473, zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, zzz481, zzz482, zzz4830, zzz4840, bh)
new_mkVBalBranch3MkVBalBranch116(zzz340, zzz341, zzz34200, zzz343, zzz344, zzz510, zzz511, zzz513, zzz514, zzz31, Succ(zzz1200), h) → new_mkVBalBranch0(zzz31, zzz514, Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), h)
new_mkVBalBranch3MkVBalBranch110(zzz461, zzz462, zzz463, zzz464, zzz465, zzz466, zzz467, zzz468, zzz469, zzz470, zzz471, Zero, bb) → new_mkVBalBranch3MkVBalBranch115(zzz461, zzz462, zzz463, zzz464, zzz465, zzz466, zzz467, Succ(zzz468), zzz469, zzz470, zzz471, Zero, Succ(Succ(zzz468)), bb)
new_mkVBalBranch3MkVBalBranch225(zzz498, zzz499, zzz500, zzz501, zzz502, zzz503, zzz504, zzz505, zzz506, zzz507, Zero, Succ(zzz5090), bg) → new_mkVBalBranch0(zzz507, Branch(zzz503, zzz504, Neg(Succ(Zero)), zzz505, zzz506), zzz501, bg)
new_mkVBalBranch3MkVBalBranch223(zzz340, zzz341, Neg(Succ(Succ(Succ(zzz3420000)))), zzz343, zzz344, zzz510, zzz511, Zero, zzz513, zzz514, zzz31, Succ(Zero), h) → new_mkVBalBranch3MkVBalBranch225(zzz340, zzz341, Succ(Succ(zzz3420000)), zzz343, zzz344, zzz510, zzz511, zzz513, zzz514, zzz31, Succ(zzz3420000), Zero, h)
new_mkVBalBranch3MkVBalBranch121(zzz473, zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, zzz481, zzz482, Zero, bh) → new_mkVBalBranch3MkVBalBranch115(zzz473, zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, Zero, zzz480, zzz481, zzz482, Zero, Succ(Zero), bh)
new_mkVBalBranch3MkVBalBranch215(zzz340, zzz341, Pos(Succ(Zero)), zzz343, zzz344, zzz510, zzz511, Succ(zzz512000), zzz513, zzz514, zzz31, Zero, h) → new_mkVBalBranch3MkVBalBranch218(zzz340, zzz341, Zero, zzz343, zzz344, zzz510, zzz511, zzz512000, zzz513, zzz514, zzz31, h)
new_mkVBalBranch3MkVBalBranch225(zzz498, zzz499, zzz500, zzz501, zzz502, zzz503, zzz504, zzz505, zzz506, zzz507, Succ(zzz5080), Zero, bg) → new_mkVBalBranch3MkVBalBranch118(zzz498, zzz499, zzz500, zzz501, zzz502, zzz503, zzz504, zzz505, zzz506, zzz507, new_primPlusNat2(new_primMulNat0(zzz500), Succ(zzz500)), bg)
new_mkVBalBranch3MkVBalBranch223(zzz340, zzz341, Neg(Succ(Zero)), zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, Succ(zzz670), h) → new_mkVBalBranch0(zzz31, Branch(zzz510, zzz511, Neg(Succ(zzz51200)), zzz513, zzz514), zzz343, h)
new_mkVBalBranch3MkVBalBranch229(zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, zzz1125, zzz1126, zzz1127, zzz1128, zzz1129, bd) → new_mkVBalBranch3MkVBalBranch119(zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, zzz1125, zzz1126, zzz1127, zzz1128, zzz1129, new_primPlusNat2(new_primMulNat0(zzz1121), Succ(zzz1121)), bd)
new_mkVBalBranch3MkVBalBranch218(zzz461, zzz462, zzz463, zzz464, zzz465, zzz466, zzz467, zzz468, zzz469, zzz470, zzz471, bb) → new_mkVBalBranch3MkVBalBranch110(zzz461, zzz462, zzz463, zzz464, zzz465, zzz466, zzz467, zzz468, zzz469, zzz470, zzz471, new_primMulNat1(zzz463), bb)
new_mkVBalBranch3MkVBalBranch223(zzz340, zzz341, Neg(Succ(Zero)), zzz343, zzz344, zzz510, zzz511, Succ(zzz512000), zzz513, zzz514, zzz31, Zero, h) → new_mkVBalBranch3MkVBalBranch227(zzz340, zzz341, Zero, zzz343, zzz344, zzz510, zzz511, zzz512000, zzz513, zzz514, zzz31, h)
new_mkVBalBranch3MkVBalBranch215(zzz340, zzz341, Pos(Succ(Zero)), zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, Succ(zzz660), h) → new_mkVBalBranch3MkVBalBranch18(zzz340, zzz341, zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, new_primMulNat1(Zero), h)
new_mkVBalBranch3MkVBalBranch226(zzz340, zzz341, zzz3420, zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, h) → new_mkVBalBranch0(zzz31, Branch(zzz510, zzz511, Neg(Succ(zzz51200)), zzz513, zzz514), zzz343, h)
new_mkVBalBranch3MkVBalBranch223(zzz340, zzz341, Neg(Succ(Succ(zzz342000))), zzz343, zzz344, zzz510, zzz511, Succ(zzz512000), zzz513, zzz514, zzz31, Zero, h) → new_mkVBalBranch3MkVBalBranch224(zzz340, zzz341, Succ(zzz342000), zzz343, zzz344, zzz510, zzz511, zzz512000, zzz513, zzz514, zzz31, zzz342000, zzz512000, h)
new_mkVBalBranch3MkVBalBranch215(zzz340, zzz341, Pos(Succ(Succ(zzz342000))), zzz343, zzz344, zzz510, zzz511, Zero, zzz513, zzz514, zzz31, Succ(Succ(zzz6600)), h) → new_mkVBalBranch3MkVBalBranch217(zzz340, zzz341, Succ(zzz342000), zzz343, zzz344, zzz510, zzz511, zzz513, zzz514, zzz31, Succ(zzz6600), zzz342000, h)
new_mkVBalBranch3MkVBalBranch117(zzz340, zzz341, zzz34200, zzz343, zzz344, zzz510, zzz511, zzz513, zzz514, zzz31, Succ(zzz1240), h) → new_mkVBalBranch0(zzz31, zzz514, Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), h)
new_mkVBalBranch3MkVBalBranch221(zzz340, zzz341, Succ(zzz34200), zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, h) → new_mkVBalBranch3MkVBalBranch19(zzz340, zzz341, zzz34200, zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, new_primPlusNat2(new_primPlusNat3(Succ(new_primPlusNat3(new_primPlusNat1(zzz34200), zzz34200)), Succ(zzz34200)), Succ(zzz34200)), h)
new_mkVBalBranch3MkVBalBranch120(zzz2050, zzz2051, zzz2052, zzz2053, zzz2054, zzz2055, zzz2056, zzz2057, zzz2058, zzz2059, zzz2060, Succ(zzz20610), Succ(zzz20620), be) → new_mkVBalBranch3MkVBalBranch120(zzz2050, zzz2051, zzz2052, zzz2053, zzz2054, zzz2055, zzz2056, zzz2057, zzz2058, zzz2059, zzz2060, zzz20610, zzz20620, be)
new_mkVBalBranch3MkVBalBranch217(zzz473, zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, zzz481, zzz482, Zero, Zero, bh) → new_mkVBalBranch3MkVBalBranch233(zzz473, zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, zzz481, zzz482, bh)
new_mkVBalBranch0(zzz31, Branch(zzz510, zzz511, Neg(Succ(zzz51200)), zzz513, zzz514), Branch(zzz340, zzz341, zzz342, zzz343, zzz344), h) → new_mkVBalBranch3MkVBalBranch223(zzz340, zzz341, zzz342, zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, new_primPlusNat3(Succ(new_primPlusNat3(new_primPlusNat1(zzz51200), zzz51200)), Succ(zzz51200)), h)
new_mkVBalBranch3MkVBalBranch223(zzz340, zzz341, Neg(Succ(Succ(zzz342000))), zzz343, zzz344, zzz510, zzz511, Zero, zzz513, zzz514, zzz31, Zero, h) → new_mkVBalBranch3MkVBalBranch118(zzz340, zzz341, Succ(zzz342000), zzz343, zzz344, zzz510, zzz511, zzz513, zzz514, zzz31, new_primMulNat1(Succ(zzz342000)), h)
new_mkVBalBranch3MkVBalBranch216(zzz1105, zzz1106, zzz1107, zzz1108, zzz1109, zzz1110, zzz1111, zzz1112, zzz1113, zzz1114, zzz1115, Succ(zzz11160), Succ(zzz11170), ba) → new_mkVBalBranch3MkVBalBranch216(zzz1105, zzz1106, zzz1107, zzz1108, zzz1109, zzz1110, zzz1111, zzz1112, zzz1113, zzz1114, zzz1115, zzz11160, zzz11170, ba)
new_mkVBalBranch3MkVBalBranch223(zzz340, zzz341, Pos(zzz3420), zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, Succ(zzz670), h) → new_mkVBalBranch0(zzz31, Branch(zzz510, zzz511, Neg(Succ(zzz51200)), zzz513, zzz514), zzz343, h)
new_mkVBalBranch3MkVBalBranch223(zzz340, zzz341, Neg(Succ(Succ(Succ(zzz3420000)))), zzz343, zzz344, zzz510, zzz511, Succ(zzz512000), zzz513, zzz514, zzz31, Succ(Zero), h) → new_mkVBalBranch3MkVBalBranch224(zzz340, zzz341, Succ(Succ(zzz3420000)), zzz343, zzz344, zzz510, zzz511, zzz512000, zzz513, zzz514, zzz31, Succ(zzz3420000), Succ(zzz512000), h)
new_mkVBalBranch3MkVBalBranch19(zzz340, zzz341, zzz34200, zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, Zero, h) → new_mkVBalBranch3MkVBalBranch122(zzz340, zzz341, zzz34200, zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, h)
new_mkVBalBranch0(zzz31, Branch(zzz510, zzz511, Neg(Zero), zzz513, zzz514), Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), h) → new_mkVBalBranch3MkVBalBranch117(zzz340, zzz341, zzz34200, zzz343, zzz344, zzz510, zzz511, zzz513, zzz514, zzz31, new_primMulNat1(zzz34200), h)
new_mkVBalBranch3MkVBalBranch215(zzz340, zzz341, Pos(Succ(Succ(zzz342000))), zzz343, zzz344, zzz510, zzz511, Zero, zzz513, zzz514, zzz31, Zero, h) → new_mkVBalBranch0(zzz31, Branch(zzz510, zzz511, Pos(Succ(Zero)), zzz513, zzz514), zzz343, h)
new_mkVBalBranch3MkVBalBranch225(zzz498, zzz499, zzz500, zzz501, zzz502, zzz503, zzz504, zzz505, zzz506, zzz507, Succ(zzz5080), Succ(zzz5090), bg) → new_mkVBalBranch3MkVBalBranch225(zzz498, zzz499, zzz500, zzz501, zzz502, zzz503, zzz504, zzz505, zzz506, zzz507, zzz5080, zzz5090, bg)
new_mkVBalBranch3MkVBalBranch19(zzz340, zzz341, zzz34200, zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, Succ(zzz1410), h) → new_mkVBalBranch0(zzz31, zzz514, Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), h)
new_mkVBalBranch3MkVBalBranch224(zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, zzz1125, zzz1126, zzz1127, zzz1128, zzz1129, Succ(zzz11300), Zero, bd) → new_mkVBalBranch3MkVBalBranch119(zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, zzz1125, zzz1126, zzz1127, zzz1128, zzz1129, new_primPlusNat2(new_primMulNat0(zzz1121), Succ(zzz1121)), bd)
new_mkVBalBranch3MkVBalBranch223(zzz340, zzz341, Pos(zzz3420), zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, Zero, h) → new_mkVBalBranch3MkVBalBranch226(zzz340, zzz341, zzz3420, zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, h)
new_mkVBalBranch3MkVBalBranch223(zzz340, zzz341, Neg(Succ(Succ(Zero))), zzz343, zzz344, zzz510, zzz511, Succ(zzz512000), zzz513, zzz514, zzz31, Succ(Zero), h) → new_mkVBalBranch3MkVBalBranch224(zzz340, zzz341, Succ(Zero), zzz343, zzz344, zzz510, zzz511, zzz512000, zzz513, zzz514, zzz31, Zero, Succ(zzz512000), h)
new_mkVBalBranch3MkVBalBranch224(zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, zzz1125, zzz1126, zzz1127, zzz1128, zzz1129, Zero, Zero, bd) → new_mkVBalBranch3MkVBalBranch229(zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, zzz1125, zzz1126, zzz1127, zzz1128, zzz1129, bd)
new_mkVBalBranch3MkVBalBranch224(zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, zzz1125, zzz1126, zzz1127, zzz1128, zzz1129, Zero, Succ(zzz11310), bd) → new_mkVBalBranch3MkVBalBranch227(zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, zzz1125, zzz1126, zzz1127, zzz1128, zzz1129, bd)
new_mkVBalBranch3MkVBalBranch230(zzz498, zzz499, zzz500, zzz501, zzz502, zzz503, zzz504, zzz505, zzz506, zzz507, bg) → new_mkVBalBranch3MkVBalBranch118(zzz498, zzz499, zzz500, zzz501, zzz502, zzz503, zzz504, zzz505, zzz506, zzz507, new_primPlusNat2(new_primMulNat0(zzz500), Succ(zzz500)), bg)
new_mkVBalBranch3MkVBalBranch223(zzz340, zzz341, Neg(Succ(Succ(Zero))), zzz343, zzz344, zzz510, zzz511, Zero, zzz513, zzz514, zzz31, Succ(Succ(zzz6700)), h) → new_mkVBalBranch3MkVBalBranch225(zzz340, zzz341, Succ(Zero), zzz343, zzz344, zzz510, zzz511, zzz513, zzz514, zzz31, Zero, Succ(zzz6700), h)
new_mkVBalBranch3MkVBalBranch223(zzz340, zzz341, Neg(Succ(Succ(Succ(zzz3420000)))), zzz343, zzz344, zzz510, zzz511, Succ(zzz512000), zzz513, zzz514, zzz31, Succ(Succ(zzz6700)), h) → new_mkVBalBranch3MkVBalBranch224(zzz340, zzz341, Succ(Succ(zzz3420000)), zzz343, zzz344, zzz510, zzz511, zzz512000, zzz513, zzz514, zzz31, Succ(zzz3420000), Succ(Succ(new_primPlusNat2(zzz6700, zzz512000))), h)
new_mkVBalBranch3MkVBalBranch115(zzz1986, zzz1987, zzz1988, zzz1989, zzz1990, zzz1991, zzz1992, zzz1993, zzz1994, zzz1995, zzz1996, Succ(zzz19970), Succ(zzz19980), bc) → new_mkVBalBranch3MkVBalBranch115(zzz1986, zzz1987, zzz1988, zzz1989, zzz1990, zzz1991, zzz1992, zzz1993, zzz1994, zzz1995, zzz1996, zzz19970, zzz19980, bc)
new_mkVBalBranch3MkVBalBranch215(zzz340, zzz341, Pos(Zero), zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, Zero, h) → new_mkVBalBranch3MkVBalBranch220(zzz340, zzz341, zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, h)
new_mkVBalBranch3MkVBalBranch215(zzz340, zzz341, Neg(Zero), zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, Succ(zzz660), h) → new_mkVBalBranch0(zzz31, zzz514, Branch(zzz340, zzz341, Neg(Zero), zzz343, zzz344), h)
new_mkVBalBranch3MkVBalBranch118(zzz498, zzz499, zzz500, zzz501, zzz502, zzz503, zzz504, zzz505, zzz506, zzz507, Succ(zzz8040), bg) → new_mkVBalBranch3MkVBalBranch120(zzz498, zzz499, zzz500, zzz501, zzz502, zzz503, zzz504, Zero, zzz505, zzz506, zzz507, Succ(Zero), Succ(zzz8040), bg)
new_mkVBalBranch3MkVBalBranch216(zzz1105, zzz1106, zzz1107, zzz1108, zzz1109, zzz1110, zzz1111, zzz1112, zzz1113, zzz1114, zzz1115, Succ(zzz11160), Zero, ba) → new_mkVBalBranch3MkVBalBranch218(zzz1105, zzz1106, zzz1107, zzz1108, zzz1109, zzz1110, zzz1111, zzz1112, zzz1113, zzz1114, zzz1115, ba)
new_mkVBalBranch3MkVBalBranch221(zzz340, zzz341, Zero, zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, h) → new_mkVBalBranch0(zzz31, zzz514, Branch(zzz340, zzz341, Neg(Zero), zzz343, zzz344), h)
new_mkVBalBranch3MkVBalBranch219(zzz340, zzz341, zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, h) → new_mkVBalBranch3MkVBalBranch18(zzz340, zzz341, zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, new_primMulNat1(Zero), h)
new_mkVBalBranch3MkVBalBranch215(zzz340, zzz341, Pos(Succ(Succ(zzz342000))), zzz343, zzz344, zzz510, zzz511, Succ(zzz512000), zzz513, zzz514, zzz31, Succ(Zero), h) → new_mkVBalBranch3MkVBalBranch216(zzz340, zzz341, Succ(zzz342000), zzz343, zzz344, zzz510, zzz511, zzz512000, zzz513, zzz514, zzz31, Succ(zzz512000), zzz342000, h)
new_mkVBalBranch3MkVBalBranch215(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, Succ(zzz660), h) → new_mkVBalBranch3MkVBalBranch19(zzz340, zzz341, zzz34200, zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, new_primPlusNat2(new_primMulNat0(zzz34200), Succ(zzz34200)), h)
new_mkVBalBranch3MkVBalBranch216(zzz1105, zzz1106, zzz1107, zzz1108, zzz1109, zzz1110, zzz1111, zzz1112, zzz1113, zzz1114, zzz1115, Zero, Zero, ba) → new_mkVBalBranch3MkVBalBranch222(zzz1105, zzz1106, zzz1107, zzz1108, zzz1109, zzz1110, zzz1111, zzz1112, zzz1113, zzz1114, zzz1115, ba)
new_mkVBalBranch3MkVBalBranch233(zzz473, zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, zzz481, zzz482, bh) → new_mkVBalBranch3MkVBalBranch121(zzz473, zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, zzz481, zzz482, new_primMulNat1(zzz475), bh)
new_mkVBalBranch3MkVBalBranch215(zzz340, zzz341, Pos(Succ(Succ(zzz342000))), zzz343, zzz344, zzz510, zzz511, Zero, zzz513, zzz514, zzz31, Succ(Zero), h) → new_mkVBalBranch3MkVBalBranch217(zzz340, zzz341, Succ(zzz342000), zzz343, zzz344, zzz510, zzz511, zzz513, zzz514, zzz31, Zero, zzz342000, h)
new_mkVBalBranch0(zzz31, Branch(zzz510, zzz511, Pos(Zero), zzz513, zzz514), Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), h) → new_mkVBalBranch3MkVBalBranch116(zzz340, zzz341, zzz34200, zzz343, zzz344, zzz510, zzz511, zzz513, zzz514, zzz31, new_primMulNat1(zzz34200), h)
new_mkVBalBranch3MkVBalBranch119(zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, zzz1125, zzz1126, zzz1127, zzz1128, zzz1129, Succ(zzz12130), bd) → new_mkVBalBranch3MkVBalBranch120(zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, zzz1125, Succ(zzz1126), zzz1127, zzz1128, zzz1129, Succ(Succ(zzz1126)), Succ(zzz12130), bd)
new_mkVBalBranch3MkVBalBranch18(zzz340, zzz341, zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, Zero, h) → new_mkVBalBranch3MkVBalBranch115(zzz340, zzz341, Zero, zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, Zero, Succ(zzz51200), h)
new_mkVBalBranch3MkVBalBranch223(zzz340, zzz341, Neg(Succ(Zero)), zzz343, zzz344, zzz510, zzz511, Zero, zzz513, zzz514, zzz31, Zero, h) → new_mkVBalBranch3MkVBalBranch118(zzz340, zzz341, Zero, zzz343, zzz344, zzz510, zzz511, zzz513, zzz514, zzz31, new_primMulNat1(Zero), h)

The TRS R consists of the following rules:

new_primPlusNat1(Zero) → Zero
new_primMulNat0(zzz6200) → new_primPlusNat3(Succ(new_primPlusNat3(new_primPlusNat1(zzz6200), zzz6200)), Succ(zzz6200))
new_primPlusNat2(Succ(zzz900), Succ(zzz9100)) → Succ(Succ(new_primPlusNat2(zzz900, zzz9100)))
new_primPlusNat3(zzz90, Succ(zzz910)) → Succ(Succ(new_primPlusNat2(zzz90, zzz910)))
new_primPlusNat3(zzz90, Zero) → Succ(zzz90)
new_primMulNat1(zzz34200) → new_primPlusNat2(new_primMulNat0(zzz34200), Succ(zzz34200))
new_primPlusNat2(Zero, Zero) → Zero
new_primPlusNat1(Succ(zzz62000)) → Succ(Succ(new_primPlusNat1(zzz62000)))
new_primPlusNat2(Succ(zzz900), Zero) → Succ(zzz900)
new_primPlusNat2(Zero, Succ(zzz9100)) → Succ(zzz9100)

The set Q consists of the following terms:

new_primPlusNat2(Zero, Succ(x0))
new_primMulNat1(x0)
new_primMulNat0(x0)
new_primPlusNat3(x0, Succ(x1))
new_primPlusNat2(Succ(x0), Succ(x1))
new_primPlusNat3(x0, Zero)
new_primPlusNat1(Zero)
new_primPlusNat2(Zero, Zero)
new_primPlusNat1(Succ(x0))
new_primPlusNat2(Succ(x0), Zero)

We have to consider all minimal (P,Q,R)-chains.
By rewriting [15] the rule new_mkVBalBranch3MkVBalBranch223(zzz340, zzz341, Neg(Succ(Succ(zzz342000))), zzz343, zzz344, zzz510, zzz511, Zero, zzz513, zzz514, zzz31, Zero, h) → new_mkVBalBranch3MkVBalBranch118(zzz340, zzz341, Succ(zzz342000), zzz343, zzz344, zzz510, zzz511, zzz513, zzz514, zzz31, new_primMulNat1(Succ(zzz342000)), h) at position [10] we obtained the following new rules:

new_mkVBalBranch3MkVBalBranch223(zzz340, zzz341, Neg(Succ(Succ(zzz342000))), zzz343, zzz344, zzz510, zzz511, Zero, zzz513, zzz514, zzz31, Zero, h) → new_mkVBalBranch3MkVBalBranch118(zzz340, zzz341, Succ(zzz342000), zzz343, zzz344, zzz510, zzz511, zzz513, zzz514, zzz31, new_primPlusNat2(new_primMulNat0(Succ(zzz342000)), Succ(Succ(zzz342000))), 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
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                    ↳ DependencyGraphProof
                                      ↳ QDP
                                        ↳ Rewriting
                                          ↳ QDP
                                            ↳ Rewriting
                                              ↳ QDP
                                                ↳ Rewriting
                                                  ↳ QDP
                                                    ↳ Rewriting
                                                      ↳ QDP
                                                        ↳ Rewriting
                                                          ↳ QDP
                                                            ↳ Rewriting
                                                              ↳ QDP
                                                                ↳ Rewriting
                                                                  ↳ QDP
                                                                    ↳ Rewriting
                                                                      ↳ QDP
                                                                        ↳ Rewriting
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP

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

new_mkVBalBranch3MkVBalBranch215(zzz340, zzz341, Neg(zzz3420), zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, Zero, h) → new_mkVBalBranch3MkVBalBranch221(zzz340, zzz341, zzz3420, zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, h)
new_mkVBalBranch3MkVBalBranch225(zzz498, zzz499, zzz500, zzz501, zzz502, zzz503, zzz504, zzz505, zzz506, zzz507, Zero, Zero, bg) → new_mkVBalBranch3MkVBalBranch230(zzz498, zzz499, zzz500, zzz501, zzz502, zzz503, zzz504, zzz505, zzz506, zzz507, bg)
new_mkVBalBranch3MkVBalBranch18(zzz340, zzz341, zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, Succ(zzz1480), h) → new_mkVBalBranch3MkVBalBranch115(zzz340, zzz341, Zero, zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, Succ(zzz1480), Succ(zzz51200), h)
new_mkVBalBranch0(zzz31, Branch(zzz510, zzz511, Neg(Zero), zzz513, zzz514), Branch(zzz340, zzz341, Pos(Succ(zzz34200)), zzz343, zzz344), h) → new_mkVBalBranch0(zzz31, Branch(zzz510, zzz511, Neg(Zero), zzz513, zzz514), zzz343, h)
new_mkVBalBranch3MkVBalBranch215(zzz340, zzz341, Pos(Succ(Succ(zzz342000))), zzz343, zzz344, zzz510, zzz511, Succ(zzz512000), zzz513, zzz514, zzz31, Succ(Succ(zzz6600)), h) → new_mkVBalBranch3MkVBalBranch216(zzz340, zzz341, Succ(zzz342000), zzz343, zzz344, zzz510, zzz511, zzz512000, zzz513, zzz514, zzz31, Succ(Succ(new_primPlusNat2(zzz6600, zzz512000))), zzz342000, h)
new_mkVBalBranch3MkVBalBranch223(zzz340, zzz341, Neg(Succ(Succ(Succ(zzz3420000)))), zzz343, zzz344, zzz510, zzz511, Zero, zzz513, zzz514, zzz31, Succ(Succ(zzz6700)), h) → new_mkVBalBranch3MkVBalBranch225(zzz340, zzz341, Succ(Succ(zzz3420000)), zzz343, zzz344, zzz510, zzz511, zzz513, zzz514, zzz31, Succ(zzz3420000), Succ(zzz6700), h)
new_mkVBalBranch3MkVBalBranch220(zzz340, zzz341, zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, h) → new_mkVBalBranch0(zzz31, zzz514, Branch(zzz340, zzz341, Pos(Zero), zzz343, zzz344), h)
new_mkVBalBranch3MkVBalBranch120(zzz2050, zzz2051, zzz2052, zzz2053, zzz2054, zzz2055, zzz2056, zzz2057, zzz2058, zzz2059, zzz2060, Zero, Succ(zzz20620), be) → new_mkVBalBranch0(zzz2060, zzz2059, Branch(zzz2050, zzz2051, Neg(Succ(zzz2052)), zzz2053, zzz2054), be)
new_mkVBalBranch3MkVBalBranch121(zzz473, zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, zzz481, zzz482, Succ(zzz7390), bh) → new_mkVBalBranch3MkVBalBranch115(zzz473, zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, Zero, zzz480, zzz481, zzz482, Succ(zzz7390), Succ(Zero), bh)
new_mkVBalBranch0(zzz31, Branch(zzz510, zzz511, Pos(Zero), zzz513, zzz514), Branch(zzz340, zzz341, Pos(Succ(zzz34200)), zzz343, zzz344), h) → new_mkVBalBranch0(zzz31, Branch(zzz510, zzz511, Pos(Zero), zzz513, zzz514), zzz343, h)
new_mkVBalBranch3MkVBalBranch228(zzz340, zzz341, zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, h) → new_mkVBalBranch0(zzz31, Branch(zzz510, zzz511, Neg(Succ(zzz51200)), zzz513, zzz514), zzz343, h)
new_mkVBalBranch3MkVBalBranch215(zzz340, zzz341, Pos(Succ(Zero)), zzz343, zzz344, zzz510, zzz511, Zero, zzz513, zzz514, zzz31, Zero, h) → new_mkVBalBranch3MkVBalBranch219(zzz340, zzz341, zzz343, zzz344, zzz510, zzz511, Zero, zzz513, zzz514, zzz31, h)
new_mkVBalBranch3MkVBalBranch223(zzz340, zzz341, Neg(Succ(Succ(Zero))), zzz343, zzz344, zzz510, zzz511, Succ(zzz512000), zzz513, zzz514, zzz31, Succ(Succ(zzz6700)), h) → new_mkVBalBranch3MkVBalBranch224(zzz340, zzz341, Succ(Zero), zzz343, zzz344, zzz510, zzz511, zzz512000, zzz513, zzz514, zzz31, Zero, Succ(Succ(new_primPlusNat2(zzz6700, zzz512000))), h)
new_mkVBalBranch3MkVBalBranch223(zzz340, zzz341, Neg(Succ(Succ(Zero))), zzz343, zzz344, zzz510, zzz511, Zero, zzz513, zzz514, zzz31, Succ(Zero), h) → new_mkVBalBranch3MkVBalBranch225(zzz340, zzz341, Succ(Zero), zzz343, zzz344, zzz510, zzz511, zzz513, zzz514, zzz31, Zero, Zero, h)
new_mkVBalBranch3MkVBalBranch224(zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, zzz1125, zzz1126, zzz1127, zzz1128, zzz1129, Succ(zzz11300), Succ(zzz11310), bd) → new_mkVBalBranch3MkVBalBranch224(zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, zzz1125, zzz1126, zzz1127, zzz1128, zzz1129, zzz11300, zzz11310, bd)
new_mkVBalBranch0(zzz31, Branch(zzz510, zzz511, Pos(Succ(zzz51200)), zzz513, zzz514), Branch(zzz340, zzz341, zzz342, zzz343, zzz344), h) → new_mkVBalBranch3MkVBalBranch215(zzz340, zzz341, zzz342, zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, new_primPlusNat3(Succ(new_primPlusNat3(new_primPlusNat1(zzz51200), zzz51200)), Succ(zzz51200)), h)
new_mkVBalBranch3MkVBalBranch217(zzz473, zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, zzz481, zzz482, Zero, Succ(zzz4840), bh) → new_mkVBalBranch0(zzz482, Branch(zzz478, zzz479, Pos(Succ(Zero)), zzz480, zzz481), zzz476, bh)
new_mkVBalBranch3MkVBalBranch215(zzz340, zzz341, Pos(Succ(Succ(zzz342000))), zzz343, zzz344, zzz510, zzz511, Succ(zzz512000), zzz513, zzz514, zzz31, Zero, h) → new_mkVBalBranch3MkVBalBranch216(zzz340, zzz341, Succ(zzz342000), zzz343, zzz344, zzz510, zzz511, zzz512000, zzz513, zzz514, zzz31, zzz512000, zzz342000, h)
new_mkVBalBranch3MkVBalBranch110(zzz461, zzz462, zzz463, zzz464, zzz465, zzz466, zzz467, zzz468, zzz469, zzz470, zzz471, Succ(zzz5800), bb) → new_mkVBalBranch3MkVBalBranch115(zzz461, zzz462, zzz463, zzz464, zzz465, zzz466, zzz467, Succ(zzz468), zzz469, zzz470, zzz471, Succ(zzz5800), Succ(Succ(zzz468)), bb)
new_mkVBalBranch3MkVBalBranch227(zzz486, zzz487, zzz488, zzz489, zzz490, zzz491, zzz492, zzz493, zzz494, zzz495, zzz496, bf) → new_mkVBalBranch0(zzz496, Branch(zzz491, zzz492, Neg(Succ(Succ(zzz493))), zzz494, zzz495), zzz489, bf)
new_mkVBalBranch3MkVBalBranch215(zzz340, zzz341, Pos(Zero), zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, Succ(zzz660), h) → new_mkVBalBranch0(zzz31, zzz514, Branch(zzz340, zzz341, Pos(Zero), zzz343, zzz344), h)
new_mkVBalBranch3MkVBalBranch223(zzz340, zzz341, Neg(Zero), zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, Succ(zzz670), h) → new_mkVBalBranch0(zzz31, Branch(zzz510, zzz511, Neg(Succ(zzz51200)), zzz513, zzz514), zzz343, h)
new_mkVBalBranch3MkVBalBranch216(zzz1105, zzz1106, zzz1107, zzz1108, zzz1109, zzz1110, zzz1111, zzz1112, zzz1113, zzz1114, zzz1115, Zero, Succ(zzz11170), ba) → new_mkVBalBranch0(zzz1115, Branch(zzz1110, zzz1111, Pos(Succ(Succ(zzz1112))), zzz1113, zzz1114), zzz1108, ba)
new_mkVBalBranch3MkVBalBranch217(zzz473, zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, zzz481, zzz482, Succ(zzz4830), Zero, bh) → new_mkVBalBranch3MkVBalBranch121(zzz473, zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, zzz481, zzz482, new_primMulNat1(zzz475), bh)
new_mkVBalBranch3MkVBalBranch222(zzz461, zzz462, zzz463, zzz464, zzz465, zzz466, zzz467, zzz468, zzz469, zzz470, zzz471, bb) → new_mkVBalBranch3MkVBalBranch110(zzz461, zzz462, zzz463, zzz464, zzz465, zzz466, zzz467, zzz468, zzz469, zzz470, zzz471, new_primMulNat1(zzz463), bb)
new_mkVBalBranch3MkVBalBranch115(zzz1986, zzz1987, zzz1988, zzz1989, zzz1990, zzz1991, zzz1992, zzz1993, zzz1994, zzz1995, zzz1996, Zero, Succ(zzz19980), bc) → new_mkVBalBranch0(zzz1996, zzz1995, Branch(zzz1986, zzz1987, Pos(Succ(zzz1988)), zzz1989, zzz1990), bc)
new_mkVBalBranch3MkVBalBranch223(zzz340, zzz341, Neg(Zero), zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, Zero, h) → new_mkVBalBranch3MkVBalBranch228(zzz340, zzz341, zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, h)
new_mkVBalBranch3MkVBalBranch122(zzz340, zzz341, zzz34200, zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, h) → new_mkVBalBranch0(zzz31, zzz514, Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), h)
new_mkVBalBranch3MkVBalBranch217(zzz473, zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, zzz481, zzz482, Succ(zzz4830), Succ(zzz4840), bh) → new_mkVBalBranch3MkVBalBranch217(zzz473, zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, zzz481, zzz482, zzz4830, zzz4840, bh)
new_mkVBalBranch3MkVBalBranch116(zzz340, zzz341, zzz34200, zzz343, zzz344, zzz510, zzz511, zzz513, zzz514, zzz31, Succ(zzz1200), h) → new_mkVBalBranch0(zzz31, zzz514, Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), h)
new_mkVBalBranch3MkVBalBranch110(zzz461, zzz462, zzz463, zzz464, zzz465, zzz466, zzz467, zzz468, zzz469, zzz470, zzz471, Zero, bb) → new_mkVBalBranch3MkVBalBranch115(zzz461, zzz462, zzz463, zzz464, zzz465, zzz466, zzz467, Succ(zzz468), zzz469, zzz470, zzz471, Zero, Succ(Succ(zzz468)), bb)
new_mkVBalBranch3MkVBalBranch225(zzz498, zzz499, zzz500, zzz501, zzz502, zzz503, zzz504, zzz505, zzz506, zzz507, Zero, Succ(zzz5090), bg) → new_mkVBalBranch0(zzz507, Branch(zzz503, zzz504, Neg(Succ(Zero)), zzz505, zzz506), zzz501, bg)
new_mkVBalBranch3MkVBalBranch223(zzz340, zzz341, Neg(Succ(Succ(Succ(zzz3420000)))), zzz343, zzz344, zzz510, zzz511, Zero, zzz513, zzz514, zzz31, Succ(Zero), h) → new_mkVBalBranch3MkVBalBranch225(zzz340, zzz341, Succ(Succ(zzz3420000)), zzz343, zzz344, zzz510, zzz511, zzz513, zzz514, zzz31, Succ(zzz3420000), Zero, h)
new_mkVBalBranch3MkVBalBranch121(zzz473, zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, zzz481, zzz482, Zero, bh) → new_mkVBalBranch3MkVBalBranch115(zzz473, zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, Zero, zzz480, zzz481, zzz482, Zero, Succ(Zero), bh)
new_mkVBalBranch3MkVBalBranch215(zzz340, zzz341, Pos(Succ(Zero)), zzz343, zzz344, zzz510, zzz511, Succ(zzz512000), zzz513, zzz514, zzz31, Zero, h) → new_mkVBalBranch3MkVBalBranch218(zzz340, zzz341, Zero, zzz343, zzz344, zzz510, zzz511, zzz512000, zzz513, zzz514, zzz31, h)
new_mkVBalBranch3MkVBalBranch223(zzz340, zzz341, Neg(Succ(Zero)), zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, Succ(zzz670), h) → new_mkVBalBranch0(zzz31, Branch(zzz510, zzz511, Neg(Succ(zzz51200)), zzz513, zzz514), zzz343, h)
new_mkVBalBranch3MkVBalBranch225(zzz498, zzz499, zzz500, zzz501, zzz502, zzz503, zzz504, zzz505, zzz506, zzz507, Succ(zzz5080), Zero, bg) → new_mkVBalBranch3MkVBalBranch118(zzz498, zzz499, zzz500, zzz501, zzz502, zzz503, zzz504, zzz505, zzz506, zzz507, new_primPlusNat2(new_primMulNat0(zzz500), Succ(zzz500)), bg)
new_mkVBalBranch3MkVBalBranch229(zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, zzz1125, zzz1126, zzz1127, zzz1128, zzz1129, bd) → new_mkVBalBranch3MkVBalBranch119(zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, zzz1125, zzz1126, zzz1127, zzz1128, zzz1129, new_primPlusNat2(new_primMulNat0(zzz1121), Succ(zzz1121)), bd)
new_mkVBalBranch3MkVBalBranch218(zzz461, zzz462, zzz463, zzz464, zzz465, zzz466, zzz467, zzz468, zzz469, zzz470, zzz471, bb) → new_mkVBalBranch3MkVBalBranch110(zzz461, zzz462, zzz463, zzz464, zzz465, zzz466, zzz467, zzz468, zzz469, zzz470, zzz471, new_primMulNat1(zzz463), bb)
new_mkVBalBranch3MkVBalBranch223(zzz340, zzz341, Neg(Succ(Zero)), zzz343, zzz344, zzz510, zzz511, Succ(zzz512000), zzz513, zzz514, zzz31, Zero, h) → new_mkVBalBranch3MkVBalBranch227(zzz340, zzz341, Zero, zzz343, zzz344, zzz510, zzz511, zzz512000, zzz513, zzz514, zzz31, h)
new_mkVBalBranch3MkVBalBranch215(zzz340, zzz341, Pos(Succ(Zero)), zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, Succ(zzz660), h) → new_mkVBalBranch3MkVBalBranch18(zzz340, zzz341, zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, new_primMulNat1(Zero), h)
new_mkVBalBranch3MkVBalBranch215(zzz340, zzz341, Pos(Succ(Succ(zzz342000))), zzz343, zzz344, zzz510, zzz511, Zero, zzz513, zzz514, zzz31, Succ(Succ(zzz6600)), h) → new_mkVBalBranch3MkVBalBranch217(zzz340, zzz341, Succ(zzz342000), zzz343, zzz344, zzz510, zzz511, zzz513, zzz514, zzz31, Succ(zzz6600), zzz342000, h)
new_mkVBalBranch3MkVBalBranch223(zzz340, zzz341, Neg(Succ(Succ(zzz342000))), zzz343, zzz344, zzz510, zzz511, Succ(zzz512000), zzz513, zzz514, zzz31, Zero, h) → new_mkVBalBranch3MkVBalBranch224(zzz340, zzz341, Succ(zzz342000), zzz343, zzz344, zzz510, zzz511, zzz512000, zzz513, zzz514, zzz31, zzz342000, zzz512000, h)
new_mkVBalBranch3MkVBalBranch226(zzz340, zzz341, zzz3420, zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, h) → new_mkVBalBranch0(zzz31, Branch(zzz510, zzz511, Neg(Succ(zzz51200)), zzz513, zzz514), zzz343, h)
new_mkVBalBranch3MkVBalBranch117(zzz340, zzz341, zzz34200, zzz343, zzz344, zzz510, zzz511, zzz513, zzz514, zzz31, Succ(zzz1240), h) → new_mkVBalBranch0(zzz31, zzz514, Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), h)
new_mkVBalBranch0(zzz31, Branch(zzz510, zzz511, Neg(Succ(zzz51200)), zzz513, zzz514), Branch(zzz340, zzz341, zzz342, zzz343, zzz344), h) → new_mkVBalBranch3MkVBalBranch223(zzz340, zzz341, zzz342, zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, new_primPlusNat3(Succ(new_primPlusNat3(new_primPlusNat1(zzz51200), zzz51200)), Succ(zzz51200)), h)
new_mkVBalBranch3MkVBalBranch217(zzz473, zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, zzz481, zzz482, Zero, Zero, bh) → new_mkVBalBranch3MkVBalBranch233(zzz473, zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, zzz481, zzz482, bh)
new_mkVBalBranch3MkVBalBranch120(zzz2050, zzz2051, zzz2052, zzz2053, zzz2054, zzz2055, zzz2056, zzz2057, zzz2058, zzz2059, zzz2060, Succ(zzz20610), Succ(zzz20620), be) → new_mkVBalBranch3MkVBalBranch120(zzz2050, zzz2051, zzz2052, zzz2053, zzz2054, zzz2055, zzz2056, zzz2057, zzz2058, zzz2059, zzz2060, zzz20610, zzz20620, be)
new_mkVBalBranch3MkVBalBranch221(zzz340, zzz341, Succ(zzz34200), zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, h) → new_mkVBalBranch3MkVBalBranch19(zzz340, zzz341, zzz34200, zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, new_primPlusNat2(new_primPlusNat3(Succ(new_primPlusNat3(new_primPlusNat1(zzz34200), zzz34200)), Succ(zzz34200)), Succ(zzz34200)), h)
new_mkVBalBranch3MkVBalBranch223(zzz340, zzz341, Pos(zzz3420), zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, Succ(zzz670), h) → new_mkVBalBranch0(zzz31, Branch(zzz510, zzz511, Neg(Succ(zzz51200)), zzz513, zzz514), zzz343, h)
new_mkVBalBranch3MkVBalBranch216(zzz1105, zzz1106, zzz1107, zzz1108, zzz1109, zzz1110, zzz1111, zzz1112, zzz1113, zzz1114, zzz1115, Succ(zzz11160), Succ(zzz11170), ba) → new_mkVBalBranch3MkVBalBranch216(zzz1105, zzz1106, zzz1107, zzz1108, zzz1109, zzz1110, zzz1111, zzz1112, zzz1113, zzz1114, zzz1115, zzz11160, zzz11170, ba)
new_mkVBalBranch3MkVBalBranch19(zzz340, zzz341, zzz34200, zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, Zero, h) → new_mkVBalBranch3MkVBalBranch122(zzz340, zzz341, zzz34200, zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, h)
new_mkVBalBranch3MkVBalBranch223(zzz340, zzz341, Neg(Succ(Succ(Succ(zzz3420000)))), zzz343, zzz344, zzz510, zzz511, Succ(zzz512000), zzz513, zzz514, zzz31, Succ(Zero), h) → new_mkVBalBranch3MkVBalBranch224(zzz340, zzz341, Succ(Succ(zzz3420000)), zzz343, zzz344, zzz510, zzz511, zzz512000, zzz513, zzz514, zzz31, Succ(zzz3420000), Succ(zzz512000), h)
new_mkVBalBranch0(zzz31, Branch(zzz510, zzz511, Neg(Zero), zzz513, zzz514), Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), h) → new_mkVBalBranch3MkVBalBranch117(zzz340, zzz341, zzz34200, zzz343, zzz344, zzz510, zzz511, zzz513, zzz514, zzz31, new_primMulNat1(zzz34200), h)
new_mkVBalBranch3MkVBalBranch215(zzz340, zzz341, Pos(Succ(Succ(zzz342000))), zzz343, zzz344, zzz510, zzz511, Zero, zzz513, zzz514, zzz31, Zero, h) → new_mkVBalBranch0(zzz31, Branch(zzz510, zzz511, Pos(Succ(Zero)), zzz513, zzz514), zzz343, h)
new_mkVBalBranch3MkVBalBranch225(zzz498, zzz499, zzz500, zzz501, zzz502, zzz503, zzz504, zzz505, zzz506, zzz507, Succ(zzz5080), Succ(zzz5090), bg) → new_mkVBalBranch3MkVBalBranch225(zzz498, zzz499, zzz500, zzz501, zzz502, zzz503, zzz504, zzz505, zzz506, zzz507, zzz5080, zzz5090, bg)
new_mkVBalBranch3MkVBalBranch19(zzz340, zzz341, zzz34200, zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, Succ(zzz1410), h) → new_mkVBalBranch0(zzz31, zzz514, Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), h)
new_mkVBalBranch3MkVBalBranch224(zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, zzz1125, zzz1126, zzz1127, zzz1128, zzz1129, Succ(zzz11300), Zero, bd) → new_mkVBalBranch3MkVBalBranch119(zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, zzz1125, zzz1126, zzz1127, zzz1128, zzz1129, new_primPlusNat2(new_primMulNat0(zzz1121), Succ(zzz1121)), bd)
new_mkVBalBranch3MkVBalBranch224(zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, zzz1125, zzz1126, zzz1127, zzz1128, zzz1129, Zero, Succ(zzz11310), bd) → new_mkVBalBranch3MkVBalBranch227(zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, zzz1125, zzz1126, zzz1127, zzz1128, zzz1129, bd)
new_mkVBalBranch3MkVBalBranch224(zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, zzz1125, zzz1126, zzz1127, zzz1128, zzz1129, Zero, Zero, bd) → new_mkVBalBranch3MkVBalBranch229(zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, zzz1125, zzz1126, zzz1127, zzz1128, zzz1129, bd)
new_mkVBalBranch3MkVBalBranch223(zzz340, zzz341, Neg(Succ(Succ(Zero))), zzz343, zzz344, zzz510, zzz511, Succ(zzz512000), zzz513, zzz514, zzz31, Succ(Zero), h) → new_mkVBalBranch3MkVBalBranch224(zzz340, zzz341, Succ(Zero), zzz343, zzz344, zzz510, zzz511, zzz512000, zzz513, zzz514, zzz31, Zero, Succ(zzz512000), h)
new_mkVBalBranch3MkVBalBranch223(zzz340, zzz341, Pos(zzz3420), zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, Zero, h) → new_mkVBalBranch3MkVBalBranch226(zzz340, zzz341, zzz3420, zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, h)
new_mkVBalBranch3MkVBalBranch223(zzz340, zzz341, Neg(Succ(Succ(zzz342000))), zzz343, zzz344, zzz510, zzz511, Zero, zzz513, zzz514, zzz31, Zero, h) → new_mkVBalBranch3MkVBalBranch118(zzz340, zzz341, Succ(zzz342000), zzz343, zzz344, zzz510, zzz511, zzz513, zzz514, zzz31, new_primPlusNat2(new_primMulNat0(Succ(zzz342000)), Succ(Succ(zzz342000))), h)
new_mkVBalBranch3MkVBalBranch230(zzz498, zzz499, zzz500, zzz501, zzz502, zzz503, zzz504, zzz505, zzz506, zzz507, bg) → new_mkVBalBranch3MkVBalBranch118(zzz498, zzz499, zzz500, zzz501, zzz502, zzz503, zzz504, zzz505, zzz506, zzz507, new_primPlusNat2(new_primMulNat0(zzz500), Succ(zzz500)), bg)
new_mkVBalBranch3MkVBalBranch223(zzz340, zzz341, Neg(Succ(Succ(Succ(zzz3420000)))), zzz343, zzz344, zzz510, zzz511, Succ(zzz512000), zzz513, zzz514, zzz31, Succ(Succ(zzz6700)), h) → new_mkVBalBranch3MkVBalBranch224(zzz340, zzz341, Succ(Succ(zzz3420000)), zzz343, zzz344, zzz510, zzz511, zzz512000, zzz513, zzz514, zzz31, Succ(zzz3420000), Succ(Succ(new_primPlusNat2(zzz6700, zzz512000))), h)
new_mkVBalBranch3MkVBalBranch223(zzz340, zzz341, Neg(Succ(Succ(Zero))), zzz343, zzz344, zzz510, zzz511, Zero, zzz513, zzz514, zzz31, Succ(Succ(zzz6700)), h) → new_mkVBalBranch3MkVBalBranch225(zzz340, zzz341, Succ(Zero), zzz343, zzz344, zzz510, zzz511, zzz513, zzz514, zzz31, Zero, Succ(zzz6700), h)
new_mkVBalBranch3MkVBalBranch215(zzz340, zzz341, Pos(Zero), zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, Zero, h) → new_mkVBalBranch3MkVBalBranch220(zzz340, zzz341, zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, h)
new_mkVBalBranch3MkVBalBranch115(zzz1986, zzz1987, zzz1988, zzz1989, zzz1990, zzz1991, zzz1992, zzz1993, zzz1994, zzz1995, zzz1996, Succ(zzz19970), Succ(zzz19980), bc) → new_mkVBalBranch3MkVBalBranch115(zzz1986, zzz1987, zzz1988, zzz1989, zzz1990, zzz1991, zzz1992, zzz1993, zzz1994, zzz1995, zzz1996, zzz19970, zzz19980, bc)
new_mkVBalBranch3MkVBalBranch215(zzz340, zzz341, Neg(Zero), zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, Succ(zzz660), h) → new_mkVBalBranch0(zzz31, zzz514, Branch(zzz340, zzz341, Neg(Zero), zzz343, zzz344), h)
new_mkVBalBranch3MkVBalBranch118(zzz498, zzz499, zzz500, zzz501, zzz502, zzz503, zzz504, zzz505, zzz506, zzz507, Succ(zzz8040), bg) → new_mkVBalBranch3MkVBalBranch120(zzz498, zzz499, zzz500, zzz501, zzz502, zzz503, zzz504, Zero, zzz505, zzz506, zzz507, Succ(Zero), Succ(zzz8040), bg)
new_mkVBalBranch3MkVBalBranch216(zzz1105, zzz1106, zzz1107, zzz1108, zzz1109, zzz1110, zzz1111, zzz1112, zzz1113, zzz1114, zzz1115, Succ(zzz11160), Zero, ba) → new_mkVBalBranch3MkVBalBranch218(zzz1105, zzz1106, zzz1107, zzz1108, zzz1109, zzz1110, zzz1111, zzz1112, zzz1113, zzz1114, zzz1115, ba)
new_mkVBalBranch3MkVBalBranch215(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, Succ(zzz660), h) → new_mkVBalBranch3MkVBalBranch19(zzz340, zzz341, zzz34200, zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, new_primPlusNat2(new_primMulNat0(zzz34200), Succ(zzz34200)), h)
new_mkVBalBranch3MkVBalBranch215(zzz340, zzz341, Pos(Succ(Succ(zzz342000))), zzz343, zzz344, zzz510, zzz511, Succ(zzz512000), zzz513, zzz514, zzz31, Succ(Zero), h) → new_mkVBalBranch3MkVBalBranch216(zzz340, zzz341, Succ(zzz342000), zzz343, zzz344, zzz510, zzz511, zzz512000, zzz513, zzz514, zzz31, Succ(zzz512000), zzz342000, h)
new_mkVBalBranch3MkVBalBranch219(zzz340, zzz341, zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, h) → new_mkVBalBranch3MkVBalBranch18(zzz340, zzz341, zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, new_primMulNat1(Zero), h)
new_mkVBalBranch3MkVBalBranch221(zzz340, zzz341, Zero, zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, h) → new_mkVBalBranch0(zzz31, zzz514, Branch(zzz340, zzz341, Neg(Zero), zzz343, zzz344), h)
new_mkVBalBranch3MkVBalBranch216(zzz1105, zzz1106, zzz1107, zzz1108, zzz1109, zzz1110, zzz1111, zzz1112, zzz1113, zzz1114, zzz1115, Zero, Zero, ba) → new_mkVBalBranch3MkVBalBranch222(zzz1105, zzz1106, zzz1107, zzz1108, zzz1109, zzz1110, zzz1111, zzz1112, zzz1113, zzz1114, zzz1115, ba)
new_mkVBalBranch3MkVBalBranch233(zzz473, zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, zzz481, zzz482, bh) → new_mkVBalBranch3MkVBalBranch121(zzz473, zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, zzz481, zzz482, new_primMulNat1(zzz475), bh)
new_mkVBalBranch3MkVBalBranch215(zzz340, zzz341, Pos(Succ(Succ(zzz342000))), zzz343, zzz344, zzz510, zzz511, Zero, zzz513, zzz514, zzz31, Succ(Zero), h) → new_mkVBalBranch3MkVBalBranch217(zzz340, zzz341, Succ(zzz342000), zzz343, zzz344, zzz510, zzz511, zzz513, zzz514, zzz31, Zero, zzz342000, h)
new_mkVBalBranch0(zzz31, Branch(zzz510, zzz511, Pos(Zero), zzz513, zzz514), Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), h) → new_mkVBalBranch3MkVBalBranch116(zzz340, zzz341, zzz34200, zzz343, zzz344, zzz510, zzz511, zzz513, zzz514, zzz31, new_primMulNat1(zzz34200), h)
new_mkVBalBranch3MkVBalBranch18(zzz340, zzz341, zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, Zero, h) → new_mkVBalBranch3MkVBalBranch115(zzz340, zzz341, Zero, zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, Zero, Succ(zzz51200), h)
new_mkVBalBranch3MkVBalBranch119(zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, zzz1125, zzz1126, zzz1127, zzz1128, zzz1129, Succ(zzz12130), bd) → new_mkVBalBranch3MkVBalBranch120(zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, zzz1125, Succ(zzz1126), zzz1127, zzz1128, zzz1129, Succ(Succ(zzz1126)), Succ(zzz12130), bd)
new_mkVBalBranch3MkVBalBranch223(zzz340, zzz341, Neg(Succ(Zero)), zzz343, zzz344, zzz510, zzz511, Zero, zzz513, zzz514, zzz31, Zero, h) → new_mkVBalBranch3MkVBalBranch118(zzz340, zzz341, Zero, zzz343, zzz344, zzz510, zzz511, zzz513, zzz514, zzz31, new_primMulNat1(Zero), h)

The TRS R consists of the following rules:

new_primPlusNat1(Zero) → Zero
new_primMulNat0(zzz6200) → new_primPlusNat3(Succ(new_primPlusNat3(new_primPlusNat1(zzz6200), zzz6200)), Succ(zzz6200))
new_primPlusNat2(Succ(zzz900), Succ(zzz9100)) → Succ(Succ(new_primPlusNat2(zzz900, zzz9100)))
new_primPlusNat3(zzz90, Succ(zzz910)) → Succ(Succ(new_primPlusNat2(zzz90, zzz910)))
new_primPlusNat3(zzz90, Zero) → Succ(zzz90)
new_primMulNat1(zzz34200) → new_primPlusNat2(new_primMulNat0(zzz34200), Succ(zzz34200))
new_primPlusNat2(Zero, Zero) → Zero
new_primPlusNat1(Succ(zzz62000)) → Succ(Succ(new_primPlusNat1(zzz62000)))
new_primPlusNat2(Succ(zzz900), Zero) → Succ(zzz900)
new_primPlusNat2(Zero, Succ(zzz9100)) → Succ(zzz9100)

The set Q consists of the following terms:

new_primPlusNat2(Zero, Succ(x0))
new_primMulNat1(x0)
new_primMulNat0(x0)
new_primPlusNat3(x0, Succ(x1))
new_primPlusNat2(Succ(x0), Succ(x1))
new_primPlusNat3(x0, Zero)
new_primPlusNat1(Zero)
new_primPlusNat2(Zero, Zero)
new_primPlusNat1(Succ(x0))
new_primPlusNat2(Succ(x0), Zero)

We have to consider all minimal (P,Q,R)-chains.
By rewriting [15] the rule new_mkVBalBranch3MkVBalBranch223(zzz340, zzz341, Neg(Succ(Zero)), zzz343, zzz344, zzz510, zzz511, Zero, zzz513, zzz514, zzz31, Zero, h) → new_mkVBalBranch3MkVBalBranch118(zzz340, zzz341, Zero, zzz343, zzz344, zzz510, zzz511, zzz513, zzz514, zzz31, new_primMulNat1(Zero), h) at position [10] we obtained the following new rules:

new_mkVBalBranch3MkVBalBranch223(zzz340, zzz341, Neg(Succ(Zero)), zzz343, zzz344, zzz510, zzz511, Zero, zzz513, zzz514, zzz31, Zero, h) → new_mkVBalBranch3MkVBalBranch118(zzz340, zzz341, Zero, zzz343, zzz344, zzz510, zzz511, zzz513, zzz514, zzz31, new_primPlusNat2(new_primMulNat0(Zero), Succ(Zero)), 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
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                    ↳ DependencyGraphProof
                                      ↳ QDP
                                        ↳ Rewriting
                                          ↳ QDP
                                            ↳ Rewriting
                                              ↳ QDP
                                                ↳ Rewriting
                                                  ↳ QDP
                                                    ↳ Rewriting
                                                      ↳ QDP
                                                        ↳ Rewriting
                                                          ↳ QDP
                                                            ↳ Rewriting
                                                              ↳ QDP
                                                                ↳ Rewriting
                                                                  ↳ QDP
                                                                    ↳ Rewriting
                                                                      ↳ QDP
                                                                        ↳ Rewriting
                                                                          ↳ QDP
                                                                            ↳ Rewriting
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP

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

new_mkVBalBranch3MkVBalBranch225(zzz498, zzz499, zzz500, zzz501, zzz502, zzz503, zzz504, zzz505, zzz506, zzz507, Zero, Zero, bg) → new_mkVBalBranch3MkVBalBranch230(zzz498, zzz499, zzz500, zzz501, zzz502, zzz503, zzz504, zzz505, zzz506, zzz507, bg)
new_mkVBalBranch3MkVBalBranch215(zzz340, zzz341, Neg(zzz3420), zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, Zero, h) → new_mkVBalBranch3MkVBalBranch221(zzz340, zzz341, zzz3420, zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, h)
new_mkVBalBranch3MkVBalBranch18(zzz340, zzz341, zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, Succ(zzz1480), h) → new_mkVBalBranch3MkVBalBranch115(zzz340, zzz341, Zero, zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, Succ(zzz1480), Succ(zzz51200), h)
new_mkVBalBranch3MkVBalBranch215(zzz340, zzz341, Pos(Succ(Succ(zzz342000))), zzz343, zzz344, zzz510, zzz511, Succ(zzz512000), zzz513, zzz514, zzz31, Succ(Succ(zzz6600)), h) → new_mkVBalBranch3MkVBalBranch216(zzz340, zzz341, Succ(zzz342000), zzz343, zzz344, zzz510, zzz511, zzz512000, zzz513, zzz514, zzz31, Succ(Succ(new_primPlusNat2(zzz6600, zzz512000))), zzz342000, h)
new_mkVBalBranch0(zzz31, Branch(zzz510, zzz511, Neg(Zero), zzz513, zzz514), Branch(zzz340, zzz341, Pos(Succ(zzz34200)), zzz343, zzz344), h) → new_mkVBalBranch0(zzz31, Branch(zzz510, zzz511, Neg(Zero), zzz513, zzz514), zzz343, h)
new_mkVBalBranch3MkVBalBranch223(zzz340, zzz341, Neg(Succ(Succ(Succ(zzz3420000)))), zzz343, zzz344, zzz510, zzz511, Zero, zzz513, zzz514, zzz31, Succ(Succ(zzz6700)), h) → new_mkVBalBranch3MkVBalBranch225(zzz340, zzz341, Succ(Succ(zzz3420000)), zzz343, zzz344, zzz510, zzz511, zzz513, zzz514, zzz31, Succ(zzz3420000), Succ(zzz6700), h)
new_mkVBalBranch3MkVBalBranch120(zzz2050, zzz2051, zzz2052, zzz2053, zzz2054, zzz2055, zzz2056, zzz2057, zzz2058, zzz2059, zzz2060, Zero, Succ(zzz20620), be) → new_mkVBalBranch0(zzz2060, zzz2059, Branch(zzz2050, zzz2051, Neg(Succ(zzz2052)), zzz2053, zzz2054), be)
new_mkVBalBranch3MkVBalBranch220(zzz340, zzz341, zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, h) → new_mkVBalBranch0(zzz31, zzz514, Branch(zzz340, zzz341, Pos(Zero), zzz343, zzz344), h)
new_mkVBalBranch3MkVBalBranch228(zzz340, zzz341, zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, h) → new_mkVBalBranch0(zzz31, Branch(zzz510, zzz511, Neg(Succ(zzz51200)), zzz513, zzz514), zzz343, h)
new_mkVBalBranch0(zzz31, Branch(zzz510, zzz511, Pos(Zero), zzz513, zzz514), Branch(zzz340, zzz341, Pos(Succ(zzz34200)), zzz343, zzz344), h) → new_mkVBalBranch0(zzz31, Branch(zzz510, zzz511, Pos(Zero), zzz513, zzz514), zzz343, h)
new_mkVBalBranch3MkVBalBranch121(zzz473, zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, zzz481, zzz482, Succ(zzz7390), bh) → new_mkVBalBranch3MkVBalBranch115(zzz473, zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, Zero, zzz480, zzz481, zzz482, Succ(zzz7390), Succ(Zero), bh)
new_mkVBalBranch3MkVBalBranch223(zzz340, zzz341, Neg(Succ(Succ(Zero))), zzz343, zzz344, zzz510, zzz511, Succ(zzz512000), zzz513, zzz514, zzz31, Succ(Succ(zzz6700)), h) → new_mkVBalBranch3MkVBalBranch224(zzz340, zzz341, Succ(Zero), zzz343, zzz344, zzz510, zzz511, zzz512000, zzz513, zzz514, zzz31, Zero, Succ(Succ(new_primPlusNat2(zzz6700, zzz512000))), h)
new_mkVBalBranch3MkVBalBranch215(zzz340, zzz341, Pos(Succ(Zero)), zzz343, zzz344, zzz510, zzz511, Zero, zzz513, zzz514, zzz31, Zero, h) → new_mkVBalBranch3MkVBalBranch219(zzz340, zzz341, zzz343, zzz344, zzz510, zzz511, Zero, zzz513, zzz514, zzz31, h)
new_mkVBalBranch3MkVBalBranch223(zzz340, zzz341, Neg(Succ(Succ(Zero))), zzz343, zzz344, zzz510, zzz511, Zero, zzz513, zzz514, zzz31, Succ(Zero), h) → new_mkVBalBranch3MkVBalBranch225(zzz340, zzz341, Succ(Zero), zzz343, zzz344, zzz510, zzz511, zzz513, zzz514, zzz31, Zero, Zero, h)
new_mkVBalBranch3MkVBalBranch224(zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, zzz1125, zzz1126, zzz1127, zzz1128, zzz1129, Succ(zzz11300), Succ(zzz11310), bd) → new_mkVBalBranch3MkVBalBranch224(zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, zzz1125, zzz1126, zzz1127, zzz1128, zzz1129, zzz11300, zzz11310, bd)
new_mkVBalBranch3MkVBalBranch217(zzz473, zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, zzz481, zzz482, Zero, Succ(zzz4840), bh) → new_mkVBalBranch0(zzz482, Branch(zzz478, zzz479, Pos(Succ(Zero)), zzz480, zzz481), zzz476, bh)
new_mkVBalBranch0(zzz31, Branch(zzz510, zzz511, Pos(Succ(zzz51200)), zzz513, zzz514), Branch(zzz340, zzz341, zzz342, zzz343, zzz344), h) → new_mkVBalBranch3MkVBalBranch215(zzz340, zzz341, zzz342, zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, new_primPlusNat3(Succ(new_primPlusNat3(new_primPlusNat1(zzz51200), zzz51200)), Succ(zzz51200)), h)
new_mkVBalBranch3MkVBalBranch215(zzz340, zzz341, Pos(Succ(Succ(zzz342000))), zzz343, zzz344, zzz510, zzz511, Succ(zzz512000), zzz513, zzz514, zzz31, Zero, h) → new_mkVBalBranch3MkVBalBranch216(zzz340, zzz341, Succ(zzz342000), zzz343, zzz344, zzz510, zzz511, zzz512000, zzz513, zzz514, zzz31, zzz512000, zzz342000, h)
new_mkVBalBranch3MkVBalBranch110(zzz461, zzz462, zzz463, zzz464, zzz465, zzz466, zzz467, zzz468, zzz469, zzz470, zzz471, Succ(zzz5800), bb) → new_mkVBalBranch3MkVBalBranch115(zzz461, zzz462, zzz463, zzz464, zzz465, zzz466, zzz467, Succ(zzz468), zzz469, zzz470, zzz471, Succ(zzz5800), Succ(Succ(zzz468)), bb)
new_mkVBalBranch3MkVBalBranch223(zzz340, zzz341, Neg(Succ(Zero)), zzz343, zzz344, zzz510, zzz511, Zero, zzz513, zzz514, zzz31, Zero, h) → new_mkVBalBranch3MkVBalBranch118(zzz340, zzz341, Zero, zzz343, zzz344, zzz510, zzz511, zzz513, zzz514, zzz31, new_primPlusNat2(new_primMulNat0(Zero), Succ(Zero)), h)
new_mkVBalBranch3MkVBalBranch227(zzz486, zzz487, zzz488, zzz489, zzz490, zzz491, zzz492, zzz493, zzz494, zzz495, zzz496, bf) → new_mkVBalBranch0(zzz496, Branch(zzz491, zzz492, Neg(Succ(Succ(zzz493))), zzz494, zzz495), zzz489, bf)
new_mkVBalBranch3MkVBalBranch215(zzz340, zzz341, Pos(Zero), zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, Succ(zzz660), h) → new_mkVBalBranch0(zzz31, zzz514, Branch(zzz340, zzz341, Pos(Zero), zzz343, zzz344), h)
new_mkVBalBranch3MkVBalBranch223(zzz340, zzz341, Neg(Zero), zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, Succ(zzz670), h) → new_mkVBalBranch0(zzz31, Branch(zzz510, zzz511, Neg(Succ(zzz51200)), zzz513, zzz514), zzz343, h)
new_mkVBalBranch3MkVBalBranch216(zzz1105, zzz1106, zzz1107, zzz1108, zzz1109, zzz1110, zzz1111, zzz1112, zzz1113, zzz1114, zzz1115, Zero, Succ(zzz11170), ba) → new_mkVBalBranch0(zzz1115, Branch(zzz1110, zzz1111, Pos(Succ(Succ(zzz1112))), zzz1113, zzz1114), zzz1108, ba)
new_mkVBalBranch3MkVBalBranch222(zzz461, zzz462, zzz463, zzz464, zzz465, zzz466, zzz467, zzz468, zzz469, zzz470, zzz471, bb) → new_mkVBalBranch3MkVBalBranch110(zzz461, zzz462, zzz463, zzz464, zzz465, zzz466, zzz467, zzz468, zzz469, zzz470, zzz471, new_primMulNat1(zzz463), bb)
new_mkVBalBranch3MkVBalBranch217(zzz473, zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, zzz481, zzz482, Succ(zzz4830), Zero, bh) → new_mkVBalBranch3MkVBalBranch121(zzz473, zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, zzz481, zzz482, new_primMulNat1(zzz475), bh)
new_mkVBalBranch3MkVBalBranch115(zzz1986, zzz1987, zzz1988, zzz1989, zzz1990, zzz1991, zzz1992, zzz1993, zzz1994, zzz1995, zzz1996, Zero, Succ(zzz19980), bc) → new_mkVBalBranch0(zzz1996, zzz1995, Branch(zzz1986, zzz1987, Pos(Succ(zzz1988)), zzz1989, zzz1990), bc)
new_mkVBalBranch3MkVBalBranch223(zzz340, zzz341, Neg(Zero), zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, Zero, h) → new_mkVBalBranch3MkVBalBranch228(zzz340, zzz341, zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, h)
new_mkVBalBranch3MkVBalBranch122(zzz340, zzz341, zzz34200, zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, h) → new_mkVBalBranch0(zzz31, zzz514, Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), h)
new_mkVBalBranch3MkVBalBranch217(zzz473, zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, zzz481, zzz482, Succ(zzz4830), Succ(zzz4840), bh) → new_mkVBalBranch3MkVBalBranch217(zzz473, zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, zzz481, zzz482, zzz4830, zzz4840, bh)
new_mkVBalBranch3MkVBalBranch116(zzz340, zzz341, zzz34200, zzz343, zzz344, zzz510, zzz511, zzz513, zzz514, zzz31, Succ(zzz1200), h) → new_mkVBalBranch0(zzz31, zzz514, Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), h)
new_mkVBalBranch3MkVBalBranch110(zzz461, zzz462, zzz463, zzz464, zzz465, zzz466, zzz467, zzz468, zzz469, zzz470, zzz471, Zero, bb) → new_mkVBalBranch3MkVBalBranch115(zzz461, zzz462, zzz463, zzz464, zzz465, zzz466, zzz467, Succ(zzz468), zzz469, zzz470, zzz471, Zero, Succ(Succ(zzz468)), bb)
new_mkVBalBranch3MkVBalBranch225(zzz498, zzz499, zzz500, zzz501, zzz502, zzz503, zzz504, zzz505, zzz506, zzz507, Zero, Succ(zzz5090), bg) → new_mkVBalBranch0(zzz507, Branch(zzz503, zzz504, Neg(Succ(Zero)), zzz505, zzz506), zzz501, bg)
new_mkVBalBranch3MkVBalBranch223(zzz340, zzz341, Neg(Succ(Succ(Succ(zzz3420000)))), zzz343, zzz344, zzz510, zzz511, Zero, zzz513, zzz514, zzz31, Succ(Zero), h) → new_mkVBalBranch3MkVBalBranch225(zzz340, zzz341, Succ(Succ(zzz3420000)), zzz343, zzz344, zzz510, zzz511, zzz513, zzz514, zzz31, Succ(zzz3420000), Zero, h)
new_mkVBalBranch3MkVBalBranch121(zzz473, zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, zzz481, zzz482, Zero, bh) → new_mkVBalBranch3MkVBalBranch115(zzz473, zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, Zero, zzz480, zzz481, zzz482, Zero, Succ(Zero), bh)
new_mkVBalBranch3MkVBalBranch215(zzz340, zzz341, Pos(Succ(Zero)), zzz343, zzz344, zzz510, zzz511, Succ(zzz512000), zzz513, zzz514, zzz31, Zero, h) → new_mkVBalBranch3MkVBalBranch218(zzz340, zzz341, Zero, zzz343, zzz344, zzz510, zzz511, zzz512000, zzz513, zzz514, zzz31, h)
new_mkVBalBranch3MkVBalBranch225(zzz498, zzz499, zzz500, zzz501, zzz502, zzz503, zzz504, zzz505, zzz506, zzz507, Succ(zzz5080), Zero, bg) → new_mkVBalBranch3MkVBalBranch118(zzz498, zzz499, zzz500, zzz501, zzz502, zzz503, zzz504, zzz505, zzz506, zzz507, new_primPlusNat2(new_primMulNat0(zzz500), Succ(zzz500)), bg)
new_mkVBalBranch3MkVBalBranch223(zzz340, zzz341, Neg(Succ(Zero)), zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, Succ(zzz670), h) → new_mkVBalBranch0(zzz31, Branch(zzz510, zzz511, Neg(Succ(zzz51200)), zzz513, zzz514), zzz343, h)
new_mkVBalBranch3MkVBalBranch229(zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, zzz1125, zzz1126, zzz1127, zzz1128, zzz1129, bd) → new_mkVBalBranch3MkVBalBranch119(zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, zzz1125, zzz1126, zzz1127, zzz1128, zzz1129, new_primPlusNat2(new_primMulNat0(zzz1121), Succ(zzz1121)), bd)
new_mkVBalBranch3MkVBalBranch218(zzz461, zzz462, zzz463, zzz464, zzz465, zzz466, zzz467, zzz468, zzz469, zzz470, zzz471, bb) → new_mkVBalBranch3MkVBalBranch110(zzz461, zzz462, zzz463, zzz464, zzz465, zzz466, zzz467, zzz468, zzz469, zzz470, zzz471, new_primMulNat1(zzz463), bb)
new_mkVBalBranch3MkVBalBranch223(zzz340, zzz341, Neg(Succ(Zero)), zzz343, zzz344, zzz510, zzz511, Succ(zzz512000), zzz513, zzz514, zzz31, Zero, h) → new_mkVBalBranch3MkVBalBranch227(zzz340, zzz341, Zero, zzz343, zzz344, zzz510, zzz511, zzz512000, zzz513, zzz514, zzz31, h)
new_mkVBalBranch3MkVBalBranch215(zzz340, zzz341, Pos(Succ(Zero)), zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, Succ(zzz660), h) → new_mkVBalBranch3MkVBalBranch18(zzz340, zzz341, zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, new_primMulNat1(Zero), h)
new_mkVBalBranch3MkVBalBranch226(zzz340, zzz341, zzz3420, zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, h) → new_mkVBalBranch0(zzz31, Branch(zzz510, zzz511, Neg(Succ(zzz51200)), zzz513, zzz514), zzz343, h)
new_mkVBalBranch3MkVBalBranch223(zzz340, zzz341, Neg(Succ(Succ(zzz342000))), zzz343, zzz344, zzz510, zzz511, Succ(zzz512000), zzz513, zzz514, zzz31, Zero, h) → new_mkVBalBranch3MkVBalBranch224(zzz340, zzz341, Succ(zzz342000), zzz343, zzz344, zzz510, zzz511, zzz512000, zzz513, zzz514, zzz31, zzz342000, zzz512000, h)
new_mkVBalBranch3MkVBalBranch215(zzz340, zzz341, Pos(Succ(Succ(zzz342000))), zzz343, zzz344, zzz510, zzz511, Zero, zzz513, zzz514, zzz31, Succ(Succ(zzz6600)), h) → new_mkVBalBranch3MkVBalBranch217(zzz340, zzz341, Succ(zzz342000), zzz343, zzz344, zzz510, zzz511, zzz513, zzz514, zzz31, Succ(zzz6600), zzz342000, h)
new_mkVBalBranch3MkVBalBranch117(zzz340, zzz341, zzz34200, zzz343, zzz344, zzz510, zzz511, zzz513, zzz514, zzz31, Succ(zzz1240), h) → new_mkVBalBranch0(zzz31, zzz514, Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), h)
new_mkVBalBranch3MkVBalBranch221(zzz340, zzz341, Succ(zzz34200), zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, h) → new_mkVBalBranch3MkVBalBranch19(zzz340, zzz341, zzz34200, zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, new_primPlusNat2(new_primPlusNat3(Succ(new_primPlusNat3(new_primPlusNat1(zzz34200), zzz34200)), Succ(zzz34200)), Succ(zzz34200)), h)
new_mkVBalBranch3MkVBalBranch120(zzz2050, zzz2051, zzz2052, zzz2053, zzz2054, zzz2055, zzz2056, zzz2057, zzz2058, zzz2059, zzz2060, Succ(zzz20610), Succ(zzz20620), be) → new_mkVBalBranch3MkVBalBranch120(zzz2050, zzz2051, zzz2052, zzz2053, zzz2054, zzz2055, zzz2056, zzz2057, zzz2058, zzz2059, zzz2060, zzz20610, zzz20620, be)
new_mkVBalBranch3MkVBalBranch217(zzz473, zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, zzz481, zzz482, Zero, Zero, bh) → new_mkVBalBranch3MkVBalBranch233(zzz473, zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, zzz481, zzz482, bh)
new_mkVBalBranch0(zzz31, Branch(zzz510, zzz511, Neg(Succ(zzz51200)), zzz513, zzz514), Branch(zzz340, zzz341, zzz342, zzz343, zzz344), h) → new_mkVBalBranch3MkVBalBranch223(zzz340, zzz341, zzz342, zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, new_primPlusNat3(Succ(new_primPlusNat3(new_primPlusNat1(zzz51200), zzz51200)), Succ(zzz51200)), h)
new_mkVBalBranch3MkVBalBranch216(zzz1105, zzz1106, zzz1107, zzz1108, zzz1109, zzz1110, zzz1111, zzz1112, zzz1113, zzz1114, zzz1115, Succ(zzz11160), Succ(zzz11170), ba) → new_mkVBalBranch3MkVBalBranch216(zzz1105, zzz1106, zzz1107, zzz1108, zzz1109, zzz1110, zzz1111, zzz1112, zzz1113, zzz1114, zzz1115, zzz11160, zzz11170, ba)
new_mkVBalBranch3MkVBalBranch223(zzz340, zzz341, Pos(zzz3420), zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, Succ(zzz670), h) → new_mkVBalBranch0(zzz31, Branch(zzz510, zzz511, Neg(Succ(zzz51200)), zzz513, zzz514), zzz343, h)
new_mkVBalBranch3MkVBalBranch223(zzz340, zzz341, Neg(Succ(Succ(Succ(zzz3420000)))), zzz343, zzz344, zzz510, zzz511, Succ(zzz512000), zzz513, zzz514, zzz31, Succ(Zero), h) → new_mkVBalBranch3MkVBalBranch224(zzz340, zzz341, Succ(Succ(zzz3420000)), zzz343, zzz344, zzz510, zzz511, zzz512000, zzz513, zzz514, zzz31, Succ(zzz3420000), Succ(zzz512000), h)
new_mkVBalBranch3MkVBalBranch19(zzz340, zzz341, zzz34200, zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, Zero, h) → new_mkVBalBranch3MkVBalBranch122(zzz340, zzz341, zzz34200, zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, h)
new_mkVBalBranch0(zzz31, Branch(zzz510, zzz511, Neg(Zero), zzz513, zzz514), Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), h) → new_mkVBalBranch3MkVBalBranch117(zzz340, zzz341, zzz34200, zzz343, zzz344, zzz510, zzz511, zzz513, zzz514, zzz31, new_primMulNat1(zzz34200), h)
new_mkVBalBranch3MkVBalBranch215(zzz340, zzz341, Pos(Succ(Succ(zzz342000))), zzz343, zzz344, zzz510, zzz511, Zero, zzz513, zzz514, zzz31, Zero, h) → new_mkVBalBranch0(zzz31, Branch(zzz510, zzz511, Pos(Succ(Zero)), zzz513, zzz514), zzz343, h)
new_mkVBalBranch3MkVBalBranch225(zzz498, zzz499, zzz500, zzz501, zzz502, zzz503, zzz504, zzz505, zzz506, zzz507, Succ(zzz5080), Succ(zzz5090), bg) → new_mkVBalBranch3MkVBalBranch225(zzz498, zzz499, zzz500, zzz501, zzz502, zzz503, zzz504, zzz505, zzz506, zzz507, zzz5080, zzz5090, bg)
new_mkVBalBranch3MkVBalBranch19(zzz340, zzz341, zzz34200, zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, Succ(zzz1410), h) → new_mkVBalBranch0(zzz31, zzz514, Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), h)
new_mkVBalBranch3MkVBalBranch224(zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, zzz1125, zzz1126, zzz1127, zzz1128, zzz1129, Succ(zzz11300), Zero, bd) → new_mkVBalBranch3MkVBalBranch119(zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, zzz1125, zzz1126, zzz1127, zzz1128, zzz1129, new_primPlusNat2(new_primMulNat0(zzz1121), Succ(zzz1121)), bd)
new_mkVBalBranch3MkVBalBranch223(zzz340, zzz341, Pos(zzz3420), zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, Zero, h) → new_mkVBalBranch3MkVBalBranch226(zzz340, zzz341, zzz3420, zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, h)
new_mkVBalBranch3MkVBalBranch223(zzz340, zzz341, Neg(Succ(Succ(Zero))), zzz343, zzz344, zzz510, zzz511, Succ(zzz512000), zzz513, zzz514, zzz31, Succ(Zero), h) → new_mkVBalBranch3MkVBalBranch224(zzz340, zzz341, Succ(Zero), zzz343, zzz344, zzz510, zzz511, zzz512000, zzz513, zzz514, zzz31, Zero, Succ(zzz512000), h)
new_mkVBalBranch3MkVBalBranch224(zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, zzz1125, zzz1126, zzz1127, zzz1128, zzz1129, Zero, Zero, bd) → new_mkVBalBranch3MkVBalBranch229(zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, zzz1125, zzz1126, zzz1127, zzz1128, zzz1129, bd)
new_mkVBalBranch3MkVBalBranch224(zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, zzz1125, zzz1126, zzz1127, zzz1128, zzz1129, Zero, Succ(zzz11310), bd) → new_mkVBalBranch3MkVBalBranch227(zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, zzz1125, zzz1126, zzz1127, zzz1128, zzz1129, bd)
new_mkVBalBranch3MkVBalBranch223(zzz340, zzz341, Neg(Succ(Succ(zzz342000))), zzz343, zzz344, zzz510, zzz511, Zero, zzz513, zzz514, zzz31, Zero, h) → new_mkVBalBranch3MkVBalBranch118(zzz340, zzz341, Succ(zzz342000), zzz343, zzz344, zzz510, zzz511, zzz513, zzz514, zzz31, new_primPlusNat2(new_primMulNat0(Succ(zzz342000)), Succ(Succ(zzz342000))), h)
new_mkVBalBranch3MkVBalBranch230(zzz498, zzz499, zzz500, zzz501, zzz502, zzz503, zzz504, zzz505, zzz506, zzz507, bg) → new_mkVBalBranch3MkVBalBranch118(zzz498, zzz499, zzz500, zzz501, zzz502, zzz503, zzz504, zzz505, zzz506, zzz507, new_primPlusNat2(new_primMulNat0(zzz500), Succ(zzz500)), bg)
new_mkVBalBranch3MkVBalBranch223(zzz340, zzz341, Neg(Succ(Succ(Zero))), zzz343, zzz344, zzz510, zzz511, Zero, zzz513, zzz514, zzz31, Succ(Succ(zzz6700)), h) → new_mkVBalBranch3MkVBalBranch225(zzz340, zzz341, Succ(Zero), zzz343, zzz344, zzz510, zzz511, zzz513, zzz514, zzz31, Zero, Succ(zzz6700), h)
new_mkVBalBranch3MkVBalBranch223(zzz340, zzz341, Neg(Succ(Succ(Succ(zzz3420000)))), zzz343, zzz344, zzz510, zzz511, Succ(zzz512000), zzz513, zzz514, zzz31, Succ(Succ(zzz6700)), h) → new_mkVBalBranch3MkVBalBranch224(zzz340, zzz341, Succ(Succ(zzz3420000)), zzz343, zzz344, zzz510, zzz511, zzz512000, zzz513, zzz514, zzz31, Succ(zzz3420000), Succ(Succ(new_primPlusNat2(zzz6700, zzz512000))), h)
new_mkVBalBranch3MkVBalBranch115(zzz1986, zzz1987, zzz1988, zzz1989, zzz1990, zzz1991, zzz1992, zzz1993, zzz1994, zzz1995, zzz1996, Succ(zzz19970), Succ(zzz19980), bc) → new_mkVBalBranch3MkVBalBranch115(zzz1986, zzz1987, zzz1988, zzz1989, zzz1990, zzz1991, zzz1992, zzz1993, zzz1994, zzz1995, zzz1996, zzz19970, zzz19980, bc)
new_mkVBalBranch3MkVBalBranch215(zzz340, zzz341, Pos(Zero), zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, Zero, h) → new_mkVBalBranch3MkVBalBranch220(zzz340, zzz341, zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, h)
new_mkVBalBranch3MkVBalBranch215(zzz340, zzz341, Neg(Zero), zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, Succ(zzz660), h) → new_mkVBalBranch0(zzz31, zzz514, Branch(zzz340, zzz341, Neg(Zero), zzz343, zzz344), h)
new_mkVBalBranch3MkVBalBranch118(zzz498, zzz499, zzz500, zzz501, zzz502, zzz503, zzz504, zzz505, zzz506, zzz507, Succ(zzz8040), bg) → new_mkVBalBranch3MkVBalBranch120(zzz498, zzz499, zzz500, zzz501, zzz502, zzz503, zzz504, Zero, zzz505, zzz506, zzz507, Succ(Zero), Succ(zzz8040), bg)
new_mkVBalBranch3MkVBalBranch216(zzz1105, zzz1106, zzz1107, zzz1108, zzz1109, zzz1110, zzz1111, zzz1112, zzz1113, zzz1114, zzz1115, Succ(zzz11160), Zero, ba) → new_mkVBalBranch3MkVBalBranch218(zzz1105, zzz1106, zzz1107, zzz1108, zzz1109, zzz1110, zzz1111, zzz1112, zzz1113, zzz1114, zzz1115, ba)
new_mkVBalBranch3MkVBalBranch221(zzz340, zzz341, Zero, zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, h) → new_mkVBalBranch0(zzz31, zzz514, Branch(zzz340, zzz341, Neg(Zero), zzz343, zzz344), h)
new_mkVBalBranch3MkVBalBranch219(zzz340, zzz341, zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, h) → new_mkVBalBranch3MkVBalBranch18(zzz340, zzz341, zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, new_primMulNat1(Zero), h)
new_mkVBalBranch3MkVBalBranch215(zzz340, zzz341, Pos(Succ(Succ(zzz342000))), zzz343, zzz344, zzz510, zzz511, Succ(zzz512000), zzz513, zzz514, zzz31, Succ(Zero), h) → new_mkVBalBranch3MkVBalBranch216(zzz340, zzz341, Succ(zzz342000), zzz343, zzz344, zzz510, zzz511, zzz512000, zzz513, zzz514, zzz31, Succ(zzz512000), zzz342000, h)
new_mkVBalBranch3MkVBalBranch215(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, Succ(zzz660), h) → new_mkVBalBranch3MkVBalBranch19(zzz340, zzz341, zzz34200, zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, new_primPlusNat2(new_primMulNat0(zzz34200), Succ(zzz34200)), h)
new_mkVBalBranch3MkVBalBranch216(zzz1105, zzz1106, zzz1107, zzz1108, zzz1109, zzz1110, zzz1111, zzz1112, zzz1113, zzz1114, zzz1115, Zero, Zero, ba) → new_mkVBalBranch3MkVBalBranch222(zzz1105, zzz1106, zzz1107, zzz1108, zzz1109, zzz1110, zzz1111, zzz1112, zzz1113, zzz1114, zzz1115, ba)
new_mkVBalBranch3MkVBalBranch233(zzz473, zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, zzz481, zzz482, bh) → new_mkVBalBranch3MkVBalBranch121(zzz473, zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, zzz481, zzz482, new_primMulNat1(zzz475), bh)
new_mkVBalBranch3MkVBalBranch215(zzz340, zzz341, Pos(Succ(Succ(zzz342000))), zzz343, zzz344, zzz510, zzz511, Zero, zzz513, zzz514, zzz31, Succ(Zero), h) → new_mkVBalBranch3MkVBalBranch217(zzz340, zzz341, Succ(zzz342000), zzz343, zzz344, zzz510, zzz511, zzz513, zzz514, zzz31, Zero, zzz342000, h)
new_mkVBalBranch0(zzz31, Branch(zzz510, zzz511, Pos(Zero), zzz513, zzz514), Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), h) → new_mkVBalBranch3MkVBalBranch116(zzz340, zzz341, zzz34200, zzz343, zzz344, zzz510, zzz511, zzz513, zzz514, zzz31, new_primMulNat1(zzz34200), h)
new_mkVBalBranch3MkVBalBranch119(zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, zzz1125, zzz1126, zzz1127, zzz1128, zzz1129, Succ(zzz12130), bd) → new_mkVBalBranch3MkVBalBranch120(zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, zzz1125, Succ(zzz1126), zzz1127, zzz1128, zzz1129, Succ(Succ(zzz1126)), Succ(zzz12130), bd)
new_mkVBalBranch3MkVBalBranch18(zzz340, zzz341, zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, Zero, h) → new_mkVBalBranch3MkVBalBranch115(zzz340, zzz341, Zero, zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, Zero, Succ(zzz51200), h)

The TRS R consists of the following rules:

new_primPlusNat1(Zero) → Zero
new_primMulNat0(zzz6200) → new_primPlusNat3(Succ(new_primPlusNat3(new_primPlusNat1(zzz6200), zzz6200)), Succ(zzz6200))
new_primPlusNat2(Succ(zzz900), Succ(zzz9100)) → Succ(Succ(new_primPlusNat2(zzz900, zzz9100)))
new_primPlusNat3(zzz90, Succ(zzz910)) → Succ(Succ(new_primPlusNat2(zzz90, zzz910)))
new_primPlusNat3(zzz90, Zero) → Succ(zzz90)
new_primMulNat1(zzz34200) → new_primPlusNat2(new_primMulNat0(zzz34200), Succ(zzz34200))
new_primPlusNat2(Zero, Zero) → Zero
new_primPlusNat1(Succ(zzz62000)) → Succ(Succ(new_primPlusNat1(zzz62000)))
new_primPlusNat2(Succ(zzz900), Zero) → Succ(zzz900)
new_primPlusNat2(Zero, Succ(zzz9100)) → Succ(zzz9100)

The set Q consists of the following terms:

new_primPlusNat2(Zero, Succ(x0))
new_primMulNat1(x0)
new_primMulNat0(x0)
new_primPlusNat3(x0, Succ(x1))
new_primPlusNat2(Succ(x0), Succ(x1))
new_primPlusNat3(x0, Zero)
new_primPlusNat1(Zero)
new_primPlusNat2(Zero, Zero)
new_primPlusNat1(Succ(x0))
new_primPlusNat2(Succ(x0), Zero)

We have to consider all minimal (P,Q,R)-chains.
By rewriting [15] the rule new_mkVBalBranch0(zzz31, Branch(zzz510, zzz511, Neg(Zero), zzz513, zzz514), Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), h) → new_mkVBalBranch3MkVBalBranch117(zzz340, zzz341, zzz34200, zzz343, zzz344, zzz510, zzz511, zzz513, zzz514, zzz31, new_primMulNat1(zzz34200), h) at position [10] we obtained the following new rules:

new_mkVBalBranch0(zzz31, Branch(zzz510, zzz511, Neg(Zero), zzz513, zzz514), Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), h) → new_mkVBalBranch3MkVBalBranch117(zzz340, zzz341, zzz34200, zzz343, zzz344, zzz510, zzz511, zzz513, zzz514, zzz31, new_primPlusNat2(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
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                    ↳ DependencyGraphProof
                                      ↳ QDP
                                        ↳ Rewriting
                                          ↳ QDP
                                            ↳ Rewriting
                                              ↳ QDP
                                                ↳ Rewriting
                                                  ↳ QDP
                                                    ↳ Rewriting
                                                      ↳ QDP
                                                        ↳ Rewriting
                                                          ↳ QDP
                                                            ↳ Rewriting
                                                              ↳ QDP
                                                                ↳ Rewriting
                                                                  ↳ QDP
                                                                    ↳ Rewriting
                                                                      ↳ QDP
                                                                        ↳ Rewriting
                                                                          ↳ QDP
                                                                            ↳ Rewriting
                                                                              ↳ QDP
                                                                                ↳ Rewriting
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP

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

new_mkVBalBranch3MkVBalBranch215(zzz340, zzz341, Neg(zzz3420), zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, Zero, h) → new_mkVBalBranch3MkVBalBranch221(zzz340, zzz341, zzz3420, zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, h)
new_mkVBalBranch3MkVBalBranch225(zzz498, zzz499, zzz500, zzz501, zzz502, zzz503, zzz504, zzz505, zzz506, zzz507, Zero, Zero, bg) → new_mkVBalBranch3MkVBalBranch230(zzz498, zzz499, zzz500, zzz501, zzz502, zzz503, zzz504, zzz505, zzz506, zzz507, bg)
new_mkVBalBranch3MkVBalBranch18(zzz340, zzz341, zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, Succ(zzz1480), h) → new_mkVBalBranch3MkVBalBranch115(zzz340, zzz341, Zero, zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, Succ(zzz1480), Succ(zzz51200), h)
new_mkVBalBranch0(zzz31, Branch(zzz510, zzz511, Neg(Zero), zzz513, zzz514), Branch(zzz340, zzz341, Pos(Succ(zzz34200)), zzz343, zzz344), h) → new_mkVBalBranch0(zzz31, Branch(zzz510, zzz511, Neg(Zero), zzz513, zzz514), zzz343, h)
new_mkVBalBranch3MkVBalBranch215(zzz340, zzz341, Pos(Succ(Succ(zzz342000))), zzz343, zzz344, zzz510, zzz511, Succ(zzz512000), zzz513, zzz514, zzz31, Succ(Succ(zzz6600)), h) → new_mkVBalBranch3MkVBalBranch216(zzz340, zzz341, Succ(zzz342000), zzz343, zzz344, zzz510, zzz511, zzz512000, zzz513, zzz514, zzz31, Succ(Succ(new_primPlusNat2(zzz6600, zzz512000))), zzz342000, h)
new_mkVBalBranch3MkVBalBranch223(zzz340, zzz341, Neg(Succ(Succ(Succ(zzz3420000)))), zzz343, zzz344, zzz510, zzz511, Zero, zzz513, zzz514, zzz31, Succ(Succ(zzz6700)), h) → new_mkVBalBranch3MkVBalBranch225(zzz340, zzz341, Succ(Succ(zzz3420000)), zzz343, zzz344, zzz510, zzz511, zzz513, zzz514, zzz31, Succ(zzz3420000), Succ(zzz6700), h)
new_mkVBalBranch3MkVBalBranch220(zzz340, zzz341, zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, h) → new_mkVBalBranch0(zzz31, zzz514, Branch(zzz340, zzz341, Pos(Zero), zzz343, zzz344), h)
new_mkVBalBranch3MkVBalBranch120(zzz2050, zzz2051, zzz2052, zzz2053, zzz2054, zzz2055, zzz2056, zzz2057, zzz2058, zzz2059, zzz2060, Zero, Succ(zzz20620), be) → new_mkVBalBranch0(zzz2060, zzz2059, Branch(zzz2050, zzz2051, Neg(Succ(zzz2052)), zzz2053, zzz2054), be)
new_mkVBalBranch3MkVBalBranch121(zzz473, zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, zzz481, zzz482, Succ(zzz7390), bh) → new_mkVBalBranch3MkVBalBranch115(zzz473, zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, Zero, zzz480, zzz481, zzz482, Succ(zzz7390), Succ(Zero), bh)
new_mkVBalBranch0(zzz31, Branch(zzz510, zzz511, Pos(Zero), zzz513, zzz514), Branch(zzz340, zzz341, Pos(Succ(zzz34200)), zzz343, zzz344), h) → new_mkVBalBranch0(zzz31, Branch(zzz510, zzz511, Pos(Zero), zzz513, zzz514), zzz343, h)
new_mkVBalBranch3MkVBalBranch228(zzz340, zzz341, zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, h) → new_mkVBalBranch0(zzz31, Branch(zzz510, zzz511, Neg(Succ(zzz51200)), zzz513, zzz514), zzz343, h)
new_mkVBalBranch3MkVBalBranch215(zzz340, zzz341, Pos(Succ(Zero)), zzz343, zzz344, zzz510, zzz511, Zero, zzz513, zzz514, zzz31, Zero, h) → new_mkVBalBranch3MkVBalBranch219(zzz340, zzz341, zzz343, zzz344, zzz510, zzz511, Zero, zzz513, zzz514, zzz31, h)
new_mkVBalBranch3MkVBalBranch223(zzz340, zzz341, Neg(Succ(Succ(Zero))), zzz343, zzz344, zzz510, zzz511, Succ(zzz512000), zzz513, zzz514, zzz31, Succ(Succ(zzz6700)), h) → new_mkVBalBranch3MkVBalBranch224(zzz340, zzz341, Succ(Zero), zzz343, zzz344, zzz510, zzz511, zzz512000, zzz513, zzz514, zzz31, Zero, Succ(Succ(new_primPlusNat2(zzz6700, zzz512000))), h)
new_mkVBalBranch3MkVBalBranch223(zzz340, zzz341, Neg(Succ(Succ(Zero))), zzz343, zzz344, zzz510, zzz511, Zero, zzz513, zzz514, zzz31, Succ(Zero), h) → new_mkVBalBranch3MkVBalBranch225(zzz340, zzz341, Succ(Zero), zzz343, zzz344, zzz510, zzz511, zzz513, zzz514, zzz31, Zero, Zero, h)
new_mkVBalBranch3MkVBalBranch224(zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, zzz1125, zzz1126, zzz1127, zzz1128, zzz1129, Succ(zzz11300), Succ(zzz11310), bd) → new_mkVBalBranch3MkVBalBranch224(zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, zzz1125, zzz1126, zzz1127, zzz1128, zzz1129, zzz11300, zzz11310, bd)
new_mkVBalBranch0(zzz31, Branch(zzz510, zzz511, Pos(Succ(zzz51200)), zzz513, zzz514), Branch(zzz340, zzz341, zzz342, zzz343, zzz344), h) → new_mkVBalBranch3MkVBalBranch215(zzz340, zzz341, zzz342, zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, new_primPlusNat3(Succ(new_primPlusNat3(new_primPlusNat1(zzz51200), zzz51200)), Succ(zzz51200)), h)
new_mkVBalBranch3MkVBalBranch217(zzz473, zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, zzz481, zzz482, Zero, Succ(zzz4840), bh) → new_mkVBalBranch0(zzz482, Branch(zzz478, zzz479, Pos(Succ(Zero)), zzz480, zzz481), zzz476, bh)
new_mkVBalBranch3MkVBalBranch215(zzz340, zzz341, Pos(Succ(Succ(zzz342000))), zzz343, zzz344, zzz510, zzz511, Succ(zzz512000), zzz513, zzz514, zzz31, Zero, h) → new_mkVBalBranch3MkVBalBranch216(zzz340, zzz341, Succ(zzz342000), zzz343, zzz344, zzz510, zzz511, zzz512000, zzz513, zzz514, zzz31, zzz512000, zzz342000, h)
new_mkVBalBranch3MkVBalBranch110(zzz461, zzz462, zzz463, zzz464, zzz465, zzz466, zzz467, zzz468, zzz469, zzz470, zzz471, Succ(zzz5800), bb) → new_mkVBalBranch3MkVBalBranch115(zzz461, zzz462, zzz463, zzz464, zzz465, zzz466, zzz467, Succ(zzz468), zzz469, zzz470, zzz471, Succ(zzz5800), Succ(Succ(zzz468)), bb)
new_mkVBalBranch3MkVBalBranch223(zzz340, zzz341, Neg(Succ(Zero)), zzz343, zzz344, zzz510, zzz511, Zero, zzz513, zzz514, zzz31, Zero, h) → new_mkVBalBranch3MkVBalBranch118(zzz340, zzz341, Zero, zzz343, zzz344, zzz510, zzz511, zzz513, zzz514, zzz31, new_primPlusNat2(new_primMulNat0(Zero), Succ(Zero)), h)
new_mkVBalBranch3MkVBalBranch227(zzz486, zzz487, zzz488, zzz489, zzz490, zzz491, zzz492, zzz493, zzz494, zzz495, zzz496, bf) → new_mkVBalBranch0(zzz496, Branch(zzz491, zzz492, Neg(Succ(Succ(zzz493))), zzz494, zzz495), zzz489, bf)
new_mkVBalBranch3MkVBalBranch215(zzz340, zzz341, Pos(Zero), zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, Succ(zzz660), h) → new_mkVBalBranch0(zzz31, zzz514, Branch(zzz340, zzz341, Pos(Zero), zzz343, zzz344), h)
new_mkVBalBranch3MkVBalBranch223(zzz340, zzz341, Neg(Zero), zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, Succ(zzz670), h) → new_mkVBalBranch0(zzz31, Branch(zzz510, zzz511, Neg(Succ(zzz51200)), zzz513, zzz514), zzz343, h)
new_mkVBalBranch3MkVBalBranch216(zzz1105, zzz1106, zzz1107, zzz1108, zzz1109, zzz1110, zzz1111, zzz1112, zzz1113, zzz1114, zzz1115, Zero, Succ(zzz11170), ba) → new_mkVBalBranch0(zzz1115, Branch(zzz1110, zzz1111, Pos(Succ(Succ(zzz1112))), zzz1113, zzz1114), zzz1108, ba)
new_mkVBalBranch3MkVBalBranch217(zzz473, zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, zzz481, zzz482, Succ(zzz4830), Zero, bh) → new_mkVBalBranch3MkVBalBranch121(zzz473, zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, zzz481, zzz482, new_primMulNat1(zzz475), bh)
new_mkVBalBranch3MkVBalBranch222(zzz461, zzz462, zzz463, zzz464, zzz465, zzz466, zzz467, zzz468, zzz469, zzz470, zzz471, bb) → new_mkVBalBranch3MkVBalBranch110(zzz461, zzz462, zzz463, zzz464, zzz465, zzz466, zzz467, zzz468, zzz469, zzz470, zzz471, new_primMulNat1(zzz463), bb)
new_mkVBalBranch3MkVBalBranch115(zzz1986, zzz1987, zzz1988, zzz1989, zzz1990, zzz1991, zzz1992, zzz1993, zzz1994, zzz1995, zzz1996, Zero, Succ(zzz19980), bc) → new_mkVBalBranch0(zzz1996, zzz1995, Branch(zzz1986, zzz1987, Pos(Succ(zzz1988)), zzz1989, zzz1990), bc)
new_mkVBalBranch0(zzz31, Branch(zzz510, zzz511, Neg(Zero), zzz513, zzz514), Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), h) → new_mkVBalBranch3MkVBalBranch117(zzz340, zzz341, zzz34200, zzz343, zzz344, zzz510, zzz511, zzz513, zzz514, zzz31, new_primPlusNat2(new_primMulNat0(zzz34200), Succ(zzz34200)), h)
new_mkVBalBranch3MkVBalBranch223(zzz340, zzz341, Neg(Zero), zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, Zero, h) → new_mkVBalBranch3MkVBalBranch228(zzz340, zzz341, zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, h)
new_mkVBalBranch3MkVBalBranch122(zzz340, zzz341, zzz34200, zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, h) → new_mkVBalBranch0(zzz31, zzz514, Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), h)
new_mkVBalBranch3MkVBalBranch217(zzz473, zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, zzz481, zzz482, Succ(zzz4830), Succ(zzz4840), bh) → new_mkVBalBranch3MkVBalBranch217(zzz473, zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, zzz481, zzz482, zzz4830, zzz4840, bh)
new_mkVBalBranch3MkVBalBranch116(zzz340, zzz341, zzz34200, zzz343, zzz344, zzz510, zzz511, zzz513, zzz514, zzz31, Succ(zzz1200), h) → new_mkVBalBranch0(zzz31, zzz514, Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), h)
new_mkVBalBranch3MkVBalBranch110(zzz461, zzz462, zzz463, zzz464, zzz465, zzz466, zzz467, zzz468, zzz469, zzz470, zzz471, Zero, bb) → new_mkVBalBranch3MkVBalBranch115(zzz461, zzz462, zzz463, zzz464, zzz465, zzz466, zzz467, Succ(zzz468), zzz469, zzz470, zzz471, Zero, Succ(Succ(zzz468)), bb)
new_mkVBalBranch3MkVBalBranch225(zzz498, zzz499, zzz500, zzz501, zzz502, zzz503, zzz504, zzz505, zzz506, zzz507, Zero, Succ(zzz5090), bg) → new_mkVBalBranch0(zzz507, Branch(zzz503, zzz504, Neg(Succ(Zero)), zzz505, zzz506), zzz501, bg)
new_mkVBalBranch3MkVBalBranch223(zzz340, zzz341, Neg(Succ(Succ(Succ(zzz3420000)))), zzz343, zzz344, zzz510, zzz511, Zero, zzz513, zzz514, zzz31, Succ(Zero), h) → new_mkVBalBranch3MkVBalBranch225(zzz340, zzz341, Succ(Succ(zzz3420000)), zzz343, zzz344, zzz510, zzz511, zzz513, zzz514, zzz31, Succ(zzz3420000), Zero, h)
new_mkVBalBranch3MkVBalBranch121(zzz473, zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, zzz481, zzz482, Zero, bh) → new_mkVBalBranch3MkVBalBranch115(zzz473, zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, Zero, zzz480, zzz481, zzz482, Zero, Succ(Zero), bh)
new_mkVBalBranch3MkVBalBranch215(zzz340, zzz341, Pos(Succ(Zero)), zzz343, zzz344, zzz510, zzz511, Succ(zzz512000), zzz513, zzz514, zzz31, Zero, h) → new_mkVBalBranch3MkVBalBranch218(zzz340, zzz341, Zero, zzz343, zzz344, zzz510, zzz511, zzz512000, zzz513, zzz514, zzz31, h)
new_mkVBalBranch3MkVBalBranch223(zzz340, zzz341, Neg(Succ(Zero)), zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, Succ(zzz670), h) → new_mkVBalBranch0(zzz31, Branch(zzz510, zzz511, Neg(Succ(zzz51200)), zzz513, zzz514), zzz343, h)
new_mkVBalBranch3MkVBalBranch225(zzz498, zzz499, zzz500, zzz501, zzz502, zzz503, zzz504, zzz505, zzz506, zzz507, Succ(zzz5080), Zero, bg) → new_mkVBalBranch3MkVBalBranch118(zzz498, zzz499, zzz500, zzz501, zzz502, zzz503, zzz504, zzz505, zzz506, zzz507, new_primPlusNat2(new_primMulNat0(zzz500), Succ(zzz500)), bg)
new_mkVBalBranch3MkVBalBranch229(zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, zzz1125, zzz1126, zzz1127, zzz1128, zzz1129, bd) → new_mkVBalBranch3MkVBalBranch119(zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, zzz1125, zzz1126, zzz1127, zzz1128, zzz1129, new_primPlusNat2(new_primMulNat0(zzz1121), Succ(zzz1121)), bd)
new_mkVBalBranch3MkVBalBranch218(zzz461, zzz462, zzz463, zzz464, zzz465, zzz466, zzz467, zzz468, zzz469, zzz470, zzz471, bb) → new_mkVBalBranch3MkVBalBranch110(zzz461, zzz462, zzz463, zzz464, zzz465, zzz466, zzz467, zzz468, zzz469, zzz470, zzz471, new_primMulNat1(zzz463), bb)
new_mkVBalBranch3MkVBalBranch223(zzz340, zzz341, Neg(Succ(Zero)), zzz343, zzz344, zzz510, zzz511, Succ(zzz512000), zzz513, zzz514, zzz31, Zero, h) → new_mkVBalBranch3MkVBalBranch227(zzz340, zzz341, Zero, zzz343, zzz344, zzz510, zzz511, zzz512000, zzz513, zzz514, zzz31, h)
new_mkVBalBranch3MkVBalBranch215(zzz340, zzz341, Pos(Succ(Zero)), zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, Succ(zzz660), h) → new_mkVBalBranch3MkVBalBranch18(zzz340, zzz341, zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, new_primMulNat1(Zero), h)
new_mkVBalBranch3MkVBalBranch215(zzz340, zzz341, Pos(Succ(Succ(zzz342000))), zzz343, zzz344, zzz510, zzz511, Zero, zzz513, zzz514, zzz31, Succ(Succ(zzz6600)), h) → new_mkVBalBranch3MkVBalBranch217(zzz340, zzz341, Succ(zzz342000), zzz343, zzz344, zzz510, zzz511, zzz513, zzz514, zzz31, Succ(zzz6600), zzz342000, h)
new_mkVBalBranch3MkVBalBranch223(zzz340, zzz341, Neg(Succ(Succ(zzz342000))), zzz343, zzz344, zzz510, zzz511, Succ(zzz512000), zzz513, zzz514, zzz31, Zero, h) → new_mkVBalBranch3MkVBalBranch224(zzz340, zzz341, Succ(zzz342000), zzz343, zzz344, zzz510, zzz511, zzz512000, zzz513, zzz514, zzz31, zzz342000, zzz512000, h)
new_mkVBalBranch3MkVBalBranch226(zzz340, zzz341, zzz3420, zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, h) → new_mkVBalBranch0(zzz31, Branch(zzz510, zzz511, Neg(Succ(zzz51200)), zzz513, zzz514), zzz343, h)
new_mkVBalBranch3MkVBalBranch117(zzz340, zzz341, zzz34200, zzz343, zzz344, zzz510, zzz511, zzz513, zzz514, zzz31, Succ(zzz1240), h) → new_mkVBalBranch0(zzz31, zzz514, Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), h)
new_mkVBalBranch0(zzz31, Branch(zzz510, zzz511, Neg(Succ(zzz51200)), zzz513, zzz514), Branch(zzz340, zzz341, zzz342, zzz343, zzz344), h) → new_mkVBalBranch3MkVBalBranch223(zzz340, zzz341, zzz342, zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, new_primPlusNat3(Succ(new_primPlusNat3(new_primPlusNat1(zzz51200), zzz51200)), Succ(zzz51200)), h)
new_mkVBalBranch3MkVBalBranch217(zzz473, zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, zzz481, zzz482, Zero, Zero, bh) → new_mkVBalBranch3MkVBalBranch233(zzz473, zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, zzz481, zzz482, bh)
new_mkVBalBranch3MkVBalBranch120(zzz2050, zzz2051, zzz2052, zzz2053, zzz2054, zzz2055, zzz2056, zzz2057, zzz2058, zzz2059, zzz2060, Succ(zzz20610), Succ(zzz20620), be) → new_mkVBalBranch3MkVBalBranch120(zzz2050, zzz2051, zzz2052, zzz2053, zzz2054, zzz2055, zzz2056, zzz2057, zzz2058, zzz2059, zzz2060, zzz20610, zzz20620, be)
new_mkVBalBranch3MkVBalBranch221(zzz340, zzz341, Succ(zzz34200), zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, h) → new_mkVBalBranch3MkVBalBranch19(zzz340, zzz341, zzz34200, zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, new_primPlusNat2(new_primPlusNat3(Succ(new_primPlusNat3(new_primPlusNat1(zzz34200), zzz34200)), Succ(zzz34200)), Succ(zzz34200)), h)
new_mkVBalBranch3MkVBalBranch223(zzz340, zzz341, Pos(zzz3420), zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, Succ(zzz670), h) → new_mkVBalBranch0(zzz31, Branch(zzz510, zzz511, Neg(Succ(zzz51200)), zzz513, zzz514), zzz343, h)
new_mkVBalBranch3MkVBalBranch216(zzz1105, zzz1106, zzz1107, zzz1108, zzz1109, zzz1110, zzz1111, zzz1112, zzz1113, zzz1114, zzz1115, Succ(zzz11160), Succ(zzz11170), ba) → new_mkVBalBranch3MkVBalBranch216(zzz1105, zzz1106, zzz1107, zzz1108, zzz1109, zzz1110, zzz1111, zzz1112, zzz1113, zzz1114, zzz1115, zzz11160, zzz11170, ba)
new_mkVBalBranch3MkVBalBranch19(zzz340, zzz341, zzz34200, zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, Zero, h) → new_mkVBalBranch3MkVBalBranch122(zzz340, zzz341, zzz34200, zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, h)
new_mkVBalBranch3MkVBalBranch223(zzz340, zzz341, Neg(Succ(Succ(Succ(zzz3420000)))), zzz343, zzz344, zzz510, zzz511, Succ(zzz512000), zzz513, zzz514, zzz31, Succ(Zero), h) → new_mkVBalBranch3MkVBalBranch224(zzz340, zzz341, Succ(Succ(zzz3420000)), zzz343, zzz344, zzz510, zzz511, zzz512000, zzz513, zzz514, zzz31, Succ(zzz3420000), Succ(zzz512000), h)
new_mkVBalBranch3MkVBalBranch215(zzz340, zzz341, Pos(Succ(Succ(zzz342000))), zzz343, zzz344, zzz510, zzz511, Zero, zzz513, zzz514, zzz31, Zero, h) → new_mkVBalBranch0(zzz31, Branch(zzz510, zzz511, Pos(Succ(Zero)), zzz513, zzz514), zzz343, h)
new_mkVBalBranch3MkVBalBranch225(zzz498, zzz499, zzz500, zzz501, zzz502, zzz503, zzz504, zzz505, zzz506, zzz507, Succ(zzz5080), Succ(zzz5090), bg) → new_mkVBalBranch3MkVBalBranch225(zzz498, zzz499, zzz500, zzz501, zzz502, zzz503, zzz504, zzz505, zzz506, zzz507, zzz5080, zzz5090, bg)
new_mkVBalBranch3MkVBalBranch19(zzz340, zzz341, zzz34200, zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, Succ(zzz1410), h) → new_mkVBalBranch0(zzz31, zzz514, Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), h)
new_mkVBalBranch3MkVBalBranch224(zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, zzz1125, zzz1126, zzz1127, zzz1128, zzz1129, Succ(zzz11300), Zero, bd) → new_mkVBalBranch3MkVBalBranch119(zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, zzz1125, zzz1126, zzz1127, zzz1128, zzz1129, new_primPlusNat2(new_primMulNat0(zzz1121), Succ(zzz1121)), bd)
new_mkVBalBranch3MkVBalBranch224(zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, zzz1125, zzz1126, zzz1127, zzz1128, zzz1129, Zero, Succ(zzz11310), bd) → new_mkVBalBranch3MkVBalBranch227(zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, zzz1125, zzz1126, zzz1127, zzz1128, zzz1129, bd)
new_mkVBalBranch3MkVBalBranch224(zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, zzz1125, zzz1126, zzz1127, zzz1128, zzz1129, Zero, Zero, bd) → new_mkVBalBranch3MkVBalBranch229(zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, zzz1125, zzz1126, zzz1127, zzz1128, zzz1129, bd)
new_mkVBalBranch3MkVBalBranch223(zzz340, zzz341, Neg(Succ(Succ(Zero))), zzz343, zzz344, zzz510, zzz511, Succ(zzz512000), zzz513, zzz514, zzz31, Succ(Zero), h) → new_mkVBalBranch3MkVBalBranch224(zzz340, zzz341, Succ(Zero), zzz343, zzz344, zzz510, zzz511, zzz512000, zzz513, zzz514, zzz31, Zero, Succ(zzz512000), h)
new_mkVBalBranch3MkVBalBranch223(zzz340, zzz341, Pos(zzz3420), zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, Zero, h) → new_mkVBalBranch3MkVBalBranch226(zzz340, zzz341, zzz3420, zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, h)
new_mkVBalBranch3MkVBalBranch223(zzz340, zzz341, Neg(Succ(Succ(zzz342000))), zzz343, zzz344, zzz510, zzz511, Zero, zzz513, zzz514, zzz31, Zero, h) → new_mkVBalBranch3MkVBalBranch118(zzz340, zzz341, Succ(zzz342000), zzz343, zzz344, zzz510, zzz511, zzz513, zzz514, zzz31, new_primPlusNat2(new_primMulNat0(Succ(zzz342000)), Succ(Succ(zzz342000))), h)
new_mkVBalBranch3MkVBalBranch230(zzz498, zzz499, zzz500, zzz501, zzz502, zzz503, zzz504, zzz505, zzz506, zzz507, bg) → new_mkVBalBranch3MkVBalBranch118(zzz498, zzz499, zzz500, zzz501, zzz502, zzz503, zzz504, zzz505, zzz506, zzz507, new_primPlusNat2(new_primMulNat0(zzz500), Succ(zzz500)), bg)
new_mkVBalBranch3MkVBalBranch223(zzz340, zzz341, Neg(Succ(Succ(Succ(zzz3420000)))), zzz343, zzz344, zzz510, zzz511, Succ(zzz512000), zzz513, zzz514, zzz31, Succ(Succ(zzz6700)), h) → new_mkVBalBranch3MkVBalBranch224(zzz340, zzz341, Succ(Succ(zzz3420000)), zzz343, zzz344, zzz510, zzz511, zzz512000, zzz513, zzz514, zzz31, Succ(zzz3420000), Succ(Succ(new_primPlusNat2(zzz6700, zzz512000))), h)
new_mkVBalBranch3MkVBalBranch223(zzz340, zzz341, Neg(Succ(Succ(Zero))), zzz343, zzz344, zzz510, zzz511, Zero, zzz513, zzz514, zzz31, Succ(Succ(zzz6700)), h) → new_mkVBalBranch3MkVBalBranch225(zzz340, zzz341, Succ(Zero), zzz343, zzz344, zzz510, zzz511, zzz513, zzz514, zzz31, Zero, Succ(zzz6700), h)
new_mkVBalBranch3MkVBalBranch215(zzz340, zzz341, Pos(Zero), zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, Zero, h) → new_mkVBalBranch3MkVBalBranch220(zzz340, zzz341, zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, h)
new_mkVBalBranch3MkVBalBranch115(zzz1986, zzz1987, zzz1988, zzz1989, zzz1990, zzz1991, zzz1992, zzz1993, zzz1994, zzz1995, zzz1996, Succ(zzz19970), Succ(zzz19980), bc) → new_mkVBalBranch3MkVBalBranch115(zzz1986, zzz1987, zzz1988, zzz1989, zzz1990, zzz1991, zzz1992, zzz1993, zzz1994, zzz1995, zzz1996, zzz19970, zzz19980, bc)
new_mkVBalBranch3MkVBalBranch215(zzz340, zzz341, Neg(Zero), zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, Succ(zzz660), h) → new_mkVBalBranch0(zzz31, zzz514, Branch(zzz340, zzz341, Neg(Zero), zzz343, zzz344), h)
new_mkVBalBranch3MkVBalBranch118(zzz498, zzz499, zzz500, zzz501, zzz502, zzz503, zzz504, zzz505, zzz506, zzz507, Succ(zzz8040), bg) → new_mkVBalBranch3MkVBalBranch120(zzz498, zzz499, zzz500, zzz501, zzz502, zzz503, zzz504, Zero, zzz505, zzz506, zzz507, Succ(Zero), Succ(zzz8040), bg)
new_mkVBalBranch3MkVBalBranch216(zzz1105, zzz1106, zzz1107, zzz1108, zzz1109, zzz1110, zzz1111, zzz1112, zzz1113, zzz1114, zzz1115, Succ(zzz11160), Zero, ba) → new_mkVBalBranch3MkVBalBranch218(zzz1105, zzz1106, zzz1107, zzz1108, zzz1109, zzz1110, zzz1111, zzz1112, zzz1113, zzz1114, zzz1115, ba)
new_mkVBalBranch3MkVBalBranch215(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, Succ(zzz660), h) → new_mkVBalBranch3MkVBalBranch19(zzz340, zzz341, zzz34200, zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, new_primPlusNat2(new_primMulNat0(zzz34200), Succ(zzz34200)), h)
new_mkVBalBranch3MkVBalBranch215(zzz340, zzz341, Pos(Succ(Succ(zzz342000))), zzz343, zzz344, zzz510, zzz511, Succ(zzz512000), zzz513, zzz514, zzz31, Succ(Zero), h) → new_mkVBalBranch3MkVBalBranch216(zzz340, zzz341, Succ(zzz342000), zzz343, zzz344, zzz510, zzz511, zzz512000, zzz513, zzz514, zzz31, Succ(zzz512000), zzz342000, h)
new_mkVBalBranch3MkVBalBranch219(zzz340, zzz341, zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, h) → new_mkVBalBranch3MkVBalBranch18(zzz340, zzz341, zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, new_primMulNat1(Zero), h)
new_mkVBalBranch3MkVBalBranch221(zzz340, zzz341, Zero, zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, h) → new_mkVBalBranch0(zzz31, zzz514, Branch(zzz340, zzz341, Neg(Zero), zzz343, zzz344), h)
new_mkVBalBranch3MkVBalBranch216(zzz1105, zzz1106, zzz1107, zzz1108, zzz1109, zzz1110, zzz1111, zzz1112, zzz1113, zzz1114, zzz1115, Zero, Zero, ba) → new_mkVBalBranch3MkVBalBranch222(zzz1105, zzz1106, zzz1107, zzz1108, zzz1109, zzz1110, zzz1111, zzz1112, zzz1113, zzz1114, zzz1115, ba)
new_mkVBalBranch3MkVBalBranch233(zzz473, zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, zzz481, zzz482, bh) → new_mkVBalBranch3MkVBalBranch121(zzz473, zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, zzz481, zzz482, new_primMulNat1(zzz475), bh)
new_mkVBalBranch3MkVBalBranch215(zzz340, zzz341, Pos(Succ(Succ(zzz342000))), zzz343, zzz344, zzz510, zzz511, Zero, zzz513, zzz514, zzz31, Succ(Zero), h) → new_mkVBalBranch3MkVBalBranch217(zzz340, zzz341, Succ(zzz342000), zzz343, zzz344, zzz510, zzz511, zzz513, zzz514, zzz31, Zero, zzz342000, h)
new_mkVBalBranch0(zzz31, Branch(zzz510, zzz511, Pos(Zero), zzz513, zzz514), Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), h) → new_mkVBalBranch3MkVBalBranch116(zzz340, zzz341, zzz34200, zzz343, zzz344, zzz510, zzz511, zzz513, zzz514, zzz31, new_primMulNat1(zzz34200), h)
new_mkVBalBranch3MkVBalBranch18(zzz340, zzz341, zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, Zero, h) → new_mkVBalBranch3MkVBalBranch115(zzz340, zzz341, Zero, zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, Zero, Succ(zzz51200), h)
new_mkVBalBranch3MkVBalBranch119(zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, zzz1125, zzz1126, zzz1127, zzz1128, zzz1129, Succ(zzz12130), bd) → new_mkVBalBranch3MkVBalBranch120(zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, zzz1125, Succ(zzz1126), zzz1127, zzz1128, zzz1129, Succ(Succ(zzz1126)), Succ(zzz12130), bd)

The TRS R consists of the following rules:

new_primPlusNat1(Zero) → Zero
new_primMulNat0(zzz6200) → new_primPlusNat3(Succ(new_primPlusNat3(new_primPlusNat1(zzz6200), zzz6200)), Succ(zzz6200))
new_primPlusNat2(Succ(zzz900), Succ(zzz9100)) → Succ(Succ(new_primPlusNat2(zzz900, zzz9100)))
new_primPlusNat3(zzz90, Succ(zzz910)) → Succ(Succ(new_primPlusNat2(zzz90, zzz910)))
new_primPlusNat3(zzz90, Zero) → Succ(zzz90)
new_primMulNat1(zzz34200) → new_primPlusNat2(new_primMulNat0(zzz34200), Succ(zzz34200))
new_primPlusNat2(Zero, Zero) → Zero
new_primPlusNat1(Succ(zzz62000)) → Succ(Succ(new_primPlusNat1(zzz62000)))
new_primPlusNat2(Succ(zzz900), Zero) → Succ(zzz900)
new_primPlusNat2(Zero, Succ(zzz9100)) → Succ(zzz9100)

The set Q consists of the following terms:

new_primPlusNat2(Zero, Succ(x0))
new_primMulNat1(x0)
new_primMulNat0(x0)
new_primPlusNat3(x0, Succ(x1))
new_primPlusNat2(Succ(x0), Succ(x1))
new_primPlusNat3(x0, Zero)
new_primPlusNat1(Zero)
new_primPlusNat2(Zero, Zero)
new_primPlusNat1(Succ(x0))
new_primPlusNat2(Succ(x0), Zero)

We have to consider all minimal (P,Q,R)-chains.
By rewriting [15] the rule new_mkVBalBranch0(zzz31, Branch(zzz510, zzz511, Pos(Zero), zzz513, zzz514), Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), h) → new_mkVBalBranch3MkVBalBranch116(zzz340, zzz341, zzz34200, zzz343, zzz344, zzz510, zzz511, zzz513, zzz514, zzz31, new_primMulNat1(zzz34200), h) at position [10] we obtained the following new rules:

new_mkVBalBranch0(zzz31, Branch(zzz510, zzz511, Pos(Zero), zzz513, zzz514), Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), h) → new_mkVBalBranch3MkVBalBranch116(zzz340, zzz341, zzz34200, zzz343, zzz344, zzz510, zzz511, zzz513, zzz514, zzz31, new_primPlusNat2(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
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                    ↳ DependencyGraphProof
                                      ↳ QDP
                                        ↳ Rewriting
                                          ↳ QDP
                                            ↳ Rewriting
                                              ↳ QDP
                                                ↳ Rewriting
                                                  ↳ QDP
                                                    ↳ Rewriting
                                                      ↳ QDP
                                                        ↳ Rewriting
                                                          ↳ QDP
                                                            ↳ Rewriting
                                                              ↳ QDP
                                                                ↳ Rewriting
                                                                  ↳ QDP
                                                                    ↳ Rewriting
                                                                      ↳ QDP
                                                                        ↳ Rewriting
                                                                          ↳ QDP
                                                                            ↳ Rewriting
                                                                              ↳ QDP
                                                                                ↳ Rewriting
                                                                                  ↳ QDP
                                                                                    ↳ Rewriting
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP

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

new_mkVBalBranch3MkVBalBranch225(zzz498, zzz499, zzz500, zzz501, zzz502, zzz503, zzz504, zzz505, zzz506, zzz507, Zero, Zero, bg) → new_mkVBalBranch3MkVBalBranch230(zzz498, zzz499, zzz500, zzz501, zzz502, zzz503, zzz504, zzz505, zzz506, zzz507, bg)
new_mkVBalBranch3MkVBalBranch215(zzz340, zzz341, Neg(zzz3420), zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, Zero, h) → new_mkVBalBranch3MkVBalBranch221(zzz340, zzz341, zzz3420, zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, h)
new_mkVBalBranch3MkVBalBranch18(zzz340, zzz341, zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, Succ(zzz1480), h) → new_mkVBalBranch3MkVBalBranch115(zzz340, zzz341, Zero, zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, Succ(zzz1480), Succ(zzz51200), h)
new_mkVBalBranch3MkVBalBranch215(zzz340, zzz341, Pos(Succ(Succ(zzz342000))), zzz343, zzz344, zzz510, zzz511, Succ(zzz512000), zzz513, zzz514, zzz31, Succ(Succ(zzz6600)), h) → new_mkVBalBranch3MkVBalBranch216(zzz340, zzz341, Succ(zzz342000), zzz343, zzz344, zzz510, zzz511, zzz512000, zzz513, zzz514, zzz31, Succ(Succ(new_primPlusNat2(zzz6600, zzz512000))), zzz342000, h)
new_mkVBalBranch0(zzz31, Branch(zzz510, zzz511, Neg(Zero), zzz513, zzz514), Branch(zzz340, zzz341, Pos(Succ(zzz34200)), zzz343, zzz344), h) → new_mkVBalBranch0(zzz31, Branch(zzz510, zzz511, Neg(Zero), zzz513, zzz514), zzz343, h)
new_mkVBalBranch3MkVBalBranch223(zzz340, zzz341, Neg(Succ(Succ(Succ(zzz3420000)))), zzz343, zzz344, zzz510, zzz511, Zero, zzz513, zzz514, zzz31, Succ(Succ(zzz6700)), h) → new_mkVBalBranch3MkVBalBranch225(zzz340, zzz341, Succ(Succ(zzz3420000)), zzz343, zzz344, zzz510, zzz511, zzz513, zzz514, zzz31, Succ(zzz3420000), Succ(zzz6700), h)
new_mkVBalBranch3MkVBalBranch120(zzz2050, zzz2051, zzz2052, zzz2053, zzz2054, zzz2055, zzz2056, zzz2057, zzz2058, zzz2059, zzz2060, Zero, Succ(zzz20620), be) → new_mkVBalBranch0(zzz2060, zzz2059, Branch(zzz2050, zzz2051, Neg(Succ(zzz2052)), zzz2053, zzz2054), be)
new_mkVBalBranch3MkVBalBranch220(zzz340, zzz341, zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, h) → new_mkVBalBranch0(zzz31, zzz514, Branch(zzz340, zzz341, Pos(Zero), zzz343, zzz344), h)
new_mkVBalBranch3MkVBalBranch228(zzz340, zzz341, zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, h) → new_mkVBalBranch0(zzz31, Branch(zzz510, zzz511, Neg(Succ(zzz51200)), zzz513, zzz514), zzz343, h)
new_mkVBalBranch0(zzz31, Branch(zzz510, zzz511, Pos(Zero), zzz513, zzz514), Branch(zzz340, zzz341, Pos(Succ(zzz34200)), zzz343, zzz344), h) → new_mkVBalBranch0(zzz31, Branch(zzz510, zzz511, Pos(Zero), zzz513, zzz514), zzz343, h)
new_mkVBalBranch3MkVBalBranch121(zzz473, zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, zzz481, zzz482, Succ(zzz7390), bh) → new_mkVBalBranch3MkVBalBranch115(zzz473, zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, Zero, zzz480, zzz481, zzz482, Succ(zzz7390), Succ(Zero), bh)
new_mkVBalBranch3MkVBalBranch223(zzz340, zzz341, Neg(Succ(Succ(Zero))), zzz343, zzz344, zzz510, zzz511, Succ(zzz512000), zzz513, zzz514, zzz31, Succ(Succ(zzz6700)), h) → new_mkVBalBranch3MkVBalBranch224(zzz340, zzz341, Succ(Zero), zzz343, zzz344, zzz510, zzz511, zzz512000, zzz513, zzz514, zzz31, Zero, Succ(Succ(new_primPlusNat2(zzz6700, zzz512000))), h)
new_mkVBalBranch3MkVBalBranch215(zzz340, zzz341, Pos(Succ(Zero)), zzz343, zzz344, zzz510, zzz511, Zero, zzz513, zzz514, zzz31, Zero, h) → new_mkVBalBranch3MkVBalBranch219(zzz340, zzz341, zzz343, zzz344, zzz510, zzz511, Zero, zzz513, zzz514, zzz31, h)
new_mkVBalBranch3MkVBalBranch223(zzz340, zzz341, Neg(Succ(Succ(Zero))), zzz343, zzz344, zzz510, zzz511, Zero, zzz513, zzz514, zzz31, Succ(Zero), h) → new_mkVBalBranch3MkVBalBranch225(zzz340, zzz341, Succ(Zero), zzz343, zzz344, zzz510, zzz511, zzz513, zzz514, zzz31, Zero, Zero, h)
new_mkVBalBranch3MkVBalBranch224(zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, zzz1125, zzz1126, zzz1127, zzz1128, zzz1129, Succ(zzz11300), Succ(zzz11310), bd) → new_mkVBalBranch3MkVBalBranch224(zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, zzz1125, zzz1126, zzz1127, zzz1128, zzz1129, zzz11300, zzz11310, bd)
new_mkVBalBranch3MkVBalBranch217(zzz473, zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, zzz481, zzz482, Zero, Succ(zzz4840), bh) → new_mkVBalBranch0(zzz482, Branch(zzz478, zzz479, Pos(Succ(Zero)), zzz480, zzz481), zzz476, bh)
new_mkVBalBranch0(zzz31, Branch(zzz510, zzz511, Pos(Succ(zzz51200)), zzz513, zzz514), Branch(zzz340, zzz341, zzz342, zzz343, zzz344), h) → new_mkVBalBranch3MkVBalBranch215(zzz340, zzz341, zzz342, zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, new_primPlusNat3(Succ(new_primPlusNat3(new_primPlusNat1(zzz51200), zzz51200)), Succ(zzz51200)), h)
new_mkVBalBranch3MkVBalBranch215(zzz340, zzz341, Pos(Succ(Succ(zzz342000))), zzz343, zzz344, zzz510, zzz511, Succ(zzz512000), zzz513, zzz514, zzz31, Zero, h) → new_mkVBalBranch3MkVBalBranch216(zzz340, zzz341, Succ(zzz342000), zzz343, zzz344, zzz510, zzz511, zzz512000, zzz513, zzz514, zzz31, zzz512000, zzz342000, h)
new_mkVBalBranch3MkVBalBranch110(zzz461, zzz462, zzz463, zzz464, zzz465, zzz466, zzz467, zzz468, zzz469, zzz470, zzz471, Succ(zzz5800), bb) → new_mkVBalBranch3MkVBalBranch115(zzz461, zzz462, zzz463, zzz464, zzz465, zzz466, zzz467, Succ(zzz468), zzz469, zzz470, zzz471, Succ(zzz5800), Succ(Succ(zzz468)), bb)
new_mkVBalBranch3MkVBalBranch223(zzz340, zzz341, Neg(Succ(Zero)), zzz343, zzz344, zzz510, zzz511, Zero, zzz513, zzz514, zzz31, Zero, h) → new_mkVBalBranch3MkVBalBranch118(zzz340, zzz341, Zero, zzz343, zzz344, zzz510, zzz511, zzz513, zzz514, zzz31, new_primPlusNat2(new_primMulNat0(Zero), Succ(Zero)), h)
new_mkVBalBranch3MkVBalBranch227(zzz486, zzz487, zzz488, zzz489, zzz490, zzz491, zzz492, zzz493, zzz494, zzz495, zzz496, bf) → new_mkVBalBranch0(zzz496, Branch(zzz491, zzz492, Neg(Succ(Succ(zzz493))), zzz494, zzz495), zzz489, bf)
new_mkVBalBranch0(zzz31, Branch(zzz510, zzz511, Pos(Zero), zzz513, zzz514), Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), h) → new_mkVBalBranch3MkVBalBranch116(zzz340, zzz341, zzz34200, zzz343, zzz344, zzz510, zzz511, zzz513, zzz514, zzz31, new_primPlusNat2(new_primMulNat0(zzz34200), Succ(zzz34200)), h)
new_mkVBalBranch3MkVBalBranch215(zzz340, zzz341, Pos(Zero), zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, Succ(zzz660), h) → new_mkVBalBranch0(zzz31, zzz514, Branch(zzz340, zzz341, Pos(Zero), zzz343, zzz344), h)
new_mkVBalBranch3MkVBalBranch223(zzz340, zzz341, Neg(Zero), zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, Succ(zzz670), h) → new_mkVBalBranch0(zzz31, Branch(zzz510, zzz511, Neg(Succ(zzz51200)), zzz513, zzz514), zzz343, h)
new_mkVBalBranch3MkVBalBranch216(zzz1105, zzz1106, zzz1107, zzz1108, zzz1109, zzz1110, zzz1111, zzz1112, zzz1113, zzz1114, zzz1115, Zero, Succ(zzz11170), ba) → new_mkVBalBranch0(zzz1115, Branch(zzz1110, zzz1111, Pos(Succ(Succ(zzz1112))), zzz1113, zzz1114), zzz1108, ba)
new_mkVBalBranch3MkVBalBranch222(zzz461, zzz462, zzz463, zzz464, zzz465, zzz466, zzz467, zzz468, zzz469, zzz470, zzz471, bb) → new_mkVBalBranch3MkVBalBranch110(zzz461, zzz462, zzz463, zzz464, zzz465, zzz466, zzz467, zzz468, zzz469, zzz470, zzz471, new_primMulNat1(zzz463), bb)
new_mkVBalBranch3MkVBalBranch217(zzz473, zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, zzz481, zzz482, Succ(zzz4830), Zero, bh) → new_mkVBalBranch3MkVBalBranch121(zzz473, zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, zzz481, zzz482, new_primMulNat1(zzz475), bh)
new_mkVBalBranch3MkVBalBranch115(zzz1986, zzz1987, zzz1988, zzz1989, zzz1990, zzz1991, zzz1992, zzz1993, zzz1994, zzz1995, zzz1996, Zero, Succ(zzz19980), bc) → new_mkVBalBranch0(zzz1996, zzz1995, Branch(zzz1986, zzz1987, Pos(Succ(zzz1988)), zzz1989, zzz1990), bc)
new_mkVBalBranch0(zzz31, Branch(zzz510, zzz511, Neg(Zero), zzz513, zzz514), Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), h) → new_mkVBalBranch3MkVBalBranch117(zzz340, zzz341, zzz34200, zzz343, zzz344, zzz510, zzz511, zzz513, zzz514, zzz31, new_primPlusNat2(new_primMulNat0(zzz34200), Succ(zzz34200)), h)
new_mkVBalBranch3MkVBalBranch223(zzz340, zzz341, Neg(Zero), zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, Zero, h) → new_mkVBalBranch3MkVBalBranch228(zzz340, zzz341, zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, h)
new_mkVBalBranch3MkVBalBranch122(zzz340, zzz341, zzz34200, zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, h) → new_mkVBalBranch0(zzz31, zzz514, Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), h)
new_mkVBalBranch3MkVBalBranch217(zzz473, zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, zzz481, zzz482, Succ(zzz4830), Succ(zzz4840), bh) → new_mkVBalBranch3MkVBalBranch217(zzz473, zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, zzz481, zzz482, zzz4830, zzz4840, bh)
new_mkVBalBranch3MkVBalBranch116(zzz340, zzz341, zzz34200, zzz343, zzz344, zzz510, zzz511, zzz513, zzz514, zzz31, Succ(zzz1200), h) → new_mkVBalBranch0(zzz31, zzz514, Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), h)
new_mkVBalBranch3MkVBalBranch110(zzz461, zzz462, zzz463, zzz464, zzz465, zzz466, zzz467, zzz468, zzz469, zzz470, zzz471, Zero, bb) → new_mkVBalBranch3MkVBalBranch115(zzz461, zzz462, zzz463, zzz464, zzz465, zzz466, zzz467, Succ(zzz468), zzz469, zzz470, zzz471, Zero, Succ(Succ(zzz468)), bb)
new_mkVBalBranch3MkVBalBranch225(zzz498, zzz499, zzz500, zzz501, zzz502, zzz503, zzz504, zzz505, zzz506, zzz507, Zero, Succ(zzz5090), bg) → new_mkVBalBranch0(zzz507, Branch(zzz503, zzz504, Neg(Succ(Zero)), zzz505, zzz506), zzz501, bg)
new_mkVBalBranch3MkVBalBranch223(zzz340, zzz341, Neg(Succ(Succ(Succ(zzz3420000)))), zzz343, zzz344, zzz510, zzz511, Zero, zzz513, zzz514, zzz31, Succ(Zero), h) → new_mkVBalBranch3MkVBalBranch225(zzz340, zzz341, Succ(Succ(zzz3420000)), zzz343, zzz344, zzz510, zzz511, zzz513, zzz514, zzz31, Succ(zzz3420000), Zero, h)
new_mkVBalBranch3MkVBalBranch121(zzz473, zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, zzz481, zzz482, Zero, bh) → new_mkVBalBranch3MkVBalBranch115(zzz473, zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, Zero, zzz480, zzz481, zzz482, Zero, Succ(Zero), bh)
new_mkVBalBranch3MkVBalBranch215(zzz340, zzz341, Pos(Succ(Zero)), zzz343, zzz344, zzz510, zzz511, Succ(zzz512000), zzz513, zzz514, zzz31, Zero, h) → new_mkVBalBranch3MkVBalBranch218(zzz340, zzz341, Zero, zzz343, zzz344, zzz510, zzz511, zzz512000, zzz513, zzz514, zzz31, h)
new_mkVBalBranch3MkVBalBranch225(zzz498, zzz499, zzz500, zzz501, zzz502, zzz503, zzz504, zzz505, zzz506, zzz507, Succ(zzz5080), Zero, bg) → new_mkVBalBranch3MkVBalBranch118(zzz498, zzz499, zzz500, zzz501, zzz502, zzz503, zzz504, zzz505, zzz506, zzz507, new_primPlusNat2(new_primMulNat0(zzz500), Succ(zzz500)), bg)
new_mkVBalBranch3MkVBalBranch223(zzz340, zzz341, Neg(Succ(Zero)), zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, Succ(zzz670), h) → new_mkVBalBranch0(zzz31, Branch(zzz510, zzz511, Neg(Succ(zzz51200)), zzz513, zzz514), zzz343, h)
new_mkVBalBranch3MkVBalBranch229(zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, zzz1125, zzz1126, zzz1127, zzz1128, zzz1129, bd) → new_mkVBalBranch3MkVBalBranch119(zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, zzz1125, zzz1126, zzz1127, zzz1128, zzz1129, new_primPlusNat2(new_primMulNat0(zzz1121), Succ(zzz1121)), bd)
new_mkVBalBranch3MkVBalBranch218(zzz461, zzz462, zzz463, zzz464, zzz465, zzz466, zzz467, zzz468, zzz469, zzz470, zzz471, bb) → new_mkVBalBranch3MkVBalBranch110(zzz461, zzz462, zzz463, zzz464, zzz465, zzz466, zzz467, zzz468, zzz469, zzz470, zzz471, new_primMulNat1(zzz463), bb)
new_mkVBalBranch3MkVBalBranch223(zzz340, zzz341, Neg(Succ(Zero)), zzz343, zzz344, zzz510, zzz511, Succ(zzz512000), zzz513, zzz514, zzz31, Zero, h) → new_mkVBalBranch3MkVBalBranch227(zzz340, zzz341, Zero, zzz343, zzz344, zzz510, zzz511, zzz512000, zzz513, zzz514, zzz31, h)
new_mkVBalBranch3MkVBalBranch215(zzz340, zzz341, Pos(Succ(Zero)), zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, Succ(zzz660), h) → new_mkVBalBranch3MkVBalBranch18(zzz340, zzz341, zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, new_primMulNat1(Zero), h)
new_mkVBalBranch3MkVBalBranch226(zzz340, zzz341, zzz3420, zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, h) → new_mkVBalBranch0(zzz31, Branch(zzz510, zzz511, Neg(Succ(zzz51200)), zzz513, zzz514), zzz343, h)
new_mkVBalBranch3MkVBalBranch223(zzz340, zzz341, Neg(Succ(Succ(zzz342000))), zzz343, zzz344, zzz510, zzz511, Succ(zzz512000), zzz513, zzz514, zzz31, Zero, h) → new_mkVBalBranch3MkVBalBranch224(zzz340, zzz341, Succ(zzz342000), zzz343, zzz344, zzz510, zzz511, zzz512000, zzz513, zzz514, zzz31, zzz342000, zzz512000, h)
new_mkVBalBranch3MkVBalBranch215(zzz340, zzz341, Pos(Succ(Succ(zzz342000))), zzz343, zzz344, zzz510, zzz511, Zero, zzz513, zzz514, zzz31, Succ(Succ(zzz6600)), h) → new_mkVBalBranch3MkVBalBranch217(zzz340, zzz341, Succ(zzz342000), zzz343, zzz344, zzz510, zzz511, zzz513, zzz514, zzz31, Succ(zzz6600), zzz342000, h)
new_mkVBalBranch3MkVBalBranch117(zzz340, zzz341, zzz34200, zzz343, zzz344, zzz510, zzz511, zzz513, zzz514, zzz31, Succ(zzz1240), h) → new_mkVBalBranch0(zzz31, zzz514, Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), h)
new_mkVBalBranch3MkVBalBranch221(zzz340, zzz341, Succ(zzz34200), zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, h) → new_mkVBalBranch3MkVBalBranch19(zzz340, zzz341, zzz34200, zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, new_primPlusNat2(new_primPlusNat3(Succ(new_primPlusNat3(new_primPlusNat1(zzz34200), zzz34200)), Succ(zzz34200)), Succ(zzz34200)), h)
new_mkVBalBranch3MkVBalBranch120(zzz2050, zzz2051, zzz2052, zzz2053, zzz2054, zzz2055, zzz2056, zzz2057, zzz2058, zzz2059, zzz2060, Succ(zzz20610), Succ(zzz20620), be) → new_mkVBalBranch3MkVBalBranch120(zzz2050, zzz2051, zzz2052, zzz2053, zzz2054, zzz2055, zzz2056, zzz2057, zzz2058, zzz2059, zzz2060, zzz20610, zzz20620, be)
new_mkVBalBranch3MkVBalBranch217(zzz473, zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, zzz481, zzz482, Zero, Zero, bh) → new_mkVBalBranch3MkVBalBranch233(zzz473, zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, zzz481, zzz482, bh)
new_mkVBalBranch0(zzz31, Branch(zzz510, zzz511, Neg(Succ(zzz51200)), zzz513, zzz514), Branch(zzz340, zzz341, zzz342, zzz343, zzz344), h) → new_mkVBalBranch3MkVBalBranch223(zzz340, zzz341, zzz342, zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, new_primPlusNat3(Succ(new_primPlusNat3(new_primPlusNat1(zzz51200), zzz51200)), Succ(zzz51200)), h)
new_mkVBalBranch3MkVBalBranch216(zzz1105, zzz1106, zzz1107, zzz1108, zzz1109, zzz1110, zzz1111, zzz1112, zzz1113, zzz1114, zzz1115, Succ(zzz11160), Succ(zzz11170), ba) → new_mkVBalBranch3MkVBalBranch216(zzz1105, zzz1106, zzz1107, zzz1108, zzz1109, zzz1110, zzz1111, zzz1112, zzz1113, zzz1114, zzz1115, zzz11160, zzz11170, ba)
new_mkVBalBranch3MkVBalBranch223(zzz340, zzz341, Pos(zzz3420), zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, Succ(zzz670), h) → new_mkVBalBranch0(zzz31, Branch(zzz510, zzz511, Neg(Succ(zzz51200)), zzz513, zzz514), zzz343, h)
new_mkVBalBranch3MkVBalBranch223(zzz340, zzz341, Neg(Succ(Succ(Succ(zzz3420000)))), zzz343, zzz344, zzz510, zzz511, Succ(zzz512000), zzz513, zzz514, zzz31, Succ(Zero), h) → new_mkVBalBranch3MkVBalBranch224(zzz340, zzz341, Succ(Succ(zzz3420000)), zzz343, zzz344, zzz510, zzz511, zzz512000, zzz513, zzz514, zzz31, Succ(zzz3420000), Succ(zzz512000), h)
new_mkVBalBranch3MkVBalBranch19(zzz340, zzz341, zzz34200, zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, Zero, h) → new_mkVBalBranch3MkVBalBranch122(zzz340, zzz341, zzz34200, zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, h)
new_mkVBalBranch3MkVBalBranch215(zzz340, zzz341, Pos(Succ(Succ(zzz342000))), zzz343, zzz344, zzz510, zzz511, Zero, zzz513, zzz514, zzz31, Zero, h) → new_mkVBalBranch0(zzz31, Branch(zzz510, zzz511, Pos(Succ(Zero)), zzz513, zzz514), zzz343, h)
new_mkVBalBranch3MkVBalBranch225(zzz498, zzz499, zzz500, zzz501, zzz502, zzz503, zzz504, zzz505, zzz506, zzz507, Succ(zzz5080), Succ(zzz5090), bg) → new_mkVBalBranch3MkVBalBranch225(zzz498, zzz499, zzz500, zzz501, zzz502, zzz503, zzz504, zzz505, zzz506, zzz507, zzz5080, zzz5090, bg)
new_mkVBalBranch3MkVBalBranch19(zzz340, zzz341, zzz34200, zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, Succ(zzz1410), h) → new_mkVBalBranch0(zzz31, zzz514, Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), h)
new_mkVBalBranch3MkVBalBranch224(zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, zzz1125, zzz1126, zzz1127, zzz1128, zzz1129, Succ(zzz11300), Zero, bd) → new_mkVBalBranch3MkVBalBranch119(zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, zzz1125, zzz1126, zzz1127, zzz1128, zzz1129, new_primPlusNat2(new_primMulNat0(zzz1121), Succ(zzz1121)), bd)
new_mkVBalBranch3MkVBalBranch223(zzz340, zzz341, Pos(zzz3420), zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, Zero, h) → new_mkVBalBranch3MkVBalBranch226(zzz340, zzz341, zzz3420, zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, h)
new_mkVBalBranch3MkVBalBranch223(zzz340, zzz341, Neg(Succ(Succ(Zero))), zzz343, zzz344, zzz510, zzz511, Succ(zzz512000), zzz513, zzz514, zzz31, Succ(Zero), h) → new_mkVBalBranch3MkVBalBranch224(zzz340, zzz341, Succ(Zero), zzz343, zzz344, zzz510, zzz511, zzz512000, zzz513, zzz514, zzz31, Zero, Succ(zzz512000), h)
new_mkVBalBranch3MkVBalBranch224(zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, zzz1125, zzz1126, zzz1127, zzz1128, zzz1129, Zero, Zero, bd) → new_mkVBalBranch3MkVBalBranch229(zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, zzz1125, zzz1126, zzz1127, zzz1128, zzz1129, bd)
new_mkVBalBranch3MkVBalBranch224(zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, zzz1125, zzz1126, zzz1127, zzz1128, zzz1129, Zero, Succ(zzz11310), bd) → new_mkVBalBranch3MkVBalBranch227(zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, zzz1125, zzz1126, zzz1127, zzz1128, zzz1129, bd)
new_mkVBalBranch3MkVBalBranch223(zzz340, zzz341, Neg(Succ(Succ(zzz342000))), zzz343, zzz344, zzz510, zzz511, Zero, zzz513, zzz514, zzz31, Zero, h) → new_mkVBalBranch3MkVBalBranch118(zzz340, zzz341, Succ(zzz342000), zzz343, zzz344, zzz510, zzz511, zzz513, zzz514, zzz31, new_primPlusNat2(new_primMulNat0(Succ(zzz342000)), Succ(Succ(zzz342000))), h)
new_mkVBalBranch3MkVBalBranch230(zzz498, zzz499, zzz500, zzz501, zzz502, zzz503, zzz504, zzz505, zzz506, zzz507, bg) → new_mkVBalBranch3MkVBalBranch118(zzz498, zzz499, zzz500, zzz501, zzz502, zzz503, zzz504, zzz505, zzz506, zzz507, new_primPlusNat2(new_primMulNat0(zzz500), Succ(zzz500)), bg)
new_mkVBalBranch3MkVBalBranch223(zzz340, zzz341, Neg(Succ(Succ(Zero))), zzz343, zzz344, zzz510, zzz511, Zero, zzz513, zzz514, zzz31, Succ(Succ(zzz6700)), h) → new_mkVBalBranch3MkVBalBranch225(zzz340, zzz341, Succ(Zero), zzz343, zzz344, zzz510, zzz511, zzz513, zzz514, zzz31, Zero, Succ(zzz6700), h)
new_mkVBalBranch3MkVBalBranch223(zzz340, zzz341, Neg(Succ(Succ(Succ(zzz3420000)))), zzz343, zzz344, zzz510, zzz511, Succ(zzz512000), zzz513, zzz514, zzz31, Succ(Succ(zzz6700)), h) → new_mkVBalBranch3MkVBalBranch224(zzz340, zzz341, Succ(Succ(zzz3420000)), zzz343, zzz344, zzz510, zzz511, zzz512000, zzz513, zzz514, zzz31, Succ(zzz3420000), Succ(Succ(new_primPlusNat2(zzz6700, zzz512000))), h)
new_mkVBalBranch3MkVBalBranch115(zzz1986, zzz1987, zzz1988, zzz1989, zzz1990, zzz1991, zzz1992, zzz1993, zzz1994, zzz1995, zzz1996, Succ(zzz19970), Succ(zzz19980), bc) → new_mkVBalBranch3MkVBalBranch115(zzz1986, zzz1987, zzz1988, zzz1989, zzz1990, zzz1991, zzz1992, zzz1993, zzz1994, zzz1995, zzz1996, zzz19970, zzz19980, bc)
new_mkVBalBranch3MkVBalBranch215(zzz340, zzz341, Pos(Zero), zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, Zero, h) → new_mkVBalBranch3MkVBalBranch220(zzz340, zzz341, zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, h)
new_mkVBalBranch3MkVBalBranch215(zzz340, zzz341, Neg(Zero), zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, Succ(zzz660), h) → new_mkVBalBranch0(zzz31, zzz514, Branch(zzz340, zzz341, Neg(Zero), zzz343, zzz344), h)
new_mkVBalBranch3MkVBalBranch118(zzz498, zzz499, zzz500, zzz501, zzz502, zzz503, zzz504, zzz505, zzz506, zzz507, Succ(zzz8040), bg) → new_mkVBalBranch3MkVBalBranch120(zzz498, zzz499, zzz500, zzz501, zzz502, zzz503, zzz504, Zero, zzz505, zzz506, zzz507, Succ(Zero), Succ(zzz8040), bg)
new_mkVBalBranch3MkVBalBranch216(zzz1105, zzz1106, zzz1107, zzz1108, zzz1109, zzz1110, zzz1111, zzz1112, zzz1113, zzz1114, zzz1115, Succ(zzz11160), Zero, ba) → new_mkVBalBranch3MkVBalBranch218(zzz1105, zzz1106, zzz1107, zzz1108, zzz1109, zzz1110, zzz1111, zzz1112, zzz1113, zzz1114, zzz1115, ba)
new_mkVBalBranch3MkVBalBranch221(zzz340, zzz341, Zero, zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, h) → new_mkVBalBranch0(zzz31, zzz514, Branch(zzz340, zzz341, Neg(Zero), zzz343, zzz344), h)
new_mkVBalBranch3MkVBalBranch219(zzz340, zzz341, zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, h) → new_mkVBalBranch3MkVBalBranch18(zzz340, zzz341, zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, new_primMulNat1(Zero), h)
new_mkVBalBranch3MkVBalBranch215(zzz340, zzz341, Pos(Succ(Succ(zzz342000))), zzz343, zzz344, zzz510, zzz511, Succ(zzz512000), zzz513, zzz514, zzz31, Succ(Zero), h) → new_mkVBalBranch3MkVBalBranch216(zzz340, zzz341, Succ(zzz342000), zzz343, zzz344, zzz510, zzz511, zzz512000, zzz513, zzz514, zzz31, Succ(zzz512000), zzz342000, h)
new_mkVBalBranch3MkVBalBranch215(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, Succ(zzz660), h) → new_mkVBalBranch3MkVBalBranch19(zzz340, zzz341, zzz34200, zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, new_primPlusNat2(new_primMulNat0(zzz34200), Succ(zzz34200)), h)
new_mkVBalBranch3MkVBalBranch216(zzz1105, zzz1106, zzz1107, zzz1108, zzz1109, zzz1110, zzz1111, zzz1112, zzz1113, zzz1114, zzz1115, Zero, Zero, ba) → new_mkVBalBranch3MkVBalBranch222(zzz1105, zzz1106, zzz1107, zzz1108, zzz1109, zzz1110, zzz1111, zzz1112, zzz1113, zzz1114, zzz1115, ba)
new_mkVBalBranch3MkVBalBranch233(zzz473, zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, zzz481, zzz482, bh) → new_mkVBalBranch3MkVBalBranch121(zzz473, zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, zzz481, zzz482, new_primMulNat1(zzz475), bh)
new_mkVBalBranch3MkVBalBranch215(zzz340, zzz341, Pos(Succ(Succ(zzz342000))), zzz343, zzz344, zzz510, zzz511, Zero, zzz513, zzz514, zzz31, Succ(Zero), h) → new_mkVBalBranch3MkVBalBranch217(zzz340, zzz341, Succ(zzz342000), zzz343, zzz344, zzz510, zzz511, zzz513, zzz514, zzz31, Zero, zzz342000, h)
new_mkVBalBranch3MkVBalBranch119(zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, zzz1125, zzz1126, zzz1127, zzz1128, zzz1129, Succ(zzz12130), bd) → new_mkVBalBranch3MkVBalBranch120(zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, zzz1125, Succ(zzz1126), zzz1127, zzz1128, zzz1129, Succ(Succ(zzz1126)), Succ(zzz12130), bd)
new_mkVBalBranch3MkVBalBranch18(zzz340, zzz341, zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, Zero, h) → new_mkVBalBranch3MkVBalBranch115(zzz340, zzz341, Zero, zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, Zero, Succ(zzz51200), h)

The TRS R consists of the following rules:

new_primPlusNat1(Zero) → Zero
new_primMulNat0(zzz6200) → new_primPlusNat3(Succ(new_primPlusNat3(new_primPlusNat1(zzz6200), zzz6200)), Succ(zzz6200))
new_primPlusNat2(Succ(zzz900), Succ(zzz9100)) → Succ(Succ(new_primPlusNat2(zzz900, zzz9100)))
new_primPlusNat3(zzz90, Succ(zzz910)) → Succ(Succ(new_primPlusNat2(zzz90, zzz910)))
new_primPlusNat3(zzz90, Zero) → Succ(zzz90)
new_primMulNat1(zzz34200) → new_primPlusNat2(new_primMulNat0(zzz34200), Succ(zzz34200))
new_primPlusNat2(Zero, Zero) → Zero
new_primPlusNat1(Succ(zzz62000)) → Succ(Succ(new_primPlusNat1(zzz62000)))
new_primPlusNat2(Succ(zzz900), Zero) → Succ(zzz900)
new_primPlusNat2(Zero, Succ(zzz9100)) → Succ(zzz9100)

The set Q consists of the following terms:

new_primPlusNat2(Zero, Succ(x0))
new_primMulNat1(x0)
new_primMulNat0(x0)
new_primPlusNat3(x0, Succ(x1))
new_primPlusNat2(Succ(x0), Succ(x1))
new_primPlusNat3(x0, Zero)
new_primPlusNat1(Zero)
new_primPlusNat2(Zero, Zero)
new_primPlusNat1(Succ(x0))
new_primPlusNat2(Succ(x0), Zero)

We have to consider all minimal (P,Q,R)-chains.
By rewriting [15] the rule new_mkVBalBranch3MkVBalBranch218(zzz461, zzz462, zzz463, zzz464, zzz465, zzz466, zzz467, zzz468, zzz469, zzz470, zzz471, bb) → new_mkVBalBranch3MkVBalBranch110(zzz461, zzz462, zzz463, zzz464, zzz465, zzz466, zzz467, zzz468, zzz469, zzz470, zzz471, new_primMulNat1(zzz463), bb) at position [11] we obtained the following new rules:

new_mkVBalBranch3MkVBalBranch218(zzz461, zzz462, zzz463, zzz464, zzz465, zzz466, zzz467, zzz468, zzz469, zzz470, zzz471, bb) → new_mkVBalBranch3MkVBalBranch110(zzz461, zzz462, zzz463, zzz464, zzz465, zzz466, zzz467, zzz468, zzz469, zzz470, zzz471, new_primPlusNat2(new_primMulNat0(zzz463), Succ(zzz463)), bb)



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

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

new_mkVBalBranch3MkVBalBranch215(zzz340, zzz341, Neg(zzz3420), zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, Zero, h) → new_mkVBalBranch3MkVBalBranch221(zzz340, zzz341, zzz3420, zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, h)
new_mkVBalBranch3MkVBalBranch225(zzz498, zzz499, zzz500, zzz501, zzz502, zzz503, zzz504, zzz505, zzz506, zzz507, Zero, Zero, bg) → new_mkVBalBranch3MkVBalBranch230(zzz498, zzz499, zzz500, zzz501, zzz502, zzz503, zzz504, zzz505, zzz506, zzz507, bg)
new_mkVBalBranch3MkVBalBranch18(zzz340, zzz341, zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, Succ(zzz1480), h) → new_mkVBalBranch3MkVBalBranch115(zzz340, zzz341, Zero, zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, Succ(zzz1480), Succ(zzz51200), h)
new_mkVBalBranch0(zzz31, Branch(zzz510, zzz511, Neg(Zero), zzz513, zzz514), Branch(zzz340, zzz341, Pos(Succ(zzz34200)), zzz343, zzz344), h) → new_mkVBalBranch0(zzz31, Branch(zzz510, zzz511, Neg(Zero), zzz513, zzz514), zzz343, h)
new_mkVBalBranch3MkVBalBranch215(zzz340, zzz341, Pos(Succ(Succ(zzz342000))), zzz343, zzz344, zzz510, zzz511, Succ(zzz512000), zzz513, zzz514, zzz31, Succ(Succ(zzz6600)), h) → new_mkVBalBranch3MkVBalBranch216(zzz340, zzz341, Succ(zzz342000), zzz343, zzz344, zzz510, zzz511, zzz512000, zzz513, zzz514, zzz31, Succ(Succ(new_primPlusNat2(zzz6600, zzz512000))), zzz342000, h)
new_mkVBalBranch3MkVBalBranch223(zzz340, zzz341, Neg(Succ(Succ(Succ(zzz3420000)))), zzz343, zzz344, zzz510, zzz511, Zero, zzz513, zzz514, zzz31, Succ(Succ(zzz6700)), h) → new_mkVBalBranch3MkVBalBranch225(zzz340, zzz341, Succ(Succ(zzz3420000)), zzz343, zzz344, zzz510, zzz511, zzz513, zzz514, zzz31, Succ(zzz3420000), Succ(zzz6700), h)
new_mkVBalBranch3MkVBalBranch220(zzz340, zzz341, zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, h) → new_mkVBalBranch0(zzz31, zzz514, Branch(zzz340, zzz341, Pos(Zero), zzz343, zzz344), h)
new_mkVBalBranch3MkVBalBranch120(zzz2050, zzz2051, zzz2052, zzz2053, zzz2054, zzz2055, zzz2056, zzz2057, zzz2058, zzz2059, zzz2060, Zero, Succ(zzz20620), be) → new_mkVBalBranch0(zzz2060, zzz2059, Branch(zzz2050, zzz2051, Neg(Succ(zzz2052)), zzz2053, zzz2054), be)
new_mkVBalBranch3MkVBalBranch121(zzz473, zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, zzz481, zzz482, Succ(zzz7390), bh) → new_mkVBalBranch3MkVBalBranch115(zzz473, zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, Zero, zzz480, zzz481, zzz482, Succ(zzz7390), Succ(Zero), bh)
new_mkVBalBranch0(zzz31, Branch(zzz510, zzz511, Pos(Zero), zzz513, zzz514), Branch(zzz340, zzz341, Pos(Succ(zzz34200)), zzz343, zzz344), h) → new_mkVBalBranch0(zzz31, Branch(zzz510, zzz511, Pos(Zero), zzz513, zzz514), zzz343, h)
new_mkVBalBranch3MkVBalBranch228(zzz340, zzz341, zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, h) → new_mkVBalBranch0(zzz31, Branch(zzz510, zzz511, Neg(Succ(zzz51200)), zzz513, zzz514), zzz343, h)
new_mkVBalBranch3MkVBalBranch215(zzz340, zzz341, Pos(Succ(Zero)), zzz343, zzz344, zzz510, zzz511, Zero, zzz513, zzz514, zzz31, Zero, h) → new_mkVBalBranch3MkVBalBranch219(zzz340, zzz341, zzz343, zzz344, zzz510, zzz511, Zero, zzz513, zzz514, zzz31, h)
new_mkVBalBranch3MkVBalBranch223(zzz340, zzz341, Neg(Succ(Succ(Zero))), zzz343, zzz344, zzz510, zzz511, Succ(zzz512000), zzz513, zzz514, zzz31, Succ(Succ(zzz6700)), h) → new_mkVBalBranch3MkVBalBranch224(zzz340, zzz341, Succ(Zero), zzz343, zzz344, zzz510, zzz511, zzz512000, zzz513, zzz514, zzz31, Zero, Succ(Succ(new_primPlusNat2(zzz6700, zzz512000))), h)
new_mkVBalBranch3MkVBalBranch223(zzz340, zzz341, Neg(Succ(Succ(Zero))), zzz343, zzz344, zzz510, zzz511, Zero, zzz513, zzz514, zzz31, Succ(Zero), h) → new_mkVBalBranch3MkVBalBranch225(zzz340, zzz341, Succ(Zero), zzz343, zzz344, zzz510, zzz511, zzz513, zzz514, zzz31, Zero, Zero, h)
new_mkVBalBranch3MkVBalBranch224(zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, zzz1125, zzz1126, zzz1127, zzz1128, zzz1129, Succ(zzz11300), Succ(zzz11310), bd) → new_mkVBalBranch3MkVBalBranch224(zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, zzz1125, zzz1126, zzz1127, zzz1128, zzz1129, zzz11300, zzz11310, bd)
new_mkVBalBranch0(zzz31, Branch(zzz510, zzz511, Pos(Succ(zzz51200)), zzz513, zzz514), Branch(zzz340, zzz341, zzz342, zzz343, zzz344), h) → new_mkVBalBranch3MkVBalBranch215(zzz340, zzz341, zzz342, zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, new_primPlusNat3(Succ(new_primPlusNat3(new_primPlusNat1(zzz51200), zzz51200)), Succ(zzz51200)), h)
new_mkVBalBranch3MkVBalBranch217(zzz473, zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, zzz481, zzz482, Zero, Succ(zzz4840), bh) → new_mkVBalBranch0(zzz482, Branch(zzz478, zzz479, Pos(Succ(Zero)), zzz480, zzz481), zzz476, bh)
new_mkVBalBranch3MkVBalBranch215(zzz340, zzz341, Pos(Succ(Succ(zzz342000))), zzz343, zzz344, zzz510, zzz511, Succ(zzz512000), zzz513, zzz514, zzz31, Zero, h) → new_mkVBalBranch3MkVBalBranch216(zzz340, zzz341, Succ(zzz342000), zzz343, zzz344, zzz510, zzz511, zzz512000, zzz513, zzz514, zzz31, zzz512000, zzz342000, h)
new_mkVBalBranch3MkVBalBranch110(zzz461, zzz462, zzz463, zzz464, zzz465, zzz466, zzz467, zzz468, zzz469, zzz470, zzz471, Succ(zzz5800), bb) → new_mkVBalBranch3MkVBalBranch115(zzz461, zzz462, zzz463, zzz464, zzz465, zzz466, zzz467, Succ(zzz468), zzz469, zzz470, zzz471, Succ(zzz5800), Succ(Succ(zzz468)), bb)
new_mkVBalBranch3MkVBalBranch223(zzz340, zzz341, Neg(Succ(Zero)), zzz343, zzz344, zzz510, zzz511, Zero, zzz513, zzz514, zzz31, Zero, h) → new_mkVBalBranch3MkVBalBranch118(zzz340, zzz341, Zero, zzz343, zzz344, zzz510, zzz511, zzz513, zzz514, zzz31, new_primPlusNat2(new_primMulNat0(Zero), Succ(Zero)), h)
new_mkVBalBranch3MkVBalBranch227(zzz486, zzz487, zzz488, zzz489, zzz490, zzz491, zzz492, zzz493, zzz494, zzz495, zzz496, bf) → new_mkVBalBranch0(zzz496, Branch(zzz491, zzz492, Neg(Succ(Succ(zzz493))), zzz494, zzz495), zzz489, bf)
new_mkVBalBranch3MkVBalBranch215(zzz340, zzz341, Pos(Zero), zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, Succ(zzz660), h) → new_mkVBalBranch0(zzz31, zzz514, Branch(zzz340, zzz341, Pos(Zero), zzz343, zzz344), h)
new_mkVBalBranch0(zzz31, Branch(zzz510, zzz511, Pos(Zero), zzz513, zzz514), Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), h) → new_mkVBalBranch3MkVBalBranch116(zzz340, zzz341, zzz34200, zzz343, zzz344, zzz510, zzz511, zzz513, zzz514, zzz31, new_primPlusNat2(new_primMulNat0(zzz34200), Succ(zzz34200)), h)
new_mkVBalBranch3MkVBalBranch223(zzz340, zzz341, Neg(Zero), zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, Succ(zzz670), h) → new_mkVBalBranch0(zzz31, Branch(zzz510, zzz511, Neg(Succ(zzz51200)), zzz513, zzz514), zzz343, h)
new_mkVBalBranch3MkVBalBranch216(zzz1105, zzz1106, zzz1107, zzz1108, zzz1109, zzz1110, zzz1111, zzz1112, zzz1113, zzz1114, zzz1115, Zero, Succ(zzz11170), ba) → new_mkVBalBranch0(zzz1115, Branch(zzz1110, zzz1111, Pos(Succ(Succ(zzz1112))), zzz1113, zzz1114), zzz1108, ba)
new_mkVBalBranch3MkVBalBranch217(zzz473, zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, zzz481, zzz482, Succ(zzz4830), Zero, bh) → new_mkVBalBranch3MkVBalBranch121(zzz473, zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, zzz481, zzz482, new_primMulNat1(zzz475), bh)
new_mkVBalBranch3MkVBalBranch222(zzz461, zzz462, zzz463, zzz464, zzz465, zzz466, zzz467, zzz468, zzz469, zzz470, zzz471, bb) → new_mkVBalBranch3MkVBalBranch110(zzz461, zzz462, zzz463, zzz464, zzz465, zzz466, zzz467, zzz468, zzz469, zzz470, zzz471, new_primMulNat1(zzz463), bb)
new_mkVBalBranch3MkVBalBranch115(zzz1986, zzz1987, zzz1988, zzz1989, zzz1990, zzz1991, zzz1992, zzz1993, zzz1994, zzz1995, zzz1996, Zero, Succ(zzz19980), bc) → new_mkVBalBranch0(zzz1996, zzz1995, Branch(zzz1986, zzz1987, Pos(Succ(zzz1988)), zzz1989, zzz1990), bc)
new_mkVBalBranch0(zzz31, Branch(zzz510, zzz511, Neg(Zero), zzz513, zzz514), Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), h) → new_mkVBalBranch3MkVBalBranch117(zzz340, zzz341, zzz34200, zzz343, zzz344, zzz510, zzz511, zzz513, zzz514, zzz31, new_primPlusNat2(new_primMulNat0(zzz34200), Succ(zzz34200)), h)
new_mkVBalBranch3MkVBalBranch223(zzz340, zzz341, Neg(Zero), zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, Zero, h) → new_mkVBalBranch3MkVBalBranch228(zzz340, zzz341, zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, h)
new_mkVBalBranch3MkVBalBranch122(zzz340, zzz341, zzz34200, zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, h) → new_mkVBalBranch0(zzz31, zzz514, Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), h)
new_mkVBalBranch3MkVBalBranch217(zzz473, zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, zzz481, zzz482, Succ(zzz4830), Succ(zzz4840), bh) → new_mkVBalBranch3MkVBalBranch217(zzz473, zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, zzz481, zzz482, zzz4830, zzz4840, bh)
new_mkVBalBranch3MkVBalBranch116(zzz340, zzz341, zzz34200, zzz343, zzz344, zzz510, zzz511, zzz513, zzz514, zzz31, Succ(zzz1200), h) → new_mkVBalBranch0(zzz31, zzz514, Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), h)
new_mkVBalBranch3MkVBalBranch110(zzz461, zzz462, zzz463, zzz464, zzz465, zzz466, zzz467, zzz468, zzz469, zzz470, zzz471, Zero, bb) → new_mkVBalBranch3MkVBalBranch115(zzz461, zzz462, zzz463, zzz464, zzz465, zzz466, zzz467, Succ(zzz468), zzz469, zzz470, zzz471, Zero, Succ(Succ(zzz468)), bb)
new_mkVBalBranch3MkVBalBranch225(zzz498, zzz499, zzz500, zzz501, zzz502, zzz503, zzz504, zzz505, zzz506, zzz507, Zero, Succ(zzz5090), bg) → new_mkVBalBranch0(zzz507, Branch(zzz503, zzz504, Neg(Succ(Zero)), zzz505, zzz506), zzz501, bg)
new_mkVBalBranch3MkVBalBranch223(zzz340, zzz341, Neg(Succ(Succ(Succ(zzz3420000)))), zzz343, zzz344, zzz510, zzz511, Zero, zzz513, zzz514, zzz31, Succ(Zero), h) → new_mkVBalBranch3MkVBalBranch225(zzz340, zzz341, Succ(Succ(zzz3420000)), zzz343, zzz344, zzz510, zzz511, zzz513, zzz514, zzz31, Succ(zzz3420000), Zero, h)
new_mkVBalBranch3MkVBalBranch121(zzz473, zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, zzz481, zzz482, Zero, bh) → new_mkVBalBranch3MkVBalBranch115(zzz473, zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, Zero, zzz480, zzz481, zzz482, Zero, Succ(Zero), bh)
new_mkVBalBranch3MkVBalBranch215(zzz340, zzz341, Pos(Succ(Zero)), zzz343, zzz344, zzz510, zzz511, Succ(zzz512000), zzz513, zzz514, zzz31, Zero, h) → new_mkVBalBranch3MkVBalBranch218(zzz340, zzz341, Zero, zzz343, zzz344, zzz510, zzz511, zzz512000, zzz513, zzz514, zzz31, h)
new_mkVBalBranch3MkVBalBranch223(zzz340, zzz341, Neg(Succ(Zero)), zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, Succ(zzz670), h) → new_mkVBalBranch0(zzz31, Branch(zzz510, zzz511, Neg(Succ(zzz51200)), zzz513, zzz514), zzz343, h)
new_mkVBalBranch3MkVBalBranch225(zzz498, zzz499, zzz500, zzz501, zzz502, zzz503, zzz504, zzz505, zzz506, zzz507, Succ(zzz5080), Zero, bg) → new_mkVBalBranch3MkVBalBranch118(zzz498, zzz499, zzz500, zzz501, zzz502, zzz503, zzz504, zzz505, zzz506, zzz507, new_primPlusNat2(new_primMulNat0(zzz500), Succ(zzz500)), bg)
new_mkVBalBranch3MkVBalBranch229(zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, zzz1125, zzz1126, zzz1127, zzz1128, zzz1129, bd) → new_mkVBalBranch3MkVBalBranch119(zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, zzz1125, zzz1126, zzz1127, zzz1128, zzz1129, new_primPlusNat2(new_primMulNat0(zzz1121), Succ(zzz1121)), bd)
new_mkVBalBranch3MkVBalBranch223(zzz340, zzz341, Neg(Succ(Zero)), zzz343, zzz344, zzz510, zzz511, Succ(zzz512000), zzz513, zzz514, zzz31, Zero, h) → new_mkVBalBranch3MkVBalBranch227(zzz340, zzz341, Zero, zzz343, zzz344, zzz510, zzz511, zzz512000, zzz513, zzz514, zzz31, h)
new_mkVBalBranch3MkVBalBranch215(zzz340, zzz341, Pos(Succ(Zero)), zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, Succ(zzz660), h) → new_mkVBalBranch3MkVBalBranch18(zzz340, zzz341, zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, new_primMulNat1(Zero), h)
new_mkVBalBranch3MkVBalBranch215(zzz340, zzz341, Pos(Succ(Succ(zzz342000))), zzz343, zzz344, zzz510, zzz511, Zero, zzz513, zzz514, zzz31, Succ(Succ(zzz6600)), h) → new_mkVBalBranch3MkVBalBranch217(zzz340, zzz341, Succ(zzz342000), zzz343, zzz344, zzz510, zzz511, zzz513, zzz514, zzz31, Succ(zzz6600), zzz342000, h)
new_mkVBalBranch3MkVBalBranch223(zzz340, zzz341, Neg(Succ(Succ(zzz342000))), zzz343, zzz344, zzz510, zzz511, Succ(zzz512000), zzz513, zzz514, zzz31, Zero, h) → new_mkVBalBranch3MkVBalBranch224(zzz340, zzz341, Succ(zzz342000), zzz343, zzz344, zzz510, zzz511, zzz512000, zzz513, zzz514, zzz31, zzz342000, zzz512000, h)
new_mkVBalBranch3MkVBalBranch226(zzz340, zzz341, zzz3420, zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, h) → new_mkVBalBranch0(zzz31, Branch(zzz510, zzz511, Neg(Succ(zzz51200)), zzz513, zzz514), zzz343, h)
new_mkVBalBranch3MkVBalBranch218(zzz461, zzz462, zzz463, zzz464, zzz465, zzz466, zzz467, zzz468, zzz469, zzz470, zzz471, bb) → new_mkVBalBranch3MkVBalBranch110(zzz461, zzz462, zzz463, zzz464, zzz465, zzz466, zzz467, zzz468, zzz469, zzz470, zzz471, new_primPlusNat2(new_primMulNat0(zzz463), Succ(zzz463)), bb)
new_mkVBalBranch3MkVBalBranch117(zzz340, zzz341, zzz34200, zzz343, zzz344, zzz510, zzz511, zzz513, zzz514, zzz31, Succ(zzz1240), h) → new_mkVBalBranch0(zzz31, zzz514, Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), h)
new_mkVBalBranch0(zzz31, Branch(zzz510, zzz511, Neg(Succ(zzz51200)), zzz513, zzz514), Branch(zzz340, zzz341, zzz342, zzz343, zzz344), h) → new_mkVBalBranch3MkVBalBranch223(zzz340, zzz341, zzz342, zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, new_primPlusNat3(Succ(new_primPlusNat3(new_primPlusNat1(zzz51200), zzz51200)), Succ(zzz51200)), h)
new_mkVBalBranch3MkVBalBranch217(zzz473, zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, zzz481, zzz482, Zero, Zero, bh) → new_mkVBalBranch3MkVBalBranch233(zzz473, zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, zzz481, zzz482, bh)
new_mkVBalBranch3MkVBalBranch120(zzz2050, zzz2051, zzz2052, zzz2053, zzz2054, zzz2055, zzz2056, zzz2057, zzz2058, zzz2059, zzz2060, Succ(zzz20610), Succ(zzz20620), be) → new_mkVBalBranch3MkVBalBranch120(zzz2050, zzz2051, zzz2052, zzz2053, zzz2054, zzz2055, zzz2056, zzz2057, zzz2058, zzz2059, zzz2060, zzz20610, zzz20620, be)
new_mkVBalBranch3MkVBalBranch221(zzz340, zzz341, Succ(zzz34200), zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, h) → new_mkVBalBranch3MkVBalBranch19(zzz340, zzz341, zzz34200, zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, new_primPlusNat2(new_primPlusNat3(Succ(new_primPlusNat3(new_primPlusNat1(zzz34200), zzz34200)), Succ(zzz34200)), Succ(zzz34200)), h)
new_mkVBalBranch3MkVBalBranch223(zzz340, zzz341, Pos(zzz3420), zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, Succ(zzz670), h) → new_mkVBalBranch0(zzz31, Branch(zzz510, zzz511, Neg(Succ(zzz51200)), zzz513, zzz514), zzz343, h)
new_mkVBalBranch3MkVBalBranch216(zzz1105, zzz1106, zzz1107, zzz1108, zzz1109, zzz1110, zzz1111, zzz1112, zzz1113, zzz1114, zzz1115, Succ(zzz11160), Succ(zzz11170), ba) → new_mkVBalBranch3MkVBalBranch216(zzz1105, zzz1106, zzz1107, zzz1108, zzz1109, zzz1110, zzz1111, zzz1112, zzz1113, zzz1114, zzz1115, zzz11160, zzz11170, ba)
new_mkVBalBranch3MkVBalBranch19(zzz340, zzz341, zzz34200, zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, Zero, h) → new_mkVBalBranch3MkVBalBranch122(zzz340, zzz341, zzz34200, zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, h)
new_mkVBalBranch3MkVBalBranch223(zzz340, zzz341, Neg(Succ(Succ(Succ(zzz3420000)))), zzz343, zzz344, zzz510, zzz511, Succ(zzz512000), zzz513, zzz514, zzz31, Succ(Zero), h) → new_mkVBalBranch3MkVBalBranch224(zzz340, zzz341, Succ(Succ(zzz3420000)), zzz343, zzz344, zzz510, zzz511, zzz512000, zzz513, zzz514, zzz31, Succ(zzz3420000), Succ(zzz512000), h)
new_mkVBalBranch3MkVBalBranch215(zzz340, zzz341, Pos(Succ(Succ(zzz342000))), zzz343, zzz344, zzz510, zzz511, Zero, zzz513, zzz514, zzz31, Zero, h) → new_mkVBalBranch0(zzz31, Branch(zzz510, zzz511, Pos(Succ(Zero)), zzz513, zzz514), zzz343, h)
new_mkVBalBranch3MkVBalBranch225(zzz498, zzz499, zzz500, zzz501, zzz502, zzz503, zzz504, zzz505, zzz506, zzz507, Succ(zzz5080), Succ(zzz5090), bg) → new_mkVBalBranch3MkVBalBranch225(zzz498, zzz499, zzz500, zzz501, zzz502, zzz503, zzz504, zzz505, zzz506, zzz507, zzz5080, zzz5090, bg)
new_mkVBalBranch3MkVBalBranch19(zzz340, zzz341, zzz34200, zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, Succ(zzz1410), h) → new_mkVBalBranch0(zzz31, zzz514, Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), h)
new_mkVBalBranch3MkVBalBranch224(zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, zzz1125, zzz1126, zzz1127, zzz1128, zzz1129, Succ(zzz11300), Zero, bd) → new_mkVBalBranch3MkVBalBranch119(zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, zzz1125, zzz1126, zzz1127, zzz1128, zzz1129, new_primPlusNat2(new_primMulNat0(zzz1121), Succ(zzz1121)), bd)
new_mkVBalBranch3MkVBalBranch224(zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, zzz1125, zzz1126, zzz1127, zzz1128, zzz1129, Zero, Succ(zzz11310), bd) → new_mkVBalBranch3MkVBalBranch227(zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, zzz1125, zzz1126, zzz1127, zzz1128, zzz1129, bd)
new_mkVBalBranch3MkVBalBranch224(zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, zzz1125, zzz1126, zzz1127, zzz1128, zzz1129, Zero, Zero, bd) → new_mkVBalBranch3MkVBalBranch229(zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, zzz1125, zzz1126, zzz1127, zzz1128, zzz1129, bd)
new_mkVBalBranch3MkVBalBranch223(zzz340, zzz341, Neg(Succ(Succ(Zero))), zzz343, zzz344, zzz510, zzz511, Succ(zzz512000), zzz513, zzz514, zzz31, Succ(Zero), h) → new_mkVBalBranch3MkVBalBranch224(zzz340, zzz341, Succ(Zero), zzz343, zzz344, zzz510, zzz511, zzz512000, zzz513, zzz514, zzz31, Zero, Succ(zzz512000), h)
new_mkVBalBranch3MkVBalBranch223(zzz340, zzz341, Pos(zzz3420), zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, Zero, h) → new_mkVBalBranch3MkVBalBranch226(zzz340, zzz341, zzz3420, zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, h)
new_mkVBalBranch3MkVBalBranch223(zzz340, zzz341, Neg(Succ(Succ(zzz342000))), zzz343, zzz344, zzz510, zzz511, Zero, zzz513, zzz514, zzz31, Zero, h) → new_mkVBalBranch3MkVBalBranch118(zzz340, zzz341, Succ(zzz342000), zzz343, zzz344, zzz510, zzz511, zzz513, zzz514, zzz31, new_primPlusNat2(new_primMulNat0(Succ(zzz342000)), Succ(Succ(zzz342000))), h)
new_mkVBalBranch3MkVBalBranch230(zzz498, zzz499, zzz500, zzz501, zzz502, zzz503, zzz504, zzz505, zzz506, zzz507, bg) → new_mkVBalBranch3MkVBalBranch118(zzz498, zzz499, zzz500, zzz501, zzz502, zzz503, zzz504, zzz505, zzz506, zzz507, new_primPlusNat2(new_primMulNat0(zzz500), Succ(zzz500)), bg)
new_mkVBalBranch3MkVBalBranch223(zzz340, zzz341, Neg(Succ(Succ(Succ(zzz3420000)))), zzz343, zzz344, zzz510, zzz511, Succ(zzz512000), zzz513, zzz514, zzz31, Succ(Succ(zzz6700)), h) → new_mkVBalBranch3MkVBalBranch224(zzz340, zzz341, Succ(Succ(zzz3420000)), zzz343, zzz344, zzz510, zzz511, zzz512000, zzz513, zzz514, zzz31, Succ(zzz3420000), Succ(Succ(new_primPlusNat2(zzz6700, zzz512000))), h)
new_mkVBalBranch3MkVBalBranch223(zzz340, zzz341, Neg(Succ(Succ(Zero))), zzz343, zzz344, zzz510, zzz511, Zero, zzz513, zzz514, zzz31, Succ(Succ(zzz6700)), h) → new_mkVBalBranch3MkVBalBranch225(zzz340, zzz341, Succ(Zero), zzz343, zzz344, zzz510, zzz511, zzz513, zzz514, zzz31, Zero, Succ(zzz6700), h)
new_mkVBalBranch3MkVBalBranch215(zzz340, zzz341, Pos(Zero), zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, Zero, h) → new_mkVBalBranch3MkVBalBranch220(zzz340, zzz341, zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, h)
new_mkVBalBranch3MkVBalBranch115(zzz1986, zzz1987, zzz1988, zzz1989, zzz1990, zzz1991, zzz1992, zzz1993, zzz1994, zzz1995, zzz1996, Succ(zzz19970), Succ(zzz19980), bc) → new_mkVBalBranch3MkVBalBranch115(zzz1986, zzz1987, zzz1988, zzz1989, zzz1990, zzz1991, zzz1992, zzz1993, zzz1994, zzz1995, zzz1996, zzz19970, zzz19980, bc)
new_mkVBalBranch3MkVBalBranch215(zzz340, zzz341, Neg(Zero), zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, Succ(zzz660), h) → new_mkVBalBranch0(zzz31, zzz514, Branch(zzz340, zzz341, Neg(Zero), zzz343, zzz344), h)
new_mkVBalBranch3MkVBalBranch118(zzz498, zzz499, zzz500, zzz501, zzz502, zzz503, zzz504, zzz505, zzz506, zzz507, Succ(zzz8040), bg) → new_mkVBalBranch3MkVBalBranch120(zzz498, zzz499, zzz500, zzz501, zzz502, zzz503, zzz504, Zero, zzz505, zzz506, zzz507, Succ(Zero), Succ(zzz8040), bg)
new_mkVBalBranch3MkVBalBranch216(zzz1105, zzz1106, zzz1107, zzz1108, zzz1109, zzz1110, zzz1111, zzz1112, zzz1113, zzz1114, zzz1115, Succ(zzz11160), Zero, ba) → new_mkVBalBranch3MkVBalBranch218(zzz1105, zzz1106, zzz1107, zzz1108, zzz1109, zzz1110, zzz1111, zzz1112, zzz1113, zzz1114, zzz1115, ba)
new_mkVBalBranch3MkVBalBranch215(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, Succ(zzz660), h) → new_mkVBalBranch3MkVBalBranch19(zzz340, zzz341, zzz34200, zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, new_primPlusNat2(new_primMulNat0(zzz34200), Succ(zzz34200)), h)
new_mkVBalBranch3MkVBalBranch215(zzz340, zzz341, Pos(Succ(Succ(zzz342000))), zzz343, zzz344, zzz510, zzz511, Succ(zzz512000), zzz513, zzz514, zzz31, Succ(Zero), h) → new_mkVBalBranch3MkVBalBranch216(zzz340, zzz341, Succ(zzz342000), zzz343, zzz344, zzz510, zzz511, zzz512000, zzz513, zzz514, zzz31, Succ(zzz512000), zzz342000, h)
new_mkVBalBranch3MkVBalBranch219(zzz340, zzz341, zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, h) → new_mkVBalBranch3MkVBalBranch18(zzz340, zzz341, zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, new_primMulNat1(Zero), h)
new_mkVBalBranch3MkVBalBranch221(zzz340, zzz341, Zero, zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, h) → new_mkVBalBranch0(zzz31, zzz514, Branch(zzz340, zzz341, Neg(Zero), zzz343, zzz344), h)
new_mkVBalBranch3MkVBalBranch216(zzz1105, zzz1106, zzz1107, zzz1108, zzz1109, zzz1110, zzz1111, zzz1112, zzz1113, zzz1114, zzz1115, Zero, Zero, ba) → new_mkVBalBranch3MkVBalBranch222(zzz1105, zzz1106, zzz1107, zzz1108, zzz1109, zzz1110, zzz1111, zzz1112, zzz1113, zzz1114, zzz1115, ba)
new_mkVBalBranch3MkVBalBranch233(zzz473, zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, zzz481, zzz482, bh) → new_mkVBalBranch3MkVBalBranch121(zzz473, zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, zzz481, zzz482, new_primMulNat1(zzz475), bh)
new_mkVBalBranch3MkVBalBranch215(zzz340, zzz341, Pos(Succ(Succ(zzz342000))), zzz343, zzz344, zzz510, zzz511, Zero, zzz513, zzz514, zzz31, Succ(Zero), h) → new_mkVBalBranch3MkVBalBranch217(zzz340, zzz341, Succ(zzz342000), zzz343, zzz344, zzz510, zzz511, zzz513, zzz514, zzz31, Zero, zzz342000, h)
new_mkVBalBranch3MkVBalBranch18(zzz340, zzz341, zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, Zero, h) → new_mkVBalBranch3MkVBalBranch115(zzz340, zzz341, Zero, zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, Zero, Succ(zzz51200), h)
new_mkVBalBranch3MkVBalBranch119(zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, zzz1125, zzz1126, zzz1127, zzz1128, zzz1129, Succ(zzz12130), bd) → new_mkVBalBranch3MkVBalBranch120(zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, zzz1125, Succ(zzz1126), zzz1127, zzz1128, zzz1129, Succ(Succ(zzz1126)), Succ(zzz12130), bd)

The TRS R consists of the following rules:

new_primPlusNat1(Zero) → Zero
new_primMulNat0(zzz6200) → new_primPlusNat3(Succ(new_primPlusNat3(new_primPlusNat1(zzz6200), zzz6200)), Succ(zzz6200))
new_primPlusNat2(Succ(zzz900), Succ(zzz9100)) → Succ(Succ(new_primPlusNat2(zzz900, zzz9100)))
new_primPlusNat3(zzz90, Succ(zzz910)) → Succ(Succ(new_primPlusNat2(zzz90, zzz910)))
new_primPlusNat3(zzz90, Zero) → Succ(zzz90)
new_primMulNat1(zzz34200) → new_primPlusNat2(new_primMulNat0(zzz34200), Succ(zzz34200))
new_primPlusNat2(Zero, Zero) → Zero
new_primPlusNat1(Succ(zzz62000)) → Succ(Succ(new_primPlusNat1(zzz62000)))
new_primPlusNat2(Succ(zzz900), Zero) → Succ(zzz900)
new_primPlusNat2(Zero, Succ(zzz9100)) → Succ(zzz9100)

The set Q consists of the following terms:

new_primPlusNat2(Zero, Succ(x0))
new_primMulNat1(x0)
new_primMulNat0(x0)
new_primPlusNat3(x0, Succ(x1))
new_primPlusNat2(Succ(x0), Succ(x1))
new_primPlusNat3(x0, Zero)
new_primPlusNat1(Zero)
new_primPlusNat2(Zero, Zero)
new_primPlusNat1(Succ(x0))
new_primPlusNat2(Succ(x0), Zero)

We have to consider all minimal (P,Q,R)-chains.
By rewriting [15] the rule new_mkVBalBranch3MkVBalBranch222(zzz461, zzz462, zzz463, zzz464, zzz465, zzz466, zzz467, zzz468, zzz469, zzz470, zzz471, bb) → new_mkVBalBranch3MkVBalBranch110(zzz461, zzz462, zzz463, zzz464, zzz465, zzz466, zzz467, zzz468, zzz469, zzz470, zzz471, new_primMulNat1(zzz463), bb) at position [11] we obtained the following new rules:

new_mkVBalBranch3MkVBalBranch222(zzz461, zzz462, zzz463, zzz464, zzz465, zzz466, zzz467, zzz468, zzz469, zzz470, zzz471, bb) → new_mkVBalBranch3MkVBalBranch110(zzz461, zzz462, zzz463, zzz464, zzz465, zzz466, zzz467, zzz468, zzz469, zzz470, zzz471, new_primPlusNat2(new_primMulNat0(zzz463), Succ(zzz463)), bb)



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

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

new_mkVBalBranch3MkVBalBranch225(zzz498, zzz499, zzz500, zzz501, zzz502, zzz503, zzz504, zzz505, zzz506, zzz507, Zero, Zero, bg) → new_mkVBalBranch3MkVBalBranch230(zzz498, zzz499, zzz500, zzz501, zzz502, zzz503, zzz504, zzz505, zzz506, zzz507, bg)
new_mkVBalBranch3MkVBalBranch215(zzz340, zzz341, Neg(zzz3420), zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, Zero, h) → new_mkVBalBranch3MkVBalBranch221(zzz340, zzz341, zzz3420, zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, h)
new_mkVBalBranch3MkVBalBranch18(zzz340, zzz341, zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, Succ(zzz1480), h) → new_mkVBalBranch3MkVBalBranch115(zzz340, zzz341, Zero, zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, Succ(zzz1480), Succ(zzz51200), h)
new_mkVBalBranch3MkVBalBranch215(zzz340, zzz341, Pos(Succ(Succ(zzz342000))), zzz343, zzz344, zzz510, zzz511, Succ(zzz512000), zzz513, zzz514, zzz31, Succ(Succ(zzz6600)), h) → new_mkVBalBranch3MkVBalBranch216(zzz340, zzz341, Succ(zzz342000), zzz343, zzz344, zzz510, zzz511, zzz512000, zzz513, zzz514, zzz31, Succ(Succ(new_primPlusNat2(zzz6600, zzz512000))), zzz342000, h)
new_mkVBalBranch0(zzz31, Branch(zzz510, zzz511, Neg(Zero), zzz513, zzz514), Branch(zzz340, zzz341, Pos(Succ(zzz34200)), zzz343, zzz344), h) → new_mkVBalBranch0(zzz31, Branch(zzz510, zzz511, Neg(Zero), zzz513, zzz514), zzz343, h)
new_mkVBalBranch3MkVBalBranch223(zzz340, zzz341, Neg(Succ(Succ(Succ(zzz3420000)))), zzz343, zzz344, zzz510, zzz511, Zero, zzz513, zzz514, zzz31, Succ(Succ(zzz6700)), h) → new_mkVBalBranch3MkVBalBranch225(zzz340, zzz341, Succ(Succ(zzz3420000)), zzz343, zzz344, zzz510, zzz511, zzz513, zzz514, zzz31, Succ(zzz3420000), Succ(zzz6700), h)
new_mkVBalBranch3MkVBalBranch120(zzz2050, zzz2051, zzz2052, zzz2053, zzz2054, zzz2055, zzz2056, zzz2057, zzz2058, zzz2059, zzz2060, Zero, Succ(zzz20620), be) → new_mkVBalBranch0(zzz2060, zzz2059, Branch(zzz2050, zzz2051, Neg(Succ(zzz2052)), zzz2053, zzz2054), be)
new_mkVBalBranch3MkVBalBranch220(zzz340, zzz341, zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, h) → new_mkVBalBranch0(zzz31, zzz514, Branch(zzz340, zzz341, Pos(Zero), zzz343, zzz344), h)
new_mkVBalBranch3MkVBalBranch222(zzz461, zzz462, zzz463, zzz464, zzz465, zzz466, zzz467, zzz468, zzz469, zzz470, zzz471, bb) → new_mkVBalBranch3MkVBalBranch110(zzz461, zzz462, zzz463, zzz464, zzz465, zzz466, zzz467, zzz468, zzz469, zzz470, zzz471, new_primPlusNat2(new_primMulNat0(zzz463), Succ(zzz463)), bb)
new_mkVBalBranch3MkVBalBranch228(zzz340, zzz341, zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, h) → new_mkVBalBranch0(zzz31, Branch(zzz510, zzz511, Neg(Succ(zzz51200)), zzz513, zzz514), zzz343, h)
new_mkVBalBranch0(zzz31, Branch(zzz510, zzz511, Pos(Zero), zzz513, zzz514), Branch(zzz340, zzz341, Pos(Succ(zzz34200)), zzz343, zzz344), h) → new_mkVBalBranch0(zzz31, Branch(zzz510, zzz511, Pos(Zero), zzz513, zzz514), zzz343, h)
new_mkVBalBranch3MkVBalBranch121(zzz473, zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, zzz481, zzz482, Succ(zzz7390), bh) → new_mkVBalBranch3MkVBalBranch115(zzz473, zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, Zero, zzz480, zzz481, zzz482, Succ(zzz7390), Succ(Zero), bh)
new_mkVBalBranch3MkVBalBranch223(zzz340, zzz341, Neg(Succ(Succ(Zero))), zzz343, zzz344, zzz510, zzz511, Succ(zzz512000), zzz513, zzz514, zzz31, Succ(Succ(zzz6700)), h) → new_mkVBalBranch3MkVBalBranch224(zzz340, zzz341, Succ(Zero), zzz343, zzz344, zzz510, zzz511, zzz512000, zzz513, zzz514, zzz31, Zero, Succ(Succ(new_primPlusNat2(zzz6700, zzz512000))), h)
new_mkVBalBranch3MkVBalBranch215(zzz340, zzz341, Pos(Succ(Zero)), zzz343, zzz344, zzz510, zzz511, Zero, zzz513, zzz514, zzz31, Zero, h) → new_mkVBalBranch3MkVBalBranch219(zzz340, zzz341, zzz343, zzz344, zzz510, zzz511, Zero, zzz513, zzz514, zzz31, h)
new_mkVBalBranch3MkVBalBranch223(zzz340, zzz341, Neg(Succ(Succ(Zero))), zzz343, zzz344, zzz510, zzz511, Zero, zzz513, zzz514, zzz31, Succ(Zero), h) → new_mkVBalBranch3MkVBalBranch225(zzz340, zzz341, Succ(Zero), zzz343, zzz344, zzz510, zzz511, zzz513, zzz514, zzz31, Zero, Zero, h)
new_mkVBalBranch3MkVBalBranch224(zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, zzz1125, zzz1126, zzz1127, zzz1128, zzz1129, Succ(zzz11300), Succ(zzz11310), bd) → new_mkVBalBranch3MkVBalBranch224(zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, zzz1125, zzz1126, zzz1127, zzz1128, zzz1129, zzz11300, zzz11310, bd)
new_mkVBalBranch3MkVBalBranch217(zzz473, zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, zzz481, zzz482, Zero, Succ(zzz4840), bh) → new_mkVBalBranch0(zzz482, Branch(zzz478, zzz479, Pos(Succ(Zero)), zzz480, zzz481), zzz476, bh)
new_mkVBalBranch0(zzz31, Branch(zzz510, zzz511, Pos(Succ(zzz51200)), zzz513, zzz514), Branch(zzz340, zzz341, zzz342, zzz343, zzz344), h) → new_mkVBalBranch3MkVBalBranch215(zzz340, zzz341, zzz342, zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, new_primPlusNat3(Succ(new_primPlusNat3(new_primPlusNat1(zzz51200), zzz51200)), Succ(zzz51200)), h)
new_mkVBalBranch3MkVBalBranch215(zzz340, zzz341, Pos(Succ(Succ(zzz342000))), zzz343, zzz344, zzz510, zzz511, Succ(zzz512000), zzz513, zzz514, zzz31, Zero, h) → new_mkVBalBranch3MkVBalBranch216(zzz340, zzz341, Succ(zzz342000), zzz343, zzz344, zzz510, zzz511, zzz512000, zzz513, zzz514, zzz31, zzz512000, zzz342000, h)
new_mkVBalBranch3MkVBalBranch110(zzz461, zzz462, zzz463, zzz464, zzz465, zzz466, zzz467, zzz468, zzz469, zzz470, zzz471, Succ(zzz5800), bb) → new_mkVBalBranch3MkVBalBranch115(zzz461, zzz462, zzz463, zzz464, zzz465, zzz466, zzz467, Succ(zzz468), zzz469, zzz470, zzz471, Succ(zzz5800), Succ(Succ(zzz468)), bb)
new_mkVBalBranch3MkVBalBranch223(zzz340, zzz341, Neg(Succ(Zero)), zzz343, zzz344, zzz510, zzz511, Zero, zzz513, zzz514, zzz31, Zero, h) → new_mkVBalBranch3MkVBalBranch118(zzz340, zzz341, Zero, zzz343, zzz344, zzz510, zzz511, zzz513, zzz514, zzz31, new_primPlusNat2(new_primMulNat0(Zero), Succ(Zero)), h)
new_mkVBalBranch3MkVBalBranch227(zzz486, zzz487, zzz488, zzz489, zzz490, zzz491, zzz492, zzz493, zzz494, zzz495, zzz496, bf) → new_mkVBalBranch0(zzz496, Branch(zzz491, zzz492, Neg(Succ(Succ(zzz493))), zzz494, zzz495), zzz489, bf)
new_mkVBalBranch0(zzz31, Branch(zzz510, zzz511, Pos(Zero), zzz513, zzz514), Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), h) → new_mkVBalBranch3MkVBalBranch116(zzz340, zzz341, zzz34200, zzz343, zzz344, zzz510, zzz511, zzz513, zzz514, zzz31, new_primPlusNat2(new_primMulNat0(zzz34200), Succ(zzz34200)), h)
new_mkVBalBranch3MkVBalBranch215(zzz340, zzz341, Pos(Zero), zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, Succ(zzz660), h) → new_mkVBalBranch0(zzz31, zzz514, Branch(zzz340, zzz341, Pos(Zero), zzz343, zzz344), h)
new_mkVBalBranch3MkVBalBranch223(zzz340, zzz341, Neg(Zero), zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, Succ(zzz670), h) → new_mkVBalBranch0(zzz31, Branch(zzz510, zzz511, Neg(Succ(zzz51200)), zzz513, zzz514), zzz343, h)
new_mkVBalBranch3MkVBalBranch216(zzz1105, zzz1106, zzz1107, zzz1108, zzz1109, zzz1110, zzz1111, zzz1112, zzz1113, zzz1114, zzz1115, Zero, Succ(zzz11170), ba) → new_mkVBalBranch0(zzz1115, Branch(zzz1110, zzz1111, Pos(Succ(Succ(zzz1112))), zzz1113, zzz1114), zzz1108, ba)
new_mkVBalBranch3MkVBalBranch217(zzz473, zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, zzz481, zzz482, Succ(zzz4830), Zero, bh) → new_mkVBalBranch3MkVBalBranch121(zzz473, zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, zzz481, zzz482, new_primMulNat1(zzz475), bh)
new_mkVBalBranch3MkVBalBranch115(zzz1986, zzz1987, zzz1988, zzz1989, zzz1990, zzz1991, zzz1992, zzz1993, zzz1994, zzz1995, zzz1996, Zero, Succ(zzz19980), bc) → new_mkVBalBranch0(zzz1996, zzz1995, Branch(zzz1986, zzz1987, Pos(Succ(zzz1988)), zzz1989, zzz1990), bc)
new_mkVBalBranch0(zzz31, Branch(zzz510, zzz511, Neg(Zero), zzz513, zzz514), Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), h) → new_mkVBalBranch3MkVBalBranch117(zzz340, zzz341, zzz34200, zzz343, zzz344, zzz510, zzz511, zzz513, zzz514, zzz31, new_primPlusNat2(new_primMulNat0(zzz34200), Succ(zzz34200)), h)
new_mkVBalBranch3MkVBalBranch223(zzz340, zzz341, Neg(Zero), zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, Zero, h) → new_mkVBalBranch3MkVBalBranch228(zzz340, zzz341, zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, h)
new_mkVBalBranch3MkVBalBranch122(zzz340, zzz341, zzz34200, zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, h) → new_mkVBalBranch0(zzz31, zzz514, Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), h)
new_mkVBalBranch3MkVBalBranch217(zzz473, zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, zzz481, zzz482, Succ(zzz4830), Succ(zzz4840), bh) → new_mkVBalBranch3MkVBalBranch217(zzz473, zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, zzz481, zzz482, zzz4830, zzz4840, bh)
new_mkVBalBranch3MkVBalBranch116(zzz340, zzz341, zzz34200, zzz343, zzz344, zzz510, zzz511, zzz513, zzz514, zzz31, Succ(zzz1200), h) → new_mkVBalBranch0(zzz31, zzz514, Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), h)
new_mkVBalBranch3MkVBalBranch110(zzz461, zzz462, zzz463, zzz464, zzz465, zzz466, zzz467, zzz468, zzz469, zzz470, zzz471, Zero, bb) → new_mkVBalBranch3MkVBalBranch115(zzz461, zzz462, zzz463, zzz464, zzz465, zzz466, zzz467, Succ(zzz468), zzz469, zzz470, zzz471, Zero, Succ(Succ(zzz468)), bb)
new_mkVBalBranch3MkVBalBranch225(zzz498, zzz499, zzz500, zzz501, zzz502, zzz503, zzz504, zzz505, zzz506, zzz507, Zero, Succ(zzz5090), bg) → new_mkVBalBranch0(zzz507, Branch(zzz503, zzz504, Neg(Succ(Zero)), zzz505, zzz506), zzz501, bg)
new_mkVBalBranch3MkVBalBranch223(zzz340, zzz341, Neg(Succ(Succ(Succ(zzz3420000)))), zzz343, zzz344, zzz510, zzz511, Zero, zzz513, zzz514, zzz31, Succ(Zero), h) → new_mkVBalBranch3MkVBalBranch225(zzz340, zzz341, Succ(Succ(zzz3420000)), zzz343, zzz344, zzz510, zzz511, zzz513, zzz514, zzz31, Succ(zzz3420000), Zero, h)
new_mkVBalBranch3MkVBalBranch121(zzz473, zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, zzz481, zzz482, Zero, bh) → new_mkVBalBranch3MkVBalBranch115(zzz473, zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, Zero, zzz480, zzz481, zzz482, Zero, Succ(Zero), bh)
new_mkVBalBranch3MkVBalBranch215(zzz340, zzz341, Pos(Succ(Zero)), zzz343, zzz344, zzz510, zzz511, Succ(zzz512000), zzz513, zzz514, zzz31, Zero, h) → new_mkVBalBranch3MkVBalBranch218(zzz340, zzz341, Zero, zzz343, zzz344, zzz510, zzz511, zzz512000, zzz513, zzz514, zzz31, h)
new_mkVBalBranch3MkVBalBranch225(zzz498, zzz499, zzz500, zzz501, zzz502, zzz503, zzz504, zzz505, zzz506, zzz507, Succ(zzz5080), Zero, bg) → new_mkVBalBranch3MkVBalBranch118(zzz498, zzz499, zzz500, zzz501, zzz502, zzz503, zzz504, zzz505, zzz506, zzz507, new_primPlusNat2(new_primMulNat0(zzz500), Succ(zzz500)), bg)
new_mkVBalBranch3MkVBalBranch223(zzz340, zzz341, Neg(Succ(Zero)), zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, Succ(zzz670), h) → new_mkVBalBranch0(zzz31, Branch(zzz510, zzz511, Neg(Succ(zzz51200)), zzz513, zzz514), zzz343, h)
new_mkVBalBranch3MkVBalBranch229(zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, zzz1125, zzz1126, zzz1127, zzz1128, zzz1129, bd) → new_mkVBalBranch3MkVBalBranch119(zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, zzz1125, zzz1126, zzz1127, zzz1128, zzz1129, new_primPlusNat2(new_primMulNat0(zzz1121), Succ(zzz1121)), bd)
new_mkVBalBranch3MkVBalBranch223(zzz340, zzz341, Neg(Succ(Zero)), zzz343, zzz344, zzz510, zzz511, Succ(zzz512000), zzz513, zzz514, zzz31, Zero, h) → new_mkVBalBranch3MkVBalBranch227(zzz340, zzz341, Zero, zzz343, zzz344, zzz510, zzz511, zzz512000, zzz513, zzz514, zzz31, h)
new_mkVBalBranch3MkVBalBranch215(zzz340, zzz341, Pos(Succ(Zero)), zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, Succ(zzz660), h) → new_mkVBalBranch3MkVBalBranch18(zzz340, zzz341, zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, new_primMulNat1(Zero), h)
new_mkVBalBranch3MkVBalBranch226(zzz340, zzz341, zzz3420, zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, h) → new_mkVBalBranch0(zzz31, Branch(zzz510, zzz511, Neg(Succ(zzz51200)), zzz513, zzz514), zzz343, h)
new_mkVBalBranch3MkVBalBranch223(zzz340, zzz341, Neg(Succ(Succ(zzz342000))), zzz343, zzz344, zzz510, zzz511, Succ(zzz512000), zzz513, zzz514, zzz31, Zero, h) → new_mkVBalBranch3MkVBalBranch224(zzz340, zzz341, Succ(zzz342000), zzz343, zzz344, zzz510, zzz511, zzz512000, zzz513, zzz514, zzz31, zzz342000, zzz512000, h)
new_mkVBalBranch3MkVBalBranch215(zzz340, zzz341, Pos(Succ(Succ(zzz342000))), zzz343, zzz344, zzz510, zzz511, Zero, zzz513, zzz514, zzz31, Succ(Succ(zzz6600)), h) → new_mkVBalBranch3MkVBalBranch217(zzz340, zzz341, Succ(zzz342000), zzz343, zzz344, zzz510, zzz511, zzz513, zzz514, zzz31, Succ(zzz6600), zzz342000, h)
new_mkVBalBranch3MkVBalBranch218(zzz461, zzz462, zzz463, zzz464, zzz465, zzz466, zzz467, zzz468, zzz469, zzz470, zzz471, bb) → new_mkVBalBranch3MkVBalBranch110(zzz461, zzz462, zzz463, zzz464, zzz465, zzz466, zzz467, zzz468, zzz469, zzz470, zzz471, new_primPlusNat2(new_primMulNat0(zzz463), Succ(zzz463)), bb)
new_mkVBalBranch3MkVBalBranch117(zzz340, zzz341, zzz34200, zzz343, zzz344, zzz510, zzz511, zzz513, zzz514, zzz31, Succ(zzz1240), h) → new_mkVBalBranch0(zzz31, zzz514, Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), h)
new_mkVBalBranch3MkVBalBranch221(zzz340, zzz341, Succ(zzz34200), zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, h) → new_mkVBalBranch3MkVBalBranch19(zzz340, zzz341, zzz34200, zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, new_primPlusNat2(new_primPlusNat3(Succ(new_primPlusNat3(new_primPlusNat1(zzz34200), zzz34200)), Succ(zzz34200)), Succ(zzz34200)), h)
new_mkVBalBranch3MkVBalBranch120(zzz2050, zzz2051, zzz2052, zzz2053, zzz2054, zzz2055, zzz2056, zzz2057, zzz2058, zzz2059, zzz2060, Succ(zzz20610), Succ(zzz20620), be) → new_mkVBalBranch3MkVBalBranch120(zzz2050, zzz2051, zzz2052, zzz2053, zzz2054, zzz2055, zzz2056, zzz2057, zzz2058, zzz2059, zzz2060, zzz20610, zzz20620, be)
new_mkVBalBranch3MkVBalBranch217(zzz473, zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, zzz481, zzz482, Zero, Zero, bh) → new_mkVBalBranch3MkVBalBranch233(zzz473, zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, zzz481, zzz482, bh)
new_mkVBalBranch0(zzz31, Branch(zzz510, zzz511, Neg(Succ(zzz51200)), zzz513, zzz514), Branch(zzz340, zzz341, zzz342, zzz343, zzz344), h) → new_mkVBalBranch3MkVBalBranch223(zzz340, zzz341, zzz342, zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, new_primPlusNat3(Succ(new_primPlusNat3(new_primPlusNat1(zzz51200), zzz51200)), Succ(zzz51200)), h)
new_mkVBalBranch3MkVBalBranch216(zzz1105, zzz1106, zzz1107, zzz1108, zzz1109, zzz1110, zzz1111, zzz1112, zzz1113, zzz1114, zzz1115, Succ(zzz11160), Succ(zzz11170), ba) → new_mkVBalBranch3MkVBalBranch216(zzz1105, zzz1106, zzz1107, zzz1108, zzz1109, zzz1110, zzz1111, zzz1112, zzz1113, zzz1114, zzz1115, zzz11160, zzz11170, ba)
new_mkVBalBranch3MkVBalBranch223(zzz340, zzz341, Pos(zzz3420), zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, Succ(zzz670), h) → new_mkVBalBranch0(zzz31, Branch(zzz510, zzz511, Neg(Succ(zzz51200)), zzz513, zzz514), zzz343, h)
new_mkVBalBranch3MkVBalBranch223(zzz340, zzz341, Neg(Succ(Succ(Succ(zzz3420000)))), zzz343, zzz344, zzz510, zzz511, Succ(zzz512000), zzz513, zzz514, zzz31, Succ(Zero), h) → new_mkVBalBranch3MkVBalBranch224(zzz340, zzz341, Succ(Succ(zzz3420000)), zzz343, zzz344, zzz510, zzz511, zzz512000, zzz513, zzz514, zzz31, Succ(zzz3420000), Succ(zzz512000), h)
new_mkVBalBranch3MkVBalBranch19(zzz340, zzz341, zzz34200, zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, Zero, h) → new_mkVBalBranch3MkVBalBranch122(zzz340, zzz341, zzz34200, zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, h)
new_mkVBalBranch3MkVBalBranch215(zzz340, zzz341, Pos(Succ(Succ(zzz342000))), zzz343, zzz344, zzz510, zzz511, Zero, zzz513, zzz514, zzz31, Zero, h) → new_mkVBalBranch0(zzz31, Branch(zzz510, zzz511, Pos(Succ(Zero)), zzz513, zzz514), zzz343, h)
new_mkVBalBranch3MkVBalBranch225(zzz498, zzz499, zzz500, zzz501, zzz502, zzz503, zzz504, zzz505, zzz506, zzz507, Succ(zzz5080), Succ(zzz5090), bg) → new_mkVBalBranch3MkVBalBranch225(zzz498, zzz499, zzz500, zzz501, zzz502, zzz503, zzz504, zzz505, zzz506, zzz507, zzz5080, zzz5090, bg)
new_mkVBalBranch3MkVBalBranch19(zzz340, zzz341, zzz34200, zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, Succ(zzz1410), h) → new_mkVBalBranch0(zzz31, zzz514, Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), h)
new_mkVBalBranch3MkVBalBranch224(zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, zzz1125, zzz1126, zzz1127, zzz1128, zzz1129, Succ(zzz11300), Zero, bd) → new_mkVBalBranch3MkVBalBranch119(zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, zzz1125, zzz1126, zzz1127, zzz1128, zzz1129, new_primPlusNat2(new_primMulNat0(zzz1121), Succ(zzz1121)), bd)
new_mkVBalBranch3MkVBalBranch223(zzz340, zzz341, Pos(zzz3420), zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, Zero, h) → new_mkVBalBranch3MkVBalBranch226(zzz340, zzz341, zzz3420, zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, h)
new_mkVBalBranch3MkVBalBranch223(zzz340, zzz341, Neg(Succ(Succ(Zero))), zzz343, zzz344, zzz510, zzz511, Succ(zzz512000), zzz513, zzz514, zzz31, Succ(Zero), h) → new_mkVBalBranch3MkVBalBranch224(zzz340, zzz341, Succ(Zero), zzz343, zzz344, zzz510, zzz511, zzz512000, zzz513, zzz514, zzz31, Zero, Succ(zzz512000), h)
new_mkVBalBranch3MkVBalBranch224(zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, zzz1125, zzz1126, zzz1127, zzz1128, zzz1129, Zero, Zero, bd) → new_mkVBalBranch3MkVBalBranch229(zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, zzz1125, zzz1126, zzz1127, zzz1128, zzz1129, bd)
new_mkVBalBranch3MkVBalBranch224(zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, zzz1125, zzz1126, zzz1127, zzz1128, zzz1129, Zero, Succ(zzz11310), bd) → new_mkVBalBranch3MkVBalBranch227(zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, zzz1125, zzz1126, zzz1127, zzz1128, zzz1129, bd)
new_mkVBalBranch3MkVBalBranch223(zzz340, zzz341, Neg(Succ(Succ(zzz342000))), zzz343, zzz344, zzz510, zzz511, Zero, zzz513, zzz514, zzz31, Zero, h) → new_mkVBalBranch3MkVBalBranch118(zzz340, zzz341, Succ(zzz342000), zzz343, zzz344, zzz510, zzz511, zzz513, zzz514, zzz31, new_primPlusNat2(new_primMulNat0(Succ(zzz342000)), Succ(Succ(zzz342000))), h)
new_mkVBalBranch3MkVBalBranch230(zzz498, zzz499, zzz500, zzz501, zzz502, zzz503, zzz504, zzz505, zzz506, zzz507, bg) → new_mkVBalBranch3MkVBalBranch118(zzz498, zzz499, zzz500, zzz501, zzz502, zzz503, zzz504, zzz505, zzz506, zzz507, new_primPlusNat2(new_primMulNat0(zzz500), Succ(zzz500)), bg)
new_mkVBalBranch3MkVBalBranch223(zzz340, zzz341, Neg(Succ(Succ(Zero))), zzz343, zzz344, zzz510, zzz511, Zero, zzz513, zzz514, zzz31, Succ(Succ(zzz6700)), h) → new_mkVBalBranch3MkVBalBranch225(zzz340, zzz341, Succ(Zero), zzz343, zzz344, zzz510, zzz511, zzz513, zzz514, zzz31, Zero, Succ(zzz6700), h)
new_mkVBalBranch3MkVBalBranch223(zzz340, zzz341, Neg(Succ(Succ(Succ(zzz3420000)))), zzz343, zzz344, zzz510, zzz511, Succ(zzz512000), zzz513, zzz514, zzz31, Succ(Succ(zzz6700)), h) → new_mkVBalBranch3MkVBalBranch224(zzz340, zzz341, Succ(Succ(zzz3420000)), zzz343, zzz344, zzz510, zzz511, zzz512000, zzz513, zzz514, zzz31, Succ(zzz3420000), Succ(Succ(new_primPlusNat2(zzz6700, zzz512000))), h)
new_mkVBalBranch3MkVBalBranch115(zzz1986, zzz1987, zzz1988, zzz1989, zzz1990, zzz1991, zzz1992, zzz1993, zzz1994, zzz1995, zzz1996, Succ(zzz19970), Succ(zzz19980), bc) → new_mkVBalBranch3MkVBalBranch115(zzz1986, zzz1987, zzz1988, zzz1989, zzz1990, zzz1991, zzz1992, zzz1993, zzz1994, zzz1995, zzz1996, zzz19970, zzz19980, bc)
new_mkVBalBranch3MkVBalBranch215(zzz340, zzz341, Pos(Zero), zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, Zero, h) → new_mkVBalBranch3MkVBalBranch220(zzz340, zzz341, zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, h)
new_mkVBalBranch3MkVBalBranch215(zzz340, zzz341, Neg(Zero), zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, Succ(zzz660), h) → new_mkVBalBranch0(zzz31, zzz514, Branch(zzz340, zzz341, Neg(Zero), zzz343, zzz344), h)
new_mkVBalBranch3MkVBalBranch118(zzz498, zzz499, zzz500, zzz501, zzz502, zzz503, zzz504, zzz505, zzz506, zzz507, Succ(zzz8040), bg) → new_mkVBalBranch3MkVBalBranch120(zzz498, zzz499, zzz500, zzz501, zzz502, zzz503, zzz504, Zero, zzz505, zzz506, zzz507, Succ(Zero), Succ(zzz8040), bg)
new_mkVBalBranch3MkVBalBranch216(zzz1105, zzz1106, zzz1107, zzz1108, zzz1109, zzz1110, zzz1111, zzz1112, zzz1113, zzz1114, zzz1115, Succ(zzz11160), Zero, ba) → new_mkVBalBranch3MkVBalBranch218(zzz1105, zzz1106, zzz1107, zzz1108, zzz1109, zzz1110, zzz1111, zzz1112, zzz1113, zzz1114, zzz1115, ba)
new_mkVBalBranch3MkVBalBranch221(zzz340, zzz341, Zero, zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, h) → new_mkVBalBranch0(zzz31, zzz514, Branch(zzz340, zzz341, Neg(Zero), zzz343, zzz344), h)
new_mkVBalBranch3MkVBalBranch219(zzz340, zzz341, zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, h) → new_mkVBalBranch3MkVBalBranch18(zzz340, zzz341, zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, new_primMulNat1(Zero), h)
new_mkVBalBranch3MkVBalBranch215(zzz340, zzz341, Pos(Succ(Succ(zzz342000))), zzz343, zzz344, zzz510, zzz511, Succ(zzz512000), zzz513, zzz514, zzz31, Succ(Zero), h) → new_mkVBalBranch3MkVBalBranch216(zzz340, zzz341, Succ(zzz342000), zzz343, zzz344, zzz510, zzz511, zzz512000, zzz513, zzz514, zzz31, Succ(zzz512000), zzz342000, h)
new_mkVBalBranch3MkVBalBranch215(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, Succ(zzz660), h) → new_mkVBalBranch3MkVBalBranch19(zzz340, zzz341, zzz34200, zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, new_primPlusNat2(new_primMulNat0(zzz34200), Succ(zzz34200)), h)
new_mkVBalBranch3MkVBalBranch216(zzz1105, zzz1106, zzz1107, zzz1108, zzz1109, zzz1110, zzz1111, zzz1112, zzz1113, zzz1114, zzz1115, Zero, Zero, ba) → new_mkVBalBranch3MkVBalBranch222(zzz1105, zzz1106, zzz1107, zzz1108, zzz1109, zzz1110, zzz1111, zzz1112, zzz1113, zzz1114, zzz1115, ba)
new_mkVBalBranch3MkVBalBranch233(zzz473, zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, zzz481, zzz482, bh) → new_mkVBalBranch3MkVBalBranch121(zzz473, zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, zzz481, zzz482, new_primMulNat1(zzz475), bh)
new_mkVBalBranch3MkVBalBranch215(zzz340, zzz341, Pos(Succ(Succ(zzz342000))), zzz343, zzz344, zzz510, zzz511, Zero, zzz513, zzz514, zzz31, Succ(Zero), h) → new_mkVBalBranch3MkVBalBranch217(zzz340, zzz341, Succ(zzz342000), zzz343, zzz344, zzz510, zzz511, zzz513, zzz514, zzz31, Zero, zzz342000, h)
new_mkVBalBranch3MkVBalBranch119(zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, zzz1125, zzz1126, zzz1127, zzz1128, zzz1129, Succ(zzz12130), bd) → new_mkVBalBranch3MkVBalBranch120(zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, zzz1125, Succ(zzz1126), zzz1127, zzz1128, zzz1129, Succ(Succ(zzz1126)), Succ(zzz12130), bd)
new_mkVBalBranch3MkVBalBranch18(zzz340, zzz341, zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, Zero, h) → new_mkVBalBranch3MkVBalBranch115(zzz340, zzz341, Zero, zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, Zero, Succ(zzz51200), h)

The TRS R consists of the following rules:

new_primPlusNat1(Zero) → Zero
new_primMulNat0(zzz6200) → new_primPlusNat3(Succ(new_primPlusNat3(new_primPlusNat1(zzz6200), zzz6200)), Succ(zzz6200))
new_primPlusNat2(Succ(zzz900), Succ(zzz9100)) → Succ(Succ(new_primPlusNat2(zzz900, zzz9100)))
new_primPlusNat3(zzz90, Succ(zzz910)) → Succ(Succ(new_primPlusNat2(zzz90, zzz910)))
new_primPlusNat3(zzz90, Zero) → Succ(zzz90)
new_primMulNat1(zzz34200) → new_primPlusNat2(new_primMulNat0(zzz34200), Succ(zzz34200))
new_primPlusNat2(Zero, Zero) → Zero
new_primPlusNat1(Succ(zzz62000)) → Succ(Succ(new_primPlusNat1(zzz62000)))
new_primPlusNat2(Succ(zzz900), Zero) → Succ(zzz900)
new_primPlusNat2(Zero, Succ(zzz9100)) → Succ(zzz9100)

The set Q consists of the following terms:

new_primPlusNat2(Zero, Succ(x0))
new_primMulNat1(x0)
new_primMulNat0(x0)
new_primPlusNat3(x0, Succ(x1))
new_primPlusNat2(Succ(x0), Succ(x1))
new_primPlusNat3(x0, Zero)
new_primPlusNat1(Zero)
new_primPlusNat2(Zero, Zero)
new_primPlusNat1(Succ(x0))
new_primPlusNat2(Succ(x0), Zero)

We have to consider all minimal (P,Q,R)-chains.
By rewriting [15] the rule new_mkVBalBranch3MkVBalBranch219(zzz340, zzz341, zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, h) → new_mkVBalBranch3MkVBalBranch18(zzz340, zzz341, zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, new_primMulNat1(Zero), h) at position [10] we obtained the following new rules:

new_mkVBalBranch3MkVBalBranch219(zzz340, zzz341, zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, h) → new_mkVBalBranch3MkVBalBranch18(zzz340, zzz341, zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, new_primPlusNat2(new_primMulNat0(Zero), Succ(Zero)), 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
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                    ↳ DependencyGraphProof
                                      ↳ QDP
                                        ↳ Rewriting
                                          ↳ QDP
                                            ↳ Rewriting
                                              ↳ QDP
                                                ↳ Rewriting
                                                  ↳ QDP
                                                    ↳ Rewriting
                                                      ↳ QDP
                                                        ↳ Rewriting
                                                          ↳ QDP
                                                            ↳ Rewriting
                                                              ↳ QDP
                                                                ↳ Rewriting
                                                                  ↳ QDP
                                                                    ↳ Rewriting
                                                                      ↳ QDP
                                                                        ↳ Rewriting
                                                                          ↳ QDP
                                                                            ↳ Rewriting
                                                                              ↳ QDP
                                                                                ↳ Rewriting
                                                                                  ↳ QDP
                                                                                    ↳ Rewriting
                                                                                      ↳ QDP
                                                                                        ↳ Rewriting
                                                                                          ↳ QDP
                                                                                            ↳ Rewriting
                                                                                              ↳ QDP
                                                                                                ↳ Rewriting
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP

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

new_mkVBalBranch3MkVBalBranch215(zzz340, zzz341, Neg(zzz3420), zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, Zero, h) → new_mkVBalBranch3MkVBalBranch221(zzz340, zzz341, zzz3420, zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, h)
new_mkVBalBranch3MkVBalBranch225(zzz498, zzz499, zzz500, zzz501, zzz502, zzz503, zzz504, zzz505, zzz506, zzz507, Zero, Zero, bg) → new_mkVBalBranch3MkVBalBranch230(zzz498, zzz499, zzz500, zzz501, zzz502, zzz503, zzz504, zzz505, zzz506, zzz507, bg)
new_mkVBalBranch3MkVBalBranch18(zzz340, zzz341, zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, Succ(zzz1480), h) → new_mkVBalBranch3MkVBalBranch115(zzz340, zzz341, Zero, zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, Succ(zzz1480), Succ(zzz51200), h)
new_mkVBalBranch0(zzz31, Branch(zzz510, zzz511, Neg(Zero), zzz513, zzz514), Branch(zzz340, zzz341, Pos(Succ(zzz34200)), zzz343, zzz344), h) → new_mkVBalBranch0(zzz31, Branch(zzz510, zzz511, Neg(Zero), zzz513, zzz514), zzz343, h)
new_mkVBalBranch3MkVBalBranch215(zzz340, zzz341, Pos(Succ(Succ(zzz342000))), zzz343, zzz344, zzz510, zzz511, Succ(zzz512000), zzz513, zzz514, zzz31, Succ(Succ(zzz6600)), h) → new_mkVBalBranch3MkVBalBranch216(zzz340, zzz341, Succ(zzz342000), zzz343, zzz344, zzz510, zzz511, zzz512000, zzz513, zzz514, zzz31, Succ(Succ(new_primPlusNat2(zzz6600, zzz512000))), zzz342000, h)
new_mkVBalBranch3MkVBalBranch223(zzz340, zzz341, Neg(Succ(Succ(Succ(zzz3420000)))), zzz343, zzz344, zzz510, zzz511, Zero, zzz513, zzz514, zzz31, Succ(Succ(zzz6700)), h) → new_mkVBalBranch3MkVBalBranch225(zzz340, zzz341, Succ(Succ(zzz3420000)), zzz343, zzz344, zzz510, zzz511, zzz513, zzz514, zzz31, Succ(zzz3420000), Succ(zzz6700), h)
new_mkVBalBranch3MkVBalBranch220(zzz340, zzz341, zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, h) → new_mkVBalBranch0(zzz31, zzz514, Branch(zzz340, zzz341, Pos(Zero), zzz343, zzz344), h)
new_mkVBalBranch3MkVBalBranch120(zzz2050, zzz2051, zzz2052, zzz2053, zzz2054, zzz2055, zzz2056, zzz2057, zzz2058, zzz2059, zzz2060, Zero, Succ(zzz20620), be) → new_mkVBalBranch0(zzz2060, zzz2059, Branch(zzz2050, zzz2051, Neg(Succ(zzz2052)), zzz2053, zzz2054), be)
new_mkVBalBranch3MkVBalBranch121(zzz473, zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, zzz481, zzz482, Succ(zzz7390), bh) → new_mkVBalBranch3MkVBalBranch115(zzz473, zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, Zero, zzz480, zzz481, zzz482, Succ(zzz7390), Succ(Zero), bh)
new_mkVBalBranch0(zzz31, Branch(zzz510, zzz511, Pos(Zero), zzz513, zzz514), Branch(zzz340, zzz341, Pos(Succ(zzz34200)), zzz343, zzz344), h) → new_mkVBalBranch0(zzz31, Branch(zzz510, zzz511, Pos(Zero), zzz513, zzz514), zzz343, h)
new_mkVBalBranch3MkVBalBranch228(zzz340, zzz341, zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, h) → new_mkVBalBranch0(zzz31, Branch(zzz510, zzz511, Neg(Succ(zzz51200)), zzz513, zzz514), zzz343, h)
new_mkVBalBranch3MkVBalBranch222(zzz461, zzz462, zzz463, zzz464, zzz465, zzz466, zzz467, zzz468, zzz469, zzz470, zzz471, bb) → new_mkVBalBranch3MkVBalBranch110(zzz461, zzz462, zzz463, zzz464, zzz465, zzz466, zzz467, zzz468, zzz469, zzz470, zzz471, new_primPlusNat2(new_primMulNat0(zzz463), Succ(zzz463)), bb)
new_mkVBalBranch3MkVBalBranch215(zzz340, zzz341, Pos(Succ(Zero)), zzz343, zzz344, zzz510, zzz511, Zero, zzz513, zzz514, zzz31, Zero, h) → new_mkVBalBranch3MkVBalBranch219(zzz340, zzz341, zzz343, zzz344, zzz510, zzz511, Zero, zzz513, zzz514, zzz31, h)
new_mkVBalBranch3MkVBalBranch223(zzz340, zzz341, Neg(Succ(Succ(Zero))), zzz343, zzz344, zzz510, zzz511, Succ(zzz512000), zzz513, zzz514, zzz31, Succ(Succ(zzz6700)), h) → new_mkVBalBranch3MkVBalBranch224(zzz340, zzz341, Succ(Zero), zzz343, zzz344, zzz510, zzz511, zzz512000, zzz513, zzz514, zzz31, Zero, Succ(Succ(new_primPlusNat2(zzz6700, zzz512000))), h)
new_mkVBalBranch3MkVBalBranch223(zzz340, zzz341, Neg(Succ(Succ(Zero))), zzz343, zzz344, zzz510, zzz511, Zero, zzz513, zzz514, zzz31, Succ(Zero), h) → new_mkVBalBranch3MkVBalBranch225(zzz340, zzz341, Succ(Zero), zzz343, zzz344, zzz510, zzz511, zzz513, zzz514, zzz31, Zero, Zero, h)
new_mkVBalBranch3MkVBalBranch224(zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, zzz1125, zzz1126, zzz1127, zzz1128, zzz1129, Succ(zzz11300), Succ(zzz11310), bd) → new_mkVBalBranch3MkVBalBranch224(zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, zzz1125, zzz1126, zzz1127, zzz1128, zzz1129, zzz11300, zzz11310, bd)
new_mkVBalBranch0(zzz31, Branch(zzz510, zzz511, Pos(Succ(zzz51200)), zzz513, zzz514), Branch(zzz340, zzz341, zzz342, zzz343, zzz344), h) → new_mkVBalBranch3MkVBalBranch215(zzz340, zzz341, zzz342, zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, new_primPlusNat3(Succ(new_primPlusNat3(new_primPlusNat1(zzz51200), zzz51200)), Succ(zzz51200)), h)
new_mkVBalBranch3MkVBalBranch217(zzz473, zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, zzz481, zzz482, Zero, Succ(zzz4840), bh) → new_mkVBalBranch0(zzz482, Branch(zzz478, zzz479, Pos(Succ(Zero)), zzz480, zzz481), zzz476, bh)
new_mkVBalBranch3MkVBalBranch215(zzz340, zzz341, Pos(Succ(Succ(zzz342000))), zzz343, zzz344, zzz510, zzz511, Succ(zzz512000), zzz513, zzz514, zzz31, Zero, h) → new_mkVBalBranch3MkVBalBranch216(zzz340, zzz341, Succ(zzz342000), zzz343, zzz344, zzz510, zzz511, zzz512000, zzz513, zzz514, zzz31, zzz512000, zzz342000, h)
new_mkVBalBranch3MkVBalBranch110(zzz461, zzz462, zzz463, zzz464, zzz465, zzz466, zzz467, zzz468, zzz469, zzz470, zzz471, Succ(zzz5800), bb) → new_mkVBalBranch3MkVBalBranch115(zzz461, zzz462, zzz463, zzz464, zzz465, zzz466, zzz467, Succ(zzz468), zzz469, zzz470, zzz471, Succ(zzz5800), Succ(Succ(zzz468)), bb)
new_mkVBalBranch3MkVBalBranch223(zzz340, zzz341, Neg(Succ(Zero)), zzz343, zzz344, zzz510, zzz511, Zero, zzz513, zzz514, zzz31, Zero, h) → new_mkVBalBranch3MkVBalBranch118(zzz340, zzz341, Zero, zzz343, zzz344, zzz510, zzz511, zzz513, zzz514, zzz31, new_primPlusNat2(new_primMulNat0(Zero), Succ(Zero)), h)
new_mkVBalBranch3MkVBalBranch227(zzz486, zzz487, zzz488, zzz489, zzz490, zzz491, zzz492, zzz493, zzz494, zzz495, zzz496, bf) → new_mkVBalBranch0(zzz496, Branch(zzz491, zzz492, Neg(Succ(Succ(zzz493))), zzz494, zzz495), zzz489, bf)
new_mkVBalBranch3MkVBalBranch215(zzz340, zzz341, Pos(Zero), zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, Succ(zzz660), h) → new_mkVBalBranch0(zzz31, zzz514, Branch(zzz340, zzz341, Pos(Zero), zzz343, zzz344), h)
new_mkVBalBranch0(zzz31, Branch(zzz510, zzz511, Pos(Zero), zzz513, zzz514), Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), h) → new_mkVBalBranch3MkVBalBranch116(zzz340, zzz341, zzz34200, zzz343, zzz344, zzz510, zzz511, zzz513, zzz514, zzz31, new_primPlusNat2(new_primMulNat0(zzz34200), Succ(zzz34200)), h)
new_mkVBalBranch3MkVBalBranch223(zzz340, zzz341, Neg(Zero), zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, Succ(zzz670), h) → new_mkVBalBranch0(zzz31, Branch(zzz510, zzz511, Neg(Succ(zzz51200)), zzz513, zzz514), zzz343, h)
new_mkVBalBranch3MkVBalBranch216(zzz1105, zzz1106, zzz1107, zzz1108, zzz1109, zzz1110, zzz1111, zzz1112, zzz1113, zzz1114, zzz1115, Zero, Succ(zzz11170), ba) → new_mkVBalBranch0(zzz1115, Branch(zzz1110, zzz1111, Pos(Succ(Succ(zzz1112))), zzz1113, zzz1114), zzz1108, ba)
new_mkVBalBranch3MkVBalBranch217(zzz473, zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, zzz481, zzz482, Succ(zzz4830), Zero, bh) → new_mkVBalBranch3MkVBalBranch121(zzz473, zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, zzz481, zzz482, new_primMulNat1(zzz475), bh)
new_mkVBalBranch3MkVBalBranch115(zzz1986, zzz1987, zzz1988, zzz1989, zzz1990, zzz1991, zzz1992, zzz1993, zzz1994, zzz1995, zzz1996, Zero, Succ(zzz19980), bc) → new_mkVBalBranch0(zzz1996, zzz1995, Branch(zzz1986, zzz1987, Pos(Succ(zzz1988)), zzz1989, zzz1990), bc)
new_mkVBalBranch0(zzz31, Branch(zzz510, zzz511, Neg(Zero), zzz513, zzz514), Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), h) → new_mkVBalBranch3MkVBalBranch117(zzz340, zzz341, zzz34200, zzz343, zzz344, zzz510, zzz511, zzz513, zzz514, zzz31, new_primPlusNat2(new_primMulNat0(zzz34200), Succ(zzz34200)), h)
new_mkVBalBranch3MkVBalBranch223(zzz340, zzz341, Neg(Zero), zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, Zero, h) → new_mkVBalBranch3MkVBalBranch228(zzz340, zzz341, zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, h)
new_mkVBalBranch3MkVBalBranch122(zzz340, zzz341, zzz34200, zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, h) → new_mkVBalBranch0(zzz31, zzz514, Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), h)
new_mkVBalBranch3MkVBalBranch217(zzz473, zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, zzz481, zzz482, Succ(zzz4830), Succ(zzz4840), bh) → new_mkVBalBranch3MkVBalBranch217(zzz473, zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, zzz481, zzz482, zzz4830, zzz4840, bh)
new_mkVBalBranch3MkVBalBranch116(zzz340, zzz341, zzz34200, zzz343, zzz344, zzz510, zzz511, zzz513, zzz514, zzz31, Succ(zzz1200), h) → new_mkVBalBranch0(zzz31, zzz514, Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), h)
new_mkVBalBranch3MkVBalBranch110(zzz461, zzz462, zzz463, zzz464, zzz465, zzz466, zzz467, zzz468, zzz469, zzz470, zzz471, Zero, bb) → new_mkVBalBranch3MkVBalBranch115(zzz461, zzz462, zzz463, zzz464, zzz465, zzz466, zzz467, Succ(zzz468), zzz469, zzz470, zzz471, Zero, Succ(Succ(zzz468)), bb)
new_mkVBalBranch3MkVBalBranch225(zzz498, zzz499, zzz500, zzz501, zzz502, zzz503, zzz504, zzz505, zzz506, zzz507, Zero, Succ(zzz5090), bg) → new_mkVBalBranch0(zzz507, Branch(zzz503, zzz504, Neg(Succ(Zero)), zzz505, zzz506), zzz501, bg)
new_mkVBalBranch3MkVBalBranch223(zzz340, zzz341, Neg(Succ(Succ(Succ(zzz3420000)))), zzz343, zzz344, zzz510, zzz511, Zero, zzz513, zzz514, zzz31, Succ(Zero), h) → new_mkVBalBranch3MkVBalBranch225(zzz340, zzz341, Succ(Succ(zzz3420000)), zzz343, zzz344, zzz510, zzz511, zzz513, zzz514, zzz31, Succ(zzz3420000), Zero, h)
new_mkVBalBranch3MkVBalBranch121(zzz473, zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, zzz481, zzz482, Zero, bh) → new_mkVBalBranch3MkVBalBranch115(zzz473, zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, Zero, zzz480, zzz481, zzz482, Zero, Succ(Zero), bh)
new_mkVBalBranch3MkVBalBranch215(zzz340, zzz341, Pos(Succ(Zero)), zzz343, zzz344, zzz510, zzz511, Succ(zzz512000), zzz513, zzz514, zzz31, Zero, h) → new_mkVBalBranch3MkVBalBranch218(zzz340, zzz341, Zero, zzz343, zzz344, zzz510, zzz511, zzz512000, zzz513, zzz514, zzz31, h)
new_mkVBalBranch3MkVBalBranch223(zzz340, zzz341, Neg(Succ(Zero)), zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, Succ(zzz670), h) → new_mkVBalBranch0(zzz31, Branch(zzz510, zzz511, Neg(Succ(zzz51200)), zzz513, zzz514), zzz343, h)
new_mkVBalBranch3MkVBalBranch225(zzz498, zzz499, zzz500, zzz501, zzz502, zzz503, zzz504, zzz505, zzz506, zzz507, Succ(zzz5080), Zero, bg) → new_mkVBalBranch3MkVBalBranch118(zzz498, zzz499, zzz500, zzz501, zzz502, zzz503, zzz504, zzz505, zzz506, zzz507, new_primPlusNat2(new_primMulNat0(zzz500), Succ(zzz500)), bg)
new_mkVBalBranch3MkVBalBranch229(zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, zzz1125, zzz1126, zzz1127, zzz1128, zzz1129, bd) → new_mkVBalBranch3MkVBalBranch119(zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, zzz1125, zzz1126, zzz1127, zzz1128, zzz1129, new_primPlusNat2(new_primMulNat0(zzz1121), Succ(zzz1121)), bd)
new_mkVBalBranch3MkVBalBranch219(zzz340, zzz341, zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, h) → new_mkVBalBranch3MkVBalBranch18(zzz340, zzz341, zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, new_primPlusNat2(new_primMulNat0(Zero), Succ(Zero)), h)
new_mkVBalBranch3MkVBalBranch223(zzz340, zzz341, Neg(Succ(Zero)), zzz343, zzz344, zzz510, zzz511, Succ(zzz512000), zzz513, zzz514, zzz31, Zero, h) → new_mkVBalBranch3MkVBalBranch227(zzz340, zzz341, Zero, zzz343, zzz344, zzz510, zzz511, zzz512000, zzz513, zzz514, zzz31, h)
new_mkVBalBranch3MkVBalBranch215(zzz340, zzz341, Pos(Succ(Zero)), zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, Succ(zzz660), h) → new_mkVBalBranch3MkVBalBranch18(zzz340, zzz341, zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, new_primMulNat1(Zero), h)
new_mkVBalBranch3MkVBalBranch215(zzz340, zzz341, Pos(Succ(Succ(zzz342000))), zzz343, zzz344, zzz510, zzz511, Zero, zzz513, zzz514, zzz31, Succ(Succ(zzz6600)), h) → new_mkVBalBranch3MkVBalBranch217(zzz340, zzz341, Succ(zzz342000), zzz343, zzz344, zzz510, zzz511, zzz513, zzz514, zzz31, Succ(zzz6600), zzz342000, h)
new_mkVBalBranch3MkVBalBranch223(zzz340, zzz341, Neg(Succ(Succ(zzz342000))), zzz343, zzz344, zzz510, zzz511, Succ(zzz512000), zzz513, zzz514, zzz31, Zero, h) → new_mkVBalBranch3MkVBalBranch224(zzz340, zzz341, Succ(zzz342000), zzz343, zzz344, zzz510, zzz511, zzz512000, zzz513, zzz514, zzz31, zzz342000, zzz512000, h)
new_mkVBalBranch3MkVBalBranch226(zzz340, zzz341, zzz3420, zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, h) → new_mkVBalBranch0(zzz31, Branch(zzz510, zzz511, Neg(Succ(zzz51200)), zzz513, zzz514), zzz343, h)
new_mkVBalBranch3MkVBalBranch218(zzz461, zzz462, zzz463, zzz464, zzz465, zzz466, zzz467, zzz468, zzz469, zzz470, zzz471, bb) → new_mkVBalBranch3MkVBalBranch110(zzz461, zzz462, zzz463, zzz464, zzz465, zzz466, zzz467, zzz468, zzz469, zzz470, zzz471, new_primPlusNat2(new_primMulNat0(zzz463), Succ(zzz463)), bb)
new_mkVBalBranch3MkVBalBranch117(zzz340, zzz341, zzz34200, zzz343, zzz344, zzz510, zzz511, zzz513, zzz514, zzz31, Succ(zzz1240), h) → new_mkVBalBranch0(zzz31, zzz514, Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), h)
new_mkVBalBranch0(zzz31, Branch(zzz510, zzz511, Neg(Succ(zzz51200)), zzz513, zzz514), Branch(zzz340, zzz341, zzz342, zzz343, zzz344), h) → new_mkVBalBranch3MkVBalBranch223(zzz340, zzz341, zzz342, zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, new_primPlusNat3(Succ(new_primPlusNat3(new_primPlusNat1(zzz51200), zzz51200)), Succ(zzz51200)), h)
new_mkVBalBranch3MkVBalBranch217(zzz473, zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, zzz481, zzz482, Zero, Zero, bh) → new_mkVBalBranch3MkVBalBranch233(zzz473, zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, zzz481, zzz482, bh)
new_mkVBalBranch3MkVBalBranch120(zzz2050, zzz2051, zzz2052, zzz2053, zzz2054, zzz2055, zzz2056, zzz2057, zzz2058, zzz2059, zzz2060, Succ(zzz20610), Succ(zzz20620), be) → new_mkVBalBranch3MkVBalBranch120(zzz2050, zzz2051, zzz2052, zzz2053, zzz2054, zzz2055, zzz2056, zzz2057, zzz2058, zzz2059, zzz2060, zzz20610, zzz20620, be)
new_mkVBalBranch3MkVBalBranch221(zzz340, zzz341, Succ(zzz34200), zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, h) → new_mkVBalBranch3MkVBalBranch19(zzz340, zzz341, zzz34200, zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, new_primPlusNat2(new_primPlusNat3(Succ(new_primPlusNat3(new_primPlusNat1(zzz34200), zzz34200)), Succ(zzz34200)), Succ(zzz34200)), h)
new_mkVBalBranch3MkVBalBranch223(zzz340, zzz341, Pos(zzz3420), zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, Succ(zzz670), h) → new_mkVBalBranch0(zzz31, Branch(zzz510, zzz511, Neg(Succ(zzz51200)), zzz513, zzz514), zzz343, h)
new_mkVBalBranch3MkVBalBranch216(zzz1105, zzz1106, zzz1107, zzz1108, zzz1109, zzz1110, zzz1111, zzz1112, zzz1113, zzz1114, zzz1115, Succ(zzz11160), Succ(zzz11170), ba) → new_mkVBalBranch3MkVBalBranch216(zzz1105, zzz1106, zzz1107, zzz1108, zzz1109, zzz1110, zzz1111, zzz1112, zzz1113, zzz1114, zzz1115, zzz11160, zzz11170, ba)
new_mkVBalBranch3MkVBalBranch19(zzz340, zzz341, zzz34200, zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, Zero, h) → new_mkVBalBranch3MkVBalBranch122(zzz340, zzz341, zzz34200, zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, h)
new_mkVBalBranch3MkVBalBranch223(zzz340, zzz341, Neg(Succ(Succ(Succ(zzz3420000)))), zzz343, zzz344, zzz510, zzz511, Succ(zzz512000), zzz513, zzz514, zzz31, Succ(Zero), h) → new_mkVBalBranch3MkVBalBranch224(zzz340, zzz341, Succ(Succ(zzz3420000)), zzz343, zzz344, zzz510, zzz511, zzz512000, zzz513, zzz514, zzz31, Succ(zzz3420000), Succ(zzz512000), h)
new_mkVBalBranch3MkVBalBranch215(zzz340, zzz341, Pos(Succ(Succ(zzz342000))), zzz343, zzz344, zzz510, zzz511, Zero, zzz513, zzz514, zzz31, Zero, h) → new_mkVBalBranch0(zzz31, Branch(zzz510, zzz511, Pos(Succ(Zero)), zzz513, zzz514), zzz343, h)
new_mkVBalBranch3MkVBalBranch225(zzz498, zzz499, zzz500, zzz501, zzz502, zzz503, zzz504, zzz505, zzz506, zzz507, Succ(zzz5080), Succ(zzz5090), bg) → new_mkVBalBranch3MkVBalBranch225(zzz498, zzz499, zzz500, zzz501, zzz502, zzz503, zzz504, zzz505, zzz506, zzz507, zzz5080, zzz5090, bg)
new_mkVBalBranch3MkVBalBranch19(zzz340, zzz341, zzz34200, zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, Succ(zzz1410), h) → new_mkVBalBranch0(zzz31, zzz514, Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), h)
new_mkVBalBranch3MkVBalBranch224(zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, zzz1125, zzz1126, zzz1127, zzz1128, zzz1129, Succ(zzz11300), Zero, bd) → new_mkVBalBranch3MkVBalBranch119(zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, zzz1125, zzz1126, zzz1127, zzz1128, zzz1129, new_primPlusNat2(new_primMulNat0(zzz1121), Succ(zzz1121)), bd)
new_mkVBalBranch3MkVBalBranch224(zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, zzz1125, zzz1126, zzz1127, zzz1128, zzz1129, Zero, Succ(zzz11310), bd) → new_mkVBalBranch3MkVBalBranch227(zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, zzz1125, zzz1126, zzz1127, zzz1128, zzz1129, bd)
new_mkVBalBranch3MkVBalBranch224(zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, zzz1125, zzz1126, zzz1127, zzz1128, zzz1129, Zero, Zero, bd) → new_mkVBalBranch3MkVBalBranch229(zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, zzz1125, zzz1126, zzz1127, zzz1128, zzz1129, bd)
new_mkVBalBranch3MkVBalBranch223(zzz340, zzz341, Neg(Succ(Succ(Zero))), zzz343, zzz344, zzz510, zzz511, Succ(zzz512000), zzz513, zzz514, zzz31, Succ(Zero), h) → new_mkVBalBranch3MkVBalBranch224(zzz340, zzz341, Succ(Zero), zzz343, zzz344, zzz510, zzz511, zzz512000, zzz513, zzz514, zzz31, Zero, Succ(zzz512000), h)
new_mkVBalBranch3MkVBalBranch223(zzz340, zzz341, Pos(zzz3420), zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, Zero, h) → new_mkVBalBranch3MkVBalBranch226(zzz340, zzz341, zzz3420, zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, h)
new_mkVBalBranch3MkVBalBranch223(zzz340, zzz341, Neg(Succ(Succ(zzz342000))), zzz343, zzz344, zzz510, zzz511, Zero, zzz513, zzz514, zzz31, Zero, h) → new_mkVBalBranch3MkVBalBranch118(zzz340, zzz341, Succ(zzz342000), zzz343, zzz344, zzz510, zzz511, zzz513, zzz514, zzz31, new_primPlusNat2(new_primMulNat0(Succ(zzz342000)), Succ(Succ(zzz342000))), h)
new_mkVBalBranch3MkVBalBranch230(zzz498, zzz499, zzz500, zzz501, zzz502, zzz503, zzz504, zzz505, zzz506, zzz507, bg) → new_mkVBalBranch3MkVBalBranch118(zzz498, zzz499, zzz500, zzz501, zzz502, zzz503, zzz504, zzz505, zzz506, zzz507, new_primPlusNat2(new_primMulNat0(zzz500), Succ(zzz500)), bg)
new_mkVBalBranch3MkVBalBranch223(zzz340, zzz341, Neg(Succ(Succ(Succ(zzz3420000)))), zzz343, zzz344, zzz510, zzz511, Succ(zzz512000), zzz513, zzz514, zzz31, Succ(Succ(zzz6700)), h) → new_mkVBalBranch3MkVBalBranch224(zzz340, zzz341, Succ(Succ(zzz3420000)), zzz343, zzz344, zzz510, zzz511, zzz512000, zzz513, zzz514, zzz31, Succ(zzz3420000), Succ(Succ(new_primPlusNat2(zzz6700, zzz512000))), h)
new_mkVBalBranch3MkVBalBranch223(zzz340, zzz341, Neg(Succ(Succ(Zero))), zzz343, zzz344, zzz510, zzz511, Zero, zzz513, zzz514, zzz31, Succ(Succ(zzz6700)), h) → new_mkVBalBranch3MkVBalBranch225(zzz340, zzz341, Succ(Zero), zzz343, zzz344, zzz510, zzz511, zzz513, zzz514, zzz31, Zero, Succ(zzz6700), h)
new_mkVBalBranch3MkVBalBranch215(zzz340, zzz341, Pos(Zero), zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, Zero, h) → new_mkVBalBranch3MkVBalBranch220(zzz340, zzz341, zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, h)
new_mkVBalBranch3MkVBalBranch115(zzz1986, zzz1987, zzz1988, zzz1989, zzz1990, zzz1991, zzz1992, zzz1993, zzz1994, zzz1995, zzz1996, Succ(zzz19970), Succ(zzz19980), bc) → new_mkVBalBranch3MkVBalBranch115(zzz1986, zzz1987, zzz1988, zzz1989, zzz1990, zzz1991, zzz1992, zzz1993, zzz1994, zzz1995, zzz1996, zzz19970, zzz19980, bc)
new_mkVBalBranch3MkVBalBranch215(zzz340, zzz341, Neg(Zero), zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, Succ(zzz660), h) → new_mkVBalBranch0(zzz31, zzz514, Branch(zzz340, zzz341, Neg(Zero), zzz343, zzz344), h)
new_mkVBalBranch3MkVBalBranch118(zzz498, zzz499, zzz500, zzz501, zzz502, zzz503, zzz504, zzz505, zzz506, zzz507, Succ(zzz8040), bg) → new_mkVBalBranch3MkVBalBranch120(zzz498, zzz499, zzz500, zzz501, zzz502, zzz503, zzz504, Zero, zzz505, zzz506, zzz507, Succ(Zero), Succ(zzz8040), bg)
new_mkVBalBranch3MkVBalBranch216(zzz1105, zzz1106, zzz1107, zzz1108, zzz1109, zzz1110, zzz1111, zzz1112, zzz1113, zzz1114, zzz1115, Succ(zzz11160), Zero, ba) → new_mkVBalBranch3MkVBalBranch218(zzz1105, zzz1106, zzz1107, zzz1108, zzz1109, zzz1110, zzz1111, zzz1112, zzz1113, zzz1114, zzz1115, ba)
new_mkVBalBranch3MkVBalBranch215(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, Succ(zzz660), h) → new_mkVBalBranch3MkVBalBranch19(zzz340, zzz341, zzz34200, zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, new_primPlusNat2(new_primMulNat0(zzz34200), Succ(zzz34200)), h)
new_mkVBalBranch3MkVBalBranch215(zzz340, zzz341, Pos(Succ(Succ(zzz342000))), zzz343, zzz344, zzz510, zzz511, Succ(zzz512000), zzz513, zzz514, zzz31, Succ(Zero), h) → new_mkVBalBranch3MkVBalBranch216(zzz340, zzz341, Succ(zzz342000), zzz343, zzz344, zzz510, zzz511, zzz512000, zzz513, zzz514, zzz31, Succ(zzz512000), zzz342000, h)
new_mkVBalBranch3MkVBalBranch221(zzz340, zzz341, Zero, zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, h) → new_mkVBalBranch0(zzz31, zzz514, Branch(zzz340, zzz341, Neg(Zero), zzz343, zzz344), h)
new_mkVBalBranch3MkVBalBranch216(zzz1105, zzz1106, zzz1107, zzz1108, zzz1109, zzz1110, zzz1111, zzz1112, zzz1113, zzz1114, zzz1115, Zero, Zero, ba) → new_mkVBalBranch3MkVBalBranch222(zzz1105, zzz1106, zzz1107, zzz1108, zzz1109, zzz1110, zzz1111, zzz1112, zzz1113, zzz1114, zzz1115, ba)
new_mkVBalBranch3MkVBalBranch233(zzz473, zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, zzz481, zzz482, bh) → new_mkVBalBranch3MkVBalBranch121(zzz473, zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, zzz481, zzz482, new_primMulNat1(zzz475), bh)
new_mkVBalBranch3MkVBalBranch215(zzz340, zzz341, Pos(Succ(Succ(zzz342000))), zzz343, zzz344, zzz510, zzz511, Zero, zzz513, zzz514, zzz31, Succ(Zero), h) → new_mkVBalBranch3MkVBalBranch217(zzz340, zzz341, Succ(zzz342000), zzz343, zzz344, zzz510, zzz511, zzz513, zzz514, zzz31, Zero, zzz342000, h)
new_mkVBalBranch3MkVBalBranch18(zzz340, zzz341, zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, Zero, h) → new_mkVBalBranch3MkVBalBranch115(zzz340, zzz341, Zero, zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, Zero, Succ(zzz51200), h)
new_mkVBalBranch3MkVBalBranch119(zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, zzz1125, zzz1126, zzz1127, zzz1128, zzz1129, Succ(zzz12130), bd) → new_mkVBalBranch3MkVBalBranch120(zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, zzz1125, Succ(zzz1126), zzz1127, zzz1128, zzz1129, Succ(Succ(zzz1126)), Succ(zzz12130), bd)

The TRS R consists of the following rules:

new_primPlusNat1(Zero) → Zero
new_primMulNat0(zzz6200) → new_primPlusNat3(Succ(new_primPlusNat3(new_primPlusNat1(zzz6200), zzz6200)), Succ(zzz6200))
new_primPlusNat2(Succ(zzz900), Succ(zzz9100)) → Succ(Succ(new_primPlusNat2(zzz900, zzz9100)))
new_primPlusNat3(zzz90, Succ(zzz910)) → Succ(Succ(new_primPlusNat2(zzz90, zzz910)))
new_primPlusNat3(zzz90, Zero) → Succ(zzz90)
new_primMulNat1(zzz34200) → new_primPlusNat2(new_primMulNat0(zzz34200), Succ(zzz34200))
new_primPlusNat2(Zero, Zero) → Zero
new_primPlusNat1(Succ(zzz62000)) → Succ(Succ(new_primPlusNat1(zzz62000)))
new_primPlusNat2(Succ(zzz900), Zero) → Succ(zzz900)
new_primPlusNat2(Zero, Succ(zzz9100)) → Succ(zzz9100)

The set Q consists of the following terms:

new_primPlusNat2(Zero, Succ(x0))
new_primMulNat1(x0)
new_primMulNat0(x0)
new_primPlusNat3(x0, Succ(x1))
new_primPlusNat2(Succ(x0), Succ(x1))
new_primPlusNat3(x0, Zero)
new_primPlusNat1(Zero)
new_primPlusNat2(Zero, Zero)
new_primPlusNat1(Succ(x0))
new_primPlusNat2(Succ(x0), Zero)

We have to consider all minimal (P,Q,R)-chains.
By rewriting [15] the rule new_mkVBalBranch3MkVBalBranch215(zzz340, zzz341, Pos(Succ(Zero)), zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, Succ(zzz660), h) → new_mkVBalBranch3MkVBalBranch18(zzz340, zzz341, zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, new_primMulNat1(Zero), h) at position [10] we obtained the following new rules:

new_mkVBalBranch3MkVBalBranch215(zzz340, zzz341, Pos(Succ(Zero)), zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, Succ(zzz660), h) → new_mkVBalBranch3MkVBalBranch18(zzz340, zzz341, zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, new_primPlusNat2(new_primMulNat0(Zero), Succ(Zero)), 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
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                    ↳ DependencyGraphProof
                                      ↳ QDP
                                        ↳ Rewriting
                                          ↳ QDP
                                            ↳ Rewriting
                                              ↳ QDP
                                                ↳ Rewriting
                                                  ↳ QDP
                                                    ↳ Rewriting
                                                      ↳ QDP
                                                        ↳ Rewriting
                                                          ↳ QDP
                                                            ↳ Rewriting
                                                              ↳ QDP
                                                                ↳ Rewriting
                                                                  ↳ QDP
                                                                    ↳ Rewriting
                                                                      ↳ QDP
                                                                        ↳ Rewriting
                                                                          ↳ QDP
                                                                            ↳ Rewriting
                                                                              ↳ QDP
                                                                                ↳ Rewriting
                                                                                  ↳ QDP
                                                                                    ↳ Rewriting
                                                                                      ↳ QDP
                                                                                        ↳ Rewriting
                                                                                          ↳ QDP
                                                                                            ↳ Rewriting
                                                                                              ↳ QDP
                                                                                                ↳ Rewriting
                                                                                                  ↳ QDP
                                                                                                    ↳ Rewriting
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP

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

new_mkVBalBranch3MkVBalBranch225(zzz498, zzz499, zzz500, zzz501, zzz502, zzz503, zzz504, zzz505, zzz506, zzz507, Zero, Zero, bg) → new_mkVBalBranch3MkVBalBranch230(zzz498, zzz499, zzz500, zzz501, zzz502, zzz503, zzz504, zzz505, zzz506, zzz507, bg)
new_mkVBalBranch3MkVBalBranch215(zzz340, zzz341, Neg(zzz3420), zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, Zero, h) → new_mkVBalBranch3MkVBalBranch221(zzz340, zzz341, zzz3420, zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, h)
new_mkVBalBranch3MkVBalBranch18(zzz340, zzz341, zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, Succ(zzz1480), h) → new_mkVBalBranch3MkVBalBranch115(zzz340, zzz341, Zero, zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, Succ(zzz1480), Succ(zzz51200), h)
new_mkVBalBranch3MkVBalBranch215(zzz340, zzz341, Pos(Succ(Succ(zzz342000))), zzz343, zzz344, zzz510, zzz511, Succ(zzz512000), zzz513, zzz514, zzz31, Succ(Succ(zzz6600)), h) → new_mkVBalBranch3MkVBalBranch216(zzz340, zzz341, Succ(zzz342000), zzz343, zzz344, zzz510, zzz511, zzz512000, zzz513, zzz514, zzz31, Succ(Succ(new_primPlusNat2(zzz6600, zzz512000))), zzz342000, h)
new_mkVBalBranch0(zzz31, Branch(zzz510, zzz511, Neg(Zero), zzz513, zzz514), Branch(zzz340, zzz341, Pos(Succ(zzz34200)), zzz343, zzz344), h) → new_mkVBalBranch0(zzz31, Branch(zzz510, zzz511, Neg(Zero), zzz513, zzz514), zzz343, h)
new_mkVBalBranch3MkVBalBranch223(zzz340, zzz341, Neg(Succ(Succ(Succ(zzz3420000)))), zzz343, zzz344, zzz510, zzz511, Zero, zzz513, zzz514, zzz31, Succ(Succ(zzz6700)), h) → new_mkVBalBranch3MkVBalBranch225(zzz340, zzz341, Succ(Succ(zzz3420000)), zzz343, zzz344, zzz510, zzz511, zzz513, zzz514, zzz31, Succ(zzz3420000), Succ(zzz6700), h)
new_mkVBalBranch3MkVBalBranch120(zzz2050, zzz2051, zzz2052, zzz2053, zzz2054, zzz2055, zzz2056, zzz2057, zzz2058, zzz2059, zzz2060, Zero, Succ(zzz20620), be) → new_mkVBalBranch0(zzz2060, zzz2059, Branch(zzz2050, zzz2051, Neg(Succ(zzz2052)), zzz2053, zzz2054), be)
new_mkVBalBranch3MkVBalBranch220(zzz340, zzz341, zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, h) → new_mkVBalBranch0(zzz31, zzz514, Branch(zzz340, zzz341, Pos(Zero), zzz343, zzz344), h)
new_mkVBalBranch3MkVBalBranch222(zzz461, zzz462, zzz463, zzz464, zzz465, zzz466, zzz467, zzz468, zzz469, zzz470, zzz471, bb) → new_mkVBalBranch3MkVBalBranch110(zzz461, zzz462, zzz463, zzz464, zzz465, zzz466, zzz467, zzz468, zzz469, zzz470, zzz471, new_primPlusNat2(new_primMulNat0(zzz463), Succ(zzz463)), bb)
new_mkVBalBranch3MkVBalBranch228(zzz340, zzz341, zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, h) → new_mkVBalBranch0(zzz31, Branch(zzz510, zzz511, Neg(Succ(zzz51200)), zzz513, zzz514), zzz343, h)
new_mkVBalBranch0(zzz31, Branch(zzz510, zzz511, Pos(Zero), zzz513, zzz514), Branch(zzz340, zzz341, Pos(Succ(zzz34200)), zzz343, zzz344), h) → new_mkVBalBranch0(zzz31, Branch(zzz510, zzz511, Pos(Zero), zzz513, zzz514), zzz343, h)
new_mkVBalBranch3MkVBalBranch121(zzz473, zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, zzz481, zzz482, Succ(zzz7390), bh) → new_mkVBalBranch3MkVBalBranch115(zzz473, zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, Zero, zzz480, zzz481, zzz482, Succ(zzz7390), Succ(Zero), bh)
new_mkVBalBranch3MkVBalBranch223(zzz340, zzz341, Neg(Succ(Succ(Zero))), zzz343, zzz344, zzz510, zzz511, Succ(zzz512000), zzz513, zzz514, zzz31, Succ(Succ(zzz6700)), h) → new_mkVBalBranch3MkVBalBranch224(zzz340, zzz341, Succ(Zero), zzz343, zzz344, zzz510, zzz511, zzz512000, zzz513, zzz514, zzz31, Zero, Succ(Succ(new_primPlusNat2(zzz6700, zzz512000))), h)
new_mkVBalBranch3MkVBalBranch215(zzz340, zzz341, Pos(Succ(Zero)), zzz343, zzz344, zzz510, zzz511, Zero, zzz513, zzz514, zzz31, Zero, h) → new_mkVBalBranch3MkVBalBranch219(zzz340, zzz341, zzz343, zzz344, zzz510, zzz511, Zero, zzz513, zzz514, zzz31, h)
new_mkVBalBranch3MkVBalBranch223(zzz340, zzz341, Neg(Succ(Succ(Zero))), zzz343, zzz344, zzz510, zzz511, Zero, zzz513, zzz514, zzz31, Succ(Zero), h) → new_mkVBalBranch3MkVBalBranch225(zzz340, zzz341, Succ(Zero), zzz343, zzz344, zzz510, zzz511, zzz513, zzz514, zzz31, Zero, Zero, h)
new_mkVBalBranch3MkVBalBranch224(zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, zzz1125, zzz1126, zzz1127, zzz1128, zzz1129, Succ(zzz11300), Succ(zzz11310), bd) → new_mkVBalBranch3MkVBalBranch224(zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, zzz1125, zzz1126, zzz1127, zzz1128, zzz1129, zzz11300, zzz11310, bd)
new_mkVBalBranch3MkVBalBranch217(zzz473, zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, zzz481, zzz482, Zero, Succ(zzz4840), bh) → new_mkVBalBranch0(zzz482, Branch(zzz478, zzz479, Pos(Succ(Zero)), zzz480, zzz481), zzz476, bh)
new_mkVBalBranch0(zzz31, Branch(zzz510, zzz511, Pos(Succ(zzz51200)), zzz513, zzz514), Branch(zzz340, zzz341, zzz342, zzz343, zzz344), h) → new_mkVBalBranch3MkVBalBranch215(zzz340, zzz341, zzz342, zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, new_primPlusNat3(Succ(new_primPlusNat3(new_primPlusNat1(zzz51200), zzz51200)), Succ(zzz51200)), h)
new_mkVBalBranch3MkVBalBranch215(zzz340, zzz341, Pos(Succ(Succ(zzz342000))), zzz343, zzz344, zzz510, zzz511, Succ(zzz512000), zzz513, zzz514, zzz31, Zero, h) → new_mkVBalBranch3MkVBalBranch216(zzz340, zzz341, Succ(zzz342000), zzz343, zzz344, zzz510, zzz511, zzz512000, zzz513, zzz514, zzz31, zzz512000, zzz342000, h)
new_mkVBalBranch3MkVBalBranch110(zzz461, zzz462, zzz463, zzz464, zzz465, zzz466, zzz467, zzz468, zzz469, zzz470, zzz471, Succ(zzz5800), bb) → new_mkVBalBranch3MkVBalBranch115(zzz461, zzz462, zzz463, zzz464, zzz465, zzz466, zzz467, Succ(zzz468), zzz469, zzz470, zzz471, Succ(zzz5800), Succ(Succ(zzz468)), bb)
new_mkVBalBranch3MkVBalBranch223(zzz340, zzz341, Neg(Succ(Zero)), zzz343, zzz344, zzz510, zzz511, Zero, zzz513, zzz514, zzz31, Zero, h) → new_mkVBalBranch3MkVBalBranch118(zzz340, zzz341, Zero, zzz343, zzz344, zzz510, zzz511, zzz513, zzz514, zzz31, new_primPlusNat2(new_primMulNat0(Zero), Succ(Zero)), h)
new_mkVBalBranch3MkVBalBranch227(zzz486, zzz487, zzz488, zzz489, zzz490, zzz491, zzz492, zzz493, zzz494, zzz495, zzz496, bf) → new_mkVBalBranch0(zzz496, Branch(zzz491, zzz492, Neg(Succ(Succ(zzz493))), zzz494, zzz495), zzz489, bf)
new_mkVBalBranch0(zzz31, Branch(zzz510, zzz511, Pos(Zero), zzz513, zzz514), Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), h) → new_mkVBalBranch3MkVBalBranch116(zzz340, zzz341, zzz34200, zzz343, zzz344, zzz510, zzz511, zzz513, zzz514, zzz31, new_primPlusNat2(new_primMulNat0(zzz34200), Succ(zzz34200)), h)
new_mkVBalBranch3MkVBalBranch215(zzz340, zzz341, Pos(Zero), zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, Succ(zzz660), h) → new_mkVBalBranch0(zzz31, zzz514, Branch(zzz340, zzz341, Pos(Zero), zzz343, zzz344), h)
new_mkVBalBranch3MkVBalBranch223(zzz340, zzz341, Neg(Zero), zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, Succ(zzz670), h) → new_mkVBalBranch0(zzz31, Branch(zzz510, zzz511, Neg(Succ(zzz51200)), zzz513, zzz514), zzz343, h)
new_mkVBalBranch3MkVBalBranch216(zzz1105, zzz1106, zzz1107, zzz1108, zzz1109, zzz1110, zzz1111, zzz1112, zzz1113, zzz1114, zzz1115, Zero, Succ(zzz11170), ba) → new_mkVBalBranch0(zzz1115, Branch(zzz1110, zzz1111, Pos(Succ(Succ(zzz1112))), zzz1113, zzz1114), zzz1108, ba)
new_mkVBalBranch3MkVBalBranch217(zzz473, zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, zzz481, zzz482, Succ(zzz4830), Zero, bh) → new_mkVBalBranch3MkVBalBranch121(zzz473, zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, zzz481, zzz482, new_primMulNat1(zzz475), bh)
new_mkVBalBranch3MkVBalBranch115(zzz1986, zzz1987, zzz1988, zzz1989, zzz1990, zzz1991, zzz1992, zzz1993, zzz1994, zzz1995, zzz1996, Zero, Succ(zzz19980), bc) → new_mkVBalBranch0(zzz1996, zzz1995, Branch(zzz1986, zzz1987, Pos(Succ(zzz1988)), zzz1989, zzz1990), bc)
new_mkVBalBranch0(zzz31, Branch(zzz510, zzz511, Neg(Zero), zzz513, zzz514), Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), h) → new_mkVBalBranch3MkVBalBranch117(zzz340, zzz341, zzz34200, zzz343, zzz344, zzz510, zzz511, zzz513, zzz514, zzz31, new_primPlusNat2(new_primMulNat0(zzz34200), Succ(zzz34200)), h)
new_mkVBalBranch3MkVBalBranch223(zzz340, zzz341, Neg(Zero), zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, Zero, h) → new_mkVBalBranch3MkVBalBranch228(zzz340, zzz341, zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, h)
new_mkVBalBranch3MkVBalBranch122(zzz340, zzz341, zzz34200, zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, h) → new_mkVBalBranch0(zzz31, zzz514, Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), h)
new_mkVBalBranch3MkVBalBranch217(zzz473, zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, zzz481, zzz482, Succ(zzz4830), Succ(zzz4840), bh) → new_mkVBalBranch3MkVBalBranch217(zzz473, zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, zzz481, zzz482, zzz4830, zzz4840, bh)
new_mkVBalBranch3MkVBalBranch116(zzz340, zzz341, zzz34200, zzz343, zzz344, zzz510, zzz511, zzz513, zzz514, zzz31, Succ(zzz1200), h) → new_mkVBalBranch0(zzz31, zzz514, Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), h)
new_mkVBalBranch3MkVBalBranch110(zzz461, zzz462, zzz463, zzz464, zzz465, zzz466, zzz467, zzz468, zzz469, zzz470, zzz471, Zero, bb) → new_mkVBalBranch3MkVBalBranch115(zzz461, zzz462, zzz463, zzz464, zzz465, zzz466, zzz467, Succ(zzz468), zzz469, zzz470, zzz471, Zero, Succ(Succ(zzz468)), bb)
new_mkVBalBranch3MkVBalBranch225(zzz498, zzz499, zzz500, zzz501, zzz502, zzz503, zzz504, zzz505, zzz506, zzz507, Zero, Succ(zzz5090), bg) → new_mkVBalBranch0(zzz507, Branch(zzz503, zzz504, Neg(Succ(Zero)), zzz505, zzz506), zzz501, bg)
new_mkVBalBranch3MkVBalBranch223(zzz340, zzz341, Neg(Succ(Succ(Succ(zzz3420000)))), zzz343, zzz344, zzz510, zzz511, Zero, zzz513, zzz514, zzz31, Succ(Zero), h) → new_mkVBalBranch3MkVBalBranch225(zzz340, zzz341, Succ(Succ(zzz3420000)), zzz343, zzz344, zzz510, zzz511, zzz513, zzz514, zzz31, Succ(zzz3420000), Zero, h)
new_mkVBalBranch3MkVBalBranch121(zzz473, zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, zzz481, zzz482, Zero, bh) → new_mkVBalBranch3MkVBalBranch115(zzz473, zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, Zero, zzz480, zzz481, zzz482, Zero, Succ(Zero), bh)
new_mkVBalBranch3MkVBalBranch215(zzz340, zzz341, Pos(Succ(Zero)), zzz343, zzz344, zzz510, zzz511, Succ(zzz512000), zzz513, zzz514, zzz31, Zero, h) → new_mkVBalBranch3MkVBalBranch218(zzz340, zzz341, Zero, zzz343, zzz344, zzz510, zzz511, zzz512000, zzz513, zzz514, zzz31, h)
new_mkVBalBranch3MkVBalBranch225(zzz498, zzz499, zzz500, zzz501, zzz502, zzz503, zzz504, zzz505, zzz506, zzz507, Succ(zzz5080), Zero, bg) → new_mkVBalBranch3MkVBalBranch118(zzz498, zzz499, zzz500, zzz501, zzz502, zzz503, zzz504, zzz505, zzz506, zzz507, new_primPlusNat2(new_primMulNat0(zzz500), Succ(zzz500)), bg)
new_mkVBalBranch3MkVBalBranch223(zzz340, zzz341, Neg(Succ(Zero)), zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, Succ(zzz670), h) → new_mkVBalBranch0(zzz31, Branch(zzz510, zzz511, Neg(Succ(zzz51200)), zzz513, zzz514), zzz343, h)
new_mkVBalBranch3MkVBalBranch215(zzz340, zzz341, Pos(Succ(Zero)), zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, Succ(zzz660), h) → new_mkVBalBranch3MkVBalBranch18(zzz340, zzz341, zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, new_primPlusNat2(new_primMulNat0(Zero), Succ(Zero)), h)
new_mkVBalBranch3MkVBalBranch229(zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, zzz1125, zzz1126, zzz1127, zzz1128, zzz1129, bd) → new_mkVBalBranch3MkVBalBranch119(zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, zzz1125, zzz1126, zzz1127, zzz1128, zzz1129, new_primPlusNat2(new_primMulNat0(zzz1121), Succ(zzz1121)), bd)
new_mkVBalBranch3MkVBalBranch219(zzz340, zzz341, zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, h) → new_mkVBalBranch3MkVBalBranch18(zzz340, zzz341, zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, new_primPlusNat2(new_primMulNat0(Zero), Succ(Zero)), h)
new_mkVBalBranch3MkVBalBranch223(zzz340, zzz341, Neg(Succ(Zero)), zzz343, zzz344, zzz510, zzz511, Succ(zzz512000), zzz513, zzz514, zzz31, Zero, h) → new_mkVBalBranch3MkVBalBranch227(zzz340, zzz341, Zero, zzz343, zzz344, zzz510, zzz511, zzz512000, zzz513, zzz514, zzz31, h)
new_mkVBalBranch3MkVBalBranch226(zzz340, zzz341, zzz3420, zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, h) → new_mkVBalBranch0(zzz31, Branch(zzz510, zzz511, Neg(Succ(zzz51200)), zzz513, zzz514), zzz343, h)
new_mkVBalBranch3MkVBalBranch223(zzz340, zzz341, Neg(Succ(Succ(zzz342000))), zzz343, zzz344, zzz510, zzz511, Succ(zzz512000), zzz513, zzz514, zzz31, Zero, h) → new_mkVBalBranch3MkVBalBranch224(zzz340, zzz341, Succ(zzz342000), zzz343, zzz344, zzz510, zzz511, zzz512000, zzz513, zzz514, zzz31, zzz342000, zzz512000, h)
new_mkVBalBranch3MkVBalBranch215(zzz340, zzz341, Pos(Succ(Succ(zzz342000))), zzz343, zzz344, zzz510, zzz511, Zero, zzz513, zzz514, zzz31, Succ(Succ(zzz6600)), h) → new_mkVBalBranch3MkVBalBranch217(zzz340, zzz341, Succ(zzz342000), zzz343, zzz344, zzz510, zzz511, zzz513, zzz514, zzz31, Succ(zzz6600), zzz342000, h)
new_mkVBalBranch3MkVBalBranch218(zzz461, zzz462, zzz463, zzz464, zzz465, zzz466, zzz467, zzz468, zzz469, zzz470, zzz471, bb) → new_mkVBalBranch3MkVBalBranch110(zzz461, zzz462, zzz463, zzz464, zzz465, zzz466, zzz467, zzz468, zzz469, zzz470, zzz471, new_primPlusNat2(new_primMulNat0(zzz463), Succ(zzz463)), bb)
new_mkVBalBranch3MkVBalBranch117(zzz340, zzz341, zzz34200, zzz343, zzz344, zzz510, zzz511, zzz513, zzz514, zzz31, Succ(zzz1240), h) → new_mkVBalBranch0(zzz31, zzz514, Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), h)
new_mkVBalBranch3MkVBalBranch221(zzz340, zzz341, Succ(zzz34200), zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, h) → new_mkVBalBranch3MkVBalBranch19(zzz340, zzz341, zzz34200, zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, new_primPlusNat2(new_primPlusNat3(Succ(new_primPlusNat3(new_primPlusNat1(zzz34200), zzz34200)), Succ(zzz34200)), Succ(zzz34200)), h)
new_mkVBalBranch3MkVBalBranch120(zzz2050, zzz2051, zzz2052, zzz2053, zzz2054, zzz2055, zzz2056, zzz2057, zzz2058, zzz2059, zzz2060, Succ(zzz20610), Succ(zzz20620), be) → new_mkVBalBranch3MkVBalBranch120(zzz2050, zzz2051, zzz2052, zzz2053, zzz2054, zzz2055, zzz2056, zzz2057, zzz2058, zzz2059, zzz2060, zzz20610, zzz20620, be)
new_mkVBalBranch3MkVBalBranch217(zzz473, zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, zzz481, zzz482, Zero, Zero, bh) → new_mkVBalBranch3MkVBalBranch233(zzz473, zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, zzz481, zzz482, bh)
new_mkVBalBranch0(zzz31, Branch(zzz510, zzz511, Neg(Succ(zzz51200)), zzz513, zzz514), Branch(zzz340, zzz341, zzz342, zzz343, zzz344), h) → new_mkVBalBranch3MkVBalBranch223(zzz340, zzz341, zzz342, zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, new_primPlusNat3(Succ(new_primPlusNat3(new_primPlusNat1(zzz51200), zzz51200)), Succ(zzz51200)), h)
new_mkVBalBranch3MkVBalBranch216(zzz1105, zzz1106, zzz1107, zzz1108, zzz1109, zzz1110, zzz1111, zzz1112, zzz1113, zzz1114, zzz1115, Succ(zzz11160), Succ(zzz11170), ba) → new_mkVBalBranch3MkVBalBranch216(zzz1105, zzz1106, zzz1107, zzz1108, zzz1109, zzz1110, zzz1111, zzz1112, zzz1113, zzz1114, zzz1115, zzz11160, zzz11170, ba)
new_mkVBalBranch3MkVBalBranch223(zzz340, zzz341, Pos(zzz3420), zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, Succ(zzz670), h) → new_mkVBalBranch0(zzz31, Branch(zzz510, zzz511, Neg(Succ(zzz51200)), zzz513, zzz514), zzz343, h)
new_mkVBalBranch3MkVBalBranch223(zzz340, zzz341, Neg(Succ(Succ(Succ(zzz3420000)))), zzz343, zzz344, zzz510, zzz511, Succ(zzz512000), zzz513, zzz514, zzz31, Succ(Zero), h) → new_mkVBalBranch3MkVBalBranch224(zzz340, zzz341, Succ(Succ(zzz3420000)), zzz343, zzz344, zzz510, zzz511, zzz512000, zzz513, zzz514, zzz31, Succ(zzz3420000), Succ(zzz512000), h)
new_mkVBalBranch3MkVBalBranch19(zzz340, zzz341, zzz34200, zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, Zero, h) → new_mkVBalBranch3MkVBalBranch122(zzz340, zzz341, zzz34200, zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, h)
new_mkVBalBranch3MkVBalBranch215(zzz340, zzz341, Pos(Succ(Succ(zzz342000))), zzz343, zzz344, zzz510, zzz511, Zero, zzz513, zzz514, zzz31, Zero, h) → new_mkVBalBranch0(zzz31, Branch(zzz510, zzz511, Pos(Succ(Zero)), zzz513, zzz514), zzz343, h)
new_mkVBalBranch3MkVBalBranch225(zzz498, zzz499, zzz500, zzz501, zzz502, zzz503, zzz504, zzz505, zzz506, zzz507, Succ(zzz5080), Succ(zzz5090), bg) → new_mkVBalBranch3MkVBalBranch225(zzz498, zzz499, zzz500, zzz501, zzz502, zzz503, zzz504, zzz505, zzz506, zzz507, zzz5080, zzz5090, bg)
new_mkVBalBranch3MkVBalBranch19(zzz340, zzz341, zzz34200, zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, Succ(zzz1410), h) → new_mkVBalBranch0(zzz31, zzz514, Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), h)
new_mkVBalBranch3MkVBalBranch224(zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, zzz1125, zzz1126, zzz1127, zzz1128, zzz1129, Succ(zzz11300), Zero, bd) → new_mkVBalBranch3MkVBalBranch119(zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, zzz1125, zzz1126, zzz1127, zzz1128, zzz1129, new_primPlusNat2(new_primMulNat0(zzz1121), Succ(zzz1121)), bd)
new_mkVBalBranch3MkVBalBranch223(zzz340, zzz341, Pos(zzz3420), zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, Zero, h) → new_mkVBalBranch3MkVBalBranch226(zzz340, zzz341, zzz3420, zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, h)
new_mkVBalBranch3MkVBalBranch223(zzz340, zzz341, Neg(Succ(Succ(Zero))), zzz343, zzz344, zzz510, zzz511, Succ(zzz512000), zzz513, zzz514, zzz31, Succ(Zero), h) → new_mkVBalBranch3MkVBalBranch224(zzz340, zzz341, Succ(Zero), zzz343, zzz344, zzz510, zzz511, zzz512000, zzz513, zzz514, zzz31, Zero, Succ(zzz512000), h)
new_mkVBalBranch3MkVBalBranch224(zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, zzz1125, zzz1126, zzz1127, zzz1128, zzz1129, Zero, Zero, bd) → new_mkVBalBranch3MkVBalBranch229(zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, zzz1125, zzz1126, zzz1127, zzz1128, zzz1129, bd)
new_mkVBalBranch3MkVBalBranch224(zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, zzz1125, zzz1126, zzz1127, zzz1128, zzz1129, Zero, Succ(zzz11310), bd) → new_mkVBalBranch3MkVBalBranch227(zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, zzz1125, zzz1126, zzz1127, zzz1128, zzz1129, bd)
new_mkVBalBranch3MkVBalBranch223(zzz340, zzz341, Neg(Succ(Succ(zzz342000))), zzz343, zzz344, zzz510, zzz511, Zero, zzz513, zzz514, zzz31, Zero, h) → new_mkVBalBranch3MkVBalBranch118(zzz340, zzz341, Succ(zzz342000), zzz343, zzz344, zzz510, zzz511, zzz513, zzz514, zzz31, new_primPlusNat2(new_primMulNat0(Succ(zzz342000)), Succ(Succ(zzz342000))), h)
new_mkVBalBranch3MkVBalBranch230(zzz498, zzz499, zzz500, zzz501, zzz502, zzz503, zzz504, zzz505, zzz506, zzz507, bg) → new_mkVBalBranch3MkVBalBranch118(zzz498, zzz499, zzz500, zzz501, zzz502, zzz503, zzz504, zzz505, zzz506, zzz507, new_primPlusNat2(new_primMulNat0(zzz500), Succ(zzz500)), bg)
new_mkVBalBranch3MkVBalBranch223(zzz340, zzz341, Neg(Succ(Succ(Zero))), zzz343, zzz344, zzz510, zzz511, Zero, zzz513, zzz514, zzz31, Succ(Succ(zzz6700)), h) → new_mkVBalBranch3MkVBalBranch225(zzz340, zzz341, Succ(Zero), zzz343, zzz344, zzz510, zzz511, zzz513, zzz514, zzz31, Zero, Succ(zzz6700), h)
new_mkVBalBranch3MkVBalBranch223(zzz340, zzz341, Neg(Succ(Succ(Succ(zzz3420000)))), zzz343, zzz344, zzz510, zzz511, Succ(zzz512000), zzz513, zzz514, zzz31, Succ(Succ(zzz6700)), h) → new_mkVBalBranch3MkVBalBranch224(zzz340, zzz341, Succ(Succ(zzz3420000)), zzz343, zzz344, zzz510, zzz511, zzz512000, zzz513, zzz514, zzz31, Succ(zzz3420000), Succ(Succ(new_primPlusNat2(zzz6700, zzz512000))), h)
new_mkVBalBranch3MkVBalBranch115(zzz1986, zzz1987, zzz1988, zzz1989, zzz1990, zzz1991, zzz1992, zzz1993, zzz1994, zzz1995, zzz1996, Succ(zzz19970), Succ(zzz19980), bc) → new_mkVBalBranch3MkVBalBranch115(zzz1986, zzz1987, zzz1988, zzz1989, zzz1990, zzz1991, zzz1992, zzz1993, zzz1994, zzz1995, zzz1996, zzz19970, zzz19980, bc)
new_mkVBalBranch3MkVBalBranch215(zzz340, zzz341, Pos(Zero), zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, Zero, h) → new_mkVBalBranch3MkVBalBranch220(zzz340, zzz341, zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, h)
new_mkVBalBranch3MkVBalBranch215(zzz340, zzz341, Neg(Zero), zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, Succ(zzz660), h) → new_mkVBalBranch0(zzz31, zzz514, Branch(zzz340, zzz341, Neg(Zero), zzz343, zzz344), h)
new_mkVBalBranch3MkVBalBranch118(zzz498, zzz499, zzz500, zzz501, zzz502, zzz503, zzz504, zzz505, zzz506, zzz507, Succ(zzz8040), bg) → new_mkVBalBranch3MkVBalBranch120(zzz498, zzz499, zzz500, zzz501, zzz502, zzz503, zzz504, Zero, zzz505, zzz506, zzz507, Succ(Zero), Succ(zzz8040), bg)
new_mkVBalBranch3MkVBalBranch216(zzz1105, zzz1106, zzz1107, zzz1108, zzz1109, zzz1110, zzz1111, zzz1112, zzz1113, zzz1114, zzz1115, Succ(zzz11160), Zero, ba) → new_mkVBalBranch3MkVBalBranch218(zzz1105, zzz1106, zzz1107, zzz1108, zzz1109, zzz1110, zzz1111, zzz1112, zzz1113, zzz1114, zzz1115, ba)
new_mkVBalBranch3MkVBalBranch221(zzz340, zzz341, Zero, zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, h) → new_mkVBalBranch0(zzz31, zzz514, Branch(zzz340, zzz341, Neg(Zero), zzz343, zzz344), h)
new_mkVBalBranch3MkVBalBranch215(zzz340, zzz341, Pos(Succ(Succ(zzz342000))), zzz343, zzz344, zzz510, zzz511, Succ(zzz512000), zzz513, zzz514, zzz31, Succ(Zero), h) → new_mkVBalBranch3MkVBalBranch216(zzz340, zzz341, Succ(zzz342000), zzz343, zzz344, zzz510, zzz511, zzz512000, zzz513, zzz514, zzz31, Succ(zzz512000), zzz342000, h)
new_mkVBalBranch3MkVBalBranch215(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, Succ(zzz660), h) → new_mkVBalBranch3MkVBalBranch19(zzz340, zzz341, zzz34200, zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, new_primPlusNat2(new_primMulNat0(zzz34200), Succ(zzz34200)), h)
new_mkVBalBranch3MkVBalBranch216(zzz1105, zzz1106, zzz1107, zzz1108, zzz1109, zzz1110, zzz1111, zzz1112, zzz1113, zzz1114, zzz1115, Zero, Zero, ba) → new_mkVBalBranch3MkVBalBranch222(zzz1105, zzz1106, zzz1107, zzz1108, zzz1109, zzz1110, zzz1111, zzz1112, zzz1113, zzz1114, zzz1115, ba)
new_mkVBalBranch3MkVBalBranch233(zzz473, zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, zzz481, zzz482, bh) → new_mkVBalBranch3MkVBalBranch121(zzz473, zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, zzz481, zzz482, new_primMulNat1(zzz475), bh)
new_mkVBalBranch3MkVBalBranch215(zzz340, zzz341, Pos(Succ(Succ(zzz342000))), zzz343, zzz344, zzz510, zzz511, Zero, zzz513, zzz514, zzz31, Succ(Zero), h) → new_mkVBalBranch3MkVBalBranch217(zzz340, zzz341, Succ(zzz342000), zzz343, zzz344, zzz510, zzz511, zzz513, zzz514, zzz31, Zero, zzz342000, h)
new_mkVBalBranch3MkVBalBranch119(zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, zzz1125, zzz1126, zzz1127, zzz1128, zzz1129, Succ(zzz12130), bd) → new_mkVBalBranch3MkVBalBranch120(zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, zzz1125, Succ(zzz1126), zzz1127, zzz1128, zzz1129, Succ(Succ(zzz1126)), Succ(zzz12130), bd)
new_mkVBalBranch3MkVBalBranch18(zzz340, zzz341, zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, Zero, h) → new_mkVBalBranch3MkVBalBranch115(zzz340, zzz341, Zero, zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, Zero, Succ(zzz51200), h)

The TRS R consists of the following rules:

new_primPlusNat1(Zero) → Zero
new_primMulNat0(zzz6200) → new_primPlusNat3(Succ(new_primPlusNat3(new_primPlusNat1(zzz6200), zzz6200)), Succ(zzz6200))
new_primPlusNat2(Succ(zzz900), Succ(zzz9100)) → Succ(Succ(new_primPlusNat2(zzz900, zzz9100)))
new_primPlusNat3(zzz90, Succ(zzz910)) → Succ(Succ(new_primPlusNat2(zzz90, zzz910)))
new_primPlusNat3(zzz90, Zero) → Succ(zzz90)
new_primMulNat1(zzz34200) → new_primPlusNat2(new_primMulNat0(zzz34200), Succ(zzz34200))
new_primPlusNat2(Zero, Zero) → Zero
new_primPlusNat1(Succ(zzz62000)) → Succ(Succ(new_primPlusNat1(zzz62000)))
new_primPlusNat2(Succ(zzz900), Zero) → Succ(zzz900)
new_primPlusNat2(Zero, Succ(zzz9100)) → Succ(zzz9100)

The set Q consists of the following terms:

new_primPlusNat2(Zero, Succ(x0))
new_primMulNat1(x0)
new_primMulNat0(x0)
new_primPlusNat3(x0, Succ(x1))
new_primPlusNat2(Succ(x0), Succ(x1))
new_primPlusNat3(x0, Zero)
new_primPlusNat1(Zero)
new_primPlusNat2(Zero, Zero)
new_primPlusNat1(Succ(x0))
new_primPlusNat2(Succ(x0), Zero)

We have to consider all minimal (P,Q,R)-chains.
By rewriting [15] the rule new_mkVBalBranch3MkVBalBranch217(zzz473, zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, zzz481, zzz482, Succ(zzz4830), Zero, bh) → new_mkVBalBranch3MkVBalBranch121(zzz473, zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, zzz481, zzz482, new_primMulNat1(zzz475), bh) at position [10] we obtained the following new rules:

new_mkVBalBranch3MkVBalBranch217(zzz473, zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, zzz481, zzz482, Succ(zzz4830), Zero, bh) → new_mkVBalBranch3MkVBalBranch121(zzz473, zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, zzz481, zzz482, new_primPlusNat2(new_primMulNat0(zzz475), Succ(zzz475)), bh)



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

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

new_mkVBalBranch3MkVBalBranch215(zzz340, zzz341, Neg(zzz3420), zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, Zero, h) → new_mkVBalBranch3MkVBalBranch221(zzz340, zzz341, zzz3420, zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, h)
new_mkVBalBranch3MkVBalBranch225(zzz498, zzz499, zzz500, zzz501, zzz502, zzz503, zzz504, zzz505, zzz506, zzz507, Zero, Zero, bg) → new_mkVBalBranch3MkVBalBranch230(zzz498, zzz499, zzz500, zzz501, zzz502, zzz503, zzz504, zzz505, zzz506, zzz507, bg)
new_mkVBalBranch3MkVBalBranch18(zzz340, zzz341, zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, Succ(zzz1480), h) → new_mkVBalBranch3MkVBalBranch115(zzz340, zzz341, Zero, zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, Succ(zzz1480), Succ(zzz51200), h)
new_mkVBalBranch0(zzz31, Branch(zzz510, zzz511, Neg(Zero), zzz513, zzz514), Branch(zzz340, zzz341, Pos(Succ(zzz34200)), zzz343, zzz344), h) → new_mkVBalBranch0(zzz31, Branch(zzz510, zzz511, Neg(Zero), zzz513, zzz514), zzz343, h)
new_mkVBalBranch3MkVBalBranch215(zzz340, zzz341, Pos(Succ(Succ(zzz342000))), zzz343, zzz344, zzz510, zzz511, Succ(zzz512000), zzz513, zzz514, zzz31, Succ(Succ(zzz6600)), h) → new_mkVBalBranch3MkVBalBranch216(zzz340, zzz341, Succ(zzz342000), zzz343, zzz344, zzz510, zzz511, zzz512000, zzz513, zzz514, zzz31, Succ(Succ(new_primPlusNat2(zzz6600, zzz512000))), zzz342000, h)
new_mkVBalBranch3MkVBalBranch223(zzz340, zzz341, Neg(Succ(Succ(Succ(zzz3420000)))), zzz343, zzz344, zzz510, zzz511, Zero, zzz513, zzz514, zzz31, Succ(Succ(zzz6700)), h) → new_mkVBalBranch3MkVBalBranch225(zzz340, zzz341, Succ(Succ(zzz3420000)), zzz343, zzz344, zzz510, zzz511, zzz513, zzz514, zzz31, Succ(zzz3420000), Succ(zzz6700), h)
new_mkVBalBranch3MkVBalBranch220(zzz340, zzz341, zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, h) → new_mkVBalBranch0(zzz31, zzz514, Branch(zzz340, zzz341, Pos(Zero), zzz343, zzz344), h)
new_mkVBalBranch3MkVBalBranch120(zzz2050, zzz2051, zzz2052, zzz2053, zzz2054, zzz2055, zzz2056, zzz2057, zzz2058, zzz2059, zzz2060, Zero, Succ(zzz20620), be) → new_mkVBalBranch0(zzz2060, zzz2059, Branch(zzz2050, zzz2051, Neg(Succ(zzz2052)), zzz2053, zzz2054), be)
new_mkVBalBranch3MkVBalBranch121(zzz473, zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, zzz481, zzz482, Succ(zzz7390), bh) → new_mkVBalBranch3MkVBalBranch115(zzz473, zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, Zero, zzz480, zzz481, zzz482, Succ(zzz7390), Succ(Zero), bh)
new_mkVBalBranch0(zzz31, Branch(zzz510, zzz511, Pos(Zero), zzz513, zzz514), Branch(zzz340, zzz341, Pos(Succ(zzz34200)), zzz343, zzz344), h) → new_mkVBalBranch0(zzz31, Branch(zzz510, zzz511, Pos(Zero), zzz513, zzz514), zzz343, h)
new_mkVBalBranch3MkVBalBranch228(zzz340, zzz341, zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, h) → new_mkVBalBranch0(zzz31, Branch(zzz510, zzz511, Neg(Succ(zzz51200)), zzz513, zzz514), zzz343, h)
new_mkVBalBranch3MkVBalBranch222(zzz461, zzz462, zzz463, zzz464, zzz465, zzz466, zzz467, zzz468, zzz469, zzz470, zzz471, bb) → new_mkVBalBranch3MkVBalBranch110(zzz461, zzz462, zzz463, zzz464, zzz465, zzz466, zzz467, zzz468, zzz469, zzz470, zzz471, new_primPlusNat2(new_primMulNat0(zzz463), Succ(zzz463)), bb)
new_mkVBalBranch3MkVBalBranch215(zzz340, zzz341, Pos(Succ(Zero)), zzz343, zzz344, zzz510, zzz511, Zero, zzz513, zzz514, zzz31, Zero, h) → new_mkVBalBranch3MkVBalBranch219(zzz340, zzz341, zzz343, zzz344, zzz510, zzz511, Zero, zzz513, zzz514, zzz31, h)
new_mkVBalBranch3MkVBalBranch223(zzz340, zzz341, Neg(Succ(Succ(Zero))), zzz343, zzz344, zzz510, zzz511, Succ(zzz512000), zzz513, zzz514, zzz31, Succ(Succ(zzz6700)), h) → new_mkVBalBranch3MkVBalBranch224(zzz340, zzz341, Succ(Zero), zzz343, zzz344, zzz510, zzz511, zzz512000, zzz513, zzz514, zzz31, Zero, Succ(Succ(new_primPlusNat2(zzz6700, zzz512000))), h)
new_mkVBalBranch3MkVBalBranch223(zzz340, zzz341, Neg(Succ(Succ(Zero))), zzz343, zzz344, zzz510, zzz511, Zero, zzz513, zzz514, zzz31, Succ(Zero), h) → new_mkVBalBranch3MkVBalBranch225(zzz340, zzz341, Succ(Zero), zzz343, zzz344, zzz510, zzz511, zzz513, zzz514, zzz31, Zero, Zero, h)
new_mkVBalBranch3MkVBalBranch224(zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, zzz1125, zzz1126, zzz1127, zzz1128, zzz1129, Succ(zzz11300), Succ(zzz11310), bd) → new_mkVBalBranch3MkVBalBranch224(zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, zzz1125, zzz1126, zzz1127, zzz1128, zzz1129, zzz11300, zzz11310, bd)
new_mkVBalBranch0(zzz31, Branch(zzz510, zzz511, Pos(Succ(zzz51200)), zzz513, zzz514), Branch(zzz340, zzz341, zzz342, zzz343, zzz344), h) → new_mkVBalBranch3MkVBalBranch215(zzz340, zzz341, zzz342, zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, new_primPlusNat3(Succ(new_primPlusNat3(new_primPlusNat1(zzz51200), zzz51200)), Succ(zzz51200)), h)
new_mkVBalBranch3MkVBalBranch217(zzz473, zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, zzz481, zzz482, Zero, Succ(zzz4840), bh) → new_mkVBalBranch0(zzz482, Branch(zzz478, zzz479, Pos(Succ(Zero)), zzz480, zzz481), zzz476, bh)
new_mkVBalBranch3MkVBalBranch215(zzz340, zzz341, Pos(Succ(Succ(zzz342000))), zzz343, zzz344, zzz510, zzz511, Succ(zzz512000), zzz513, zzz514, zzz31, Zero, h) → new_mkVBalBranch3MkVBalBranch216(zzz340, zzz341, Succ(zzz342000), zzz343, zzz344, zzz510, zzz511, zzz512000, zzz513, zzz514, zzz31, zzz512000, zzz342000, h)
new_mkVBalBranch3MkVBalBranch110(zzz461, zzz462, zzz463, zzz464, zzz465, zzz466, zzz467, zzz468, zzz469, zzz470, zzz471, Succ(zzz5800), bb) → new_mkVBalBranch3MkVBalBranch115(zzz461, zzz462, zzz463, zzz464, zzz465, zzz466, zzz467, Succ(zzz468), zzz469, zzz470, zzz471, Succ(zzz5800), Succ(Succ(zzz468)), bb)
new_mkVBalBranch3MkVBalBranch223(zzz340, zzz341, Neg(Succ(Zero)), zzz343, zzz344, zzz510, zzz511, Zero, zzz513, zzz514, zzz31, Zero, h) → new_mkVBalBranch3MkVBalBranch118(zzz340, zzz341, Zero, zzz343, zzz344, zzz510, zzz511, zzz513, zzz514, zzz31, new_primPlusNat2(new_primMulNat0(Zero), Succ(Zero)), h)
new_mkVBalBranch3MkVBalBranch227(zzz486, zzz487, zzz488, zzz489, zzz490, zzz491, zzz492, zzz493, zzz494, zzz495, zzz496, bf) → new_mkVBalBranch0(zzz496, Branch(zzz491, zzz492, Neg(Succ(Succ(zzz493))), zzz494, zzz495), zzz489, bf)
new_mkVBalBranch3MkVBalBranch215(zzz340, zzz341, Pos(Zero), zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, Succ(zzz660), h) → new_mkVBalBranch0(zzz31, zzz514, Branch(zzz340, zzz341, Pos(Zero), zzz343, zzz344), h)
new_mkVBalBranch0(zzz31, Branch(zzz510, zzz511, Pos(Zero), zzz513, zzz514), Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), h) → new_mkVBalBranch3MkVBalBranch116(zzz340, zzz341, zzz34200, zzz343, zzz344, zzz510, zzz511, zzz513, zzz514, zzz31, new_primPlusNat2(new_primMulNat0(zzz34200), Succ(zzz34200)), h)
new_mkVBalBranch3MkVBalBranch217(zzz473, zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, zzz481, zzz482, Succ(zzz4830), Zero, bh) → new_mkVBalBranch3MkVBalBranch121(zzz473, zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, zzz481, zzz482, new_primPlusNat2(new_primMulNat0(zzz475), Succ(zzz475)), bh)
new_mkVBalBranch3MkVBalBranch223(zzz340, zzz341, Neg(Zero), zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, Succ(zzz670), h) → new_mkVBalBranch0(zzz31, Branch(zzz510, zzz511, Neg(Succ(zzz51200)), zzz513, zzz514), zzz343, h)
new_mkVBalBranch3MkVBalBranch216(zzz1105, zzz1106, zzz1107, zzz1108, zzz1109, zzz1110, zzz1111, zzz1112, zzz1113, zzz1114, zzz1115, Zero, Succ(zzz11170), ba) → new_mkVBalBranch0(zzz1115, Branch(zzz1110, zzz1111, Pos(Succ(Succ(zzz1112))), zzz1113, zzz1114), zzz1108, ba)
new_mkVBalBranch3MkVBalBranch115(zzz1986, zzz1987, zzz1988, zzz1989, zzz1990, zzz1991, zzz1992, zzz1993, zzz1994, zzz1995, zzz1996, Zero, Succ(zzz19980), bc) → new_mkVBalBranch0(zzz1996, zzz1995, Branch(zzz1986, zzz1987, Pos(Succ(zzz1988)), zzz1989, zzz1990), bc)
new_mkVBalBranch0(zzz31, Branch(zzz510, zzz511, Neg(Zero), zzz513, zzz514), Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), h) → new_mkVBalBranch3MkVBalBranch117(zzz340, zzz341, zzz34200, zzz343, zzz344, zzz510, zzz511, zzz513, zzz514, zzz31, new_primPlusNat2(new_primMulNat0(zzz34200), Succ(zzz34200)), h)
new_mkVBalBranch3MkVBalBranch223(zzz340, zzz341, Neg(Zero), zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, Zero, h) → new_mkVBalBranch3MkVBalBranch228(zzz340, zzz341, zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, h)
new_mkVBalBranch3MkVBalBranch122(zzz340, zzz341, zzz34200, zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, h) → new_mkVBalBranch0(zzz31, zzz514, Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), h)
new_mkVBalBranch3MkVBalBranch217(zzz473, zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, zzz481, zzz482, Succ(zzz4830), Succ(zzz4840), bh) → new_mkVBalBranch3MkVBalBranch217(zzz473, zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, zzz481, zzz482, zzz4830, zzz4840, bh)
new_mkVBalBranch3MkVBalBranch116(zzz340, zzz341, zzz34200, zzz343, zzz344, zzz510, zzz511, zzz513, zzz514, zzz31, Succ(zzz1200), h) → new_mkVBalBranch0(zzz31, zzz514, Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), h)
new_mkVBalBranch3MkVBalBranch110(zzz461, zzz462, zzz463, zzz464, zzz465, zzz466, zzz467, zzz468, zzz469, zzz470, zzz471, Zero, bb) → new_mkVBalBranch3MkVBalBranch115(zzz461, zzz462, zzz463, zzz464, zzz465, zzz466, zzz467, Succ(zzz468), zzz469, zzz470, zzz471, Zero, Succ(Succ(zzz468)), bb)
new_mkVBalBranch3MkVBalBranch225(zzz498, zzz499, zzz500, zzz501, zzz502, zzz503, zzz504, zzz505, zzz506, zzz507, Zero, Succ(zzz5090), bg) → new_mkVBalBranch0(zzz507, Branch(zzz503, zzz504, Neg(Succ(Zero)), zzz505, zzz506), zzz501, bg)
new_mkVBalBranch3MkVBalBranch223(zzz340, zzz341, Neg(Succ(Succ(Succ(zzz3420000)))), zzz343, zzz344, zzz510, zzz511, Zero, zzz513, zzz514, zzz31, Succ(Zero), h) → new_mkVBalBranch3MkVBalBranch225(zzz340, zzz341, Succ(Succ(zzz3420000)), zzz343, zzz344, zzz510, zzz511, zzz513, zzz514, zzz31, Succ(zzz3420000), Zero, h)
new_mkVBalBranch3MkVBalBranch121(zzz473, zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, zzz481, zzz482, Zero, bh) → new_mkVBalBranch3MkVBalBranch115(zzz473, zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, Zero, zzz480, zzz481, zzz482, Zero, Succ(Zero), bh)
new_mkVBalBranch3MkVBalBranch215(zzz340, zzz341, Pos(Succ(Zero)), zzz343, zzz344, zzz510, zzz511, Succ(zzz512000), zzz513, zzz514, zzz31, Zero, h) → new_mkVBalBranch3MkVBalBranch218(zzz340, zzz341, Zero, zzz343, zzz344, zzz510, zzz511, zzz512000, zzz513, zzz514, zzz31, h)
new_mkVBalBranch3MkVBalBranch223(zzz340, zzz341, Neg(Succ(Zero)), zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, Succ(zzz670), h) → new_mkVBalBranch0(zzz31, Branch(zzz510, zzz511, Neg(Succ(zzz51200)), zzz513, zzz514), zzz343, h)
new_mkVBalBranch3MkVBalBranch225(zzz498, zzz499, zzz500, zzz501, zzz502, zzz503, zzz504, zzz505, zzz506, zzz507, Succ(zzz5080), Zero, bg) → new_mkVBalBranch3MkVBalBranch118(zzz498, zzz499, zzz500, zzz501, zzz502, zzz503, zzz504, zzz505, zzz506, zzz507, new_primPlusNat2(new_primMulNat0(zzz500), Succ(zzz500)), bg)
new_mkVBalBranch3MkVBalBranch215(zzz340, zzz341, Pos(Succ(Zero)), zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, Succ(zzz660), h) → new_mkVBalBranch3MkVBalBranch18(zzz340, zzz341, zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, new_primPlusNat2(new_primMulNat0(Zero), Succ(Zero)), h)
new_mkVBalBranch3MkVBalBranch229(zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, zzz1125, zzz1126, zzz1127, zzz1128, zzz1129, bd) → new_mkVBalBranch3MkVBalBranch119(zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, zzz1125, zzz1126, zzz1127, zzz1128, zzz1129, new_primPlusNat2(new_primMulNat0(zzz1121), Succ(zzz1121)), bd)
new_mkVBalBranch3MkVBalBranch219(zzz340, zzz341, zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, h) → new_mkVBalBranch3MkVBalBranch18(zzz340, zzz341, zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, new_primPlusNat2(new_primMulNat0(Zero), Succ(Zero)), h)
new_mkVBalBranch3MkVBalBranch223(zzz340, zzz341, Neg(Succ(Zero)), zzz343, zzz344, zzz510, zzz511, Succ(zzz512000), zzz513, zzz514, zzz31, Zero, h) → new_mkVBalBranch3MkVBalBranch227(zzz340, zzz341, Zero, zzz343, zzz344, zzz510, zzz511, zzz512000, zzz513, zzz514, zzz31, h)
new_mkVBalBranch3MkVBalBranch215(zzz340, zzz341, Pos(Succ(Succ(zzz342000))), zzz343, zzz344, zzz510, zzz511, Zero, zzz513, zzz514, zzz31, Succ(Succ(zzz6600)), h) → new_mkVBalBranch3MkVBalBranch217(zzz340, zzz341, Succ(zzz342000), zzz343, zzz344, zzz510, zzz511, zzz513, zzz514, zzz31, Succ(zzz6600), zzz342000, h)
new_mkVBalBranch3MkVBalBranch223(zzz340, zzz341, Neg(Succ(Succ(zzz342000))), zzz343, zzz344, zzz510, zzz511, Succ(zzz512000), zzz513, zzz514, zzz31, Zero, h) → new_mkVBalBranch3MkVBalBranch224(zzz340, zzz341, Succ(zzz342000), zzz343, zzz344, zzz510, zzz511, zzz512000, zzz513, zzz514, zzz31, zzz342000, zzz512000, h)
new_mkVBalBranch3MkVBalBranch226(zzz340, zzz341, zzz3420, zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, h) → new_mkVBalBranch0(zzz31, Branch(zzz510, zzz511, Neg(Succ(zzz51200)), zzz513, zzz514), zzz343, h)
new_mkVBalBranch3MkVBalBranch218(zzz461, zzz462, zzz463, zzz464, zzz465, zzz466, zzz467, zzz468, zzz469, zzz470, zzz471, bb) → new_mkVBalBranch3MkVBalBranch110(zzz461, zzz462, zzz463, zzz464, zzz465, zzz466, zzz467, zzz468, zzz469, zzz470, zzz471, new_primPlusNat2(new_primMulNat0(zzz463), Succ(zzz463)), bb)
new_mkVBalBranch3MkVBalBranch117(zzz340, zzz341, zzz34200, zzz343, zzz344, zzz510, zzz511, zzz513, zzz514, zzz31, Succ(zzz1240), h) → new_mkVBalBranch0(zzz31, zzz514, Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), h)
new_mkVBalBranch0(zzz31, Branch(zzz510, zzz511, Neg(Succ(zzz51200)), zzz513, zzz514), Branch(zzz340, zzz341, zzz342, zzz343, zzz344), h) → new_mkVBalBranch3MkVBalBranch223(zzz340, zzz341, zzz342, zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, new_primPlusNat3(Succ(new_primPlusNat3(new_primPlusNat1(zzz51200), zzz51200)), Succ(zzz51200)), h)
new_mkVBalBranch3MkVBalBranch217(zzz473, zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, zzz481, zzz482, Zero, Zero, bh) → new_mkVBalBranch3MkVBalBranch233(zzz473, zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, zzz481, zzz482, bh)
new_mkVBalBranch3MkVBalBranch120(zzz2050, zzz2051, zzz2052, zzz2053, zzz2054, zzz2055, zzz2056, zzz2057, zzz2058, zzz2059, zzz2060, Succ(zzz20610), Succ(zzz20620), be) → new_mkVBalBranch3MkVBalBranch120(zzz2050, zzz2051, zzz2052, zzz2053, zzz2054, zzz2055, zzz2056, zzz2057, zzz2058, zzz2059, zzz2060, zzz20610, zzz20620, be)
new_mkVBalBranch3MkVBalBranch221(zzz340, zzz341, Succ(zzz34200), zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, h) → new_mkVBalBranch3MkVBalBranch19(zzz340, zzz341, zzz34200, zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, new_primPlusNat2(new_primPlusNat3(Succ(new_primPlusNat3(new_primPlusNat1(zzz34200), zzz34200)), Succ(zzz34200)), Succ(zzz34200)), h)
new_mkVBalBranch3MkVBalBranch223(zzz340, zzz341, Pos(zzz3420), zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, Succ(zzz670), h) → new_mkVBalBranch0(zzz31, Branch(zzz510, zzz511, Neg(Succ(zzz51200)), zzz513, zzz514), zzz343, h)
new_mkVBalBranch3MkVBalBranch216(zzz1105, zzz1106, zzz1107, zzz1108, zzz1109, zzz1110, zzz1111, zzz1112, zzz1113, zzz1114, zzz1115, Succ(zzz11160), Succ(zzz11170), ba) → new_mkVBalBranch3MkVBalBranch216(zzz1105, zzz1106, zzz1107, zzz1108, zzz1109, zzz1110, zzz1111, zzz1112, zzz1113, zzz1114, zzz1115, zzz11160, zzz11170, ba)
new_mkVBalBranch3MkVBalBranch19(zzz340, zzz341, zzz34200, zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, Zero, h) → new_mkVBalBranch3MkVBalBranch122(zzz340, zzz341, zzz34200, zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, h)
new_mkVBalBranch3MkVBalBranch223(zzz340, zzz341, Neg(Succ(Succ(Succ(zzz3420000)))), zzz343, zzz344, zzz510, zzz511, Succ(zzz512000), zzz513, zzz514, zzz31, Succ(Zero), h) → new_mkVBalBranch3MkVBalBranch224(zzz340, zzz341, Succ(Succ(zzz3420000)), zzz343, zzz344, zzz510, zzz511, zzz512000, zzz513, zzz514, zzz31, Succ(zzz3420000), Succ(zzz512000), h)
new_mkVBalBranch3MkVBalBranch215(zzz340, zzz341, Pos(Succ(Succ(zzz342000))), zzz343, zzz344, zzz510, zzz511, Zero, zzz513, zzz514, zzz31, Zero, h) → new_mkVBalBranch0(zzz31, Branch(zzz510, zzz511, Pos(Succ(Zero)), zzz513, zzz514), zzz343, h)
new_mkVBalBranch3MkVBalBranch225(zzz498, zzz499, zzz500, zzz501, zzz502, zzz503, zzz504, zzz505, zzz506, zzz507, Succ(zzz5080), Succ(zzz5090), bg) → new_mkVBalBranch3MkVBalBranch225(zzz498, zzz499, zzz500, zzz501, zzz502, zzz503, zzz504, zzz505, zzz506, zzz507, zzz5080, zzz5090, bg)
new_mkVBalBranch3MkVBalBranch19(zzz340, zzz341, zzz34200, zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, Succ(zzz1410), h) → new_mkVBalBranch0(zzz31, zzz514, Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), h)
new_mkVBalBranch3MkVBalBranch224(zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, zzz1125, zzz1126, zzz1127, zzz1128, zzz1129, Succ(zzz11300), Zero, bd) → new_mkVBalBranch3MkVBalBranch119(zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, zzz1125, zzz1126, zzz1127, zzz1128, zzz1129, new_primPlusNat2(new_primMulNat0(zzz1121), Succ(zzz1121)), bd)
new_mkVBalBranch3MkVBalBranch224(zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, zzz1125, zzz1126, zzz1127, zzz1128, zzz1129, Zero, Succ(zzz11310), bd) → new_mkVBalBranch3MkVBalBranch227(zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, zzz1125, zzz1126, zzz1127, zzz1128, zzz1129, bd)
new_mkVBalBranch3MkVBalBranch224(zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, zzz1125, zzz1126, zzz1127, zzz1128, zzz1129, Zero, Zero, bd) → new_mkVBalBranch3MkVBalBranch229(zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, zzz1125, zzz1126, zzz1127, zzz1128, zzz1129, bd)
new_mkVBalBranch3MkVBalBranch223(zzz340, zzz341, Neg(Succ(Succ(Zero))), zzz343, zzz344, zzz510, zzz511, Succ(zzz512000), zzz513, zzz514, zzz31, Succ(Zero), h) → new_mkVBalBranch3MkVBalBranch224(zzz340, zzz341, Succ(Zero), zzz343, zzz344, zzz510, zzz511, zzz512000, zzz513, zzz514, zzz31, Zero, Succ(zzz512000), h)
new_mkVBalBranch3MkVBalBranch223(zzz340, zzz341, Pos(zzz3420), zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, Zero, h) → new_mkVBalBranch3MkVBalBranch226(zzz340, zzz341, zzz3420, zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, h)
new_mkVBalBranch3MkVBalBranch223(zzz340, zzz341, Neg(Succ(Succ(zzz342000))), zzz343, zzz344, zzz510, zzz511, Zero, zzz513, zzz514, zzz31, Zero, h) → new_mkVBalBranch3MkVBalBranch118(zzz340, zzz341, Succ(zzz342000), zzz343, zzz344, zzz510, zzz511, zzz513, zzz514, zzz31, new_primPlusNat2(new_primMulNat0(Succ(zzz342000)), Succ(Succ(zzz342000))), h)
new_mkVBalBranch3MkVBalBranch230(zzz498, zzz499, zzz500, zzz501, zzz502, zzz503, zzz504, zzz505, zzz506, zzz507, bg) → new_mkVBalBranch3MkVBalBranch118(zzz498, zzz499, zzz500, zzz501, zzz502, zzz503, zzz504, zzz505, zzz506, zzz507, new_primPlusNat2(new_primMulNat0(zzz500), Succ(zzz500)), bg)
new_mkVBalBranch3MkVBalBranch223(zzz340, zzz341, Neg(Succ(Succ(Succ(zzz3420000)))), zzz343, zzz344, zzz510, zzz511, Succ(zzz512000), zzz513, zzz514, zzz31, Succ(Succ(zzz6700)), h) → new_mkVBalBranch3MkVBalBranch224(zzz340, zzz341, Succ(Succ(zzz3420000)), zzz343, zzz344, zzz510, zzz511, zzz512000, zzz513, zzz514, zzz31, Succ(zzz3420000), Succ(Succ(new_primPlusNat2(zzz6700, zzz512000))), h)
new_mkVBalBranch3MkVBalBranch223(zzz340, zzz341, Neg(Succ(Succ(Zero))), zzz343, zzz344, zzz510, zzz511, Zero, zzz513, zzz514, zzz31, Succ(Succ(zzz6700)), h) → new_mkVBalBranch3MkVBalBranch225(zzz340, zzz341, Succ(Zero), zzz343, zzz344, zzz510, zzz511, zzz513, zzz514, zzz31, Zero, Succ(zzz6700), h)
new_mkVBalBranch3MkVBalBranch215(zzz340, zzz341, Pos(Zero), zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, Zero, h) → new_mkVBalBranch3MkVBalBranch220(zzz340, zzz341, zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, h)
new_mkVBalBranch3MkVBalBranch115(zzz1986, zzz1987, zzz1988, zzz1989, zzz1990, zzz1991, zzz1992, zzz1993, zzz1994, zzz1995, zzz1996, Succ(zzz19970), Succ(zzz19980), bc) → new_mkVBalBranch3MkVBalBranch115(zzz1986, zzz1987, zzz1988, zzz1989, zzz1990, zzz1991, zzz1992, zzz1993, zzz1994, zzz1995, zzz1996, zzz19970, zzz19980, bc)
new_mkVBalBranch3MkVBalBranch215(zzz340, zzz341, Neg(Zero), zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, Succ(zzz660), h) → new_mkVBalBranch0(zzz31, zzz514, Branch(zzz340, zzz341, Neg(Zero), zzz343, zzz344), h)
new_mkVBalBranch3MkVBalBranch118(zzz498, zzz499, zzz500, zzz501, zzz502, zzz503, zzz504, zzz505, zzz506, zzz507, Succ(zzz8040), bg) → new_mkVBalBranch3MkVBalBranch120(zzz498, zzz499, zzz500, zzz501, zzz502, zzz503, zzz504, Zero, zzz505, zzz506, zzz507, Succ(Zero), Succ(zzz8040), bg)
new_mkVBalBranch3MkVBalBranch216(zzz1105, zzz1106, zzz1107, zzz1108, zzz1109, zzz1110, zzz1111, zzz1112, zzz1113, zzz1114, zzz1115, Succ(zzz11160), Zero, ba) → new_mkVBalBranch3MkVBalBranch218(zzz1105, zzz1106, zzz1107, zzz1108, zzz1109, zzz1110, zzz1111, zzz1112, zzz1113, zzz1114, zzz1115, ba)
new_mkVBalBranch3MkVBalBranch215(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, Succ(zzz660), h) → new_mkVBalBranch3MkVBalBranch19(zzz340, zzz341, zzz34200, zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, new_primPlusNat2(new_primMulNat0(zzz34200), Succ(zzz34200)), h)
new_mkVBalBranch3MkVBalBranch215(zzz340, zzz341, Pos(Succ(Succ(zzz342000))), zzz343, zzz344, zzz510, zzz511, Succ(zzz512000), zzz513, zzz514, zzz31, Succ(Zero), h) → new_mkVBalBranch3MkVBalBranch216(zzz340, zzz341, Succ(zzz342000), zzz343, zzz344, zzz510, zzz511, zzz512000, zzz513, zzz514, zzz31, Succ(zzz512000), zzz342000, h)
new_mkVBalBranch3MkVBalBranch221(zzz340, zzz341, Zero, zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, h) → new_mkVBalBranch0(zzz31, zzz514, Branch(zzz340, zzz341, Neg(Zero), zzz343, zzz344), h)
new_mkVBalBranch3MkVBalBranch216(zzz1105, zzz1106, zzz1107, zzz1108, zzz1109, zzz1110, zzz1111, zzz1112, zzz1113, zzz1114, zzz1115, Zero, Zero, ba) → new_mkVBalBranch3MkVBalBranch222(zzz1105, zzz1106, zzz1107, zzz1108, zzz1109, zzz1110, zzz1111, zzz1112, zzz1113, zzz1114, zzz1115, ba)
new_mkVBalBranch3MkVBalBranch233(zzz473, zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, zzz481, zzz482, bh) → new_mkVBalBranch3MkVBalBranch121(zzz473, zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, zzz481, zzz482, new_primMulNat1(zzz475), bh)
new_mkVBalBranch3MkVBalBranch215(zzz340, zzz341, Pos(Succ(Succ(zzz342000))), zzz343, zzz344, zzz510, zzz511, Zero, zzz513, zzz514, zzz31, Succ(Zero), h) → new_mkVBalBranch3MkVBalBranch217(zzz340, zzz341, Succ(zzz342000), zzz343, zzz344, zzz510, zzz511, zzz513, zzz514, zzz31, Zero, zzz342000, h)
new_mkVBalBranch3MkVBalBranch18(zzz340, zzz341, zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, Zero, h) → new_mkVBalBranch3MkVBalBranch115(zzz340, zzz341, Zero, zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, Zero, Succ(zzz51200), h)
new_mkVBalBranch3MkVBalBranch119(zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, zzz1125, zzz1126, zzz1127, zzz1128, zzz1129, Succ(zzz12130), bd) → new_mkVBalBranch3MkVBalBranch120(zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, zzz1125, Succ(zzz1126), zzz1127, zzz1128, zzz1129, Succ(Succ(zzz1126)), Succ(zzz12130), bd)

The TRS R consists of the following rules:

new_primPlusNat1(Zero) → Zero
new_primMulNat0(zzz6200) → new_primPlusNat3(Succ(new_primPlusNat3(new_primPlusNat1(zzz6200), zzz6200)), Succ(zzz6200))
new_primPlusNat2(Succ(zzz900), Succ(zzz9100)) → Succ(Succ(new_primPlusNat2(zzz900, zzz9100)))
new_primPlusNat3(zzz90, Succ(zzz910)) → Succ(Succ(new_primPlusNat2(zzz90, zzz910)))
new_primPlusNat3(zzz90, Zero) → Succ(zzz90)
new_primMulNat1(zzz34200) → new_primPlusNat2(new_primMulNat0(zzz34200), Succ(zzz34200))
new_primPlusNat2(Zero, Zero) → Zero
new_primPlusNat1(Succ(zzz62000)) → Succ(Succ(new_primPlusNat1(zzz62000)))
new_primPlusNat2(Succ(zzz900), Zero) → Succ(zzz900)
new_primPlusNat2(Zero, Succ(zzz9100)) → Succ(zzz9100)

The set Q consists of the following terms:

new_primPlusNat2(Zero, Succ(x0))
new_primMulNat1(x0)
new_primMulNat0(x0)
new_primPlusNat3(x0, Succ(x1))
new_primPlusNat2(Succ(x0), Succ(x1))
new_primPlusNat3(x0, Zero)
new_primPlusNat1(Zero)
new_primPlusNat2(Zero, Zero)
new_primPlusNat1(Succ(x0))
new_primPlusNat2(Succ(x0), Zero)

We have to consider all minimal (P,Q,R)-chains.
By rewriting [15] the rule new_mkVBalBranch3MkVBalBranch233(zzz473, zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, zzz481, zzz482, bh) → new_mkVBalBranch3MkVBalBranch121(zzz473, zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, zzz481, zzz482, new_primMulNat1(zzz475), bh) at position [10] we obtained the following new rules:

new_mkVBalBranch3MkVBalBranch233(zzz473, zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, zzz481, zzz482, bh) → new_mkVBalBranch3MkVBalBranch121(zzz473, zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, zzz481, zzz482, new_primPlusNat2(new_primMulNat0(zzz475), Succ(zzz475)), bh)



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

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

new_mkVBalBranch3MkVBalBranch225(zzz498, zzz499, zzz500, zzz501, zzz502, zzz503, zzz504, zzz505, zzz506, zzz507, Zero, Zero, bg) → new_mkVBalBranch3MkVBalBranch230(zzz498, zzz499, zzz500, zzz501, zzz502, zzz503, zzz504, zzz505, zzz506, zzz507, bg)
new_mkVBalBranch3MkVBalBranch215(zzz340, zzz341, Neg(zzz3420), zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, Zero, h) → new_mkVBalBranch3MkVBalBranch221(zzz340, zzz341, zzz3420, zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, h)
new_mkVBalBranch3MkVBalBranch18(zzz340, zzz341, zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, Succ(zzz1480), h) → new_mkVBalBranch3MkVBalBranch115(zzz340, zzz341, Zero, zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, Succ(zzz1480), Succ(zzz51200), h)
new_mkVBalBranch3MkVBalBranch215(zzz340, zzz341, Pos(Succ(Succ(zzz342000))), zzz343, zzz344, zzz510, zzz511, Succ(zzz512000), zzz513, zzz514, zzz31, Succ(Succ(zzz6600)), h) → new_mkVBalBranch3MkVBalBranch216(zzz340, zzz341, Succ(zzz342000), zzz343, zzz344, zzz510, zzz511, zzz512000, zzz513, zzz514, zzz31, Succ(Succ(new_primPlusNat2(zzz6600, zzz512000))), zzz342000, h)
new_mkVBalBranch0(zzz31, Branch(zzz510, zzz511, Neg(Zero), zzz513, zzz514), Branch(zzz340, zzz341, Pos(Succ(zzz34200)), zzz343, zzz344), h) → new_mkVBalBranch0(zzz31, Branch(zzz510, zzz511, Neg(Zero), zzz513, zzz514), zzz343, h)
new_mkVBalBranch3MkVBalBranch223(zzz340, zzz341, Neg(Succ(Succ(Succ(zzz3420000)))), zzz343, zzz344, zzz510, zzz511, Zero, zzz513, zzz514, zzz31, Succ(Succ(zzz6700)), h) → new_mkVBalBranch3MkVBalBranch225(zzz340, zzz341, Succ(Succ(zzz3420000)), zzz343, zzz344, zzz510, zzz511, zzz513, zzz514, zzz31, Succ(zzz3420000), Succ(zzz6700), h)
new_mkVBalBranch3MkVBalBranch120(zzz2050, zzz2051, zzz2052, zzz2053, zzz2054, zzz2055, zzz2056, zzz2057, zzz2058, zzz2059, zzz2060, Zero, Succ(zzz20620), be) → new_mkVBalBranch0(zzz2060, zzz2059, Branch(zzz2050, zzz2051, Neg(Succ(zzz2052)), zzz2053, zzz2054), be)
new_mkVBalBranch3MkVBalBranch220(zzz340, zzz341, zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, h) → new_mkVBalBranch0(zzz31, zzz514, Branch(zzz340, zzz341, Pos(Zero), zzz343, zzz344), h)
new_mkVBalBranch3MkVBalBranch222(zzz461, zzz462, zzz463, zzz464, zzz465, zzz466, zzz467, zzz468, zzz469, zzz470, zzz471, bb) → new_mkVBalBranch3MkVBalBranch110(zzz461, zzz462, zzz463, zzz464, zzz465, zzz466, zzz467, zzz468, zzz469, zzz470, zzz471, new_primPlusNat2(new_primMulNat0(zzz463), Succ(zzz463)), bb)
new_mkVBalBranch3MkVBalBranch228(zzz340, zzz341, zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, h) → new_mkVBalBranch0(zzz31, Branch(zzz510, zzz511, Neg(Succ(zzz51200)), zzz513, zzz514), zzz343, h)
new_mkVBalBranch0(zzz31, Branch(zzz510, zzz511, Pos(Zero), zzz513, zzz514), Branch(zzz340, zzz341, Pos(Succ(zzz34200)), zzz343, zzz344), h) → new_mkVBalBranch0(zzz31, Branch(zzz510, zzz511, Pos(Zero), zzz513, zzz514), zzz343, h)
new_mkVBalBranch3MkVBalBranch121(zzz473, zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, zzz481, zzz482, Succ(zzz7390), bh) → new_mkVBalBranch3MkVBalBranch115(zzz473, zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, Zero, zzz480, zzz481, zzz482, Succ(zzz7390), Succ(Zero), bh)
new_mkVBalBranch3MkVBalBranch223(zzz340, zzz341, Neg(Succ(Succ(Zero))), zzz343, zzz344, zzz510, zzz511, Succ(zzz512000), zzz513, zzz514, zzz31, Succ(Succ(zzz6700)), h) → new_mkVBalBranch3MkVBalBranch224(zzz340, zzz341, Succ(Zero), zzz343, zzz344, zzz510, zzz511, zzz512000, zzz513, zzz514, zzz31, Zero, Succ(Succ(new_primPlusNat2(zzz6700, zzz512000))), h)
new_mkVBalBranch3MkVBalBranch215(zzz340, zzz341, Pos(Succ(Zero)), zzz343, zzz344, zzz510, zzz511, Zero, zzz513, zzz514, zzz31, Zero, h) → new_mkVBalBranch3MkVBalBranch219(zzz340, zzz341, zzz343, zzz344, zzz510, zzz511, Zero, zzz513, zzz514, zzz31, h)
new_mkVBalBranch3MkVBalBranch223(zzz340, zzz341, Neg(Succ(Succ(Zero))), zzz343, zzz344, zzz510, zzz511, Zero, zzz513, zzz514, zzz31, Succ(Zero), h) → new_mkVBalBranch3MkVBalBranch225(zzz340, zzz341, Succ(Zero), zzz343, zzz344, zzz510, zzz511, zzz513, zzz514, zzz31, Zero, Zero, h)
new_mkVBalBranch3MkVBalBranch224(zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, zzz1125, zzz1126, zzz1127, zzz1128, zzz1129, Succ(zzz11300), Succ(zzz11310), bd) → new_mkVBalBranch3MkVBalBranch224(zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, zzz1125, zzz1126, zzz1127, zzz1128, zzz1129, zzz11300, zzz11310, bd)
new_mkVBalBranch3MkVBalBranch217(zzz473, zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, zzz481, zzz482, Zero, Succ(zzz4840), bh) → new_mkVBalBranch0(zzz482, Branch(zzz478, zzz479, Pos(Succ(Zero)), zzz480, zzz481), zzz476, bh)
new_mkVBalBranch0(zzz31, Branch(zzz510, zzz511, Pos(Succ(zzz51200)), zzz513, zzz514), Branch(zzz340, zzz341, zzz342, zzz343, zzz344), h) → new_mkVBalBranch3MkVBalBranch215(zzz340, zzz341, zzz342, zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, new_primPlusNat3(Succ(new_primPlusNat3(new_primPlusNat1(zzz51200), zzz51200)), Succ(zzz51200)), h)
new_mkVBalBranch3MkVBalBranch215(zzz340, zzz341, Pos(Succ(Succ(zzz342000))), zzz343, zzz344, zzz510, zzz511, Succ(zzz512000), zzz513, zzz514, zzz31, Zero, h) → new_mkVBalBranch3MkVBalBranch216(zzz340, zzz341, Succ(zzz342000), zzz343, zzz344, zzz510, zzz511, zzz512000, zzz513, zzz514, zzz31, zzz512000, zzz342000, h)
new_mkVBalBranch3MkVBalBranch110(zzz461, zzz462, zzz463, zzz464, zzz465, zzz466, zzz467, zzz468, zzz469, zzz470, zzz471, Succ(zzz5800), bb) → new_mkVBalBranch3MkVBalBranch115(zzz461, zzz462, zzz463, zzz464, zzz465, zzz466, zzz467, Succ(zzz468), zzz469, zzz470, zzz471, Succ(zzz5800), Succ(Succ(zzz468)), bb)
new_mkVBalBranch3MkVBalBranch223(zzz340, zzz341, Neg(Succ(Zero)), zzz343, zzz344, zzz510, zzz511, Zero, zzz513, zzz514, zzz31, Zero, h) → new_mkVBalBranch3MkVBalBranch118(zzz340, zzz341, Zero, zzz343, zzz344, zzz510, zzz511, zzz513, zzz514, zzz31, new_primPlusNat2(new_primMulNat0(Zero), Succ(Zero)), h)
new_mkVBalBranch3MkVBalBranch227(zzz486, zzz487, zzz488, zzz489, zzz490, zzz491, zzz492, zzz493, zzz494, zzz495, zzz496, bf) → new_mkVBalBranch0(zzz496, Branch(zzz491, zzz492, Neg(Succ(Succ(zzz493))), zzz494, zzz495), zzz489, bf)
new_mkVBalBranch0(zzz31, Branch(zzz510, zzz511, Pos(Zero), zzz513, zzz514), Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), h) → new_mkVBalBranch3MkVBalBranch116(zzz340, zzz341, zzz34200, zzz343, zzz344, zzz510, zzz511, zzz513, zzz514, zzz31, new_primPlusNat2(new_primMulNat0(zzz34200), Succ(zzz34200)), h)
new_mkVBalBranch3MkVBalBranch215(zzz340, zzz341, Pos(Zero), zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, Succ(zzz660), h) → new_mkVBalBranch0(zzz31, zzz514, Branch(zzz340, zzz341, Pos(Zero), zzz343, zzz344), h)
new_mkVBalBranch3MkVBalBranch223(zzz340, zzz341, Neg(Zero), zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, Succ(zzz670), h) → new_mkVBalBranch0(zzz31, Branch(zzz510, zzz511, Neg(Succ(zzz51200)), zzz513, zzz514), zzz343, h)
new_mkVBalBranch3MkVBalBranch217(zzz473, zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, zzz481, zzz482, Succ(zzz4830), Zero, bh) → new_mkVBalBranch3MkVBalBranch121(zzz473, zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, zzz481, zzz482, new_primPlusNat2(new_primMulNat0(zzz475), Succ(zzz475)), bh)
new_mkVBalBranch3MkVBalBranch216(zzz1105, zzz1106, zzz1107, zzz1108, zzz1109, zzz1110, zzz1111, zzz1112, zzz1113, zzz1114, zzz1115, Zero, Succ(zzz11170), ba) → new_mkVBalBranch0(zzz1115, Branch(zzz1110, zzz1111, Pos(Succ(Succ(zzz1112))), zzz1113, zzz1114), zzz1108, ba)
new_mkVBalBranch3MkVBalBranch115(zzz1986, zzz1987, zzz1988, zzz1989, zzz1990, zzz1991, zzz1992, zzz1993, zzz1994, zzz1995, zzz1996, Zero, Succ(zzz19980), bc) → new_mkVBalBranch0(zzz1996, zzz1995, Branch(zzz1986, zzz1987, Pos(Succ(zzz1988)), zzz1989, zzz1990), bc)
new_mkVBalBranch0(zzz31, Branch(zzz510, zzz511, Neg(Zero), zzz513, zzz514), Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), h) → new_mkVBalBranch3MkVBalBranch117(zzz340, zzz341, zzz34200, zzz343, zzz344, zzz510, zzz511, zzz513, zzz514, zzz31, new_primPlusNat2(new_primMulNat0(zzz34200), Succ(zzz34200)), h)
new_mkVBalBranch3MkVBalBranch223(zzz340, zzz341, Neg(Zero), zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, Zero, h) → new_mkVBalBranch3MkVBalBranch228(zzz340, zzz341, zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, h)
new_mkVBalBranch3MkVBalBranch122(zzz340, zzz341, zzz34200, zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, h) → new_mkVBalBranch0(zzz31, zzz514, Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), h)
new_mkVBalBranch3MkVBalBranch217(zzz473, zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, zzz481, zzz482, Succ(zzz4830), Succ(zzz4840), bh) → new_mkVBalBranch3MkVBalBranch217(zzz473, zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, zzz481, zzz482, zzz4830, zzz4840, bh)
new_mkVBalBranch3MkVBalBranch116(zzz340, zzz341, zzz34200, zzz343, zzz344, zzz510, zzz511, zzz513, zzz514, zzz31, Succ(zzz1200), h) → new_mkVBalBranch0(zzz31, zzz514, Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), h)
new_mkVBalBranch3MkVBalBranch110(zzz461, zzz462, zzz463, zzz464, zzz465, zzz466, zzz467, zzz468, zzz469, zzz470, zzz471, Zero, bb) → new_mkVBalBranch3MkVBalBranch115(zzz461, zzz462, zzz463, zzz464, zzz465, zzz466, zzz467, Succ(zzz468), zzz469, zzz470, zzz471, Zero, Succ(Succ(zzz468)), bb)
new_mkVBalBranch3MkVBalBranch225(zzz498, zzz499, zzz500, zzz501, zzz502, zzz503, zzz504, zzz505, zzz506, zzz507, Zero, Succ(zzz5090), bg) → new_mkVBalBranch0(zzz507, Branch(zzz503, zzz504, Neg(Succ(Zero)), zzz505, zzz506), zzz501, bg)
new_mkVBalBranch3MkVBalBranch223(zzz340, zzz341, Neg(Succ(Succ(Succ(zzz3420000)))), zzz343, zzz344, zzz510, zzz511, Zero, zzz513, zzz514, zzz31, Succ(Zero), h) → new_mkVBalBranch3MkVBalBranch225(zzz340, zzz341, Succ(Succ(zzz3420000)), zzz343, zzz344, zzz510, zzz511, zzz513, zzz514, zzz31, Succ(zzz3420000), Zero, h)
new_mkVBalBranch3MkVBalBranch121(zzz473, zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, zzz481, zzz482, Zero, bh) → new_mkVBalBranch3MkVBalBranch115(zzz473, zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, Zero, zzz480, zzz481, zzz482, Zero, Succ(Zero), bh)
new_mkVBalBranch3MkVBalBranch215(zzz340, zzz341, Pos(Succ(Zero)), zzz343, zzz344, zzz510, zzz511, Succ(zzz512000), zzz513, zzz514, zzz31, Zero, h) → new_mkVBalBranch3MkVBalBranch218(zzz340, zzz341, Zero, zzz343, zzz344, zzz510, zzz511, zzz512000, zzz513, zzz514, zzz31, h)
new_mkVBalBranch3MkVBalBranch225(zzz498, zzz499, zzz500, zzz501, zzz502, zzz503, zzz504, zzz505, zzz506, zzz507, Succ(zzz5080), Zero, bg) → new_mkVBalBranch3MkVBalBranch118(zzz498, zzz499, zzz500, zzz501, zzz502, zzz503, zzz504, zzz505, zzz506, zzz507, new_primPlusNat2(new_primMulNat0(zzz500), Succ(zzz500)), bg)
new_mkVBalBranch3MkVBalBranch223(zzz340, zzz341, Neg(Succ(Zero)), zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, Succ(zzz670), h) → new_mkVBalBranch0(zzz31, Branch(zzz510, zzz511, Neg(Succ(zzz51200)), zzz513, zzz514), zzz343, h)
new_mkVBalBranch3MkVBalBranch215(zzz340, zzz341, Pos(Succ(Zero)), zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, Succ(zzz660), h) → new_mkVBalBranch3MkVBalBranch18(zzz340, zzz341, zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, new_primPlusNat2(new_primMulNat0(Zero), Succ(Zero)), h)
new_mkVBalBranch3MkVBalBranch229(zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, zzz1125, zzz1126, zzz1127, zzz1128, zzz1129, bd) → new_mkVBalBranch3MkVBalBranch119(zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, zzz1125, zzz1126, zzz1127, zzz1128, zzz1129, new_primPlusNat2(new_primMulNat0(zzz1121), Succ(zzz1121)), bd)
new_mkVBalBranch3MkVBalBranch219(zzz340, zzz341, zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, h) → new_mkVBalBranch3MkVBalBranch18(zzz340, zzz341, zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, new_primPlusNat2(new_primMulNat0(Zero), Succ(Zero)), h)
new_mkVBalBranch3MkVBalBranch233(zzz473, zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, zzz481, zzz482, bh) → new_mkVBalBranch3MkVBalBranch121(zzz473, zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, zzz481, zzz482, new_primPlusNat2(new_primMulNat0(zzz475), Succ(zzz475)), bh)
new_mkVBalBranch3MkVBalBranch223(zzz340, zzz341, Neg(Succ(Zero)), zzz343, zzz344, zzz510, zzz511, Succ(zzz512000), zzz513, zzz514, zzz31, Zero, h) → new_mkVBalBranch3MkVBalBranch227(zzz340, zzz341, Zero, zzz343, zzz344, zzz510, zzz511, zzz512000, zzz513, zzz514, zzz31, h)
new_mkVBalBranch3MkVBalBranch226(zzz340, zzz341, zzz3420, zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, h) → new_mkVBalBranch0(zzz31, Branch(zzz510, zzz511, Neg(Succ(zzz51200)), zzz513, zzz514), zzz343, h)
new_mkVBalBranch3MkVBalBranch223(zzz340, zzz341, Neg(Succ(Succ(zzz342000))), zzz343, zzz344, zzz510, zzz511, Succ(zzz512000), zzz513, zzz514, zzz31, Zero, h) → new_mkVBalBranch3MkVBalBranch224(zzz340, zzz341, Succ(zzz342000), zzz343, zzz344, zzz510, zzz511, zzz512000, zzz513, zzz514, zzz31, zzz342000, zzz512000, h)
new_mkVBalBranch3MkVBalBranch215(zzz340, zzz341, Pos(Succ(Succ(zzz342000))), zzz343, zzz344, zzz510, zzz511, Zero, zzz513, zzz514, zzz31, Succ(Succ(zzz6600)), h) → new_mkVBalBranch3MkVBalBranch217(zzz340, zzz341, Succ(zzz342000), zzz343, zzz344, zzz510, zzz511, zzz513, zzz514, zzz31, Succ(zzz6600), zzz342000, h)
new_mkVBalBranch3MkVBalBranch218(zzz461, zzz462, zzz463, zzz464, zzz465, zzz466, zzz467, zzz468, zzz469, zzz470, zzz471, bb) → new_mkVBalBranch3MkVBalBranch110(zzz461, zzz462, zzz463, zzz464, zzz465, zzz466, zzz467, zzz468, zzz469, zzz470, zzz471, new_primPlusNat2(new_primMulNat0(zzz463), Succ(zzz463)), bb)
new_mkVBalBranch3MkVBalBranch117(zzz340, zzz341, zzz34200, zzz343, zzz344, zzz510, zzz511, zzz513, zzz514, zzz31, Succ(zzz1240), h) → new_mkVBalBranch0(zzz31, zzz514, Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), h)
new_mkVBalBranch3MkVBalBranch221(zzz340, zzz341, Succ(zzz34200), zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, h) → new_mkVBalBranch3MkVBalBranch19(zzz340, zzz341, zzz34200, zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, new_primPlusNat2(new_primPlusNat3(Succ(new_primPlusNat3(new_primPlusNat1(zzz34200), zzz34200)), Succ(zzz34200)), Succ(zzz34200)), h)
new_mkVBalBranch3MkVBalBranch120(zzz2050, zzz2051, zzz2052, zzz2053, zzz2054, zzz2055, zzz2056, zzz2057, zzz2058, zzz2059, zzz2060, Succ(zzz20610), Succ(zzz20620), be) → new_mkVBalBranch3MkVBalBranch120(zzz2050, zzz2051, zzz2052, zzz2053, zzz2054, zzz2055, zzz2056, zzz2057, zzz2058, zzz2059, zzz2060, zzz20610, zzz20620, be)
new_mkVBalBranch3MkVBalBranch217(zzz473, zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, zzz481, zzz482, Zero, Zero, bh) → new_mkVBalBranch3MkVBalBranch233(zzz473, zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, zzz481, zzz482, bh)
new_mkVBalBranch0(zzz31, Branch(zzz510, zzz511, Neg(Succ(zzz51200)), zzz513, zzz514), Branch(zzz340, zzz341, zzz342, zzz343, zzz344), h) → new_mkVBalBranch3MkVBalBranch223(zzz340, zzz341, zzz342, zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, new_primPlusNat3(Succ(new_primPlusNat3(new_primPlusNat1(zzz51200), zzz51200)), Succ(zzz51200)), h)
new_mkVBalBranch3MkVBalBranch216(zzz1105, zzz1106, zzz1107, zzz1108, zzz1109, zzz1110, zzz1111, zzz1112, zzz1113, zzz1114, zzz1115, Succ(zzz11160), Succ(zzz11170), ba) → new_mkVBalBranch3MkVBalBranch216(zzz1105, zzz1106, zzz1107, zzz1108, zzz1109, zzz1110, zzz1111, zzz1112, zzz1113, zzz1114, zzz1115, zzz11160, zzz11170, ba)
new_mkVBalBranch3MkVBalBranch223(zzz340, zzz341, Pos(zzz3420), zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, Succ(zzz670), h) → new_mkVBalBranch0(zzz31, Branch(zzz510, zzz511, Neg(Succ(zzz51200)), zzz513, zzz514), zzz343, h)
new_mkVBalBranch3MkVBalBranch223(zzz340, zzz341, Neg(Succ(Succ(Succ(zzz3420000)))), zzz343, zzz344, zzz510, zzz511, Succ(zzz512000), zzz513, zzz514, zzz31, Succ(Zero), h) → new_mkVBalBranch3MkVBalBranch224(zzz340, zzz341, Succ(Succ(zzz3420000)), zzz343, zzz344, zzz510, zzz511, zzz512000, zzz513, zzz514, zzz31, Succ(zzz3420000), Succ(zzz512000), h)
new_mkVBalBranch3MkVBalBranch19(zzz340, zzz341, zzz34200, zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, Zero, h) → new_mkVBalBranch3MkVBalBranch122(zzz340, zzz341, zzz34200, zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, h)
new_mkVBalBranch3MkVBalBranch215(zzz340, zzz341, Pos(Succ(Succ(zzz342000))), zzz343, zzz344, zzz510, zzz511, Zero, zzz513, zzz514, zzz31, Zero, h) → new_mkVBalBranch0(zzz31, Branch(zzz510, zzz511, Pos(Succ(Zero)), zzz513, zzz514), zzz343, h)
new_mkVBalBranch3MkVBalBranch225(zzz498, zzz499, zzz500, zzz501, zzz502, zzz503, zzz504, zzz505, zzz506, zzz507, Succ(zzz5080), Succ(zzz5090), bg) → new_mkVBalBranch3MkVBalBranch225(zzz498, zzz499, zzz500, zzz501, zzz502, zzz503, zzz504, zzz505, zzz506, zzz507, zzz5080, zzz5090, bg)
new_mkVBalBranch3MkVBalBranch19(zzz340, zzz341, zzz34200, zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, Succ(zzz1410), h) → new_mkVBalBranch0(zzz31, zzz514, Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), h)
new_mkVBalBranch3MkVBalBranch224(zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, zzz1125, zzz1126, zzz1127, zzz1128, zzz1129, Succ(zzz11300), Zero, bd) → new_mkVBalBranch3MkVBalBranch119(zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, zzz1125, zzz1126, zzz1127, zzz1128, zzz1129, new_primPlusNat2(new_primMulNat0(zzz1121), Succ(zzz1121)), bd)
new_mkVBalBranch3MkVBalBranch223(zzz340, zzz341, Pos(zzz3420), zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, Zero, h) → new_mkVBalBranch3MkVBalBranch226(zzz340, zzz341, zzz3420, zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, h)
new_mkVBalBranch3MkVBalBranch223(zzz340, zzz341, Neg(Succ(Succ(Zero))), zzz343, zzz344, zzz510, zzz511, Succ(zzz512000), zzz513, zzz514, zzz31, Succ(Zero), h) → new_mkVBalBranch3MkVBalBranch224(zzz340, zzz341, Succ(Zero), zzz343, zzz344, zzz510, zzz511, zzz512000, zzz513, zzz514, zzz31, Zero, Succ(zzz512000), h)
new_mkVBalBranch3MkVBalBranch224(zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, zzz1125, zzz1126, zzz1127, zzz1128, zzz1129, Zero, Zero, bd) → new_mkVBalBranch3MkVBalBranch229(zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, zzz1125, zzz1126, zzz1127, zzz1128, zzz1129, bd)
new_mkVBalBranch3MkVBalBranch224(zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, zzz1125, zzz1126, zzz1127, zzz1128, zzz1129, Zero, Succ(zzz11310), bd) → new_mkVBalBranch3MkVBalBranch227(zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, zzz1125, zzz1126, zzz1127, zzz1128, zzz1129, bd)
new_mkVBalBranch3MkVBalBranch223(zzz340, zzz341, Neg(Succ(Succ(zzz342000))), zzz343, zzz344, zzz510, zzz511, Zero, zzz513, zzz514, zzz31, Zero, h) → new_mkVBalBranch3MkVBalBranch118(zzz340, zzz341, Succ(zzz342000), zzz343, zzz344, zzz510, zzz511, zzz513, zzz514, zzz31, new_primPlusNat2(new_primMulNat0(Succ(zzz342000)), Succ(Succ(zzz342000))), h)
new_mkVBalBranch3MkVBalBranch230(zzz498, zzz499, zzz500, zzz501, zzz502, zzz503, zzz504, zzz505, zzz506, zzz507, bg) → new_mkVBalBranch3MkVBalBranch118(zzz498, zzz499, zzz500, zzz501, zzz502, zzz503, zzz504, zzz505, zzz506, zzz507, new_primPlusNat2(new_primMulNat0(zzz500), Succ(zzz500)), bg)
new_mkVBalBranch3MkVBalBranch223(zzz340, zzz341, Neg(Succ(Succ(Zero))), zzz343, zzz344, zzz510, zzz511, Zero, zzz513, zzz514, zzz31, Succ(Succ(zzz6700)), h) → new_mkVBalBranch3MkVBalBranch225(zzz340, zzz341, Succ(Zero), zzz343, zzz344, zzz510, zzz511, zzz513, zzz514, zzz31, Zero, Succ(zzz6700), h)
new_mkVBalBranch3MkVBalBranch223(zzz340, zzz341, Neg(Succ(Succ(Succ(zzz3420000)))), zzz343, zzz344, zzz510, zzz511, Succ(zzz512000), zzz513, zzz514, zzz31, Succ(Succ(zzz6700)), h) → new_mkVBalBranch3MkVBalBranch224(zzz340, zzz341, Succ(Succ(zzz3420000)), zzz343, zzz344, zzz510, zzz511, zzz512000, zzz513, zzz514, zzz31, Succ(zzz3420000), Succ(Succ(new_primPlusNat2(zzz6700, zzz512000))), h)
new_mkVBalBranch3MkVBalBranch115(zzz1986, zzz1987, zzz1988, zzz1989, zzz1990, zzz1991, zzz1992, zzz1993, zzz1994, zzz1995, zzz1996, Succ(zzz19970), Succ(zzz19980), bc) → new_mkVBalBranch3MkVBalBranch115(zzz1986, zzz1987, zzz1988, zzz1989, zzz1990, zzz1991, zzz1992, zzz1993, zzz1994, zzz1995, zzz1996, zzz19970, zzz19980, bc)
new_mkVBalBranch3MkVBalBranch215(zzz340, zzz341, Pos(Zero), zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, Zero, h) → new_mkVBalBranch3MkVBalBranch220(zzz340, zzz341, zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, h)
new_mkVBalBranch3MkVBalBranch215(zzz340, zzz341, Neg(Zero), zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, Succ(zzz660), h) → new_mkVBalBranch0(zzz31, zzz514, Branch(zzz340, zzz341, Neg(Zero), zzz343, zzz344), h)
new_mkVBalBranch3MkVBalBranch118(zzz498, zzz499, zzz500, zzz501, zzz502, zzz503, zzz504, zzz505, zzz506, zzz507, Succ(zzz8040), bg) → new_mkVBalBranch3MkVBalBranch120(zzz498, zzz499, zzz500, zzz501, zzz502, zzz503, zzz504, Zero, zzz505, zzz506, zzz507, Succ(Zero), Succ(zzz8040), bg)
new_mkVBalBranch3MkVBalBranch216(zzz1105, zzz1106, zzz1107, zzz1108, zzz1109, zzz1110, zzz1111, zzz1112, zzz1113, zzz1114, zzz1115, Succ(zzz11160), Zero, ba) → new_mkVBalBranch3MkVBalBranch218(zzz1105, zzz1106, zzz1107, zzz1108, zzz1109, zzz1110, zzz1111, zzz1112, zzz1113, zzz1114, zzz1115, ba)
new_mkVBalBranch3MkVBalBranch221(zzz340, zzz341, Zero, zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, h) → new_mkVBalBranch0(zzz31, zzz514, Branch(zzz340, zzz341, Neg(Zero), zzz343, zzz344), h)
new_mkVBalBranch3MkVBalBranch215(zzz340, zzz341, Pos(Succ(Succ(zzz342000))), zzz343, zzz344, zzz510, zzz511, Succ(zzz512000), zzz513, zzz514, zzz31, Succ(Zero), h) → new_mkVBalBranch3MkVBalBranch216(zzz340, zzz341, Succ(zzz342000), zzz343, zzz344, zzz510, zzz511, zzz512000, zzz513, zzz514, zzz31, Succ(zzz512000), zzz342000, h)
new_mkVBalBranch3MkVBalBranch215(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, Succ(zzz660), h) → new_mkVBalBranch3MkVBalBranch19(zzz340, zzz341, zzz34200, zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, new_primPlusNat2(new_primMulNat0(zzz34200), Succ(zzz34200)), h)
new_mkVBalBranch3MkVBalBranch216(zzz1105, zzz1106, zzz1107, zzz1108, zzz1109, zzz1110, zzz1111, zzz1112, zzz1113, zzz1114, zzz1115, Zero, Zero, ba) → new_mkVBalBranch3MkVBalBranch222(zzz1105, zzz1106, zzz1107, zzz1108, zzz1109, zzz1110, zzz1111, zzz1112, zzz1113, zzz1114, zzz1115, ba)
new_mkVBalBranch3MkVBalBranch215(zzz340, zzz341, Pos(Succ(Succ(zzz342000))), zzz343, zzz344, zzz510, zzz511, Zero, zzz513, zzz514, zzz31, Succ(Zero), h) → new_mkVBalBranch3MkVBalBranch217(zzz340, zzz341, Succ(zzz342000), zzz343, zzz344, zzz510, zzz511, zzz513, zzz514, zzz31, Zero, zzz342000, h)
new_mkVBalBranch3MkVBalBranch119(zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, zzz1125, zzz1126, zzz1127, zzz1128, zzz1129, Succ(zzz12130), bd) → new_mkVBalBranch3MkVBalBranch120(zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, zzz1125, Succ(zzz1126), zzz1127, zzz1128, zzz1129, Succ(Succ(zzz1126)), Succ(zzz12130), bd)
new_mkVBalBranch3MkVBalBranch18(zzz340, zzz341, zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, Zero, h) → new_mkVBalBranch3MkVBalBranch115(zzz340, zzz341, Zero, zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, Zero, Succ(zzz51200), h)

The TRS R consists of the following rules:

new_primPlusNat1(Zero) → Zero
new_primMulNat0(zzz6200) → new_primPlusNat3(Succ(new_primPlusNat3(new_primPlusNat1(zzz6200), zzz6200)), Succ(zzz6200))
new_primPlusNat2(Succ(zzz900), Succ(zzz9100)) → Succ(Succ(new_primPlusNat2(zzz900, zzz9100)))
new_primPlusNat3(zzz90, Succ(zzz910)) → Succ(Succ(new_primPlusNat2(zzz90, zzz910)))
new_primPlusNat3(zzz90, Zero) → Succ(zzz90)
new_primMulNat1(zzz34200) → new_primPlusNat2(new_primMulNat0(zzz34200), Succ(zzz34200))
new_primPlusNat2(Zero, Zero) → Zero
new_primPlusNat1(Succ(zzz62000)) → Succ(Succ(new_primPlusNat1(zzz62000)))
new_primPlusNat2(Succ(zzz900), Zero) → Succ(zzz900)
new_primPlusNat2(Zero, Succ(zzz9100)) → Succ(zzz9100)

The set Q consists of the following terms:

new_primPlusNat2(Zero, Succ(x0))
new_primMulNat1(x0)
new_primMulNat0(x0)
new_primPlusNat3(x0, Succ(x1))
new_primPlusNat2(Succ(x0), Succ(x1))
new_primPlusNat3(x0, Zero)
new_primPlusNat1(Zero)
new_primPlusNat2(Zero, Zero)
new_primPlusNat1(Succ(x0))
new_primPlusNat2(Succ(x0), Zero)

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

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

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

new_mkVBalBranch3MkVBalBranch215(zzz340, zzz341, Neg(zzz3420), zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, Zero, h) → new_mkVBalBranch3MkVBalBranch221(zzz340, zzz341, zzz3420, zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, h)
new_mkVBalBranch3MkVBalBranch225(zzz498, zzz499, zzz500, zzz501, zzz502, zzz503, zzz504, zzz505, zzz506, zzz507, Zero, Zero, bg) → new_mkVBalBranch3MkVBalBranch230(zzz498, zzz499, zzz500, zzz501, zzz502, zzz503, zzz504, zzz505, zzz506, zzz507, bg)
new_mkVBalBranch3MkVBalBranch18(zzz340, zzz341, zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, Succ(zzz1480), h) → new_mkVBalBranch3MkVBalBranch115(zzz340, zzz341, Zero, zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, Succ(zzz1480), Succ(zzz51200), h)
new_mkVBalBranch3MkVBalBranch215(zzz340, zzz341, Pos(Succ(Succ(zzz342000))), zzz343, zzz344, zzz510, zzz511, Succ(zzz512000), zzz513, zzz514, zzz31, Succ(Succ(zzz6600)), h) → new_mkVBalBranch3MkVBalBranch216(zzz340, zzz341, Succ(zzz342000), zzz343, zzz344, zzz510, zzz511, zzz512000, zzz513, zzz514, zzz31, Succ(Succ(new_primPlusNat2(zzz6600, zzz512000))), zzz342000, h)
new_mkVBalBranch0(zzz31, Branch(zzz510, zzz511, Neg(Zero), zzz513, zzz514), Branch(zzz340, zzz341, Pos(Succ(zzz34200)), zzz343, zzz344), h) → new_mkVBalBranch0(zzz31, Branch(zzz510, zzz511, Neg(Zero), zzz513, zzz514), zzz343, h)
new_mkVBalBranch3MkVBalBranch223(zzz340, zzz341, Neg(Succ(Succ(Succ(zzz3420000)))), zzz343, zzz344, zzz510, zzz511, Zero, zzz513, zzz514, zzz31, Succ(Succ(zzz6700)), h) → new_mkVBalBranch3MkVBalBranch225(zzz340, zzz341, Succ(Succ(zzz3420000)), zzz343, zzz344, zzz510, zzz511, zzz513, zzz514, zzz31, Succ(zzz3420000), Succ(zzz6700), h)
new_mkVBalBranch3MkVBalBranch220(zzz340, zzz341, zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, h) → new_mkVBalBranch0(zzz31, zzz514, Branch(zzz340, zzz341, Pos(Zero), zzz343, zzz344), h)
new_mkVBalBranch3MkVBalBranch120(zzz2050, zzz2051, zzz2052, zzz2053, zzz2054, zzz2055, zzz2056, zzz2057, zzz2058, zzz2059, zzz2060, Zero, Succ(zzz20620), be) → new_mkVBalBranch0(zzz2060, zzz2059, Branch(zzz2050, zzz2051, Neg(Succ(zzz2052)), zzz2053, zzz2054), be)
new_mkVBalBranch3MkVBalBranch222(zzz461, zzz462, zzz463, zzz464, zzz465, zzz466, zzz467, zzz468, zzz469, zzz470, zzz471, bb) → new_mkVBalBranch3MkVBalBranch110(zzz461, zzz462, zzz463, zzz464, zzz465, zzz466, zzz467, zzz468, zzz469, zzz470, zzz471, new_primPlusNat2(new_primMulNat0(zzz463), Succ(zzz463)), bb)
new_mkVBalBranch3MkVBalBranch121(zzz473, zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, zzz481, zzz482, Succ(zzz7390), bh) → new_mkVBalBranch3MkVBalBranch115(zzz473, zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, Zero, zzz480, zzz481, zzz482, Succ(zzz7390), Succ(Zero), bh)
new_mkVBalBranch3MkVBalBranch228(zzz340, zzz341, zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, h) → new_mkVBalBranch0(zzz31, Branch(zzz510, zzz511, Neg(Succ(zzz51200)), zzz513, zzz514), zzz343, h)
new_mkVBalBranch0(zzz31, Branch(zzz510, zzz511, Pos(Zero), zzz513, zzz514), Branch(zzz340, zzz341, Pos(Succ(zzz34200)), zzz343, zzz344), h) → new_mkVBalBranch0(zzz31, Branch(zzz510, zzz511, Pos(Zero), zzz513, zzz514), zzz343, h)
new_mkVBalBranch3MkVBalBranch223(zzz340, zzz341, Neg(Succ(Succ(Zero))), zzz343, zzz344, zzz510, zzz511, Succ(zzz512000), zzz513, zzz514, zzz31, Succ(Succ(zzz6700)), h) → new_mkVBalBranch3MkVBalBranch224(zzz340, zzz341, Succ(Zero), zzz343, zzz344, zzz510, zzz511, zzz512000, zzz513, zzz514, zzz31, Zero, Succ(Succ(new_primPlusNat2(zzz6700, zzz512000))), h)
new_mkVBalBranch3MkVBalBranch215(zzz340, zzz341, Pos(Succ(Zero)), zzz343, zzz344, zzz510, zzz511, Zero, zzz513, zzz514, zzz31, Zero, h) → new_mkVBalBranch3MkVBalBranch219(zzz340, zzz341, zzz343, zzz344, zzz510, zzz511, Zero, zzz513, zzz514, zzz31, h)
new_mkVBalBranch3MkVBalBranch223(zzz340, zzz341, Neg(Succ(Succ(Zero))), zzz343, zzz344, zzz510, zzz511, Zero, zzz513, zzz514, zzz31, Succ(Zero), h) → new_mkVBalBranch3MkVBalBranch225(zzz340, zzz341, Succ(Zero), zzz343, zzz344, zzz510, zzz511, zzz513, zzz514, zzz31, Zero, Zero, h)
new_mkVBalBranch3MkVBalBranch224(zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, zzz1125, zzz1126, zzz1127, zzz1128, zzz1129, Succ(zzz11300), Succ(zzz11310), bd) → new_mkVBalBranch3MkVBalBranch224(zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, zzz1125, zzz1126, zzz1127, zzz1128, zzz1129, zzz11300, zzz11310, bd)
new_mkVBalBranch0(zzz31, Branch(zzz510, zzz511, Pos(Succ(zzz51200)), zzz513, zzz514), Branch(zzz340, zzz341, zzz342, zzz343, zzz344), h) → new_mkVBalBranch3MkVBalBranch215(zzz340, zzz341, zzz342, zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, new_primPlusNat3(Succ(new_primPlusNat3(new_primPlusNat1(zzz51200), zzz51200)), Succ(zzz51200)), h)
new_mkVBalBranch3MkVBalBranch217(zzz473, zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, zzz481, zzz482, Zero, Succ(zzz4840), bh) → new_mkVBalBranch0(zzz482, Branch(zzz478, zzz479, Pos(Succ(Zero)), zzz480, zzz481), zzz476, bh)
new_mkVBalBranch3MkVBalBranch215(zzz340, zzz341, Pos(Succ(Succ(zzz342000))), zzz343, zzz344, zzz510, zzz511, Succ(zzz512000), zzz513, zzz514, zzz31, Zero, h) → new_mkVBalBranch3MkVBalBranch216(zzz340, zzz341, Succ(zzz342000), zzz343, zzz344, zzz510, zzz511, zzz512000, zzz513, zzz514, zzz31, zzz512000, zzz342000, h)
new_mkVBalBranch3MkVBalBranch110(zzz461, zzz462, zzz463, zzz464, zzz465, zzz466, zzz467, zzz468, zzz469, zzz470, zzz471, Succ(zzz5800), bb) → new_mkVBalBranch3MkVBalBranch115(zzz461, zzz462, zzz463, zzz464, zzz465, zzz466, zzz467, Succ(zzz468), zzz469, zzz470, zzz471, Succ(zzz5800), Succ(Succ(zzz468)), bb)
new_mkVBalBranch3MkVBalBranch223(zzz340, zzz341, Neg(Succ(Zero)), zzz343, zzz344, zzz510, zzz511, Zero, zzz513, zzz514, zzz31, Zero, h) → new_mkVBalBranch3MkVBalBranch118(zzz340, zzz341, Zero, zzz343, zzz344, zzz510, zzz511, zzz513, zzz514, zzz31, new_primPlusNat2(new_primMulNat0(Zero), Succ(Zero)), h)
new_mkVBalBranch3MkVBalBranch227(zzz486, zzz487, zzz488, zzz489, zzz490, zzz491, zzz492, zzz493, zzz494, zzz495, zzz496, bf) → new_mkVBalBranch0(zzz496, Branch(zzz491, zzz492, Neg(Succ(Succ(zzz493))), zzz494, zzz495), zzz489, bf)
new_mkVBalBranch0(zzz31, Branch(zzz510, zzz511, Pos(Zero), zzz513, zzz514), Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), h) → new_mkVBalBranch3MkVBalBranch116(zzz340, zzz341, zzz34200, zzz343, zzz344, zzz510, zzz511, zzz513, zzz514, zzz31, new_primPlusNat2(new_primMulNat0(zzz34200), Succ(zzz34200)), h)
new_mkVBalBranch3MkVBalBranch215(zzz340, zzz341, Pos(Zero), zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, Succ(zzz660), h) → new_mkVBalBranch0(zzz31, zzz514, Branch(zzz340, zzz341, Pos(Zero), zzz343, zzz344), h)
new_mkVBalBranch3MkVBalBranch217(zzz473, zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, zzz481, zzz482, Succ(zzz4830), Zero, bh) → new_mkVBalBranch3MkVBalBranch121(zzz473, zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, zzz481, zzz482, new_primPlusNat2(new_primMulNat0(zzz475), Succ(zzz475)), bh)
new_mkVBalBranch3MkVBalBranch223(zzz340, zzz341, Neg(Zero), zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, Succ(zzz670), h) → new_mkVBalBranch0(zzz31, Branch(zzz510, zzz511, Neg(Succ(zzz51200)), zzz513, zzz514), zzz343, h)
new_mkVBalBranch3MkVBalBranch216(zzz1105, zzz1106, zzz1107, zzz1108, zzz1109, zzz1110, zzz1111, zzz1112, zzz1113, zzz1114, zzz1115, Zero, Succ(zzz11170), ba) → new_mkVBalBranch0(zzz1115, Branch(zzz1110, zzz1111, Pos(Succ(Succ(zzz1112))), zzz1113, zzz1114), zzz1108, ba)
new_mkVBalBranch3MkVBalBranch115(zzz1986, zzz1987, zzz1988, zzz1989, zzz1990, zzz1991, zzz1992, zzz1993, zzz1994, zzz1995, zzz1996, Zero, Succ(zzz19980), bc) → new_mkVBalBranch0(zzz1996, zzz1995, Branch(zzz1986, zzz1987, Pos(Succ(zzz1988)), zzz1989, zzz1990), bc)
new_mkVBalBranch0(zzz31, Branch(zzz510, zzz511, Neg(Zero), zzz513, zzz514), Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), h) → new_mkVBalBranch3MkVBalBranch117(zzz340, zzz341, zzz34200, zzz343, zzz344, zzz510, zzz511, zzz513, zzz514, zzz31, new_primPlusNat2(new_primMulNat0(zzz34200), Succ(zzz34200)), h)
new_mkVBalBranch3MkVBalBranch223(zzz340, zzz341, Neg(Zero), zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, Zero, h) → new_mkVBalBranch3MkVBalBranch228(zzz340, zzz341, zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, h)
new_mkVBalBranch3MkVBalBranch122(zzz340, zzz341, zzz34200, zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, h) → new_mkVBalBranch0(zzz31, zzz514, Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), h)
new_mkVBalBranch3MkVBalBranch217(zzz473, zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, zzz481, zzz482, Succ(zzz4830), Succ(zzz4840), bh) → new_mkVBalBranch3MkVBalBranch217(zzz473, zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, zzz481, zzz482, zzz4830, zzz4840, bh)
new_mkVBalBranch3MkVBalBranch116(zzz340, zzz341, zzz34200, zzz343, zzz344, zzz510, zzz511, zzz513, zzz514, zzz31, Succ(zzz1200), h) → new_mkVBalBranch0(zzz31, zzz514, Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), h)
new_mkVBalBranch3MkVBalBranch110(zzz461, zzz462, zzz463, zzz464, zzz465, zzz466, zzz467, zzz468, zzz469, zzz470, zzz471, Zero, bb) → new_mkVBalBranch3MkVBalBranch115(zzz461, zzz462, zzz463, zzz464, zzz465, zzz466, zzz467, Succ(zzz468), zzz469, zzz470, zzz471, Zero, Succ(Succ(zzz468)), bb)
new_mkVBalBranch3MkVBalBranch225(zzz498, zzz499, zzz500, zzz501, zzz502, zzz503, zzz504, zzz505, zzz506, zzz507, Zero, Succ(zzz5090), bg) → new_mkVBalBranch0(zzz507, Branch(zzz503, zzz504, Neg(Succ(Zero)), zzz505, zzz506), zzz501, bg)
new_mkVBalBranch3MkVBalBranch223(zzz340, zzz341, Neg(Succ(Succ(Succ(zzz3420000)))), zzz343, zzz344, zzz510, zzz511, Zero, zzz513, zzz514, zzz31, Succ(Zero), h) → new_mkVBalBranch3MkVBalBranch225(zzz340, zzz341, Succ(Succ(zzz3420000)), zzz343, zzz344, zzz510, zzz511, zzz513, zzz514, zzz31, Succ(zzz3420000), Zero, h)
new_mkVBalBranch3MkVBalBranch121(zzz473, zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, zzz481, zzz482, Zero, bh) → new_mkVBalBranch3MkVBalBranch115(zzz473, zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, Zero, zzz480, zzz481, zzz482, Zero, Succ(Zero), bh)
new_mkVBalBranch3MkVBalBranch215(zzz340, zzz341, Pos(Succ(Zero)), zzz343, zzz344, zzz510, zzz511, Succ(zzz512000), zzz513, zzz514, zzz31, Zero, h) → new_mkVBalBranch3MkVBalBranch218(zzz340, zzz341, Zero, zzz343, zzz344, zzz510, zzz511, zzz512000, zzz513, zzz514, zzz31, h)
new_mkVBalBranch3MkVBalBranch225(zzz498, zzz499, zzz500, zzz501, zzz502, zzz503, zzz504, zzz505, zzz506, zzz507, Succ(zzz5080), Zero, bg) → new_mkVBalBranch3MkVBalBranch118(zzz498, zzz499, zzz500, zzz501, zzz502, zzz503, zzz504, zzz505, zzz506, zzz507, new_primPlusNat2(new_primMulNat0(zzz500), Succ(zzz500)), bg)
new_mkVBalBranch3MkVBalBranch223(zzz340, zzz341, Neg(Succ(Zero)), zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, Succ(zzz670), h) → new_mkVBalBranch0(zzz31, Branch(zzz510, zzz511, Neg(Succ(zzz51200)), zzz513, zzz514), zzz343, h)
new_mkVBalBranch3MkVBalBranch215(zzz340, zzz341, Pos(Succ(Zero)), zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, Succ(zzz660), h) → new_mkVBalBranch3MkVBalBranch18(zzz340, zzz341, zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, new_primPlusNat2(new_primMulNat0(Zero), Succ(Zero)), h)
new_mkVBalBranch3MkVBalBranch229(zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, zzz1125, zzz1126, zzz1127, zzz1128, zzz1129, bd) → new_mkVBalBranch3MkVBalBranch119(zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, zzz1125, zzz1126, zzz1127, zzz1128, zzz1129, new_primPlusNat2(new_primMulNat0(zzz1121), Succ(zzz1121)), bd)
new_mkVBalBranch3MkVBalBranch219(zzz340, zzz341, zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, h) → new_mkVBalBranch3MkVBalBranch18(zzz340, zzz341, zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, new_primPlusNat2(new_primMulNat0(Zero), Succ(Zero)), h)
new_mkVBalBranch3MkVBalBranch233(zzz473, zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, zzz481, zzz482, bh) → new_mkVBalBranch3MkVBalBranch121(zzz473, zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, zzz481, zzz482, new_primPlusNat2(new_primMulNat0(zzz475), Succ(zzz475)), bh)
new_mkVBalBranch3MkVBalBranch223(zzz340, zzz341, Neg(Succ(Zero)), zzz343, zzz344, zzz510, zzz511, Succ(zzz512000), zzz513, zzz514, zzz31, Zero, h) → new_mkVBalBranch3MkVBalBranch227(zzz340, zzz341, Zero, zzz343, zzz344, zzz510, zzz511, zzz512000, zzz513, zzz514, zzz31, h)
new_mkVBalBranch3MkVBalBranch215(zzz340, zzz341, Pos(Succ(Succ(zzz342000))), zzz343, zzz344, zzz510, zzz511, Zero, zzz513, zzz514, zzz31, Succ(Succ(zzz6600)), h) → new_mkVBalBranch3MkVBalBranch217(zzz340, zzz341, Succ(zzz342000), zzz343, zzz344, zzz510, zzz511, zzz513, zzz514, zzz31, Succ(zzz6600), zzz342000, h)
new_mkVBalBranch3MkVBalBranch223(zzz340, zzz341, Neg(Succ(Succ(zzz342000))), zzz343, zzz344, zzz510, zzz511, Succ(zzz512000), zzz513, zzz514, zzz31, Zero, h) → new_mkVBalBranch3MkVBalBranch224(zzz340, zzz341, Succ(zzz342000), zzz343, zzz344, zzz510, zzz511, zzz512000, zzz513, zzz514, zzz31, zzz342000, zzz512000, h)
new_mkVBalBranch3MkVBalBranch226(zzz340, zzz341, zzz3420, zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, h) → new_mkVBalBranch0(zzz31, Branch(zzz510, zzz511, Neg(Succ(zzz51200)), zzz513, zzz514), zzz343, h)
new_mkVBalBranch3MkVBalBranch218(zzz461, zzz462, zzz463, zzz464, zzz465, zzz466, zzz467, zzz468, zzz469, zzz470, zzz471, bb) → new_mkVBalBranch3MkVBalBranch110(zzz461, zzz462, zzz463, zzz464, zzz465, zzz466, zzz467, zzz468, zzz469, zzz470, zzz471, new_primPlusNat2(new_primMulNat0(zzz463), Succ(zzz463)), bb)
new_mkVBalBranch3MkVBalBranch117(zzz340, zzz341, zzz34200, zzz343, zzz344, zzz510, zzz511, zzz513, zzz514, zzz31, Succ(zzz1240), h) → new_mkVBalBranch0(zzz31, zzz514, Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), h)
new_mkVBalBranch0(zzz31, Branch(zzz510, zzz511, Neg(Succ(zzz51200)), zzz513, zzz514), Branch(zzz340, zzz341, zzz342, zzz343, zzz344), h) → new_mkVBalBranch3MkVBalBranch223(zzz340, zzz341, zzz342, zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, new_primPlusNat3(Succ(new_primPlusNat3(new_primPlusNat1(zzz51200), zzz51200)), Succ(zzz51200)), h)
new_mkVBalBranch3MkVBalBranch221(zzz340, zzz341, Succ(zzz34200), zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, h) → new_mkVBalBranch3MkVBalBranch19(zzz340, zzz341, zzz34200, zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, new_primPlusNat2(new_primPlusNat3(Succ(new_primPlusNat3(new_primPlusNat1(zzz34200), zzz34200)), Succ(zzz34200)), Succ(zzz34200)), h)
new_mkVBalBranch3MkVBalBranch217(zzz473, zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, zzz481, zzz482, Zero, Zero, bh) → new_mkVBalBranch3MkVBalBranch233(zzz473, zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, zzz481, zzz482, bh)
new_mkVBalBranch3MkVBalBranch120(zzz2050, zzz2051, zzz2052, zzz2053, zzz2054, zzz2055, zzz2056, zzz2057, zzz2058, zzz2059, zzz2060, Succ(zzz20610), Succ(zzz20620), be) → new_mkVBalBranch3MkVBalBranch120(zzz2050, zzz2051, zzz2052, zzz2053, zzz2054, zzz2055, zzz2056, zzz2057, zzz2058, zzz2059, zzz2060, zzz20610, zzz20620, be)
new_mkVBalBranch3MkVBalBranch223(zzz340, zzz341, Pos(zzz3420), zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, Succ(zzz670), h) → new_mkVBalBranch0(zzz31, Branch(zzz510, zzz511, Neg(Succ(zzz51200)), zzz513, zzz514), zzz343, h)
new_mkVBalBranch3MkVBalBranch216(zzz1105, zzz1106, zzz1107, zzz1108, zzz1109, zzz1110, zzz1111, zzz1112, zzz1113, zzz1114, zzz1115, Succ(zzz11160), Succ(zzz11170), ba) → new_mkVBalBranch3MkVBalBranch216(zzz1105, zzz1106, zzz1107, zzz1108, zzz1109, zzz1110, zzz1111, zzz1112, zzz1113, zzz1114, zzz1115, zzz11160, zzz11170, ba)
new_mkVBalBranch3MkVBalBranch19(zzz340, zzz341, zzz34200, zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, Zero, h) → new_mkVBalBranch3MkVBalBranch122(zzz340, zzz341, zzz34200, zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, h)
new_mkVBalBranch3MkVBalBranch223(zzz340, zzz341, Neg(Succ(Succ(Succ(zzz3420000)))), zzz343, zzz344, zzz510, zzz511, Succ(zzz512000), zzz513, zzz514, zzz31, Succ(Zero), h) → new_mkVBalBranch3MkVBalBranch224(zzz340, zzz341, Succ(Succ(zzz3420000)), zzz343, zzz344, zzz510, zzz511, zzz512000, zzz513, zzz514, zzz31, Succ(zzz3420000), Succ(zzz512000), h)
new_mkVBalBranch3MkVBalBranch215(zzz340, zzz341, Pos(Succ(Succ(zzz342000))), zzz343, zzz344, zzz510, zzz511, Zero, zzz513, zzz514, zzz31, Zero, h) → new_mkVBalBranch0(zzz31, Branch(zzz510, zzz511, Pos(Succ(Zero)), zzz513, zzz514), zzz343, h)
new_mkVBalBranch3MkVBalBranch225(zzz498, zzz499, zzz500, zzz501, zzz502, zzz503, zzz504, zzz505, zzz506, zzz507, Succ(zzz5080), Succ(zzz5090), bg) → new_mkVBalBranch3MkVBalBranch225(zzz498, zzz499, zzz500, zzz501, zzz502, zzz503, zzz504, zzz505, zzz506, zzz507, zzz5080, zzz5090, bg)
new_mkVBalBranch3MkVBalBranch19(zzz340, zzz341, zzz34200, zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, Succ(zzz1410), h) → new_mkVBalBranch0(zzz31, zzz514, Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), h)
new_mkVBalBranch3MkVBalBranch224(zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, zzz1125, zzz1126, zzz1127, zzz1128, zzz1129, Succ(zzz11300), Zero, bd) → new_mkVBalBranch3MkVBalBranch119(zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, zzz1125, zzz1126, zzz1127, zzz1128, zzz1129, new_primPlusNat2(new_primMulNat0(zzz1121), Succ(zzz1121)), bd)
new_mkVBalBranch3MkVBalBranch224(zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, zzz1125, zzz1126, zzz1127, zzz1128, zzz1129, Zero, Zero, bd) → new_mkVBalBranch3MkVBalBranch229(zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, zzz1125, zzz1126, zzz1127, zzz1128, zzz1129, bd)
new_mkVBalBranch3MkVBalBranch224(zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, zzz1125, zzz1126, zzz1127, zzz1128, zzz1129, Zero, Succ(zzz11310), bd) → new_mkVBalBranch3MkVBalBranch227(zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, zzz1125, zzz1126, zzz1127, zzz1128, zzz1129, bd)
new_mkVBalBranch3MkVBalBranch223(zzz340, zzz341, Neg(Succ(Succ(Zero))), zzz343, zzz344, zzz510, zzz511, Succ(zzz512000), zzz513, zzz514, zzz31, Succ(Zero), h) → new_mkVBalBranch3MkVBalBranch224(zzz340, zzz341, Succ(Zero), zzz343, zzz344, zzz510, zzz511, zzz512000, zzz513, zzz514, zzz31, Zero, Succ(zzz512000), h)
new_mkVBalBranch3MkVBalBranch223(zzz340, zzz341, Pos(zzz3420), zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, Zero, h) → new_mkVBalBranch3MkVBalBranch226(zzz340, zzz341, zzz3420, zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, h)
new_mkVBalBranch3MkVBalBranch223(zzz340, zzz341, Neg(Succ(Succ(zzz342000))), zzz343, zzz344, zzz510, zzz511, Zero, zzz513, zzz514, zzz31, Zero, h) → new_mkVBalBranch3MkVBalBranch118(zzz340, zzz341, Succ(zzz342000), zzz343, zzz344, zzz510, zzz511, zzz513, zzz514, zzz31, new_primPlusNat2(new_primMulNat0(Succ(zzz342000)), Succ(Succ(zzz342000))), h)
new_mkVBalBranch3MkVBalBranch230(zzz498, zzz499, zzz500, zzz501, zzz502, zzz503, zzz504, zzz505, zzz506, zzz507, bg) → new_mkVBalBranch3MkVBalBranch118(zzz498, zzz499, zzz500, zzz501, zzz502, zzz503, zzz504, zzz505, zzz506, zzz507, new_primPlusNat2(new_primMulNat0(zzz500), Succ(zzz500)), bg)
new_mkVBalBranch3MkVBalBranch223(zzz340, zzz341, Neg(Succ(Succ(Succ(zzz3420000)))), zzz343, zzz344, zzz510, zzz511, Succ(zzz512000), zzz513, zzz514, zzz31, Succ(Succ(zzz6700)), h) → new_mkVBalBranch3MkVBalBranch224(zzz340, zzz341, Succ(Succ(zzz3420000)), zzz343, zzz344, zzz510, zzz511, zzz512000, zzz513, zzz514, zzz31, Succ(zzz3420000), Succ(Succ(new_primPlusNat2(zzz6700, zzz512000))), h)
new_mkVBalBranch3MkVBalBranch223(zzz340, zzz341, Neg(Succ(Succ(Zero))), zzz343, zzz344, zzz510, zzz511, Zero, zzz513, zzz514, zzz31, Succ(Succ(zzz6700)), h) → new_mkVBalBranch3MkVBalBranch225(zzz340, zzz341, Succ(Zero), zzz343, zzz344, zzz510, zzz511, zzz513, zzz514, zzz31, Zero, Succ(zzz6700), h)
new_mkVBalBranch3MkVBalBranch215(zzz340, zzz341, Pos(Zero), zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, Zero, h) → new_mkVBalBranch3MkVBalBranch220(zzz340, zzz341, zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, h)
new_mkVBalBranch3MkVBalBranch115(zzz1986, zzz1987, zzz1988, zzz1989, zzz1990, zzz1991, zzz1992, zzz1993, zzz1994, zzz1995, zzz1996, Succ(zzz19970), Succ(zzz19980), bc) → new_mkVBalBranch3MkVBalBranch115(zzz1986, zzz1987, zzz1988, zzz1989, zzz1990, zzz1991, zzz1992, zzz1993, zzz1994, zzz1995, zzz1996, zzz19970, zzz19980, bc)
new_mkVBalBranch3MkVBalBranch215(zzz340, zzz341, Neg(Zero), zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, Succ(zzz660), h) → new_mkVBalBranch0(zzz31, zzz514, Branch(zzz340, zzz341, Neg(Zero), zzz343, zzz344), h)
new_mkVBalBranch3MkVBalBranch118(zzz498, zzz499, zzz500, zzz501, zzz502, zzz503, zzz504, zzz505, zzz506, zzz507, Succ(zzz8040), bg) → new_mkVBalBranch3MkVBalBranch120(zzz498, zzz499, zzz500, zzz501, zzz502, zzz503, zzz504, Zero, zzz505, zzz506, zzz507, Succ(Zero), Succ(zzz8040), bg)
new_mkVBalBranch3MkVBalBranch216(zzz1105, zzz1106, zzz1107, zzz1108, zzz1109, zzz1110, zzz1111, zzz1112, zzz1113, zzz1114, zzz1115, Succ(zzz11160), Zero, ba) → new_mkVBalBranch3MkVBalBranch218(zzz1105, zzz1106, zzz1107, zzz1108, zzz1109, zzz1110, zzz1111, zzz1112, zzz1113, zzz1114, zzz1115, ba)
new_mkVBalBranch3MkVBalBranch215(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, Succ(zzz660), h) → new_mkVBalBranch3MkVBalBranch19(zzz340, zzz341, zzz34200, zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, new_primPlusNat2(new_primMulNat0(zzz34200), Succ(zzz34200)), h)
new_mkVBalBranch3MkVBalBranch215(zzz340, zzz341, Pos(Succ(Succ(zzz342000))), zzz343, zzz344, zzz510, zzz511, Succ(zzz512000), zzz513, zzz514, zzz31, Succ(Zero), h) → new_mkVBalBranch3MkVBalBranch216(zzz340, zzz341, Succ(zzz342000), zzz343, zzz344, zzz510, zzz511, zzz512000, zzz513, zzz514, zzz31, Succ(zzz512000), zzz342000, h)
new_mkVBalBranch3MkVBalBranch221(zzz340, zzz341, Zero, zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, h) → new_mkVBalBranch0(zzz31, zzz514, Branch(zzz340, zzz341, Neg(Zero), zzz343, zzz344), h)
new_mkVBalBranch3MkVBalBranch216(zzz1105, zzz1106, zzz1107, zzz1108, zzz1109, zzz1110, zzz1111, zzz1112, zzz1113, zzz1114, zzz1115, Zero, Zero, ba) → new_mkVBalBranch3MkVBalBranch222(zzz1105, zzz1106, zzz1107, zzz1108, zzz1109, zzz1110, zzz1111, zzz1112, zzz1113, zzz1114, zzz1115, ba)
new_mkVBalBranch3MkVBalBranch215(zzz340, zzz341, Pos(Succ(Succ(zzz342000))), zzz343, zzz344, zzz510, zzz511, Zero, zzz513, zzz514, zzz31, Succ(Zero), h) → new_mkVBalBranch3MkVBalBranch217(zzz340, zzz341, Succ(zzz342000), zzz343, zzz344, zzz510, zzz511, zzz513, zzz514, zzz31, Zero, zzz342000, h)
new_mkVBalBranch3MkVBalBranch119(zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, zzz1125, zzz1126, zzz1127, zzz1128, zzz1129, Succ(zzz12130), bd) → new_mkVBalBranch3MkVBalBranch120(zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, zzz1125, Succ(zzz1126), zzz1127, zzz1128, zzz1129, Succ(Succ(zzz1126)), Succ(zzz12130), bd)
new_mkVBalBranch3MkVBalBranch18(zzz340, zzz341, zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, Zero, h) → new_mkVBalBranch3MkVBalBranch115(zzz340, zzz341, Zero, zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, Zero, Succ(zzz51200), h)

The TRS R consists of the following rules:

new_primMulNat0(zzz6200) → new_primPlusNat3(Succ(new_primPlusNat3(new_primPlusNat1(zzz6200), zzz6200)), Succ(zzz6200))
new_primPlusNat2(Succ(zzz900), Succ(zzz9100)) → Succ(Succ(new_primPlusNat2(zzz900, zzz9100)))
new_primPlusNat2(Zero, Succ(zzz9100)) → Succ(zzz9100)
new_primPlusNat2(Zero, Zero) → Zero
new_primPlusNat2(Succ(zzz900), Zero) → Succ(zzz900)
new_primPlusNat1(Zero) → Zero
new_primPlusNat1(Succ(zzz62000)) → Succ(Succ(new_primPlusNat1(zzz62000)))
new_primPlusNat3(zzz90, Succ(zzz910)) → Succ(Succ(new_primPlusNat2(zzz90, zzz910)))
new_primPlusNat3(zzz90, Zero) → Succ(zzz90)

The set Q consists of the following terms:

new_primPlusNat2(Zero, Succ(x0))
new_primMulNat1(x0)
new_primMulNat0(x0)
new_primPlusNat3(x0, Succ(x1))
new_primPlusNat2(Succ(x0), Succ(x1))
new_primPlusNat3(x0, Zero)
new_primPlusNat1(Zero)
new_primPlusNat2(Zero, Zero)
new_primPlusNat1(Succ(x0))
new_primPlusNat2(Succ(x0), Zero)

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

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

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

new_mkVBalBranch3MkVBalBranch215(zzz340, zzz341, Neg(zzz3420), zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, Zero, h) → new_mkVBalBranch3MkVBalBranch221(zzz340, zzz341, zzz3420, zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, h)
new_mkVBalBranch3MkVBalBranch225(zzz498, zzz499, zzz500, zzz501, zzz502, zzz503, zzz504, zzz505, zzz506, zzz507, Zero, Zero, bg) → new_mkVBalBranch3MkVBalBranch230(zzz498, zzz499, zzz500, zzz501, zzz502, zzz503, zzz504, zzz505, zzz506, zzz507, bg)
new_mkVBalBranch3MkVBalBranch18(zzz340, zzz341, zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, Succ(zzz1480), h) → new_mkVBalBranch3MkVBalBranch115(zzz340, zzz341, Zero, zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, Succ(zzz1480), Succ(zzz51200), h)
new_mkVBalBranch3MkVBalBranch215(zzz340, zzz341, Pos(Succ(Succ(zzz342000))), zzz343, zzz344, zzz510, zzz511, Succ(zzz512000), zzz513, zzz514, zzz31, Succ(Succ(zzz6600)), h) → new_mkVBalBranch3MkVBalBranch216(zzz340, zzz341, Succ(zzz342000), zzz343, zzz344, zzz510, zzz511, zzz512000, zzz513, zzz514, zzz31, Succ(Succ(new_primPlusNat2(zzz6600, zzz512000))), zzz342000, h)
new_mkVBalBranch0(zzz31, Branch(zzz510, zzz511, Neg(Zero), zzz513, zzz514), Branch(zzz340, zzz341, Pos(Succ(zzz34200)), zzz343, zzz344), h) → new_mkVBalBranch0(zzz31, Branch(zzz510, zzz511, Neg(Zero), zzz513, zzz514), zzz343, h)
new_mkVBalBranch3MkVBalBranch223(zzz340, zzz341, Neg(Succ(Succ(Succ(zzz3420000)))), zzz343, zzz344, zzz510, zzz511, Zero, zzz513, zzz514, zzz31, Succ(Succ(zzz6700)), h) → new_mkVBalBranch3MkVBalBranch225(zzz340, zzz341, Succ(Succ(zzz3420000)), zzz343, zzz344, zzz510, zzz511, zzz513, zzz514, zzz31, Succ(zzz3420000), Succ(zzz6700), h)
new_mkVBalBranch3MkVBalBranch220(zzz340, zzz341, zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, h) → new_mkVBalBranch0(zzz31, zzz514, Branch(zzz340, zzz341, Pos(Zero), zzz343, zzz344), h)
new_mkVBalBranch3MkVBalBranch120(zzz2050, zzz2051, zzz2052, zzz2053, zzz2054, zzz2055, zzz2056, zzz2057, zzz2058, zzz2059, zzz2060, Zero, Succ(zzz20620), be) → new_mkVBalBranch0(zzz2060, zzz2059, Branch(zzz2050, zzz2051, Neg(Succ(zzz2052)), zzz2053, zzz2054), be)
new_mkVBalBranch3MkVBalBranch222(zzz461, zzz462, zzz463, zzz464, zzz465, zzz466, zzz467, zzz468, zzz469, zzz470, zzz471, bb) → new_mkVBalBranch3MkVBalBranch110(zzz461, zzz462, zzz463, zzz464, zzz465, zzz466, zzz467, zzz468, zzz469, zzz470, zzz471, new_primPlusNat2(new_primMulNat0(zzz463), Succ(zzz463)), bb)
new_mkVBalBranch3MkVBalBranch121(zzz473, zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, zzz481, zzz482, Succ(zzz7390), bh) → new_mkVBalBranch3MkVBalBranch115(zzz473, zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, Zero, zzz480, zzz481, zzz482, Succ(zzz7390), Succ(Zero), bh)
new_mkVBalBranch3MkVBalBranch228(zzz340, zzz341, zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, h) → new_mkVBalBranch0(zzz31, Branch(zzz510, zzz511, Neg(Succ(zzz51200)), zzz513, zzz514), zzz343, h)
new_mkVBalBranch0(zzz31, Branch(zzz510, zzz511, Pos(Zero), zzz513, zzz514), Branch(zzz340, zzz341, Pos(Succ(zzz34200)), zzz343, zzz344), h) → new_mkVBalBranch0(zzz31, Branch(zzz510, zzz511, Pos(Zero), zzz513, zzz514), zzz343, h)
new_mkVBalBranch3MkVBalBranch215(zzz340, zzz341, Pos(Succ(Zero)), zzz343, zzz344, zzz510, zzz511, Zero, zzz513, zzz514, zzz31, Zero, h) → new_mkVBalBranch3MkVBalBranch219(zzz340, zzz341, zzz343, zzz344, zzz510, zzz511, Zero, zzz513, zzz514, zzz31, h)
new_mkVBalBranch3MkVBalBranch223(zzz340, zzz341, Neg(Succ(Succ(Zero))), zzz343, zzz344, zzz510, zzz511, Succ(zzz512000), zzz513, zzz514, zzz31, Succ(Succ(zzz6700)), h) → new_mkVBalBranch3MkVBalBranch224(zzz340, zzz341, Succ(Zero), zzz343, zzz344, zzz510, zzz511, zzz512000, zzz513, zzz514, zzz31, Zero, Succ(Succ(new_primPlusNat2(zzz6700, zzz512000))), h)
new_mkVBalBranch3MkVBalBranch223(zzz340, zzz341, Neg(Succ(Succ(Zero))), zzz343, zzz344, zzz510, zzz511, Zero, zzz513, zzz514, zzz31, Succ(Zero), h) → new_mkVBalBranch3MkVBalBranch225(zzz340, zzz341, Succ(Zero), zzz343, zzz344, zzz510, zzz511, zzz513, zzz514, zzz31, Zero, Zero, h)
new_mkVBalBranch3MkVBalBranch224(zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, zzz1125, zzz1126, zzz1127, zzz1128, zzz1129, Succ(zzz11300), Succ(zzz11310), bd) → new_mkVBalBranch3MkVBalBranch224(zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, zzz1125, zzz1126, zzz1127, zzz1128, zzz1129, zzz11300, zzz11310, bd)
new_mkVBalBranch3MkVBalBranch217(zzz473, zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, zzz481, zzz482, Zero, Succ(zzz4840), bh) → new_mkVBalBranch0(zzz482, Branch(zzz478, zzz479, Pos(Succ(Zero)), zzz480, zzz481), zzz476, bh)
new_mkVBalBranch0(zzz31, Branch(zzz510, zzz511, Pos(Succ(zzz51200)), zzz513, zzz514), Branch(zzz340, zzz341, zzz342, zzz343, zzz344), h) → new_mkVBalBranch3MkVBalBranch215(zzz340, zzz341, zzz342, zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, new_primPlusNat3(Succ(new_primPlusNat3(new_primPlusNat1(zzz51200), zzz51200)), Succ(zzz51200)), h)
new_mkVBalBranch3MkVBalBranch215(zzz340, zzz341, Pos(Succ(Succ(zzz342000))), zzz343, zzz344, zzz510, zzz511, Succ(zzz512000), zzz513, zzz514, zzz31, Zero, h) → new_mkVBalBranch3MkVBalBranch216(zzz340, zzz341, Succ(zzz342000), zzz343, zzz344, zzz510, zzz511, zzz512000, zzz513, zzz514, zzz31, zzz512000, zzz342000, h)
new_mkVBalBranch3MkVBalBranch110(zzz461, zzz462, zzz463, zzz464, zzz465, zzz466, zzz467, zzz468, zzz469, zzz470, zzz471, Succ(zzz5800), bb) → new_mkVBalBranch3MkVBalBranch115(zzz461, zzz462, zzz463, zzz464, zzz465, zzz466, zzz467, Succ(zzz468), zzz469, zzz470, zzz471, Succ(zzz5800), Succ(Succ(zzz468)), bb)
new_mkVBalBranch3MkVBalBranch223(zzz340, zzz341, Neg(Succ(Zero)), zzz343, zzz344, zzz510, zzz511, Zero, zzz513, zzz514, zzz31, Zero, h) → new_mkVBalBranch3MkVBalBranch118(zzz340, zzz341, Zero, zzz343, zzz344, zzz510, zzz511, zzz513, zzz514, zzz31, new_primPlusNat2(new_primMulNat0(Zero), Succ(Zero)), h)
new_mkVBalBranch3MkVBalBranch227(zzz486, zzz487, zzz488, zzz489, zzz490, zzz491, zzz492, zzz493, zzz494, zzz495, zzz496, bf) → new_mkVBalBranch0(zzz496, Branch(zzz491, zzz492, Neg(Succ(Succ(zzz493))), zzz494, zzz495), zzz489, bf)
new_mkVBalBranch3MkVBalBranch215(zzz340, zzz341, Pos(Zero), zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, Succ(zzz660), h) → new_mkVBalBranch0(zzz31, zzz514, Branch(zzz340, zzz341, Pos(Zero), zzz343, zzz344), h)
new_mkVBalBranch0(zzz31, Branch(zzz510, zzz511, Pos(Zero), zzz513, zzz514), Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), h) → new_mkVBalBranch3MkVBalBranch116(zzz340, zzz341, zzz34200, zzz343, zzz344, zzz510, zzz511, zzz513, zzz514, zzz31, new_primPlusNat2(new_primMulNat0(zzz34200), Succ(zzz34200)), h)
new_mkVBalBranch3MkVBalBranch217(zzz473, zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, zzz481, zzz482, Succ(zzz4830), Zero, bh) → new_mkVBalBranch3MkVBalBranch121(zzz473, zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, zzz481, zzz482, new_primPlusNat2(new_primMulNat0(zzz475), Succ(zzz475)), bh)
new_mkVBalBranch3MkVBalBranch223(zzz340, zzz341, Neg(Zero), zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, Succ(zzz670), h) → new_mkVBalBranch0(zzz31, Branch(zzz510, zzz511, Neg(Succ(zzz51200)), zzz513, zzz514), zzz343, h)
new_mkVBalBranch3MkVBalBranch216(zzz1105, zzz1106, zzz1107, zzz1108, zzz1109, zzz1110, zzz1111, zzz1112, zzz1113, zzz1114, zzz1115, Zero, Succ(zzz11170), ba) → new_mkVBalBranch0(zzz1115, Branch(zzz1110, zzz1111, Pos(Succ(Succ(zzz1112))), zzz1113, zzz1114), zzz1108, ba)
new_mkVBalBranch3MkVBalBranch115(zzz1986, zzz1987, zzz1988, zzz1989, zzz1990, zzz1991, zzz1992, zzz1993, zzz1994, zzz1995, zzz1996, Zero, Succ(zzz19980), bc) → new_mkVBalBranch0(zzz1996, zzz1995, Branch(zzz1986, zzz1987, Pos(Succ(zzz1988)), zzz1989, zzz1990), bc)
new_mkVBalBranch0(zzz31, Branch(zzz510, zzz511, Neg(Zero), zzz513, zzz514), Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), h) → new_mkVBalBranch3MkVBalBranch117(zzz340, zzz341, zzz34200, zzz343, zzz344, zzz510, zzz511, zzz513, zzz514, zzz31, new_primPlusNat2(new_primMulNat0(zzz34200), Succ(zzz34200)), h)
new_mkVBalBranch3MkVBalBranch223(zzz340, zzz341, Neg(Zero), zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, Zero, h) → new_mkVBalBranch3MkVBalBranch228(zzz340, zzz341, zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, h)
new_mkVBalBranch3MkVBalBranch122(zzz340, zzz341, zzz34200, zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, h) → new_mkVBalBranch0(zzz31, zzz514, Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), h)
new_mkVBalBranch3MkVBalBranch217(zzz473, zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, zzz481, zzz482, Succ(zzz4830), Succ(zzz4840), bh) → new_mkVBalBranch3MkVBalBranch217(zzz473, zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, zzz481, zzz482, zzz4830, zzz4840, bh)
new_mkVBalBranch3MkVBalBranch116(zzz340, zzz341, zzz34200, zzz343, zzz344, zzz510, zzz511, zzz513, zzz514, zzz31, Succ(zzz1200), h) → new_mkVBalBranch0(zzz31, zzz514, Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), h)
new_mkVBalBranch3MkVBalBranch110(zzz461, zzz462, zzz463, zzz464, zzz465, zzz466, zzz467, zzz468, zzz469, zzz470, zzz471, Zero, bb) → new_mkVBalBranch3MkVBalBranch115(zzz461, zzz462, zzz463, zzz464, zzz465, zzz466, zzz467, Succ(zzz468), zzz469, zzz470, zzz471, Zero, Succ(Succ(zzz468)), bb)
new_mkVBalBranch3MkVBalBranch225(zzz498, zzz499, zzz500, zzz501, zzz502, zzz503, zzz504, zzz505, zzz506, zzz507, Zero, Succ(zzz5090), bg) → new_mkVBalBranch0(zzz507, Branch(zzz503, zzz504, Neg(Succ(Zero)), zzz505, zzz506), zzz501, bg)
new_mkVBalBranch3MkVBalBranch223(zzz340, zzz341, Neg(Succ(Succ(Succ(zzz3420000)))), zzz343, zzz344, zzz510, zzz511, Zero, zzz513, zzz514, zzz31, Succ(Zero), h) → new_mkVBalBranch3MkVBalBranch225(zzz340, zzz341, Succ(Succ(zzz3420000)), zzz343, zzz344, zzz510, zzz511, zzz513, zzz514, zzz31, Succ(zzz3420000), Zero, h)
new_mkVBalBranch3MkVBalBranch121(zzz473, zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, zzz481, zzz482, Zero, bh) → new_mkVBalBranch3MkVBalBranch115(zzz473, zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, Zero, zzz480, zzz481, zzz482, Zero, Succ(Zero), bh)
new_mkVBalBranch3MkVBalBranch215(zzz340, zzz341, Pos(Succ(Zero)), zzz343, zzz344, zzz510, zzz511, Succ(zzz512000), zzz513, zzz514, zzz31, Zero, h) → new_mkVBalBranch3MkVBalBranch218(zzz340, zzz341, Zero, zzz343, zzz344, zzz510, zzz511, zzz512000, zzz513, zzz514, zzz31, h)
new_mkVBalBranch3MkVBalBranch225(zzz498, zzz499, zzz500, zzz501, zzz502, zzz503, zzz504, zzz505, zzz506, zzz507, Succ(zzz5080), Zero, bg) → new_mkVBalBranch3MkVBalBranch118(zzz498, zzz499, zzz500, zzz501, zzz502, zzz503, zzz504, zzz505, zzz506, zzz507, new_primPlusNat2(new_primMulNat0(zzz500), Succ(zzz500)), bg)
new_mkVBalBranch3MkVBalBranch223(zzz340, zzz341, Neg(Succ(Zero)), zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, Succ(zzz670), h) → new_mkVBalBranch0(zzz31, Branch(zzz510, zzz511, Neg(Succ(zzz51200)), zzz513, zzz514), zzz343, h)
new_mkVBalBranch3MkVBalBranch215(zzz340, zzz341, Pos(Succ(Zero)), zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, Succ(zzz660), h) → new_mkVBalBranch3MkVBalBranch18(zzz340, zzz341, zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, new_primPlusNat2(new_primMulNat0(Zero), Succ(Zero)), h)
new_mkVBalBranch3MkVBalBranch229(zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, zzz1125, zzz1126, zzz1127, zzz1128, zzz1129, bd) → new_mkVBalBranch3MkVBalBranch119(zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, zzz1125, zzz1126, zzz1127, zzz1128, zzz1129, new_primPlusNat2(new_primMulNat0(zzz1121), Succ(zzz1121)), bd)
new_mkVBalBranch3MkVBalBranch219(zzz340, zzz341, zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, h) → new_mkVBalBranch3MkVBalBranch18(zzz340, zzz341, zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, new_primPlusNat2(new_primMulNat0(Zero), Succ(Zero)), h)
new_mkVBalBranch3MkVBalBranch233(zzz473, zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, zzz481, zzz482, bh) → new_mkVBalBranch3MkVBalBranch121(zzz473, zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, zzz481, zzz482, new_primPlusNat2(new_primMulNat0(zzz475), Succ(zzz475)), bh)
new_mkVBalBranch3MkVBalBranch223(zzz340, zzz341, Neg(Succ(Zero)), zzz343, zzz344, zzz510, zzz511, Succ(zzz512000), zzz513, zzz514, zzz31, Zero, h) → new_mkVBalBranch3MkVBalBranch227(zzz340, zzz341, Zero, zzz343, zzz344, zzz510, zzz511, zzz512000, zzz513, zzz514, zzz31, h)
new_mkVBalBranch3MkVBalBranch215(zzz340, zzz341, Pos(Succ(Succ(zzz342000))), zzz343, zzz344, zzz510, zzz511, Zero, zzz513, zzz514, zzz31, Succ(Succ(zzz6600)), h) → new_mkVBalBranch3MkVBalBranch217(zzz340, zzz341, Succ(zzz342000), zzz343, zzz344, zzz510, zzz511, zzz513, zzz514, zzz31, Succ(zzz6600), zzz342000, h)
new_mkVBalBranch3MkVBalBranch223(zzz340, zzz341, Neg(Succ(Succ(zzz342000))), zzz343, zzz344, zzz510, zzz511, Succ(zzz512000), zzz513, zzz514, zzz31, Zero, h) → new_mkVBalBranch3MkVBalBranch224(zzz340, zzz341, Succ(zzz342000), zzz343, zzz344, zzz510, zzz511, zzz512000, zzz513, zzz514, zzz31, zzz342000, zzz512000, h)
new_mkVBalBranch3MkVBalBranch226(zzz340, zzz341, zzz3420, zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, h) → new_mkVBalBranch0(zzz31, Branch(zzz510, zzz511, Neg(Succ(zzz51200)), zzz513, zzz514), zzz343, h)
new_mkVBalBranch3MkVBalBranch218(zzz461, zzz462, zzz463, zzz464, zzz465, zzz466, zzz467, zzz468, zzz469, zzz470, zzz471, bb) → new_mkVBalBranch3MkVBalBranch110(zzz461, zzz462, zzz463, zzz464, zzz465, zzz466, zzz467, zzz468, zzz469, zzz470, zzz471, new_primPlusNat2(new_primMulNat0(zzz463), Succ(zzz463)), bb)
new_mkVBalBranch3MkVBalBranch117(zzz340, zzz341, zzz34200, zzz343, zzz344, zzz510, zzz511, zzz513, zzz514, zzz31, Succ(zzz1240), h) → new_mkVBalBranch0(zzz31, zzz514, Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), h)
new_mkVBalBranch3MkVBalBranch120(zzz2050, zzz2051, zzz2052, zzz2053, zzz2054, zzz2055, zzz2056, zzz2057, zzz2058, zzz2059, zzz2060, Succ(zzz20610), Succ(zzz20620), be) → new_mkVBalBranch3MkVBalBranch120(zzz2050, zzz2051, zzz2052, zzz2053, zzz2054, zzz2055, zzz2056, zzz2057, zzz2058, zzz2059, zzz2060, zzz20610, zzz20620, be)
new_mkVBalBranch3MkVBalBranch217(zzz473, zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, zzz481, zzz482, Zero, Zero, bh) → new_mkVBalBranch3MkVBalBranch233(zzz473, zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, zzz481, zzz482, bh)
new_mkVBalBranch3MkVBalBranch221(zzz340, zzz341, Succ(zzz34200), zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, h) → new_mkVBalBranch3MkVBalBranch19(zzz340, zzz341, zzz34200, zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, new_primPlusNat2(new_primPlusNat3(Succ(new_primPlusNat3(new_primPlusNat1(zzz34200), zzz34200)), Succ(zzz34200)), Succ(zzz34200)), h)
new_mkVBalBranch0(zzz31, Branch(zzz510, zzz511, Neg(Succ(zzz51200)), zzz513, zzz514), Branch(zzz340, zzz341, zzz342, zzz343, zzz344), h) → new_mkVBalBranch3MkVBalBranch223(zzz340, zzz341, zzz342, zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, new_primPlusNat3(Succ(new_primPlusNat3(new_primPlusNat1(zzz51200), zzz51200)), Succ(zzz51200)), h)
new_mkVBalBranch3MkVBalBranch216(zzz1105, zzz1106, zzz1107, zzz1108, zzz1109, zzz1110, zzz1111, zzz1112, zzz1113, zzz1114, zzz1115, Succ(zzz11160), Succ(zzz11170), ba) → new_mkVBalBranch3MkVBalBranch216(zzz1105, zzz1106, zzz1107, zzz1108, zzz1109, zzz1110, zzz1111, zzz1112, zzz1113, zzz1114, zzz1115, zzz11160, zzz11170, ba)
new_mkVBalBranch3MkVBalBranch223(zzz340, zzz341, Pos(zzz3420), zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, Succ(zzz670), h) → new_mkVBalBranch0(zzz31, Branch(zzz510, zzz511, Neg(Succ(zzz51200)), zzz513, zzz514), zzz343, h)
new_mkVBalBranch3MkVBalBranch223(zzz340, zzz341, Neg(Succ(Succ(Succ(zzz3420000)))), zzz343, zzz344, zzz510, zzz511, Succ(zzz512000), zzz513, zzz514, zzz31, Succ(Zero), h) → new_mkVBalBranch3MkVBalBranch224(zzz340, zzz341, Succ(Succ(zzz3420000)), zzz343, zzz344, zzz510, zzz511, zzz512000, zzz513, zzz514, zzz31, Succ(zzz3420000), Succ(zzz512000), h)
new_mkVBalBranch3MkVBalBranch19(zzz340, zzz341, zzz34200, zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, Zero, h) → new_mkVBalBranch3MkVBalBranch122(zzz340, zzz341, zzz34200, zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, h)
new_mkVBalBranch3MkVBalBranch215(zzz340, zzz341, Pos(Succ(Succ(zzz342000))), zzz343, zzz344, zzz510, zzz511, Zero, zzz513, zzz514, zzz31, Zero, h) → new_mkVBalBranch0(zzz31, Branch(zzz510, zzz511, Pos(Succ(Zero)), zzz513, zzz514), zzz343, h)
new_mkVBalBranch3MkVBalBranch225(zzz498, zzz499, zzz500, zzz501, zzz502, zzz503, zzz504, zzz505, zzz506, zzz507, Succ(zzz5080), Succ(zzz5090), bg) → new_mkVBalBranch3MkVBalBranch225(zzz498, zzz499, zzz500, zzz501, zzz502, zzz503, zzz504, zzz505, zzz506, zzz507, zzz5080, zzz5090, bg)
new_mkVBalBranch3MkVBalBranch19(zzz340, zzz341, zzz34200, zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, Succ(zzz1410), h) → new_mkVBalBranch0(zzz31, zzz514, Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), h)
new_mkVBalBranch3MkVBalBranch224(zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, zzz1125, zzz1126, zzz1127, zzz1128, zzz1129, Succ(zzz11300), Zero, bd) → new_mkVBalBranch3MkVBalBranch119(zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, zzz1125, zzz1126, zzz1127, zzz1128, zzz1129, new_primPlusNat2(new_primMulNat0(zzz1121), Succ(zzz1121)), bd)
new_mkVBalBranch3MkVBalBranch223(zzz340, zzz341, Pos(zzz3420), zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, Zero, h) → new_mkVBalBranch3MkVBalBranch226(zzz340, zzz341, zzz3420, zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, h)
new_mkVBalBranch3MkVBalBranch223(zzz340, zzz341, Neg(Succ(Succ(Zero))), zzz343, zzz344, zzz510, zzz511, Succ(zzz512000), zzz513, zzz514, zzz31, Succ(Zero), h) → new_mkVBalBranch3MkVBalBranch224(zzz340, zzz341, Succ(Zero), zzz343, zzz344, zzz510, zzz511, zzz512000, zzz513, zzz514, zzz31, Zero, Succ(zzz512000), h)
new_mkVBalBranch3MkVBalBranch224(zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, zzz1125, zzz1126, zzz1127, zzz1128, zzz1129, Zero, Succ(zzz11310), bd) → new_mkVBalBranch3MkVBalBranch227(zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, zzz1125, zzz1126, zzz1127, zzz1128, zzz1129, bd)
new_mkVBalBranch3MkVBalBranch224(zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, zzz1125, zzz1126, zzz1127, zzz1128, zzz1129, Zero, Zero, bd) → new_mkVBalBranch3MkVBalBranch229(zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, zzz1125, zzz1126, zzz1127, zzz1128, zzz1129, bd)
new_mkVBalBranch3MkVBalBranch223(zzz340, zzz341, Neg(Succ(Succ(zzz342000))), zzz343, zzz344, zzz510, zzz511, Zero, zzz513, zzz514, zzz31, Zero, h) → new_mkVBalBranch3MkVBalBranch118(zzz340, zzz341, Succ(zzz342000), zzz343, zzz344, zzz510, zzz511, zzz513, zzz514, zzz31, new_primPlusNat2(new_primMulNat0(Succ(zzz342000)), Succ(Succ(zzz342000))), h)
new_mkVBalBranch3MkVBalBranch230(zzz498, zzz499, zzz500, zzz501, zzz502, zzz503, zzz504, zzz505, zzz506, zzz507, bg) → new_mkVBalBranch3MkVBalBranch118(zzz498, zzz499, zzz500, zzz501, zzz502, zzz503, zzz504, zzz505, zzz506, zzz507, new_primPlusNat2(new_primMulNat0(zzz500), Succ(zzz500)), bg)
new_mkVBalBranch3MkVBalBranch223(zzz340, zzz341, Neg(Succ(Succ(Zero))), zzz343, zzz344, zzz510, zzz511, Zero, zzz513, zzz514, zzz31, Succ(Succ(zzz6700)), h) → new_mkVBalBranch3MkVBalBranch225(zzz340, zzz341, Succ(Zero), zzz343, zzz344, zzz510, zzz511, zzz513, zzz514, zzz31, Zero, Succ(zzz6700), h)
new_mkVBalBranch3MkVBalBranch223(zzz340, zzz341, Neg(Succ(Succ(Succ(zzz3420000)))), zzz343, zzz344, zzz510, zzz511, Succ(zzz512000), zzz513, zzz514, zzz31, Succ(Succ(zzz6700)), h) → new_mkVBalBranch3MkVBalBranch224(zzz340, zzz341, Succ(Succ(zzz3420000)), zzz343, zzz344, zzz510, zzz511, zzz512000, zzz513, zzz514, zzz31, Succ(zzz3420000), Succ(Succ(new_primPlusNat2(zzz6700, zzz512000))), h)
new_mkVBalBranch3MkVBalBranch115(zzz1986, zzz1987, zzz1988, zzz1989, zzz1990, zzz1991, zzz1992, zzz1993, zzz1994, zzz1995, zzz1996, Succ(zzz19970), Succ(zzz19980), bc) → new_mkVBalBranch3MkVBalBranch115(zzz1986, zzz1987, zzz1988, zzz1989, zzz1990, zzz1991, zzz1992, zzz1993, zzz1994, zzz1995, zzz1996, zzz19970, zzz19980, bc)
new_mkVBalBranch3MkVBalBranch215(zzz340, zzz341, Pos(Zero), zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, Zero, h) → new_mkVBalBranch3MkVBalBranch220(zzz340, zzz341, zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, h)
new_mkVBalBranch3MkVBalBranch215(zzz340, zzz341, Neg(Zero), zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, Succ(zzz660), h) → new_mkVBalBranch0(zzz31, zzz514, Branch(zzz340, zzz341, Neg(Zero), zzz343, zzz344), h)
new_mkVBalBranch3MkVBalBranch118(zzz498, zzz499, zzz500, zzz501, zzz502, zzz503, zzz504, zzz505, zzz506, zzz507, Succ(zzz8040), bg) → new_mkVBalBranch3MkVBalBranch120(zzz498, zzz499, zzz500, zzz501, zzz502, zzz503, zzz504, Zero, zzz505, zzz506, zzz507, Succ(Zero), Succ(zzz8040), bg)
new_mkVBalBranch3MkVBalBranch216(zzz1105, zzz1106, zzz1107, zzz1108, zzz1109, zzz1110, zzz1111, zzz1112, zzz1113, zzz1114, zzz1115, Succ(zzz11160), Zero, ba) → new_mkVBalBranch3MkVBalBranch218(zzz1105, zzz1106, zzz1107, zzz1108, zzz1109, zzz1110, zzz1111, zzz1112, zzz1113, zzz1114, zzz1115, ba)
new_mkVBalBranch3MkVBalBranch221(zzz340, zzz341, Zero, zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, h) → new_mkVBalBranch0(zzz31, zzz514, Branch(zzz340, zzz341, Neg(Zero), zzz343, zzz344), h)
new_mkVBalBranch3MkVBalBranch215(zzz340, zzz341, Pos(Succ(Succ(zzz342000))), zzz343, zzz344, zzz510, zzz511, Succ(zzz512000), zzz513, zzz514, zzz31, Succ(Zero), h) → new_mkVBalBranch3MkVBalBranch216(zzz340, zzz341, Succ(zzz342000), zzz343, zzz344, zzz510, zzz511, zzz512000, zzz513, zzz514, zzz31, Succ(zzz512000), zzz342000, h)
new_mkVBalBranch3MkVBalBranch215(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, Succ(zzz660), h) → new_mkVBalBranch3MkVBalBranch19(zzz340, zzz341, zzz34200, zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, new_primPlusNat2(new_primMulNat0(zzz34200), Succ(zzz34200)), h)
new_mkVBalBranch3MkVBalBranch216(zzz1105, zzz1106, zzz1107, zzz1108, zzz1109, zzz1110, zzz1111, zzz1112, zzz1113, zzz1114, zzz1115, Zero, Zero, ba) → new_mkVBalBranch3MkVBalBranch222(zzz1105, zzz1106, zzz1107, zzz1108, zzz1109, zzz1110, zzz1111, zzz1112, zzz1113, zzz1114, zzz1115, ba)
new_mkVBalBranch3MkVBalBranch215(zzz340, zzz341, Pos(Succ(Succ(zzz342000))), zzz343, zzz344, zzz510, zzz511, Zero, zzz513, zzz514, zzz31, Succ(Zero), h) → new_mkVBalBranch3MkVBalBranch217(zzz340, zzz341, Succ(zzz342000), zzz343, zzz344, zzz510, zzz511, zzz513, zzz514, zzz31, Zero, zzz342000, h)
new_mkVBalBranch3MkVBalBranch18(zzz340, zzz341, zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, Zero, h) → new_mkVBalBranch3MkVBalBranch115(zzz340, zzz341, Zero, zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, Zero, Succ(zzz51200), h)
new_mkVBalBranch3MkVBalBranch119(zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, zzz1125, zzz1126, zzz1127, zzz1128, zzz1129, Succ(zzz12130), bd) → new_mkVBalBranch3MkVBalBranch120(zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, zzz1125, Succ(zzz1126), zzz1127, zzz1128, zzz1129, Succ(Succ(zzz1126)), Succ(zzz12130), bd)

The TRS R consists of the following rules:

new_primMulNat0(zzz6200) → new_primPlusNat3(Succ(new_primPlusNat3(new_primPlusNat1(zzz6200), zzz6200)), Succ(zzz6200))
new_primPlusNat2(Succ(zzz900), Succ(zzz9100)) → Succ(Succ(new_primPlusNat2(zzz900, zzz9100)))
new_primPlusNat2(Zero, Succ(zzz9100)) → Succ(zzz9100)
new_primPlusNat2(Zero, Zero) → Zero
new_primPlusNat2(Succ(zzz900), Zero) → Succ(zzz900)
new_primPlusNat1(Zero) → Zero
new_primPlusNat1(Succ(zzz62000)) → Succ(Succ(new_primPlusNat1(zzz62000)))
new_primPlusNat3(zzz90, Succ(zzz910)) → Succ(Succ(new_primPlusNat2(zzz90, zzz910)))
new_primPlusNat3(zzz90, Zero) → Succ(zzz90)

The set Q consists of the following terms:

new_primPlusNat2(Zero, Succ(x0))
new_primMulNat0(x0)
new_primPlusNat3(x0, Succ(x1))
new_primPlusNat2(Succ(x0), Succ(x1))
new_primPlusNat3(x0, Zero)
new_primPlusNat1(Zero)
new_primPlusNat2(Zero, Zero)
new_primPlusNat1(Succ(x0))
new_primPlusNat2(Succ(x0), Zero)

We have to consider all minimal (P,Q,R)-chains.
By rewriting [15] the rule new_mkVBalBranch3MkVBalBranch222(zzz461, zzz462, zzz463, zzz464, zzz465, zzz466, zzz467, zzz468, zzz469, zzz470, zzz471, bb) → new_mkVBalBranch3MkVBalBranch110(zzz461, zzz462, zzz463, zzz464, zzz465, zzz466, zzz467, zzz468, zzz469, zzz470, zzz471, new_primPlusNat2(new_primMulNat0(zzz463), Succ(zzz463)), bb) at position [11,0] we obtained the following new rules:

new_mkVBalBranch3MkVBalBranch222(zzz461, zzz462, zzz463, zzz464, zzz465, zzz466, zzz467, zzz468, zzz469, zzz470, zzz471, bb) → new_mkVBalBranch3MkVBalBranch110(zzz461, zzz462, zzz463, zzz464, zzz465, zzz466, zzz467, zzz468, zzz469, zzz470, zzz471, new_primPlusNat2(new_primPlusNat3(Succ(new_primPlusNat3(new_primPlusNat1(zzz463), zzz463)), Succ(zzz463)), Succ(zzz463)), bb)



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

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

new_mkVBalBranch3MkVBalBranch225(zzz498, zzz499, zzz500, zzz501, zzz502, zzz503, zzz504, zzz505, zzz506, zzz507, Zero, Zero, bg) → new_mkVBalBranch3MkVBalBranch230(zzz498, zzz499, zzz500, zzz501, zzz502, zzz503, zzz504, zzz505, zzz506, zzz507, bg)
new_mkVBalBranch3MkVBalBranch215(zzz340, zzz341, Neg(zzz3420), zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, Zero, h) → new_mkVBalBranch3MkVBalBranch221(zzz340, zzz341, zzz3420, zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, h)
new_mkVBalBranch3MkVBalBranch18(zzz340, zzz341, zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, Succ(zzz1480), h) → new_mkVBalBranch3MkVBalBranch115(zzz340, zzz341, Zero, zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, Succ(zzz1480), Succ(zzz51200), h)
new_mkVBalBranch0(zzz31, Branch(zzz510, zzz511, Neg(Zero), zzz513, zzz514), Branch(zzz340, zzz341, Pos(Succ(zzz34200)), zzz343, zzz344), h) → new_mkVBalBranch0(zzz31, Branch(zzz510, zzz511, Neg(Zero), zzz513, zzz514), zzz343, h)
new_mkVBalBranch3MkVBalBranch215(zzz340, zzz341, Pos(Succ(Succ(zzz342000))), zzz343, zzz344, zzz510, zzz511, Succ(zzz512000), zzz513, zzz514, zzz31, Succ(Succ(zzz6600)), h) → new_mkVBalBranch3MkVBalBranch216(zzz340, zzz341, Succ(zzz342000), zzz343, zzz344, zzz510, zzz511, zzz512000, zzz513, zzz514, zzz31, Succ(Succ(new_primPlusNat2(zzz6600, zzz512000))), zzz342000, h)
new_mkVBalBranch3MkVBalBranch223(zzz340, zzz341, Neg(Succ(Succ(Succ(zzz3420000)))), zzz343, zzz344, zzz510, zzz511, Zero, zzz513, zzz514, zzz31, Succ(Succ(zzz6700)), h) → new_mkVBalBranch3MkVBalBranch225(zzz340, zzz341, Succ(Succ(zzz3420000)), zzz343, zzz344, zzz510, zzz511, zzz513, zzz514, zzz31, Succ(zzz3420000), Succ(zzz6700), h)
new_mkVBalBranch3MkVBalBranch120(zzz2050, zzz2051, zzz2052, zzz2053, zzz2054, zzz2055, zzz2056, zzz2057, zzz2058, zzz2059, zzz2060, Zero, Succ(zzz20620), be) → new_mkVBalBranch0(zzz2060, zzz2059, Branch(zzz2050, zzz2051, Neg(Succ(zzz2052)), zzz2053, zzz2054), be)
new_mkVBalBranch3MkVBalBranch220(zzz340, zzz341, zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, h) → new_mkVBalBranch0(zzz31, zzz514, Branch(zzz340, zzz341, Pos(Zero), zzz343, zzz344), h)
new_mkVBalBranch0(zzz31, Branch(zzz510, zzz511, Pos(Zero), zzz513, zzz514), Branch(zzz340, zzz341, Pos(Succ(zzz34200)), zzz343, zzz344), h) → new_mkVBalBranch0(zzz31, Branch(zzz510, zzz511, Pos(Zero), zzz513, zzz514), zzz343, h)
new_mkVBalBranch3MkVBalBranch228(zzz340, zzz341, zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, h) → new_mkVBalBranch0(zzz31, Branch(zzz510, zzz511, Neg(Succ(zzz51200)), zzz513, zzz514), zzz343, h)
new_mkVBalBranch3MkVBalBranch121(zzz473, zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, zzz481, zzz482, Succ(zzz7390), bh) → new_mkVBalBranch3MkVBalBranch115(zzz473, zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, Zero, zzz480, zzz481, zzz482, Succ(zzz7390), Succ(Zero), bh)
new_mkVBalBranch3MkVBalBranch223(zzz340, zzz341, Neg(Succ(Succ(Zero))), zzz343, zzz344, zzz510, zzz511, Succ(zzz512000), zzz513, zzz514, zzz31, Succ(Succ(zzz6700)), h) → new_mkVBalBranch3MkVBalBranch224(zzz340, zzz341, Succ(Zero), zzz343, zzz344, zzz510, zzz511, zzz512000, zzz513, zzz514, zzz31, Zero, Succ(Succ(new_primPlusNat2(zzz6700, zzz512000))), h)
new_mkVBalBranch3MkVBalBranch215(zzz340, zzz341, Pos(Succ(Zero)), zzz343, zzz344, zzz510, zzz511, Zero, zzz513, zzz514, zzz31, Zero, h) → new_mkVBalBranch3MkVBalBranch219(zzz340, zzz341, zzz343, zzz344, zzz510, zzz511, Zero, zzz513, zzz514, zzz31, h)
new_mkVBalBranch3MkVBalBranch223(zzz340, zzz341, Neg(Succ(Succ(Zero))), zzz343, zzz344, zzz510, zzz511, Zero, zzz513, zzz514, zzz31, Succ(Zero), h) → new_mkVBalBranch3MkVBalBranch225(zzz340, zzz341, Succ(Zero), zzz343, zzz344, zzz510, zzz511, zzz513, zzz514, zzz31, Zero, Zero, h)
new_mkVBalBranch3MkVBalBranch224(zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, zzz1125, zzz1126, zzz1127, zzz1128, zzz1129, Succ(zzz11300), Succ(zzz11310), bd) → new_mkVBalBranch3MkVBalBranch224(zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, zzz1125, zzz1126, zzz1127, zzz1128, zzz1129, zzz11300, zzz11310, bd)
new_mkVBalBranch0(zzz31, Branch(zzz510, zzz511, Pos(Succ(zzz51200)), zzz513, zzz514), Branch(zzz340, zzz341, zzz342, zzz343, zzz344), h) → new_mkVBalBranch3MkVBalBranch215(zzz340, zzz341, zzz342, zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, new_primPlusNat3(Succ(new_primPlusNat3(new_primPlusNat1(zzz51200), zzz51200)), Succ(zzz51200)), h)
new_mkVBalBranch3MkVBalBranch217(zzz473, zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, zzz481, zzz482, Zero, Succ(zzz4840), bh) → new_mkVBalBranch0(zzz482, Branch(zzz478, zzz479, Pos(Succ(Zero)), zzz480, zzz481), zzz476, bh)
new_mkVBalBranch3MkVBalBranch215(zzz340, zzz341, Pos(Succ(Succ(zzz342000))), zzz343, zzz344, zzz510, zzz511, Succ(zzz512000), zzz513, zzz514, zzz31, Zero, h) → new_mkVBalBranch3MkVBalBranch216(zzz340, zzz341, Succ(zzz342000), zzz343, zzz344, zzz510, zzz511, zzz512000, zzz513, zzz514, zzz31, zzz512000, zzz342000, h)
new_mkVBalBranch3MkVBalBranch110(zzz461, zzz462, zzz463, zzz464, zzz465, zzz466, zzz467, zzz468, zzz469, zzz470, zzz471, Succ(zzz5800), bb) → new_mkVBalBranch3MkVBalBranch115(zzz461, zzz462, zzz463, zzz464, zzz465, zzz466, zzz467, Succ(zzz468), zzz469, zzz470, zzz471, Succ(zzz5800), Succ(Succ(zzz468)), bb)
new_mkVBalBranch3MkVBalBranch223(zzz340, zzz341, Neg(Succ(Zero)), zzz343, zzz344, zzz510, zzz511, Zero, zzz513, zzz514, zzz31, Zero, h) → new_mkVBalBranch3MkVBalBranch118(zzz340, zzz341, Zero, zzz343, zzz344, zzz510, zzz511, zzz513, zzz514, zzz31, new_primPlusNat2(new_primMulNat0(Zero), Succ(Zero)), h)
new_mkVBalBranch3MkVBalBranch227(zzz486, zzz487, zzz488, zzz489, zzz490, zzz491, zzz492, zzz493, zzz494, zzz495, zzz496, bf) → new_mkVBalBranch0(zzz496, Branch(zzz491, zzz492, Neg(Succ(Succ(zzz493))), zzz494, zzz495), zzz489, bf)
new_mkVBalBranch0(zzz31, Branch(zzz510, zzz511, Pos(Zero), zzz513, zzz514), Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), h) → new_mkVBalBranch3MkVBalBranch116(zzz340, zzz341, zzz34200, zzz343, zzz344, zzz510, zzz511, zzz513, zzz514, zzz31, new_primPlusNat2(new_primMulNat0(zzz34200), Succ(zzz34200)), h)
new_mkVBalBranch3MkVBalBranch215(zzz340, zzz341, Pos(Zero), zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, Succ(zzz660), h) → new_mkVBalBranch0(zzz31, zzz514, Branch(zzz340, zzz341, Pos(Zero), zzz343, zzz344), h)
new_mkVBalBranch3MkVBalBranch223(zzz340, zzz341, Neg(Zero), zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, Succ(zzz670), h) → new_mkVBalBranch0(zzz31, Branch(zzz510, zzz511, Neg(Succ(zzz51200)), zzz513, zzz514), zzz343, h)
new_mkVBalBranch3MkVBalBranch217(zzz473, zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, zzz481, zzz482, Succ(zzz4830), Zero, bh) → new_mkVBalBranch3MkVBalBranch121(zzz473, zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, zzz481, zzz482, new_primPlusNat2(new_primMulNat0(zzz475), Succ(zzz475)), bh)
new_mkVBalBranch3MkVBalBranch216(zzz1105, zzz1106, zzz1107, zzz1108, zzz1109, zzz1110, zzz1111, zzz1112, zzz1113, zzz1114, zzz1115, Zero, Succ(zzz11170), ba) → new_mkVBalBranch0(zzz1115, Branch(zzz1110, zzz1111, Pos(Succ(Succ(zzz1112))), zzz1113, zzz1114), zzz1108, ba)
new_mkVBalBranch3MkVBalBranch115(zzz1986, zzz1987, zzz1988, zzz1989, zzz1990, zzz1991, zzz1992, zzz1993, zzz1994, zzz1995, zzz1996, Zero, Succ(zzz19980), bc) → new_mkVBalBranch0(zzz1996, zzz1995, Branch(zzz1986, zzz1987, Pos(Succ(zzz1988)), zzz1989, zzz1990), bc)
new_mkVBalBranch0(zzz31, Branch(zzz510, zzz511, Neg(Zero), zzz513, zzz514), Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), h) → new_mkVBalBranch3MkVBalBranch117(zzz340, zzz341, zzz34200, zzz343, zzz344, zzz510, zzz511, zzz513, zzz514, zzz31, new_primPlusNat2(new_primMulNat0(zzz34200), Succ(zzz34200)), h)
new_mkVBalBranch3MkVBalBranch223(zzz340, zzz341, Neg(Zero), zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, Zero, h) → new_mkVBalBranch3MkVBalBranch228(zzz340, zzz341, zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, h)
new_mkVBalBranch3MkVBalBranch122(zzz340, zzz341, zzz34200, zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, h) → new_mkVBalBranch0(zzz31, zzz514, Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), h)
new_mkVBalBranch3MkVBalBranch217(zzz473, zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, zzz481, zzz482, Succ(zzz4830), Succ(zzz4840), bh) → new_mkVBalBranch3MkVBalBranch217(zzz473, zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, zzz481, zzz482, zzz4830, zzz4840, bh)
new_mkVBalBranch3MkVBalBranch116(zzz340, zzz341, zzz34200, zzz343, zzz344, zzz510, zzz511, zzz513, zzz514, zzz31, Succ(zzz1200), h) → new_mkVBalBranch0(zzz31, zzz514, Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), h)
new_mkVBalBranch3MkVBalBranch110(zzz461, zzz462, zzz463, zzz464, zzz465, zzz466, zzz467, zzz468, zzz469, zzz470, zzz471, Zero, bb) → new_mkVBalBranch3MkVBalBranch115(zzz461, zzz462, zzz463, zzz464, zzz465, zzz466, zzz467, Succ(zzz468), zzz469, zzz470, zzz471, Zero, Succ(Succ(zzz468)), bb)
new_mkVBalBranch3MkVBalBranch225(zzz498, zzz499, zzz500, zzz501, zzz502, zzz503, zzz504, zzz505, zzz506, zzz507, Zero, Succ(zzz5090), bg) → new_mkVBalBranch0(zzz507, Branch(zzz503, zzz504, Neg(Succ(Zero)), zzz505, zzz506), zzz501, bg)
new_mkVBalBranch3MkVBalBranch222(zzz461, zzz462, zzz463, zzz464, zzz465, zzz466, zzz467, zzz468, zzz469, zzz470, zzz471, bb) → new_mkVBalBranch3MkVBalBranch110(zzz461, zzz462, zzz463, zzz464, zzz465, zzz466, zzz467, zzz468, zzz469, zzz470, zzz471, new_primPlusNat2(new_primPlusNat3(Succ(new_primPlusNat3(new_primPlusNat1(zzz463), zzz463)), Succ(zzz463)), Succ(zzz463)), bb)
new_mkVBalBranch3MkVBalBranch223(zzz340, zzz341, Neg(Succ(Succ(Succ(zzz3420000)))), zzz343, zzz344, zzz510, zzz511, Zero, zzz513, zzz514, zzz31, Succ(Zero), h) → new_mkVBalBranch3MkVBalBranch225(zzz340, zzz341, Succ(Succ(zzz3420000)), zzz343, zzz344, zzz510, zzz511, zzz513, zzz514, zzz31, Succ(zzz3420000), Zero, h)
new_mkVBalBranch3MkVBalBranch121(zzz473, zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, zzz481, zzz482, Zero, bh) → new_mkVBalBranch3MkVBalBranch115(zzz473, zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, Zero, zzz480, zzz481, zzz482, Zero, Succ(Zero), bh)
new_mkVBalBranch3MkVBalBranch215(zzz340, zzz341, Pos(Succ(Zero)), zzz343, zzz344, zzz510, zzz511, Succ(zzz512000), zzz513, zzz514, zzz31, Zero, h) → new_mkVBalBranch3MkVBalBranch218(zzz340, zzz341, Zero, zzz343, zzz344, zzz510, zzz511, zzz512000, zzz513, zzz514, zzz31, h)
new_mkVBalBranch3MkVBalBranch223(zzz340, zzz341, Neg(Succ(Zero)), zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, Succ(zzz670), h) → new_mkVBalBranch0(zzz31, Branch(zzz510, zzz511, Neg(Succ(zzz51200)), zzz513, zzz514), zzz343, h)
new_mkVBalBranch3MkVBalBranch225(zzz498, zzz499, zzz500, zzz501, zzz502, zzz503, zzz504, zzz505, zzz506, zzz507, Succ(zzz5080), Zero, bg) → new_mkVBalBranch3MkVBalBranch118(zzz498, zzz499, zzz500, zzz501, zzz502, zzz503, zzz504, zzz505, zzz506, zzz507, new_primPlusNat2(new_primMulNat0(zzz500), Succ(zzz500)), bg)
new_mkVBalBranch3MkVBalBranch215(zzz340, zzz341, Pos(Succ(Zero)), zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, Succ(zzz660), h) → new_mkVBalBranch3MkVBalBranch18(zzz340, zzz341, zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, new_primPlusNat2(new_primMulNat0(Zero), Succ(Zero)), h)
new_mkVBalBranch3MkVBalBranch229(zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, zzz1125, zzz1126, zzz1127, zzz1128, zzz1129, bd) → new_mkVBalBranch3MkVBalBranch119(zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, zzz1125, zzz1126, zzz1127, zzz1128, zzz1129, new_primPlusNat2(new_primMulNat0(zzz1121), Succ(zzz1121)), bd)
new_mkVBalBranch3MkVBalBranch219(zzz340, zzz341, zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, h) → new_mkVBalBranch3MkVBalBranch18(zzz340, zzz341, zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, new_primPlusNat2(new_primMulNat0(Zero), Succ(Zero)), h)
new_mkVBalBranch3MkVBalBranch223(zzz340, zzz341, Neg(Succ(Zero)), zzz343, zzz344, zzz510, zzz511, Succ(zzz512000), zzz513, zzz514, zzz31, Zero, h) → new_mkVBalBranch3MkVBalBranch227(zzz340, zzz341, Zero, zzz343, zzz344, zzz510, zzz511, zzz512000, zzz513, zzz514, zzz31, h)
new_mkVBalBranch3MkVBalBranch233(zzz473, zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, zzz481, zzz482, bh) → new_mkVBalBranch3MkVBalBranch121(zzz473, zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, zzz481, zzz482, new_primPlusNat2(new_primMulNat0(zzz475), Succ(zzz475)), bh)
new_mkVBalBranch3MkVBalBranch226(zzz340, zzz341, zzz3420, zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, h) → new_mkVBalBranch0(zzz31, Branch(zzz510, zzz511, Neg(Succ(zzz51200)), zzz513, zzz514), zzz343, h)
new_mkVBalBranch3MkVBalBranch223(zzz340, zzz341, Neg(Succ(Succ(zzz342000))), zzz343, zzz344, zzz510, zzz511, Succ(zzz512000), zzz513, zzz514, zzz31, Zero, h) → new_mkVBalBranch3MkVBalBranch224(zzz340, zzz341, Succ(zzz342000), zzz343, zzz344, zzz510, zzz511, zzz512000, zzz513, zzz514, zzz31, zzz342000, zzz512000, h)
new_mkVBalBranch3MkVBalBranch215(zzz340, zzz341, Pos(Succ(Succ(zzz342000))), zzz343, zzz344, zzz510, zzz511, Zero, zzz513, zzz514, zzz31, Succ(Succ(zzz6600)), h) → new_mkVBalBranch3MkVBalBranch217(zzz340, zzz341, Succ(zzz342000), zzz343, zzz344, zzz510, zzz511, zzz513, zzz514, zzz31, Succ(zzz6600), zzz342000, h)
new_mkVBalBranch3MkVBalBranch218(zzz461, zzz462, zzz463, zzz464, zzz465, zzz466, zzz467, zzz468, zzz469, zzz470, zzz471, bb) → new_mkVBalBranch3MkVBalBranch110(zzz461, zzz462, zzz463, zzz464, zzz465, zzz466, zzz467, zzz468, zzz469, zzz470, zzz471, new_primPlusNat2(new_primMulNat0(zzz463), Succ(zzz463)), bb)
new_mkVBalBranch3MkVBalBranch117(zzz340, zzz341, zzz34200, zzz343, zzz344, zzz510, zzz511, zzz513, zzz514, zzz31, Succ(zzz1240), h) → new_mkVBalBranch0(zzz31, zzz514, Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), h)
new_mkVBalBranch0(zzz31, Branch(zzz510, zzz511, Neg(Succ(zzz51200)), zzz513, zzz514), Branch(zzz340, zzz341, zzz342, zzz343, zzz344), h) → new_mkVBalBranch3MkVBalBranch223(zzz340, zzz341, zzz342, zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, new_primPlusNat3(Succ(new_primPlusNat3(new_primPlusNat1(zzz51200), zzz51200)), Succ(zzz51200)), h)
new_mkVBalBranch3MkVBalBranch221(zzz340, zzz341, Succ(zzz34200), zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, h) → new_mkVBalBranch3MkVBalBranch19(zzz340, zzz341, zzz34200, zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, new_primPlusNat2(new_primPlusNat3(Succ(new_primPlusNat3(new_primPlusNat1(zzz34200), zzz34200)), Succ(zzz34200)), Succ(zzz34200)), h)
new_mkVBalBranch3MkVBalBranch217(zzz473, zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, zzz481, zzz482, Zero, Zero, bh) → new_mkVBalBranch3MkVBalBranch233(zzz473, zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, zzz481, zzz482, bh)
new_mkVBalBranch3MkVBalBranch120(zzz2050, zzz2051, zzz2052, zzz2053, zzz2054, zzz2055, zzz2056, zzz2057, zzz2058, zzz2059, zzz2060, Succ(zzz20610), Succ(zzz20620), be) → new_mkVBalBranch3MkVBalBranch120(zzz2050, zzz2051, zzz2052, zzz2053, zzz2054, zzz2055, zzz2056, zzz2057, zzz2058, zzz2059, zzz2060, zzz20610, zzz20620, be)
new_mkVBalBranch3MkVBalBranch223(zzz340, zzz341, Pos(zzz3420), zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, Succ(zzz670), h) → new_mkVBalBranch0(zzz31, Branch(zzz510, zzz511, Neg(Succ(zzz51200)), zzz513, zzz514), zzz343, h)
new_mkVBalBranch3MkVBalBranch216(zzz1105, zzz1106, zzz1107, zzz1108, zzz1109, zzz1110, zzz1111, zzz1112, zzz1113, zzz1114, zzz1115, Succ(zzz11160), Succ(zzz11170), ba) → new_mkVBalBranch3MkVBalBranch216(zzz1105, zzz1106, zzz1107, zzz1108, zzz1109, zzz1110, zzz1111, zzz1112, zzz1113, zzz1114, zzz1115, zzz11160, zzz11170, ba)
new_mkVBalBranch3MkVBalBranch19(zzz340, zzz341, zzz34200, zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, Zero, h) → new_mkVBalBranch3MkVBalBranch122(zzz340, zzz341, zzz34200, zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, h)
new_mkVBalBranch3MkVBalBranch223(zzz340, zzz341, Neg(Succ(Succ(Succ(zzz3420000)))), zzz343, zzz344, zzz510, zzz511, Succ(zzz512000), zzz513, zzz514, zzz31, Succ(Zero), h) → new_mkVBalBranch3MkVBalBranch224(zzz340, zzz341, Succ(Succ(zzz3420000)), zzz343, zzz344, zzz510, zzz511, zzz512000, zzz513, zzz514, zzz31, Succ(zzz3420000), Succ(zzz512000), h)
new_mkVBalBranch3MkVBalBranch215(zzz340, zzz341, Pos(Succ(Succ(zzz342000))), zzz343, zzz344, zzz510, zzz511, Zero, zzz513, zzz514, zzz31, Zero, h) → new_mkVBalBranch0(zzz31, Branch(zzz510, zzz511, Pos(Succ(Zero)), zzz513, zzz514), zzz343, h)
new_mkVBalBranch3MkVBalBranch225(zzz498, zzz499, zzz500, zzz501, zzz502, zzz503, zzz504, zzz505, zzz506, zzz507, Succ(zzz5080), Succ(zzz5090), bg) → new_mkVBalBranch3MkVBalBranch225(zzz498, zzz499, zzz500, zzz501, zzz502, zzz503, zzz504, zzz505, zzz506, zzz507, zzz5080, zzz5090, bg)
new_mkVBalBranch3MkVBalBranch19(zzz340, zzz341, zzz34200, zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, Succ(zzz1410), h) → new_mkVBalBranch0(zzz31, zzz514, Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), h)
new_mkVBalBranch3MkVBalBranch224(zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, zzz1125, zzz1126, zzz1127, zzz1128, zzz1129, Succ(zzz11300), Zero, bd) → new_mkVBalBranch3MkVBalBranch119(zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, zzz1125, zzz1126, zzz1127, zzz1128, zzz1129, new_primPlusNat2(new_primMulNat0(zzz1121), Succ(zzz1121)), bd)
new_mkVBalBranch3MkVBalBranch224(zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, zzz1125, zzz1126, zzz1127, zzz1128, zzz1129, Zero, Zero, bd) → new_mkVBalBranch3MkVBalBranch229(zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, zzz1125, zzz1126, zzz1127, zzz1128, zzz1129, bd)
new_mkVBalBranch3MkVBalBranch224(zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, zzz1125, zzz1126, zzz1127, zzz1128, zzz1129, Zero, Succ(zzz11310), bd) → new_mkVBalBranch3MkVBalBranch227(zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, zzz1125, zzz1126, zzz1127, zzz1128, zzz1129, bd)
new_mkVBalBranch3MkVBalBranch223(zzz340, zzz341, Neg(Succ(Succ(Zero))), zzz343, zzz344, zzz510, zzz511, Succ(zzz512000), zzz513, zzz514, zzz31, Succ(Zero), h) → new_mkVBalBranch3MkVBalBranch224(zzz340, zzz341, Succ(Zero), zzz343, zzz344, zzz510, zzz511, zzz512000, zzz513, zzz514, zzz31, Zero, Succ(zzz512000), h)
new_mkVBalBranch3MkVBalBranch223(zzz340, zzz341, Pos(zzz3420), zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, Zero, h) → new_mkVBalBranch3MkVBalBranch226(zzz340, zzz341, zzz3420, zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, h)
new_mkVBalBranch3MkVBalBranch223(zzz340, zzz341, Neg(Succ(Succ(zzz342000))), zzz343, zzz344, zzz510, zzz511, Zero, zzz513, zzz514, zzz31, Zero, h) → new_mkVBalBranch3MkVBalBranch118(zzz340, zzz341, Succ(zzz342000), zzz343, zzz344, zzz510, zzz511, zzz513, zzz514, zzz31, new_primPlusNat2(new_primMulNat0(Succ(zzz342000)), Succ(Succ(zzz342000))), h)
new_mkVBalBranch3MkVBalBranch230(zzz498, zzz499, zzz500, zzz501, zzz502, zzz503, zzz504, zzz505, zzz506, zzz507, bg) → new_mkVBalBranch3MkVBalBranch118(zzz498, zzz499, zzz500, zzz501, zzz502, zzz503, zzz504, zzz505, zzz506, zzz507, new_primPlusNat2(new_primMulNat0(zzz500), Succ(zzz500)), bg)
new_mkVBalBranch3MkVBalBranch223(zzz340, zzz341, Neg(Succ(Succ(Succ(zzz3420000)))), zzz343, zzz344, zzz510, zzz511, Succ(zzz512000), zzz513, zzz514, zzz31, Succ(Succ(zzz6700)), h) → new_mkVBalBranch3MkVBalBranch224(zzz340, zzz341, Succ(Succ(zzz3420000)), zzz343, zzz344, zzz510, zzz511, zzz512000, zzz513, zzz514, zzz31, Succ(zzz3420000), Succ(Succ(new_primPlusNat2(zzz6700, zzz512000))), h)
new_mkVBalBranch3MkVBalBranch223(zzz340, zzz341, Neg(Succ(Succ(Zero))), zzz343, zzz344, zzz510, zzz511, Zero, zzz513, zzz514, zzz31, Succ(Succ(zzz6700)), h) → new_mkVBalBranch3MkVBalBranch225(zzz340, zzz341, Succ(Zero), zzz343, zzz344, zzz510, zzz511, zzz513, zzz514, zzz31, Zero, Succ(zzz6700), h)
new_mkVBalBranch3MkVBalBranch215(zzz340, zzz341, Pos(Zero), zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, Zero, h) → new_mkVBalBranch3MkVBalBranch220(zzz340, zzz341, zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, h)
new_mkVBalBranch3MkVBalBranch115(zzz1986, zzz1987, zzz1988, zzz1989, zzz1990, zzz1991, zzz1992, zzz1993, zzz1994, zzz1995, zzz1996, Succ(zzz19970), Succ(zzz19980), bc) → new_mkVBalBranch3MkVBalBranch115(zzz1986, zzz1987, zzz1988, zzz1989, zzz1990, zzz1991, zzz1992, zzz1993, zzz1994, zzz1995, zzz1996, zzz19970, zzz19980, bc)
new_mkVBalBranch3MkVBalBranch215(zzz340, zzz341, Neg(Zero), zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, Succ(zzz660), h) → new_mkVBalBranch0(zzz31, zzz514, Branch(zzz340, zzz341, Neg(Zero), zzz343, zzz344), h)
new_mkVBalBranch3MkVBalBranch118(zzz498, zzz499, zzz500, zzz501, zzz502, zzz503, zzz504, zzz505, zzz506, zzz507, Succ(zzz8040), bg) → new_mkVBalBranch3MkVBalBranch120(zzz498, zzz499, zzz500, zzz501, zzz502, zzz503, zzz504, Zero, zzz505, zzz506, zzz507, Succ(Zero), Succ(zzz8040), bg)
new_mkVBalBranch3MkVBalBranch216(zzz1105, zzz1106, zzz1107, zzz1108, zzz1109, zzz1110, zzz1111, zzz1112, zzz1113, zzz1114, zzz1115, Succ(zzz11160), Zero, ba) → new_mkVBalBranch3MkVBalBranch218(zzz1105, zzz1106, zzz1107, zzz1108, zzz1109, zzz1110, zzz1111, zzz1112, zzz1113, zzz1114, zzz1115, ba)
new_mkVBalBranch3MkVBalBranch215(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, Succ(zzz660), h) → new_mkVBalBranch3MkVBalBranch19(zzz340, zzz341, zzz34200, zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, new_primPlusNat2(new_primMulNat0(zzz34200), Succ(zzz34200)), h)
new_mkVBalBranch3MkVBalBranch215(zzz340, zzz341, Pos(Succ(Succ(zzz342000))), zzz343, zzz344, zzz510, zzz511, Succ(zzz512000), zzz513, zzz514, zzz31, Succ(Zero), h) → new_mkVBalBranch3MkVBalBranch216(zzz340, zzz341, Succ(zzz342000), zzz343, zzz344, zzz510, zzz511, zzz512000, zzz513, zzz514, zzz31, Succ(zzz512000), zzz342000, h)
new_mkVBalBranch3MkVBalBranch221(zzz340, zzz341, Zero, zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, h) → new_mkVBalBranch0(zzz31, zzz514, Branch(zzz340, zzz341, Neg(Zero), zzz343, zzz344), h)
new_mkVBalBranch3MkVBalBranch216(zzz1105, zzz1106, zzz1107, zzz1108, zzz1109, zzz1110, zzz1111, zzz1112, zzz1113, zzz1114, zzz1115, Zero, Zero, ba) → new_mkVBalBranch3MkVBalBranch222(zzz1105, zzz1106, zzz1107, zzz1108, zzz1109, zzz1110, zzz1111, zzz1112, zzz1113, zzz1114, zzz1115, ba)
new_mkVBalBranch3MkVBalBranch215(zzz340, zzz341, Pos(Succ(Succ(zzz342000))), zzz343, zzz344, zzz510, zzz511, Zero, zzz513, zzz514, zzz31, Succ(Zero), h) → new_mkVBalBranch3MkVBalBranch217(zzz340, zzz341, Succ(zzz342000), zzz343, zzz344, zzz510, zzz511, zzz513, zzz514, zzz31, Zero, zzz342000, h)
new_mkVBalBranch3MkVBalBranch119(zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, zzz1125, zzz1126, zzz1127, zzz1128, zzz1129, Succ(zzz12130), bd) → new_mkVBalBranch3MkVBalBranch120(zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, zzz1125, Succ(zzz1126), zzz1127, zzz1128, zzz1129, Succ(Succ(zzz1126)), Succ(zzz12130), bd)
new_mkVBalBranch3MkVBalBranch18(zzz340, zzz341, zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, Zero, h) → new_mkVBalBranch3MkVBalBranch115(zzz340, zzz341, Zero, zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, Zero, Succ(zzz51200), h)

The TRS R consists of the following rules:

new_primMulNat0(zzz6200) → new_primPlusNat3(Succ(new_primPlusNat3(new_primPlusNat1(zzz6200), zzz6200)), Succ(zzz6200))
new_primPlusNat2(Succ(zzz900), Succ(zzz9100)) → Succ(Succ(new_primPlusNat2(zzz900, zzz9100)))
new_primPlusNat2(Zero, Succ(zzz9100)) → Succ(zzz9100)
new_primPlusNat2(Zero, Zero) → Zero
new_primPlusNat2(Succ(zzz900), Zero) → Succ(zzz900)
new_primPlusNat1(Zero) → Zero
new_primPlusNat1(Succ(zzz62000)) → Succ(Succ(new_primPlusNat1(zzz62000)))
new_primPlusNat3(zzz90, Succ(zzz910)) → Succ(Succ(new_primPlusNat2(zzz90, zzz910)))
new_primPlusNat3(zzz90, Zero) → Succ(zzz90)

The set Q consists of the following terms:

new_primPlusNat2(Zero, Succ(x0))
new_primMulNat0(x0)
new_primPlusNat3(x0, Succ(x1))
new_primPlusNat2(Succ(x0), Succ(x1))
new_primPlusNat3(x0, Zero)
new_primPlusNat1(Zero)
new_primPlusNat2(Zero, Zero)
new_primPlusNat1(Succ(x0))
new_primPlusNat2(Succ(x0), Zero)

We have to consider all minimal (P,Q,R)-chains.
By rewriting [15] the rule new_mkVBalBranch0(zzz31, Branch(zzz510, zzz511, Pos(Succ(zzz51200)), zzz513, zzz514), Branch(zzz340, zzz341, zzz342, zzz343, zzz344), h) → new_mkVBalBranch3MkVBalBranch215(zzz340, zzz341, zzz342, zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, new_primPlusNat3(Succ(new_primPlusNat3(new_primPlusNat1(zzz51200), zzz51200)), Succ(zzz51200)), h) at position [11] we obtained the following new rules:

new_mkVBalBranch0(zzz31, Branch(zzz510, zzz511, Pos(Succ(zzz51200)), zzz513, zzz514), Branch(zzz340, zzz341, zzz342, zzz343, zzz344), h) → new_mkVBalBranch3MkVBalBranch215(zzz340, zzz341, zzz342, zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat3(new_primPlusNat1(zzz51200), zzz51200)), zzz51200))), 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
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                    ↳ DependencyGraphProof
                                      ↳ QDP
                                        ↳ Rewriting
                                          ↳ QDP
                                            ↳ Rewriting
                                              ↳ QDP
                                                ↳ Rewriting
                                                  ↳ QDP
                                                    ↳ Rewriting
                                                      ↳ QDP
                                                        ↳ Rewriting
                                                          ↳ QDP
                                                            ↳ Rewriting
                                                              ↳ QDP
                                                                ↳ Rewriting
                                                                  ↳ QDP
                                                                    ↳ Rewriting
                                                                      ↳ QDP
                                                                        ↳ Rewriting
                                                                          ↳ QDP
                                                                            ↳ Rewriting
                                                                              ↳ QDP
                                                                                ↳ Rewriting
                                                                                  ↳ QDP
                                                                                    ↳ Rewriting
                                                                                      ↳ QDP
                                                                                        ↳ Rewriting
                                                                                          ↳ QDP
                                                                                            ↳ Rewriting
                                                                                              ↳ QDP
                                                                                                ↳ Rewriting
                                                                                                  ↳ QDP
                                                                                                    ↳ Rewriting
                                                                                                      ↳ QDP
                                                                                                        ↳ Rewriting
                                                                                                          ↳ QDP
                                                                                                            ↳ UsableRulesProof
                                                                                                              ↳ QDP
                                                                                                                ↳ QReductionProof
                                                                                                                  ↳ QDP
                                                                                                                    ↳ Rewriting
                                                                                                                      ↳ QDP
                                                                                                                        ↳ Rewriting
                                                                                                                          ↳ QDP
                                                                                                                            ↳ DependencyGraphProof
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP

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

new_mkVBalBranch3MkVBalBranch215(zzz340, zzz341, Neg(zzz3420), zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, Zero, h) → new_mkVBalBranch3MkVBalBranch221(zzz340, zzz341, zzz3420, zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, h)
new_mkVBalBranch3MkVBalBranch225(zzz498, zzz499, zzz500, zzz501, zzz502, zzz503, zzz504, zzz505, zzz506, zzz507, Zero, Zero, bg) → new_mkVBalBranch3MkVBalBranch230(zzz498, zzz499, zzz500, zzz501, zzz502, zzz503, zzz504, zzz505, zzz506, zzz507, bg)
new_mkVBalBranch3MkVBalBranch18(zzz340, zzz341, zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, Succ(zzz1480), h) → new_mkVBalBranch3MkVBalBranch115(zzz340, zzz341, Zero, zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, Succ(zzz1480), Succ(zzz51200), h)
new_mkVBalBranch3MkVBalBranch215(zzz340, zzz341, Pos(Succ(Succ(zzz342000))), zzz343, zzz344, zzz510, zzz511, Succ(zzz512000), zzz513, zzz514, zzz31, Succ(Succ(zzz6600)), h) → new_mkVBalBranch3MkVBalBranch216(zzz340, zzz341, Succ(zzz342000), zzz343, zzz344, zzz510, zzz511, zzz512000, zzz513, zzz514, zzz31, Succ(Succ(new_primPlusNat2(zzz6600, zzz512000))), zzz342000, h)
new_mkVBalBranch0(zzz31, Branch(zzz510, zzz511, Neg(Zero), zzz513, zzz514), Branch(zzz340, zzz341, Pos(Succ(zzz34200)), zzz343, zzz344), h) → new_mkVBalBranch0(zzz31, Branch(zzz510, zzz511, Neg(Zero), zzz513, zzz514), zzz343, h)
new_mkVBalBranch3MkVBalBranch223(zzz340, zzz341, Neg(Succ(Succ(Succ(zzz3420000)))), zzz343, zzz344, zzz510, zzz511, Zero, zzz513, zzz514, zzz31, Succ(Succ(zzz6700)), h) → new_mkVBalBranch3MkVBalBranch225(zzz340, zzz341, Succ(Succ(zzz3420000)), zzz343, zzz344, zzz510, zzz511, zzz513, zzz514, zzz31, Succ(zzz3420000), Succ(zzz6700), h)
new_mkVBalBranch3MkVBalBranch220(zzz340, zzz341, zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, h) → new_mkVBalBranch0(zzz31, zzz514, Branch(zzz340, zzz341, Pos(Zero), zzz343, zzz344), h)
new_mkVBalBranch3MkVBalBranch120(zzz2050, zzz2051, zzz2052, zzz2053, zzz2054, zzz2055, zzz2056, zzz2057, zzz2058, zzz2059, zzz2060, Zero, Succ(zzz20620), be) → new_mkVBalBranch0(zzz2060, zzz2059, Branch(zzz2050, zzz2051, Neg(Succ(zzz2052)), zzz2053, zzz2054), be)
new_mkVBalBranch3MkVBalBranch121(zzz473, zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, zzz481, zzz482, Succ(zzz7390), bh) → new_mkVBalBranch3MkVBalBranch115(zzz473, zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, Zero, zzz480, zzz481, zzz482, Succ(zzz7390), Succ(Zero), bh)
new_mkVBalBranch3MkVBalBranch228(zzz340, zzz341, zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, h) → new_mkVBalBranch0(zzz31, Branch(zzz510, zzz511, Neg(Succ(zzz51200)), zzz513, zzz514), zzz343, h)
new_mkVBalBranch0(zzz31, Branch(zzz510, zzz511, Pos(Zero), zzz513, zzz514), Branch(zzz340, zzz341, Pos(Succ(zzz34200)), zzz343, zzz344), h) → new_mkVBalBranch0(zzz31, Branch(zzz510, zzz511, Pos(Zero), zzz513, zzz514), zzz343, h)
new_mkVBalBranch0(zzz31, Branch(zzz510, zzz511, Pos(Succ(zzz51200)), zzz513, zzz514), Branch(zzz340, zzz341, zzz342, zzz343, zzz344), h) → new_mkVBalBranch3MkVBalBranch215(zzz340, zzz341, zzz342, zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat3(new_primPlusNat1(zzz51200), zzz51200)), zzz51200))), h)
new_mkVBalBranch3MkVBalBranch215(zzz340, zzz341, Pos(Succ(Zero)), zzz343, zzz344, zzz510, zzz511, Zero, zzz513, zzz514, zzz31, Zero, h) → new_mkVBalBranch3MkVBalBranch219(zzz340, zzz341, zzz343, zzz344, zzz510, zzz511, Zero, zzz513, zzz514, zzz31, h)
new_mkVBalBranch3MkVBalBranch223(zzz340, zzz341, Neg(Succ(Succ(Zero))), zzz343, zzz344, zzz510, zzz511, Succ(zzz512000), zzz513, zzz514, zzz31, Succ(Succ(zzz6700)), h) → new_mkVBalBranch3MkVBalBranch224(zzz340, zzz341, Succ(Zero), zzz343, zzz344, zzz510, zzz511, zzz512000, zzz513, zzz514, zzz31, Zero, Succ(Succ(new_primPlusNat2(zzz6700, zzz512000))), h)
new_mkVBalBranch3MkVBalBranch223(zzz340, zzz341, Neg(Succ(Succ(Zero))), zzz343, zzz344, zzz510, zzz511, Zero, zzz513, zzz514, zzz31, Succ(Zero), h) → new_mkVBalBranch3MkVBalBranch225(zzz340, zzz341, Succ(Zero), zzz343, zzz344, zzz510, zzz511, zzz513, zzz514, zzz31, Zero, Zero, h)
new_mkVBalBranch3MkVBalBranch224(zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, zzz1125, zzz1126, zzz1127, zzz1128, zzz1129, Succ(zzz11300), Succ(zzz11310), bd) → new_mkVBalBranch3MkVBalBranch224(zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, zzz1125, zzz1126, zzz1127, zzz1128, zzz1129, zzz11300, zzz11310, bd)
new_mkVBalBranch3MkVBalBranch217(zzz473, zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, zzz481, zzz482, Zero, Succ(zzz4840), bh) → new_mkVBalBranch0(zzz482, Branch(zzz478, zzz479, Pos(Succ(Zero)), zzz480, zzz481), zzz476, bh)
new_mkVBalBranch3MkVBalBranch215(zzz340, zzz341, Pos(Succ(Succ(zzz342000))), zzz343, zzz344, zzz510, zzz511, Succ(zzz512000), zzz513, zzz514, zzz31, Zero, h) → new_mkVBalBranch3MkVBalBranch216(zzz340, zzz341, Succ(zzz342000), zzz343, zzz344, zzz510, zzz511, zzz512000, zzz513, zzz514, zzz31, zzz512000, zzz342000, h)
new_mkVBalBranch3MkVBalBranch110(zzz461, zzz462, zzz463, zzz464, zzz465, zzz466, zzz467, zzz468, zzz469, zzz470, zzz471, Succ(zzz5800), bb) → new_mkVBalBranch3MkVBalBranch115(zzz461, zzz462, zzz463, zzz464, zzz465, zzz466, zzz467, Succ(zzz468), zzz469, zzz470, zzz471, Succ(zzz5800), Succ(Succ(zzz468)), bb)
new_mkVBalBranch3MkVBalBranch223(zzz340, zzz341, Neg(Succ(Zero)), zzz343, zzz344, zzz510, zzz511, Zero, zzz513, zzz514, zzz31, Zero, h) → new_mkVBalBranch3MkVBalBranch118(zzz340, zzz341, Zero, zzz343, zzz344, zzz510, zzz511, zzz513, zzz514, zzz31, new_primPlusNat2(new_primMulNat0(Zero), Succ(Zero)), h)
new_mkVBalBranch3MkVBalBranch227(zzz486, zzz487, zzz488, zzz489, zzz490, zzz491, zzz492, zzz493, zzz494, zzz495, zzz496, bf) → new_mkVBalBranch0(zzz496, Branch(zzz491, zzz492, Neg(Succ(Succ(zzz493))), zzz494, zzz495), zzz489, bf)
new_mkVBalBranch3MkVBalBranch215(zzz340, zzz341, Pos(Zero), zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, Succ(zzz660), h) → new_mkVBalBranch0(zzz31, zzz514, Branch(zzz340, zzz341, Pos(Zero), zzz343, zzz344), h)
new_mkVBalBranch0(zzz31, Branch(zzz510, zzz511, Pos(Zero), zzz513, zzz514), Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), h) → new_mkVBalBranch3MkVBalBranch116(zzz340, zzz341, zzz34200, zzz343, zzz344, zzz510, zzz511, zzz513, zzz514, zzz31, new_primPlusNat2(new_primMulNat0(zzz34200), Succ(zzz34200)), h)
new_mkVBalBranch3MkVBalBranch217(zzz473, zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, zzz481, zzz482, Succ(zzz4830), Zero, bh) → new_mkVBalBranch3MkVBalBranch121(zzz473, zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, zzz481, zzz482, new_primPlusNat2(new_primMulNat0(zzz475), Succ(zzz475)), bh)
new_mkVBalBranch3MkVBalBranch223(zzz340, zzz341, Neg(Zero), zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, Succ(zzz670), h) → new_mkVBalBranch0(zzz31, Branch(zzz510, zzz511, Neg(Succ(zzz51200)), zzz513, zzz514), zzz343, h)
new_mkVBalBranch3MkVBalBranch216(zzz1105, zzz1106, zzz1107, zzz1108, zzz1109, zzz1110, zzz1111, zzz1112, zzz1113, zzz1114, zzz1115, Zero, Succ(zzz11170), ba) → new_mkVBalBranch0(zzz1115, Branch(zzz1110, zzz1111, Pos(Succ(Succ(zzz1112))), zzz1113, zzz1114), zzz1108, ba)
new_mkVBalBranch3MkVBalBranch115(zzz1986, zzz1987, zzz1988, zzz1989, zzz1990, zzz1991, zzz1992, zzz1993, zzz1994, zzz1995, zzz1996, Zero, Succ(zzz19980), bc) → new_mkVBalBranch0(zzz1996, zzz1995, Branch(zzz1986, zzz1987, Pos(Succ(zzz1988)), zzz1989, zzz1990), bc)
new_mkVBalBranch0(zzz31, Branch(zzz510, zzz511, Neg(Zero), zzz513, zzz514), Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), h) → new_mkVBalBranch3MkVBalBranch117(zzz340, zzz341, zzz34200, zzz343, zzz344, zzz510, zzz511, zzz513, zzz514, zzz31, new_primPlusNat2(new_primMulNat0(zzz34200), Succ(zzz34200)), h)
new_mkVBalBranch3MkVBalBranch223(zzz340, zzz341, Neg(Zero), zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, Zero, h) → new_mkVBalBranch3MkVBalBranch228(zzz340, zzz341, zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, h)
new_mkVBalBranch3MkVBalBranch122(zzz340, zzz341, zzz34200, zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, h) → new_mkVBalBranch0(zzz31, zzz514, Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), h)
new_mkVBalBranch3MkVBalBranch217(zzz473, zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, zzz481, zzz482, Succ(zzz4830), Succ(zzz4840), bh) → new_mkVBalBranch3MkVBalBranch217(zzz473, zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, zzz481, zzz482, zzz4830, zzz4840, bh)
new_mkVBalBranch3MkVBalBranch116(zzz340, zzz341, zzz34200, zzz343, zzz344, zzz510, zzz511, zzz513, zzz514, zzz31, Succ(zzz1200), h) → new_mkVBalBranch0(zzz31, zzz514, Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), h)
new_mkVBalBranch3MkVBalBranch110(zzz461, zzz462, zzz463, zzz464, zzz465, zzz466, zzz467, zzz468, zzz469, zzz470, zzz471, Zero, bb) → new_mkVBalBranch3MkVBalBranch115(zzz461, zzz462, zzz463, zzz464, zzz465, zzz466, zzz467, Succ(zzz468), zzz469, zzz470, zzz471, Zero, Succ(Succ(zzz468)), bb)
new_mkVBalBranch3MkVBalBranch225(zzz498, zzz499, zzz500, zzz501, zzz502, zzz503, zzz504, zzz505, zzz506, zzz507, Zero, Succ(zzz5090), bg) → new_mkVBalBranch0(zzz507, Branch(zzz503, zzz504, Neg(Succ(Zero)), zzz505, zzz506), zzz501, bg)
new_mkVBalBranch3MkVBalBranch222(zzz461, zzz462, zzz463, zzz464, zzz465, zzz466, zzz467, zzz468, zzz469, zzz470, zzz471, bb) → new_mkVBalBranch3MkVBalBranch110(zzz461, zzz462, zzz463, zzz464, zzz465, zzz466, zzz467, zzz468, zzz469, zzz470, zzz471, new_primPlusNat2(new_primPlusNat3(Succ(new_primPlusNat3(new_primPlusNat1(zzz463), zzz463)), Succ(zzz463)), Succ(zzz463)), bb)
new_mkVBalBranch3MkVBalBranch223(zzz340, zzz341, Neg(Succ(Succ(Succ(zzz3420000)))), zzz343, zzz344, zzz510, zzz511, Zero, zzz513, zzz514, zzz31, Succ(Zero), h) → new_mkVBalBranch3MkVBalBranch225(zzz340, zzz341, Succ(Succ(zzz3420000)), zzz343, zzz344, zzz510, zzz511, zzz513, zzz514, zzz31, Succ(zzz3420000), Zero, h)
new_mkVBalBranch3MkVBalBranch121(zzz473, zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, zzz481, zzz482, Zero, bh) → new_mkVBalBranch3MkVBalBranch115(zzz473, zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, Zero, zzz480, zzz481, zzz482, Zero, Succ(Zero), bh)
new_mkVBalBranch3MkVBalBranch215(zzz340, zzz341, Pos(Succ(Zero)), zzz343, zzz344, zzz510, zzz511, Succ(zzz512000), zzz513, zzz514, zzz31, Zero, h) → new_mkVBalBranch3MkVBalBranch218(zzz340, zzz341, Zero, zzz343, zzz344, zzz510, zzz511, zzz512000, zzz513, zzz514, zzz31, h)
new_mkVBalBranch3MkVBalBranch225(zzz498, zzz499, zzz500, zzz501, zzz502, zzz503, zzz504, zzz505, zzz506, zzz507, Succ(zzz5080), Zero, bg) → new_mkVBalBranch3MkVBalBranch118(zzz498, zzz499, zzz500, zzz501, zzz502, zzz503, zzz504, zzz505, zzz506, zzz507, new_primPlusNat2(new_primMulNat0(zzz500), Succ(zzz500)), bg)
new_mkVBalBranch3MkVBalBranch223(zzz340, zzz341, Neg(Succ(Zero)), zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, Succ(zzz670), h) → new_mkVBalBranch0(zzz31, Branch(zzz510, zzz511, Neg(Succ(zzz51200)), zzz513, zzz514), zzz343, h)
new_mkVBalBranch3MkVBalBranch215(zzz340, zzz341, Pos(Succ(Zero)), zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, Succ(zzz660), h) → new_mkVBalBranch3MkVBalBranch18(zzz340, zzz341, zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, new_primPlusNat2(new_primMulNat0(Zero), Succ(Zero)), h)
new_mkVBalBranch3MkVBalBranch229(zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, zzz1125, zzz1126, zzz1127, zzz1128, zzz1129, bd) → new_mkVBalBranch3MkVBalBranch119(zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, zzz1125, zzz1126, zzz1127, zzz1128, zzz1129, new_primPlusNat2(new_primMulNat0(zzz1121), Succ(zzz1121)), bd)
new_mkVBalBranch3MkVBalBranch219(zzz340, zzz341, zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, h) → new_mkVBalBranch3MkVBalBranch18(zzz340, zzz341, zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, new_primPlusNat2(new_primMulNat0(Zero), Succ(Zero)), h)
new_mkVBalBranch3MkVBalBranch233(zzz473, zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, zzz481, zzz482, bh) → new_mkVBalBranch3MkVBalBranch121(zzz473, zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, zzz481, zzz482, new_primPlusNat2(new_primMulNat0(zzz475), Succ(zzz475)), bh)
new_mkVBalBranch3MkVBalBranch223(zzz340, zzz341, Neg(Succ(Zero)), zzz343, zzz344, zzz510, zzz511, Succ(zzz512000), zzz513, zzz514, zzz31, Zero, h) → new_mkVBalBranch3MkVBalBranch227(zzz340, zzz341, Zero, zzz343, zzz344, zzz510, zzz511, zzz512000, zzz513, zzz514, zzz31, h)
new_mkVBalBranch3MkVBalBranch215(zzz340, zzz341, Pos(Succ(Succ(zzz342000))), zzz343, zzz344, zzz510, zzz511, Zero, zzz513, zzz514, zzz31, Succ(Succ(zzz6600)), h) → new_mkVBalBranch3MkVBalBranch217(zzz340, zzz341, Succ(zzz342000), zzz343, zzz344, zzz510, zzz511, zzz513, zzz514, zzz31, Succ(zzz6600), zzz342000, h)
new_mkVBalBranch3MkVBalBranch223(zzz340, zzz341, Neg(Succ(Succ(zzz342000))), zzz343, zzz344, zzz510, zzz511, Succ(zzz512000), zzz513, zzz514, zzz31, Zero, h) → new_mkVBalBranch3MkVBalBranch224(zzz340, zzz341, Succ(zzz342000), zzz343, zzz344, zzz510, zzz511, zzz512000, zzz513, zzz514, zzz31, zzz342000, zzz512000, h)
new_mkVBalBranch3MkVBalBranch226(zzz340, zzz341, zzz3420, zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, h) → new_mkVBalBranch0(zzz31, Branch(zzz510, zzz511, Neg(Succ(zzz51200)), zzz513, zzz514), zzz343, h)
new_mkVBalBranch3MkVBalBranch218(zzz461, zzz462, zzz463, zzz464, zzz465, zzz466, zzz467, zzz468, zzz469, zzz470, zzz471, bb) → new_mkVBalBranch3MkVBalBranch110(zzz461, zzz462, zzz463, zzz464, zzz465, zzz466, zzz467, zzz468, zzz469, zzz470, zzz471, new_primPlusNat2(new_primMulNat0(zzz463), Succ(zzz463)), bb)
new_mkVBalBranch3MkVBalBranch117(zzz340, zzz341, zzz34200, zzz343, zzz344, zzz510, zzz511, zzz513, zzz514, zzz31, Succ(zzz1240), h) → new_mkVBalBranch0(zzz31, zzz514, Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), h)
new_mkVBalBranch3MkVBalBranch120(zzz2050, zzz2051, zzz2052, zzz2053, zzz2054, zzz2055, zzz2056, zzz2057, zzz2058, zzz2059, zzz2060, Succ(zzz20610), Succ(zzz20620), be) → new_mkVBalBranch3MkVBalBranch120(zzz2050, zzz2051, zzz2052, zzz2053, zzz2054, zzz2055, zzz2056, zzz2057, zzz2058, zzz2059, zzz2060, zzz20610, zzz20620, be)
new_mkVBalBranch3MkVBalBranch217(zzz473, zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, zzz481, zzz482, Zero, Zero, bh) → new_mkVBalBranch3MkVBalBranch233(zzz473, zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, zzz481, zzz482, bh)
new_mkVBalBranch3MkVBalBranch221(zzz340, zzz341, Succ(zzz34200), zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, h) → new_mkVBalBranch3MkVBalBranch19(zzz340, zzz341, zzz34200, zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, new_primPlusNat2(new_primPlusNat3(Succ(new_primPlusNat3(new_primPlusNat1(zzz34200), zzz34200)), Succ(zzz34200)), Succ(zzz34200)), h)
new_mkVBalBranch0(zzz31, Branch(zzz510, zzz511, Neg(Succ(zzz51200)), zzz513, zzz514), Branch(zzz340, zzz341, zzz342, zzz343, zzz344), h) → new_mkVBalBranch3MkVBalBranch223(zzz340, zzz341, zzz342, zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, new_primPlusNat3(Succ(new_primPlusNat3(new_primPlusNat1(zzz51200), zzz51200)), Succ(zzz51200)), h)
new_mkVBalBranch3MkVBalBranch216(zzz1105, zzz1106, zzz1107, zzz1108, zzz1109, zzz1110, zzz1111, zzz1112, zzz1113, zzz1114, zzz1115, Succ(zzz11160), Succ(zzz11170), ba) → new_mkVBalBranch3MkVBalBranch216(zzz1105, zzz1106, zzz1107, zzz1108, zzz1109, zzz1110, zzz1111, zzz1112, zzz1113, zzz1114, zzz1115, zzz11160, zzz11170, ba)
new_mkVBalBranch3MkVBalBranch223(zzz340, zzz341, Pos(zzz3420), zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, Succ(zzz670), h) → new_mkVBalBranch0(zzz31, Branch(zzz510, zzz511, Neg(Succ(zzz51200)), zzz513, zzz514), zzz343, h)
new_mkVBalBranch3MkVBalBranch223(zzz340, zzz341, Neg(Succ(Succ(Succ(zzz3420000)))), zzz343, zzz344, zzz510, zzz511, Succ(zzz512000), zzz513, zzz514, zzz31, Succ(Zero), h) → new_mkVBalBranch3MkVBalBranch224(zzz340, zzz341, Succ(Succ(zzz3420000)), zzz343, zzz344, zzz510, zzz511, zzz512000, zzz513, zzz514, zzz31, Succ(zzz3420000), Succ(zzz512000), h)
new_mkVBalBranch3MkVBalBranch19(zzz340, zzz341, zzz34200, zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, Zero, h) → new_mkVBalBranch3MkVBalBranch122(zzz340, zzz341, zzz34200, zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, h)
new_mkVBalBranch3MkVBalBranch215(zzz340, zzz341, Pos(Succ(Succ(zzz342000))), zzz343, zzz344, zzz510, zzz511, Zero, zzz513, zzz514, zzz31, Zero, h) → new_mkVBalBranch0(zzz31, Branch(zzz510, zzz511, Pos(Succ(Zero)), zzz513, zzz514), zzz343, h)
new_mkVBalBranch3MkVBalBranch225(zzz498, zzz499, zzz500, zzz501, zzz502, zzz503, zzz504, zzz505, zzz506, zzz507, Succ(zzz5080), Succ(zzz5090), bg) → new_mkVBalBranch3MkVBalBranch225(zzz498, zzz499, zzz500, zzz501, zzz502, zzz503, zzz504, zzz505, zzz506, zzz507, zzz5080, zzz5090, bg)
new_mkVBalBranch3MkVBalBranch19(zzz340, zzz341, zzz34200, zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, Succ(zzz1410), h) → new_mkVBalBranch0(zzz31, zzz514, Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), h)
new_mkVBalBranch3MkVBalBranch224(zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, zzz1125, zzz1126, zzz1127, zzz1128, zzz1129, Succ(zzz11300), Zero, bd) → new_mkVBalBranch3MkVBalBranch119(zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, zzz1125, zzz1126, zzz1127, zzz1128, zzz1129, new_primPlusNat2(new_primMulNat0(zzz1121), Succ(zzz1121)), bd)
new_mkVBalBranch3MkVBalBranch223(zzz340, zzz341, Pos(zzz3420), zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, Zero, h) → new_mkVBalBranch3MkVBalBranch226(zzz340, zzz341, zzz3420, zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, h)
new_mkVBalBranch3MkVBalBranch223(zzz340, zzz341, Neg(Succ(Succ(Zero))), zzz343, zzz344, zzz510, zzz511, Succ(zzz512000), zzz513, zzz514, zzz31, Succ(Zero), h) → new_mkVBalBranch3MkVBalBranch224(zzz340, zzz341, Succ(Zero), zzz343, zzz344, zzz510, zzz511, zzz512000, zzz513, zzz514, zzz31, Zero, Succ(zzz512000), h)
new_mkVBalBranch3MkVBalBranch224(zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, zzz1125, zzz1126, zzz1127, zzz1128, zzz1129, Zero, Succ(zzz11310), bd) → new_mkVBalBranch3MkVBalBranch227(zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, zzz1125, zzz1126, zzz1127, zzz1128, zzz1129, bd)
new_mkVBalBranch3MkVBalBranch224(zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, zzz1125, zzz1126, zzz1127, zzz1128, zzz1129, Zero, Zero, bd) → new_mkVBalBranch3MkVBalBranch229(zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, zzz1125, zzz1126, zzz1127, zzz1128, zzz1129, bd)
new_mkVBalBranch3MkVBalBranch223(zzz340, zzz341, Neg(Succ(Succ(zzz342000))), zzz343, zzz344, zzz510, zzz511, Zero, zzz513, zzz514, zzz31, Zero, h) → new_mkVBalBranch3MkVBalBranch118(zzz340, zzz341, Succ(zzz342000), zzz343, zzz344, zzz510, zzz511, zzz513, zzz514, zzz31, new_primPlusNat2(new_primMulNat0(Succ(zzz342000)), Succ(Succ(zzz342000))), h)
new_mkVBalBranch3MkVBalBranch230(zzz498, zzz499, zzz500, zzz501, zzz502, zzz503, zzz504, zzz505, zzz506, zzz507, bg) → new_mkVBalBranch3MkVBalBranch118(zzz498, zzz499, zzz500, zzz501, zzz502, zzz503, zzz504, zzz505, zzz506, zzz507, new_primPlusNat2(new_primMulNat0(zzz500), Succ(zzz500)), bg)
new_mkVBalBranch3MkVBalBranch223(zzz340, zzz341, Neg(Succ(Succ(Zero))), zzz343, zzz344, zzz510, zzz511, Zero, zzz513, zzz514, zzz31, Succ(Succ(zzz6700)), h) → new_mkVBalBranch3MkVBalBranch225(zzz340, zzz341, Succ(Zero), zzz343, zzz344, zzz510, zzz511, zzz513, zzz514, zzz31, Zero, Succ(zzz6700), h)
new_mkVBalBranch3MkVBalBranch223(zzz340, zzz341, Neg(Succ(Succ(Succ(zzz3420000)))), zzz343, zzz344, zzz510, zzz511, Succ(zzz512000), zzz513, zzz514, zzz31, Succ(Succ(zzz6700)), h) → new_mkVBalBranch3MkVBalBranch224(zzz340, zzz341, Succ(Succ(zzz3420000)), zzz343, zzz344, zzz510, zzz511, zzz512000, zzz513, zzz514, zzz31, Succ(zzz3420000), Succ(Succ(new_primPlusNat2(zzz6700, zzz512000))), h)
new_mkVBalBranch3MkVBalBranch115(zzz1986, zzz1987, zzz1988, zzz1989, zzz1990, zzz1991, zzz1992, zzz1993, zzz1994, zzz1995, zzz1996, Succ(zzz19970), Succ(zzz19980), bc) → new_mkVBalBranch3MkVBalBranch115(zzz1986, zzz1987, zzz1988, zzz1989, zzz1990, zzz1991, zzz1992, zzz1993, zzz1994, zzz1995, zzz1996, zzz19970, zzz19980, bc)
new_mkVBalBranch3MkVBalBranch215(zzz340, zzz341, Pos(Zero), zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, Zero, h) → new_mkVBalBranch3MkVBalBranch220(zzz340, zzz341, zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, h)
new_mkVBalBranch3MkVBalBranch215(zzz340, zzz341, Neg(Zero), zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, Succ(zzz660), h) → new_mkVBalBranch0(zzz31, zzz514, Branch(zzz340, zzz341, Neg(Zero), zzz343, zzz344), h)
new_mkVBalBranch3MkVBalBranch118(zzz498, zzz499, zzz500, zzz501, zzz502, zzz503, zzz504, zzz505, zzz506, zzz507, Succ(zzz8040), bg) → new_mkVBalBranch3MkVBalBranch120(zzz498, zzz499, zzz500, zzz501, zzz502, zzz503, zzz504, Zero, zzz505, zzz506, zzz507, Succ(Zero), Succ(zzz8040), bg)
new_mkVBalBranch3MkVBalBranch216(zzz1105, zzz1106, zzz1107, zzz1108, zzz1109, zzz1110, zzz1111, zzz1112, zzz1113, zzz1114, zzz1115, Succ(zzz11160), Zero, ba) → new_mkVBalBranch3MkVBalBranch218(zzz1105, zzz1106, zzz1107, zzz1108, zzz1109, zzz1110, zzz1111, zzz1112, zzz1113, zzz1114, zzz1115, ba)
new_mkVBalBranch3MkVBalBranch221(zzz340, zzz341, Zero, zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, h) → new_mkVBalBranch0(zzz31, zzz514, Branch(zzz340, zzz341, Neg(Zero), zzz343, zzz344), h)
new_mkVBalBranch3MkVBalBranch215(zzz340, zzz341, Pos(Succ(Succ(zzz342000))), zzz343, zzz344, zzz510, zzz511, Succ(zzz512000), zzz513, zzz514, zzz31, Succ(Zero), h) → new_mkVBalBranch3MkVBalBranch216(zzz340, zzz341, Succ(zzz342000), zzz343, zzz344, zzz510, zzz511, zzz512000, zzz513, zzz514, zzz31, Succ(zzz512000), zzz342000, h)
new_mkVBalBranch3MkVBalBranch215(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, Succ(zzz660), h) → new_mkVBalBranch3MkVBalBranch19(zzz340, zzz341, zzz34200, zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, new_primPlusNat2(new_primMulNat0(zzz34200), Succ(zzz34200)), h)
new_mkVBalBranch3MkVBalBranch216(zzz1105, zzz1106, zzz1107, zzz1108, zzz1109, zzz1110, zzz1111, zzz1112, zzz1113, zzz1114, zzz1115, Zero, Zero, ba) → new_mkVBalBranch3MkVBalBranch222(zzz1105, zzz1106, zzz1107, zzz1108, zzz1109, zzz1110, zzz1111, zzz1112, zzz1113, zzz1114, zzz1115, ba)
new_mkVBalBranch3MkVBalBranch215(zzz340, zzz341, Pos(Succ(Succ(zzz342000))), zzz343, zzz344, zzz510, zzz511, Zero, zzz513, zzz514, zzz31, Succ(Zero), h) → new_mkVBalBranch3MkVBalBranch217(zzz340, zzz341, Succ(zzz342000), zzz343, zzz344, zzz510, zzz511, zzz513, zzz514, zzz31, Zero, zzz342000, h)
new_mkVBalBranch3MkVBalBranch18(zzz340, zzz341, zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, Zero, h) → new_mkVBalBranch3MkVBalBranch115(zzz340, zzz341, Zero, zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, Zero, Succ(zzz51200), h)
new_mkVBalBranch3MkVBalBranch119(zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, zzz1125, zzz1126, zzz1127, zzz1128, zzz1129, Succ(zzz12130), bd) → new_mkVBalBranch3MkVBalBranch120(zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, zzz1125, Succ(zzz1126), zzz1127, zzz1128, zzz1129, Succ(Succ(zzz1126)), Succ(zzz12130), bd)

The TRS R consists of the following rules:

new_primMulNat0(zzz6200) → new_primPlusNat3(Succ(new_primPlusNat3(new_primPlusNat1(zzz6200), zzz6200)), Succ(zzz6200))
new_primPlusNat2(Succ(zzz900), Succ(zzz9100)) → Succ(Succ(new_primPlusNat2(zzz900, zzz9100)))
new_primPlusNat2(Zero, Succ(zzz9100)) → Succ(zzz9100)
new_primPlusNat2(Zero, Zero) → Zero
new_primPlusNat2(Succ(zzz900), Zero) → Succ(zzz900)
new_primPlusNat1(Zero) → Zero
new_primPlusNat1(Succ(zzz62000)) → Succ(Succ(new_primPlusNat1(zzz62000)))
new_primPlusNat3(zzz90, Succ(zzz910)) → Succ(Succ(new_primPlusNat2(zzz90, zzz910)))
new_primPlusNat3(zzz90, Zero) → Succ(zzz90)

The set Q consists of the following terms:

new_primPlusNat2(Zero, Succ(x0))
new_primMulNat0(x0)
new_primPlusNat3(x0, Succ(x1))
new_primPlusNat2(Succ(x0), Succ(x1))
new_primPlusNat3(x0, Zero)
new_primPlusNat1(Zero)
new_primPlusNat2(Zero, Zero)
new_primPlusNat1(Succ(x0))
new_primPlusNat2(Succ(x0), Zero)

We have to consider all minimal (P,Q,R)-chains.
The approximation of the Dependency Graph [15,17,22] contains 1 SCC with 12 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
                                    ↳ DependencyGraphProof
                                      ↳ QDP
                                        ↳ Rewriting
                                          ↳ QDP
                                            ↳ Rewriting
                                              ↳ QDP
                                                ↳ Rewriting
                                                  ↳ QDP
                                                    ↳ Rewriting
                                                      ↳ QDP
                                                        ↳ Rewriting
                                                          ↳ QDP
                                                            ↳ Rewriting
                                                              ↳ QDP
                                                                ↳ Rewriting
                                                                  ↳ QDP
                                                                    ↳ Rewriting
                                                                      ↳ QDP
                                                                        ↳ Rewriting
                                                                          ↳ QDP
                                                                            ↳ Rewriting
                                                                              ↳ QDP
                                                                                ↳ Rewriting
                                                                                  ↳ QDP
                                                                                    ↳ Rewriting
                                                                                      ↳ QDP
                                                                                        ↳ Rewriting
                                                                                          ↳ QDP
                                                                                            ↳ Rewriting
                                                                                              ↳ QDP
                                                                                                ↳ Rewriting
                                                                                                  ↳ QDP
                                                                                                    ↳ Rewriting
                                                                                                      ↳ QDP
                                                                                                        ↳ Rewriting
                                                                                                          ↳ QDP
                                                                                                            ↳ UsableRulesProof
                                                                                                              ↳ QDP
                                                                                                                ↳ QReductionProof
                                                                                                                  ↳ QDP
                                                                                                                    ↳ Rewriting
                                                                                                                      ↳ QDP
                                                                                                                        ↳ Rewriting
                                                                                                                          ↳ QDP
                                                                                                                            ↳ DependencyGraphProof
                                                                                                                              ↳ QDP
                                                                                                                                ↳ Rewriting
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP

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

new_mkVBalBranch3MkVBalBranch225(zzz498, zzz499, zzz500, zzz501, zzz502, zzz503, zzz504, zzz505, zzz506, zzz507, Zero, Zero, bg) → new_mkVBalBranch3MkVBalBranch230(zzz498, zzz499, zzz500, zzz501, zzz502, zzz503, zzz504, zzz505, zzz506, zzz507, bg)
new_mkVBalBranch3MkVBalBranch18(zzz340, zzz341, zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, Succ(zzz1480), h) → new_mkVBalBranch3MkVBalBranch115(zzz340, zzz341, Zero, zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, Succ(zzz1480), Succ(zzz51200), h)
new_mkVBalBranch3MkVBalBranch215(zzz340, zzz341, Pos(Succ(Succ(zzz342000))), zzz343, zzz344, zzz510, zzz511, Succ(zzz512000), zzz513, zzz514, zzz31, Succ(Succ(zzz6600)), h) → new_mkVBalBranch3MkVBalBranch216(zzz340, zzz341, Succ(zzz342000), zzz343, zzz344, zzz510, zzz511, zzz512000, zzz513, zzz514, zzz31, Succ(Succ(new_primPlusNat2(zzz6600, zzz512000))), zzz342000, h)
new_mkVBalBranch0(zzz31, Branch(zzz510, zzz511, Neg(Zero), zzz513, zzz514), Branch(zzz340, zzz341, Pos(Succ(zzz34200)), zzz343, zzz344), h) → new_mkVBalBranch0(zzz31, Branch(zzz510, zzz511, Neg(Zero), zzz513, zzz514), zzz343, h)
new_mkVBalBranch3MkVBalBranch223(zzz340, zzz341, Neg(Succ(Succ(Succ(zzz3420000)))), zzz343, zzz344, zzz510, zzz511, Zero, zzz513, zzz514, zzz31, Succ(Succ(zzz6700)), h) → new_mkVBalBranch3MkVBalBranch225(zzz340, zzz341, Succ(Succ(zzz3420000)), zzz343, zzz344, zzz510, zzz511, zzz513, zzz514, zzz31, Succ(zzz3420000), Succ(zzz6700), h)
new_mkVBalBranch3MkVBalBranch120(zzz2050, zzz2051, zzz2052, zzz2053, zzz2054, zzz2055, zzz2056, zzz2057, zzz2058, zzz2059, zzz2060, Zero, Succ(zzz20620), be) → new_mkVBalBranch0(zzz2060, zzz2059, Branch(zzz2050, zzz2051, Neg(Succ(zzz2052)), zzz2053, zzz2054), be)
new_mkVBalBranch3MkVBalBranch121(zzz473, zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, zzz481, zzz482, Succ(zzz7390), bh) → new_mkVBalBranch3MkVBalBranch115(zzz473, zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, Zero, zzz480, zzz481, zzz482, Succ(zzz7390), Succ(Zero), bh)
new_mkVBalBranch0(zzz31, Branch(zzz510, zzz511, Pos(Zero), zzz513, zzz514), Branch(zzz340, zzz341, Pos(Succ(zzz34200)), zzz343, zzz344), h) → new_mkVBalBranch0(zzz31, Branch(zzz510, zzz511, Pos(Zero), zzz513, zzz514), zzz343, h)
new_mkVBalBranch3MkVBalBranch228(zzz340, zzz341, zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, h) → new_mkVBalBranch0(zzz31, Branch(zzz510, zzz511, Neg(Succ(zzz51200)), zzz513, zzz514), zzz343, h)
new_mkVBalBranch0(zzz31, Branch(zzz510, zzz511, Pos(Succ(zzz51200)), zzz513, zzz514), Branch(zzz340, zzz341, zzz342, zzz343, zzz344), h) → new_mkVBalBranch3MkVBalBranch215(zzz340, zzz341, zzz342, zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat3(new_primPlusNat1(zzz51200), zzz51200)), zzz51200))), h)
new_mkVBalBranch3MkVBalBranch223(zzz340, zzz341, Neg(Succ(Succ(Zero))), zzz343, zzz344, zzz510, zzz511, Succ(zzz512000), zzz513, zzz514, zzz31, Succ(Succ(zzz6700)), h) → new_mkVBalBranch3MkVBalBranch224(zzz340, zzz341, Succ(Zero), zzz343, zzz344, zzz510, zzz511, zzz512000, zzz513, zzz514, zzz31, Zero, Succ(Succ(new_primPlusNat2(zzz6700, zzz512000))), h)
new_mkVBalBranch3MkVBalBranch223(zzz340, zzz341, Neg(Succ(Succ(Zero))), zzz343, zzz344, zzz510, zzz511, Zero, zzz513, zzz514, zzz31, Succ(Zero), h) → new_mkVBalBranch3MkVBalBranch225(zzz340, zzz341, Succ(Zero), zzz343, zzz344, zzz510, zzz511, zzz513, zzz514, zzz31, Zero, Zero, h)
new_mkVBalBranch3MkVBalBranch224(zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, zzz1125, zzz1126, zzz1127, zzz1128, zzz1129, Succ(zzz11300), Succ(zzz11310), bd) → new_mkVBalBranch3MkVBalBranch224(zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, zzz1125, zzz1126, zzz1127, zzz1128, zzz1129, zzz11300, zzz11310, bd)
new_mkVBalBranch3MkVBalBranch217(zzz473, zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, zzz481, zzz482, Zero, Succ(zzz4840), bh) → new_mkVBalBranch0(zzz482, Branch(zzz478, zzz479, Pos(Succ(Zero)), zzz480, zzz481), zzz476, bh)
new_mkVBalBranch3MkVBalBranch110(zzz461, zzz462, zzz463, zzz464, zzz465, zzz466, zzz467, zzz468, zzz469, zzz470, zzz471, Succ(zzz5800), bb) → new_mkVBalBranch3MkVBalBranch115(zzz461, zzz462, zzz463, zzz464, zzz465, zzz466, zzz467, Succ(zzz468), zzz469, zzz470, zzz471, Succ(zzz5800), Succ(Succ(zzz468)), bb)
new_mkVBalBranch3MkVBalBranch223(zzz340, zzz341, Neg(Succ(Zero)), zzz343, zzz344, zzz510, zzz511, Zero, zzz513, zzz514, zzz31, Zero, h) → new_mkVBalBranch3MkVBalBranch118(zzz340, zzz341, Zero, zzz343, zzz344, zzz510, zzz511, zzz513, zzz514, zzz31, new_primPlusNat2(new_primMulNat0(Zero), Succ(Zero)), h)
new_mkVBalBranch3MkVBalBranch227(zzz486, zzz487, zzz488, zzz489, zzz490, zzz491, zzz492, zzz493, zzz494, zzz495, zzz496, bf) → new_mkVBalBranch0(zzz496, Branch(zzz491, zzz492, Neg(Succ(Succ(zzz493))), zzz494, zzz495), zzz489, bf)
new_mkVBalBranch3MkVBalBranch215(zzz340, zzz341, Pos(Zero), zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, Succ(zzz660), h) → new_mkVBalBranch0(zzz31, zzz514, Branch(zzz340, zzz341, Pos(Zero), zzz343, zzz344), h)
new_mkVBalBranch0(zzz31, Branch(zzz510, zzz511, Pos(Zero), zzz513, zzz514), Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), h) → new_mkVBalBranch3MkVBalBranch116(zzz340, zzz341, zzz34200, zzz343, zzz344, zzz510, zzz511, zzz513, zzz514, zzz31, new_primPlusNat2(new_primMulNat0(zzz34200), Succ(zzz34200)), h)
new_mkVBalBranch3MkVBalBranch217(zzz473, zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, zzz481, zzz482, Succ(zzz4830), Zero, bh) → new_mkVBalBranch3MkVBalBranch121(zzz473, zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, zzz481, zzz482, new_primPlusNat2(new_primMulNat0(zzz475), Succ(zzz475)), bh)
new_mkVBalBranch3MkVBalBranch223(zzz340, zzz341, Neg(Zero), zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, Succ(zzz670), h) → new_mkVBalBranch0(zzz31, Branch(zzz510, zzz511, Neg(Succ(zzz51200)), zzz513, zzz514), zzz343, h)
new_mkVBalBranch3MkVBalBranch216(zzz1105, zzz1106, zzz1107, zzz1108, zzz1109, zzz1110, zzz1111, zzz1112, zzz1113, zzz1114, zzz1115, Zero, Succ(zzz11170), ba) → new_mkVBalBranch0(zzz1115, Branch(zzz1110, zzz1111, Pos(Succ(Succ(zzz1112))), zzz1113, zzz1114), zzz1108, ba)
new_mkVBalBranch3MkVBalBranch115(zzz1986, zzz1987, zzz1988, zzz1989, zzz1990, zzz1991, zzz1992, zzz1993, zzz1994, zzz1995, zzz1996, Zero, Succ(zzz19980), bc) → new_mkVBalBranch0(zzz1996, zzz1995, Branch(zzz1986, zzz1987, Pos(Succ(zzz1988)), zzz1989, zzz1990), bc)
new_mkVBalBranch0(zzz31, Branch(zzz510, zzz511, Neg(Zero), zzz513, zzz514), Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), h) → new_mkVBalBranch3MkVBalBranch117(zzz340, zzz341, zzz34200, zzz343, zzz344, zzz510, zzz511, zzz513, zzz514, zzz31, new_primPlusNat2(new_primMulNat0(zzz34200), Succ(zzz34200)), h)
new_mkVBalBranch3MkVBalBranch223(zzz340, zzz341, Neg(Zero), zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, Zero, h) → new_mkVBalBranch3MkVBalBranch228(zzz340, zzz341, zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, h)
new_mkVBalBranch3MkVBalBranch122(zzz340, zzz341, zzz34200, zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, h) → new_mkVBalBranch0(zzz31, zzz514, Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), h)
new_mkVBalBranch3MkVBalBranch217(zzz473, zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, zzz481, zzz482, Succ(zzz4830), Succ(zzz4840), bh) → new_mkVBalBranch3MkVBalBranch217(zzz473, zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, zzz481, zzz482, zzz4830, zzz4840, bh)
new_mkVBalBranch3MkVBalBranch116(zzz340, zzz341, zzz34200, zzz343, zzz344, zzz510, zzz511, zzz513, zzz514, zzz31, Succ(zzz1200), h) → new_mkVBalBranch0(zzz31, zzz514, Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), h)
new_mkVBalBranch3MkVBalBranch110(zzz461, zzz462, zzz463, zzz464, zzz465, zzz466, zzz467, zzz468, zzz469, zzz470, zzz471, Zero, bb) → new_mkVBalBranch3MkVBalBranch115(zzz461, zzz462, zzz463, zzz464, zzz465, zzz466, zzz467, Succ(zzz468), zzz469, zzz470, zzz471, Zero, Succ(Succ(zzz468)), bb)
new_mkVBalBranch3MkVBalBranch225(zzz498, zzz499, zzz500, zzz501, zzz502, zzz503, zzz504, zzz505, zzz506, zzz507, Zero, Succ(zzz5090), bg) → new_mkVBalBranch0(zzz507, Branch(zzz503, zzz504, Neg(Succ(Zero)), zzz505, zzz506), zzz501, bg)
new_mkVBalBranch3MkVBalBranch222(zzz461, zzz462, zzz463, zzz464, zzz465, zzz466, zzz467, zzz468, zzz469, zzz470, zzz471, bb) → new_mkVBalBranch3MkVBalBranch110(zzz461, zzz462, zzz463, zzz464, zzz465, zzz466, zzz467, zzz468, zzz469, zzz470, zzz471, new_primPlusNat2(new_primPlusNat3(Succ(new_primPlusNat3(new_primPlusNat1(zzz463), zzz463)), Succ(zzz463)), Succ(zzz463)), bb)
new_mkVBalBranch3MkVBalBranch223(zzz340, zzz341, Neg(Succ(Succ(Succ(zzz3420000)))), zzz343, zzz344, zzz510, zzz511, Zero, zzz513, zzz514, zzz31, Succ(Zero), h) → new_mkVBalBranch3MkVBalBranch225(zzz340, zzz341, Succ(Succ(zzz3420000)), zzz343, zzz344, zzz510, zzz511, zzz513, zzz514, zzz31, Succ(zzz3420000), Zero, h)
new_mkVBalBranch3MkVBalBranch121(zzz473, zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, zzz481, zzz482, Zero, bh) → new_mkVBalBranch3MkVBalBranch115(zzz473, zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, Zero, zzz480, zzz481, zzz482, Zero, Succ(Zero), bh)
new_mkVBalBranch3MkVBalBranch223(zzz340, zzz341, Neg(Succ(Zero)), zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, Succ(zzz670), h) → new_mkVBalBranch0(zzz31, Branch(zzz510, zzz511, Neg(Succ(zzz51200)), zzz513, zzz514), zzz343, h)
new_mkVBalBranch3MkVBalBranch225(zzz498, zzz499, zzz500, zzz501, zzz502, zzz503, zzz504, zzz505, zzz506, zzz507, Succ(zzz5080), Zero, bg) → new_mkVBalBranch3MkVBalBranch118(zzz498, zzz499, zzz500, zzz501, zzz502, zzz503, zzz504, zzz505, zzz506, zzz507, new_primPlusNat2(new_primMulNat0(zzz500), Succ(zzz500)), bg)
new_mkVBalBranch3MkVBalBranch215(zzz340, zzz341, Pos(Succ(Zero)), zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, Succ(zzz660), h) → new_mkVBalBranch3MkVBalBranch18(zzz340, zzz341, zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, new_primPlusNat2(new_primMulNat0(Zero), Succ(Zero)), h)
new_mkVBalBranch3MkVBalBranch229(zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, zzz1125, zzz1126, zzz1127, zzz1128, zzz1129, bd) → new_mkVBalBranch3MkVBalBranch119(zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, zzz1125, zzz1126, zzz1127, zzz1128, zzz1129, new_primPlusNat2(new_primMulNat0(zzz1121), Succ(zzz1121)), bd)
new_mkVBalBranch3MkVBalBranch233(zzz473, zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, zzz481, zzz482, bh) → new_mkVBalBranch3MkVBalBranch121(zzz473, zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, zzz481, zzz482, new_primPlusNat2(new_primMulNat0(zzz475), Succ(zzz475)), bh)
new_mkVBalBranch3MkVBalBranch223(zzz340, zzz341, Neg(Succ(Zero)), zzz343, zzz344, zzz510, zzz511, Succ(zzz512000), zzz513, zzz514, zzz31, Zero, h) → new_mkVBalBranch3MkVBalBranch227(zzz340, zzz341, Zero, zzz343, zzz344, zzz510, zzz511, zzz512000, zzz513, zzz514, zzz31, h)
new_mkVBalBranch3MkVBalBranch215(zzz340, zzz341, Pos(Succ(Succ(zzz342000))), zzz343, zzz344, zzz510, zzz511, Zero, zzz513, zzz514, zzz31, Succ(Succ(zzz6600)), h) → new_mkVBalBranch3MkVBalBranch217(zzz340, zzz341, Succ(zzz342000), zzz343, zzz344, zzz510, zzz511, zzz513, zzz514, zzz31, Succ(zzz6600), zzz342000, h)
new_mkVBalBranch3MkVBalBranch223(zzz340, zzz341, Neg(Succ(Succ(zzz342000))), zzz343, zzz344, zzz510, zzz511, Succ(zzz512000), zzz513, zzz514, zzz31, Zero, h) → new_mkVBalBranch3MkVBalBranch224(zzz340, zzz341, Succ(zzz342000), zzz343, zzz344, zzz510, zzz511, zzz512000, zzz513, zzz514, zzz31, zzz342000, zzz512000, h)
new_mkVBalBranch3MkVBalBranch226(zzz340, zzz341, zzz3420, zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, h) → new_mkVBalBranch0(zzz31, Branch(zzz510, zzz511, Neg(Succ(zzz51200)), zzz513, zzz514), zzz343, h)
new_mkVBalBranch3MkVBalBranch218(zzz461, zzz462, zzz463, zzz464, zzz465, zzz466, zzz467, zzz468, zzz469, zzz470, zzz471, bb) → new_mkVBalBranch3MkVBalBranch110(zzz461, zzz462, zzz463, zzz464, zzz465, zzz466, zzz467, zzz468, zzz469, zzz470, zzz471, new_primPlusNat2(new_primMulNat0(zzz463), Succ(zzz463)), bb)
new_mkVBalBranch3MkVBalBranch117(zzz340, zzz341, zzz34200, zzz343, zzz344, zzz510, zzz511, zzz513, zzz514, zzz31, Succ(zzz1240), h) → new_mkVBalBranch0(zzz31, zzz514, Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), h)
new_mkVBalBranch3MkVBalBranch217(zzz473, zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, zzz481, zzz482, Zero, Zero, bh) → new_mkVBalBranch3MkVBalBranch233(zzz473, zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, zzz481, zzz482, bh)
new_mkVBalBranch3MkVBalBranch120(zzz2050, zzz2051, zzz2052, zzz2053, zzz2054, zzz2055, zzz2056, zzz2057, zzz2058, zzz2059, zzz2060, Succ(zzz20610), Succ(zzz20620), be) → new_mkVBalBranch3MkVBalBranch120(zzz2050, zzz2051, zzz2052, zzz2053, zzz2054, zzz2055, zzz2056, zzz2057, zzz2058, zzz2059, zzz2060, zzz20610, zzz20620, be)
new_mkVBalBranch0(zzz31, Branch(zzz510, zzz511, Neg(Succ(zzz51200)), zzz513, zzz514), Branch(zzz340, zzz341, zzz342, zzz343, zzz344), h) → new_mkVBalBranch3MkVBalBranch223(zzz340, zzz341, zzz342, zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, new_primPlusNat3(Succ(new_primPlusNat3(new_primPlusNat1(zzz51200), zzz51200)), Succ(zzz51200)), h)
new_mkVBalBranch3MkVBalBranch223(zzz340, zzz341, Pos(zzz3420), zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, Succ(zzz670), h) → new_mkVBalBranch0(zzz31, Branch(zzz510, zzz511, Neg(Succ(zzz51200)), zzz513, zzz514), zzz343, h)
new_mkVBalBranch3MkVBalBranch216(zzz1105, zzz1106, zzz1107, zzz1108, zzz1109, zzz1110, zzz1111, zzz1112, zzz1113, zzz1114, zzz1115, Succ(zzz11160), Succ(zzz11170), ba) → new_mkVBalBranch3MkVBalBranch216(zzz1105, zzz1106, zzz1107, zzz1108, zzz1109, zzz1110, zzz1111, zzz1112, zzz1113, zzz1114, zzz1115, zzz11160, zzz11170, ba)
new_mkVBalBranch3MkVBalBranch19(zzz340, zzz341, zzz34200, zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, Zero, h) → new_mkVBalBranch3MkVBalBranch122(zzz340, zzz341, zzz34200, zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, h)
new_mkVBalBranch3MkVBalBranch223(zzz340, zzz341, Neg(Succ(Succ(Succ(zzz3420000)))), zzz343, zzz344, zzz510, zzz511, Succ(zzz512000), zzz513, zzz514, zzz31, Succ(Zero), h) → new_mkVBalBranch3MkVBalBranch224(zzz340, zzz341, Succ(Succ(zzz3420000)), zzz343, zzz344, zzz510, zzz511, zzz512000, zzz513, zzz514, zzz31, Succ(zzz3420000), Succ(zzz512000), h)
new_mkVBalBranch3MkVBalBranch225(zzz498, zzz499, zzz500, zzz501, zzz502, zzz503, zzz504, zzz505, zzz506, zzz507, Succ(zzz5080), Succ(zzz5090), bg) → new_mkVBalBranch3MkVBalBranch225(zzz498, zzz499, zzz500, zzz501, zzz502, zzz503, zzz504, zzz505, zzz506, zzz507, zzz5080, zzz5090, bg)
new_mkVBalBranch3MkVBalBranch19(zzz340, zzz341, zzz34200, zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, Succ(zzz1410), h) → new_mkVBalBranch0(zzz31, zzz514, Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), h)
new_mkVBalBranch3MkVBalBranch224(zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, zzz1125, zzz1126, zzz1127, zzz1128, zzz1129, Succ(zzz11300), Zero, bd) → new_mkVBalBranch3MkVBalBranch119(zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, zzz1125, zzz1126, zzz1127, zzz1128, zzz1129, new_primPlusNat2(new_primMulNat0(zzz1121), Succ(zzz1121)), bd)
new_mkVBalBranch3MkVBalBranch224(zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, zzz1125, zzz1126, zzz1127, zzz1128, zzz1129, Zero, Zero, bd) → new_mkVBalBranch3MkVBalBranch229(zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, zzz1125, zzz1126, zzz1127, zzz1128, zzz1129, bd)
new_mkVBalBranch3MkVBalBranch224(zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, zzz1125, zzz1126, zzz1127, zzz1128, zzz1129, Zero, Succ(zzz11310), bd) → new_mkVBalBranch3MkVBalBranch227(zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, zzz1125, zzz1126, zzz1127, zzz1128, zzz1129, bd)
new_mkVBalBranch3MkVBalBranch223(zzz340, zzz341, Neg(Succ(Succ(Zero))), zzz343, zzz344, zzz510, zzz511, Succ(zzz512000), zzz513, zzz514, zzz31, Succ(Zero), h) → new_mkVBalBranch3MkVBalBranch224(zzz340, zzz341, Succ(Zero), zzz343, zzz344, zzz510, zzz511, zzz512000, zzz513, zzz514, zzz31, Zero, Succ(zzz512000), h)
new_mkVBalBranch3MkVBalBranch223(zzz340, zzz341, Pos(zzz3420), zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, Zero, h) → new_mkVBalBranch3MkVBalBranch226(zzz340, zzz341, zzz3420, zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, h)
new_mkVBalBranch3MkVBalBranch223(zzz340, zzz341, Neg(Succ(Succ(zzz342000))), zzz343, zzz344, zzz510, zzz511, Zero, zzz513, zzz514, zzz31, Zero, h) → new_mkVBalBranch3MkVBalBranch118(zzz340, zzz341, Succ(zzz342000), zzz343, zzz344, zzz510, zzz511, zzz513, zzz514, zzz31, new_primPlusNat2(new_primMulNat0(Succ(zzz342000)), Succ(Succ(zzz342000))), h)
new_mkVBalBranch3MkVBalBranch230(zzz498, zzz499, zzz500, zzz501, zzz502, zzz503, zzz504, zzz505, zzz506, zzz507, bg) → new_mkVBalBranch3MkVBalBranch118(zzz498, zzz499, zzz500, zzz501, zzz502, zzz503, zzz504, zzz505, zzz506, zzz507, new_primPlusNat2(new_primMulNat0(zzz500), Succ(zzz500)), bg)
new_mkVBalBranch3MkVBalBranch223(zzz340, zzz341, Neg(Succ(Succ(Succ(zzz3420000)))), zzz343, zzz344, zzz510, zzz511, Succ(zzz512000), zzz513, zzz514, zzz31, Succ(Succ(zzz6700)), h) → new_mkVBalBranch3MkVBalBranch224(zzz340, zzz341, Succ(Succ(zzz3420000)), zzz343, zzz344, zzz510, zzz511, zzz512000, zzz513, zzz514, zzz31, Succ(zzz3420000), Succ(Succ(new_primPlusNat2(zzz6700, zzz512000))), h)
new_mkVBalBranch3MkVBalBranch223(zzz340, zzz341, Neg(Succ(Succ(Zero))), zzz343, zzz344, zzz510, zzz511, Zero, zzz513, zzz514, zzz31, Succ(Succ(zzz6700)), h) → new_mkVBalBranch3MkVBalBranch225(zzz340, zzz341, Succ(Zero), zzz343, zzz344, zzz510, zzz511, zzz513, zzz514, zzz31, Zero, Succ(zzz6700), h)
new_mkVBalBranch3MkVBalBranch115(zzz1986, zzz1987, zzz1988, zzz1989, zzz1990, zzz1991, zzz1992, zzz1993, zzz1994, zzz1995, zzz1996, Succ(zzz19970), Succ(zzz19980), bc) → new_mkVBalBranch3MkVBalBranch115(zzz1986, zzz1987, zzz1988, zzz1989, zzz1990, zzz1991, zzz1992, zzz1993, zzz1994, zzz1995, zzz1996, zzz19970, zzz19980, bc)
new_mkVBalBranch3MkVBalBranch215(zzz340, zzz341, Neg(Zero), zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, Succ(zzz660), h) → new_mkVBalBranch0(zzz31, zzz514, Branch(zzz340, zzz341, Neg(Zero), zzz343, zzz344), h)
new_mkVBalBranch3MkVBalBranch118(zzz498, zzz499, zzz500, zzz501, zzz502, zzz503, zzz504, zzz505, zzz506, zzz507, Succ(zzz8040), bg) → new_mkVBalBranch3MkVBalBranch120(zzz498, zzz499, zzz500, zzz501, zzz502, zzz503, zzz504, Zero, zzz505, zzz506, zzz507, Succ(Zero), Succ(zzz8040), bg)
new_mkVBalBranch3MkVBalBranch216(zzz1105, zzz1106, zzz1107, zzz1108, zzz1109, zzz1110, zzz1111, zzz1112, zzz1113, zzz1114, zzz1115, Succ(zzz11160), Zero, ba) → new_mkVBalBranch3MkVBalBranch218(zzz1105, zzz1106, zzz1107, zzz1108, zzz1109, zzz1110, zzz1111, zzz1112, zzz1113, zzz1114, zzz1115, ba)
new_mkVBalBranch3MkVBalBranch215(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, Succ(zzz660), h) → new_mkVBalBranch3MkVBalBranch19(zzz340, zzz341, zzz34200, zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, new_primPlusNat2(new_primMulNat0(zzz34200), Succ(zzz34200)), h)
new_mkVBalBranch3MkVBalBranch216(zzz1105, zzz1106, zzz1107, zzz1108, zzz1109, zzz1110, zzz1111, zzz1112, zzz1113, zzz1114, zzz1115, Zero, Zero, ba) → new_mkVBalBranch3MkVBalBranch222(zzz1105, zzz1106, zzz1107, zzz1108, zzz1109, zzz1110, zzz1111, zzz1112, zzz1113, zzz1114, zzz1115, ba)
new_mkVBalBranch3MkVBalBranch18(zzz340, zzz341, zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, Zero, h) → new_mkVBalBranch3MkVBalBranch115(zzz340, zzz341, Zero, zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, Zero, Succ(zzz51200), h)
new_mkVBalBranch3MkVBalBranch119(zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, zzz1125, zzz1126, zzz1127, zzz1128, zzz1129, Succ(zzz12130), bd) → new_mkVBalBranch3MkVBalBranch120(zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, zzz1125, Succ(zzz1126), zzz1127, zzz1128, zzz1129, Succ(Succ(zzz1126)), Succ(zzz12130), bd)

The TRS R consists of the following rules:

new_primMulNat0(zzz6200) → new_primPlusNat3(Succ(new_primPlusNat3(new_primPlusNat1(zzz6200), zzz6200)), Succ(zzz6200))
new_primPlusNat2(Succ(zzz900), Succ(zzz9100)) → Succ(Succ(new_primPlusNat2(zzz900, zzz9100)))
new_primPlusNat2(Zero, Succ(zzz9100)) → Succ(zzz9100)
new_primPlusNat2(Zero, Zero) → Zero
new_primPlusNat2(Succ(zzz900), Zero) → Succ(zzz900)
new_primPlusNat1(Zero) → Zero
new_primPlusNat1(Succ(zzz62000)) → Succ(Succ(new_primPlusNat1(zzz62000)))
new_primPlusNat3(zzz90, Succ(zzz910)) → Succ(Succ(new_primPlusNat2(zzz90, zzz910)))
new_primPlusNat3(zzz90, Zero) → Succ(zzz90)

The set Q consists of the following terms:

new_primPlusNat2(Zero, Succ(x0))
new_primMulNat0(x0)
new_primPlusNat3(x0, Succ(x1))
new_primPlusNat2(Succ(x0), Succ(x1))
new_primPlusNat3(x0, Zero)
new_primPlusNat1(Zero)
new_primPlusNat2(Zero, Zero)
new_primPlusNat1(Succ(x0))
new_primPlusNat2(Succ(x0), Zero)

We have to consider all minimal (P,Q,R)-chains.
By rewriting [15] the rule new_mkVBalBranch3MkVBalBranch230(zzz498, zzz499, zzz500, zzz501, zzz502, zzz503, zzz504, zzz505, zzz506, zzz507, bg) → new_mkVBalBranch3MkVBalBranch118(zzz498, zzz499, zzz500, zzz501, zzz502, zzz503, zzz504, zzz505, zzz506, zzz507, new_primPlusNat2(new_primMulNat0(zzz500), Succ(zzz500)), bg) at position [10,0] we obtained the following new rules:

new_mkVBalBranch3MkVBalBranch230(zzz498, zzz499, zzz500, zzz501, zzz502, zzz503, zzz504, zzz505, zzz506, zzz507, bg) → new_mkVBalBranch3MkVBalBranch118(zzz498, zzz499, zzz500, zzz501, zzz502, zzz503, zzz504, zzz505, zzz506, zzz507, new_primPlusNat2(new_primPlusNat3(Succ(new_primPlusNat3(new_primPlusNat1(zzz500), zzz500)), Succ(zzz500)), Succ(zzz500)), bg)



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

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

new_mkVBalBranch3MkVBalBranch225(zzz498, zzz499, zzz500, zzz501, zzz502, zzz503, zzz504, zzz505, zzz506, zzz507, Zero, Zero, bg) → new_mkVBalBranch3MkVBalBranch230(zzz498, zzz499, zzz500, zzz501, zzz502, zzz503, zzz504, zzz505, zzz506, zzz507, bg)
new_mkVBalBranch3MkVBalBranch18(zzz340, zzz341, zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, Succ(zzz1480), h) → new_mkVBalBranch3MkVBalBranch115(zzz340, zzz341, Zero, zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, Succ(zzz1480), Succ(zzz51200), h)
new_mkVBalBranch0(zzz31, Branch(zzz510, zzz511, Neg(Zero), zzz513, zzz514), Branch(zzz340, zzz341, Pos(Succ(zzz34200)), zzz343, zzz344), h) → new_mkVBalBranch0(zzz31, Branch(zzz510, zzz511, Neg(Zero), zzz513, zzz514), zzz343, h)
new_mkVBalBranch3MkVBalBranch215(zzz340, zzz341, Pos(Succ(Succ(zzz342000))), zzz343, zzz344, zzz510, zzz511, Succ(zzz512000), zzz513, zzz514, zzz31, Succ(Succ(zzz6600)), h) → new_mkVBalBranch3MkVBalBranch216(zzz340, zzz341, Succ(zzz342000), zzz343, zzz344, zzz510, zzz511, zzz512000, zzz513, zzz514, zzz31, Succ(Succ(new_primPlusNat2(zzz6600, zzz512000))), zzz342000, h)
new_mkVBalBranch3MkVBalBranch223(zzz340, zzz341, Neg(Succ(Succ(Succ(zzz3420000)))), zzz343, zzz344, zzz510, zzz511, Zero, zzz513, zzz514, zzz31, Succ(Succ(zzz6700)), h) → new_mkVBalBranch3MkVBalBranch225(zzz340, zzz341, Succ(Succ(zzz3420000)), zzz343, zzz344, zzz510, zzz511, zzz513, zzz514, zzz31, Succ(zzz3420000), Succ(zzz6700), h)
new_mkVBalBranch3MkVBalBranch120(zzz2050, zzz2051, zzz2052, zzz2053, zzz2054, zzz2055, zzz2056, zzz2057, zzz2058, zzz2059, zzz2060, Zero, Succ(zzz20620), be) → new_mkVBalBranch0(zzz2060, zzz2059, Branch(zzz2050, zzz2051, Neg(Succ(zzz2052)), zzz2053, zzz2054), be)
new_mkVBalBranch3MkVBalBranch228(zzz340, zzz341, zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, h) → new_mkVBalBranch0(zzz31, Branch(zzz510, zzz511, Neg(Succ(zzz51200)), zzz513, zzz514), zzz343, h)
new_mkVBalBranch0(zzz31, Branch(zzz510, zzz511, Pos(Zero), zzz513, zzz514), Branch(zzz340, zzz341, Pos(Succ(zzz34200)), zzz343, zzz344), h) → new_mkVBalBranch0(zzz31, Branch(zzz510, zzz511, Pos(Zero), zzz513, zzz514), zzz343, h)
new_mkVBalBranch3MkVBalBranch121(zzz473, zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, zzz481, zzz482, Succ(zzz7390), bh) → new_mkVBalBranch3MkVBalBranch115(zzz473, zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, Zero, zzz480, zzz481, zzz482, Succ(zzz7390), Succ(Zero), bh)
new_mkVBalBranch0(zzz31, Branch(zzz510, zzz511, Pos(Succ(zzz51200)), zzz513, zzz514), Branch(zzz340, zzz341, zzz342, zzz343, zzz344), h) → new_mkVBalBranch3MkVBalBranch215(zzz340, zzz341, zzz342, zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat3(new_primPlusNat1(zzz51200), zzz51200)), zzz51200))), h)
new_mkVBalBranch3MkVBalBranch223(zzz340, zzz341, Neg(Succ(Succ(Zero))), zzz343, zzz344, zzz510, zzz511, Succ(zzz512000), zzz513, zzz514, zzz31, Succ(Succ(zzz6700)), h) → new_mkVBalBranch3MkVBalBranch224(zzz340, zzz341, Succ(Zero), zzz343, zzz344, zzz510, zzz511, zzz512000, zzz513, zzz514, zzz31, Zero, Succ(Succ(new_primPlusNat2(zzz6700, zzz512000))), h)
new_mkVBalBranch3MkVBalBranch230(zzz498, zzz499, zzz500, zzz501, zzz502, zzz503, zzz504, zzz505, zzz506, zzz507, bg) → new_mkVBalBranch3MkVBalBranch118(zzz498, zzz499, zzz500, zzz501, zzz502, zzz503, zzz504, zzz505, zzz506, zzz507, new_primPlusNat2(new_primPlusNat3(Succ(new_primPlusNat3(new_primPlusNat1(zzz500), zzz500)), Succ(zzz500)), Succ(zzz500)), bg)
new_mkVBalBranch3MkVBalBranch223(zzz340, zzz341, Neg(Succ(Succ(Zero))), zzz343, zzz344, zzz510, zzz511, Zero, zzz513, zzz514, zzz31, Succ(Zero), h) → new_mkVBalBranch3MkVBalBranch225(zzz340, zzz341, Succ(Zero), zzz343, zzz344, zzz510, zzz511, zzz513, zzz514, zzz31, Zero, Zero, h)
new_mkVBalBranch3MkVBalBranch224(zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, zzz1125, zzz1126, zzz1127, zzz1128, zzz1129, Succ(zzz11300), Succ(zzz11310), bd) → new_mkVBalBranch3MkVBalBranch224(zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, zzz1125, zzz1126, zzz1127, zzz1128, zzz1129, zzz11300, zzz11310, bd)
new_mkVBalBranch3MkVBalBranch217(zzz473, zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, zzz481, zzz482, Zero, Succ(zzz4840), bh) → new_mkVBalBranch0(zzz482, Branch(zzz478, zzz479, Pos(Succ(Zero)), zzz480, zzz481), zzz476, bh)
new_mkVBalBranch3MkVBalBranch110(zzz461, zzz462, zzz463, zzz464, zzz465, zzz466, zzz467, zzz468, zzz469, zzz470, zzz471, Succ(zzz5800), bb) → new_mkVBalBranch3MkVBalBranch115(zzz461, zzz462, zzz463, zzz464, zzz465, zzz466, zzz467, Succ(zzz468), zzz469, zzz470, zzz471, Succ(zzz5800), Succ(Succ(zzz468)), bb)
new_mkVBalBranch3MkVBalBranch223(zzz340, zzz341, Neg(Succ(Zero)), zzz343, zzz344, zzz510, zzz511, Zero, zzz513, zzz514, zzz31, Zero, h) → new_mkVBalBranch3MkVBalBranch118(zzz340, zzz341, Zero, zzz343, zzz344, zzz510, zzz511, zzz513, zzz514, zzz31, new_primPlusNat2(new_primMulNat0(Zero), Succ(Zero)), h)
new_mkVBalBranch3MkVBalBranch227(zzz486, zzz487, zzz488, zzz489, zzz490, zzz491, zzz492, zzz493, zzz494, zzz495, zzz496, bf) → new_mkVBalBranch0(zzz496, Branch(zzz491, zzz492, Neg(Succ(Succ(zzz493))), zzz494, zzz495), zzz489, bf)
new_mkVBalBranch0(zzz31, Branch(zzz510, zzz511, Pos(Zero), zzz513, zzz514), Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), h) → new_mkVBalBranch3MkVBalBranch116(zzz340, zzz341, zzz34200, zzz343, zzz344, zzz510, zzz511, zzz513, zzz514, zzz31, new_primPlusNat2(new_primMulNat0(zzz34200), Succ(zzz34200)), h)
new_mkVBalBranch3MkVBalBranch215(zzz340, zzz341, Pos(Zero), zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, Succ(zzz660), h) → new_mkVBalBranch0(zzz31, zzz514, Branch(zzz340, zzz341, Pos(Zero), zzz343, zzz344), h)
new_mkVBalBranch3MkVBalBranch223(zzz340, zzz341, Neg(Zero), zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, Succ(zzz670), h) → new_mkVBalBranch0(zzz31, Branch(zzz510, zzz511, Neg(Succ(zzz51200)), zzz513, zzz514), zzz343, h)
new_mkVBalBranch3MkVBalBranch217(zzz473, zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, zzz481, zzz482, Succ(zzz4830), Zero, bh) → new_mkVBalBranch3MkVBalBranch121(zzz473, zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, zzz481, zzz482, new_primPlusNat2(new_primMulNat0(zzz475), Succ(zzz475)), bh)
new_mkVBalBranch3MkVBalBranch216(zzz1105, zzz1106, zzz1107, zzz1108, zzz1109, zzz1110, zzz1111, zzz1112, zzz1113, zzz1114, zzz1115, Zero, Succ(zzz11170), ba) → new_mkVBalBranch0(zzz1115, Branch(zzz1110, zzz1111, Pos(Succ(Succ(zzz1112))), zzz1113, zzz1114), zzz1108, ba)
new_mkVBalBranch3MkVBalBranch115(zzz1986, zzz1987, zzz1988, zzz1989, zzz1990, zzz1991, zzz1992, zzz1993, zzz1994, zzz1995, zzz1996, Zero, Succ(zzz19980), bc) → new_mkVBalBranch0(zzz1996, zzz1995, Branch(zzz1986, zzz1987, Pos(Succ(zzz1988)), zzz1989, zzz1990), bc)
new_mkVBalBranch0(zzz31, Branch(zzz510, zzz511, Neg(Zero), zzz513, zzz514), Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), h) → new_mkVBalBranch3MkVBalBranch117(zzz340, zzz341, zzz34200, zzz343, zzz344, zzz510, zzz511, zzz513, zzz514, zzz31, new_primPlusNat2(new_primMulNat0(zzz34200), Succ(zzz34200)), h)
new_mkVBalBranch3MkVBalBranch223(zzz340, zzz341, Neg(Zero), zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, Zero, h) → new_mkVBalBranch3MkVBalBranch228(zzz340, zzz341, zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, h)
new_mkVBalBranch3MkVBalBranch122(zzz340, zzz341, zzz34200, zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, h) → new_mkVBalBranch0(zzz31, zzz514, Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), h)
new_mkVBalBranch3MkVBalBranch217(zzz473, zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, zzz481, zzz482, Succ(zzz4830), Succ(zzz4840), bh) → new_mkVBalBranch3MkVBalBranch217(zzz473, zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, zzz481, zzz482, zzz4830, zzz4840, bh)
new_mkVBalBranch3MkVBalBranch116(zzz340, zzz341, zzz34200, zzz343, zzz344, zzz510, zzz511, zzz513, zzz514, zzz31, Succ(zzz1200), h) → new_mkVBalBranch0(zzz31, zzz514, Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), h)
new_mkVBalBranch3MkVBalBranch110(zzz461, zzz462, zzz463, zzz464, zzz465, zzz466, zzz467, zzz468, zzz469, zzz470, zzz471, Zero, bb) → new_mkVBalBranch3MkVBalBranch115(zzz461, zzz462, zzz463, zzz464, zzz465, zzz466, zzz467, Succ(zzz468), zzz469, zzz470, zzz471, Zero, Succ(Succ(zzz468)), bb)
new_mkVBalBranch3MkVBalBranch225(zzz498, zzz499, zzz500, zzz501, zzz502, zzz503, zzz504, zzz505, zzz506, zzz507, Zero, Succ(zzz5090), bg) → new_mkVBalBranch0(zzz507, Branch(zzz503, zzz504, Neg(Succ(Zero)), zzz505, zzz506), zzz501, bg)
new_mkVBalBranch3MkVBalBranch222(zzz461, zzz462, zzz463, zzz464, zzz465, zzz466, zzz467, zzz468, zzz469, zzz470, zzz471, bb) → new_mkVBalBranch3MkVBalBranch110(zzz461, zzz462, zzz463, zzz464, zzz465, zzz466, zzz467, zzz468, zzz469, zzz470, zzz471, new_primPlusNat2(new_primPlusNat3(Succ(new_primPlusNat3(new_primPlusNat1(zzz463), zzz463)), Succ(zzz463)), Succ(zzz463)), bb)
new_mkVBalBranch3MkVBalBranch223(zzz340, zzz341, Neg(Succ(Succ(Succ(zzz3420000)))), zzz343, zzz344, zzz510, zzz511, Zero, zzz513, zzz514, zzz31, Succ(Zero), h) → new_mkVBalBranch3MkVBalBranch225(zzz340, zzz341, Succ(Succ(zzz3420000)), zzz343, zzz344, zzz510, zzz511, zzz513, zzz514, zzz31, Succ(zzz3420000), Zero, h)
new_mkVBalBranch3MkVBalBranch121(zzz473, zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, zzz481, zzz482, Zero, bh) → new_mkVBalBranch3MkVBalBranch115(zzz473, zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, Zero, zzz480, zzz481, zzz482, Zero, Succ(Zero), bh)
new_mkVBalBranch3MkVBalBranch225(zzz498, zzz499, zzz500, zzz501, zzz502, zzz503, zzz504, zzz505, zzz506, zzz507, Succ(zzz5080), Zero, bg) → new_mkVBalBranch3MkVBalBranch118(zzz498, zzz499, zzz500, zzz501, zzz502, zzz503, zzz504, zzz505, zzz506, zzz507, new_primPlusNat2(new_primMulNat0(zzz500), Succ(zzz500)), bg)
new_mkVBalBranch3MkVBalBranch223(zzz340, zzz341, Neg(Succ(Zero)), zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, Succ(zzz670), h) → new_mkVBalBranch0(zzz31, Branch(zzz510, zzz511, Neg(Succ(zzz51200)), zzz513, zzz514), zzz343, h)
new_mkVBalBranch3MkVBalBranch215(zzz340, zzz341, Pos(Succ(Zero)), zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, Succ(zzz660), h) → new_mkVBalBranch3MkVBalBranch18(zzz340, zzz341, zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, new_primPlusNat2(new_primMulNat0(Zero), Succ(Zero)), h)
new_mkVBalBranch3MkVBalBranch229(zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, zzz1125, zzz1126, zzz1127, zzz1128, zzz1129, bd) → new_mkVBalBranch3MkVBalBranch119(zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, zzz1125, zzz1126, zzz1127, zzz1128, zzz1129, new_primPlusNat2(new_primMulNat0(zzz1121), Succ(zzz1121)), bd)
new_mkVBalBranch3MkVBalBranch223(zzz340, zzz341, Neg(Succ(Zero)), zzz343, zzz344, zzz510, zzz511, Succ(zzz512000), zzz513, zzz514, zzz31, Zero, h) → new_mkVBalBranch3MkVBalBranch227(zzz340, zzz341, Zero, zzz343, zzz344, zzz510, zzz511, zzz512000, zzz513, zzz514, zzz31, h)
new_mkVBalBranch3MkVBalBranch233(zzz473, zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, zzz481, zzz482, bh) → new_mkVBalBranch3MkVBalBranch121(zzz473, zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, zzz481, zzz482, new_primPlusNat2(new_primMulNat0(zzz475), Succ(zzz475)), bh)
new_mkVBalBranch3MkVBalBranch226(zzz340, zzz341, zzz3420, zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, h) → new_mkVBalBranch0(zzz31, Branch(zzz510, zzz511, Neg(Succ(zzz51200)), zzz513, zzz514), zzz343, h)
new_mkVBalBranch3MkVBalBranch223(zzz340, zzz341, Neg(Succ(Succ(zzz342000))), zzz343, zzz344, zzz510, zzz511, Succ(zzz512000), zzz513, zzz514, zzz31, Zero, h) → new_mkVBalBranch3MkVBalBranch224(zzz340, zzz341, Succ(zzz342000), zzz343, zzz344, zzz510, zzz511, zzz512000, zzz513, zzz514, zzz31, zzz342000, zzz512000, h)
new_mkVBalBranch3MkVBalBranch215(zzz340, zzz341, Pos(Succ(Succ(zzz342000))), zzz343, zzz344, zzz510, zzz511, Zero, zzz513, zzz514, zzz31, Succ(Succ(zzz6600)), h) → new_mkVBalBranch3MkVBalBranch217(zzz340, zzz341, Succ(zzz342000), zzz343, zzz344, zzz510, zzz511, zzz513, zzz514, zzz31, Succ(zzz6600), zzz342000, h)
new_mkVBalBranch3MkVBalBranch218(zzz461, zzz462, zzz463, zzz464, zzz465, zzz466, zzz467, zzz468, zzz469, zzz470, zzz471, bb) → new_mkVBalBranch3MkVBalBranch110(zzz461, zzz462, zzz463, zzz464, zzz465, zzz466, zzz467, zzz468, zzz469, zzz470, zzz471, new_primPlusNat2(new_primMulNat0(zzz463), Succ(zzz463)), bb)
new_mkVBalBranch3MkVBalBranch117(zzz340, zzz341, zzz34200, zzz343, zzz344, zzz510, zzz511, zzz513, zzz514, zzz31, Succ(zzz1240), h) → new_mkVBalBranch0(zzz31, zzz514, Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), h)
new_mkVBalBranch0(zzz31, Branch(zzz510, zzz511, Neg(Succ(zzz51200)), zzz513, zzz514), Branch(zzz340, zzz341, zzz342, zzz343, zzz344), h) → new_mkVBalBranch3MkVBalBranch223(zzz340, zzz341, zzz342, zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, new_primPlusNat3(Succ(new_primPlusNat3(new_primPlusNat1(zzz51200), zzz51200)), Succ(zzz51200)), h)
new_mkVBalBranch3MkVBalBranch120(zzz2050, zzz2051, zzz2052, zzz2053, zzz2054, zzz2055, zzz2056, zzz2057, zzz2058, zzz2059, zzz2060, Succ(zzz20610), Succ(zzz20620), be) → new_mkVBalBranch3MkVBalBranch120(zzz2050, zzz2051, zzz2052, zzz2053, zzz2054, zzz2055, zzz2056, zzz2057, zzz2058, zzz2059, zzz2060, zzz20610, zzz20620, be)
new_mkVBalBranch3MkVBalBranch217(zzz473, zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, zzz481, zzz482, Zero, Zero, bh) → new_mkVBalBranch3MkVBalBranch233(zzz473, zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, zzz481, zzz482, bh)
new_mkVBalBranch3MkVBalBranch216(zzz1105, zzz1106, zzz1107, zzz1108, zzz1109, zzz1110, zzz1111, zzz1112, zzz1113, zzz1114, zzz1115, Succ(zzz11160), Succ(zzz11170), ba) → new_mkVBalBranch3MkVBalBranch216(zzz1105, zzz1106, zzz1107, zzz1108, zzz1109, zzz1110, zzz1111, zzz1112, zzz1113, zzz1114, zzz1115, zzz11160, zzz11170, ba)
new_mkVBalBranch3MkVBalBranch223(zzz340, zzz341, Pos(zzz3420), zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, Succ(zzz670), h) → new_mkVBalBranch0(zzz31, Branch(zzz510, zzz511, Neg(Succ(zzz51200)), zzz513, zzz514), zzz343, h)
new_mkVBalBranch3MkVBalBranch223(zzz340, zzz341, Neg(Succ(Succ(Succ(zzz3420000)))), zzz343, zzz344, zzz510, zzz511, Succ(zzz512000), zzz513, zzz514, zzz31, Succ(Zero), h) → new_mkVBalBranch3MkVBalBranch224(zzz340, zzz341, Succ(Succ(zzz3420000)), zzz343, zzz344, zzz510, zzz511, zzz512000, zzz513, zzz514, zzz31, Succ(zzz3420000), Succ(zzz512000), h)
new_mkVBalBranch3MkVBalBranch19(zzz340, zzz341, zzz34200, zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, Zero, h) → new_mkVBalBranch3MkVBalBranch122(zzz340, zzz341, zzz34200, zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, h)
new_mkVBalBranch3MkVBalBranch225(zzz498, zzz499, zzz500, zzz501, zzz502, zzz503, zzz504, zzz505, zzz506, zzz507, Succ(zzz5080), Succ(zzz5090), bg) → new_mkVBalBranch3MkVBalBranch225(zzz498, zzz499, zzz500, zzz501, zzz502, zzz503, zzz504, zzz505, zzz506, zzz507, zzz5080, zzz5090, bg)
new_mkVBalBranch3MkVBalBranch19(zzz340, zzz341, zzz34200, zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, Succ(zzz1410), h) → new_mkVBalBranch0(zzz31, zzz514, Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), h)
new_mkVBalBranch3MkVBalBranch224(zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, zzz1125, zzz1126, zzz1127, zzz1128, zzz1129, Succ(zzz11300), Zero, bd) → new_mkVBalBranch3MkVBalBranch119(zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, zzz1125, zzz1126, zzz1127, zzz1128, zzz1129, new_primPlusNat2(new_primMulNat0(zzz1121), Succ(zzz1121)), bd)
new_mkVBalBranch3MkVBalBranch223(zzz340, zzz341, Pos(zzz3420), zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, Zero, h) → new_mkVBalBranch3MkVBalBranch226(zzz340, zzz341, zzz3420, zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, h)
new_mkVBalBranch3MkVBalBranch223(zzz340, zzz341, Neg(Succ(Succ(Zero))), zzz343, zzz344, zzz510, zzz511, Succ(zzz512000), zzz513, zzz514, zzz31, Succ(Zero), h) → new_mkVBalBranch3MkVBalBranch224(zzz340, zzz341, Succ(Zero), zzz343, zzz344, zzz510, zzz511, zzz512000, zzz513, zzz514, zzz31, Zero, Succ(zzz512000), h)
new_mkVBalBranch3MkVBalBranch224(zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, zzz1125, zzz1126, zzz1127, zzz1128, zzz1129, Zero, Succ(zzz11310), bd) → new_mkVBalBranch3MkVBalBranch227(zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, zzz1125, zzz1126, zzz1127, zzz1128, zzz1129, bd)
new_mkVBalBranch3MkVBalBranch224(zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, zzz1125, zzz1126, zzz1127, zzz1128, zzz1129, Zero, Zero, bd) → new_mkVBalBranch3MkVBalBranch229(zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, zzz1125, zzz1126, zzz1127, zzz1128, zzz1129, bd)
new_mkVBalBranch3MkVBalBranch223(zzz340, zzz341, Neg(Succ(Succ(zzz342000))), zzz343, zzz344, zzz510, zzz511, Zero, zzz513, zzz514, zzz31, Zero, h) → new_mkVBalBranch3MkVBalBranch118(zzz340, zzz341, Succ(zzz342000), zzz343, zzz344, zzz510, zzz511, zzz513, zzz514, zzz31, new_primPlusNat2(new_primMulNat0(Succ(zzz342000)), Succ(Succ(zzz342000))), h)
new_mkVBalBranch3MkVBalBranch223(zzz340, zzz341, Neg(Succ(Succ(Zero))), zzz343, zzz344, zzz510, zzz511, Zero, zzz513, zzz514, zzz31, Succ(Succ(zzz6700)), h) → new_mkVBalBranch3MkVBalBranch225(zzz340, zzz341, Succ(Zero), zzz343, zzz344, zzz510, zzz511, zzz513, zzz514, zzz31, Zero, Succ(zzz6700), h)
new_mkVBalBranch3MkVBalBranch223(zzz340, zzz341, Neg(Succ(Succ(Succ(zzz3420000)))), zzz343, zzz344, zzz510, zzz511, Succ(zzz512000), zzz513, zzz514, zzz31, Succ(Succ(zzz6700)), h) → new_mkVBalBranch3MkVBalBranch224(zzz340, zzz341, Succ(Succ(zzz3420000)), zzz343, zzz344, zzz510, zzz511, zzz512000, zzz513, zzz514, zzz31, Succ(zzz3420000), Succ(Succ(new_primPlusNat2(zzz6700, zzz512000))), h)
new_mkVBalBranch3MkVBalBranch115(zzz1986, zzz1987, zzz1988, zzz1989, zzz1990, zzz1991, zzz1992, zzz1993, zzz1994, zzz1995, zzz1996, Succ(zzz19970), Succ(zzz19980), bc) → new_mkVBalBranch3MkVBalBranch115(zzz1986, zzz1987, zzz1988, zzz1989, zzz1990, zzz1991, zzz1992, zzz1993, zzz1994, zzz1995, zzz1996, zzz19970, zzz19980, bc)
new_mkVBalBranch3MkVBalBranch215(zzz340, zzz341, Neg(Zero), zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, Succ(zzz660), h) → new_mkVBalBranch0(zzz31, zzz514, Branch(zzz340, zzz341, Neg(Zero), zzz343, zzz344), h)
new_mkVBalBranch3MkVBalBranch118(zzz498, zzz499, zzz500, zzz501, zzz502, zzz503, zzz504, zzz505, zzz506, zzz507, Succ(zzz8040), bg) → new_mkVBalBranch3MkVBalBranch120(zzz498, zzz499, zzz500, zzz501, zzz502, zzz503, zzz504, Zero, zzz505, zzz506, zzz507, Succ(Zero), Succ(zzz8040), bg)
new_mkVBalBranch3MkVBalBranch216(zzz1105, zzz1106, zzz1107, zzz1108, zzz1109, zzz1110, zzz1111, zzz1112, zzz1113, zzz1114, zzz1115, Succ(zzz11160), Zero, ba) → new_mkVBalBranch3MkVBalBranch218(zzz1105, zzz1106, zzz1107, zzz1108, zzz1109, zzz1110, zzz1111, zzz1112, zzz1113, zzz1114, zzz1115, ba)
new_mkVBalBranch3MkVBalBranch215(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, Succ(zzz660), h) → new_mkVBalBranch3MkVBalBranch19(zzz340, zzz341, zzz34200, zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, new_primPlusNat2(new_primMulNat0(zzz34200), Succ(zzz34200)), h)
new_mkVBalBranch3MkVBalBranch216(zzz1105, zzz1106, zzz1107, zzz1108, zzz1109, zzz1110, zzz1111, zzz1112, zzz1113, zzz1114, zzz1115, Zero, Zero, ba) → new_mkVBalBranch3MkVBalBranch222(zzz1105, zzz1106, zzz1107, zzz1108, zzz1109, zzz1110, zzz1111, zzz1112, zzz1113, zzz1114, zzz1115, ba)
new_mkVBalBranch3MkVBalBranch119(zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, zzz1125, zzz1126, zzz1127, zzz1128, zzz1129, Succ(zzz12130), bd) → new_mkVBalBranch3MkVBalBranch120(zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, zzz1125, Succ(zzz1126), zzz1127, zzz1128, zzz1129, Succ(Succ(zzz1126)), Succ(zzz12130), bd)
new_mkVBalBranch3MkVBalBranch18(zzz340, zzz341, zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, Zero, h) → new_mkVBalBranch3MkVBalBranch115(zzz340, zzz341, Zero, zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, Zero, Succ(zzz51200), h)

The TRS R consists of the following rules:

new_primMulNat0(zzz6200) → new_primPlusNat3(Succ(new_primPlusNat3(new_primPlusNat1(zzz6200), zzz6200)), Succ(zzz6200))
new_primPlusNat2(Succ(zzz900), Succ(zzz9100)) → Succ(Succ(new_primPlusNat2(zzz900, zzz9100)))
new_primPlusNat2(Zero, Succ(zzz9100)) → Succ(zzz9100)
new_primPlusNat2(Zero, Zero) → Zero
new_primPlusNat2(Succ(zzz900), Zero) → Succ(zzz900)
new_primPlusNat1(Zero) → Zero
new_primPlusNat1(Succ(zzz62000)) → Succ(Succ(new_primPlusNat1(zzz62000)))
new_primPlusNat3(zzz90, Succ(zzz910)) → Succ(Succ(new_primPlusNat2(zzz90, zzz910)))
new_primPlusNat3(zzz90, Zero) → Succ(zzz90)

The set Q consists of the following terms:

new_primPlusNat2(Zero, Succ(x0))
new_primMulNat0(x0)
new_primPlusNat3(x0, Succ(x1))
new_primPlusNat2(Succ(x0), Succ(x1))
new_primPlusNat3(x0, Zero)
new_primPlusNat1(Zero)
new_primPlusNat2(Zero, Zero)
new_primPlusNat1(Succ(x0))
new_primPlusNat2(Succ(x0), Zero)

We have to consider all minimal (P,Q,R)-chains.
By rewriting [15] the rule new_mkVBalBranch0(zzz31, Branch(zzz510, zzz511, Neg(Succ(zzz51200)), zzz513, zzz514), Branch(zzz340, zzz341, zzz342, zzz343, zzz344), h) → new_mkVBalBranch3MkVBalBranch223(zzz340, zzz341, zzz342, zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, new_primPlusNat3(Succ(new_primPlusNat3(new_primPlusNat1(zzz51200), zzz51200)), Succ(zzz51200)), h) at position [11] we obtained the following new rules:

new_mkVBalBranch0(zzz31, Branch(zzz510, zzz511, Neg(Succ(zzz51200)), zzz513, zzz514), Branch(zzz340, zzz341, zzz342, zzz343, zzz344), h) → new_mkVBalBranch3MkVBalBranch223(zzz340, zzz341, zzz342, zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat3(new_primPlusNat1(zzz51200), zzz51200)), zzz51200))), 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
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                    ↳ DependencyGraphProof
                                      ↳ QDP
                                        ↳ Rewriting
                                          ↳ QDP
                                            ↳ Rewriting
                                              ↳ QDP
                                                ↳ Rewriting
                                                  ↳ QDP
                                                    ↳ Rewriting
                                                      ↳ QDP
                                                        ↳ Rewriting
                                                          ↳ QDP
                                                            ↳ Rewriting
                                                              ↳ QDP
                                                                ↳ Rewriting
                                                                  ↳ QDP
                                                                    ↳ Rewriting
                                                                      ↳ QDP
                                                                        ↳ Rewriting
                                                                          ↳ QDP
                                                                            ↳ Rewriting
                                                                              ↳ QDP
                                                                                ↳ Rewriting
                                                                                  ↳ QDP
                                                                                    ↳ Rewriting
                                                                                      ↳ QDP
                                                                                        ↳ Rewriting
                                                                                          ↳ QDP
                                                                                            ↳ Rewriting
                                                                                              ↳ QDP
                                                                                                ↳ Rewriting
                                                                                                  ↳ QDP
                                                                                                    ↳ Rewriting
                                                                                                      ↳ QDP
                                                                                                        ↳ Rewriting
                                                                                                          ↳ QDP
                                                                                                            ↳ UsableRulesProof
                                                                                                              ↳ QDP
                                                                                                                ↳ QReductionProof
                                                                                                                  ↳ QDP
                                                                                                                    ↳ Rewriting
                                                                                                                      ↳ QDP
                                                                                                                        ↳ Rewriting
                                                                                                                          ↳ QDP
                                                                                                                            ↳ DependencyGraphProof
                                                                                                                              ↳ QDP
                                                                                                                                ↳ Rewriting
                                                                                                                                  ↳ QDP
                                                                                                                                    ↳ Rewriting
                                                                                                                                      ↳ QDP
                                                                                                                                        ↳ DependencyGraphProof
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP

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

new_mkVBalBranch3MkVBalBranch225(zzz498, zzz499, zzz500, zzz501, zzz502, zzz503, zzz504, zzz505, zzz506, zzz507, Zero, Zero, bg) → new_mkVBalBranch3MkVBalBranch230(zzz498, zzz499, zzz500, zzz501, zzz502, zzz503, zzz504, zzz505, zzz506, zzz507, bg)
new_mkVBalBranch3MkVBalBranch18(zzz340, zzz341, zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, Succ(zzz1480), h) → new_mkVBalBranch3MkVBalBranch115(zzz340, zzz341, Zero, zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, Succ(zzz1480), Succ(zzz51200), h)
new_mkVBalBranch3MkVBalBranch215(zzz340, zzz341, Pos(Succ(Succ(zzz342000))), zzz343, zzz344, zzz510, zzz511, Succ(zzz512000), zzz513, zzz514, zzz31, Succ(Succ(zzz6600)), h) → new_mkVBalBranch3MkVBalBranch216(zzz340, zzz341, Succ(zzz342000), zzz343, zzz344, zzz510, zzz511, zzz512000, zzz513, zzz514, zzz31, Succ(Succ(new_primPlusNat2(zzz6600, zzz512000))), zzz342000, h)
new_mkVBalBranch0(zzz31, Branch(zzz510, zzz511, Neg(Zero), zzz513, zzz514), Branch(zzz340, zzz341, Pos(Succ(zzz34200)), zzz343, zzz344), h) → new_mkVBalBranch0(zzz31, Branch(zzz510, zzz511, Neg(Zero), zzz513, zzz514), zzz343, h)
new_mkVBalBranch3MkVBalBranch223(zzz340, zzz341, Neg(Succ(Succ(Succ(zzz3420000)))), zzz343, zzz344, zzz510, zzz511, Zero, zzz513, zzz514, zzz31, Succ(Succ(zzz6700)), h) → new_mkVBalBranch3MkVBalBranch225(zzz340, zzz341, Succ(Succ(zzz3420000)), zzz343, zzz344, zzz510, zzz511, zzz513, zzz514, zzz31, Succ(zzz3420000), Succ(zzz6700), h)
new_mkVBalBranch3MkVBalBranch120(zzz2050, zzz2051, zzz2052, zzz2053, zzz2054, zzz2055, zzz2056, zzz2057, zzz2058, zzz2059, zzz2060, Zero, Succ(zzz20620), be) → new_mkVBalBranch0(zzz2060, zzz2059, Branch(zzz2050, zzz2051, Neg(Succ(zzz2052)), zzz2053, zzz2054), be)
new_mkVBalBranch3MkVBalBranch121(zzz473, zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, zzz481, zzz482, Succ(zzz7390), bh) → new_mkVBalBranch3MkVBalBranch115(zzz473, zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, Zero, zzz480, zzz481, zzz482, Succ(zzz7390), Succ(Zero), bh)
new_mkVBalBranch0(zzz31, Branch(zzz510, zzz511, Pos(Zero), zzz513, zzz514), Branch(zzz340, zzz341, Pos(Succ(zzz34200)), zzz343, zzz344), h) → new_mkVBalBranch0(zzz31, Branch(zzz510, zzz511, Pos(Zero), zzz513, zzz514), zzz343, h)
new_mkVBalBranch3MkVBalBranch228(zzz340, zzz341, zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, h) → new_mkVBalBranch0(zzz31, Branch(zzz510, zzz511, Neg(Succ(zzz51200)), zzz513, zzz514), zzz343, h)
new_mkVBalBranch0(zzz31, Branch(zzz510, zzz511, Pos(Succ(zzz51200)), zzz513, zzz514), Branch(zzz340, zzz341, zzz342, zzz343, zzz344), h) → new_mkVBalBranch3MkVBalBranch215(zzz340, zzz341, zzz342, zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat3(new_primPlusNat1(zzz51200), zzz51200)), zzz51200))), h)
new_mkVBalBranch3MkVBalBranch223(zzz340, zzz341, Neg(Succ(Succ(Zero))), zzz343, zzz344, zzz510, zzz511, Succ(zzz512000), zzz513, zzz514, zzz31, Succ(Succ(zzz6700)), h) → new_mkVBalBranch3MkVBalBranch224(zzz340, zzz341, Succ(Zero), zzz343, zzz344, zzz510, zzz511, zzz512000, zzz513, zzz514, zzz31, Zero, Succ(Succ(new_primPlusNat2(zzz6700, zzz512000))), h)
new_mkVBalBranch3MkVBalBranch230(zzz498, zzz499, zzz500, zzz501, zzz502, zzz503, zzz504, zzz505, zzz506, zzz507, bg) → new_mkVBalBranch3MkVBalBranch118(zzz498, zzz499, zzz500, zzz501, zzz502, zzz503, zzz504, zzz505, zzz506, zzz507, new_primPlusNat2(new_primPlusNat3(Succ(new_primPlusNat3(new_primPlusNat1(zzz500), zzz500)), Succ(zzz500)), Succ(zzz500)), bg)
new_mkVBalBranch3MkVBalBranch223(zzz340, zzz341, Neg(Succ(Succ(Zero))), zzz343, zzz344, zzz510, zzz511, Zero, zzz513, zzz514, zzz31, Succ(Zero), h) → new_mkVBalBranch3MkVBalBranch225(zzz340, zzz341, Succ(Zero), zzz343, zzz344, zzz510, zzz511, zzz513, zzz514, zzz31, Zero, Zero, h)
new_mkVBalBranch3MkVBalBranch224(zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, zzz1125, zzz1126, zzz1127, zzz1128, zzz1129, Succ(zzz11300), Succ(zzz11310), bd) → new_mkVBalBranch3MkVBalBranch224(zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, zzz1125, zzz1126, zzz1127, zzz1128, zzz1129, zzz11300, zzz11310, bd)
new_mkVBalBranch3MkVBalBranch217(zzz473, zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, zzz481, zzz482, Zero, Succ(zzz4840), bh) → new_mkVBalBranch0(zzz482, Branch(zzz478, zzz479, Pos(Succ(Zero)), zzz480, zzz481), zzz476, bh)
new_mkVBalBranch3MkVBalBranch110(zzz461, zzz462, zzz463, zzz464, zzz465, zzz466, zzz467, zzz468, zzz469, zzz470, zzz471, Succ(zzz5800), bb) → new_mkVBalBranch3MkVBalBranch115(zzz461, zzz462, zzz463, zzz464, zzz465, zzz466, zzz467, Succ(zzz468), zzz469, zzz470, zzz471, Succ(zzz5800), Succ(Succ(zzz468)), bb)
new_mkVBalBranch3MkVBalBranch223(zzz340, zzz341, Neg(Succ(Zero)), zzz343, zzz344, zzz510, zzz511, Zero, zzz513, zzz514, zzz31, Zero, h) → new_mkVBalBranch3MkVBalBranch118(zzz340, zzz341, Zero, zzz343, zzz344, zzz510, zzz511, zzz513, zzz514, zzz31, new_primPlusNat2(new_primMulNat0(Zero), Succ(Zero)), h)
new_mkVBalBranch3MkVBalBranch227(zzz486, zzz487, zzz488, zzz489, zzz490, zzz491, zzz492, zzz493, zzz494, zzz495, zzz496, bf) → new_mkVBalBranch0(zzz496, Branch(zzz491, zzz492, Neg(Succ(Succ(zzz493))), zzz494, zzz495), zzz489, bf)
new_mkVBalBranch3MkVBalBranch215(zzz340, zzz341, Pos(Zero), zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, Succ(zzz660), h) → new_mkVBalBranch0(zzz31, zzz514, Branch(zzz340, zzz341, Pos(Zero), zzz343, zzz344), h)
new_mkVBalBranch0(zzz31, Branch(zzz510, zzz511, Pos(Zero), zzz513, zzz514), Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), h) → new_mkVBalBranch3MkVBalBranch116(zzz340, zzz341, zzz34200, zzz343, zzz344, zzz510, zzz511, zzz513, zzz514, zzz31, new_primPlusNat2(new_primMulNat0(zzz34200), Succ(zzz34200)), h)
new_mkVBalBranch3MkVBalBranch217(zzz473, zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, zzz481, zzz482, Succ(zzz4830), Zero, bh) → new_mkVBalBranch3MkVBalBranch121(zzz473, zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, zzz481, zzz482, new_primPlusNat2(new_primMulNat0(zzz475), Succ(zzz475)), bh)
new_mkVBalBranch3MkVBalBranch223(zzz340, zzz341, Neg(Zero), zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, Succ(zzz670), h) → new_mkVBalBranch0(zzz31, Branch(zzz510, zzz511, Neg(Succ(zzz51200)), zzz513, zzz514), zzz343, h)
new_mkVBalBranch3MkVBalBranch216(zzz1105, zzz1106, zzz1107, zzz1108, zzz1109, zzz1110, zzz1111, zzz1112, zzz1113, zzz1114, zzz1115, Zero, Succ(zzz11170), ba) → new_mkVBalBranch0(zzz1115, Branch(zzz1110, zzz1111, Pos(Succ(Succ(zzz1112))), zzz1113, zzz1114), zzz1108, ba)
new_mkVBalBranch3MkVBalBranch115(zzz1986, zzz1987, zzz1988, zzz1989, zzz1990, zzz1991, zzz1992, zzz1993, zzz1994, zzz1995, zzz1996, Zero, Succ(zzz19980), bc) → new_mkVBalBranch0(zzz1996, zzz1995, Branch(zzz1986, zzz1987, Pos(Succ(zzz1988)), zzz1989, zzz1990), bc)
new_mkVBalBranch0(zzz31, Branch(zzz510, zzz511, Neg(Zero), zzz513, zzz514), Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), h) → new_mkVBalBranch3MkVBalBranch117(zzz340, zzz341, zzz34200, zzz343, zzz344, zzz510, zzz511, zzz513, zzz514, zzz31, new_primPlusNat2(new_primMulNat0(zzz34200), Succ(zzz34200)), h)
new_mkVBalBranch3MkVBalBranch223(zzz340, zzz341, Neg(Zero), zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, Zero, h) → new_mkVBalBranch3MkVBalBranch228(zzz340, zzz341, zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, h)
new_mkVBalBranch3MkVBalBranch122(zzz340, zzz341, zzz34200, zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, h) → new_mkVBalBranch0(zzz31, zzz514, Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), h)
new_mkVBalBranch3MkVBalBranch217(zzz473, zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, zzz481, zzz482, Succ(zzz4830), Succ(zzz4840), bh) → new_mkVBalBranch3MkVBalBranch217(zzz473, zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, zzz481, zzz482, zzz4830, zzz4840, bh)
new_mkVBalBranch3MkVBalBranch116(zzz340, zzz341, zzz34200, zzz343, zzz344, zzz510, zzz511, zzz513, zzz514, zzz31, Succ(zzz1200), h) → new_mkVBalBranch0(zzz31, zzz514, Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), h)
new_mkVBalBranch3MkVBalBranch110(zzz461, zzz462, zzz463, zzz464, zzz465, zzz466, zzz467, zzz468, zzz469, zzz470, zzz471, Zero, bb) → new_mkVBalBranch3MkVBalBranch115(zzz461, zzz462, zzz463, zzz464, zzz465, zzz466, zzz467, Succ(zzz468), zzz469, zzz470, zzz471, Zero, Succ(Succ(zzz468)), bb)
new_mkVBalBranch3MkVBalBranch225(zzz498, zzz499, zzz500, zzz501, zzz502, zzz503, zzz504, zzz505, zzz506, zzz507, Zero, Succ(zzz5090), bg) → new_mkVBalBranch0(zzz507, Branch(zzz503, zzz504, Neg(Succ(Zero)), zzz505, zzz506), zzz501, bg)
new_mkVBalBranch0(zzz31, Branch(zzz510, zzz511, Neg(Succ(zzz51200)), zzz513, zzz514), Branch(zzz340, zzz341, zzz342, zzz343, zzz344), h) → new_mkVBalBranch3MkVBalBranch223(zzz340, zzz341, zzz342, zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat3(new_primPlusNat1(zzz51200), zzz51200)), zzz51200))), h)
new_mkVBalBranch3MkVBalBranch222(zzz461, zzz462, zzz463, zzz464, zzz465, zzz466, zzz467, zzz468, zzz469, zzz470, zzz471, bb) → new_mkVBalBranch3MkVBalBranch110(zzz461, zzz462, zzz463, zzz464, zzz465, zzz466, zzz467, zzz468, zzz469, zzz470, zzz471, new_primPlusNat2(new_primPlusNat3(Succ(new_primPlusNat3(new_primPlusNat1(zzz463), zzz463)), Succ(zzz463)), Succ(zzz463)), bb)
new_mkVBalBranch3MkVBalBranch223(zzz340, zzz341, Neg(Succ(Succ(Succ(zzz3420000)))), zzz343, zzz344, zzz510, zzz511, Zero, zzz513, zzz514, zzz31, Succ(Zero), h) → new_mkVBalBranch3MkVBalBranch225(zzz340, zzz341, Succ(Succ(zzz3420000)), zzz343, zzz344, zzz510, zzz511, zzz513, zzz514, zzz31, Succ(zzz3420000), Zero, h)
new_mkVBalBranch3MkVBalBranch121(zzz473, zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, zzz481, zzz482, Zero, bh) → new_mkVBalBranch3MkVBalBranch115(zzz473, zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, Zero, zzz480, zzz481, zzz482, Zero, Succ(Zero), bh)
new_mkVBalBranch3MkVBalBranch223(zzz340, zzz341, Neg(Succ(Zero)), zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, Succ(zzz670), h) → new_mkVBalBranch0(zzz31, Branch(zzz510, zzz511, Neg(Succ(zzz51200)), zzz513, zzz514), zzz343, h)
new_mkVBalBranch3MkVBalBranch225(zzz498, zzz499, zzz500, zzz501, zzz502, zzz503, zzz504, zzz505, zzz506, zzz507, Succ(zzz5080), Zero, bg) → new_mkVBalBranch3MkVBalBranch118(zzz498, zzz499, zzz500, zzz501, zzz502, zzz503, zzz504, zzz505, zzz506, zzz507, new_primPlusNat2(new_primMulNat0(zzz500), Succ(zzz500)), bg)
new_mkVBalBranch3MkVBalBranch215(zzz340, zzz341, Pos(Succ(Zero)), zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, Succ(zzz660), h) → new_mkVBalBranch3MkVBalBranch18(zzz340, zzz341, zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, new_primPlusNat2(new_primMulNat0(Zero), Succ(Zero)), h)
new_mkVBalBranch3MkVBalBranch229(zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, zzz1125, zzz1126, zzz1127, zzz1128, zzz1129, bd) → new_mkVBalBranch3MkVBalBranch119(zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, zzz1125, zzz1126, zzz1127, zzz1128, zzz1129, new_primPlusNat2(new_primMulNat0(zzz1121), Succ(zzz1121)), bd)
new_mkVBalBranch3MkVBalBranch233(zzz473, zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, zzz481, zzz482, bh) → new_mkVBalBranch3MkVBalBranch121(zzz473, zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, zzz481, zzz482, new_primPlusNat2(new_primMulNat0(zzz475), Succ(zzz475)), bh)
new_mkVBalBranch3MkVBalBranch223(zzz340, zzz341, Neg(Succ(Zero)), zzz343, zzz344, zzz510, zzz511, Succ(zzz512000), zzz513, zzz514, zzz31, Zero, h) → new_mkVBalBranch3MkVBalBranch227(zzz340, zzz341, Zero, zzz343, zzz344, zzz510, zzz511, zzz512000, zzz513, zzz514, zzz31, h)
new_mkVBalBranch3MkVBalBranch215(zzz340, zzz341, Pos(Succ(Succ(zzz342000))), zzz343, zzz344, zzz510, zzz511, Zero, zzz513, zzz514, zzz31, Succ(Succ(zzz6600)), h) → new_mkVBalBranch3MkVBalBranch217(zzz340, zzz341, Succ(zzz342000), zzz343, zzz344, zzz510, zzz511, zzz513, zzz514, zzz31, Succ(zzz6600), zzz342000, h)
new_mkVBalBranch3MkVBalBranch223(zzz340, zzz341, Neg(Succ(Succ(zzz342000))), zzz343, zzz344, zzz510, zzz511, Succ(zzz512000), zzz513, zzz514, zzz31, Zero, h) → new_mkVBalBranch3MkVBalBranch224(zzz340, zzz341, Succ(zzz342000), zzz343, zzz344, zzz510, zzz511, zzz512000, zzz513, zzz514, zzz31, zzz342000, zzz512000, h)
new_mkVBalBranch3MkVBalBranch226(zzz340, zzz341, zzz3420, zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, h) → new_mkVBalBranch0(zzz31, Branch(zzz510, zzz511, Neg(Succ(zzz51200)), zzz513, zzz514), zzz343, h)
new_mkVBalBranch3MkVBalBranch218(zzz461, zzz462, zzz463, zzz464, zzz465, zzz466, zzz467, zzz468, zzz469, zzz470, zzz471, bb) → new_mkVBalBranch3MkVBalBranch110(zzz461, zzz462, zzz463, zzz464, zzz465, zzz466, zzz467, zzz468, zzz469, zzz470, zzz471, new_primPlusNat2(new_primMulNat0(zzz463), Succ(zzz463)), bb)
new_mkVBalBranch3MkVBalBranch117(zzz340, zzz341, zzz34200, zzz343, zzz344, zzz510, zzz511, zzz513, zzz514, zzz31, Succ(zzz1240), h) → new_mkVBalBranch0(zzz31, zzz514, Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), h)
new_mkVBalBranch3MkVBalBranch217(zzz473, zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, zzz481, zzz482, Zero, Zero, bh) → new_mkVBalBranch3MkVBalBranch233(zzz473, zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, zzz481, zzz482, bh)
new_mkVBalBranch3MkVBalBranch120(zzz2050, zzz2051, zzz2052, zzz2053, zzz2054, zzz2055, zzz2056, zzz2057, zzz2058, zzz2059, zzz2060, Succ(zzz20610), Succ(zzz20620), be) → new_mkVBalBranch3MkVBalBranch120(zzz2050, zzz2051, zzz2052, zzz2053, zzz2054, zzz2055, zzz2056, zzz2057, zzz2058, zzz2059, zzz2060, zzz20610, zzz20620, be)
new_mkVBalBranch3MkVBalBranch223(zzz340, zzz341, Pos(zzz3420), zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, Succ(zzz670), h) → new_mkVBalBranch0(zzz31, Branch(zzz510, zzz511, Neg(Succ(zzz51200)), zzz513, zzz514), zzz343, h)
new_mkVBalBranch3MkVBalBranch216(zzz1105, zzz1106, zzz1107, zzz1108, zzz1109, zzz1110, zzz1111, zzz1112, zzz1113, zzz1114, zzz1115, Succ(zzz11160), Succ(zzz11170), ba) → new_mkVBalBranch3MkVBalBranch216(zzz1105, zzz1106, zzz1107, zzz1108, zzz1109, zzz1110, zzz1111, zzz1112, zzz1113, zzz1114, zzz1115, zzz11160, zzz11170, ba)
new_mkVBalBranch3MkVBalBranch19(zzz340, zzz341, zzz34200, zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, Zero, h) → new_mkVBalBranch3MkVBalBranch122(zzz340, zzz341, zzz34200, zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, h)
new_mkVBalBranch3MkVBalBranch223(zzz340, zzz341, Neg(Succ(Succ(Succ(zzz3420000)))), zzz343, zzz344, zzz510, zzz511, Succ(zzz512000), zzz513, zzz514, zzz31, Succ(Zero), h) → new_mkVBalBranch3MkVBalBranch224(zzz340, zzz341, Succ(Succ(zzz3420000)), zzz343, zzz344, zzz510, zzz511, zzz512000, zzz513, zzz514, zzz31, Succ(zzz3420000), Succ(zzz512000), h)
new_mkVBalBranch3MkVBalBranch225(zzz498, zzz499, zzz500, zzz501, zzz502, zzz503, zzz504, zzz505, zzz506, zzz507, Succ(zzz5080), Succ(zzz5090), bg) → new_mkVBalBranch3MkVBalBranch225(zzz498, zzz499, zzz500, zzz501, zzz502, zzz503, zzz504, zzz505, zzz506, zzz507, zzz5080, zzz5090, bg)
new_mkVBalBranch3MkVBalBranch19(zzz340, zzz341, zzz34200, zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, Succ(zzz1410), h) → new_mkVBalBranch0(zzz31, zzz514, Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), h)
new_mkVBalBranch3MkVBalBranch224(zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, zzz1125, zzz1126, zzz1127, zzz1128, zzz1129, Succ(zzz11300), Zero, bd) → new_mkVBalBranch3MkVBalBranch119(zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, zzz1125, zzz1126, zzz1127, zzz1128, zzz1129, new_primPlusNat2(new_primMulNat0(zzz1121), Succ(zzz1121)), bd)
new_mkVBalBranch3MkVBalBranch224(zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, zzz1125, zzz1126, zzz1127, zzz1128, zzz1129, Zero, Zero, bd) → new_mkVBalBranch3MkVBalBranch229(zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, zzz1125, zzz1126, zzz1127, zzz1128, zzz1129, bd)
new_mkVBalBranch3MkVBalBranch224(zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, zzz1125, zzz1126, zzz1127, zzz1128, zzz1129, Zero, Succ(zzz11310), bd) → new_mkVBalBranch3MkVBalBranch227(zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, zzz1125, zzz1126, zzz1127, zzz1128, zzz1129, bd)
new_mkVBalBranch3MkVBalBranch223(zzz340, zzz341, Neg(Succ(Succ(Zero))), zzz343, zzz344, zzz510, zzz511, Succ(zzz512000), zzz513, zzz514, zzz31, Succ(Zero), h) → new_mkVBalBranch3MkVBalBranch224(zzz340, zzz341, Succ(Zero), zzz343, zzz344, zzz510, zzz511, zzz512000, zzz513, zzz514, zzz31, Zero, Succ(zzz512000), h)
new_mkVBalBranch3MkVBalBranch223(zzz340, zzz341, Pos(zzz3420), zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, Zero, h) → new_mkVBalBranch3MkVBalBranch226(zzz340, zzz341, zzz3420, zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, h)
new_mkVBalBranch3MkVBalBranch223(zzz340, zzz341, Neg(Succ(Succ(zzz342000))), zzz343, zzz344, zzz510, zzz511, Zero, zzz513, zzz514, zzz31, Zero, h) → new_mkVBalBranch3MkVBalBranch118(zzz340, zzz341, Succ(zzz342000), zzz343, zzz344, zzz510, zzz511, zzz513, zzz514, zzz31, new_primPlusNat2(new_primMulNat0(Succ(zzz342000)), Succ(Succ(zzz342000))), h)
new_mkVBalBranch3MkVBalBranch223(zzz340, zzz341, Neg(Succ(Succ(Succ(zzz3420000)))), zzz343, zzz344, zzz510, zzz511, Succ(zzz512000), zzz513, zzz514, zzz31, Succ(Succ(zzz6700)), h) → new_mkVBalBranch3MkVBalBranch224(zzz340, zzz341, Succ(Succ(zzz3420000)), zzz343, zzz344, zzz510, zzz511, zzz512000, zzz513, zzz514, zzz31, Succ(zzz3420000), Succ(Succ(new_primPlusNat2(zzz6700, zzz512000))), h)
new_mkVBalBranch3MkVBalBranch223(zzz340, zzz341, Neg(Succ(Succ(Zero))), zzz343, zzz344, zzz510, zzz511, Zero, zzz513, zzz514, zzz31, Succ(Succ(zzz6700)), h) → new_mkVBalBranch3MkVBalBranch225(zzz340, zzz341, Succ(Zero), zzz343, zzz344, zzz510, zzz511, zzz513, zzz514, zzz31, Zero, Succ(zzz6700), h)
new_mkVBalBranch3MkVBalBranch115(zzz1986, zzz1987, zzz1988, zzz1989, zzz1990, zzz1991, zzz1992, zzz1993, zzz1994, zzz1995, zzz1996, Succ(zzz19970), Succ(zzz19980), bc) → new_mkVBalBranch3MkVBalBranch115(zzz1986, zzz1987, zzz1988, zzz1989, zzz1990, zzz1991, zzz1992, zzz1993, zzz1994, zzz1995, zzz1996, zzz19970, zzz19980, bc)
new_mkVBalBranch3MkVBalBranch215(zzz340, zzz341, Neg(Zero), zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, Succ(zzz660), h) → new_mkVBalBranch0(zzz31, zzz514, Branch(zzz340, zzz341, Neg(Zero), zzz343, zzz344), h)
new_mkVBalBranch3MkVBalBranch118(zzz498, zzz499, zzz500, zzz501, zzz502, zzz503, zzz504, zzz505, zzz506, zzz507, Succ(zzz8040), bg) → new_mkVBalBranch3MkVBalBranch120(zzz498, zzz499, zzz500, zzz501, zzz502, zzz503, zzz504, Zero, zzz505, zzz506, zzz507, Succ(Zero), Succ(zzz8040), bg)
new_mkVBalBranch3MkVBalBranch216(zzz1105, zzz1106, zzz1107, zzz1108, zzz1109, zzz1110, zzz1111, zzz1112, zzz1113, zzz1114, zzz1115, Succ(zzz11160), Zero, ba) → new_mkVBalBranch3MkVBalBranch218(zzz1105, zzz1106, zzz1107, zzz1108, zzz1109, zzz1110, zzz1111, zzz1112, zzz1113, zzz1114, zzz1115, ba)
new_mkVBalBranch3MkVBalBranch215(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, Succ(zzz660), h) → new_mkVBalBranch3MkVBalBranch19(zzz340, zzz341, zzz34200, zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, new_primPlusNat2(new_primMulNat0(zzz34200), Succ(zzz34200)), h)
new_mkVBalBranch3MkVBalBranch216(zzz1105, zzz1106, zzz1107, zzz1108, zzz1109, zzz1110, zzz1111, zzz1112, zzz1113, zzz1114, zzz1115, Zero, Zero, ba) → new_mkVBalBranch3MkVBalBranch222(zzz1105, zzz1106, zzz1107, zzz1108, zzz1109, zzz1110, zzz1111, zzz1112, zzz1113, zzz1114, zzz1115, ba)
new_mkVBalBranch3MkVBalBranch18(zzz340, zzz341, zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, Zero, h) → new_mkVBalBranch3MkVBalBranch115(zzz340, zzz341, Zero, zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, Zero, Succ(zzz51200), h)
new_mkVBalBranch3MkVBalBranch119(zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, zzz1125, zzz1126, zzz1127, zzz1128, zzz1129, Succ(zzz12130), bd) → new_mkVBalBranch3MkVBalBranch120(zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, zzz1125, Succ(zzz1126), zzz1127, zzz1128, zzz1129, Succ(Succ(zzz1126)), Succ(zzz12130), bd)

The TRS R consists of the following rules:

new_primMulNat0(zzz6200) → new_primPlusNat3(Succ(new_primPlusNat3(new_primPlusNat1(zzz6200), zzz6200)), Succ(zzz6200))
new_primPlusNat2(Succ(zzz900), Succ(zzz9100)) → Succ(Succ(new_primPlusNat2(zzz900, zzz9100)))
new_primPlusNat2(Zero, Succ(zzz9100)) → Succ(zzz9100)
new_primPlusNat2(Zero, Zero) → Zero
new_primPlusNat2(Succ(zzz900), Zero) → Succ(zzz900)
new_primPlusNat1(Zero) → Zero
new_primPlusNat1(Succ(zzz62000)) → Succ(Succ(new_primPlusNat1(zzz62000)))
new_primPlusNat3(zzz90, Succ(zzz910)) → Succ(Succ(new_primPlusNat2(zzz90, zzz910)))
new_primPlusNat3(zzz90, Zero) → Succ(zzz90)

The set Q consists of the following terms:

new_primPlusNat2(Zero, Succ(x0))
new_primMulNat0(x0)
new_primPlusNat3(x0, Succ(x1))
new_primPlusNat2(Succ(x0), Succ(x1))
new_primPlusNat3(x0, Zero)
new_primPlusNat1(Zero)
new_primPlusNat2(Zero, Zero)
new_primPlusNat1(Succ(x0))
new_primPlusNat2(Succ(x0), Zero)

We have to consider all minimal (P,Q,R)-chains.
The approximation of the Dependency Graph [15,17,22] contains 1 SCC with 12 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
                                    ↳ DependencyGraphProof
                                      ↳ QDP
                                        ↳ Rewriting
                                          ↳ QDP
                                            ↳ Rewriting
                                              ↳ QDP
                                                ↳ Rewriting
                                                  ↳ QDP
                                                    ↳ Rewriting
                                                      ↳ QDP
                                                        ↳ Rewriting
                                                          ↳ QDP
                                                            ↳ Rewriting
                                                              ↳ QDP
                                                                ↳ Rewriting
                                                                  ↳ QDP
                                                                    ↳ Rewriting
                                                                      ↳ QDP
                                                                        ↳ Rewriting
                                                                          ↳ QDP
                                                                            ↳ Rewriting
                                                                              ↳ QDP
                                                                                ↳ Rewriting
                                                                                  ↳ QDP
                                                                                    ↳ Rewriting
                                                                                      ↳ QDP
                                                                                        ↳ Rewriting
                                                                                          ↳ QDP
                                                                                            ↳ Rewriting
                                                                                              ↳ QDP
                                                                                                ↳ Rewriting
                                                                                                  ↳ QDP
                                                                                                    ↳ Rewriting
                                                                                                      ↳ QDP
                                                                                                        ↳ Rewriting
                                                                                                          ↳ QDP
                                                                                                            ↳ UsableRulesProof
                                                                                                              ↳ QDP
                                                                                                                ↳ QReductionProof
                                                                                                                  ↳ QDP
                                                                                                                    ↳ Rewriting
                                                                                                                      ↳ QDP
                                                                                                                        ↳ Rewriting
                                                                                                                          ↳ QDP
                                                                                                                            ↳ DependencyGraphProof
                                                                                                                              ↳ QDP
                                                                                                                                ↳ Rewriting
                                                                                                                                  ↳ QDP
                                                                                                                                    ↳ Rewriting
                                                                                                                                      ↳ QDP
                                                                                                                                        ↳ DependencyGraphProof
                                                                                                                                          ↳ QDP
                                                                                                                                            ↳ Rewriting
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP

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

new_mkVBalBranch3MkVBalBranch225(zzz498, zzz499, zzz500, zzz501, zzz502, zzz503, zzz504, zzz505, zzz506, zzz507, Zero, Zero, bg) → new_mkVBalBranch3MkVBalBranch230(zzz498, zzz499, zzz500, zzz501, zzz502, zzz503, zzz504, zzz505, zzz506, zzz507, bg)
new_mkVBalBranch3MkVBalBranch18(zzz340, zzz341, zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, Succ(zzz1480), h) → new_mkVBalBranch3MkVBalBranch115(zzz340, zzz341, Zero, zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, Succ(zzz1480), Succ(zzz51200), h)
new_mkVBalBranch0(zzz31, Branch(zzz510, zzz511, Neg(Zero), zzz513, zzz514), Branch(zzz340, zzz341, Pos(Succ(zzz34200)), zzz343, zzz344), h) → new_mkVBalBranch0(zzz31, Branch(zzz510, zzz511, Neg(Zero), zzz513, zzz514), zzz343, h)
new_mkVBalBranch3MkVBalBranch215(zzz340, zzz341, Pos(Succ(Succ(zzz342000))), zzz343, zzz344, zzz510, zzz511, Succ(zzz512000), zzz513, zzz514, zzz31, Succ(Succ(zzz6600)), h) → new_mkVBalBranch3MkVBalBranch216(zzz340, zzz341, Succ(zzz342000), zzz343, zzz344, zzz510, zzz511, zzz512000, zzz513, zzz514, zzz31, Succ(Succ(new_primPlusNat2(zzz6600, zzz512000))), zzz342000, h)
new_mkVBalBranch3MkVBalBranch223(zzz340, zzz341, Neg(Succ(Succ(Succ(zzz3420000)))), zzz343, zzz344, zzz510, zzz511, Zero, zzz513, zzz514, zzz31, Succ(Succ(zzz6700)), h) → new_mkVBalBranch3MkVBalBranch225(zzz340, zzz341, Succ(Succ(zzz3420000)), zzz343, zzz344, zzz510, zzz511, zzz513, zzz514, zzz31, Succ(zzz3420000), Succ(zzz6700), h)
new_mkVBalBranch3MkVBalBranch120(zzz2050, zzz2051, zzz2052, zzz2053, zzz2054, zzz2055, zzz2056, zzz2057, zzz2058, zzz2059, zzz2060, Zero, Succ(zzz20620), be) → new_mkVBalBranch0(zzz2060, zzz2059, Branch(zzz2050, zzz2051, Neg(Succ(zzz2052)), zzz2053, zzz2054), be)
new_mkVBalBranch0(zzz31, Branch(zzz510, zzz511, Pos(Zero), zzz513, zzz514), Branch(zzz340, zzz341, Pos(Succ(zzz34200)), zzz343, zzz344), h) → new_mkVBalBranch0(zzz31, Branch(zzz510, zzz511, Pos(Zero), zzz513, zzz514), zzz343, h)
new_mkVBalBranch3MkVBalBranch121(zzz473, zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, zzz481, zzz482, Succ(zzz7390), bh) → new_mkVBalBranch3MkVBalBranch115(zzz473, zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, Zero, zzz480, zzz481, zzz482, Succ(zzz7390), Succ(Zero), bh)
new_mkVBalBranch0(zzz31, Branch(zzz510, zzz511, Pos(Succ(zzz51200)), zzz513, zzz514), Branch(zzz340, zzz341, zzz342, zzz343, zzz344), h) → new_mkVBalBranch3MkVBalBranch215(zzz340, zzz341, zzz342, zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat3(new_primPlusNat1(zzz51200), zzz51200)), zzz51200))), h)
new_mkVBalBranch3MkVBalBranch223(zzz340, zzz341, Neg(Succ(Succ(Zero))), zzz343, zzz344, zzz510, zzz511, Succ(zzz512000), zzz513, zzz514, zzz31, Succ(Succ(zzz6700)), h) → new_mkVBalBranch3MkVBalBranch224(zzz340, zzz341, Succ(Zero), zzz343, zzz344, zzz510, zzz511, zzz512000, zzz513, zzz514, zzz31, Zero, Succ(Succ(new_primPlusNat2(zzz6700, zzz512000))), h)
new_mkVBalBranch3MkVBalBranch230(zzz498, zzz499, zzz500, zzz501, zzz502, zzz503, zzz504, zzz505, zzz506, zzz507, bg) → new_mkVBalBranch3MkVBalBranch118(zzz498, zzz499, zzz500, zzz501, zzz502, zzz503, zzz504, zzz505, zzz506, zzz507, new_primPlusNat2(new_primPlusNat3(Succ(new_primPlusNat3(new_primPlusNat1(zzz500), zzz500)), Succ(zzz500)), Succ(zzz500)), bg)
new_mkVBalBranch3MkVBalBranch224(zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, zzz1125, zzz1126, zzz1127, zzz1128, zzz1129, Succ(zzz11300), Succ(zzz11310), bd) → new_mkVBalBranch3MkVBalBranch224(zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, zzz1125, zzz1126, zzz1127, zzz1128, zzz1129, zzz11300, zzz11310, bd)
new_mkVBalBranch3MkVBalBranch217(zzz473, zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, zzz481, zzz482, Zero, Succ(zzz4840), bh) → new_mkVBalBranch0(zzz482, Branch(zzz478, zzz479, Pos(Succ(Zero)), zzz480, zzz481), zzz476, bh)
new_mkVBalBranch3MkVBalBranch110(zzz461, zzz462, zzz463, zzz464, zzz465, zzz466, zzz467, zzz468, zzz469, zzz470, zzz471, Succ(zzz5800), bb) → new_mkVBalBranch3MkVBalBranch115(zzz461, zzz462, zzz463, zzz464, zzz465, zzz466, zzz467, Succ(zzz468), zzz469, zzz470, zzz471, Succ(zzz5800), Succ(Succ(zzz468)), bb)
new_mkVBalBranch3MkVBalBranch227(zzz486, zzz487, zzz488, zzz489, zzz490, zzz491, zzz492, zzz493, zzz494, zzz495, zzz496, bf) → new_mkVBalBranch0(zzz496, Branch(zzz491, zzz492, Neg(Succ(Succ(zzz493))), zzz494, zzz495), zzz489, bf)
new_mkVBalBranch0(zzz31, Branch(zzz510, zzz511, Pos(Zero), zzz513, zzz514), Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), h) → new_mkVBalBranch3MkVBalBranch116(zzz340, zzz341, zzz34200, zzz343, zzz344, zzz510, zzz511, zzz513, zzz514, zzz31, new_primPlusNat2(new_primMulNat0(zzz34200), Succ(zzz34200)), h)
new_mkVBalBranch3MkVBalBranch215(zzz340, zzz341, Pos(Zero), zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, Succ(zzz660), h) → new_mkVBalBranch0(zzz31, zzz514, Branch(zzz340, zzz341, Pos(Zero), zzz343, zzz344), h)
new_mkVBalBranch3MkVBalBranch217(zzz473, zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, zzz481, zzz482, Succ(zzz4830), Zero, bh) → new_mkVBalBranch3MkVBalBranch121(zzz473, zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, zzz481, zzz482, new_primPlusNat2(new_primMulNat0(zzz475), Succ(zzz475)), bh)
new_mkVBalBranch3MkVBalBranch223(zzz340, zzz341, Neg(Zero), zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, Succ(zzz670), h) → new_mkVBalBranch0(zzz31, Branch(zzz510, zzz511, Neg(Succ(zzz51200)), zzz513, zzz514), zzz343, h)
new_mkVBalBranch3MkVBalBranch216(zzz1105, zzz1106, zzz1107, zzz1108, zzz1109, zzz1110, zzz1111, zzz1112, zzz1113, zzz1114, zzz1115, Zero, Succ(zzz11170), ba) → new_mkVBalBranch0(zzz1115, Branch(zzz1110, zzz1111, Pos(Succ(Succ(zzz1112))), zzz1113, zzz1114), zzz1108, ba)
new_mkVBalBranch3MkVBalBranch115(zzz1986, zzz1987, zzz1988, zzz1989, zzz1990, zzz1991, zzz1992, zzz1993, zzz1994, zzz1995, zzz1996, Zero, Succ(zzz19980), bc) → new_mkVBalBranch0(zzz1996, zzz1995, Branch(zzz1986, zzz1987, Pos(Succ(zzz1988)), zzz1989, zzz1990), bc)
new_mkVBalBranch0(zzz31, Branch(zzz510, zzz511, Neg(Zero), zzz513, zzz514), Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), h) → new_mkVBalBranch3MkVBalBranch117(zzz340, zzz341, zzz34200, zzz343, zzz344, zzz510, zzz511, zzz513, zzz514, zzz31, new_primPlusNat2(new_primMulNat0(zzz34200), Succ(zzz34200)), h)
new_mkVBalBranch3MkVBalBranch122(zzz340, zzz341, zzz34200, zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, h) → new_mkVBalBranch0(zzz31, zzz514, Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), h)
new_mkVBalBranch3MkVBalBranch217(zzz473, zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, zzz481, zzz482, Succ(zzz4830), Succ(zzz4840), bh) → new_mkVBalBranch3MkVBalBranch217(zzz473, zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, zzz481, zzz482, zzz4830, zzz4840, bh)
new_mkVBalBranch3MkVBalBranch116(zzz340, zzz341, zzz34200, zzz343, zzz344, zzz510, zzz511, zzz513, zzz514, zzz31, Succ(zzz1200), h) → new_mkVBalBranch0(zzz31, zzz514, Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), h)
new_mkVBalBranch3MkVBalBranch110(zzz461, zzz462, zzz463, zzz464, zzz465, zzz466, zzz467, zzz468, zzz469, zzz470, zzz471, Zero, bb) → new_mkVBalBranch3MkVBalBranch115(zzz461, zzz462, zzz463, zzz464, zzz465, zzz466, zzz467, Succ(zzz468), zzz469, zzz470, zzz471, Zero, Succ(Succ(zzz468)), bb)
new_mkVBalBranch3MkVBalBranch225(zzz498, zzz499, zzz500, zzz501, zzz502, zzz503, zzz504, zzz505, zzz506, zzz507, Zero, Succ(zzz5090), bg) → new_mkVBalBranch0(zzz507, Branch(zzz503, zzz504, Neg(Succ(Zero)), zzz505, zzz506), zzz501, bg)
new_mkVBalBranch0(zzz31, Branch(zzz510, zzz511, Neg(Succ(zzz51200)), zzz513, zzz514), Branch(zzz340, zzz341, zzz342, zzz343, zzz344), h) → new_mkVBalBranch3MkVBalBranch223(zzz340, zzz341, zzz342, zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat3(new_primPlusNat1(zzz51200), zzz51200)), zzz51200))), h)
new_mkVBalBranch3MkVBalBranch222(zzz461, zzz462, zzz463, zzz464, zzz465, zzz466, zzz467, zzz468, zzz469, zzz470, zzz471, bb) → new_mkVBalBranch3MkVBalBranch110(zzz461, zzz462, zzz463, zzz464, zzz465, zzz466, zzz467, zzz468, zzz469, zzz470, zzz471, new_primPlusNat2(new_primPlusNat3(Succ(new_primPlusNat3(new_primPlusNat1(zzz463), zzz463)), Succ(zzz463)), Succ(zzz463)), bb)
new_mkVBalBranch3MkVBalBranch121(zzz473, zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, zzz481, zzz482, Zero, bh) → new_mkVBalBranch3MkVBalBranch115(zzz473, zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, Zero, zzz480, zzz481, zzz482, Zero, Succ(Zero), bh)
new_mkVBalBranch3MkVBalBranch225(zzz498, zzz499, zzz500, zzz501, zzz502, zzz503, zzz504, zzz505, zzz506, zzz507, Succ(zzz5080), Zero, bg) → new_mkVBalBranch3MkVBalBranch118(zzz498, zzz499, zzz500, zzz501, zzz502, zzz503, zzz504, zzz505, zzz506, zzz507, new_primPlusNat2(new_primMulNat0(zzz500), Succ(zzz500)), bg)
new_mkVBalBranch3MkVBalBranch223(zzz340, zzz341, Neg(Succ(Zero)), zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, Succ(zzz670), h) → new_mkVBalBranch0(zzz31, Branch(zzz510, zzz511, Neg(Succ(zzz51200)), zzz513, zzz514), zzz343, h)
new_mkVBalBranch3MkVBalBranch215(zzz340, zzz341, Pos(Succ(Zero)), zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, Succ(zzz660), h) → new_mkVBalBranch3MkVBalBranch18(zzz340, zzz341, zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, new_primPlusNat2(new_primMulNat0(Zero), Succ(Zero)), h)
new_mkVBalBranch3MkVBalBranch229(zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, zzz1125, zzz1126, zzz1127, zzz1128, zzz1129, bd) → new_mkVBalBranch3MkVBalBranch119(zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, zzz1125, zzz1126, zzz1127, zzz1128, zzz1129, new_primPlusNat2(new_primMulNat0(zzz1121), Succ(zzz1121)), bd)
new_mkVBalBranch3MkVBalBranch233(zzz473, zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, zzz481, zzz482, bh) → new_mkVBalBranch3MkVBalBranch121(zzz473, zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, zzz481, zzz482, new_primPlusNat2(new_primMulNat0(zzz475), Succ(zzz475)), bh)
new_mkVBalBranch3MkVBalBranch215(zzz340, zzz341, Pos(Succ(Succ(zzz342000))), zzz343, zzz344, zzz510, zzz511, Zero, zzz513, zzz514, zzz31, Succ(Succ(zzz6600)), h) → new_mkVBalBranch3MkVBalBranch217(zzz340, zzz341, Succ(zzz342000), zzz343, zzz344, zzz510, zzz511, zzz513, zzz514, zzz31, Succ(zzz6600), zzz342000, h)
new_mkVBalBranch3MkVBalBranch218(zzz461, zzz462, zzz463, zzz464, zzz465, zzz466, zzz467, zzz468, zzz469, zzz470, zzz471, bb) → new_mkVBalBranch3MkVBalBranch110(zzz461, zzz462, zzz463, zzz464, zzz465, zzz466, zzz467, zzz468, zzz469, zzz470, zzz471, new_primPlusNat2(new_primMulNat0(zzz463), Succ(zzz463)), bb)
new_mkVBalBranch3MkVBalBranch117(zzz340, zzz341, zzz34200, zzz343, zzz344, zzz510, zzz511, zzz513, zzz514, zzz31, Succ(zzz1240), h) → new_mkVBalBranch0(zzz31, zzz514, Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), h)
new_mkVBalBranch3MkVBalBranch120(zzz2050, zzz2051, zzz2052, zzz2053, zzz2054, zzz2055, zzz2056, zzz2057, zzz2058, zzz2059, zzz2060, Succ(zzz20610), Succ(zzz20620), be) → new_mkVBalBranch3MkVBalBranch120(zzz2050, zzz2051, zzz2052, zzz2053, zzz2054, zzz2055, zzz2056, zzz2057, zzz2058, zzz2059, zzz2060, zzz20610, zzz20620, be)
new_mkVBalBranch3MkVBalBranch217(zzz473, zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, zzz481, zzz482, Zero, Zero, bh) → new_mkVBalBranch3MkVBalBranch233(zzz473, zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, zzz481, zzz482, bh)
new_mkVBalBranch3MkVBalBranch216(zzz1105, zzz1106, zzz1107, zzz1108, zzz1109, zzz1110, zzz1111, zzz1112, zzz1113, zzz1114, zzz1115, Succ(zzz11160), Succ(zzz11170), ba) → new_mkVBalBranch3MkVBalBranch216(zzz1105, zzz1106, zzz1107, zzz1108, zzz1109, zzz1110, zzz1111, zzz1112, zzz1113, zzz1114, zzz1115, zzz11160, zzz11170, ba)
new_mkVBalBranch3MkVBalBranch223(zzz340, zzz341, Pos(zzz3420), zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, Succ(zzz670), h) → new_mkVBalBranch0(zzz31, Branch(zzz510, zzz511, Neg(Succ(zzz51200)), zzz513, zzz514), zzz343, h)
new_mkVBalBranch3MkVBalBranch19(zzz340, zzz341, zzz34200, zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, Zero, h) → new_mkVBalBranch3MkVBalBranch122(zzz340, zzz341, zzz34200, zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, h)
new_mkVBalBranch3MkVBalBranch225(zzz498, zzz499, zzz500, zzz501, zzz502, zzz503, zzz504, zzz505, zzz506, zzz507, Succ(zzz5080), Succ(zzz5090), bg) → new_mkVBalBranch3MkVBalBranch225(zzz498, zzz499, zzz500, zzz501, zzz502, zzz503, zzz504, zzz505, zzz506, zzz507, zzz5080, zzz5090, bg)
new_mkVBalBranch3MkVBalBranch19(zzz340, zzz341, zzz34200, zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, Succ(zzz1410), h) → new_mkVBalBranch0(zzz31, zzz514, Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), h)
new_mkVBalBranch3MkVBalBranch224(zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, zzz1125, zzz1126, zzz1127, zzz1128, zzz1129, Succ(zzz11300), Zero, bd) → new_mkVBalBranch3MkVBalBranch119(zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, zzz1125, zzz1126, zzz1127, zzz1128, zzz1129, new_primPlusNat2(new_primMulNat0(zzz1121), Succ(zzz1121)), bd)
new_mkVBalBranch3MkVBalBranch224(zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, zzz1125, zzz1126, zzz1127, zzz1128, zzz1129, Zero, Succ(zzz11310), bd) → new_mkVBalBranch3MkVBalBranch227(zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, zzz1125, zzz1126, zzz1127, zzz1128, zzz1129, bd)
new_mkVBalBranch3MkVBalBranch224(zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, zzz1125, zzz1126, zzz1127, zzz1128, zzz1129, Zero, Zero, bd) → new_mkVBalBranch3MkVBalBranch229(zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, zzz1125, zzz1126, zzz1127, zzz1128, zzz1129, bd)
new_mkVBalBranch3MkVBalBranch223(zzz340, zzz341, Neg(Succ(Succ(Succ(zzz3420000)))), zzz343, zzz344, zzz510, zzz511, Succ(zzz512000), zzz513, zzz514, zzz31, Succ(Succ(zzz6700)), h) → new_mkVBalBranch3MkVBalBranch224(zzz340, zzz341, Succ(Succ(zzz3420000)), zzz343, zzz344, zzz510, zzz511, zzz512000, zzz513, zzz514, zzz31, Succ(zzz3420000), Succ(Succ(new_primPlusNat2(zzz6700, zzz512000))), h)
new_mkVBalBranch3MkVBalBranch223(zzz340, zzz341, Neg(Succ(Succ(Zero))), zzz343, zzz344, zzz510, zzz511, Zero, zzz513, zzz514, zzz31, Succ(Succ(zzz6700)), h) → new_mkVBalBranch3MkVBalBranch225(zzz340, zzz341, Succ(Zero), zzz343, zzz344, zzz510, zzz511, zzz513, zzz514, zzz31, Zero, Succ(zzz6700), h)
new_mkVBalBranch3MkVBalBranch115(zzz1986, zzz1987, zzz1988, zzz1989, zzz1990, zzz1991, zzz1992, zzz1993, zzz1994, zzz1995, zzz1996, Succ(zzz19970), Succ(zzz19980), bc) → new_mkVBalBranch3MkVBalBranch115(zzz1986, zzz1987, zzz1988, zzz1989, zzz1990, zzz1991, zzz1992, zzz1993, zzz1994, zzz1995, zzz1996, zzz19970, zzz19980, bc)
new_mkVBalBranch3MkVBalBranch215(zzz340, zzz341, Neg(Zero), zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, Succ(zzz660), h) → new_mkVBalBranch0(zzz31, zzz514, Branch(zzz340, zzz341, Neg(Zero), zzz343, zzz344), h)
new_mkVBalBranch3MkVBalBranch118(zzz498, zzz499, zzz500, zzz501, zzz502, zzz503, zzz504, zzz505, zzz506, zzz507, Succ(zzz8040), bg) → new_mkVBalBranch3MkVBalBranch120(zzz498, zzz499, zzz500, zzz501, zzz502, zzz503, zzz504, Zero, zzz505, zzz506, zzz507, Succ(Zero), Succ(zzz8040), bg)
new_mkVBalBranch3MkVBalBranch216(zzz1105, zzz1106, zzz1107, zzz1108, zzz1109, zzz1110, zzz1111, zzz1112, zzz1113, zzz1114, zzz1115, Succ(zzz11160), Zero, ba) → new_mkVBalBranch3MkVBalBranch218(zzz1105, zzz1106, zzz1107, zzz1108, zzz1109, zzz1110, zzz1111, zzz1112, zzz1113, zzz1114, zzz1115, ba)
new_mkVBalBranch3MkVBalBranch215(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, Succ(zzz660), h) → new_mkVBalBranch3MkVBalBranch19(zzz340, zzz341, zzz34200, zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, new_primPlusNat2(new_primMulNat0(zzz34200), Succ(zzz34200)), h)
new_mkVBalBranch3MkVBalBranch216(zzz1105, zzz1106, zzz1107, zzz1108, zzz1109, zzz1110, zzz1111, zzz1112, zzz1113, zzz1114, zzz1115, Zero, Zero, ba) → new_mkVBalBranch3MkVBalBranch222(zzz1105, zzz1106, zzz1107, zzz1108, zzz1109, zzz1110, zzz1111, zzz1112, zzz1113, zzz1114, zzz1115, ba)
new_mkVBalBranch3MkVBalBranch18(zzz340, zzz341, zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, Zero, h) → new_mkVBalBranch3MkVBalBranch115(zzz340, zzz341, Zero, zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, Zero, Succ(zzz51200), h)
new_mkVBalBranch3MkVBalBranch119(zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, zzz1125, zzz1126, zzz1127, zzz1128, zzz1129, Succ(zzz12130), bd) → new_mkVBalBranch3MkVBalBranch120(zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, zzz1125, Succ(zzz1126), zzz1127, zzz1128, zzz1129, Succ(Succ(zzz1126)), Succ(zzz12130), bd)

The TRS R consists of the following rules:

new_primMulNat0(zzz6200) → new_primPlusNat3(Succ(new_primPlusNat3(new_primPlusNat1(zzz6200), zzz6200)), Succ(zzz6200))
new_primPlusNat2(Succ(zzz900), Succ(zzz9100)) → Succ(Succ(new_primPlusNat2(zzz900, zzz9100)))
new_primPlusNat2(Zero, Succ(zzz9100)) → Succ(zzz9100)
new_primPlusNat2(Zero, Zero) → Zero
new_primPlusNat2(Succ(zzz900), Zero) → Succ(zzz900)
new_primPlusNat1(Zero) → Zero
new_primPlusNat1(Succ(zzz62000)) → Succ(Succ(new_primPlusNat1(zzz62000)))
new_primPlusNat3(zzz90, Succ(zzz910)) → Succ(Succ(new_primPlusNat2(zzz90, zzz910)))
new_primPlusNat3(zzz90, Zero) → Succ(zzz90)

The set Q consists of the following terms:

new_primPlusNat2(Zero, Succ(x0))
new_primMulNat0(x0)
new_primPlusNat3(x0, Succ(x1))
new_primPlusNat2(Succ(x0), Succ(x1))
new_primPlusNat3(x0, Zero)
new_primPlusNat1(Zero)
new_primPlusNat2(Zero, Zero)
new_primPlusNat1(Succ(x0))
new_primPlusNat2(Succ(x0), Zero)

We have to consider all minimal (P,Q,R)-chains.
By rewriting [15] the rule new_mkVBalBranch0(zzz31, Branch(zzz510, zzz511, Neg(Zero), zzz513, zzz514), Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), h) → new_mkVBalBranch3MkVBalBranch117(zzz340, zzz341, zzz34200, zzz343, zzz344, zzz510, zzz511, zzz513, zzz514, zzz31, new_primPlusNat2(new_primMulNat0(zzz34200), Succ(zzz34200)), h) at position [10,0] we obtained the following new rules:

new_mkVBalBranch0(zzz31, Branch(zzz510, zzz511, Neg(Zero), zzz513, zzz514), Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), h) → new_mkVBalBranch3MkVBalBranch117(zzz340, zzz341, zzz34200, zzz343, zzz344, zzz510, zzz511, zzz513, zzz514, zzz31, new_primPlusNat2(new_primPlusNat3(Succ(new_primPlusNat3(new_primPlusNat1(zzz34200), zzz34200)), Succ(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
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                    ↳ DependencyGraphProof
                                      ↳ QDP
                                        ↳ Rewriting
                                          ↳ QDP
                                            ↳ Rewriting
                                              ↳ QDP
                                                ↳ Rewriting
                                                  ↳ QDP
                                                    ↳ Rewriting
                                                      ↳ QDP
                                                        ↳ Rewriting
                                                          ↳ QDP
                                                            ↳ Rewriting
                                                              ↳ QDP
                                                                ↳ Rewriting
                                                                  ↳ QDP
                                                                    ↳ Rewriting
                                                                      ↳ QDP
                                                                        ↳ Rewriting
                                                                          ↳ QDP
                                                                            ↳ Rewriting
                                                                              ↳ QDP
                                                                                ↳ Rewriting
                                                                                  ↳ QDP
                                                                                    ↳ Rewriting
                                                                                      ↳ QDP
                                                                                        ↳ Rewriting
                                                                                          ↳ QDP
                                                                                            ↳ Rewriting
                                                                                              ↳ QDP
                                                                                                ↳ Rewriting
                                                                                                  ↳ QDP
                                                                                                    ↳ Rewriting
                                                                                                      ↳ QDP
                                                                                                        ↳ Rewriting
                                                                                                          ↳ QDP
                                                                                                            ↳ UsableRulesProof
                                                                                                              ↳ QDP
                                                                                                                ↳ QReductionProof
                                                                                                                  ↳ QDP
                                                                                                                    ↳ Rewriting
                                                                                                                      ↳ QDP
                                                                                                                        ↳ Rewriting
                                                                                                                          ↳ QDP
                                                                                                                            ↳ DependencyGraphProof
                                                                                                                              ↳ QDP
                                                                                                                                ↳ Rewriting
                                                                                                                                  ↳ QDP
                                                                                                                                    ↳ Rewriting
                                                                                                                                      ↳ QDP
                                                                                                                                        ↳ DependencyGraphProof
                                                                                                                                          ↳ QDP
                                                                                                                                            ↳ Rewriting
                                                                                                                                              ↳ QDP
                                                                                                                                                ↳ Rewriting
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP

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

new_mkVBalBranch3MkVBalBranch225(zzz498, zzz499, zzz500, zzz501, zzz502, zzz503, zzz504, zzz505, zzz506, zzz507, Zero, Zero, bg) → new_mkVBalBranch3MkVBalBranch230(zzz498, zzz499, zzz500, zzz501, zzz502, zzz503, zzz504, zzz505, zzz506, zzz507, bg)
new_mkVBalBranch3MkVBalBranch18(zzz340, zzz341, zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, Succ(zzz1480), h) → new_mkVBalBranch3MkVBalBranch115(zzz340, zzz341, Zero, zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, Succ(zzz1480), Succ(zzz51200), h)
new_mkVBalBranch3MkVBalBranch215(zzz340, zzz341, Pos(Succ(Succ(zzz342000))), zzz343, zzz344, zzz510, zzz511, Succ(zzz512000), zzz513, zzz514, zzz31, Succ(Succ(zzz6600)), h) → new_mkVBalBranch3MkVBalBranch216(zzz340, zzz341, Succ(zzz342000), zzz343, zzz344, zzz510, zzz511, zzz512000, zzz513, zzz514, zzz31, Succ(Succ(new_primPlusNat2(zzz6600, zzz512000))), zzz342000, h)
new_mkVBalBranch0(zzz31, Branch(zzz510, zzz511, Neg(Zero), zzz513, zzz514), Branch(zzz340, zzz341, Pos(Succ(zzz34200)), zzz343, zzz344), h) → new_mkVBalBranch0(zzz31, Branch(zzz510, zzz511, Neg(Zero), zzz513, zzz514), zzz343, h)
new_mkVBalBranch3MkVBalBranch223(zzz340, zzz341, Neg(Succ(Succ(Succ(zzz3420000)))), zzz343, zzz344, zzz510, zzz511, Zero, zzz513, zzz514, zzz31, Succ(Succ(zzz6700)), h) → new_mkVBalBranch3MkVBalBranch225(zzz340, zzz341, Succ(Succ(zzz3420000)), zzz343, zzz344, zzz510, zzz511, zzz513, zzz514, zzz31, Succ(zzz3420000), Succ(zzz6700), h)
new_mkVBalBranch3MkVBalBranch120(zzz2050, zzz2051, zzz2052, zzz2053, zzz2054, zzz2055, zzz2056, zzz2057, zzz2058, zzz2059, zzz2060, Zero, Succ(zzz20620), be) → new_mkVBalBranch0(zzz2060, zzz2059, Branch(zzz2050, zzz2051, Neg(Succ(zzz2052)), zzz2053, zzz2054), be)
new_mkVBalBranch3MkVBalBranch121(zzz473, zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, zzz481, zzz482, Succ(zzz7390), bh) → new_mkVBalBranch3MkVBalBranch115(zzz473, zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, Zero, zzz480, zzz481, zzz482, Succ(zzz7390), Succ(Zero), bh)
new_mkVBalBranch0(zzz31, Branch(zzz510, zzz511, Pos(Zero), zzz513, zzz514), Branch(zzz340, zzz341, Pos(Succ(zzz34200)), zzz343, zzz344), h) → new_mkVBalBranch0(zzz31, Branch(zzz510, zzz511, Pos(Zero), zzz513, zzz514), zzz343, h)
new_mkVBalBranch0(zzz31, Branch(zzz510, zzz511, Pos(Succ(zzz51200)), zzz513, zzz514), Branch(zzz340, zzz341, zzz342, zzz343, zzz344), h) → new_mkVBalBranch3MkVBalBranch215(zzz340, zzz341, zzz342, zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat3(new_primPlusNat1(zzz51200), zzz51200)), zzz51200))), h)
new_mkVBalBranch3MkVBalBranch223(zzz340, zzz341, Neg(Succ(Succ(Zero))), zzz343, zzz344, zzz510, zzz511, Succ(zzz512000), zzz513, zzz514, zzz31, Succ(Succ(zzz6700)), h) → new_mkVBalBranch3MkVBalBranch224(zzz340, zzz341, Succ(Zero), zzz343, zzz344, zzz510, zzz511, zzz512000, zzz513, zzz514, zzz31, Zero, Succ(Succ(new_primPlusNat2(zzz6700, zzz512000))), h)
new_mkVBalBranch3MkVBalBranch230(zzz498, zzz499, zzz500, zzz501, zzz502, zzz503, zzz504, zzz505, zzz506, zzz507, bg) → new_mkVBalBranch3MkVBalBranch118(zzz498, zzz499, zzz500, zzz501, zzz502, zzz503, zzz504, zzz505, zzz506, zzz507, new_primPlusNat2(new_primPlusNat3(Succ(new_primPlusNat3(new_primPlusNat1(zzz500), zzz500)), Succ(zzz500)), Succ(zzz500)), bg)
new_mkVBalBranch3MkVBalBranch224(zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, zzz1125, zzz1126, zzz1127, zzz1128, zzz1129, Succ(zzz11300), Succ(zzz11310), bd) → new_mkVBalBranch3MkVBalBranch224(zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, zzz1125, zzz1126, zzz1127, zzz1128, zzz1129, zzz11300, zzz11310, bd)
new_mkVBalBranch3MkVBalBranch217(zzz473, zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, zzz481, zzz482, Zero, Succ(zzz4840), bh) → new_mkVBalBranch0(zzz482, Branch(zzz478, zzz479, Pos(Succ(Zero)), zzz480, zzz481), zzz476, bh)
new_mkVBalBranch3MkVBalBranch110(zzz461, zzz462, zzz463, zzz464, zzz465, zzz466, zzz467, zzz468, zzz469, zzz470, zzz471, Succ(zzz5800), bb) → new_mkVBalBranch3MkVBalBranch115(zzz461, zzz462, zzz463, zzz464, zzz465, zzz466, zzz467, Succ(zzz468), zzz469, zzz470, zzz471, Succ(zzz5800), Succ(Succ(zzz468)), bb)
new_mkVBalBranch3MkVBalBranch227(zzz486, zzz487, zzz488, zzz489, zzz490, zzz491, zzz492, zzz493, zzz494, zzz495, zzz496, bf) → new_mkVBalBranch0(zzz496, Branch(zzz491, zzz492, Neg(Succ(Succ(zzz493))), zzz494, zzz495), zzz489, bf)
new_mkVBalBranch3MkVBalBranch215(zzz340, zzz341, Pos(Zero), zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, Succ(zzz660), h) → new_mkVBalBranch0(zzz31, zzz514, Branch(zzz340, zzz341, Pos(Zero), zzz343, zzz344), h)
new_mkVBalBranch0(zzz31, Branch(zzz510, zzz511, Pos(Zero), zzz513, zzz514), Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), h) → new_mkVBalBranch3MkVBalBranch116(zzz340, zzz341, zzz34200, zzz343, zzz344, zzz510, zzz511, zzz513, zzz514, zzz31, new_primPlusNat2(new_primMulNat0(zzz34200), Succ(zzz34200)), h)
new_mkVBalBranch3MkVBalBranch223(zzz340, zzz341, Neg(Zero), zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, Succ(zzz670), h) → new_mkVBalBranch0(zzz31, Branch(zzz510, zzz511, Neg(Succ(zzz51200)), zzz513, zzz514), zzz343, h)
new_mkVBalBranch3MkVBalBranch217(zzz473, zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, zzz481, zzz482, Succ(zzz4830), Zero, bh) → new_mkVBalBranch3MkVBalBranch121(zzz473, zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, zzz481, zzz482, new_primPlusNat2(new_primMulNat0(zzz475), Succ(zzz475)), bh)
new_mkVBalBranch3MkVBalBranch216(zzz1105, zzz1106, zzz1107, zzz1108, zzz1109, zzz1110, zzz1111, zzz1112, zzz1113, zzz1114, zzz1115, Zero, Succ(zzz11170), ba) → new_mkVBalBranch0(zzz1115, Branch(zzz1110, zzz1111, Pos(Succ(Succ(zzz1112))), zzz1113, zzz1114), zzz1108, ba)
new_mkVBalBranch3MkVBalBranch115(zzz1986, zzz1987, zzz1988, zzz1989, zzz1990, zzz1991, zzz1992, zzz1993, zzz1994, zzz1995, zzz1996, Zero, Succ(zzz19980), bc) → new_mkVBalBranch0(zzz1996, zzz1995, Branch(zzz1986, zzz1987, Pos(Succ(zzz1988)), zzz1989, zzz1990), bc)
new_mkVBalBranch3MkVBalBranch122(zzz340, zzz341, zzz34200, zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, h) → new_mkVBalBranch0(zzz31, zzz514, Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), h)
new_mkVBalBranch3MkVBalBranch217(zzz473, zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, zzz481, zzz482, Succ(zzz4830), Succ(zzz4840), bh) → new_mkVBalBranch3MkVBalBranch217(zzz473, zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, zzz481, zzz482, zzz4830, zzz4840, bh)
new_mkVBalBranch3MkVBalBranch116(zzz340, zzz341, zzz34200, zzz343, zzz344, zzz510, zzz511, zzz513, zzz514, zzz31, Succ(zzz1200), h) → new_mkVBalBranch0(zzz31, zzz514, Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), h)
new_mkVBalBranch3MkVBalBranch110(zzz461, zzz462, zzz463, zzz464, zzz465, zzz466, zzz467, zzz468, zzz469, zzz470, zzz471, Zero, bb) → new_mkVBalBranch3MkVBalBranch115(zzz461, zzz462, zzz463, zzz464, zzz465, zzz466, zzz467, Succ(zzz468), zzz469, zzz470, zzz471, Zero, Succ(Succ(zzz468)), bb)
new_mkVBalBranch3MkVBalBranch225(zzz498, zzz499, zzz500, zzz501, zzz502, zzz503, zzz504, zzz505, zzz506, zzz507, Zero, Succ(zzz5090), bg) → new_mkVBalBranch0(zzz507, Branch(zzz503, zzz504, Neg(Succ(Zero)), zzz505, zzz506), zzz501, bg)
new_mkVBalBranch0(zzz31, Branch(zzz510, zzz511, Neg(Succ(zzz51200)), zzz513, zzz514), Branch(zzz340, zzz341, zzz342, zzz343, zzz344), h) → new_mkVBalBranch3MkVBalBranch223(zzz340, zzz341, zzz342, zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat3(new_primPlusNat1(zzz51200), zzz51200)), zzz51200))), h)
new_mkVBalBranch3MkVBalBranch222(zzz461, zzz462, zzz463, zzz464, zzz465, zzz466, zzz467, zzz468, zzz469, zzz470, zzz471, bb) → new_mkVBalBranch3MkVBalBranch110(zzz461, zzz462, zzz463, zzz464, zzz465, zzz466, zzz467, zzz468, zzz469, zzz470, zzz471, new_primPlusNat2(new_primPlusNat3(Succ(new_primPlusNat3(new_primPlusNat1(zzz463), zzz463)), Succ(zzz463)), Succ(zzz463)), bb)
new_mkVBalBranch0(zzz31, Branch(zzz510, zzz511, Neg(Zero), zzz513, zzz514), Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), h) → new_mkVBalBranch3MkVBalBranch117(zzz340, zzz341, zzz34200, zzz343, zzz344, zzz510, zzz511, zzz513, zzz514, zzz31, new_primPlusNat2(new_primPlusNat3(Succ(new_primPlusNat3(new_primPlusNat1(zzz34200), zzz34200)), Succ(zzz34200)), Succ(zzz34200)), h)
new_mkVBalBranch3MkVBalBranch121(zzz473, zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, zzz481, zzz482, Zero, bh) → new_mkVBalBranch3MkVBalBranch115(zzz473, zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, Zero, zzz480, zzz481, zzz482, Zero, Succ(Zero), bh)
new_mkVBalBranch3MkVBalBranch223(zzz340, zzz341, Neg(Succ(Zero)), zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, Succ(zzz670), h) → new_mkVBalBranch0(zzz31, Branch(zzz510, zzz511, Neg(Succ(zzz51200)), zzz513, zzz514), zzz343, h)
new_mkVBalBranch3MkVBalBranch225(zzz498, zzz499, zzz500, zzz501, zzz502, zzz503, zzz504, zzz505, zzz506, zzz507, Succ(zzz5080), Zero, bg) → new_mkVBalBranch3MkVBalBranch118(zzz498, zzz499, zzz500, zzz501, zzz502, zzz503, zzz504, zzz505, zzz506, zzz507, new_primPlusNat2(new_primMulNat0(zzz500), Succ(zzz500)), bg)
new_mkVBalBranch3MkVBalBranch215(zzz340, zzz341, Pos(Succ(Zero)), zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, Succ(zzz660), h) → new_mkVBalBranch3MkVBalBranch18(zzz340, zzz341, zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, new_primPlusNat2(new_primMulNat0(Zero), Succ(Zero)), h)
new_mkVBalBranch3MkVBalBranch229(zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, zzz1125, zzz1126, zzz1127, zzz1128, zzz1129, bd) → new_mkVBalBranch3MkVBalBranch119(zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, zzz1125, zzz1126, zzz1127, zzz1128, zzz1129, new_primPlusNat2(new_primMulNat0(zzz1121), Succ(zzz1121)), bd)
new_mkVBalBranch3MkVBalBranch233(zzz473, zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, zzz481, zzz482, bh) → new_mkVBalBranch3MkVBalBranch121(zzz473, zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, zzz481, zzz482, new_primPlusNat2(new_primMulNat0(zzz475), Succ(zzz475)), bh)
new_mkVBalBranch3MkVBalBranch215(zzz340, zzz341, Pos(Succ(Succ(zzz342000))), zzz343, zzz344, zzz510, zzz511, Zero, zzz513, zzz514, zzz31, Succ(Succ(zzz6600)), h) → new_mkVBalBranch3MkVBalBranch217(zzz340, zzz341, Succ(zzz342000), zzz343, zzz344, zzz510, zzz511, zzz513, zzz514, zzz31, Succ(zzz6600), zzz342000, h)
new_mkVBalBranch3MkVBalBranch218(zzz461, zzz462, zzz463, zzz464, zzz465, zzz466, zzz467, zzz468, zzz469, zzz470, zzz471, bb) → new_mkVBalBranch3MkVBalBranch110(zzz461, zzz462, zzz463, zzz464, zzz465, zzz466, zzz467, zzz468, zzz469, zzz470, zzz471, new_primPlusNat2(new_primMulNat0(zzz463), Succ(zzz463)), bb)
new_mkVBalBranch3MkVBalBranch117(zzz340, zzz341, zzz34200, zzz343, zzz344, zzz510, zzz511, zzz513, zzz514, zzz31, Succ(zzz1240), h) → new_mkVBalBranch0(zzz31, zzz514, Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), h)
new_mkVBalBranch3MkVBalBranch217(zzz473, zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, zzz481, zzz482, Zero, Zero, bh) → new_mkVBalBranch3MkVBalBranch233(zzz473, zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, zzz481, zzz482, bh)
new_mkVBalBranch3MkVBalBranch120(zzz2050, zzz2051, zzz2052, zzz2053, zzz2054, zzz2055, zzz2056, zzz2057, zzz2058, zzz2059, zzz2060, Succ(zzz20610), Succ(zzz20620), be) → new_mkVBalBranch3MkVBalBranch120(zzz2050, zzz2051, zzz2052, zzz2053, zzz2054, zzz2055, zzz2056, zzz2057, zzz2058, zzz2059, zzz2060, zzz20610, zzz20620, be)
new_mkVBalBranch3MkVBalBranch223(zzz340, zzz341, Pos(zzz3420), zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, Succ(zzz670), h) → new_mkVBalBranch0(zzz31, Branch(zzz510, zzz511, Neg(Succ(zzz51200)), zzz513, zzz514), zzz343, h)
new_mkVBalBranch3MkVBalBranch216(zzz1105, zzz1106, zzz1107, zzz1108, zzz1109, zzz1110, zzz1111, zzz1112, zzz1113, zzz1114, zzz1115, Succ(zzz11160), Succ(zzz11170), ba) → new_mkVBalBranch3MkVBalBranch216(zzz1105, zzz1106, zzz1107, zzz1108, zzz1109, zzz1110, zzz1111, zzz1112, zzz1113, zzz1114, zzz1115, zzz11160, zzz11170, ba)
new_mkVBalBranch3MkVBalBranch19(zzz340, zzz341, zzz34200, zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, Zero, h) → new_mkVBalBranch3MkVBalBranch122(zzz340, zzz341, zzz34200, zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, h)
new_mkVBalBranch3MkVBalBranch225(zzz498, zzz499, zzz500, zzz501, zzz502, zzz503, zzz504, zzz505, zzz506, zzz507, Succ(zzz5080), Succ(zzz5090), bg) → new_mkVBalBranch3MkVBalBranch225(zzz498, zzz499, zzz500, zzz501, zzz502, zzz503, zzz504, zzz505, zzz506, zzz507, zzz5080, zzz5090, bg)
new_mkVBalBranch3MkVBalBranch19(zzz340, zzz341, zzz34200, zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, Succ(zzz1410), h) → new_mkVBalBranch0(zzz31, zzz514, Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), h)
new_mkVBalBranch3MkVBalBranch224(zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, zzz1125, zzz1126, zzz1127, zzz1128, zzz1129, Succ(zzz11300), Zero, bd) → new_mkVBalBranch3MkVBalBranch119(zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, zzz1125, zzz1126, zzz1127, zzz1128, zzz1129, new_primPlusNat2(new_primMulNat0(zzz1121), Succ(zzz1121)), bd)
new_mkVBalBranch3MkVBalBranch224(zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, zzz1125, zzz1126, zzz1127, zzz1128, zzz1129, Zero, Zero, bd) → new_mkVBalBranch3MkVBalBranch229(zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, zzz1125, zzz1126, zzz1127, zzz1128, zzz1129, bd)
new_mkVBalBranch3MkVBalBranch224(zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, zzz1125, zzz1126, zzz1127, zzz1128, zzz1129, Zero, Succ(zzz11310), bd) → new_mkVBalBranch3MkVBalBranch227(zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, zzz1125, zzz1126, zzz1127, zzz1128, zzz1129, bd)
new_mkVBalBranch3MkVBalBranch223(zzz340, zzz341, Neg(Succ(Succ(Zero))), zzz343, zzz344, zzz510, zzz511, Zero, zzz513, zzz514, zzz31, Succ(Succ(zzz6700)), h) → new_mkVBalBranch3MkVBalBranch225(zzz340, zzz341, Succ(Zero), zzz343, zzz344, zzz510, zzz511, zzz513, zzz514, zzz31, Zero, Succ(zzz6700), h)
new_mkVBalBranch3MkVBalBranch223(zzz340, zzz341, Neg(Succ(Succ(Succ(zzz3420000)))), zzz343, zzz344, zzz510, zzz511, Succ(zzz512000), zzz513, zzz514, zzz31, Succ(Succ(zzz6700)), h) → new_mkVBalBranch3MkVBalBranch224(zzz340, zzz341, Succ(Succ(zzz3420000)), zzz343, zzz344, zzz510, zzz511, zzz512000, zzz513, zzz514, zzz31, Succ(zzz3420000), Succ(Succ(new_primPlusNat2(zzz6700, zzz512000))), h)
new_mkVBalBranch3MkVBalBranch115(zzz1986, zzz1987, zzz1988, zzz1989, zzz1990, zzz1991, zzz1992, zzz1993, zzz1994, zzz1995, zzz1996, Succ(zzz19970), Succ(zzz19980), bc) → new_mkVBalBranch3MkVBalBranch115(zzz1986, zzz1987, zzz1988, zzz1989, zzz1990, zzz1991, zzz1992, zzz1993, zzz1994, zzz1995, zzz1996, zzz19970, zzz19980, bc)
new_mkVBalBranch3MkVBalBranch215(zzz340, zzz341, Neg(Zero), zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, Succ(zzz660), h) → new_mkVBalBranch0(zzz31, zzz514, Branch(zzz340, zzz341, Neg(Zero), zzz343, zzz344), h)
new_mkVBalBranch3MkVBalBranch118(zzz498, zzz499, zzz500, zzz501, zzz502, zzz503, zzz504, zzz505, zzz506, zzz507, Succ(zzz8040), bg) → new_mkVBalBranch3MkVBalBranch120(zzz498, zzz499, zzz500, zzz501, zzz502, zzz503, zzz504, Zero, zzz505, zzz506, zzz507, Succ(Zero), Succ(zzz8040), bg)
new_mkVBalBranch3MkVBalBranch216(zzz1105, zzz1106, zzz1107, zzz1108, zzz1109, zzz1110, zzz1111, zzz1112, zzz1113, zzz1114, zzz1115, Succ(zzz11160), Zero, ba) → new_mkVBalBranch3MkVBalBranch218(zzz1105, zzz1106, zzz1107, zzz1108, zzz1109, zzz1110, zzz1111, zzz1112, zzz1113, zzz1114, zzz1115, ba)
new_mkVBalBranch3MkVBalBranch215(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, Succ(zzz660), h) → new_mkVBalBranch3MkVBalBranch19(zzz340, zzz341, zzz34200, zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, new_primPlusNat2(new_primMulNat0(zzz34200), Succ(zzz34200)), h)
new_mkVBalBranch3MkVBalBranch216(zzz1105, zzz1106, zzz1107, zzz1108, zzz1109, zzz1110, zzz1111, zzz1112, zzz1113, zzz1114, zzz1115, Zero, Zero, ba) → new_mkVBalBranch3MkVBalBranch222(zzz1105, zzz1106, zzz1107, zzz1108, zzz1109, zzz1110, zzz1111, zzz1112, zzz1113, zzz1114, zzz1115, ba)
new_mkVBalBranch3MkVBalBranch119(zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, zzz1125, zzz1126, zzz1127, zzz1128, zzz1129, Succ(zzz12130), bd) → new_mkVBalBranch3MkVBalBranch120(zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, zzz1125, Succ(zzz1126), zzz1127, zzz1128, zzz1129, Succ(Succ(zzz1126)), Succ(zzz12130), bd)
new_mkVBalBranch3MkVBalBranch18(zzz340, zzz341, zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, Zero, h) → new_mkVBalBranch3MkVBalBranch115(zzz340, zzz341, Zero, zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, Zero, Succ(zzz51200), h)

The TRS R consists of the following rules:

new_primMulNat0(zzz6200) → new_primPlusNat3(Succ(new_primPlusNat3(new_primPlusNat1(zzz6200), zzz6200)), Succ(zzz6200))
new_primPlusNat2(Succ(zzz900), Succ(zzz9100)) → Succ(Succ(new_primPlusNat2(zzz900, zzz9100)))
new_primPlusNat2(Zero, Succ(zzz9100)) → Succ(zzz9100)
new_primPlusNat2(Zero, Zero) → Zero
new_primPlusNat2(Succ(zzz900), Zero) → Succ(zzz900)
new_primPlusNat1(Zero) → Zero
new_primPlusNat1(Succ(zzz62000)) → Succ(Succ(new_primPlusNat1(zzz62000)))
new_primPlusNat3(zzz90, Succ(zzz910)) → Succ(Succ(new_primPlusNat2(zzz90, zzz910)))
new_primPlusNat3(zzz90, Zero) → Succ(zzz90)

The set Q consists of the following terms:

new_primPlusNat2(Zero, Succ(x0))
new_primMulNat0(x0)
new_primPlusNat3(x0, Succ(x1))
new_primPlusNat2(Succ(x0), Succ(x1))
new_primPlusNat3(x0, Zero)
new_primPlusNat1(Zero)
new_primPlusNat2(Zero, Zero)
new_primPlusNat1(Succ(x0))
new_primPlusNat2(Succ(x0), Zero)

We have to consider all minimal (P,Q,R)-chains.
By rewriting [15] the rule new_mkVBalBranch0(zzz31, Branch(zzz510, zzz511, Pos(Zero), zzz513, zzz514), Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), h) → new_mkVBalBranch3MkVBalBranch116(zzz340, zzz341, zzz34200, zzz343, zzz344, zzz510, zzz511, zzz513, zzz514, zzz31, new_primPlusNat2(new_primMulNat0(zzz34200), Succ(zzz34200)), h) at position [10,0] we obtained the following new rules:

new_mkVBalBranch0(zzz31, Branch(zzz510, zzz511, Pos(Zero), zzz513, zzz514), Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), h) → new_mkVBalBranch3MkVBalBranch116(zzz340, zzz341, zzz34200, zzz343, zzz344, zzz510, zzz511, zzz513, zzz514, zzz31, new_primPlusNat2(new_primPlusNat3(Succ(new_primPlusNat3(new_primPlusNat1(zzz34200), zzz34200)), Succ(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
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                    ↳ DependencyGraphProof
                                      ↳ QDP
                                        ↳ Rewriting
                                          ↳ QDP
                                            ↳ Rewriting
                                              ↳ QDP
                                                ↳ Rewriting
                                                  ↳ QDP
                                                    ↳ Rewriting
                                                      ↳ QDP
                                                        ↳ Rewriting
                                                          ↳ QDP
                                                            ↳ Rewriting
                                                              ↳ QDP
                                                                ↳ Rewriting
                                                                  ↳ QDP
                                                                    ↳ Rewriting
                                                                      ↳ QDP
                                                                        ↳ Rewriting
                                                                          ↳ QDP
                                                                            ↳ Rewriting
                                                                              ↳ QDP
                                                                                ↳ Rewriting
                                                                                  ↳ QDP
                                                                                    ↳ Rewriting
                                                                                      ↳ QDP
                                                                                        ↳ Rewriting
                                                                                          ↳ QDP
                                                                                            ↳ Rewriting
                                                                                              ↳ QDP
                                                                                                ↳ Rewriting
                                                                                                  ↳ QDP
                                                                                                    ↳ Rewriting
                                                                                                      ↳ QDP
                                                                                                        ↳ Rewriting
                                                                                                          ↳ QDP
                                                                                                            ↳ UsableRulesProof
                                                                                                              ↳ QDP
                                                                                                                ↳ QReductionProof
                                                                                                                  ↳ QDP
                                                                                                                    ↳ Rewriting
                                                                                                                      ↳ QDP
                                                                                                                        ↳ Rewriting
                                                                                                                          ↳ QDP
                                                                                                                            ↳ DependencyGraphProof
                                                                                                                              ↳ QDP
                                                                                                                                ↳ Rewriting
                                                                                                                                  ↳ QDP
                                                                                                                                    ↳ Rewriting
                                                                                                                                      ↳ QDP
                                                                                                                                        ↳ DependencyGraphProof
                                                                                                                                          ↳ QDP
                                                                                                                                            ↳ Rewriting
                                                                                                                                              ↳ QDP
                                                                                                                                                ↳ Rewriting
                                                                                                                                                  ↳ QDP
                                                                                                                                                    ↳ Rewriting
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP

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

new_mkVBalBranch3MkVBalBranch225(zzz498, zzz499, zzz500, zzz501, zzz502, zzz503, zzz504, zzz505, zzz506, zzz507, Zero, Zero, bg) → new_mkVBalBranch3MkVBalBranch230(zzz498, zzz499, zzz500, zzz501, zzz502, zzz503, zzz504, zzz505, zzz506, zzz507, bg)
new_mkVBalBranch3MkVBalBranch18(zzz340, zzz341, zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, Succ(zzz1480), h) → new_mkVBalBranch3MkVBalBranch115(zzz340, zzz341, Zero, zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, Succ(zzz1480), Succ(zzz51200), h)
new_mkVBalBranch0(zzz31, Branch(zzz510, zzz511, Neg(Zero), zzz513, zzz514), Branch(zzz340, zzz341, Pos(Succ(zzz34200)), zzz343, zzz344), h) → new_mkVBalBranch0(zzz31, Branch(zzz510, zzz511, Neg(Zero), zzz513, zzz514), zzz343, h)
new_mkVBalBranch3MkVBalBranch215(zzz340, zzz341, Pos(Succ(Succ(zzz342000))), zzz343, zzz344, zzz510, zzz511, Succ(zzz512000), zzz513, zzz514, zzz31, Succ(Succ(zzz6600)), h) → new_mkVBalBranch3MkVBalBranch216(zzz340, zzz341, Succ(zzz342000), zzz343, zzz344, zzz510, zzz511, zzz512000, zzz513, zzz514, zzz31, Succ(Succ(new_primPlusNat2(zzz6600, zzz512000))), zzz342000, h)
new_mkVBalBranch3MkVBalBranch223(zzz340, zzz341, Neg(Succ(Succ(Succ(zzz3420000)))), zzz343, zzz344, zzz510, zzz511, Zero, zzz513, zzz514, zzz31, Succ(Succ(zzz6700)), h) → new_mkVBalBranch3MkVBalBranch225(zzz340, zzz341, Succ(Succ(zzz3420000)), zzz343, zzz344, zzz510, zzz511, zzz513, zzz514, zzz31, Succ(zzz3420000), Succ(zzz6700), h)
new_mkVBalBranch3MkVBalBranch120(zzz2050, zzz2051, zzz2052, zzz2053, zzz2054, zzz2055, zzz2056, zzz2057, zzz2058, zzz2059, zzz2060, Zero, Succ(zzz20620), be) → new_mkVBalBranch0(zzz2060, zzz2059, Branch(zzz2050, zzz2051, Neg(Succ(zzz2052)), zzz2053, zzz2054), be)
new_mkVBalBranch0(zzz31, Branch(zzz510, zzz511, Pos(Zero), zzz513, zzz514), Branch(zzz340, zzz341, Pos(Succ(zzz34200)), zzz343, zzz344), h) → new_mkVBalBranch0(zzz31, Branch(zzz510, zzz511, Pos(Zero), zzz513, zzz514), zzz343, h)
new_mkVBalBranch3MkVBalBranch121(zzz473, zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, zzz481, zzz482, Succ(zzz7390), bh) → new_mkVBalBranch3MkVBalBranch115(zzz473, zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, Zero, zzz480, zzz481, zzz482, Succ(zzz7390), Succ(Zero), bh)
new_mkVBalBranch0(zzz31, Branch(zzz510, zzz511, Pos(Succ(zzz51200)), zzz513, zzz514), Branch(zzz340, zzz341, zzz342, zzz343, zzz344), h) → new_mkVBalBranch3MkVBalBranch215(zzz340, zzz341, zzz342, zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat3(new_primPlusNat1(zzz51200), zzz51200)), zzz51200))), h)
new_mkVBalBranch3MkVBalBranch223(zzz340, zzz341, Neg(Succ(Succ(Zero))), zzz343, zzz344, zzz510, zzz511, Succ(zzz512000), zzz513, zzz514, zzz31, Succ(Succ(zzz6700)), h) → new_mkVBalBranch3MkVBalBranch224(zzz340, zzz341, Succ(Zero), zzz343, zzz344, zzz510, zzz511, zzz512000, zzz513, zzz514, zzz31, Zero, Succ(Succ(new_primPlusNat2(zzz6700, zzz512000))), h)
new_mkVBalBranch3MkVBalBranch230(zzz498, zzz499, zzz500, zzz501, zzz502, zzz503, zzz504, zzz505, zzz506, zzz507, bg) → new_mkVBalBranch3MkVBalBranch118(zzz498, zzz499, zzz500, zzz501, zzz502, zzz503, zzz504, zzz505, zzz506, zzz507, new_primPlusNat2(new_primPlusNat3(Succ(new_primPlusNat3(new_primPlusNat1(zzz500), zzz500)), Succ(zzz500)), Succ(zzz500)), bg)
new_mkVBalBranch3MkVBalBranch224(zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, zzz1125, zzz1126, zzz1127, zzz1128, zzz1129, Succ(zzz11300), Succ(zzz11310), bd) → new_mkVBalBranch3MkVBalBranch224(zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, zzz1125, zzz1126, zzz1127, zzz1128, zzz1129, zzz11300, zzz11310, bd)
new_mkVBalBranch3MkVBalBranch217(zzz473, zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, zzz481, zzz482, Zero, Succ(zzz4840), bh) → new_mkVBalBranch0(zzz482, Branch(zzz478, zzz479, Pos(Succ(Zero)), zzz480, zzz481), zzz476, bh)
new_mkVBalBranch3MkVBalBranch110(zzz461, zzz462, zzz463, zzz464, zzz465, zzz466, zzz467, zzz468, zzz469, zzz470, zzz471, Succ(zzz5800), bb) → new_mkVBalBranch3MkVBalBranch115(zzz461, zzz462, zzz463, zzz464, zzz465, zzz466, zzz467, Succ(zzz468), zzz469, zzz470, zzz471, Succ(zzz5800), Succ(Succ(zzz468)), bb)
new_mkVBalBranch3MkVBalBranch227(zzz486, zzz487, zzz488, zzz489, zzz490, zzz491, zzz492, zzz493, zzz494, zzz495, zzz496, bf) → new_mkVBalBranch0(zzz496, Branch(zzz491, zzz492, Neg(Succ(Succ(zzz493))), zzz494, zzz495), zzz489, bf)
new_mkVBalBranch3MkVBalBranch215(zzz340, zzz341, Pos(Zero), zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, Succ(zzz660), h) → new_mkVBalBranch0(zzz31, zzz514, Branch(zzz340, zzz341, Pos(Zero), zzz343, zzz344), h)
new_mkVBalBranch3MkVBalBranch217(zzz473, zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, zzz481, zzz482, Succ(zzz4830), Zero, bh) → new_mkVBalBranch3MkVBalBranch121(zzz473, zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, zzz481, zzz482, new_primPlusNat2(new_primMulNat0(zzz475), Succ(zzz475)), bh)
new_mkVBalBranch3MkVBalBranch223(zzz340, zzz341, Neg(Zero), zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, Succ(zzz670), h) → new_mkVBalBranch0(zzz31, Branch(zzz510, zzz511, Neg(Succ(zzz51200)), zzz513, zzz514), zzz343, h)
new_mkVBalBranch3MkVBalBranch216(zzz1105, zzz1106, zzz1107, zzz1108, zzz1109, zzz1110, zzz1111, zzz1112, zzz1113, zzz1114, zzz1115, Zero, Succ(zzz11170), ba) → new_mkVBalBranch0(zzz1115, Branch(zzz1110, zzz1111, Pos(Succ(Succ(zzz1112))), zzz1113, zzz1114), zzz1108, ba)
new_mkVBalBranch3MkVBalBranch115(zzz1986, zzz1987, zzz1988, zzz1989, zzz1990, zzz1991, zzz1992, zzz1993, zzz1994, zzz1995, zzz1996, Zero, Succ(zzz19980), bc) → new_mkVBalBranch0(zzz1996, zzz1995, Branch(zzz1986, zzz1987, Pos(Succ(zzz1988)), zzz1989, zzz1990), bc)
new_mkVBalBranch3MkVBalBranch122(zzz340, zzz341, zzz34200, zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, h) → new_mkVBalBranch0(zzz31, zzz514, Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), h)
new_mkVBalBranch3MkVBalBranch217(zzz473, zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, zzz481, zzz482, Succ(zzz4830), Succ(zzz4840), bh) → new_mkVBalBranch3MkVBalBranch217(zzz473, zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, zzz481, zzz482, zzz4830, zzz4840, bh)
new_mkVBalBranch3MkVBalBranch116(zzz340, zzz341, zzz34200, zzz343, zzz344, zzz510, zzz511, zzz513, zzz514, zzz31, Succ(zzz1200), h) → new_mkVBalBranch0(zzz31, zzz514, Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), h)
new_mkVBalBranch3MkVBalBranch110(zzz461, zzz462, zzz463, zzz464, zzz465, zzz466, zzz467, zzz468, zzz469, zzz470, zzz471, Zero, bb) → new_mkVBalBranch3MkVBalBranch115(zzz461, zzz462, zzz463, zzz464, zzz465, zzz466, zzz467, Succ(zzz468), zzz469, zzz470, zzz471, Zero, Succ(Succ(zzz468)), bb)
new_mkVBalBranch3MkVBalBranch225(zzz498, zzz499, zzz500, zzz501, zzz502, zzz503, zzz504, zzz505, zzz506, zzz507, Zero, Succ(zzz5090), bg) → new_mkVBalBranch0(zzz507, Branch(zzz503, zzz504, Neg(Succ(Zero)), zzz505, zzz506), zzz501, bg)
new_mkVBalBranch0(zzz31, Branch(zzz510, zzz511, Neg(Succ(zzz51200)), zzz513, zzz514), Branch(zzz340, zzz341, zzz342, zzz343, zzz344), h) → new_mkVBalBranch3MkVBalBranch223(zzz340, zzz341, zzz342, zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat3(new_primPlusNat1(zzz51200), zzz51200)), zzz51200))), h)
new_mkVBalBranch3MkVBalBranch222(zzz461, zzz462, zzz463, zzz464, zzz465, zzz466, zzz467, zzz468, zzz469, zzz470, zzz471, bb) → new_mkVBalBranch3MkVBalBranch110(zzz461, zzz462, zzz463, zzz464, zzz465, zzz466, zzz467, zzz468, zzz469, zzz470, zzz471, new_primPlusNat2(new_primPlusNat3(Succ(new_primPlusNat3(new_primPlusNat1(zzz463), zzz463)), Succ(zzz463)), Succ(zzz463)), bb)
new_mkVBalBranch0(zzz31, Branch(zzz510, zzz511, Neg(Zero), zzz513, zzz514), Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), h) → new_mkVBalBranch3MkVBalBranch117(zzz340, zzz341, zzz34200, zzz343, zzz344, zzz510, zzz511, zzz513, zzz514, zzz31, new_primPlusNat2(new_primPlusNat3(Succ(new_primPlusNat3(new_primPlusNat1(zzz34200), zzz34200)), Succ(zzz34200)), Succ(zzz34200)), h)
new_mkVBalBranch3MkVBalBranch121(zzz473, zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, zzz481, zzz482, Zero, bh) → new_mkVBalBranch3MkVBalBranch115(zzz473, zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, Zero, zzz480, zzz481, zzz482, Zero, Succ(Zero), bh)
new_mkVBalBranch3MkVBalBranch225(zzz498, zzz499, zzz500, zzz501, zzz502, zzz503, zzz504, zzz505, zzz506, zzz507, Succ(zzz5080), Zero, bg) → new_mkVBalBranch3MkVBalBranch118(zzz498, zzz499, zzz500, zzz501, zzz502, zzz503, zzz504, zzz505, zzz506, zzz507, new_primPlusNat2(new_primMulNat0(zzz500), Succ(zzz500)), bg)
new_mkVBalBranch3MkVBalBranch223(zzz340, zzz341, Neg(Succ(Zero)), zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, Succ(zzz670), h) → new_mkVBalBranch0(zzz31, Branch(zzz510, zzz511, Neg(Succ(zzz51200)), zzz513, zzz514), zzz343, h)
new_mkVBalBranch3MkVBalBranch215(zzz340, zzz341, Pos(Succ(Zero)), zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, Succ(zzz660), h) → new_mkVBalBranch3MkVBalBranch18(zzz340, zzz341, zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, new_primPlusNat2(new_primMulNat0(Zero), Succ(Zero)), h)
new_mkVBalBranch3MkVBalBranch229(zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, zzz1125, zzz1126, zzz1127, zzz1128, zzz1129, bd) → new_mkVBalBranch3MkVBalBranch119(zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, zzz1125, zzz1126, zzz1127, zzz1128, zzz1129, new_primPlusNat2(new_primMulNat0(zzz1121), Succ(zzz1121)), bd)
new_mkVBalBranch3MkVBalBranch233(zzz473, zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, zzz481, zzz482, bh) → new_mkVBalBranch3MkVBalBranch121(zzz473, zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, zzz481, zzz482, new_primPlusNat2(new_primMulNat0(zzz475), Succ(zzz475)), bh)
new_mkVBalBranch0(zzz31, Branch(zzz510, zzz511, Pos(Zero), zzz513, zzz514), Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), h) → new_mkVBalBranch3MkVBalBranch116(zzz340, zzz341, zzz34200, zzz343, zzz344, zzz510, zzz511, zzz513, zzz514, zzz31, new_primPlusNat2(new_primPlusNat3(Succ(new_primPlusNat3(new_primPlusNat1(zzz34200), zzz34200)), Succ(zzz34200)), Succ(zzz34200)), h)
new_mkVBalBranch3MkVBalBranch215(zzz340, zzz341, Pos(Succ(Succ(zzz342000))), zzz343, zzz344, zzz510, zzz511, Zero, zzz513, zzz514, zzz31, Succ(Succ(zzz6600)), h) → new_mkVBalBranch3MkVBalBranch217(zzz340, zzz341, Succ(zzz342000), zzz343, zzz344, zzz510, zzz511, zzz513, zzz514, zzz31, Succ(zzz6600), zzz342000, h)
new_mkVBalBranch3MkVBalBranch218(zzz461, zzz462, zzz463, zzz464, zzz465, zzz466, zzz467, zzz468, zzz469, zzz470, zzz471, bb) → new_mkVBalBranch3MkVBalBranch110(zzz461, zzz462, zzz463, zzz464, zzz465, zzz466, zzz467, zzz468, zzz469, zzz470, zzz471, new_primPlusNat2(new_primMulNat0(zzz463), Succ(zzz463)), bb)
new_mkVBalBranch3MkVBalBranch117(zzz340, zzz341, zzz34200, zzz343, zzz344, zzz510, zzz511, zzz513, zzz514, zzz31, Succ(zzz1240), h) → new_mkVBalBranch0(zzz31, zzz514, Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), h)
new_mkVBalBranch3MkVBalBranch120(zzz2050, zzz2051, zzz2052, zzz2053, zzz2054, zzz2055, zzz2056, zzz2057, zzz2058, zzz2059, zzz2060, Succ(zzz20610), Succ(zzz20620), be) → new_mkVBalBranch3MkVBalBranch120(zzz2050, zzz2051, zzz2052, zzz2053, zzz2054, zzz2055, zzz2056, zzz2057, zzz2058, zzz2059, zzz2060, zzz20610, zzz20620, be)
new_mkVBalBranch3MkVBalBranch217(zzz473, zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, zzz481, zzz482, Zero, Zero, bh) → new_mkVBalBranch3MkVBalBranch233(zzz473, zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, zzz481, zzz482, bh)
new_mkVBalBranch3MkVBalBranch216(zzz1105, zzz1106, zzz1107, zzz1108, zzz1109, zzz1110, zzz1111, zzz1112, zzz1113, zzz1114, zzz1115, Succ(zzz11160), Succ(zzz11170), ba) → new_mkVBalBranch3MkVBalBranch216(zzz1105, zzz1106, zzz1107, zzz1108, zzz1109, zzz1110, zzz1111, zzz1112, zzz1113, zzz1114, zzz1115, zzz11160, zzz11170, ba)
new_mkVBalBranch3MkVBalBranch223(zzz340, zzz341, Pos(zzz3420), zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, Succ(zzz670), h) → new_mkVBalBranch0(zzz31, Branch(zzz510, zzz511, Neg(Succ(zzz51200)), zzz513, zzz514), zzz343, h)
new_mkVBalBranch3MkVBalBranch19(zzz340, zzz341, zzz34200, zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, Zero, h) → new_mkVBalBranch3MkVBalBranch122(zzz340, zzz341, zzz34200, zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, h)
new_mkVBalBranch3MkVBalBranch225(zzz498, zzz499, zzz500, zzz501, zzz502, zzz503, zzz504, zzz505, zzz506, zzz507, Succ(zzz5080), Succ(zzz5090), bg) → new_mkVBalBranch3MkVBalBranch225(zzz498, zzz499, zzz500, zzz501, zzz502, zzz503, zzz504, zzz505, zzz506, zzz507, zzz5080, zzz5090, bg)
new_mkVBalBranch3MkVBalBranch19(zzz340, zzz341, zzz34200, zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, Succ(zzz1410), h) → new_mkVBalBranch0(zzz31, zzz514, Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), h)
new_mkVBalBranch3MkVBalBranch224(zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, zzz1125, zzz1126, zzz1127, zzz1128, zzz1129, Succ(zzz11300), Zero, bd) → new_mkVBalBranch3MkVBalBranch119(zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, zzz1125, zzz1126, zzz1127, zzz1128, zzz1129, new_primPlusNat2(new_primMulNat0(zzz1121), Succ(zzz1121)), bd)
new_mkVBalBranch3MkVBalBranch224(zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, zzz1125, zzz1126, zzz1127, zzz1128, zzz1129, Zero, Succ(zzz11310), bd) → new_mkVBalBranch3MkVBalBranch227(zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, zzz1125, zzz1126, zzz1127, zzz1128, zzz1129, bd)
new_mkVBalBranch3MkVBalBranch224(zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, zzz1125, zzz1126, zzz1127, zzz1128, zzz1129, Zero, Zero, bd) → new_mkVBalBranch3MkVBalBranch229(zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, zzz1125, zzz1126, zzz1127, zzz1128, zzz1129, bd)
new_mkVBalBranch3MkVBalBranch223(zzz340, zzz341, Neg(Succ(Succ(Succ(zzz3420000)))), zzz343, zzz344, zzz510, zzz511, Succ(zzz512000), zzz513, zzz514, zzz31, Succ(Succ(zzz6700)), h) → new_mkVBalBranch3MkVBalBranch224(zzz340, zzz341, Succ(Succ(zzz3420000)), zzz343, zzz344, zzz510, zzz511, zzz512000, zzz513, zzz514, zzz31, Succ(zzz3420000), Succ(Succ(new_primPlusNat2(zzz6700, zzz512000))), h)
new_mkVBalBranch3MkVBalBranch223(zzz340, zzz341, Neg(Succ(Succ(Zero))), zzz343, zzz344, zzz510, zzz511, Zero, zzz513, zzz514, zzz31, Succ(Succ(zzz6700)), h) → new_mkVBalBranch3MkVBalBranch225(zzz340, zzz341, Succ(Zero), zzz343, zzz344, zzz510, zzz511, zzz513, zzz514, zzz31, Zero, Succ(zzz6700), h)
new_mkVBalBranch3MkVBalBranch115(zzz1986, zzz1987, zzz1988, zzz1989, zzz1990, zzz1991, zzz1992, zzz1993, zzz1994, zzz1995, zzz1996, Succ(zzz19970), Succ(zzz19980), bc) → new_mkVBalBranch3MkVBalBranch115(zzz1986, zzz1987, zzz1988, zzz1989, zzz1990, zzz1991, zzz1992, zzz1993, zzz1994, zzz1995, zzz1996, zzz19970, zzz19980, bc)
new_mkVBalBranch3MkVBalBranch215(zzz340, zzz341, Neg(Zero), zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, Succ(zzz660), h) → new_mkVBalBranch0(zzz31, zzz514, Branch(zzz340, zzz341, Neg(Zero), zzz343, zzz344), h)
new_mkVBalBranch3MkVBalBranch118(zzz498, zzz499, zzz500, zzz501, zzz502, zzz503, zzz504, zzz505, zzz506, zzz507, Succ(zzz8040), bg) → new_mkVBalBranch3MkVBalBranch120(zzz498, zzz499, zzz500, zzz501, zzz502, zzz503, zzz504, Zero, zzz505, zzz506, zzz507, Succ(Zero), Succ(zzz8040), bg)
new_mkVBalBranch3MkVBalBranch216(zzz1105, zzz1106, zzz1107, zzz1108, zzz1109, zzz1110, zzz1111, zzz1112, zzz1113, zzz1114, zzz1115, Succ(zzz11160), Zero, ba) → new_mkVBalBranch3MkVBalBranch218(zzz1105, zzz1106, zzz1107, zzz1108, zzz1109, zzz1110, zzz1111, zzz1112, zzz1113, zzz1114, zzz1115, ba)
new_mkVBalBranch3MkVBalBranch215(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, Succ(zzz660), h) → new_mkVBalBranch3MkVBalBranch19(zzz340, zzz341, zzz34200, zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, new_primPlusNat2(new_primMulNat0(zzz34200), Succ(zzz34200)), h)
new_mkVBalBranch3MkVBalBranch216(zzz1105, zzz1106, zzz1107, zzz1108, zzz1109, zzz1110, zzz1111, zzz1112, zzz1113, zzz1114, zzz1115, Zero, Zero, ba) → new_mkVBalBranch3MkVBalBranch222(zzz1105, zzz1106, zzz1107, zzz1108, zzz1109, zzz1110, zzz1111, zzz1112, zzz1113, zzz1114, zzz1115, ba)
new_mkVBalBranch3MkVBalBranch18(zzz340, zzz341, zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, Zero, h) → new_mkVBalBranch3MkVBalBranch115(zzz340, zzz341, Zero, zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, Zero, Succ(zzz51200), h)
new_mkVBalBranch3MkVBalBranch119(zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, zzz1125, zzz1126, zzz1127, zzz1128, zzz1129, Succ(zzz12130), bd) → new_mkVBalBranch3MkVBalBranch120(zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, zzz1125, Succ(zzz1126), zzz1127, zzz1128, zzz1129, Succ(Succ(zzz1126)), Succ(zzz12130), bd)

The TRS R consists of the following rules:

new_primMulNat0(zzz6200) → new_primPlusNat3(Succ(new_primPlusNat3(new_primPlusNat1(zzz6200), zzz6200)), Succ(zzz6200))
new_primPlusNat2(Succ(zzz900), Succ(zzz9100)) → Succ(Succ(new_primPlusNat2(zzz900, zzz9100)))
new_primPlusNat2(Zero, Succ(zzz9100)) → Succ(zzz9100)
new_primPlusNat2(Zero, Zero) → Zero
new_primPlusNat2(Succ(zzz900), Zero) → Succ(zzz900)
new_primPlusNat1(Zero) → Zero
new_primPlusNat1(Succ(zzz62000)) → Succ(Succ(new_primPlusNat1(zzz62000)))
new_primPlusNat3(zzz90, Succ(zzz910)) → Succ(Succ(new_primPlusNat2(zzz90, zzz910)))
new_primPlusNat3(zzz90, Zero) → Succ(zzz90)

The set Q consists of the following terms:

new_primPlusNat2(Zero, Succ(x0))
new_primMulNat0(x0)
new_primPlusNat3(x0, Succ(x1))
new_primPlusNat2(Succ(x0), Succ(x1))
new_primPlusNat3(x0, Zero)
new_primPlusNat1(Zero)
new_primPlusNat2(Zero, Zero)
new_primPlusNat1(Succ(x0))
new_primPlusNat2(Succ(x0), Zero)

We have to consider all minimal (P,Q,R)-chains.
By rewriting [15] the rule new_mkVBalBranch3MkVBalBranch218(zzz461, zzz462, zzz463, zzz464, zzz465, zzz466, zzz467, zzz468, zzz469, zzz470, zzz471, bb) → new_mkVBalBranch3MkVBalBranch110(zzz461, zzz462, zzz463, zzz464, zzz465, zzz466, zzz467, zzz468, zzz469, zzz470, zzz471, new_primPlusNat2(new_primMulNat0(zzz463), Succ(zzz463)), bb) at position [11,0] we obtained the following new rules:

new_mkVBalBranch3MkVBalBranch218(zzz461, zzz462, zzz463, zzz464, zzz465, zzz466, zzz467, zzz468, zzz469, zzz470, zzz471, bb) → new_mkVBalBranch3MkVBalBranch110(zzz461, zzz462, zzz463, zzz464, zzz465, zzz466, zzz467, zzz468, zzz469, zzz470, zzz471, new_primPlusNat2(new_primPlusNat3(Succ(new_primPlusNat3(new_primPlusNat1(zzz463), zzz463)), Succ(zzz463)), Succ(zzz463)), bb)



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

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

new_mkVBalBranch3MkVBalBranch225(zzz498, zzz499, zzz500, zzz501, zzz502, zzz503, zzz504, zzz505, zzz506, zzz507, Zero, Zero, bg) → new_mkVBalBranch3MkVBalBranch230(zzz498, zzz499, zzz500, zzz501, zzz502, zzz503, zzz504, zzz505, zzz506, zzz507, bg)
new_mkVBalBranch3MkVBalBranch18(zzz340, zzz341, zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, Succ(zzz1480), h) → new_mkVBalBranch3MkVBalBranch115(zzz340, zzz341, Zero, zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, Succ(zzz1480), Succ(zzz51200), h)
new_mkVBalBranch3MkVBalBranch215(zzz340, zzz341, Pos(Succ(Succ(zzz342000))), zzz343, zzz344, zzz510, zzz511, Succ(zzz512000), zzz513, zzz514, zzz31, Succ(Succ(zzz6600)), h) → new_mkVBalBranch3MkVBalBranch216(zzz340, zzz341, Succ(zzz342000), zzz343, zzz344, zzz510, zzz511, zzz512000, zzz513, zzz514, zzz31, Succ(Succ(new_primPlusNat2(zzz6600, zzz512000))), zzz342000, h)
new_mkVBalBranch0(zzz31, Branch(zzz510, zzz511, Neg(Zero), zzz513, zzz514), Branch(zzz340, zzz341, Pos(Succ(zzz34200)), zzz343, zzz344), h) → new_mkVBalBranch0(zzz31, Branch(zzz510, zzz511, Neg(Zero), zzz513, zzz514), zzz343, h)
new_mkVBalBranch3MkVBalBranch223(zzz340, zzz341, Neg(Succ(Succ(Succ(zzz3420000)))), zzz343, zzz344, zzz510, zzz511, Zero, zzz513, zzz514, zzz31, Succ(Succ(zzz6700)), h) → new_mkVBalBranch3MkVBalBranch225(zzz340, zzz341, Succ(Succ(zzz3420000)), zzz343, zzz344, zzz510, zzz511, zzz513, zzz514, zzz31, Succ(zzz3420000), Succ(zzz6700), h)
new_mkVBalBranch3MkVBalBranch120(zzz2050, zzz2051, zzz2052, zzz2053, zzz2054, zzz2055, zzz2056, zzz2057, zzz2058, zzz2059, zzz2060, Zero, Succ(zzz20620), be) → new_mkVBalBranch0(zzz2060, zzz2059, Branch(zzz2050, zzz2051, Neg(Succ(zzz2052)), zzz2053, zzz2054), be)
new_mkVBalBranch3MkVBalBranch121(zzz473, zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, zzz481, zzz482, Succ(zzz7390), bh) → new_mkVBalBranch3MkVBalBranch115(zzz473, zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, Zero, zzz480, zzz481, zzz482, Succ(zzz7390), Succ(Zero), bh)
new_mkVBalBranch0(zzz31, Branch(zzz510, zzz511, Pos(Zero), zzz513, zzz514), Branch(zzz340, zzz341, Pos(Succ(zzz34200)), zzz343, zzz344), h) → new_mkVBalBranch0(zzz31, Branch(zzz510, zzz511, Pos(Zero), zzz513, zzz514), zzz343, h)
new_mkVBalBranch0(zzz31, Branch(zzz510, zzz511, Pos(Succ(zzz51200)), zzz513, zzz514), Branch(zzz340, zzz341, zzz342, zzz343, zzz344), h) → new_mkVBalBranch3MkVBalBranch215(zzz340, zzz341, zzz342, zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat3(new_primPlusNat1(zzz51200), zzz51200)), zzz51200))), h)
new_mkVBalBranch3MkVBalBranch223(zzz340, zzz341, Neg(Succ(Succ(Zero))), zzz343, zzz344, zzz510, zzz511, Succ(zzz512000), zzz513, zzz514, zzz31, Succ(Succ(zzz6700)), h) → new_mkVBalBranch3MkVBalBranch224(zzz340, zzz341, Succ(Zero), zzz343, zzz344, zzz510, zzz511, zzz512000, zzz513, zzz514, zzz31, Zero, Succ(Succ(new_primPlusNat2(zzz6700, zzz512000))), h)
new_mkVBalBranch3MkVBalBranch230(zzz498, zzz499, zzz500, zzz501, zzz502, zzz503, zzz504, zzz505, zzz506, zzz507, bg) → new_mkVBalBranch3MkVBalBranch118(zzz498, zzz499, zzz500, zzz501, zzz502, zzz503, zzz504, zzz505, zzz506, zzz507, new_primPlusNat2(new_primPlusNat3(Succ(new_primPlusNat3(new_primPlusNat1(zzz500), zzz500)), Succ(zzz500)), Succ(zzz500)), bg)
new_mkVBalBranch3MkVBalBranch224(zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, zzz1125, zzz1126, zzz1127, zzz1128, zzz1129, Succ(zzz11300), Succ(zzz11310), bd) → new_mkVBalBranch3MkVBalBranch224(zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, zzz1125, zzz1126, zzz1127, zzz1128, zzz1129, zzz11300, zzz11310, bd)
new_mkVBalBranch3MkVBalBranch217(zzz473, zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, zzz481, zzz482, Zero, Succ(zzz4840), bh) → new_mkVBalBranch0(zzz482, Branch(zzz478, zzz479, Pos(Succ(Zero)), zzz480, zzz481), zzz476, bh)
new_mkVBalBranch3MkVBalBranch218(zzz461, zzz462, zzz463, zzz464, zzz465, zzz466, zzz467, zzz468, zzz469, zzz470, zzz471, bb) → new_mkVBalBranch3MkVBalBranch110(zzz461, zzz462, zzz463, zzz464, zzz465, zzz466, zzz467, zzz468, zzz469, zzz470, zzz471, new_primPlusNat2(new_primPlusNat3(Succ(new_primPlusNat3(new_primPlusNat1(zzz463), zzz463)), Succ(zzz463)), Succ(zzz463)), bb)
new_mkVBalBranch3MkVBalBranch110(zzz461, zzz462, zzz463, zzz464, zzz465, zzz466, zzz467, zzz468, zzz469, zzz470, zzz471, Succ(zzz5800), bb) → new_mkVBalBranch3MkVBalBranch115(zzz461, zzz462, zzz463, zzz464, zzz465, zzz466, zzz467, Succ(zzz468), zzz469, zzz470, zzz471, Succ(zzz5800), Succ(Succ(zzz468)), bb)
new_mkVBalBranch3MkVBalBranch227(zzz486, zzz487, zzz488, zzz489, zzz490, zzz491, zzz492, zzz493, zzz494, zzz495, zzz496, bf) → new_mkVBalBranch0(zzz496, Branch(zzz491, zzz492, Neg(Succ(Succ(zzz493))), zzz494, zzz495), zzz489, bf)
new_mkVBalBranch3MkVBalBranch215(zzz340, zzz341, Pos(Zero), zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, Succ(zzz660), h) → new_mkVBalBranch0(zzz31, zzz514, Branch(zzz340, zzz341, Pos(Zero), zzz343, zzz344), h)
new_mkVBalBranch3MkVBalBranch223(zzz340, zzz341, Neg(Zero), zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, Succ(zzz670), h) → new_mkVBalBranch0(zzz31, Branch(zzz510, zzz511, Neg(Succ(zzz51200)), zzz513, zzz514), zzz343, h)
new_mkVBalBranch3MkVBalBranch217(zzz473, zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, zzz481, zzz482, Succ(zzz4830), Zero, bh) → new_mkVBalBranch3MkVBalBranch121(zzz473, zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, zzz481, zzz482, new_primPlusNat2(new_primMulNat0(zzz475), Succ(zzz475)), bh)
new_mkVBalBranch3MkVBalBranch216(zzz1105, zzz1106, zzz1107, zzz1108, zzz1109, zzz1110, zzz1111, zzz1112, zzz1113, zzz1114, zzz1115, Zero, Succ(zzz11170), ba) → new_mkVBalBranch0(zzz1115, Branch(zzz1110, zzz1111, Pos(Succ(Succ(zzz1112))), zzz1113, zzz1114), zzz1108, ba)
new_mkVBalBranch3MkVBalBranch115(zzz1986, zzz1987, zzz1988, zzz1989, zzz1990, zzz1991, zzz1992, zzz1993, zzz1994, zzz1995, zzz1996, Zero, Succ(zzz19980), bc) → new_mkVBalBranch0(zzz1996, zzz1995, Branch(zzz1986, zzz1987, Pos(Succ(zzz1988)), zzz1989, zzz1990), bc)
new_mkVBalBranch3MkVBalBranch122(zzz340, zzz341, zzz34200, zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, h) → new_mkVBalBranch0(zzz31, zzz514, Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), h)
new_mkVBalBranch3MkVBalBranch217(zzz473, zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, zzz481, zzz482, Succ(zzz4830), Succ(zzz4840), bh) → new_mkVBalBranch3MkVBalBranch217(zzz473, zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, zzz481, zzz482, zzz4830, zzz4840, bh)
new_mkVBalBranch3MkVBalBranch116(zzz340, zzz341, zzz34200, zzz343, zzz344, zzz510, zzz511, zzz513, zzz514, zzz31, Succ(zzz1200), h) → new_mkVBalBranch0(zzz31, zzz514, Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), h)
new_mkVBalBranch3MkVBalBranch110(zzz461, zzz462, zzz463, zzz464, zzz465, zzz466, zzz467, zzz468, zzz469, zzz470, zzz471, Zero, bb) → new_mkVBalBranch3MkVBalBranch115(zzz461, zzz462, zzz463, zzz464, zzz465, zzz466, zzz467, Succ(zzz468), zzz469, zzz470, zzz471, Zero, Succ(Succ(zzz468)), bb)
new_mkVBalBranch3MkVBalBranch225(zzz498, zzz499, zzz500, zzz501, zzz502, zzz503, zzz504, zzz505, zzz506, zzz507, Zero, Succ(zzz5090), bg) → new_mkVBalBranch0(zzz507, Branch(zzz503, zzz504, Neg(Succ(Zero)), zzz505, zzz506), zzz501, bg)
new_mkVBalBranch0(zzz31, Branch(zzz510, zzz511, Neg(Succ(zzz51200)), zzz513, zzz514), Branch(zzz340, zzz341, zzz342, zzz343, zzz344), h) → new_mkVBalBranch3MkVBalBranch223(zzz340, zzz341, zzz342, zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat3(new_primPlusNat1(zzz51200), zzz51200)), zzz51200))), h)
new_mkVBalBranch3MkVBalBranch222(zzz461, zzz462, zzz463, zzz464, zzz465, zzz466, zzz467, zzz468, zzz469, zzz470, zzz471, bb) → new_mkVBalBranch3MkVBalBranch110(zzz461, zzz462, zzz463, zzz464, zzz465, zzz466, zzz467, zzz468, zzz469, zzz470, zzz471, new_primPlusNat2(new_primPlusNat3(Succ(new_primPlusNat3(new_primPlusNat1(zzz463), zzz463)), Succ(zzz463)), Succ(zzz463)), bb)
new_mkVBalBranch0(zzz31, Branch(zzz510, zzz511, Neg(Zero), zzz513, zzz514), Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), h) → new_mkVBalBranch3MkVBalBranch117(zzz340, zzz341, zzz34200, zzz343, zzz344, zzz510, zzz511, zzz513, zzz514, zzz31, new_primPlusNat2(new_primPlusNat3(Succ(new_primPlusNat3(new_primPlusNat1(zzz34200), zzz34200)), Succ(zzz34200)), Succ(zzz34200)), h)
new_mkVBalBranch3MkVBalBranch121(zzz473, zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, zzz481, zzz482, Zero, bh) → new_mkVBalBranch3MkVBalBranch115(zzz473, zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, Zero, zzz480, zzz481, zzz482, Zero, Succ(Zero), bh)
new_mkVBalBranch3MkVBalBranch223(zzz340, zzz341, Neg(Succ(Zero)), zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, Succ(zzz670), h) → new_mkVBalBranch0(zzz31, Branch(zzz510, zzz511, Neg(Succ(zzz51200)), zzz513, zzz514), zzz343, h)
new_mkVBalBranch3MkVBalBranch225(zzz498, zzz499, zzz500, zzz501, zzz502, zzz503, zzz504, zzz505, zzz506, zzz507, Succ(zzz5080), Zero, bg) → new_mkVBalBranch3MkVBalBranch118(zzz498, zzz499, zzz500, zzz501, zzz502, zzz503, zzz504, zzz505, zzz506, zzz507, new_primPlusNat2(new_primMulNat0(zzz500), Succ(zzz500)), bg)
new_mkVBalBranch3MkVBalBranch215(zzz340, zzz341, Pos(Succ(Zero)), zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, Succ(zzz660), h) → new_mkVBalBranch3MkVBalBranch18(zzz340, zzz341, zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, new_primPlusNat2(new_primMulNat0(Zero), Succ(Zero)), h)
new_mkVBalBranch3MkVBalBranch229(zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, zzz1125, zzz1126, zzz1127, zzz1128, zzz1129, bd) → new_mkVBalBranch3MkVBalBranch119(zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, zzz1125, zzz1126, zzz1127, zzz1128, zzz1129, new_primPlusNat2(new_primMulNat0(zzz1121), Succ(zzz1121)), bd)
new_mkVBalBranch3MkVBalBranch233(zzz473, zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, zzz481, zzz482, bh) → new_mkVBalBranch3MkVBalBranch121(zzz473, zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, zzz481, zzz482, new_primPlusNat2(new_primMulNat0(zzz475), Succ(zzz475)), bh)
new_mkVBalBranch0(zzz31, Branch(zzz510, zzz511, Pos(Zero), zzz513, zzz514), Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), h) → new_mkVBalBranch3MkVBalBranch116(zzz340, zzz341, zzz34200, zzz343, zzz344, zzz510, zzz511, zzz513, zzz514, zzz31, new_primPlusNat2(new_primPlusNat3(Succ(new_primPlusNat3(new_primPlusNat1(zzz34200), zzz34200)), Succ(zzz34200)), Succ(zzz34200)), h)
new_mkVBalBranch3MkVBalBranch215(zzz340, zzz341, Pos(Succ(Succ(zzz342000))), zzz343, zzz344, zzz510, zzz511, Zero, zzz513, zzz514, zzz31, Succ(Succ(zzz6600)), h) → new_mkVBalBranch3MkVBalBranch217(zzz340, zzz341, Succ(zzz342000), zzz343, zzz344, zzz510, zzz511, zzz513, zzz514, zzz31, Succ(zzz6600), zzz342000, h)
new_mkVBalBranch3MkVBalBranch117(zzz340, zzz341, zzz34200, zzz343, zzz344, zzz510, zzz511, zzz513, zzz514, zzz31, Succ(zzz1240), h) → new_mkVBalBranch0(zzz31, zzz514, Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), h)
new_mkVBalBranch3MkVBalBranch217(zzz473, zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, zzz481, zzz482, Zero, Zero, bh) → new_mkVBalBranch3MkVBalBranch233(zzz473, zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, zzz481, zzz482, bh)
new_mkVBalBranch3MkVBalBranch120(zzz2050, zzz2051, zzz2052, zzz2053, zzz2054, zzz2055, zzz2056, zzz2057, zzz2058, zzz2059, zzz2060, Succ(zzz20610), Succ(zzz20620), be) → new_mkVBalBranch3MkVBalBranch120(zzz2050, zzz2051, zzz2052, zzz2053, zzz2054, zzz2055, zzz2056, zzz2057, zzz2058, zzz2059, zzz2060, zzz20610, zzz20620, be)
new_mkVBalBranch3MkVBalBranch223(zzz340, zzz341, Pos(zzz3420), zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, Succ(zzz670), h) → new_mkVBalBranch0(zzz31, Branch(zzz510, zzz511, Neg(Succ(zzz51200)), zzz513, zzz514), zzz343, h)
new_mkVBalBranch3MkVBalBranch216(zzz1105, zzz1106, zzz1107, zzz1108, zzz1109, zzz1110, zzz1111, zzz1112, zzz1113, zzz1114, zzz1115, Succ(zzz11160), Succ(zzz11170), ba) → new_mkVBalBranch3MkVBalBranch216(zzz1105, zzz1106, zzz1107, zzz1108, zzz1109, zzz1110, zzz1111, zzz1112, zzz1113, zzz1114, zzz1115, zzz11160, zzz11170, ba)
new_mkVBalBranch3MkVBalBranch19(zzz340, zzz341, zzz34200, zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, Zero, h) → new_mkVBalBranch3MkVBalBranch122(zzz340, zzz341, zzz34200, zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, h)
new_mkVBalBranch3MkVBalBranch225(zzz498, zzz499, zzz500, zzz501, zzz502, zzz503, zzz504, zzz505, zzz506, zzz507, Succ(zzz5080), Succ(zzz5090), bg) → new_mkVBalBranch3MkVBalBranch225(zzz498, zzz499, zzz500, zzz501, zzz502, zzz503, zzz504, zzz505, zzz506, zzz507, zzz5080, zzz5090, bg)
new_mkVBalBranch3MkVBalBranch19(zzz340, zzz341, zzz34200, zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, Succ(zzz1410), h) → new_mkVBalBranch0(zzz31, zzz514, Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), h)
new_mkVBalBranch3MkVBalBranch224(zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, zzz1125, zzz1126, zzz1127, zzz1128, zzz1129, Succ(zzz11300), Zero, bd) → new_mkVBalBranch3MkVBalBranch119(zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, zzz1125, zzz1126, zzz1127, zzz1128, zzz1129, new_primPlusNat2(new_primMulNat0(zzz1121), Succ(zzz1121)), bd)
new_mkVBalBranch3MkVBalBranch224(zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, zzz1125, zzz1126, zzz1127, zzz1128, zzz1129, Zero, Zero, bd) → new_mkVBalBranch3MkVBalBranch229(zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, zzz1125, zzz1126, zzz1127, zzz1128, zzz1129, bd)
new_mkVBalBranch3MkVBalBranch224(zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, zzz1125, zzz1126, zzz1127, zzz1128, zzz1129, Zero, Succ(zzz11310), bd) → new_mkVBalBranch3MkVBalBranch227(zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, zzz1125, zzz1126, zzz1127, zzz1128, zzz1129, bd)
new_mkVBalBranch3MkVBalBranch223(zzz340, zzz341, Neg(Succ(Succ(Zero))), zzz343, zzz344, zzz510, zzz511, Zero, zzz513, zzz514, zzz31, Succ(Succ(zzz6700)), h) → new_mkVBalBranch3MkVBalBranch225(zzz340, zzz341, Succ(Zero), zzz343, zzz344, zzz510, zzz511, zzz513, zzz514, zzz31, Zero, Succ(zzz6700), h)
new_mkVBalBranch3MkVBalBranch223(zzz340, zzz341, Neg(Succ(Succ(Succ(zzz3420000)))), zzz343, zzz344, zzz510, zzz511, Succ(zzz512000), zzz513, zzz514, zzz31, Succ(Succ(zzz6700)), h) → new_mkVBalBranch3MkVBalBranch224(zzz340, zzz341, Succ(Succ(zzz3420000)), zzz343, zzz344, zzz510, zzz511, zzz512000, zzz513, zzz514, zzz31, Succ(zzz3420000), Succ(Succ(new_primPlusNat2(zzz6700, zzz512000))), h)
new_mkVBalBranch3MkVBalBranch115(zzz1986, zzz1987, zzz1988, zzz1989, zzz1990, zzz1991, zzz1992, zzz1993, zzz1994, zzz1995, zzz1996, Succ(zzz19970), Succ(zzz19980), bc) → new_mkVBalBranch3MkVBalBranch115(zzz1986, zzz1987, zzz1988, zzz1989, zzz1990, zzz1991, zzz1992, zzz1993, zzz1994, zzz1995, zzz1996, zzz19970, zzz19980, bc)
new_mkVBalBranch3MkVBalBranch215(zzz340, zzz341, Neg(Zero), zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, Succ(zzz660), h) → new_mkVBalBranch0(zzz31, zzz514, Branch(zzz340, zzz341, Neg(Zero), zzz343, zzz344), h)
new_mkVBalBranch3MkVBalBranch118(zzz498, zzz499, zzz500, zzz501, zzz502, zzz503, zzz504, zzz505, zzz506, zzz507, Succ(zzz8040), bg) → new_mkVBalBranch3MkVBalBranch120(zzz498, zzz499, zzz500, zzz501, zzz502, zzz503, zzz504, Zero, zzz505, zzz506, zzz507, Succ(Zero), Succ(zzz8040), bg)
new_mkVBalBranch3MkVBalBranch216(zzz1105, zzz1106, zzz1107, zzz1108, zzz1109, zzz1110, zzz1111, zzz1112, zzz1113, zzz1114, zzz1115, Succ(zzz11160), Zero, ba) → new_mkVBalBranch3MkVBalBranch218(zzz1105, zzz1106, zzz1107, zzz1108, zzz1109, zzz1110, zzz1111, zzz1112, zzz1113, zzz1114, zzz1115, ba)
new_mkVBalBranch3MkVBalBranch215(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, Succ(zzz660), h) → new_mkVBalBranch3MkVBalBranch19(zzz340, zzz341, zzz34200, zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, new_primPlusNat2(new_primMulNat0(zzz34200), Succ(zzz34200)), h)
new_mkVBalBranch3MkVBalBranch216(zzz1105, zzz1106, zzz1107, zzz1108, zzz1109, zzz1110, zzz1111, zzz1112, zzz1113, zzz1114, zzz1115, Zero, Zero, ba) → new_mkVBalBranch3MkVBalBranch222(zzz1105, zzz1106, zzz1107, zzz1108, zzz1109, zzz1110, zzz1111, zzz1112, zzz1113, zzz1114, zzz1115, ba)
new_mkVBalBranch3MkVBalBranch119(zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, zzz1125, zzz1126, zzz1127, zzz1128, zzz1129, Succ(zzz12130), bd) → new_mkVBalBranch3MkVBalBranch120(zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, zzz1125, Succ(zzz1126), zzz1127, zzz1128, zzz1129, Succ(Succ(zzz1126)), Succ(zzz12130), bd)
new_mkVBalBranch3MkVBalBranch18(zzz340, zzz341, zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, Zero, h) → new_mkVBalBranch3MkVBalBranch115(zzz340, zzz341, Zero, zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, Zero, Succ(zzz51200), h)

The TRS R consists of the following rules:

new_primMulNat0(zzz6200) → new_primPlusNat3(Succ(new_primPlusNat3(new_primPlusNat1(zzz6200), zzz6200)), Succ(zzz6200))
new_primPlusNat2(Succ(zzz900), Succ(zzz9100)) → Succ(Succ(new_primPlusNat2(zzz900, zzz9100)))
new_primPlusNat2(Zero, Succ(zzz9100)) → Succ(zzz9100)
new_primPlusNat2(Zero, Zero) → Zero
new_primPlusNat2(Succ(zzz900), Zero) → Succ(zzz900)
new_primPlusNat1(Zero) → Zero
new_primPlusNat1(Succ(zzz62000)) → Succ(Succ(new_primPlusNat1(zzz62000)))
new_primPlusNat3(zzz90, Succ(zzz910)) → Succ(Succ(new_primPlusNat2(zzz90, zzz910)))
new_primPlusNat3(zzz90, Zero) → Succ(zzz90)

The set Q consists of the following terms:

new_primPlusNat2(Zero, Succ(x0))
new_primMulNat0(x0)
new_primPlusNat3(x0, Succ(x1))
new_primPlusNat2(Succ(x0), Succ(x1))
new_primPlusNat3(x0, Zero)
new_primPlusNat1(Zero)
new_primPlusNat2(Zero, Zero)
new_primPlusNat1(Succ(x0))
new_primPlusNat2(Succ(x0), Zero)

We have to consider all minimal (P,Q,R)-chains.
By rewriting [15] the rule new_mkVBalBranch3MkVBalBranch230(zzz498, zzz499, zzz500, zzz501, zzz502, zzz503, zzz504, zzz505, zzz506, zzz507, bg) → new_mkVBalBranch3MkVBalBranch118(zzz498, zzz499, zzz500, zzz501, zzz502, zzz503, zzz504, zzz505, zzz506, zzz507, new_primPlusNat2(new_primPlusNat3(Succ(new_primPlusNat3(new_primPlusNat1(zzz500), zzz500)), Succ(zzz500)), Succ(zzz500)), bg) at position [10,0] we obtained the following new rules:

new_mkVBalBranch3MkVBalBranch230(zzz498, zzz499, zzz500, zzz501, zzz502, zzz503, zzz504, zzz505, zzz506, zzz507, bg) → new_mkVBalBranch3MkVBalBranch118(zzz498, zzz499, zzz500, zzz501, zzz502, zzz503, zzz504, zzz505, zzz506, zzz507, new_primPlusNat2(Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat3(new_primPlusNat1(zzz500), zzz500)), zzz500))), Succ(zzz500)), bg)



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

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

new_mkVBalBranch3MkVBalBranch225(zzz498, zzz499, zzz500, zzz501, zzz502, zzz503, zzz504, zzz505, zzz506, zzz507, Zero, Zero, bg) → new_mkVBalBranch3MkVBalBranch230(zzz498, zzz499, zzz500, zzz501, zzz502, zzz503, zzz504, zzz505, zzz506, zzz507, bg)
new_mkVBalBranch3MkVBalBranch18(zzz340, zzz341, zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, Succ(zzz1480), h) → new_mkVBalBranch3MkVBalBranch115(zzz340, zzz341, Zero, zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, Succ(zzz1480), Succ(zzz51200), h)
new_mkVBalBranch0(zzz31, Branch(zzz510, zzz511, Neg(Zero), zzz513, zzz514), Branch(zzz340, zzz341, Pos(Succ(zzz34200)), zzz343, zzz344), h) → new_mkVBalBranch0(zzz31, Branch(zzz510, zzz511, Neg(Zero), zzz513, zzz514), zzz343, h)
new_mkVBalBranch3MkVBalBranch215(zzz340, zzz341, Pos(Succ(Succ(zzz342000))), zzz343, zzz344, zzz510, zzz511, Succ(zzz512000), zzz513, zzz514, zzz31, Succ(Succ(zzz6600)), h) → new_mkVBalBranch3MkVBalBranch216(zzz340, zzz341, Succ(zzz342000), zzz343, zzz344, zzz510, zzz511, zzz512000, zzz513, zzz514, zzz31, Succ(Succ(new_primPlusNat2(zzz6600, zzz512000))), zzz342000, h)
new_mkVBalBranch3MkVBalBranch223(zzz340, zzz341, Neg(Succ(Succ(Succ(zzz3420000)))), zzz343, zzz344, zzz510, zzz511, Zero, zzz513, zzz514, zzz31, Succ(Succ(zzz6700)), h) → new_mkVBalBranch3MkVBalBranch225(zzz340, zzz341, Succ(Succ(zzz3420000)), zzz343, zzz344, zzz510, zzz511, zzz513, zzz514, zzz31, Succ(zzz3420000), Succ(zzz6700), h)
new_mkVBalBranch3MkVBalBranch120(zzz2050, zzz2051, zzz2052, zzz2053, zzz2054, zzz2055, zzz2056, zzz2057, zzz2058, zzz2059, zzz2060, Zero, Succ(zzz20620), be) → new_mkVBalBranch0(zzz2060, zzz2059, Branch(zzz2050, zzz2051, Neg(Succ(zzz2052)), zzz2053, zzz2054), be)
new_mkVBalBranch0(zzz31, Branch(zzz510, zzz511, Pos(Zero), zzz513, zzz514), Branch(zzz340, zzz341, Pos(Succ(zzz34200)), zzz343, zzz344), h) → new_mkVBalBranch0(zzz31, Branch(zzz510, zzz511, Pos(Zero), zzz513, zzz514), zzz343, h)
new_mkVBalBranch3MkVBalBranch121(zzz473, zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, zzz481, zzz482, Succ(zzz7390), bh) → new_mkVBalBranch3MkVBalBranch115(zzz473, zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, Zero, zzz480, zzz481, zzz482, Succ(zzz7390), Succ(Zero), bh)
new_mkVBalBranch0(zzz31, Branch(zzz510, zzz511, Pos(Succ(zzz51200)), zzz513, zzz514), Branch(zzz340, zzz341, zzz342, zzz343, zzz344), h) → new_mkVBalBranch3MkVBalBranch215(zzz340, zzz341, zzz342, zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat3(new_primPlusNat1(zzz51200), zzz51200)), zzz51200))), h)
new_mkVBalBranch3MkVBalBranch223(zzz340, zzz341, Neg(Succ(Succ(Zero))), zzz343, zzz344, zzz510, zzz511, Succ(zzz512000), zzz513, zzz514, zzz31, Succ(Succ(zzz6700)), h) → new_mkVBalBranch3MkVBalBranch224(zzz340, zzz341, Succ(Zero), zzz343, zzz344, zzz510, zzz511, zzz512000, zzz513, zzz514, zzz31, Zero, Succ(Succ(new_primPlusNat2(zzz6700, zzz512000))), h)
new_mkVBalBranch3MkVBalBranch224(zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, zzz1125, zzz1126, zzz1127, zzz1128, zzz1129, Succ(zzz11300), Succ(zzz11310), bd) → new_mkVBalBranch3MkVBalBranch224(zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, zzz1125, zzz1126, zzz1127, zzz1128, zzz1129, zzz11300, zzz11310, bd)
new_mkVBalBranch3MkVBalBranch217(zzz473, zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, zzz481, zzz482, Zero, Succ(zzz4840), bh) → new_mkVBalBranch0(zzz482, Branch(zzz478, zzz479, Pos(Succ(Zero)), zzz480, zzz481), zzz476, bh)
new_mkVBalBranch3MkVBalBranch218(zzz461, zzz462, zzz463, zzz464, zzz465, zzz466, zzz467, zzz468, zzz469, zzz470, zzz471, bb) → new_mkVBalBranch3MkVBalBranch110(zzz461, zzz462, zzz463, zzz464, zzz465, zzz466, zzz467, zzz468, zzz469, zzz470, zzz471, new_primPlusNat2(new_primPlusNat3(Succ(new_primPlusNat3(new_primPlusNat1(zzz463), zzz463)), Succ(zzz463)), Succ(zzz463)), bb)
new_mkVBalBranch3MkVBalBranch110(zzz461, zzz462, zzz463, zzz464, zzz465, zzz466, zzz467, zzz468, zzz469, zzz470, zzz471, Succ(zzz5800), bb) → new_mkVBalBranch3MkVBalBranch115(zzz461, zzz462, zzz463, zzz464, zzz465, zzz466, zzz467, Succ(zzz468), zzz469, zzz470, zzz471, Succ(zzz5800), Succ(Succ(zzz468)), bb)
new_mkVBalBranch3MkVBalBranch227(zzz486, zzz487, zzz488, zzz489, zzz490, zzz491, zzz492, zzz493, zzz494, zzz495, zzz496, bf) → new_mkVBalBranch0(zzz496, Branch(zzz491, zzz492, Neg(Succ(Succ(zzz493))), zzz494, zzz495), zzz489, bf)
new_mkVBalBranch3MkVBalBranch215(zzz340, zzz341, Pos(Zero), zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, Succ(zzz660), h) → new_mkVBalBranch0(zzz31, zzz514, Branch(zzz340, zzz341, Pos(Zero), zzz343, zzz344), h)
new_mkVBalBranch3MkVBalBranch217(zzz473, zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, zzz481, zzz482, Succ(zzz4830), Zero, bh) → new_mkVBalBranch3MkVBalBranch121(zzz473, zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, zzz481, zzz482, new_primPlusNat2(new_primMulNat0(zzz475), Succ(zzz475)), bh)
new_mkVBalBranch3MkVBalBranch223(zzz340, zzz341, Neg(Zero), zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, Succ(zzz670), h) → new_mkVBalBranch0(zzz31, Branch(zzz510, zzz511, Neg(Succ(zzz51200)), zzz513, zzz514), zzz343, h)
new_mkVBalBranch3MkVBalBranch216(zzz1105, zzz1106, zzz1107, zzz1108, zzz1109, zzz1110, zzz1111, zzz1112, zzz1113, zzz1114, zzz1115, Zero, Succ(zzz11170), ba) → new_mkVBalBranch0(zzz1115, Branch(zzz1110, zzz1111, Pos(Succ(Succ(zzz1112))), zzz1113, zzz1114), zzz1108, ba)
new_mkVBalBranch3MkVBalBranch115(zzz1986, zzz1987, zzz1988, zzz1989, zzz1990, zzz1991, zzz1992, zzz1993, zzz1994, zzz1995, zzz1996, Zero, Succ(zzz19980), bc) → new_mkVBalBranch0(zzz1996, zzz1995, Branch(zzz1986, zzz1987, Pos(Succ(zzz1988)), zzz1989, zzz1990), bc)
new_mkVBalBranch3MkVBalBranch230(zzz498, zzz499, zzz500, zzz501, zzz502, zzz503, zzz504, zzz505, zzz506, zzz507, bg) → new_mkVBalBranch3MkVBalBranch118(zzz498, zzz499, zzz500, zzz501, zzz502, zzz503, zzz504, zzz505, zzz506, zzz507, new_primPlusNat2(Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat3(new_primPlusNat1(zzz500), zzz500)), zzz500))), Succ(zzz500)), bg)
new_mkVBalBranch3MkVBalBranch122(zzz340, zzz341, zzz34200, zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, h) → new_mkVBalBranch0(zzz31, zzz514, Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), h)
new_mkVBalBranch3MkVBalBranch217(zzz473, zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, zzz481, zzz482, Succ(zzz4830), Succ(zzz4840), bh) → new_mkVBalBranch3MkVBalBranch217(zzz473, zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, zzz481, zzz482, zzz4830, zzz4840, bh)
new_mkVBalBranch3MkVBalBranch116(zzz340, zzz341, zzz34200, zzz343, zzz344, zzz510, zzz511, zzz513, zzz514, zzz31, Succ(zzz1200), h) → new_mkVBalBranch0(zzz31, zzz514, Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), h)
new_mkVBalBranch3MkVBalBranch110(zzz461, zzz462, zzz463, zzz464, zzz465, zzz466, zzz467, zzz468, zzz469, zzz470, zzz471, Zero, bb) → new_mkVBalBranch3MkVBalBranch115(zzz461, zzz462, zzz463, zzz464, zzz465, zzz466, zzz467, Succ(zzz468), zzz469, zzz470, zzz471, Zero, Succ(Succ(zzz468)), bb)
new_mkVBalBranch3MkVBalBranch225(zzz498, zzz499, zzz500, zzz501, zzz502, zzz503, zzz504, zzz505, zzz506, zzz507, Zero, Succ(zzz5090), bg) → new_mkVBalBranch0(zzz507, Branch(zzz503, zzz504, Neg(Succ(Zero)), zzz505, zzz506), zzz501, bg)
new_mkVBalBranch0(zzz31, Branch(zzz510, zzz511, Neg(Succ(zzz51200)), zzz513, zzz514), Branch(zzz340, zzz341, zzz342, zzz343, zzz344), h) → new_mkVBalBranch3MkVBalBranch223(zzz340, zzz341, zzz342, zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat3(new_primPlusNat1(zzz51200), zzz51200)), zzz51200))), h)
new_mkVBalBranch3MkVBalBranch222(zzz461, zzz462, zzz463, zzz464, zzz465, zzz466, zzz467, zzz468, zzz469, zzz470, zzz471, bb) → new_mkVBalBranch3MkVBalBranch110(zzz461, zzz462, zzz463, zzz464, zzz465, zzz466, zzz467, zzz468, zzz469, zzz470, zzz471, new_primPlusNat2(new_primPlusNat3(Succ(new_primPlusNat3(new_primPlusNat1(zzz463), zzz463)), Succ(zzz463)), Succ(zzz463)), bb)
new_mkVBalBranch0(zzz31, Branch(zzz510, zzz511, Neg(Zero), zzz513, zzz514), Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), h) → new_mkVBalBranch3MkVBalBranch117(zzz340, zzz341, zzz34200, zzz343, zzz344, zzz510, zzz511, zzz513, zzz514, zzz31, new_primPlusNat2(new_primPlusNat3(Succ(new_primPlusNat3(new_primPlusNat1(zzz34200), zzz34200)), Succ(zzz34200)), Succ(zzz34200)), h)
new_mkVBalBranch3MkVBalBranch121(zzz473, zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, zzz481, zzz482, Zero, bh) → new_mkVBalBranch3MkVBalBranch115(zzz473, zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, Zero, zzz480, zzz481, zzz482, Zero, Succ(Zero), bh)
new_mkVBalBranch3MkVBalBranch225(zzz498, zzz499, zzz500, zzz501, zzz502, zzz503, zzz504, zzz505, zzz506, zzz507, Succ(zzz5080), Zero, bg) → new_mkVBalBranch3MkVBalBranch118(zzz498, zzz499, zzz500, zzz501, zzz502, zzz503, zzz504, zzz505, zzz506, zzz507, new_primPlusNat2(new_primMulNat0(zzz500), Succ(zzz500)), bg)
new_mkVBalBranch3MkVBalBranch223(zzz340, zzz341, Neg(Succ(Zero)), zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, Succ(zzz670), h) → new_mkVBalBranch0(zzz31, Branch(zzz510, zzz511, Neg(Succ(zzz51200)), zzz513, zzz514), zzz343, h)
new_mkVBalBranch3MkVBalBranch215(zzz340, zzz341, Pos(Succ(Zero)), zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, Succ(zzz660), h) → new_mkVBalBranch3MkVBalBranch18(zzz340, zzz341, zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, new_primPlusNat2(new_primMulNat0(Zero), Succ(Zero)), h)
new_mkVBalBranch3MkVBalBranch229(zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, zzz1125, zzz1126, zzz1127, zzz1128, zzz1129, bd) → new_mkVBalBranch3MkVBalBranch119(zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, zzz1125, zzz1126, zzz1127, zzz1128, zzz1129, new_primPlusNat2(new_primMulNat0(zzz1121), Succ(zzz1121)), bd)
new_mkVBalBranch3MkVBalBranch233(zzz473, zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, zzz481, zzz482, bh) → new_mkVBalBranch3MkVBalBranch121(zzz473, zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, zzz481, zzz482, new_primPlusNat2(new_primMulNat0(zzz475), Succ(zzz475)), bh)
new_mkVBalBranch0(zzz31, Branch(zzz510, zzz511, Pos(Zero), zzz513, zzz514), Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), h) → new_mkVBalBranch3MkVBalBranch116(zzz340, zzz341, zzz34200, zzz343, zzz344, zzz510, zzz511, zzz513, zzz514, zzz31, new_primPlusNat2(new_primPlusNat3(Succ(new_primPlusNat3(new_primPlusNat1(zzz34200), zzz34200)), Succ(zzz34200)), Succ(zzz34200)), h)
new_mkVBalBranch3MkVBalBranch215(zzz340, zzz341, Pos(Succ(Succ(zzz342000))), zzz343, zzz344, zzz510, zzz511, Zero, zzz513, zzz514, zzz31, Succ(Succ(zzz6600)), h) → new_mkVBalBranch3MkVBalBranch217(zzz340, zzz341, Succ(zzz342000), zzz343, zzz344, zzz510, zzz511, zzz513, zzz514, zzz31, Succ(zzz6600), zzz342000, h)
new_mkVBalBranch3MkVBalBranch117(zzz340, zzz341, zzz34200, zzz343, zzz344, zzz510, zzz511, zzz513, zzz514, zzz31, Succ(zzz1240), h) → new_mkVBalBranch0(zzz31, zzz514, Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), h)
new_mkVBalBranch3MkVBalBranch120(zzz2050, zzz2051, zzz2052, zzz2053, zzz2054, zzz2055, zzz2056, zzz2057, zzz2058, zzz2059, zzz2060, Succ(zzz20610), Succ(zzz20620), be) → new_mkVBalBranch3MkVBalBranch120(zzz2050, zzz2051, zzz2052, zzz2053, zzz2054, zzz2055, zzz2056, zzz2057, zzz2058, zzz2059, zzz2060, zzz20610, zzz20620, be)
new_mkVBalBranch3MkVBalBranch217(zzz473, zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, zzz481, zzz482, Zero, Zero, bh) → new_mkVBalBranch3MkVBalBranch233(zzz473, zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, zzz481, zzz482, bh)
new_mkVBalBranch3MkVBalBranch216(zzz1105, zzz1106, zzz1107, zzz1108, zzz1109, zzz1110, zzz1111, zzz1112, zzz1113, zzz1114, zzz1115, Succ(zzz11160), Succ(zzz11170), ba) → new_mkVBalBranch3MkVBalBranch216(zzz1105, zzz1106, zzz1107, zzz1108, zzz1109, zzz1110, zzz1111, zzz1112, zzz1113, zzz1114, zzz1115, zzz11160, zzz11170, ba)
new_mkVBalBranch3MkVBalBranch223(zzz340, zzz341, Pos(zzz3420), zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, Succ(zzz670), h) → new_mkVBalBranch0(zzz31, Branch(zzz510, zzz511, Neg(Succ(zzz51200)), zzz513, zzz514), zzz343, h)
new_mkVBalBranch3MkVBalBranch19(zzz340, zzz341, zzz34200, zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, Zero, h) → new_mkVBalBranch3MkVBalBranch122(zzz340, zzz341, zzz34200, zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, h)
new_mkVBalBranch3MkVBalBranch225(zzz498, zzz499, zzz500, zzz501, zzz502, zzz503, zzz504, zzz505, zzz506, zzz507, Succ(zzz5080), Succ(zzz5090), bg) → new_mkVBalBranch3MkVBalBranch225(zzz498, zzz499, zzz500, zzz501, zzz502, zzz503, zzz504, zzz505, zzz506, zzz507, zzz5080, zzz5090, bg)
new_mkVBalBranch3MkVBalBranch19(zzz340, zzz341, zzz34200, zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, Succ(zzz1410), h) → new_mkVBalBranch0(zzz31, zzz514, Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), h)
new_mkVBalBranch3MkVBalBranch224(zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, zzz1125, zzz1126, zzz1127, zzz1128, zzz1129, Succ(zzz11300), Zero, bd) → new_mkVBalBranch3MkVBalBranch119(zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, zzz1125, zzz1126, zzz1127, zzz1128, zzz1129, new_primPlusNat2(new_primMulNat0(zzz1121), Succ(zzz1121)), bd)
new_mkVBalBranch3MkVBalBranch224(zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, zzz1125, zzz1126, zzz1127, zzz1128, zzz1129, Zero, Succ(zzz11310), bd) → new_mkVBalBranch3MkVBalBranch227(zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, zzz1125, zzz1126, zzz1127, zzz1128, zzz1129, bd)
new_mkVBalBranch3MkVBalBranch224(zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, zzz1125, zzz1126, zzz1127, zzz1128, zzz1129, Zero, Zero, bd) → new_mkVBalBranch3MkVBalBranch229(zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, zzz1125, zzz1126, zzz1127, zzz1128, zzz1129, bd)
new_mkVBalBranch3MkVBalBranch223(zzz340, zzz341, Neg(Succ(Succ(Succ(zzz3420000)))), zzz343, zzz344, zzz510, zzz511, Succ(zzz512000), zzz513, zzz514, zzz31, Succ(Succ(zzz6700)), h) → new_mkVBalBranch3MkVBalBranch224(zzz340, zzz341, Succ(Succ(zzz3420000)), zzz343, zzz344, zzz510, zzz511, zzz512000, zzz513, zzz514, zzz31, Succ(zzz3420000), Succ(Succ(new_primPlusNat2(zzz6700, zzz512000))), h)
new_mkVBalBranch3MkVBalBranch223(zzz340, zzz341, Neg(Succ(Succ(Zero))), zzz343, zzz344, zzz510, zzz511, Zero, zzz513, zzz514, zzz31, Succ(Succ(zzz6700)), h) → new_mkVBalBranch3MkVBalBranch225(zzz340, zzz341, Succ(Zero), zzz343, zzz344, zzz510, zzz511, zzz513, zzz514, zzz31, Zero, Succ(zzz6700), h)
new_mkVBalBranch3MkVBalBranch115(zzz1986, zzz1987, zzz1988, zzz1989, zzz1990, zzz1991, zzz1992, zzz1993, zzz1994, zzz1995, zzz1996, Succ(zzz19970), Succ(zzz19980), bc) → new_mkVBalBranch3MkVBalBranch115(zzz1986, zzz1987, zzz1988, zzz1989, zzz1990, zzz1991, zzz1992, zzz1993, zzz1994, zzz1995, zzz1996, zzz19970, zzz19980, bc)
new_mkVBalBranch3MkVBalBranch215(zzz340, zzz341, Neg(Zero), zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, Succ(zzz660), h) → new_mkVBalBranch0(zzz31, zzz514, Branch(zzz340, zzz341, Neg(Zero), zzz343, zzz344), h)
new_mkVBalBranch3MkVBalBranch118(zzz498, zzz499, zzz500, zzz501, zzz502, zzz503, zzz504, zzz505, zzz506, zzz507, Succ(zzz8040), bg) → new_mkVBalBranch3MkVBalBranch120(zzz498, zzz499, zzz500, zzz501, zzz502, zzz503, zzz504, Zero, zzz505, zzz506, zzz507, Succ(Zero), Succ(zzz8040), bg)
new_mkVBalBranch3MkVBalBranch216(zzz1105, zzz1106, zzz1107, zzz1108, zzz1109, zzz1110, zzz1111, zzz1112, zzz1113, zzz1114, zzz1115, Succ(zzz11160), Zero, ba) → new_mkVBalBranch3MkVBalBranch218(zzz1105, zzz1106, zzz1107, zzz1108, zzz1109, zzz1110, zzz1111, zzz1112, zzz1113, zzz1114, zzz1115, ba)
new_mkVBalBranch3MkVBalBranch215(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, Succ(zzz660), h) → new_mkVBalBranch3MkVBalBranch19(zzz340, zzz341, zzz34200, zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, new_primPlusNat2(new_primMulNat0(zzz34200), Succ(zzz34200)), h)
new_mkVBalBranch3MkVBalBranch216(zzz1105, zzz1106, zzz1107, zzz1108, zzz1109, zzz1110, zzz1111, zzz1112, zzz1113, zzz1114, zzz1115, Zero, Zero, ba) → new_mkVBalBranch3MkVBalBranch222(zzz1105, zzz1106, zzz1107, zzz1108, zzz1109, zzz1110, zzz1111, zzz1112, zzz1113, zzz1114, zzz1115, ba)
new_mkVBalBranch3MkVBalBranch18(zzz340, zzz341, zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, Zero, h) → new_mkVBalBranch3MkVBalBranch115(zzz340, zzz341, Zero, zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, Zero, Succ(zzz51200), h)
new_mkVBalBranch3MkVBalBranch119(zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, zzz1125, zzz1126, zzz1127, zzz1128, zzz1129, Succ(zzz12130), bd) → new_mkVBalBranch3MkVBalBranch120(zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, zzz1125, Succ(zzz1126), zzz1127, zzz1128, zzz1129, Succ(Succ(zzz1126)), Succ(zzz12130), bd)

The TRS R consists of the following rules:

new_primMulNat0(zzz6200) → new_primPlusNat3(Succ(new_primPlusNat3(new_primPlusNat1(zzz6200), zzz6200)), Succ(zzz6200))
new_primPlusNat2(Succ(zzz900), Succ(zzz9100)) → Succ(Succ(new_primPlusNat2(zzz900, zzz9100)))
new_primPlusNat2(Zero, Succ(zzz9100)) → Succ(zzz9100)
new_primPlusNat2(Zero, Zero) → Zero
new_primPlusNat2(Succ(zzz900), Zero) → Succ(zzz900)
new_primPlusNat1(Zero) → Zero
new_primPlusNat1(Succ(zzz62000)) → Succ(Succ(new_primPlusNat1(zzz62000)))
new_primPlusNat3(zzz90, Succ(zzz910)) → Succ(Succ(new_primPlusNat2(zzz90, zzz910)))
new_primPlusNat3(zzz90, Zero) → Succ(zzz90)

The set Q consists of the following terms:

new_primPlusNat2(Zero, Succ(x0))
new_primMulNat0(x0)
new_primPlusNat3(x0, Succ(x1))
new_primPlusNat2(Succ(x0), Succ(x1))
new_primPlusNat3(x0, Zero)
new_primPlusNat1(Zero)
new_primPlusNat2(Zero, Zero)
new_primPlusNat1(Succ(x0))
new_primPlusNat2(Succ(x0), Zero)

We have to consider all minimal (P,Q,R)-chains.
By rewriting [15] the rule new_mkVBalBranch3MkVBalBranch225(zzz498, zzz499, zzz500, zzz501, zzz502, zzz503, zzz504, zzz505, zzz506, zzz507, Succ(zzz5080), Zero, bg) → new_mkVBalBranch3MkVBalBranch118(zzz498, zzz499, zzz500, zzz501, zzz502, zzz503, zzz504, zzz505, zzz506, zzz507, new_primPlusNat2(new_primMulNat0(zzz500), Succ(zzz500)), bg) at position [10,0] we obtained the following new rules:

new_mkVBalBranch3MkVBalBranch225(zzz498, zzz499, zzz500, zzz501, zzz502, zzz503, zzz504, zzz505, zzz506, zzz507, Succ(zzz5080), Zero, bg) → new_mkVBalBranch3MkVBalBranch118(zzz498, zzz499, zzz500, zzz501, zzz502, zzz503, zzz504, zzz505, zzz506, zzz507, new_primPlusNat2(new_primPlusNat3(Succ(new_primPlusNat3(new_primPlusNat1(zzz500), zzz500)), Succ(zzz500)), Succ(zzz500)), bg)



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

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

new_mkVBalBranch3MkVBalBranch225(zzz498, zzz499, zzz500, zzz501, zzz502, zzz503, zzz504, zzz505, zzz506, zzz507, Zero, Zero, bg) → new_mkVBalBranch3MkVBalBranch230(zzz498, zzz499, zzz500, zzz501, zzz502, zzz503, zzz504, zzz505, zzz506, zzz507, bg)
new_mkVBalBranch3MkVBalBranch18(zzz340, zzz341, zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, Succ(zzz1480), h) → new_mkVBalBranch3MkVBalBranch115(zzz340, zzz341, Zero, zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, Succ(zzz1480), Succ(zzz51200), h)
new_mkVBalBranch3MkVBalBranch215(zzz340, zzz341, Pos(Succ(Succ(zzz342000))), zzz343, zzz344, zzz510, zzz511, Succ(zzz512000), zzz513, zzz514, zzz31, Succ(Succ(zzz6600)), h) → new_mkVBalBranch3MkVBalBranch216(zzz340, zzz341, Succ(zzz342000), zzz343, zzz344, zzz510, zzz511, zzz512000, zzz513, zzz514, zzz31, Succ(Succ(new_primPlusNat2(zzz6600, zzz512000))), zzz342000, h)
new_mkVBalBranch0(zzz31, Branch(zzz510, zzz511, Neg(Zero), zzz513, zzz514), Branch(zzz340, zzz341, Pos(Succ(zzz34200)), zzz343, zzz344), h) → new_mkVBalBranch0(zzz31, Branch(zzz510, zzz511, Neg(Zero), zzz513, zzz514), zzz343, h)
new_mkVBalBranch3MkVBalBranch223(zzz340, zzz341, Neg(Succ(Succ(Succ(zzz3420000)))), zzz343, zzz344, zzz510, zzz511, Zero, zzz513, zzz514, zzz31, Succ(Succ(zzz6700)), h) → new_mkVBalBranch3MkVBalBranch225(zzz340, zzz341, Succ(Succ(zzz3420000)), zzz343, zzz344, zzz510, zzz511, zzz513, zzz514, zzz31, Succ(zzz3420000), Succ(zzz6700), h)
new_mkVBalBranch3MkVBalBranch120(zzz2050, zzz2051, zzz2052, zzz2053, zzz2054, zzz2055, zzz2056, zzz2057, zzz2058, zzz2059, zzz2060, Zero, Succ(zzz20620), be) → new_mkVBalBranch0(zzz2060, zzz2059, Branch(zzz2050, zzz2051, Neg(Succ(zzz2052)), zzz2053, zzz2054), be)
new_mkVBalBranch3MkVBalBranch121(zzz473, zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, zzz481, zzz482, Succ(zzz7390), bh) → new_mkVBalBranch3MkVBalBranch115(zzz473, zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, Zero, zzz480, zzz481, zzz482, Succ(zzz7390), Succ(Zero), bh)
new_mkVBalBranch0(zzz31, Branch(zzz510, zzz511, Pos(Zero), zzz513, zzz514), Branch(zzz340, zzz341, Pos(Succ(zzz34200)), zzz343, zzz344), h) → new_mkVBalBranch0(zzz31, Branch(zzz510, zzz511, Pos(Zero), zzz513, zzz514), zzz343, h)
new_mkVBalBranch0(zzz31, Branch(zzz510, zzz511, Pos(Succ(zzz51200)), zzz513, zzz514), Branch(zzz340, zzz341, zzz342, zzz343, zzz344), h) → new_mkVBalBranch3MkVBalBranch215(zzz340, zzz341, zzz342, zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat3(new_primPlusNat1(zzz51200), zzz51200)), zzz51200))), h)
new_mkVBalBranch3MkVBalBranch223(zzz340, zzz341, Neg(Succ(Succ(Zero))), zzz343, zzz344, zzz510, zzz511, Succ(zzz512000), zzz513, zzz514, zzz31, Succ(Succ(zzz6700)), h) → new_mkVBalBranch3MkVBalBranch224(zzz340, zzz341, Succ(Zero), zzz343, zzz344, zzz510, zzz511, zzz512000, zzz513, zzz514, zzz31, Zero, Succ(Succ(new_primPlusNat2(zzz6700, zzz512000))), h)
new_mkVBalBranch3MkVBalBranch224(zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, zzz1125, zzz1126, zzz1127, zzz1128, zzz1129, Succ(zzz11300), Succ(zzz11310), bd) → new_mkVBalBranch3MkVBalBranch224(zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, zzz1125, zzz1126, zzz1127, zzz1128, zzz1129, zzz11300, zzz11310, bd)
new_mkVBalBranch3MkVBalBranch217(zzz473, zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, zzz481, zzz482, Zero, Succ(zzz4840), bh) → new_mkVBalBranch0(zzz482, Branch(zzz478, zzz479, Pos(Succ(Zero)), zzz480, zzz481), zzz476, bh)
new_mkVBalBranch3MkVBalBranch218(zzz461, zzz462, zzz463, zzz464, zzz465, zzz466, zzz467, zzz468, zzz469, zzz470, zzz471, bb) → new_mkVBalBranch3MkVBalBranch110(zzz461, zzz462, zzz463, zzz464, zzz465, zzz466, zzz467, zzz468, zzz469, zzz470, zzz471, new_primPlusNat2(new_primPlusNat3(Succ(new_primPlusNat3(new_primPlusNat1(zzz463), zzz463)), Succ(zzz463)), Succ(zzz463)), bb)
new_mkVBalBranch3MkVBalBranch110(zzz461, zzz462, zzz463, zzz464, zzz465, zzz466, zzz467, zzz468, zzz469, zzz470, zzz471, Succ(zzz5800), bb) → new_mkVBalBranch3MkVBalBranch115(zzz461, zzz462, zzz463, zzz464, zzz465, zzz466, zzz467, Succ(zzz468), zzz469, zzz470, zzz471, Succ(zzz5800), Succ(Succ(zzz468)), bb)
new_mkVBalBranch3MkVBalBranch227(zzz486, zzz487, zzz488, zzz489, zzz490, zzz491, zzz492, zzz493, zzz494, zzz495, zzz496, bf) → new_mkVBalBranch0(zzz496, Branch(zzz491, zzz492, Neg(Succ(Succ(zzz493))), zzz494, zzz495), zzz489, bf)
new_mkVBalBranch3MkVBalBranch215(zzz340, zzz341, Pos(Zero), zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, Succ(zzz660), h) → new_mkVBalBranch0(zzz31, zzz514, Branch(zzz340, zzz341, Pos(Zero), zzz343, zzz344), h)
new_mkVBalBranch3MkVBalBranch223(zzz340, zzz341, Neg(Zero), zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, Succ(zzz670), h) → new_mkVBalBranch0(zzz31, Branch(zzz510, zzz511, Neg(Succ(zzz51200)), zzz513, zzz514), zzz343, h)
new_mkVBalBranch3MkVBalBranch217(zzz473, zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, zzz481, zzz482, Succ(zzz4830), Zero, bh) → new_mkVBalBranch3MkVBalBranch121(zzz473, zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, zzz481, zzz482, new_primPlusNat2(new_primMulNat0(zzz475), Succ(zzz475)), bh)
new_mkVBalBranch3MkVBalBranch216(zzz1105, zzz1106, zzz1107, zzz1108, zzz1109, zzz1110, zzz1111, zzz1112, zzz1113, zzz1114, zzz1115, Zero, Succ(zzz11170), ba) → new_mkVBalBranch0(zzz1115, Branch(zzz1110, zzz1111, Pos(Succ(Succ(zzz1112))), zzz1113, zzz1114), zzz1108, ba)
new_mkVBalBranch3MkVBalBranch115(zzz1986, zzz1987, zzz1988, zzz1989, zzz1990, zzz1991, zzz1992, zzz1993, zzz1994, zzz1995, zzz1996, Zero, Succ(zzz19980), bc) → new_mkVBalBranch0(zzz1996, zzz1995, Branch(zzz1986, zzz1987, Pos(Succ(zzz1988)), zzz1989, zzz1990), bc)
new_mkVBalBranch3MkVBalBranch122(zzz340, zzz341, zzz34200, zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, h) → new_mkVBalBranch0(zzz31, zzz514, Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), h)
new_mkVBalBranch3MkVBalBranch230(zzz498, zzz499, zzz500, zzz501, zzz502, zzz503, zzz504, zzz505, zzz506, zzz507, bg) → new_mkVBalBranch3MkVBalBranch118(zzz498, zzz499, zzz500, zzz501, zzz502, zzz503, zzz504, zzz505, zzz506, zzz507, new_primPlusNat2(Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat3(new_primPlusNat1(zzz500), zzz500)), zzz500))), Succ(zzz500)), bg)
new_mkVBalBranch3MkVBalBranch217(zzz473, zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, zzz481, zzz482, Succ(zzz4830), Succ(zzz4840), bh) → new_mkVBalBranch3MkVBalBranch217(zzz473, zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, zzz481, zzz482, zzz4830, zzz4840, bh)
new_mkVBalBranch3MkVBalBranch116(zzz340, zzz341, zzz34200, zzz343, zzz344, zzz510, zzz511, zzz513, zzz514, zzz31, Succ(zzz1200), h) → new_mkVBalBranch0(zzz31, zzz514, Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), h)
new_mkVBalBranch3MkVBalBranch110(zzz461, zzz462, zzz463, zzz464, zzz465, zzz466, zzz467, zzz468, zzz469, zzz470, zzz471, Zero, bb) → new_mkVBalBranch3MkVBalBranch115(zzz461, zzz462, zzz463, zzz464, zzz465, zzz466, zzz467, Succ(zzz468), zzz469, zzz470, zzz471, Zero, Succ(Succ(zzz468)), bb)
new_mkVBalBranch3MkVBalBranch225(zzz498, zzz499, zzz500, zzz501, zzz502, zzz503, zzz504, zzz505, zzz506, zzz507, Zero, Succ(zzz5090), bg) → new_mkVBalBranch0(zzz507, Branch(zzz503, zzz504, Neg(Succ(Zero)), zzz505, zzz506), zzz501, bg)
new_mkVBalBranch0(zzz31, Branch(zzz510, zzz511, Neg(Succ(zzz51200)), zzz513, zzz514), Branch(zzz340, zzz341, zzz342, zzz343, zzz344), h) → new_mkVBalBranch3MkVBalBranch223(zzz340, zzz341, zzz342, zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat3(new_primPlusNat1(zzz51200), zzz51200)), zzz51200))), h)
new_mkVBalBranch3MkVBalBranch222(zzz461, zzz462, zzz463, zzz464, zzz465, zzz466, zzz467, zzz468, zzz469, zzz470, zzz471, bb) → new_mkVBalBranch3MkVBalBranch110(zzz461, zzz462, zzz463, zzz464, zzz465, zzz466, zzz467, zzz468, zzz469, zzz470, zzz471, new_primPlusNat2(new_primPlusNat3(Succ(new_primPlusNat3(new_primPlusNat1(zzz463), zzz463)), Succ(zzz463)), Succ(zzz463)), bb)
new_mkVBalBranch0(zzz31, Branch(zzz510, zzz511, Neg(Zero), zzz513, zzz514), Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), h) → new_mkVBalBranch3MkVBalBranch117(zzz340, zzz341, zzz34200, zzz343, zzz344, zzz510, zzz511, zzz513, zzz514, zzz31, new_primPlusNat2(new_primPlusNat3(Succ(new_primPlusNat3(new_primPlusNat1(zzz34200), zzz34200)), Succ(zzz34200)), Succ(zzz34200)), h)
new_mkVBalBranch3MkVBalBranch121(zzz473, zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, zzz481, zzz482, Zero, bh) → new_mkVBalBranch3MkVBalBranch115(zzz473, zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, Zero, zzz480, zzz481, zzz482, Zero, Succ(Zero), bh)
new_mkVBalBranch3MkVBalBranch223(zzz340, zzz341, Neg(Succ(Zero)), zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, Succ(zzz670), h) → new_mkVBalBranch0(zzz31, Branch(zzz510, zzz511, Neg(Succ(zzz51200)), zzz513, zzz514), zzz343, h)
new_mkVBalBranch3MkVBalBranch225(zzz498, zzz499, zzz500, zzz501, zzz502, zzz503, zzz504, zzz505, zzz506, zzz507, Succ(zzz5080), Zero, bg) → new_mkVBalBranch3MkVBalBranch118(zzz498, zzz499, zzz500, zzz501, zzz502, zzz503, zzz504, zzz505, zzz506, zzz507, new_primPlusNat2(new_primPlusNat3(Succ(new_primPlusNat3(new_primPlusNat1(zzz500), zzz500)), Succ(zzz500)), Succ(zzz500)), bg)
new_mkVBalBranch3MkVBalBranch215(zzz340, zzz341, Pos(Succ(Zero)), zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, Succ(zzz660), h) → new_mkVBalBranch3MkVBalBranch18(zzz340, zzz341, zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, new_primPlusNat2(new_primMulNat0(Zero), Succ(Zero)), h)
new_mkVBalBranch3MkVBalBranch229(zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, zzz1125, zzz1126, zzz1127, zzz1128, zzz1129, bd) → new_mkVBalBranch3MkVBalBranch119(zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, zzz1125, zzz1126, zzz1127, zzz1128, zzz1129, new_primPlusNat2(new_primMulNat0(zzz1121), Succ(zzz1121)), bd)
new_mkVBalBranch3MkVBalBranch233(zzz473, zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, zzz481, zzz482, bh) → new_mkVBalBranch3MkVBalBranch121(zzz473, zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, zzz481, zzz482, new_primPlusNat2(new_primMulNat0(zzz475), Succ(zzz475)), bh)
new_mkVBalBranch0(zzz31, Branch(zzz510, zzz511, Pos(Zero), zzz513, zzz514), Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), h) → new_mkVBalBranch3MkVBalBranch116(zzz340, zzz341, zzz34200, zzz343, zzz344, zzz510, zzz511, zzz513, zzz514, zzz31, new_primPlusNat2(new_primPlusNat3(Succ(new_primPlusNat3(new_primPlusNat1(zzz34200), zzz34200)), Succ(zzz34200)), Succ(zzz34200)), h)
new_mkVBalBranch3MkVBalBranch215(zzz340, zzz341, Pos(Succ(Succ(zzz342000))), zzz343, zzz344, zzz510, zzz511, Zero, zzz513, zzz514, zzz31, Succ(Succ(zzz6600)), h) → new_mkVBalBranch3MkVBalBranch217(zzz340, zzz341, Succ(zzz342000), zzz343, zzz344, zzz510, zzz511, zzz513, zzz514, zzz31, Succ(zzz6600), zzz342000, h)
new_mkVBalBranch3MkVBalBranch117(zzz340, zzz341, zzz34200, zzz343, zzz344, zzz510, zzz511, zzz513, zzz514, zzz31, Succ(zzz1240), h) → new_mkVBalBranch0(zzz31, zzz514, Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), h)
new_mkVBalBranch3MkVBalBranch217(zzz473, zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, zzz481, zzz482, Zero, Zero, bh) → new_mkVBalBranch3MkVBalBranch233(zzz473, zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, zzz481, zzz482, bh)
new_mkVBalBranch3MkVBalBranch120(zzz2050, zzz2051, zzz2052, zzz2053, zzz2054, zzz2055, zzz2056, zzz2057, zzz2058, zzz2059, zzz2060, Succ(zzz20610), Succ(zzz20620), be) → new_mkVBalBranch3MkVBalBranch120(zzz2050, zzz2051, zzz2052, zzz2053, zzz2054, zzz2055, zzz2056, zzz2057, zzz2058, zzz2059, zzz2060, zzz20610, zzz20620, be)
new_mkVBalBranch3MkVBalBranch223(zzz340, zzz341, Pos(zzz3420), zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, Succ(zzz670), h) → new_mkVBalBranch0(zzz31, Branch(zzz510, zzz511, Neg(Succ(zzz51200)), zzz513, zzz514), zzz343, h)
new_mkVBalBranch3MkVBalBranch216(zzz1105, zzz1106, zzz1107, zzz1108, zzz1109, zzz1110, zzz1111, zzz1112, zzz1113, zzz1114, zzz1115, Succ(zzz11160), Succ(zzz11170), ba) → new_mkVBalBranch3MkVBalBranch216(zzz1105, zzz1106, zzz1107, zzz1108, zzz1109, zzz1110, zzz1111, zzz1112, zzz1113, zzz1114, zzz1115, zzz11160, zzz11170, ba)
new_mkVBalBranch3MkVBalBranch19(zzz340, zzz341, zzz34200, zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, Zero, h) → new_mkVBalBranch3MkVBalBranch122(zzz340, zzz341, zzz34200, zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, h)
new_mkVBalBranch3MkVBalBranch225(zzz498, zzz499, zzz500, zzz501, zzz502, zzz503, zzz504, zzz505, zzz506, zzz507, Succ(zzz5080), Succ(zzz5090), bg) → new_mkVBalBranch3MkVBalBranch225(zzz498, zzz499, zzz500, zzz501, zzz502, zzz503, zzz504, zzz505, zzz506, zzz507, zzz5080, zzz5090, bg)
new_mkVBalBranch3MkVBalBranch19(zzz340, zzz341, zzz34200, zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, Succ(zzz1410), h) → new_mkVBalBranch0(zzz31, zzz514, Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), h)
new_mkVBalBranch3MkVBalBranch224(zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, zzz1125, zzz1126, zzz1127, zzz1128, zzz1129, Succ(zzz11300), Zero, bd) → new_mkVBalBranch3MkVBalBranch119(zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, zzz1125, zzz1126, zzz1127, zzz1128, zzz1129, new_primPlusNat2(new_primMulNat0(zzz1121), Succ(zzz1121)), bd)
new_mkVBalBranch3MkVBalBranch224(zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, zzz1125, zzz1126, zzz1127, zzz1128, zzz1129, Zero, Zero, bd) → new_mkVBalBranch3MkVBalBranch229(zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, zzz1125, zzz1126, zzz1127, zzz1128, zzz1129, bd)
new_mkVBalBranch3MkVBalBranch224(zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, zzz1125, zzz1126, zzz1127, zzz1128, zzz1129, Zero, Succ(zzz11310), bd) → new_mkVBalBranch3MkVBalBranch227(zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, zzz1125, zzz1126, zzz1127, zzz1128, zzz1129, bd)
new_mkVBalBranch3MkVBalBranch223(zzz340, zzz341, Neg(Succ(Succ(Zero))), zzz343, zzz344, zzz510, zzz511, Zero, zzz513, zzz514, zzz31, Succ(Succ(zzz6700)), h) → new_mkVBalBranch3MkVBalBranch225(zzz340, zzz341, Succ(Zero), zzz343, zzz344, zzz510, zzz511, zzz513, zzz514, zzz31, Zero, Succ(zzz6700), h)
new_mkVBalBranch3MkVBalBranch223(zzz340, zzz341, Neg(Succ(Succ(Succ(zzz3420000)))), zzz343, zzz344, zzz510, zzz511, Succ(zzz512000), zzz513, zzz514, zzz31, Succ(Succ(zzz6700)), h) → new_mkVBalBranch3MkVBalBranch224(zzz340, zzz341, Succ(Succ(zzz3420000)), zzz343, zzz344, zzz510, zzz511, zzz512000, zzz513, zzz514, zzz31, Succ(zzz3420000), Succ(Succ(new_primPlusNat2(zzz6700, zzz512000))), h)
new_mkVBalBranch3MkVBalBranch115(zzz1986, zzz1987, zzz1988, zzz1989, zzz1990, zzz1991, zzz1992, zzz1993, zzz1994, zzz1995, zzz1996, Succ(zzz19970), Succ(zzz19980), bc) → new_mkVBalBranch3MkVBalBranch115(zzz1986, zzz1987, zzz1988, zzz1989, zzz1990, zzz1991, zzz1992, zzz1993, zzz1994, zzz1995, zzz1996, zzz19970, zzz19980, bc)
new_mkVBalBranch3MkVBalBranch215(zzz340, zzz341, Neg(Zero), zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, Succ(zzz660), h) → new_mkVBalBranch0(zzz31, zzz514, Branch(zzz340, zzz341, Neg(Zero), zzz343, zzz344), h)
new_mkVBalBranch3MkVBalBranch118(zzz498, zzz499, zzz500, zzz501, zzz502, zzz503, zzz504, zzz505, zzz506, zzz507, Succ(zzz8040), bg) → new_mkVBalBranch3MkVBalBranch120(zzz498, zzz499, zzz500, zzz501, zzz502, zzz503, zzz504, Zero, zzz505, zzz506, zzz507, Succ(Zero), Succ(zzz8040), bg)
new_mkVBalBranch3MkVBalBranch216(zzz1105, zzz1106, zzz1107, zzz1108, zzz1109, zzz1110, zzz1111, zzz1112, zzz1113, zzz1114, zzz1115, Succ(zzz11160), Zero, ba) → new_mkVBalBranch3MkVBalBranch218(zzz1105, zzz1106, zzz1107, zzz1108, zzz1109, zzz1110, zzz1111, zzz1112, zzz1113, zzz1114, zzz1115, ba)
new_mkVBalBranch3MkVBalBranch215(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, Succ(zzz660), h) → new_mkVBalBranch3MkVBalBranch19(zzz340, zzz341, zzz34200, zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, new_primPlusNat2(new_primMulNat0(zzz34200), Succ(zzz34200)), h)
new_mkVBalBranch3MkVBalBranch216(zzz1105, zzz1106, zzz1107, zzz1108, zzz1109, zzz1110, zzz1111, zzz1112, zzz1113, zzz1114, zzz1115, Zero, Zero, ba) → new_mkVBalBranch3MkVBalBranch222(zzz1105, zzz1106, zzz1107, zzz1108, zzz1109, zzz1110, zzz1111, zzz1112, zzz1113, zzz1114, zzz1115, ba)
new_mkVBalBranch3MkVBalBranch119(zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, zzz1125, zzz1126, zzz1127, zzz1128, zzz1129, Succ(zzz12130), bd) → new_mkVBalBranch3MkVBalBranch120(zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, zzz1125, Succ(zzz1126), zzz1127, zzz1128, zzz1129, Succ(Succ(zzz1126)), Succ(zzz12130), bd)
new_mkVBalBranch3MkVBalBranch18(zzz340, zzz341, zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, Zero, h) → new_mkVBalBranch3MkVBalBranch115(zzz340, zzz341, Zero, zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, Zero, Succ(zzz51200), h)

The TRS R consists of the following rules:

new_primMulNat0(zzz6200) → new_primPlusNat3(Succ(new_primPlusNat3(new_primPlusNat1(zzz6200), zzz6200)), Succ(zzz6200))
new_primPlusNat2(Succ(zzz900), Succ(zzz9100)) → Succ(Succ(new_primPlusNat2(zzz900, zzz9100)))
new_primPlusNat2(Zero, Succ(zzz9100)) → Succ(zzz9100)
new_primPlusNat2(Zero, Zero) → Zero
new_primPlusNat2(Succ(zzz900), Zero) → Succ(zzz900)
new_primPlusNat1(Zero) → Zero
new_primPlusNat1(Succ(zzz62000)) → Succ(Succ(new_primPlusNat1(zzz62000)))
new_primPlusNat3(zzz90, Succ(zzz910)) → Succ(Succ(new_primPlusNat2(zzz90, zzz910)))
new_primPlusNat3(zzz90, Zero) → Succ(zzz90)

The set Q consists of the following terms:

new_primPlusNat2(Zero, Succ(x0))
new_primMulNat0(x0)
new_primPlusNat3(x0, Succ(x1))
new_primPlusNat2(Succ(x0), Succ(x1))
new_primPlusNat3(x0, Zero)
new_primPlusNat1(Zero)
new_primPlusNat2(Zero, Zero)
new_primPlusNat1(Succ(x0))
new_primPlusNat2(Succ(x0), Zero)

We have to consider all minimal (P,Q,R)-chains.
By rewriting [15] the rule new_mkVBalBranch3MkVBalBranch229(zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, zzz1125, zzz1126, zzz1127, zzz1128, zzz1129, bd) → new_mkVBalBranch3MkVBalBranch119(zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, zzz1125, zzz1126, zzz1127, zzz1128, zzz1129, new_primPlusNat2(new_primMulNat0(zzz1121), Succ(zzz1121)), bd) at position [11,0] we obtained the following new rules:

new_mkVBalBranch3MkVBalBranch229(zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, zzz1125, zzz1126, zzz1127, zzz1128, zzz1129, bd) → new_mkVBalBranch3MkVBalBranch119(zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, zzz1125, zzz1126, zzz1127, zzz1128, zzz1129, new_primPlusNat2(new_primPlusNat3(Succ(new_primPlusNat3(new_primPlusNat1(zzz1121), zzz1121)), Succ(zzz1121)), Succ(zzz1121)), bd)



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

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

new_mkVBalBranch3MkVBalBranch225(zzz498, zzz499, zzz500, zzz501, zzz502, zzz503, zzz504, zzz505, zzz506, zzz507, Zero, Zero, bg) → new_mkVBalBranch3MkVBalBranch230(zzz498, zzz499, zzz500, zzz501, zzz502, zzz503, zzz504, zzz505, zzz506, zzz507, bg)
new_mkVBalBranch3MkVBalBranch18(zzz340, zzz341, zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, Succ(zzz1480), h) → new_mkVBalBranch3MkVBalBranch115(zzz340, zzz341, Zero, zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, Succ(zzz1480), Succ(zzz51200), h)
new_mkVBalBranch0(zzz31, Branch(zzz510, zzz511, Neg(Zero), zzz513, zzz514), Branch(zzz340, zzz341, Pos(Succ(zzz34200)), zzz343, zzz344), h) → new_mkVBalBranch0(zzz31, Branch(zzz510, zzz511, Neg(Zero), zzz513, zzz514), zzz343, h)
new_mkVBalBranch3MkVBalBranch215(zzz340, zzz341, Pos(Succ(Succ(zzz342000))), zzz343, zzz344, zzz510, zzz511, Succ(zzz512000), zzz513, zzz514, zzz31, Succ(Succ(zzz6600)), h) → new_mkVBalBranch3MkVBalBranch216(zzz340, zzz341, Succ(zzz342000), zzz343, zzz344, zzz510, zzz511, zzz512000, zzz513, zzz514, zzz31, Succ(Succ(new_primPlusNat2(zzz6600, zzz512000))), zzz342000, h)
new_mkVBalBranch3MkVBalBranch223(zzz340, zzz341, Neg(Succ(Succ(Succ(zzz3420000)))), zzz343, zzz344, zzz510, zzz511, Zero, zzz513, zzz514, zzz31, Succ(Succ(zzz6700)), h) → new_mkVBalBranch3MkVBalBranch225(zzz340, zzz341, Succ(Succ(zzz3420000)), zzz343, zzz344, zzz510, zzz511, zzz513, zzz514, zzz31, Succ(zzz3420000), Succ(zzz6700), h)
new_mkVBalBranch3MkVBalBranch120(zzz2050, zzz2051, zzz2052, zzz2053, zzz2054, zzz2055, zzz2056, zzz2057, zzz2058, zzz2059, zzz2060, Zero, Succ(zzz20620), be) → new_mkVBalBranch0(zzz2060, zzz2059, Branch(zzz2050, zzz2051, Neg(Succ(zzz2052)), zzz2053, zzz2054), be)
new_mkVBalBranch0(zzz31, Branch(zzz510, zzz511, Pos(Zero), zzz513, zzz514), Branch(zzz340, zzz341, Pos(Succ(zzz34200)), zzz343, zzz344), h) → new_mkVBalBranch0(zzz31, Branch(zzz510, zzz511, Pos(Zero), zzz513, zzz514), zzz343, h)
new_mkVBalBranch3MkVBalBranch121(zzz473, zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, zzz481, zzz482, Succ(zzz7390), bh) → new_mkVBalBranch3MkVBalBranch115(zzz473, zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, Zero, zzz480, zzz481, zzz482, Succ(zzz7390), Succ(Zero), bh)
new_mkVBalBranch0(zzz31, Branch(zzz510, zzz511, Pos(Succ(zzz51200)), zzz513, zzz514), Branch(zzz340, zzz341, zzz342, zzz343, zzz344), h) → new_mkVBalBranch3MkVBalBranch215(zzz340, zzz341, zzz342, zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat3(new_primPlusNat1(zzz51200), zzz51200)), zzz51200))), h)
new_mkVBalBranch3MkVBalBranch223(zzz340, zzz341, Neg(Succ(Succ(Zero))), zzz343, zzz344, zzz510, zzz511, Succ(zzz512000), zzz513, zzz514, zzz31, Succ(Succ(zzz6700)), h) → new_mkVBalBranch3MkVBalBranch224(zzz340, zzz341, Succ(Zero), zzz343, zzz344, zzz510, zzz511, zzz512000, zzz513, zzz514, zzz31, Zero, Succ(Succ(new_primPlusNat2(zzz6700, zzz512000))), h)
new_mkVBalBranch3MkVBalBranch224(zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, zzz1125, zzz1126, zzz1127, zzz1128, zzz1129, Succ(zzz11300), Succ(zzz11310), bd) → new_mkVBalBranch3MkVBalBranch224(zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, zzz1125, zzz1126, zzz1127, zzz1128, zzz1129, zzz11300, zzz11310, bd)
new_mkVBalBranch3MkVBalBranch217(zzz473, zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, zzz481, zzz482, Zero, Succ(zzz4840), bh) → new_mkVBalBranch0(zzz482, Branch(zzz478, zzz479, Pos(Succ(Zero)), zzz480, zzz481), zzz476, bh)
new_mkVBalBranch3MkVBalBranch218(zzz461, zzz462, zzz463, zzz464, zzz465, zzz466, zzz467, zzz468, zzz469, zzz470, zzz471, bb) → new_mkVBalBranch3MkVBalBranch110(zzz461, zzz462, zzz463, zzz464, zzz465, zzz466, zzz467, zzz468, zzz469, zzz470, zzz471, new_primPlusNat2(new_primPlusNat3(Succ(new_primPlusNat3(new_primPlusNat1(zzz463), zzz463)), Succ(zzz463)), Succ(zzz463)), bb)
new_mkVBalBranch3MkVBalBranch110(zzz461, zzz462, zzz463, zzz464, zzz465, zzz466, zzz467, zzz468, zzz469, zzz470, zzz471, Succ(zzz5800), bb) → new_mkVBalBranch3MkVBalBranch115(zzz461, zzz462, zzz463, zzz464, zzz465, zzz466, zzz467, Succ(zzz468), zzz469, zzz470, zzz471, Succ(zzz5800), Succ(Succ(zzz468)), bb)
new_mkVBalBranch3MkVBalBranch227(zzz486, zzz487, zzz488, zzz489, zzz490, zzz491, zzz492, zzz493, zzz494, zzz495, zzz496, bf) → new_mkVBalBranch0(zzz496, Branch(zzz491, zzz492, Neg(Succ(Succ(zzz493))), zzz494, zzz495), zzz489, bf)
new_mkVBalBranch3MkVBalBranch215(zzz340, zzz341, Pos(Zero), zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, Succ(zzz660), h) → new_mkVBalBranch0(zzz31, zzz514, Branch(zzz340, zzz341, Pos(Zero), zzz343, zzz344), h)
new_mkVBalBranch3MkVBalBranch217(zzz473, zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, zzz481, zzz482, Succ(zzz4830), Zero, bh) → new_mkVBalBranch3MkVBalBranch121(zzz473, zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, zzz481, zzz482, new_primPlusNat2(new_primMulNat0(zzz475), Succ(zzz475)), bh)
new_mkVBalBranch3MkVBalBranch223(zzz340, zzz341, Neg(Zero), zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, Succ(zzz670), h) → new_mkVBalBranch0(zzz31, Branch(zzz510, zzz511, Neg(Succ(zzz51200)), zzz513, zzz514), zzz343, h)
new_mkVBalBranch3MkVBalBranch216(zzz1105, zzz1106, zzz1107, zzz1108, zzz1109, zzz1110, zzz1111, zzz1112, zzz1113, zzz1114, zzz1115, Zero, Succ(zzz11170), ba) → new_mkVBalBranch0(zzz1115, Branch(zzz1110, zzz1111, Pos(Succ(Succ(zzz1112))), zzz1113, zzz1114), zzz1108, ba)
new_mkVBalBranch3MkVBalBranch115(zzz1986, zzz1987, zzz1988, zzz1989, zzz1990, zzz1991, zzz1992, zzz1993, zzz1994, zzz1995, zzz1996, Zero, Succ(zzz19980), bc) → new_mkVBalBranch0(zzz1996, zzz1995, Branch(zzz1986, zzz1987, Pos(Succ(zzz1988)), zzz1989, zzz1990), bc)
new_mkVBalBranch3MkVBalBranch230(zzz498, zzz499, zzz500, zzz501, zzz502, zzz503, zzz504, zzz505, zzz506, zzz507, bg) → new_mkVBalBranch3MkVBalBranch118(zzz498, zzz499, zzz500, zzz501, zzz502, zzz503, zzz504, zzz505, zzz506, zzz507, new_primPlusNat2(Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat3(new_primPlusNat1(zzz500), zzz500)), zzz500))), Succ(zzz500)), bg)
new_mkVBalBranch3MkVBalBranch122(zzz340, zzz341, zzz34200, zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, h) → new_mkVBalBranch0(zzz31, zzz514, Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), h)
new_mkVBalBranch3MkVBalBranch217(zzz473, zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, zzz481, zzz482, Succ(zzz4830), Succ(zzz4840), bh) → new_mkVBalBranch3MkVBalBranch217(zzz473, zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, zzz481, zzz482, zzz4830, zzz4840, bh)
new_mkVBalBranch3MkVBalBranch116(zzz340, zzz341, zzz34200, zzz343, zzz344, zzz510, zzz511, zzz513, zzz514, zzz31, Succ(zzz1200), h) → new_mkVBalBranch0(zzz31, zzz514, Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), h)
new_mkVBalBranch3MkVBalBranch110(zzz461, zzz462, zzz463, zzz464, zzz465, zzz466, zzz467, zzz468, zzz469, zzz470, zzz471, Zero, bb) → new_mkVBalBranch3MkVBalBranch115(zzz461, zzz462, zzz463, zzz464, zzz465, zzz466, zzz467, Succ(zzz468), zzz469, zzz470, zzz471, Zero, Succ(Succ(zzz468)), bb)
new_mkVBalBranch3MkVBalBranch225(zzz498, zzz499, zzz500, zzz501, zzz502, zzz503, zzz504, zzz505, zzz506, zzz507, Zero, Succ(zzz5090), bg) → new_mkVBalBranch0(zzz507, Branch(zzz503, zzz504, Neg(Succ(Zero)), zzz505, zzz506), zzz501, bg)
new_mkVBalBranch0(zzz31, Branch(zzz510, zzz511, Neg(Succ(zzz51200)), zzz513, zzz514), Branch(zzz340, zzz341, zzz342, zzz343, zzz344), h) → new_mkVBalBranch3MkVBalBranch223(zzz340, zzz341, zzz342, zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat3(new_primPlusNat1(zzz51200), zzz51200)), zzz51200))), h)
new_mkVBalBranch3MkVBalBranch222(zzz461, zzz462, zzz463, zzz464, zzz465, zzz466, zzz467, zzz468, zzz469, zzz470, zzz471, bb) → new_mkVBalBranch3MkVBalBranch110(zzz461, zzz462, zzz463, zzz464, zzz465, zzz466, zzz467, zzz468, zzz469, zzz470, zzz471, new_primPlusNat2(new_primPlusNat3(Succ(new_primPlusNat3(new_primPlusNat1(zzz463), zzz463)), Succ(zzz463)), Succ(zzz463)), bb)
new_mkVBalBranch0(zzz31, Branch(zzz510, zzz511, Neg(Zero), zzz513, zzz514), Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), h) → new_mkVBalBranch3MkVBalBranch117(zzz340, zzz341, zzz34200, zzz343, zzz344, zzz510, zzz511, zzz513, zzz514, zzz31, new_primPlusNat2(new_primPlusNat3(Succ(new_primPlusNat3(new_primPlusNat1(zzz34200), zzz34200)), Succ(zzz34200)), Succ(zzz34200)), h)
new_mkVBalBranch3MkVBalBranch121(zzz473, zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, zzz481, zzz482, Zero, bh) → new_mkVBalBranch3MkVBalBranch115(zzz473, zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, Zero, zzz480, zzz481, zzz482, Zero, Succ(Zero), bh)
new_mkVBalBranch3MkVBalBranch223(zzz340, zzz341, Neg(Succ(Zero)), zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, Succ(zzz670), h) → new_mkVBalBranch0(zzz31, Branch(zzz510, zzz511, Neg(Succ(zzz51200)), zzz513, zzz514), zzz343, h)
new_mkVBalBranch3MkVBalBranch229(zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, zzz1125, zzz1126, zzz1127, zzz1128, zzz1129, bd) → new_mkVBalBranch3MkVBalBranch119(zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, zzz1125, zzz1126, zzz1127, zzz1128, zzz1129, new_primPlusNat2(new_primPlusNat3(Succ(new_primPlusNat3(new_primPlusNat1(zzz1121), zzz1121)), Succ(zzz1121)), Succ(zzz1121)), bd)
new_mkVBalBranch3MkVBalBranch225(zzz498, zzz499, zzz500, zzz501, zzz502, zzz503, zzz504, zzz505, zzz506, zzz507, Succ(zzz5080), Zero, bg) → new_mkVBalBranch3MkVBalBranch118(zzz498, zzz499, zzz500, zzz501, zzz502, zzz503, zzz504, zzz505, zzz506, zzz507, new_primPlusNat2(new_primPlusNat3(Succ(new_primPlusNat3(new_primPlusNat1(zzz500), zzz500)), Succ(zzz500)), Succ(zzz500)), bg)
new_mkVBalBranch3MkVBalBranch215(zzz340, zzz341, Pos(Succ(Zero)), zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, Succ(zzz660), h) → new_mkVBalBranch3MkVBalBranch18(zzz340, zzz341, zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, new_primPlusNat2(new_primMulNat0(Zero), Succ(Zero)), h)
new_mkVBalBranch3MkVBalBranch233(zzz473, zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, zzz481, zzz482, bh) → new_mkVBalBranch3MkVBalBranch121(zzz473, zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, zzz481, zzz482, new_primPlusNat2(new_primMulNat0(zzz475), Succ(zzz475)), bh)
new_mkVBalBranch0(zzz31, Branch(zzz510, zzz511, Pos(Zero), zzz513, zzz514), Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), h) → new_mkVBalBranch3MkVBalBranch116(zzz340, zzz341, zzz34200, zzz343, zzz344, zzz510, zzz511, zzz513, zzz514, zzz31, new_primPlusNat2(new_primPlusNat3(Succ(new_primPlusNat3(new_primPlusNat1(zzz34200), zzz34200)), Succ(zzz34200)), Succ(zzz34200)), h)
new_mkVBalBranch3MkVBalBranch215(zzz340, zzz341, Pos(Succ(Succ(zzz342000))), zzz343, zzz344, zzz510, zzz511, Zero, zzz513, zzz514, zzz31, Succ(Succ(zzz6600)), h) → new_mkVBalBranch3MkVBalBranch217(zzz340, zzz341, Succ(zzz342000), zzz343, zzz344, zzz510, zzz511, zzz513, zzz514, zzz31, Succ(zzz6600), zzz342000, h)
new_mkVBalBranch3MkVBalBranch117(zzz340, zzz341, zzz34200, zzz343, zzz344, zzz510, zzz511, zzz513, zzz514, zzz31, Succ(zzz1240), h) → new_mkVBalBranch0(zzz31, zzz514, Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), h)
new_mkVBalBranch3MkVBalBranch120(zzz2050, zzz2051, zzz2052, zzz2053, zzz2054, zzz2055, zzz2056, zzz2057, zzz2058, zzz2059, zzz2060, Succ(zzz20610), Succ(zzz20620), be) → new_mkVBalBranch3MkVBalBranch120(zzz2050, zzz2051, zzz2052, zzz2053, zzz2054, zzz2055, zzz2056, zzz2057, zzz2058, zzz2059, zzz2060, zzz20610, zzz20620, be)
new_mkVBalBranch3MkVBalBranch217(zzz473, zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, zzz481, zzz482, Zero, Zero, bh) → new_mkVBalBranch3MkVBalBranch233(zzz473, zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, zzz481, zzz482, bh)
new_mkVBalBranch3MkVBalBranch216(zzz1105, zzz1106, zzz1107, zzz1108, zzz1109, zzz1110, zzz1111, zzz1112, zzz1113, zzz1114, zzz1115, Succ(zzz11160), Succ(zzz11170), ba) → new_mkVBalBranch3MkVBalBranch216(zzz1105, zzz1106, zzz1107, zzz1108, zzz1109, zzz1110, zzz1111, zzz1112, zzz1113, zzz1114, zzz1115, zzz11160, zzz11170, ba)
new_mkVBalBranch3MkVBalBranch223(zzz340, zzz341, Pos(zzz3420), zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, Succ(zzz670), h) → new_mkVBalBranch0(zzz31, Branch(zzz510, zzz511, Neg(Succ(zzz51200)), zzz513, zzz514), zzz343, h)
new_mkVBalBranch3MkVBalBranch19(zzz340, zzz341, zzz34200, zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, Zero, h) → new_mkVBalBranch3MkVBalBranch122(zzz340, zzz341, zzz34200, zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, h)
new_mkVBalBranch3MkVBalBranch225(zzz498, zzz499, zzz500, zzz501, zzz502, zzz503, zzz504, zzz505, zzz506, zzz507, Succ(zzz5080), Succ(zzz5090), bg) → new_mkVBalBranch3MkVBalBranch225(zzz498, zzz499, zzz500, zzz501, zzz502, zzz503, zzz504, zzz505, zzz506, zzz507, zzz5080, zzz5090, bg)
new_mkVBalBranch3MkVBalBranch19(zzz340, zzz341, zzz34200, zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, Succ(zzz1410), h) → new_mkVBalBranch0(zzz31, zzz514, Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), h)
new_mkVBalBranch3MkVBalBranch224(zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, zzz1125, zzz1126, zzz1127, zzz1128, zzz1129, Succ(zzz11300), Zero, bd) → new_mkVBalBranch3MkVBalBranch119(zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, zzz1125, zzz1126, zzz1127, zzz1128, zzz1129, new_primPlusNat2(new_primMulNat0(zzz1121), Succ(zzz1121)), bd)
new_mkVBalBranch3MkVBalBranch224(zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, zzz1125, zzz1126, zzz1127, zzz1128, zzz1129, Zero, Succ(zzz11310), bd) → new_mkVBalBranch3MkVBalBranch227(zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, zzz1125, zzz1126, zzz1127, zzz1128, zzz1129, bd)
new_mkVBalBranch3MkVBalBranch224(zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, zzz1125, zzz1126, zzz1127, zzz1128, zzz1129, Zero, Zero, bd) → new_mkVBalBranch3MkVBalBranch229(zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, zzz1125, zzz1126, zzz1127, zzz1128, zzz1129, bd)
new_mkVBalBranch3MkVBalBranch223(zzz340, zzz341, Neg(Succ(Succ(Succ(zzz3420000)))), zzz343, zzz344, zzz510, zzz511, Succ(zzz512000), zzz513, zzz514, zzz31, Succ(Succ(zzz6700)), h) → new_mkVBalBranch3MkVBalBranch224(zzz340, zzz341, Succ(Succ(zzz3420000)), zzz343, zzz344, zzz510, zzz511, zzz512000, zzz513, zzz514, zzz31, Succ(zzz3420000), Succ(Succ(new_primPlusNat2(zzz6700, zzz512000))), h)
new_mkVBalBranch3MkVBalBranch223(zzz340, zzz341, Neg(Succ(Succ(Zero))), zzz343, zzz344, zzz510, zzz511, Zero, zzz513, zzz514, zzz31, Succ(Succ(zzz6700)), h) → new_mkVBalBranch3MkVBalBranch225(zzz340, zzz341, Succ(Zero), zzz343, zzz344, zzz510, zzz511, zzz513, zzz514, zzz31, Zero, Succ(zzz6700), h)
new_mkVBalBranch3MkVBalBranch115(zzz1986, zzz1987, zzz1988, zzz1989, zzz1990, zzz1991, zzz1992, zzz1993, zzz1994, zzz1995, zzz1996, Succ(zzz19970), Succ(zzz19980), bc) → new_mkVBalBranch3MkVBalBranch115(zzz1986, zzz1987, zzz1988, zzz1989, zzz1990, zzz1991, zzz1992, zzz1993, zzz1994, zzz1995, zzz1996, zzz19970, zzz19980, bc)
new_mkVBalBranch3MkVBalBranch215(zzz340, zzz341, Neg(Zero), zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, Succ(zzz660), h) → new_mkVBalBranch0(zzz31, zzz514, Branch(zzz340, zzz341, Neg(Zero), zzz343, zzz344), h)
new_mkVBalBranch3MkVBalBranch118(zzz498, zzz499, zzz500, zzz501, zzz502, zzz503, zzz504, zzz505, zzz506, zzz507, Succ(zzz8040), bg) → new_mkVBalBranch3MkVBalBranch120(zzz498, zzz499, zzz500, zzz501, zzz502, zzz503, zzz504, Zero, zzz505, zzz506, zzz507, Succ(Zero), Succ(zzz8040), bg)
new_mkVBalBranch3MkVBalBranch216(zzz1105, zzz1106, zzz1107, zzz1108, zzz1109, zzz1110, zzz1111, zzz1112, zzz1113, zzz1114, zzz1115, Succ(zzz11160), Zero, ba) → new_mkVBalBranch3MkVBalBranch218(zzz1105, zzz1106, zzz1107, zzz1108, zzz1109, zzz1110, zzz1111, zzz1112, zzz1113, zzz1114, zzz1115, ba)
new_mkVBalBranch3MkVBalBranch215(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, Succ(zzz660), h) → new_mkVBalBranch3MkVBalBranch19(zzz340, zzz341, zzz34200, zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, new_primPlusNat2(new_primMulNat0(zzz34200), Succ(zzz34200)), h)
new_mkVBalBranch3MkVBalBranch216(zzz1105, zzz1106, zzz1107, zzz1108, zzz1109, zzz1110, zzz1111, zzz1112, zzz1113, zzz1114, zzz1115, Zero, Zero, ba) → new_mkVBalBranch3MkVBalBranch222(zzz1105, zzz1106, zzz1107, zzz1108, zzz1109, zzz1110, zzz1111, zzz1112, zzz1113, zzz1114, zzz1115, ba)
new_mkVBalBranch3MkVBalBranch18(zzz340, zzz341, zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, Zero, h) → new_mkVBalBranch3MkVBalBranch115(zzz340, zzz341, Zero, zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, Zero, Succ(zzz51200), h)
new_mkVBalBranch3MkVBalBranch119(zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, zzz1125, zzz1126, zzz1127, zzz1128, zzz1129, Succ(zzz12130), bd) → new_mkVBalBranch3MkVBalBranch120(zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, zzz1125, Succ(zzz1126), zzz1127, zzz1128, zzz1129, Succ(Succ(zzz1126)), Succ(zzz12130), bd)

The TRS R consists of the following rules:

new_primMulNat0(zzz6200) → new_primPlusNat3(Succ(new_primPlusNat3(new_primPlusNat1(zzz6200), zzz6200)), Succ(zzz6200))
new_primPlusNat2(Succ(zzz900), Succ(zzz9100)) → Succ(Succ(new_primPlusNat2(zzz900, zzz9100)))
new_primPlusNat2(Zero, Succ(zzz9100)) → Succ(zzz9100)
new_primPlusNat2(Zero, Zero) → Zero
new_primPlusNat2(Succ(zzz900), Zero) → Succ(zzz900)
new_primPlusNat1(Zero) → Zero
new_primPlusNat1(Succ(zzz62000)) → Succ(Succ(new_primPlusNat1(zzz62000)))
new_primPlusNat3(zzz90, Succ(zzz910)) → Succ(Succ(new_primPlusNat2(zzz90, zzz910)))
new_primPlusNat3(zzz90, Zero) → Succ(zzz90)

The set Q consists of the following terms:

new_primPlusNat2(Zero, Succ(x0))
new_primMulNat0(x0)
new_primPlusNat3(x0, Succ(x1))
new_primPlusNat2(Succ(x0), Succ(x1))
new_primPlusNat3(x0, Zero)
new_primPlusNat1(Zero)
new_primPlusNat2(Zero, Zero)
new_primPlusNat1(Succ(x0))
new_primPlusNat2(Succ(x0), Zero)

We have to consider all minimal (P,Q,R)-chains.
By rewriting [15] the rule new_mkVBalBranch3MkVBalBranch224(zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, zzz1125, zzz1126, zzz1127, zzz1128, zzz1129, Succ(zzz11300), Zero, bd) → new_mkVBalBranch3MkVBalBranch119(zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, zzz1125, zzz1126, zzz1127, zzz1128, zzz1129, new_primPlusNat2(new_primMulNat0(zzz1121), Succ(zzz1121)), bd) at position [11,0] we obtained the following new rules:

new_mkVBalBranch3MkVBalBranch224(zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, zzz1125, zzz1126, zzz1127, zzz1128, zzz1129, Succ(zzz11300), Zero, bd) → new_mkVBalBranch3MkVBalBranch119(zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, zzz1125, zzz1126, zzz1127, zzz1128, zzz1129, new_primPlusNat2(new_primPlusNat3(Succ(new_primPlusNat3(new_primPlusNat1(zzz1121), zzz1121)), Succ(zzz1121)), Succ(zzz1121)), bd)



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

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

new_mkVBalBranch3MkVBalBranch225(zzz498, zzz499, zzz500, zzz501, zzz502, zzz503, zzz504, zzz505, zzz506, zzz507, Zero, Zero, bg) → new_mkVBalBranch3MkVBalBranch230(zzz498, zzz499, zzz500, zzz501, zzz502, zzz503, zzz504, zzz505, zzz506, zzz507, bg)
new_mkVBalBranch3MkVBalBranch18(zzz340, zzz341, zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, Succ(zzz1480), h) → new_mkVBalBranch3MkVBalBranch115(zzz340, zzz341, Zero, zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, Succ(zzz1480), Succ(zzz51200), h)
new_mkVBalBranch3MkVBalBranch215(zzz340, zzz341, Pos(Succ(Succ(zzz342000))), zzz343, zzz344, zzz510, zzz511, Succ(zzz512000), zzz513, zzz514, zzz31, Succ(Succ(zzz6600)), h) → new_mkVBalBranch3MkVBalBranch216(zzz340, zzz341, Succ(zzz342000), zzz343, zzz344, zzz510, zzz511, zzz512000, zzz513, zzz514, zzz31, Succ(Succ(new_primPlusNat2(zzz6600, zzz512000))), zzz342000, h)
new_mkVBalBranch0(zzz31, Branch(zzz510, zzz511, Neg(Zero), zzz513, zzz514), Branch(zzz340, zzz341, Pos(Succ(zzz34200)), zzz343, zzz344), h) → new_mkVBalBranch0(zzz31, Branch(zzz510, zzz511, Neg(Zero), zzz513, zzz514), zzz343, h)
new_mkVBalBranch3MkVBalBranch223(zzz340, zzz341, Neg(Succ(Succ(Succ(zzz3420000)))), zzz343, zzz344, zzz510, zzz511, Zero, zzz513, zzz514, zzz31, Succ(Succ(zzz6700)), h) → new_mkVBalBranch3MkVBalBranch225(zzz340, zzz341, Succ(Succ(zzz3420000)), zzz343, zzz344, zzz510, zzz511, zzz513, zzz514, zzz31, Succ(zzz3420000), Succ(zzz6700), h)
new_mkVBalBranch3MkVBalBranch120(zzz2050, zzz2051, zzz2052, zzz2053, zzz2054, zzz2055, zzz2056, zzz2057, zzz2058, zzz2059, zzz2060, Zero, Succ(zzz20620), be) → new_mkVBalBranch0(zzz2060, zzz2059, Branch(zzz2050, zzz2051, Neg(Succ(zzz2052)), zzz2053, zzz2054), be)
new_mkVBalBranch3MkVBalBranch121(zzz473, zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, zzz481, zzz482, Succ(zzz7390), bh) → new_mkVBalBranch3MkVBalBranch115(zzz473, zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, Zero, zzz480, zzz481, zzz482, Succ(zzz7390), Succ(Zero), bh)
new_mkVBalBranch0(zzz31, Branch(zzz510, zzz511, Pos(Zero), zzz513, zzz514), Branch(zzz340, zzz341, Pos(Succ(zzz34200)), zzz343, zzz344), h) → new_mkVBalBranch0(zzz31, Branch(zzz510, zzz511, Pos(Zero), zzz513, zzz514), zzz343, h)
new_mkVBalBranch0(zzz31, Branch(zzz510, zzz511, Pos(Succ(zzz51200)), zzz513, zzz514), Branch(zzz340, zzz341, zzz342, zzz343, zzz344), h) → new_mkVBalBranch3MkVBalBranch215(zzz340, zzz341, zzz342, zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat3(new_primPlusNat1(zzz51200), zzz51200)), zzz51200))), h)
new_mkVBalBranch3MkVBalBranch223(zzz340, zzz341, Neg(Succ(Succ(Zero))), zzz343, zzz344, zzz510, zzz511, Succ(zzz512000), zzz513, zzz514, zzz31, Succ(Succ(zzz6700)), h) → new_mkVBalBranch3MkVBalBranch224(zzz340, zzz341, Succ(Zero), zzz343, zzz344, zzz510, zzz511, zzz512000, zzz513, zzz514, zzz31, Zero, Succ(Succ(new_primPlusNat2(zzz6700, zzz512000))), h)
new_mkVBalBranch3MkVBalBranch224(zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, zzz1125, zzz1126, zzz1127, zzz1128, zzz1129, Succ(zzz11300), Succ(zzz11310), bd) → new_mkVBalBranch3MkVBalBranch224(zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, zzz1125, zzz1126, zzz1127, zzz1128, zzz1129, zzz11300, zzz11310, bd)
new_mkVBalBranch3MkVBalBranch224(zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, zzz1125, zzz1126, zzz1127, zzz1128, zzz1129, Succ(zzz11300), Zero, bd) → new_mkVBalBranch3MkVBalBranch119(zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, zzz1125, zzz1126, zzz1127, zzz1128, zzz1129, new_primPlusNat2(new_primPlusNat3(Succ(new_primPlusNat3(new_primPlusNat1(zzz1121), zzz1121)), Succ(zzz1121)), Succ(zzz1121)), bd)
new_mkVBalBranch3MkVBalBranch217(zzz473, zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, zzz481, zzz482, Zero, Succ(zzz4840), bh) → new_mkVBalBranch0(zzz482, Branch(zzz478, zzz479, Pos(Succ(Zero)), zzz480, zzz481), zzz476, bh)
new_mkVBalBranch3MkVBalBranch218(zzz461, zzz462, zzz463, zzz464, zzz465, zzz466, zzz467, zzz468, zzz469, zzz470, zzz471, bb) → new_mkVBalBranch3MkVBalBranch110(zzz461, zzz462, zzz463, zzz464, zzz465, zzz466, zzz467, zzz468, zzz469, zzz470, zzz471, new_primPlusNat2(new_primPlusNat3(Succ(new_primPlusNat3(new_primPlusNat1(zzz463), zzz463)), Succ(zzz463)), Succ(zzz463)), bb)
new_mkVBalBranch3MkVBalBranch110(zzz461, zzz462, zzz463, zzz464, zzz465, zzz466, zzz467, zzz468, zzz469, zzz470, zzz471, Succ(zzz5800), bb) → new_mkVBalBranch3MkVBalBranch115(zzz461, zzz462, zzz463, zzz464, zzz465, zzz466, zzz467, Succ(zzz468), zzz469, zzz470, zzz471, Succ(zzz5800), Succ(Succ(zzz468)), bb)
new_mkVBalBranch3MkVBalBranch227(zzz486, zzz487, zzz488, zzz489, zzz490, zzz491, zzz492, zzz493, zzz494, zzz495, zzz496, bf) → new_mkVBalBranch0(zzz496, Branch(zzz491, zzz492, Neg(Succ(Succ(zzz493))), zzz494, zzz495), zzz489, bf)
new_mkVBalBranch3MkVBalBranch215(zzz340, zzz341, Pos(Zero), zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, Succ(zzz660), h) → new_mkVBalBranch0(zzz31, zzz514, Branch(zzz340, zzz341, Pos(Zero), zzz343, zzz344), h)
new_mkVBalBranch3MkVBalBranch223(zzz340, zzz341, Neg(Zero), zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, Succ(zzz670), h) → new_mkVBalBranch0(zzz31, Branch(zzz510, zzz511, Neg(Succ(zzz51200)), zzz513, zzz514), zzz343, h)
new_mkVBalBranch3MkVBalBranch217(zzz473, zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, zzz481, zzz482, Succ(zzz4830), Zero, bh) → new_mkVBalBranch3MkVBalBranch121(zzz473, zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, zzz481, zzz482, new_primPlusNat2(new_primMulNat0(zzz475), Succ(zzz475)), bh)
new_mkVBalBranch3MkVBalBranch216(zzz1105, zzz1106, zzz1107, zzz1108, zzz1109, zzz1110, zzz1111, zzz1112, zzz1113, zzz1114, zzz1115, Zero, Succ(zzz11170), ba) → new_mkVBalBranch0(zzz1115, Branch(zzz1110, zzz1111, Pos(Succ(Succ(zzz1112))), zzz1113, zzz1114), zzz1108, ba)
new_mkVBalBranch3MkVBalBranch115(zzz1986, zzz1987, zzz1988, zzz1989, zzz1990, zzz1991, zzz1992, zzz1993, zzz1994, zzz1995, zzz1996, Zero, Succ(zzz19980), bc) → new_mkVBalBranch0(zzz1996, zzz1995, Branch(zzz1986, zzz1987, Pos(Succ(zzz1988)), zzz1989, zzz1990), bc)
new_mkVBalBranch3MkVBalBranch122(zzz340, zzz341, zzz34200, zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, h) → new_mkVBalBranch0(zzz31, zzz514, Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), h)
new_mkVBalBranch3MkVBalBranch230(zzz498, zzz499, zzz500, zzz501, zzz502, zzz503, zzz504, zzz505, zzz506, zzz507, bg) → new_mkVBalBranch3MkVBalBranch118(zzz498, zzz499, zzz500, zzz501, zzz502, zzz503, zzz504, zzz505, zzz506, zzz507, new_primPlusNat2(Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat3(new_primPlusNat1(zzz500), zzz500)), zzz500))), Succ(zzz500)), bg)
new_mkVBalBranch3MkVBalBranch217(zzz473, zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, zzz481, zzz482, Succ(zzz4830), Succ(zzz4840), bh) → new_mkVBalBranch3MkVBalBranch217(zzz473, zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, zzz481, zzz482, zzz4830, zzz4840, bh)
new_mkVBalBranch3MkVBalBranch116(zzz340, zzz341, zzz34200, zzz343, zzz344, zzz510, zzz511, zzz513, zzz514, zzz31, Succ(zzz1200), h) → new_mkVBalBranch0(zzz31, zzz514, Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), h)
new_mkVBalBranch3MkVBalBranch110(zzz461, zzz462, zzz463, zzz464, zzz465, zzz466, zzz467, zzz468, zzz469, zzz470, zzz471, Zero, bb) → new_mkVBalBranch3MkVBalBranch115(zzz461, zzz462, zzz463, zzz464, zzz465, zzz466, zzz467, Succ(zzz468), zzz469, zzz470, zzz471, Zero, Succ(Succ(zzz468)), bb)
new_mkVBalBranch3MkVBalBranch225(zzz498, zzz499, zzz500, zzz501, zzz502, zzz503, zzz504, zzz505, zzz506, zzz507, Zero, Succ(zzz5090), bg) → new_mkVBalBranch0(zzz507, Branch(zzz503, zzz504, Neg(Succ(Zero)), zzz505, zzz506), zzz501, bg)
new_mkVBalBranch0(zzz31, Branch(zzz510, zzz511, Neg(Succ(zzz51200)), zzz513, zzz514), Branch(zzz340, zzz341, zzz342, zzz343, zzz344), h) → new_mkVBalBranch3MkVBalBranch223(zzz340, zzz341, zzz342, zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat3(new_primPlusNat1(zzz51200), zzz51200)), zzz51200))), h)
new_mkVBalBranch3MkVBalBranch222(zzz461, zzz462, zzz463, zzz464, zzz465, zzz466, zzz467, zzz468, zzz469, zzz470, zzz471, bb) → new_mkVBalBranch3MkVBalBranch110(zzz461, zzz462, zzz463, zzz464, zzz465, zzz466, zzz467, zzz468, zzz469, zzz470, zzz471, new_primPlusNat2(new_primPlusNat3(Succ(new_primPlusNat3(new_primPlusNat1(zzz463), zzz463)), Succ(zzz463)), Succ(zzz463)), bb)
new_mkVBalBranch0(zzz31, Branch(zzz510, zzz511, Neg(Zero), zzz513, zzz514), Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), h) → new_mkVBalBranch3MkVBalBranch117(zzz340, zzz341, zzz34200, zzz343, zzz344, zzz510, zzz511, zzz513, zzz514, zzz31, new_primPlusNat2(new_primPlusNat3(Succ(new_primPlusNat3(new_primPlusNat1(zzz34200), zzz34200)), Succ(zzz34200)), Succ(zzz34200)), h)
new_mkVBalBranch3MkVBalBranch121(zzz473, zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, zzz481, zzz482, Zero, bh) → new_mkVBalBranch3MkVBalBranch115(zzz473, zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, Zero, zzz480, zzz481, zzz482, Zero, Succ(Zero), bh)
new_mkVBalBranch3MkVBalBranch223(zzz340, zzz341, Neg(Succ(Zero)), zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, Succ(zzz670), h) → new_mkVBalBranch0(zzz31, Branch(zzz510, zzz511, Neg(Succ(zzz51200)), zzz513, zzz514), zzz343, h)
new_mkVBalBranch3MkVBalBranch225(zzz498, zzz499, zzz500, zzz501, zzz502, zzz503, zzz504, zzz505, zzz506, zzz507, Succ(zzz5080), Zero, bg) → new_mkVBalBranch3MkVBalBranch118(zzz498, zzz499, zzz500, zzz501, zzz502, zzz503, zzz504, zzz505, zzz506, zzz507, new_primPlusNat2(new_primPlusNat3(Succ(new_primPlusNat3(new_primPlusNat1(zzz500), zzz500)), Succ(zzz500)), Succ(zzz500)), bg)
new_mkVBalBranch3MkVBalBranch229(zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, zzz1125, zzz1126, zzz1127, zzz1128, zzz1129, bd) → new_mkVBalBranch3MkVBalBranch119(zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, zzz1125, zzz1126, zzz1127, zzz1128, zzz1129, new_primPlusNat2(new_primPlusNat3(Succ(new_primPlusNat3(new_primPlusNat1(zzz1121), zzz1121)), Succ(zzz1121)), Succ(zzz1121)), bd)
new_mkVBalBranch3MkVBalBranch215(zzz340, zzz341, Pos(Succ(Zero)), zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, Succ(zzz660), h) → new_mkVBalBranch3MkVBalBranch18(zzz340, zzz341, zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, new_primPlusNat2(new_primMulNat0(Zero), Succ(Zero)), h)
new_mkVBalBranch3MkVBalBranch233(zzz473, zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, zzz481, zzz482, bh) → new_mkVBalBranch3MkVBalBranch121(zzz473, zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, zzz481, zzz482, new_primPlusNat2(new_primMulNat0(zzz475), Succ(zzz475)), bh)
new_mkVBalBranch0(zzz31, Branch(zzz510, zzz511, Pos(Zero), zzz513, zzz514), Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), h) → new_mkVBalBranch3MkVBalBranch116(zzz340, zzz341, zzz34200, zzz343, zzz344, zzz510, zzz511, zzz513, zzz514, zzz31, new_primPlusNat2(new_primPlusNat3(Succ(new_primPlusNat3(new_primPlusNat1(zzz34200), zzz34200)), Succ(zzz34200)), Succ(zzz34200)), h)
new_mkVBalBranch3MkVBalBranch215(zzz340, zzz341, Pos(Succ(Succ(zzz342000))), zzz343, zzz344, zzz510, zzz511, Zero, zzz513, zzz514, zzz31, Succ(Succ(zzz6600)), h) → new_mkVBalBranch3MkVBalBranch217(zzz340, zzz341, Succ(zzz342000), zzz343, zzz344, zzz510, zzz511, zzz513, zzz514, zzz31, Succ(zzz6600), zzz342000, h)
new_mkVBalBranch3MkVBalBranch117(zzz340, zzz341, zzz34200, zzz343, zzz344, zzz510, zzz511, zzz513, zzz514, zzz31, Succ(zzz1240), h) → new_mkVBalBranch0(zzz31, zzz514, Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), h)
new_mkVBalBranch3MkVBalBranch217(zzz473, zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, zzz481, zzz482, Zero, Zero, bh) → new_mkVBalBranch3MkVBalBranch233(zzz473, zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, zzz481, zzz482, bh)
new_mkVBalBranch3MkVBalBranch120(zzz2050, zzz2051, zzz2052, zzz2053, zzz2054, zzz2055, zzz2056, zzz2057, zzz2058, zzz2059, zzz2060, Succ(zzz20610), Succ(zzz20620), be) → new_mkVBalBranch3MkVBalBranch120(zzz2050, zzz2051, zzz2052, zzz2053, zzz2054, zzz2055, zzz2056, zzz2057, zzz2058, zzz2059, zzz2060, zzz20610, zzz20620, be)
new_mkVBalBranch3MkVBalBranch223(zzz340, zzz341, Pos(zzz3420), zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, Succ(zzz670), h) → new_mkVBalBranch0(zzz31, Branch(zzz510, zzz511, Neg(Succ(zzz51200)), zzz513, zzz514), zzz343, h)
new_mkVBalBranch3MkVBalBranch216(zzz1105, zzz1106, zzz1107, zzz1108, zzz1109, zzz1110, zzz1111, zzz1112, zzz1113, zzz1114, zzz1115, Succ(zzz11160), Succ(zzz11170), ba) → new_mkVBalBranch3MkVBalBranch216(zzz1105, zzz1106, zzz1107, zzz1108, zzz1109, zzz1110, zzz1111, zzz1112, zzz1113, zzz1114, zzz1115, zzz11160, zzz11170, ba)
new_mkVBalBranch3MkVBalBranch19(zzz340, zzz341, zzz34200, zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, Zero, h) → new_mkVBalBranch3MkVBalBranch122(zzz340, zzz341, zzz34200, zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, h)
new_mkVBalBranch3MkVBalBranch225(zzz498, zzz499, zzz500, zzz501, zzz502, zzz503, zzz504, zzz505, zzz506, zzz507, Succ(zzz5080), Succ(zzz5090), bg) → new_mkVBalBranch3MkVBalBranch225(zzz498, zzz499, zzz500, zzz501, zzz502, zzz503, zzz504, zzz505, zzz506, zzz507, zzz5080, zzz5090, bg)
new_mkVBalBranch3MkVBalBranch19(zzz340, zzz341, zzz34200, zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, Succ(zzz1410), h) → new_mkVBalBranch0(zzz31, zzz514, Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), h)
new_mkVBalBranch3MkVBalBranch224(zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, zzz1125, zzz1126, zzz1127, zzz1128, zzz1129, Zero, Zero, bd) → new_mkVBalBranch3MkVBalBranch229(zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, zzz1125, zzz1126, zzz1127, zzz1128, zzz1129, bd)
new_mkVBalBranch3MkVBalBranch224(zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, zzz1125, zzz1126, zzz1127, zzz1128, zzz1129, Zero, Succ(zzz11310), bd) → new_mkVBalBranch3MkVBalBranch227(zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, zzz1125, zzz1126, zzz1127, zzz1128, zzz1129, bd)
new_mkVBalBranch3MkVBalBranch223(zzz340, zzz341, Neg(Succ(Succ(Zero))), zzz343, zzz344, zzz510, zzz511, Zero, zzz513, zzz514, zzz31, Succ(Succ(zzz6700)), h) → new_mkVBalBranch3MkVBalBranch225(zzz340, zzz341, Succ(Zero), zzz343, zzz344, zzz510, zzz511, zzz513, zzz514, zzz31, Zero, Succ(zzz6700), h)
new_mkVBalBranch3MkVBalBranch223(zzz340, zzz341, Neg(Succ(Succ(Succ(zzz3420000)))), zzz343, zzz344, zzz510, zzz511, Succ(zzz512000), zzz513, zzz514, zzz31, Succ(Succ(zzz6700)), h) → new_mkVBalBranch3MkVBalBranch224(zzz340, zzz341, Succ(Succ(zzz3420000)), zzz343, zzz344, zzz510, zzz511, zzz512000, zzz513, zzz514, zzz31, Succ(zzz3420000), Succ(Succ(new_primPlusNat2(zzz6700, zzz512000))), h)
new_mkVBalBranch3MkVBalBranch115(zzz1986, zzz1987, zzz1988, zzz1989, zzz1990, zzz1991, zzz1992, zzz1993, zzz1994, zzz1995, zzz1996, Succ(zzz19970), Succ(zzz19980), bc) → new_mkVBalBranch3MkVBalBranch115(zzz1986, zzz1987, zzz1988, zzz1989, zzz1990, zzz1991, zzz1992, zzz1993, zzz1994, zzz1995, zzz1996, zzz19970, zzz19980, bc)
new_mkVBalBranch3MkVBalBranch215(zzz340, zzz341, Neg(Zero), zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, Succ(zzz660), h) → new_mkVBalBranch0(zzz31, zzz514, Branch(zzz340, zzz341, Neg(Zero), zzz343, zzz344), h)
new_mkVBalBranch3MkVBalBranch118(zzz498, zzz499, zzz500, zzz501, zzz502, zzz503, zzz504, zzz505, zzz506, zzz507, Succ(zzz8040), bg) → new_mkVBalBranch3MkVBalBranch120(zzz498, zzz499, zzz500, zzz501, zzz502, zzz503, zzz504, Zero, zzz505, zzz506, zzz507, Succ(Zero), Succ(zzz8040), bg)
new_mkVBalBranch3MkVBalBranch216(zzz1105, zzz1106, zzz1107, zzz1108, zzz1109, zzz1110, zzz1111, zzz1112, zzz1113, zzz1114, zzz1115, Succ(zzz11160), Zero, ba) → new_mkVBalBranch3MkVBalBranch218(zzz1105, zzz1106, zzz1107, zzz1108, zzz1109, zzz1110, zzz1111, zzz1112, zzz1113, zzz1114, zzz1115, ba)
new_mkVBalBranch3MkVBalBranch215(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, Succ(zzz660), h) → new_mkVBalBranch3MkVBalBranch19(zzz340, zzz341, zzz34200, zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, new_primPlusNat2(new_primMulNat0(zzz34200), Succ(zzz34200)), h)
new_mkVBalBranch3MkVBalBranch216(zzz1105, zzz1106, zzz1107, zzz1108, zzz1109, zzz1110, zzz1111, zzz1112, zzz1113, zzz1114, zzz1115, Zero, Zero, ba) → new_mkVBalBranch3MkVBalBranch222(zzz1105, zzz1106, zzz1107, zzz1108, zzz1109, zzz1110, zzz1111, zzz1112, zzz1113, zzz1114, zzz1115, ba)
new_mkVBalBranch3MkVBalBranch119(zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, zzz1125, zzz1126, zzz1127, zzz1128, zzz1129, Succ(zzz12130), bd) → new_mkVBalBranch3MkVBalBranch120(zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, zzz1125, Succ(zzz1126), zzz1127, zzz1128, zzz1129, Succ(Succ(zzz1126)), Succ(zzz12130), bd)
new_mkVBalBranch3MkVBalBranch18(zzz340, zzz341, zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, Zero, h) → new_mkVBalBranch3MkVBalBranch115(zzz340, zzz341, Zero, zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, Zero, Succ(zzz51200), h)

The TRS R consists of the following rules:

new_primMulNat0(zzz6200) → new_primPlusNat3(Succ(new_primPlusNat3(new_primPlusNat1(zzz6200), zzz6200)), Succ(zzz6200))
new_primPlusNat2(Succ(zzz900), Succ(zzz9100)) → Succ(Succ(new_primPlusNat2(zzz900, zzz9100)))
new_primPlusNat2(Zero, Succ(zzz9100)) → Succ(zzz9100)
new_primPlusNat2(Zero, Zero) → Zero
new_primPlusNat2(Succ(zzz900), Zero) → Succ(zzz900)
new_primPlusNat1(Zero) → Zero
new_primPlusNat1(Succ(zzz62000)) → Succ(Succ(new_primPlusNat1(zzz62000)))
new_primPlusNat3(zzz90, Succ(zzz910)) → Succ(Succ(new_primPlusNat2(zzz90, zzz910)))
new_primPlusNat3(zzz90, Zero) → Succ(zzz90)

The set Q consists of the following terms:

new_primPlusNat2(Zero, Succ(x0))
new_primMulNat0(x0)
new_primPlusNat3(x0, Succ(x1))
new_primPlusNat2(Succ(x0), Succ(x1))
new_primPlusNat3(x0, Zero)
new_primPlusNat1(Zero)
new_primPlusNat2(Zero, Zero)
new_primPlusNat1(Succ(x0))
new_primPlusNat2(Succ(x0), Zero)

We have to consider all minimal (P,Q,R)-chains.
By rewriting [15] the rule new_mkVBalBranch3MkVBalBranch222(zzz461, zzz462, zzz463, zzz464, zzz465, zzz466, zzz467, zzz468, zzz469, zzz470, zzz471, bb) → new_mkVBalBranch3MkVBalBranch110(zzz461, zzz462, zzz463, zzz464, zzz465, zzz466, zzz467, zzz468, zzz469, zzz470, zzz471, new_primPlusNat2(new_primPlusNat3(Succ(new_primPlusNat3(new_primPlusNat1(zzz463), zzz463)), Succ(zzz463)), Succ(zzz463)), bb) at position [11,0] we obtained the following new rules:

new_mkVBalBranch3MkVBalBranch222(zzz461, zzz462, zzz463, zzz464, zzz465, zzz466, zzz467, zzz468, zzz469, zzz470, zzz471, bb) → new_mkVBalBranch3MkVBalBranch110(zzz461, zzz462, zzz463, zzz464, zzz465, zzz466, zzz467, zzz468, zzz469, zzz470, zzz471, new_primPlusNat2(Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat3(new_primPlusNat1(zzz463), zzz463)), zzz463))), Succ(zzz463)), bb)



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

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

new_mkVBalBranch3MkVBalBranch225(zzz498, zzz499, zzz500, zzz501, zzz502, zzz503, zzz504, zzz505, zzz506, zzz507, Zero, Zero, bg) → new_mkVBalBranch3MkVBalBranch230(zzz498, zzz499, zzz500, zzz501, zzz502, zzz503, zzz504, zzz505, zzz506, zzz507, bg)
new_mkVBalBranch3MkVBalBranch18(zzz340, zzz341, zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, Succ(zzz1480), h) → new_mkVBalBranch3MkVBalBranch115(zzz340, zzz341, Zero, zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, Succ(zzz1480), Succ(zzz51200), h)
new_mkVBalBranch0(zzz31, Branch(zzz510, zzz511, Neg(Zero), zzz513, zzz514), Branch(zzz340, zzz341, Pos(Succ(zzz34200)), zzz343, zzz344), h) → new_mkVBalBranch0(zzz31, Branch(zzz510, zzz511, Neg(Zero), zzz513, zzz514), zzz343, h)
new_mkVBalBranch3MkVBalBranch215(zzz340, zzz341, Pos(Succ(Succ(zzz342000))), zzz343, zzz344, zzz510, zzz511, Succ(zzz512000), zzz513, zzz514, zzz31, Succ(Succ(zzz6600)), h) → new_mkVBalBranch3MkVBalBranch216(zzz340, zzz341, Succ(zzz342000), zzz343, zzz344, zzz510, zzz511, zzz512000, zzz513, zzz514, zzz31, Succ(Succ(new_primPlusNat2(zzz6600, zzz512000))), zzz342000, h)
new_mkVBalBranch3MkVBalBranch223(zzz340, zzz341, Neg(Succ(Succ(Succ(zzz3420000)))), zzz343, zzz344, zzz510, zzz511, Zero, zzz513, zzz514, zzz31, Succ(Succ(zzz6700)), h) → new_mkVBalBranch3MkVBalBranch225(zzz340, zzz341, Succ(Succ(zzz3420000)), zzz343, zzz344, zzz510, zzz511, zzz513, zzz514, zzz31, Succ(zzz3420000), Succ(zzz6700), h)
new_mkVBalBranch3MkVBalBranch120(zzz2050, zzz2051, zzz2052, zzz2053, zzz2054, zzz2055, zzz2056, zzz2057, zzz2058, zzz2059, zzz2060, Zero, Succ(zzz20620), be) → new_mkVBalBranch0(zzz2060, zzz2059, Branch(zzz2050, zzz2051, Neg(Succ(zzz2052)), zzz2053, zzz2054), be)
new_mkVBalBranch0(zzz31, Branch(zzz510, zzz511, Pos(Zero), zzz513, zzz514), Branch(zzz340, zzz341, Pos(Succ(zzz34200)), zzz343, zzz344), h) → new_mkVBalBranch0(zzz31, Branch(zzz510, zzz511, Pos(Zero), zzz513, zzz514), zzz343, h)
new_mkVBalBranch3MkVBalBranch121(zzz473, zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, zzz481, zzz482, Succ(zzz7390), bh) → new_mkVBalBranch3MkVBalBranch115(zzz473, zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, Zero, zzz480, zzz481, zzz482, Succ(zzz7390), Succ(Zero), bh)
new_mkVBalBranch0(zzz31, Branch(zzz510, zzz511, Pos(Succ(zzz51200)), zzz513, zzz514), Branch(zzz340, zzz341, zzz342, zzz343, zzz344), h) → new_mkVBalBranch3MkVBalBranch215(zzz340, zzz341, zzz342, zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat3(new_primPlusNat1(zzz51200), zzz51200)), zzz51200))), h)
new_mkVBalBranch3MkVBalBranch223(zzz340, zzz341, Neg(Succ(Succ(Zero))), zzz343, zzz344, zzz510, zzz511, Succ(zzz512000), zzz513, zzz514, zzz31, Succ(Succ(zzz6700)), h) → new_mkVBalBranch3MkVBalBranch224(zzz340, zzz341, Succ(Zero), zzz343, zzz344, zzz510, zzz511, zzz512000, zzz513, zzz514, zzz31, Zero, Succ(Succ(new_primPlusNat2(zzz6700, zzz512000))), h)
new_mkVBalBranch3MkVBalBranch224(zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, zzz1125, zzz1126, zzz1127, zzz1128, zzz1129, Succ(zzz11300), Succ(zzz11310), bd) → new_mkVBalBranch3MkVBalBranch224(zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, zzz1125, zzz1126, zzz1127, zzz1128, zzz1129, zzz11300, zzz11310, bd)
new_mkVBalBranch3MkVBalBranch224(zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, zzz1125, zzz1126, zzz1127, zzz1128, zzz1129, Succ(zzz11300), Zero, bd) → new_mkVBalBranch3MkVBalBranch119(zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, zzz1125, zzz1126, zzz1127, zzz1128, zzz1129, new_primPlusNat2(new_primPlusNat3(Succ(new_primPlusNat3(new_primPlusNat1(zzz1121), zzz1121)), Succ(zzz1121)), Succ(zzz1121)), bd)
new_mkVBalBranch3MkVBalBranch217(zzz473, zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, zzz481, zzz482, Zero, Succ(zzz4840), bh) → new_mkVBalBranch0(zzz482, Branch(zzz478, zzz479, Pos(Succ(Zero)), zzz480, zzz481), zzz476, bh)
new_mkVBalBranch3MkVBalBranch218(zzz461, zzz462, zzz463, zzz464, zzz465, zzz466, zzz467, zzz468, zzz469, zzz470, zzz471, bb) → new_mkVBalBranch3MkVBalBranch110(zzz461, zzz462, zzz463, zzz464, zzz465, zzz466, zzz467, zzz468, zzz469, zzz470, zzz471, new_primPlusNat2(new_primPlusNat3(Succ(new_primPlusNat3(new_primPlusNat1(zzz463), zzz463)), Succ(zzz463)), Succ(zzz463)), bb)
new_mkVBalBranch3MkVBalBranch110(zzz461, zzz462, zzz463, zzz464, zzz465, zzz466, zzz467, zzz468, zzz469, zzz470, zzz471, Succ(zzz5800), bb) → new_mkVBalBranch3MkVBalBranch115(zzz461, zzz462, zzz463, zzz464, zzz465, zzz466, zzz467, Succ(zzz468), zzz469, zzz470, zzz471, Succ(zzz5800), Succ(Succ(zzz468)), bb)
new_mkVBalBranch3MkVBalBranch227(zzz486, zzz487, zzz488, zzz489, zzz490, zzz491, zzz492, zzz493, zzz494, zzz495, zzz496, bf) → new_mkVBalBranch0(zzz496, Branch(zzz491, zzz492, Neg(Succ(Succ(zzz493))), zzz494, zzz495), zzz489, bf)
new_mkVBalBranch3MkVBalBranch215(zzz340, zzz341, Pos(Zero), zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, Succ(zzz660), h) → new_mkVBalBranch0(zzz31, zzz514, Branch(zzz340, zzz341, Pos(Zero), zzz343, zzz344), h)
new_mkVBalBranch3MkVBalBranch217(zzz473, zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, zzz481, zzz482, Succ(zzz4830), Zero, bh) → new_mkVBalBranch3MkVBalBranch121(zzz473, zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, zzz481, zzz482, new_primPlusNat2(new_primMulNat0(zzz475), Succ(zzz475)), bh)
new_mkVBalBranch3MkVBalBranch223(zzz340, zzz341, Neg(Zero), zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, Succ(zzz670), h) → new_mkVBalBranch0(zzz31, Branch(zzz510, zzz511, Neg(Succ(zzz51200)), zzz513, zzz514), zzz343, h)
new_mkVBalBranch3MkVBalBranch216(zzz1105, zzz1106, zzz1107, zzz1108, zzz1109, zzz1110, zzz1111, zzz1112, zzz1113, zzz1114, zzz1115, Zero, Succ(zzz11170), ba) → new_mkVBalBranch0(zzz1115, Branch(zzz1110, zzz1111, Pos(Succ(Succ(zzz1112))), zzz1113, zzz1114), zzz1108, ba)
new_mkVBalBranch3MkVBalBranch115(zzz1986, zzz1987, zzz1988, zzz1989, zzz1990, zzz1991, zzz1992, zzz1993, zzz1994, zzz1995, zzz1996, Zero, Succ(zzz19980), bc) → new_mkVBalBranch0(zzz1996, zzz1995, Branch(zzz1986, zzz1987, Pos(Succ(zzz1988)), zzz1989, zzz1990), bc)
new_mkVBalBranch3MkVBalBranch230(zzz498, zzz499, zzz500, zzz501, zzz502, zzz503, zzz504, zzz505, zzz506, zzz507, bg) → new_mkVBalBranch3MkVBalBranch118(zzz498, zzz499, zzz500, zzz501, zzz502, zzz503, zzz504, zzz505, zzz506, zzz507, new_primPlusNat2(Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat3(new_primPlusNat1(zzz500), zzz500)), zzz500))), Succ(zzz500)), bg)
new_mkVBalBranch3MkVBalBranch122(zzz340, zzz341, zzz34200, zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, h) → new_mkVBalBranch0(zzz31, zzz514, Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), h)
new_mkVBalBranch3MkVBalBranch217(zzz473, zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, zzz481, zzz482, Succ(zzz4830), Succ(zzz4840), bh) → new_mkVBalBranch3MkVBalBranch217(zzz473, zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, zzz481, zzz482, zzz4830, zzz4840, bh)
new_mkVBalBranch3MkVBalBranch116(zzz340, zzz341, zzz34200, zzz343, zzz344, zzz510, zzz511, zzz513, zzz514, zzz31, Succ(zzz1200), h) → new_mkVBalBranch0(zzz31, zzz514, Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), h)
new_mkVBalBranch3MkVBalBranch110(zzz461, zzz462, zzz463, zzz464, zzz465, zzz466, zzz467, zzz468, zzz469, zzz470, zzz471, Zero, bb) → new_mkVBalBranch3MkVBalBranch115(zzz461, zzz462, zzz463, zzz464, zzz465, zzz466, zzz467, Succ(zzz468), zzz469, zzz470, zzz471, Zero, Succ(Succ(zzz468)), bb)
new_mkVBalBranch3MkVBalBranch225(zzz498, zzz499, zzz500, zzz501, zzz502, zzz503, zzz504, zzz505, zzz506, zzz507, Zero, Succ(zzz5090), bg) → new_mkVBalBranch0(zzz507, Branch(zzz503, zzz504, Neg(Succ(Zero)), zzz505, zzz506), zzz501, bg)
new_mkVBalBranch0(zzz31, Branch(zzz510, zzz511, Neg(Succ(zzz51200)), zzz513, zzz514), Branch(zzz340, zzz341, zzz342, zzz343, zzz344), h) → new_mkVBalBranch3MkVBalBranch223(zzz340, zzz341, zzz342, zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat3(new_primPlusNat1(zzz51200), zzz51200)), zzz51200))), h)
new_mkVBalBranch0(zzz31, Branch(zzz510, zzz511, Neg(Zero), zzz513, zzz514), Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), h) → new_mkVBalBranch3MkVBalBranch117(zzz340, zzz341, zzz34200, zzz343, zzz344, zzz510, zzz511, zzz513, zzz514, zzz31, new_primPlusNat2(new_primPlusNat3(Succ(new_primPlusNat3(new_primPlusNat1(zzz34200), zzz34200)), Succ(zzz34200)), Succ(zzz34200)), h)
new_mkVBalBranch3MkVBalBranch121(zzz473, zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, zzz481, zzz482, Zero, bh) → new_mkVBalBranch3MkVBalBranch115(zzz473, zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, Zero, zzz480, zzz481, zzz482, Zero, Succ(Zero), bh)
new_mkVBalBranch3MkVBalBranch223(zzz340, zzz341, Neg(Succ(Zero)), zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, Succ(zzz670), h) → new_mkVBalBranch0(zzz31, Branch(zzz510, zzz511, Neg(Succ(zzz51200)), zzz513, zzz514), zzz343, h)
new_mkVBalBranch3MkVBalBranch229(zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, zzz1125, zzz1126, zzz1127, zzz1128, zzz1129, bd) → new_mkVBalBranch3MkVBalBranch119(zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, zzz1125, zzz1126, zzz1127, zzz1128, zzz1129, new_primPlusNat2(new_primPlusNat3(Succ(new_primPlusNat3(new_primPlusNat1(zzz1121), zzz1121)), Succ(zzz1121)), Succ(zzz1121)), bd)
new_mkVBalBranch3MkVBalBranch225(zzz498, zzz499, zzz500, zzz501, zzz502, zzz503, zzz504, zzz505, zzz506, zzz507, Succ(zzz5080), Zero, bg) → new_mkVBalBranch3MkVBalBranch118(zzz498, zzz499, zzz500, zzz501, zzz502, zzz503, zzz504, zzz505, zzz506, zzz507, new_primPlusNat2(new_primPlusNat3(Succ(new_primPlusNat3(new_primPlusNat1(zzz500), zzz500)), Succ(zzz500)), Succ(zzz500)), bg)
new_mkVBalBranch3MkVBalBranch215(zzz340, zzz341, Pos(Succ(Zero)), zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, Succ(zzz660), h) → new_mkVBalBranch3MkVBalBranch18(zzz340, zzz341, zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, new_primPlusNat2(new_primMulNat0(Zero), Succ(Zero)), h)
new_mkVBalBranch3MkVBalBranch233(zzz473, zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, zzz481, zzz482, bh) → new_mkVBalBranch3MkVBalBranch121(zzz473, zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, zzz481, zzz482, new_primPlusNat2(new_primMulNat0(zzz475), Succ(zzz475)), bh)
new_mkVBalBranch0(zzz31, Branch(zzz510, zzz511, Pos(Zero), zzz513, zzz514), Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), h) → new_mkVBalBranch3MkVBalBranch116(zzz340, zzz341, zzz34200, zzz343, zzz344, zzz510, zzz511, zzz513, zzz514, zzz31, new_primPlusNat2(new_primPlusNat3(Succ(new_primPlusNat3(new_primPlusNat1(zzz34200), zzz34200)), Succ(zzz34200)), Succ(zzz34200)), h)
new_mkVBalBranch3MkVBalBranch222(zzz461, zzz462, zzz463, zzz464, zzz465, zzz466, zzz467, zzz468, zzz469, zzz470, zzz471, bb) → new_mkVBalBranch3MkVBalBranch110(zzz461, zzz462, zzz463, zzz464, zzz465, zzz466, zzz467, zzz468, zzz469, zzz470, zzz471, new_primPlusNat2(Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat3(new_primPlusNat1(zzz463), zzz463)), zzz463))), Succ(zzz463)), bb)
new_mkVBalBranch3MkVBalBranch215(zzz340, zzz341, Pos(Succ(Succ(zzz342000))), zzz343, zzz344, zzz510, zzz511, Zero, zzz513, zzz514, zzz31, Succ(Succ(zzz6600)), h) → new_mkVBalBranch3MkVBalBranch217(zzz340, zzz341, Succ(zzz342000), zzz343, zzz344, zzz510, zzz511, zzz513, zzz514, zzz31, Succ(zzz6600), zzz342000, h)
new_mkVBalBranch3MkVBalBranch117(zzz340, zzz341, zzz34200, zzz343, zzz344, zzz510, zzz511, zzz513, zzz514, zzz31, Succ(zzz1240), h) → new_mkVBalBranch0(zzz31, zzz514, Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), h)
new_mkVBalBranch3MkVBalBranch120(zzz2050, zzz2051, zzz2052, zzz2053, zzz2054, zzz2055, zzz2056, zzz2057, zzz2058, zzz2059, zzz2060, Succ(zzz20610), Succ(zzz20620), be) → new_mkVBalBranch3MkVBalBranch120(zzz2050, zzz2051, zzz2052, zzz2053, zzz2054, zzz2055, zzz2056, zzz2057, zzz2058, zzz2059, zzz2060, zzz20610, zzz20620, be)
new_mkVBalBranch3MkVBalBranch217(zzz473, zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, zzz481, zzz482, Zero, Zero, bh) → new_mkVBalBranch3MkVBalBranch233(zzz473, zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, zzz481, zzz482, bh)
new_mkVBalBranch3MkVBalBranch216(zzz1105, zzz1106, zzz1107, zzz1108, zzz1109, zzz1110, zzz1111, zzz1112, zzz1113, zzz1114, zzz1115, Succ(zzz11160), Succ(zzz11170), ba) → new_mkVBalBranch3MkVBalBranch216(zzz1105, zzz1106, zzz1107, zzz1108, zzz1109, zzz1110, zzz1111, zzz1112, zzz1113, zzz1114, zzz1115, zzz11160, zzz11170, ba)
new_mkVBalBranch3MkVBalBranch223(zzz340, zzz341, Pos(zzz3420), zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, Succ(zzz670), h) → new_mkVBalBranch0(zzz31, Branch(zzz510, zzz511, Neg(Succ(zzz51200)), zzz513, zzz514), zzz343, h)
new_mkVBalBranch3MkVBalBranch19(zzz340, zzz341, zzz34200, zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, Zero, h) → new_mkVBalBranch3MkVBalBranch122(zzz340, zzz341, zzz34200, zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, h)
new_mkVBalBranch3MkVBalBranch225(zzz498, zzz499, zzz500, zzz501, zzz502, zzz503, zzz504, zzz505, zzz506, zzz507, Succ(zzz5080), Succ(zzz5090), bg) → new_mkVBalBranch3MkVBalBranch225(zzz498, zzz499, zzz500, zzz501, zzz502, zzz503, zzz504, zzz505, zzz506, zzz507, zzz5080, zzz5090, bg)
new_mkVBalBranch3MkVBalBranch19(zzz340, zzz341, zzz34200, zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, Succ(zzz1410), h) → new_mkVBalBranch0(zzz31, zzz514, Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), h)
new_mkVBalBranch3MkVBalBranch224(zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, zzz1125, zzz1126, zzz1127, zzz1128, zzz1129, Zero, Succ(zzz11310), bd) → new_mkVBalBranch3MkVBalBranch227(zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, zzz1125, zzz1126, zzz1127, zzz1128, zzz1129, bd)
new_mkVBalBranch3MkVBalBranch224(zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, zzz1125, zzz1126, zzz1127, zzz1128, zzz1129, Zero, Zero, bd) → new_mkVBalBranch3MkVBalBranch229(zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, zzz1125, zzz1126, zzz1127, zzz1128, zzz1129, bd)
new_mkVBalBranch3MkVBalBranch223(zzz340, zzz341, Neg(Succ(Succ(Succ(zzz3420000)))), zzz343, zzz344, zzz510, zzz511, Succ(zzz512000), zzz513, zzz514, zzz31, Succ(Succ(zzz6700)), h) → new_mkVBalBranch3MkVBalBranch224(zzz340, zzz341, Succ(Succ(zzz3420000)), zzz343, zzz344, zzz510, zzz511, zzz512000, zzz513, zzz514, zzz31, Succ(zzz3420000), Succ(Succ(new_primPlusNat2(zzz6700, zzz512000))), h)
new_mkVBalBranch3MkVBalBranch223(zzz340, zzz341, Neg(Succ(Succ(Zero))), zzz343, zzz344, zzz510, zzz511, Zero, zzz513, zzz514, zzz31, Succ(Succ(zzz6700)), h) → new_mkVBalBranch3MkVBalBranch225(zzz340, zzz341, Succ(Zero), zzz343, zzz344, zzz510, zzz511, zzz513, zzz514, zzz31, Zero, Succ(zzz6700), h)
new_mkVBalBranch3MkVBalBranch115(zzz1986, zzz1987, zzz1988, zzz1989, zzz1990, zzz1991, zzz1992, zzz1993, zzz1994, zzz1995, zzz1996, Succ(zzz19970), Succ(zzz19980), bc) → new_mkVBalBranch3MkVBalBranch115(zzz1986, zzz1987, zzz1988, zzz1989, zzz1990, zzz1991, zzz1992, zzz1993, zzz1994, zzz1995, zzz1996, zzz19970, zzz19980, bc)
new_mkVBalBranch3MkVBalBranch215(zzz340, zzz341, Neg(Zero), zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, Succ(zzz660), h) → new_mkVBalBranch0(zzz31, zzz514, Branch(zzz340, zzz341, Neg(Zero), zzz343, zzz344), h)
new_mkVBalBranch3MkVBalBranch118(zzz498, zzz499, zzz500, zzz501, zzz502, zzz503, zzz504, zzz505, zzz506, zzz507, Succ(zzz8040), bg) → new_mkVBalBranch3MkVBalBranch120(zzz498, zzz499, zzz500, zzz501, zzz502, zzz503, zzz504, Zero, zzz505, zzz506, zzz507, Succ(Zero), Succ(zzz8040), bg)
new_mkVBalBranch3MkVBalBranch216(zzz1105, zzz1106, zzz1107, zzz1108, zzz1109, zzz1110, zzz1111, zzz1112, zzz1113, zzz1114, zzz1115, Succ(zzz11160), Zero, ba) → new_mkVBalBranch3MkVBalBranch218(zzz1105, zzz1106, zzz1107, zzz1108, zzz1109, zzz1110, zzz1111, zzz1112, zzz1113, zzz1114, zzz1115, ba)
new_mkVBalBranch3MkVBalBranch215(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, Succ(zzz660), h) → new_mkVBalBranch3MkVBalBranch19(zzz340, zzz341, zzz34200, zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, new_primPlusNat2(new_primMulNat0(zzz34200), Succ(zzz34200)), h)
new_mkVBalBranch3MkVBalBranch216(zzz1105, zzz1106, zzz1107, zzz1108, zzz1109, zzz1110, zzz1111, zzz1112, zzz1113, zzz1114, zzz1115, Zero, Zero, ba) → new_mkVBalBranch3MkVBalBranch222(zzz1105, zzz1106, zzz1107, zzz1108, zzz1109, zzz1110, zzz1111, zzz1112, zzz1113, zzz1114, zzz1115, ba)
new_mkVBalBranch3MkVBalBranch18(zzz340, zzz341, zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, Zero, h) → new_mkVBalBranch3MkVBalBranch115(zzz340, zzz341, Zero, zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, Zero, Succ(zzz51200), h)
new_mkVBalBranch3MkVBalBranch119(zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, zzz1125, zzz1126, zzz1127, zzz1128, zzz1129, Succ(zzz12130), bd) → new_mkVBalBranch3MkVBalBranch120(zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, zzz1125, Succ(zzz1126), zzz1127, zzz1128, zzz1129, Succ(Succ(zzz1126)), Succ(zzz12130), bd)

The TRS R consists of the following rules:

new_primMulNat0(zzz6200) → new_primPlusNat3(Succ(new_primPlusNat3(new_primPlusNat1(zzz6200), zzz6200)), Succ(zzz6200))
new_primPlusNat2(Succ(zzz900), Succ(zzz9100)) → Succ(Succ(new_primPlusNat2(zzz900, zzz9100)))
new_primPlusNat2(Zero, Succ(zzz9100)) → Succ(zzz9100)
new_primPlusNat2(Zero, Zero) → Zero
new_primPlusNat2(Succ(zzz900), Zero) → Succ(zzz900)
new_primPlusNat1(Zero) → Zero
new_primPlusNat1(Succ(zzz62000)) → Succ(Succ(new_primPlusNat1(zzz62000)))
new_primPlusNat3(zzz90, Succ(zzz910)) → Succ(Succ(new_primPlusNat2(zzz90, zzz910)))
new_primPlusNat3(zzz90, Zero) → Succ(zzz90)

The set Q consists of the following terms:

new_primPlusNat2(Zero, Succ(x0))
new_primMulNat0(x0)
new_primPlusNat3(x0, Succ(x1))
new_primPlusNat2(Succ(x0), Succ(x1))
new_primPlusNat3(x0, Zero)
new_primPlusNat1(Zero)
new_primPlusNat2(Zero, Zero)
new_primPlusNat1(Succ(x0))
new_primPlusNat2(Succ(x0), Zero)

We have to consider all minimal (P,Q,R)-chains.
By rewriting [15] the rule new_mkVBalBranch3MkVBalBranch233(zzz473, zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, zzz481, zzz482, bh) → new_mkVBalBranch3MkVBalBranch121(zzz473, zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, zzz481, zzz482, new_primPlusNat2(new_primMulNat0(zzz475), Succ(zzz475)), bh) at position [10,0] we obtained the following new rules:

new_mkVBalBranch3MkVBalBranch233(zzz473, zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, zzz481, zzz482, bh) → new_mkVBalBranch3MkVBalBranch121(zzz473, zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, zzz481, zzz482, new_primPlusNat2(new_primPlusNat3(Succ(new_primPlusNat3(new_primPlusNat1(zzz475), zzz475)), Succ(zzz475)), Succ(zzz475)), bh)



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

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

new_mkVBalBranch3MkVBalBranch225(zzz498, zzz499, zzz500, zzz501, zzz502, zzz503, zzz504, zzz505, zzz506, zzz507, Zero, Zero, bg) → new_mkVBalBranch3MkVBalBranch230(zzz498, zzz499, zzz500, zzz501, zzz502, zzz503, zzz504, zzz505, zzz506, zzz507, bg)
new_mkVBalBranch3MkVBalBranch18(zzz340, zzz341, zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, Succ(zzz1480), h) → new_mkVBalBranch3MkVBalBranch115(zzz340, zzz341, Zero, zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, Succ(zzz1480), Succ(zzz51200), h)
new_mkVBalBranch3MkVBalBranch215(zzz340, zzz341, Pos(Succ(Succ(zzz342000))), zzz343, zzz344, zzz510, zzz511, Succ(zzz512000), zzz513, zzz514, zzz31, Succ(Succ(zzz6600)), h) → new_mkVBalBranch3MkVBalBranch216(zzz340, zzz341, Succ(zzz342000), zzz343, zzz344, zzz510, zzz511, zzz512000, zzz513, zzz514, zzz31, Succ(Succ(new_primPlusNat2(zzz6600, zzz512000))), zzz342000, h)
new_mkVBalBranch0(zzz31, Branch(zzz510, zzz511, Neg(Zero), zzz513, zzz514), Branch(zzz340, zzz341, Pos(Succ(zzz34200)), zzz343, zzz344), h) → new_mkVBalBranch0(zzz31, Branch(zzz510, zzz511, Neg(Zero), zzz513, zzz514), zzz343, h)
new_mkVBalBranch3MkVBalBranch223(zzz340, zzz341, Neg(Succ(Succ(Succ(zzz3420000)))), zzz343, zzz344, zzz510, zzz511, Zero, zzz513, zzz514, zzz31, Succ(Succ(zzz6700)), h) → new_mkVBalBranch3MkVBalBranch225(zzz340, zzz341, Succ(Succ(zzz3420000)), zzz343, zzz344, zzz510, zzz511, zzz513, zzz514, zzz31, Succ(zzz3420000), Succ(zzz6700), h)
new_mkVBalBranch3MkVBalBranch120(zzz2050, zzz2051, zzz2052, zzz2053, zzz2054, zzz2055, zzz2056, zzz2057, zzz2058, zzz2059, zzz2060, Zero, Succ(zzz20620), be) → new_mkVBalBranch0(zzz2060, zzz2059, Branch(zzz2050, zzz2051, Neg(Succ(zzz2052)), zzz2053, zzz2054), be)
new_mkVBalBranch3MkVBalBranch121(zzz473, zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, zzz481, zzz482, Succ(zzz7390), bh) → new_mkVBalBranch3MkVBalBranch115(zzz473, zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, Zero, zzz480, zzz481, zzz482, Succ(zzz7390), Succ(Zero), bh)
new_mkVBalBranch0(zzz31, Branch(zzz510, zzz511, Pos(Zero), zzz513, zzz514), Branch(zzz340, zzz341, Pos(Succ(zzz34200)), zzz343, zzz344), h) → new_mkVBalBranch0(zzz31, Branch(zzz510, zzz511, Pos(Zero), zzz513, zzz514), zzz343, h)
new_mkVBalBranch0(zzz31, Branch(zzz510, zzz511, Pos(Succ(zzz51200)), zzz513, zzz514), Branch(zzz340, zzz341, zzz342, zzz343, zzz344), h) → new_mkVBalBranch3MkVBalBranch215(zzz340, zzz341, zzz342, zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat3(new_primPlusNat1(zzz51200), zzz51200)), zzz51200))), h)
new_mkVBalBranch3MkVBalBranch223(zzz340, zzz341, Neg(Succ(Succ(Zero))), zzz343, zzz344, zzz510, zzz511, Succ(zzz512000), zzz513, zzz514, zzz31, Succ(Succ(zzz6700)), h) → new_mkVBalBranch3MkVBalBranch224(zzz340, zzz341, Succ(Zero), zzz343, zzz344, zzz510, zzz511, zzz512000, zzz513, zzz514, zzz31, Zero, Succ(Succ(new_primPlusNat2(zzz6700, zzz512000))), h)
new_mkVBalBranch3MkVBalBranch224(zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, zzz1125, zzz1126, zzz1127, zzz1128, zzz1129, Succ(zzz11300), Succ(zzz11310), bd) → new_mkVBalBranch3MkVBalBranch224(zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, zzz1125, zzz1126, zzz1127, zzz1128, zzz1129, zzz11300, zzz11310, bd)
new_mkVBalBranch3MkVBalBranch224(zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, zzz1125, zzz1126, zzz1127, zzz1128, zzz1129, Succ(zzz11300), Zero, bd) → new_mkVBalBranch3MkVBalBranch119(zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, zzz1125, zzz1126, zzz1127, zzz1128, zzz1129, new_primPlusNat2(new_primPlusNat3(Succ(new_primPlusNat3(new_primPlusNat1(zzz1121), zzz1121)), Succ(zzz1121)), Succ(zzz1121)), bd)
new_mkVBalBranch3MkVBalBranch217(zzz473, zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, zzz481, zzz482, Zero, Succ(zzz4840), bh) → new_mkVBalBranch0(zzz482, Branch(zzz478, zzz479, Pos(Succ(Zero)), zzz480, zzz481), zzz476, bh)
new_mkVBalBranch3MkVBalBranch218(zzz461, zzz462, zzz463, zzz464, zzz465, zzz466, zzz467, zzz468, zzz469, zzz470, zzz471, bb) → new_mkVBalBranch3MkVBalBranch110(zzz461, zzz462, zzz463, zzz464, zzz465, zzz466, zzz467, zzz468, zzz469, zzz470, zzz471, new_primPlusNat2(new_primPlusNat3(Succ(new_primPlusNat3(new_primPlusNat1(zzz463), zzz463)), Succ(zzz463)), Succ(zzz463)), bb)
new_mkVBalBranch3MkVBalBranch233(zzz473, zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, zzz481, zzz482, bh) → new_mkVBalBranch3MkVBalBranch121(zzz473, zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, zzz481, zzz482, new_primPlusNat2(new_primPlusNat3(Succ(new_primPlusNat3(new_primPlusNat1(zzz475), zzz475)), Succ(zzz475)), Succ(zzz475)), bh)
new_mkVBalBranch3MkVBalBranch110(zzz461, zzz462, zzz463, zzz464, zzz465, zzz466, zzz467, zzz468, zzz469, zzz470, zzz471, Succ(zzz5800), bb) → new_mkVBalBranch3MkVBalBranch115(zzz461, zzz462, zzz463, zzz464, zzz465, zzz466, zzz467, Succ(zzz468), zzz469, zzz470, zzz471, Succ(zzz5800), Succ(Succ(zzz468)), bb)
new_mkVBalBranch3MkVBalBranch227(zzz486, zzz487, zzz488, zzz489, zzz490, zzz491, zzz492, zzz493, zzz494, zzz495, zzz496, bf) → new_mkVBalBranch0(zzz496, Branch(zzz491, zzz492, Neg(Succ(Succ(zzz493))), zzz494, zzz495), zzz489, bf)
new_mkVBalBranch3MkVBalBranch215(zzz340, zzz341, Pos(Zero), zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, Succ(zzz660), h) → new_mkVBalBranch0(zzz31, zzz514, Branch(zzz340, zzz341, Pos(Zero), zzz343, zzz344), h)
new_mkVBalBranch3MkVBalBranch223(zzz340, zzz341, Neg(Zero), zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, Succ(zzz670), h) → new_mkVBalBranch0(zzz31, Branch(zzz510, zzz511, Neg(Succ(zzz51200)), zzz513, zzz514), zzz343, h)
new_mkVBalBranch3MkVBalBranch217(zzz473, zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, zzz481, zzz482, Succ(zzz4830), Zero, bh) → new_mkVBalBranch3MkVBalBranch121(zzz473, zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, zzz481, zzz482, new_primPlusNat2(new_primMulNat0(zzz475), Succ(zzz475)), bh)
new_mkVBalBranch3MkVBalBranch216(zzz1105, zzz1106, zzz1107, zzz1108, zzz1109, zzz1110, zzz1111, zzz1112, zzz1113, zzz1114, zzz1115, Zero, Succ(zzz11170), ba) → new_mkVBalBranch0(zzz1115, Branch(zzz1110, zzz1111, Pos(Succ(Succ(zzz1112))), zzz1113, zzz1114), zzz1108, ba)
new_mkVBalBranch3MkVBalBranch115(zzz1986, zzz1987, zzz1988, zzz1989, zzz1990, zzz1991, zzz1992, zzz1993, zzz1994, zzz1995, zzz1996, Zero, Succ(zzz19980), bc) → new_mkVBalBranch0(zzz1996, zzz1995, Branch(zzz1986, zzz1987, Pos(Succ(zzz1988)), zzz1989, zzz1990), bc)
new_mkVBalBranch3MkVBalBranch122(zzz340, zzz341, zzz34200, zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, h) → new_mkVBalBranch0(zzz31, zzz514, Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), h)
new_mkVBalBranch3MkVBalBranch230(zzz498, zzz499, zzz500, zzz501, zzz502, zzz503, zzz504, zzz505, zzz506, zzz507, bg) → new_mkVBalBranch3MkVBalBranch118(zzz498, zzz499, zzz500, zzz501, zzz502, zzz503, zzz504, zzz505, zzz506, zzz507, new_primPlusNat2(Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat3(new_primPlusNat1(zzz500), zzz500)), zzz500))), Succ(zzz500)), bg)
new_mkVBalBranch3MkVBalBranch217(zzz473, zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, zzz481, zzz482, Succ(zzz4830), Succ(zzz4840), bh) → new_mkVBalBranch3MkVBalBranch217(zzz473, zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, zzz481, zzz482, zzz4830, zzz4840, bh)
new_mkVBalBranch3MkVBalBranch116(zzz340, zzz341, zzz34200, zzz343, zzz344, zzz510, zzz511, zzz513, zzz514, zzz31, Succ(zzz1200), h) → new_mkVBalBranch0(zzz31, zzz514, Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), h)
new_mkVBalBranch3MkVBalBranch110(zzz461, zzz462, zzz463, zzz464, zzz465, zzz466, zzz467, zzz468, zzz469, zzz470, zzz471, Zero, bb) → new_mkVBalBranch3MkVBalBranch115(zzz461, zzz462, zzz463, zzz464, zzz465, zzz466, zzz467, Succ(zzz468), zzz469, zzz470, zzz471, Zero, Succ(Succ(zzz468)), bb)
new_mkVBalBranch3MkVBalBranch225(zzz498, zzz499, zzz500, zzz501, zzz502, zzz503, zzz504, zzz505, zzz506, zzz507, Zero, Succ(zzz5090), bg) → new_mkVBalBranch0(zzz507, Branch(zzz503, zzz504, Neg(Succ(Zero)), zzz505, zzz506), zzz501, bg)
new_mkVBalBranch0(zzz31, Branch(zzz510, zzz511, Neg(Succ(zzz51200)), zzz513, zzz514), Branch(zzz340, zzz341, zzz342, zzz343, zzz344), h) → new_mkVBalBranch3MkVBalBranch223(zzz340, zzz341, zzz342, zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat3(new_primPlusNat1(zzz51200), zzz51200)), zzz51200))), h)
new_mkVBalBranch0(zzz31, Branch(zzz510, zzz511, Neg(Zero), zzz513, zzz514), Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), h) → new_mkVBalBranch3MkVBalBranch117(zzz340, zzz341, zzz34200, zzz343, zzz344, zzz510, zzz511, zzz513, zzz514, zzz31, new_primPlusNat2(new_primPlusNat3(Succ(new_primPlusNat3(new_primPlusNat1(zzz34200), zzz34200)), Succ(zzz34200)), Succ(zzz34200)), h)
new_mkVBalBranch3MkVBalBranch121(zzz473, zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, zzz481, zzz482, Zero, bh) → new_mkVBalBranch3MkVBalBranch115(zzz473, zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, Zero, zzz480, zzz481, zzz482, Zero, Succ(Zero), bh)
new_mkVBalBranch3MkVBalBranch223(zzz340, zzz341, Neg(Succ(Zero)), zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, Succ(zzz670), h) → new_mkVBalBranch0(zzz31, Branch(zzz510, zzz511, Neg(Succ(zzz51200)), zzz513, zzz514), zzz343, h)
new_mkVBalBranch3MkVBalBranch225(zzz498, zzz499, zzz500, zzz501, zzz502, zzz503, zzz504, zzz505, zzz506, zzz507, Succ(zzz5080), Zero, bg) → new_mkVBalBranch3MkVBalBranch118(zzz498, zzz499, zzz500, zzz501, zzz502, zzz503, zzz504, zzz505, zzz506, zzz507, new_primPlusNat2(new_primPlusNat3(Succ(new_primPlusNat3(new_primPlusNat1(zzz500), zzz500)), Succ(zzz500)), Succ(zzz500)), bg)
new_mkVBalBranch3MkVBalBranch229(zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, zzz1125, zzz1126, zzz1127, zzz1128, zzz1129, bd) → new_mkVBalBranch3MkVBalBranch119(zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, zzz1125, zzz1126, zzz1127, zzz1128, zzz1129, new_primPlusNat2(new_primPlusNat3(Succ(new_primPlusNat3(new_primPlusNat1(zzz1121), zzz1121)), Succ(zzz1121)), Succ(zzz1121)), bd)
new_mkVBalBranch3MkVBalBranch215(zzz340, zzz341, Pos(Succ(Zero)), zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, Succ(zzz660), h) → new_mkVBalBranch3MkVBalBranch18(zzz340, zzz341, zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, new_primPlusNat2(new_primMulNat0(Zero), Succ(Zero)), h)
new_mkVBalBranch0(zzz31, Branch(zzz510, zzz511, Pos(Zero), zzz513, zzz514), Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), h) → new_mkVBalBranch3MkVBalBranch116(zzz340, zzz341, zzz34200, zzz343, zzz344, zzz510, zzz511, zzz513, zzz514, zzz31, new_primPlusNat2(new_primPlusNat3(Succ(new_primPlusNat3(new_primPlusNat1(zzz34200), zzz34200)), Succ(zzz34200)), Succ(zzz34200)), h)
new_mkVBalBranch3MkVBalBranch222(zzz461, zzz462, zzz463, zzz464, zzz465, zzz466, zzz467, zzz468, zzz469, zzz470, zzz471, bb) → new_mkVBalBranch3MkVBalBranch110(zzz461, zzz462, zzz463, zzz464, zzz465, zzz466, zzz467, zzz468, zzz469, zzz470, zzz471, new_primPlusNat2(Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat3(new_primPlusNat1(zzz463), zzz463)), zzz463))), Succ(zzz463)), bb)
new_mkVBalBranch3MkVBalBranch215(zzz340, zzz341, Pos(Succ(Succ(zzz342000))), zzz343, zzz344, zzz510, zzz511, Zero, zzz513, zzz514, zzz31, Succ(Succ(zzz6600)), h) → new_mkVBalBranch3MkVBalBranch217(zzz340, zzz341, Succ(zzz342000), zzz343, zzz344, zzz510, zzz511, zzz513, zzz514, zzz31, Succ(zzz6600), zzz342000, h)
new_mkVBalBranch3MkVBalBranch117(zzz340, zzz341, zzz34200, zzz343, zzz344, zzz510, zzz511, zzz513, zzz514, zzz31, Succ(zzz1240), h) → new_mkVBalBranch0(zzz31, zzz514, Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), h)
new_mkVBalBranch3MkVBalBranch217(zzz473, zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, zzz481, zzz482, Zero, Zero, bh) → new_mkVBalBranch3MkVBalBranch233(zzz473, zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, zzz481, zzz482, bh)
new_mkVBalBranch3MkVBalBranch120(zzz2050, zzz2051, zzz2052, zzz2053, zzz2054, zzz2055, zzz2056, zzz2057, zzz2058, zzz2059, zzz2060, Succ(zzz20610), Succ(zzz20620), be) → new_mkVBalBranch3MkVBalBranch120(zzz2050, zzz2051, zzz2052, zzz2053, zzz2054, zzz2055, zzz2056, zzz2057, zzz2058, zzz2059, zzz2060, zzz20610, zzz20620, be)
new_mkVBalBranch3MkVBalBranch223(zzz340, zzz341, Pos(zzz3420), zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, Succ(zzz670), h) → new_mkVBalBranch0(zzz31, Branch(zzz510, zzz511, Neg(Succ(zzz51200)), zzz513, zzz514), zzz343, h)
new_mkVBalBranch3MkVBalBranch216(zzz1105, zzz1106, zzz1107, zzz1108, zzz1109, zzz1110, zzz1111, zzz1112, zzz1113, zzz1114, zzz1115, Succ(zzz11160), Succ(zzz11170), ba) → new_mkVBalBranch3MkVBalBranch216(zzz1105, zzz1106, zzz1107, zzz1108, zzz1109, zzz1110, zzz1111, zzz1112, zzz1113, zzz1114, zzz1115, zzz11160, zzz11170, ba)
new_mkVBalBranch3MkVBalBranch19(zzz340, zzz341, zzz34200, zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, Zero, h) → new_mkVBalBranch3MkVBalBranch122(zzz340, zzz341, zzz34200, zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, h)
new_mkVBalBranch3MkVBalBranch225(zzz498, zzz499, zzz500, zzz501, zzz502, zzz503, zzz504, zzz505, zzz506, zzz507, Succ(zzz5080), Succ(zzz5090), bg) → new_mkVBalBranch3MkVBalBranch225(zzz498, zzz499, zzz500, zzz501, zzz502, zzz503, zzz504, zzz505, zzz506, zzz507, zzz5080, zzz5090, bg)
new_mkVBalBranch3MkVBalBranch19(zzz340, zzz341, zzz34200, zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, Succ(zzz1410), h) → new_mkVBalBranch0(zzz31, zzz514, Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), h)
new_mkVBalBranch3MkVBalBranch224(zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, zzz1125, zzz1126, zzz1127, zzz1128, zzz1129, Zero, Zero, bd) → new_mkVBalBranch3MkVBalBranch229(zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, zzz1125, zzz1126, zzz1127, zzz1128, zzz1129, bd)
new_mkVBalBranch3MkVBalBranch224(zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, zzz1125, zzz1126, zzz1127, zzz1128, zzz1129, Zero, Succ(zzz11310), bd) → new_mkVBalBranch3MkVBalBranch227(zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, zzz1125, zzz1126, zzz1127, zzz1128, zzz1129, bd)
new_mkVBalBranch3MkVBalBranch223(zzz340, zzz341, Neg(Succ(Succ(Zero))), zzz343, zzz344, zzz510, zzz511, Zero, zzz513, zzz514, zzz31, Succ(Succ(zzz6700)), h) → new_mkVBalBranch3MkVBalBranch225(zzz340, zzz341, Succ(Zero), zzz343, zzz344, zzz510, zzz511, zzz513, zzz514, zzz31, Zero, Succ(zzz6700), h)
new_mkVBalBranch3MkVBalBranch223(zzz340, zzz341, Neg(Succ(Succ(Succ(zzz3420000)))), zzz343, zzz344, zzz510, zzz511, Succ(zzz512000), zzz513, zzz514, zzz31, Succ(Succ(zzz6700)), h) → new_mkVBalBranch3MkVBalBranch224(zzz340, zzz341, Succ(Succ(zzz3420000)), zzz343, zzz344, zzz510, zzz511, zzz512000, zzz513, zzz514, zzz31, Succ(zzz3420000), Succ(Succ(new_primPlusNat2(zzz6700, zzz512000))), h)
new_mkVBalBranch3MkVBalBranch115(zzz1986, zzz1987, zzz1988, zzz1989, zzz1990, zzz1991, zzz1992, zzz1993, zzz1994, zzz1995, zzz1996, Succ(zzz19970), Succ(zzz19980), bc) → new_mkVBalBranch3MkVBalBranch115(zzz1986, zzz1987, zzz1988, zzz1989, zzz1990, zzz1991, zzz1992, zzz1993, zzz1994, zzz1995, zzz1996, zzz19970, zzz19980, bc)
new_mkVBalBranch3MkVBalBranch215(zzz340, zzz341, Neg(Zero), zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, Succ(zzz660), h) → new_mkVBalBranch0(zzz31, zzz514, Branch(zzz340, zzz341, Neg(Zero), zzz343, zzz344), h)
new_mkVBalBranch3MkVBalBranch118(zzz498, zzz499, zzz500, zzz501, zzz502, zzz503, zzz504, zzz505, zzz506, zzz507, Succ(zzz8040), bg) → new_mkVBalBranch3MkVBalBranch120(zzz498, zzz499, zzz500, zzz501, zzz502, zzz503, zzz504, Zero, zzz505, zzz506, zzz507, Succ(Zero), Succ(zzz8040), bg)
new_mkVBalBranch3MkVBalBranch216(zzz1105, zzz1106, zzz1107, zzz1108, zzz1109, zzz1110, zzz1111, zzz1112, zzz1113, zzz1114, zzz1115, Succ(zzz11160), Zero, ba) → new_mkVBalBranch3MkVBalBranch218(zzz1105, zzz1106, zzz1107, zzz1108, zzz1109, zzz1110, zzz1111, zzz1112, zzz1113, zzz1114, zzz1115, ba)
new_mkVBalBranch3MkVBalBranch215(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, Succ(zzz660), h) → new_mkVBalBranch3MkVBalBranch19(zzz340, zzz341, zzz34200, zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, new_primPlusNat2(new_primMulNat0(zzz34200), Succ(zzz34200)), h)
new_mkVBalBranch3MkVBalBranch216(zzz1105, zzz1106, zzz1107, zzz1108, zzz1109, zzz1110, zzz1111, zzz1112, zzz1113, zzz1114, zzz1115, Zero, Zero, ba) → new_mkVBalBranch3MkVBalBranch222(zzz1105, zzz1106, zzz1107, zzz1108, zzz1109, zzz1110, zzz1111, zzz1112, zzz1113, zzz1114, zzz1115, ba)
new_mkVBalBranch3MkVBalBranch119(zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, zzz1125, zzz1126, zzz1127, zzz1128, zzz1129, Succ(zzz12130), bd) → new_mkVBalBranch3MkVBalBranch120(zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, zzz1125, Succ(zzz1126), zzz1127, zzz1128, zzz1129, Succ(Succ(zzz1126)), Succ(zzz12130), bd)
new_mkVBalBranch3MkVBalBranch18(zzz340, zzz341, zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, Zero, h) → new_mkVBalBranch3MkVBalBranch115(zzz340, zzz341, Zero, zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, Zero, Succ(zzz51200), h)

The TRS R consists of the following rules:

new_primMulNat0(zzz6200) → new_primPlusNat3(Succ(new_primPlusNat3(new_primPlusNat1(zzz6200), zzz6200)), Succ(zzz6200))
new_primPlusNat2(Succ(zzz900), Succ(zzz9100)) → Succ(Succ(new_primPlusNat2(zzz900, zzz9100)))
new_primPlusNat2(Zero, Succ(zzz9100)) → Succ(zzz9100)
new_primPlusNat2(Zero, Zero) → Zero
new_primPlusNat2(Succ(zzz900), Zero) → Succ(zzz900)
new_primPlusNat1(Zero) → Zero
new_primPlusNat1(Succ(zzz62000)) → Succ(Succ(new_primPlusNat1(zzz62000)))
new_primPlusNat3(zzz90, Succ(zzz910)) → Succ(Succ(new_primPlusNat2(zzz90, zzz910)))
new_primPlusNat3(zzz90, Zero) → Succ(zzz90)

The set Q consists of the following terms:

new_primPlusNat2(Zero, Succ(x0))
new_primMulNat0(x0)
new_primPlusNat3(x0, Succ(x1))
new_primPlusNat2(Succ(x0), Succ(x1))
new_primPlusNat3(x0, Zero)
new_primPlusNat1(Zero)
new_primPlusNat2(Zero, Zero)
new_primPlusNat1(Succ(x0))
new_primPlusNat2(Succ(x0), Zero)

We have to consider all minimal (P,Q,R)-chains.
By rewriting [15] the rule new_mkVBalBranch3MkVBalBranch217(zzz473, zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, zzz481, zzz482, Succ(zzz4830), Zero, bh) → new_mkVBalBranch3MkVBalBranch121(zzz473, zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, zzz481, zzz482, new_primPlusNat2(new_primMulNat0(zzz475), Succ(zzz475)), bh) at position [10,0] we obtained the following new rules:

new_mkVBalBranch3MkVBalBranch217(zzz473, zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, zzz481, zzz482, Succ(zzz4830), Zero, bh) → new_mkVBalBranch3MkVBalBranch121(zzz473, zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, zzz481, zzz482, new_primPlusNat2(new_primPlusNat3(Succ(new_primPlusNat3(new_primPlusNat1(zzz475), zzz475)), Succ(zzz475)), Succ(zzz475)), bh)



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

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

new_mkVBalBranch3MkVBalBranch225(zzz498, zzz499, zzz500, zzz501, zzz502, zzz503, zzz504, zzz505, zzz506, zzz507, Zero, Zero, bg) → new_mkVBalBranch3MkVBalBranch230(zzz498, zzz499, zzz500, zzz501, zzz502, zzz503, zzz504, zzz505, zzz506, zzz507, bg)
new_mkVBalBranch3MkVBalBranch18(zzz340, zzz341, zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, Succ(zzz1480), h) → new_mkVBalBranch3MkVBalBranch115(zzz340, zzz341, Zero, zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, Succ(zzz1480), Succ(zzz51200), h)
new_mkVBalBranch0(zzz31, Branch(zzz510, zzz511, Neg(Zero), zzz513, zzz514), Branch(zzz340, zzz341, Pos(Succ(zzz34200)), zzz343, zzz344), h) → new_mkVBalBranch0(zzz31, Branch(zzz510, zzz511, Neg(Zero), zzz513, zzz514), zzz343, h)
new_mkVBalBranch3MkVBalBranch215(zzz340, zzz341, Pos(Succ(Succ(zzz342000))), zzz343, zzz344, zzz510, zzz511, Succ(zzz512000), zzz513, zzz514, zzz31, Succ(Succ(zzz6600)), h) → new_mkVBalBranch3MkVBalBranch216(zzz340, zzz341, Succ(zzz342000), zzz343, zzz344, zzz510, zzz511, zzz512000, zzz513, zzz514, zzz31, Succ(Succ(new_primPlusNat2(zzz6600, zzz512000))), zzz342000, h)
new_mkVBalBranch3MkVBalBranch223(zzz340, zzz341, Neg(Succ(Succ(Succ(zzz3420000)))), zzz343, zzz344, zzz510, zzz511, Zero, zzz513, zzz514, zzz31, Succ(Succ(zzz6700)), h) → new_mkVBalBranch3MkVBalBranch225(zzz340, zzz341, Succ(Succ(zzz3420000)), zzz343, zzz344, zzz510, zzz511, zzz513, zzz514, zzz31, Succ(zzz3420000), Succ(zzz6700), h)
new_mkVBalBranch3MkVBalBranch120(zzz2050, zzz2051, zzz2052, zzz2053, zzz2054, zzz2055, zzz2056, zzz2057, zzz2058, zzz2059, zzz2060, Zero, Succ(zzz20620), be) → new_mkVBalBranch0(zzz2060, zzz2059, Branch(zzz2050, zzz2051, Neg(Succ(zzz2052)), zzz2053, zzz2054), be)
new_mkVBalBranch0(zzz31, Branch(zzz510, zzz511, Pos(Zero), zzz513, zzz514), Branch(zzz340, zzz341, Pos(Succ(zzz34200)), zzz343, zzz344), h) → new_mkVBalBranch0(zzz31, Branch(zzz510, zzz511, Pos(Zero), zzz513, zzz514), zzz343, h)
new_mkVBalBranch3MkVBalBranch121(zzz473, zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, zzz481, zzz482, Succ(zzz7390), bh) → new_mkVBalBranch3MkVBalBranch115(zzz473, zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, Zero, zzz480, zzz481, zzz482, Succ(zzz7390), Succ(Zero), bh)
new_mkVBalBranch0(zzz31, Branch(zzz510, zzz511, Pos(Succ(zzz51200)), zzz513, zzz514), Branch(zzz340, zzz341, zzz342, zzz343, zzz344), h) → new_mkVBalBranch3MkVBalBranch215(zzz340, zzz341, zzz342, zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat3(new_primPlusNat1(zzz51200), zzz51200)), zzz51200))), h)
new_mkVBalBranch3MkVBalBranch223(zzz340, zzz341, Neg(Succ(Succ(Zero))), zzz343, zzz344, zzz510, zzz511, Succ(zzz512000), zzz513, zzz514, zzz31, Succ(Succ(zzz6700)), h) → new_mkVBalBranch3MkVBalBranch224(zzz340, zzz341, Succ(Zero), zzz343, zzz344, zzz510, zzz511, zzz512000, zzz513, zzz514, zzz31, Zero, Succ(Succ(new_primPlusNat2(zzz6700, zzz512000))), h)
new_mkVBalBranch3MkVBalBranch224(zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, zzz1125, zzz1126, zzz1127, zzz1128, zzz1129, Succ(zzz11300), Succ(zzz11310), bd) → new_mkVBalBranch3MkVBalBranch224(zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, zzz1125, zzz1126, zzz1127, zzz1128, zzz1129, zzz11300, zzz11310, bd)
new_mkVBalBranch3MkVBalBranch224(zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, zzz1125, zzz1126, zzz1127, zzz1128, zzz1129, Succ(zzz11300), Zero, bd) → new_mkVBalBranch3MkVBalBranch119(zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, zzz1125, zzz1126, zzz1127, zzz1128, zzz1129, new_primPlusNat2(new_primPlusNat3(Succ(new_primPlusNat3(new_primPlusNat1(zzz1121), zzz1121)), Succ(zzz1121)), Succ(zzz1121)), bd)
new_mkVBalBranch3MkVBalBranch217(zzz473, zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, zzz481, zzz482, Zero, Succ(zzz4840), bh) → new_mkVBalBranch0(zzz482, Branch(zzz478, zzz479, Pos(Succ(Zero)), zzz480, zzz481), zzz476, bh)
new_mkVBalBranch3MkVBalBranch218(zzz461, zzz462, zzz463, zzz464, zzz465, zzz466, zzz467, zzz468, zzz469, zzz470, zzz471, bb) → new_mkVBalBranch3MkVBalBranch110(zzz461, zzz462, zzz463, zzz464, zzz465, zzz466, zzz467, zzz468, zzz469, zzz470, zzz471, new_primPlusNat2(new_primPlusNat3(Succ(new_primPlusNat3(new_primPlusNat1(zzz463), zzz463)), Succ(zzz463)), Succ(zzz463)), bb)
new_mkVBalBranch3MkVBalBranch233(zzz473, zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, zzz481, zzz482, bh) → new_mkVBalBranch3MkVBalBranch121(zzz473, zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, zzz481, zzz482, new_primPlusNat2(new_primPlusNat3(Succ(new_primPlusNat3(new_primPlusNat1(zzz475), zzz475)), Succ(zzz475)), Succ(zzz475)), bh)
new_mkVBalBranch3MkVBalBranch110(zzz461, zzz462, zzz463, zzz464, zzz465, zzz466, zzz467, zzz468, zzz469, zzz470, zzz471, Succ(zzz5800), bb) → new_mkVBalBranch3MkVBalBranch115(zzz461, zzz462, zzz463, zzz464, zzz465, zzz466, zzz467, Succ(zzz468), zzz469, zzz470, zzz471, Succ(zzz5800), Succ(Succ(zzz468)), bb)
new_mkVBalBranch3MkVBalBranch227(zzz486, zzz487, zzz488, zzz489, zzz490, zzz491, zzz492, zzz493, zzz494, zzz495, zzz496, bf) → new_mkVBalBranch0(zzz496, Branch(zzz491, zzz492, Neg(Succ(Succ(zzz493))), zzz494, zzz495), zzz489, bf)
new_mkVBalBranch3MkVBalBranch215(zzz340, zzz341, Pos(Zero), zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, Succ(zzz660), h) → new_mkVBalBranch0(zzz31, zzz514, Branch(zzz340, zzz341, Pos(Zero), zzz343, zzz344), h)
new_mkVBalBranch3MkVBalBranch223(zzz340, zzz341, Neg(Zero), zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, Succ(zzz670), h) → new_mkVBalBranch0(zzz31, Branch(zzz510, zzz511, Neg(Succ(zzz51200)), zzz513, zzz514), zzz343, h)
new_mkVBalBranch3MkVBalBranch216(zzz1105, zzz1106, zzz1107, zzz1108, zzz1109, zzz1110, zzz1111, zzz1112, zzz1113, zzz1114, zzz1115, Zero, Succ(zzz11170), ba) → new_mkVBalBranch0(zzz1115, Branch(zzz1110, zzz1111, Pos(Succ(Succ(zzz1112))), zzz1113, zzz1114), zzz1108, ba)
new_mkVBalBranch3MkVBalBranch115(zzz1986, zzz1987, zzz1988, zzz1989, zzz1990, zzz1991, zzz1992, zzz1993, zzz1994, zzz1995, zzz1996, Zero, Succ(zzz19980), bc) → new_mkVBalBranch0(zzz1996, zzz1995, Branch(zzz1986, zzz1987, Pos(Succ(zzz1988)), zzz1989, zzz1990), bc)
new_mkVBalBranch3MkVBalBranch230(zzz498, zzz499, zzz500, zzz501, zzz502, zzz503, zzz504, zzz505, zzz506, zzz507, bg) → new_mkVBalBranch3MkVBalBranch118(zzz498, zzz499, zzz500, zzz501, zzz502, zzz503, zzz504, zzz505, zzz506, zzz507, new_primPlusNat2(Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat3(new_primPlusNat1(zzz500), zzz500)), zzz500))), Succ(zzz500)), bg)
new_mkVBalBranch3MkVBalBranch122(zzz340, zzz341, zzz34200, zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, h) → new_mkVBalBranch0(zzz31, zzz514, Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), h)
new_mkVBalBranch3MkVBalBranch217(zzz473, zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, zzz481, zzz482, Succ(zzz4830), Succ(zzz4840), bh) → new_mkVBalBranch3MkVBalBranch217(zzz473, zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, zzz481, zzz482, zzz4830, zzz4840, bh)
new_mkVBalBranch3MkVBalBranch116(zzz340, zzz341, zzz34200, zzz343, zzz344, zzz510, zzz511, zzz513, zzz514, zzz31, Succ(zzz1200), h) → new_mkVBalBranch0(zzz31, zzz514, Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), h)
new_mkVBalBranch3MkVBalBranch110(zzz461, zzz462, zzz463, zzz464, zzz465, zzz466, zzz467, zzz468, zzz469, zzz470, zzz471, Zero, bb) → new_mkVBalBranch3MkVBalBranch115(zzz461, zzz462, zzz463, zzz464, zzz465, zzz466, zzz467, Succ(zzz468), zzz469, zzz470, zzz471, Zero, Succ(Succ(zzz468)), bb)
new_mkVBalBranch3MkVBalBranch225(zzz498, zzz499, zzz500, zzz501, zzz502, zzz503, zzz504, zzz505, zzz506, zzz507, Zero, Succ(zzz5090), bg) → new_mkVBalBranch0(zzz507, Branch(zzz503, zzz504, Neg(Succ(Zero)), zzz505, zzz506), zzz501, bg)
new_mkVBalBranch0(zzz31, Branch(zzz510, zzz511, Neg(Succ(zzz51200)), zzz513, zzz514), Branch(zzz340, zzz341, zzz342, zzz343, zzz344), h) → new_mkVBalBranch3MkVBalBranch223(zzz340, zzz341, zzz342, zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat3(new_primPlusNat1(zzz51200), zzz51200)), zzz51200))), h)
new_mkVBalBranch0(zzz31, Branch(zzz510, zzz511, Neg(Zero), zzz513, zzz514), Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), h) → new_mkVBalBranch3MkVBalBranch117(zzz340, zzz341, zzz34200, zzz343, zzz344, zzz510, zzz511, zzz513, zzz514, zzz31, new_primPlusNat2(new_primPlusNat3(Succ(new_primPlusNat3(new_primPlusNat1(zzz34200), zzz34200)), Succ(zzz34200)), Succ(zzz34200)), h)
new_mkVBalBranch3MkVBalBranch217(zzz473, zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, zzz481, zzz482, Succ(zzz4830), Zero, bh) → new_mkVBalBranch3MkVBalBranch121(zzz473, zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, zzz481, zzz482, new_primPlusNat2(new_primPlusNat3(Succ(new_primPlusNat3(new_primPlusNat1(zzz475), zzz475)), Succ(zzz475)), Succ(zzz475)), bh)
new_mkVBalBranch3MkVBalBranch121(zzz473, zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, zzz481, zzz482, Zero, bh) → new_mkVBalBranch3MkVBalBranch115(zzz473, zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, Zero, zzz480, zzz481, zzz482, Zero, Succ(Zero), bh)
new_mkVBalBranch3MkVBalBranch223(zzz340, zzz341, Neg(Succ(Zero)), zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, Succ(zzz670), h) → new_mkVBalBranch0(zzz31, Branch(zzz510, zzz511, Neg(Succ(zzz51200)), zzz513, zzz514), zzz343, h)
new_mkVBalBranch3MkVBalBranch229(zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, zzz1125, zzz1126, zzz1127, zzz1128, zzz1129, bd) → new_mkVBalBranch3MkVBalBranch119(zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, zzz1125, zzz1126, zzz1127, zzz1128, zzz1129, new_primPlusNat2(new_primPlusNat3(Succ(new_primPlusNat3(new_primPlusNat1(zzz1121), zzz1121)), Succ(zzz1121)), Succ(zzz1121)), bd)
new_mkVBalBranch3MkVBalBranch225(zzz498, zzz499, zzz500, zzz501, zzz502, zzz503, zzz504, zzz505, zzz506, zzz507, Succ(zzz5080), Zero, bg) → new_mkVBalBranch3MkVBalBranch118(zzz498, zzz499, zzz500, zzz501, zzz502, zzz503, zzz504, zzz505, zzz506, zzz507, new_primPlusNat2(new_primPlusNat3(Succ(new_primPlusNat3(new_primPlusNat1(zzz500), zzz500)), Succ(zzz500)), Succ(zzz500)), bg)
new_mkVBalBranch3MkVBalBranch215(zzz340, zzz341, Pos(Succ(Zero)), zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, Succ(zzz660), h) → new_mkVBalBranch3MkVBalBranch18(zzz340, zzz341, zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, new_primPlusNat2(new_primMulNat0(Zero), Succ(Zero)), h)
new_mkVBalBranch0(zzz31, Branch(zzz510, zzz511, Pos(Zero), zzz513, zzz514), Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), h) → new_mkVBalBranch3MkVBalBranch116(zzz340, zzz341, zzz34200, zzz343, zzz344, zzz510, zzz511, zzz513, zzz514, zzz31, new_primPlusNat2(new_primPlusNat3(Succ(new_primPlusNat3(new_primPlusNat1(zzz34200), zzz34200)), Succ(zzz34200)), Succ(zzz34200)), h)
new_mkVBalBranch3MkVBalBranch222(zzz461, zzz462, zzz463, zzz464, zzz465, zzz466, zzz467, zzz468, zzz469, zzz470, zzz471, bb) → new_mkVBalBranch3MkVBalBranch110(zzz461, zzz462, zzz463, zzz464, zzz465, zzz466, zzz467, zzz468, zzz469, zzz470, zzz471, new_primPlusNat2(Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat3(new_primPlusNat1(zzz463), zzz463)), zzz463))), Succ(zzz463)), bb)
new_mkVBalBranch3MkVBalBranch215(zzz340, zzz341, Pos(Succ(Succ(zzz342000))), zzz343, zzz344, zzz510, zzz511, Zero, zzz513, zzz514, zzz31, Succ(Succ(zzz6600)), h) → new_mkVBalBranch3MkVBalBranch217(zzz340, zzz341, Succ(zzz342000), zzz343, zzz344, zzz510, zzz511, zzz513, zzz514, zzz31, Succ(zzz6600), zzz342000, h)
new_mkVBalBranch3MkVBalBranch117(zzz340, zzz341, zzz34200, zzz343, zzz344, zzz510, zzz511, zzz513, zzz514, zzz31, Succ(zzz1240), h) → new_mkVBalBranch0(zzz31, zzz514, Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), h)
new_mkVBalBranch3MkVBalBranch120(zzz2050, zzz2051, zzz2052, zzz2053, zzz2054, zzz2055, zzz2056, zzz2057, zzz2058, zzz2059, zzz2060, Succ(zzz20610), Succ(zzz20620), be) → new_mkVBalBranch3MkVBalBranch120(zzz2050, zzz2051, zzz2052, zzz2053, zzz2054, zzz2055, zzz2056, zzz2057, zzz2058, zzz2059, zzz2060, zzz20610, zzz20620, be)
new_mkVBalBranch3MkVBalBranch217(zzz473, zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, zzz481, zzz482, Zero, Zero, bh) → new_mkVBalBranch3MkVBalBranch233(zzz473, zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, zzz481, zzz482, bh)
new_mkVBalBranch3MkVBalBranch216(zzz1105, zzz1106, zzz1107, zzz1108, zzz1109, zzz1110, zzz1111, zzz1112, zzz1113, zzz1114, zzz1115, Succ(zzz11160), Succ(zzz11170), ba) → new_mkVBalBranch3MkVBalBranch216(zzz1105, zzz1106, zzz1107, zzz1108, zzz1109, zzz1110, zzz1111, zzz1112, zzz1113, zzz1114, zzz1115, zzz11160, zzz11170, ba)
new_mkVBalBranch3MkVBalBranch223(zzz340, zzz341, Pos(zzz3420), zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, Succ(zzz670), h) → new_mkVBalBranch0(zzz31, Branch(zzz510, zzz511, Neg(Succ(zzz51200)), zzz513, zzz514), zzz343, h)
new_mkVBalBranch3MkVBalBranch19(zzz340, zzz341, zzz34200, zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, Zero, h) → new_mkVBalBranch3MkVBalBranch122(zzz340, zzz341, zzz34200, zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, h)
new_mkVBalBranch3MkVBalBranch225(zzz498, zzz499, zzz500, zzz501, zzz502, zzz503, zzz504, zzz505, zzz506, zzz507, Succ(zzz5080), Succ(zzz5090), bg) → new_mkVBalBranch3MkVBalBranch225(zzz498, zzz499, zzz500, zzz501, zzz502, zzz503, zzz504, zzz505, zzz506, zzz507, zzz5080, zzz5090, bg)
new_mkVBalBranch3MkVBalBranch19(zzz340, zzz341, zzz34200, zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, Succ(zzz1410), h) → new_mkVBalBranch0(zzz31, zzz514, Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), h)
new_mkVBalBranch3MkVBalBranch224(zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, zzz1125, zzz1126, zzz1127, zzz1128, zzz1129, Zero, Succ(zzz11310), bd) → new_mkVBalBranch3MkVBalBranch227(zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, zzz1125, zzz1126, zzz1127, zzz1128, zzz1129, bd)
new_mkVBalBranch3MkVBalBranch224(zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, zzz1125, zzz1126, zzz1127, zzz1128, zzz1129, Zero, Zero, bd) → new_mkVBalBranch3MkVBalBranch229(zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, zzz1125, zzz1126, zzz1127, zzz1128, zzz1129, bd)
new_mkVBalBranch3MkVBalBranch223(zzz340, zzz341, Neg(Succ(Succ(Succ(zzz3420000)))), zzz343, zzz344, zzz510, zzz511, Succ(zzz512000), zzz513, zzz514, zzz31, Succ(Succ(zzz6700)), h) → new_mkVBalBranch3MkVBalBranch224(zzz340, zzz341, Succ(Succ(zzz3420000)), zzz343, zzz344, zzz510, zzz511, zzz512000, zzz513, zzz514, zzz31, Succ(zzz3420000), Succ(Succ(new_primPlusNat2(zzz6700, zzz512000))), h)
new_mkVBalBranch3MkVBalBranch223(zzz340, zzz341, Neg(Succ(Succ(Zero))), zzz343, zzz344, zzz510, zzz511, Zero, zzz513, zzz514, zzz31, Succ(Succ(zzz6700)), h) → new_mkVBalBranch3MkVBalBranch225(zzz340, zzz341, Succ(Zero), zzz343, zzz344, zzz510, zzz511, zzz513, zzz514, zzz31, Zero, Succ(zzz6700), h)
new_mkVBalBranch3MkVBalBranch115(zzz1986, zzz1987, zzz1988, zzz1989, zzz1990, zzz1991, zzz1992, zzz1993, zzz1994, zzz1995, zzz1996, Succ(zzz19970), Succ(zzz19980), bc) → new_mkVBalBranch3MkVBalBranch115(zzz1986, zzz1987, zzz1988, zzz1989, zzz1990, zzz1991, zzz1992, zzz1993, zzz1994, zzz1995, zzz1996, zzz19970, zzz19980, bc)
new_mkVBalBranch3MkVBalBranch215(zzz340, zzz341, Neg(Zero), zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, Succ(zzz660), h) → new_mkVBalBranch0(zzz31, zzz514, Branch(zzz340, zzz341, Neg(Zero), zzz343, zzz344), h)
new_mkVBalBranch3MkVBalBranch118(zzz498, zzz499, zzz500, zzz501, zzz502, zzz503, zzz504, zzz505, zzz506, zzz507, Succ(zzz8040), bg) → new_mkVBalBranch3MkVBalBranch120(zzz498, zzz499, zzz500, zzz501, zzz502, zzz503, zzz504, Zero, zzz505, zzz506, zzz507, Succ(Zero), Succ(zzz8040), bg)
new_mkVBalBranch3MkVBalBranch216(zzz1105, zzz1106, zzz1107, zzz1108, zzz1109, zzz1110, zzz1111, zzz1112, zzz1113, zzz1114, zzz1115, Succ(zzz11160), Zero, ba) → new_mkVBalBranch3MkVBalBranch218(zzz1105, zzz1106, zzz1107, zzz1108, zzz1109, zzz1110, zzz1111, zzz1112, zzz1113, zzz1114, zzz1115, ba)
new_mkVBalBranch3MkVBalBranch215(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, Succ(zzz660), h) → new_mkVBalBranch3MkVBalBranch19(zzz340, zzz341, zzz34200, zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, new_primPlusNat2(new_primMulNat0(zzz34200), Succ(zzz34200)), h)
new_mkVBalBranch3MkVBalBranch216(zzz1105, zzz1106, zzz1107, zzz1108, zzz1109, zzz1110, zzz1111, zzz1112, zzz1113, zzz1114, zzz1115, Zero, Zero, ba) → new_mkVBalBranch3MkVBalBranch222(zzz1105, zzz1106, zzz1107, zzz1108, zzz1109, zzz1110, zzz1111, zzz1112, zzz1113, zzz1114, zzz1115, ba)
new_mkVBalBranch3MkVBalBranch18(zzz340, zzz341, zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, Zero, h) → new_mkVBalBranch3MkVBalBranch115(zzz340, zzz341, Zero, zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, Zero, Succ(zzz51200), h)
new_mkVBalBranch3MkVBalBranch119(zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, zzz1125, zzz1126, zzz1127, zzz1128, zzz1129, Succ(zzz12130), bd) → new_mkVBalBranch3MkVBalBranch120(zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, zzz1125, Succ(zzz1126), zzz1127, zzz1128, zzz1129, Succ(Succ(zzz1126)), Succ(zzz12130), bd)

The TRS R consists of the following rules:

new_primMulNat0(zzz6200) → new_primPlusNat3(Succ(new_primPlusNat3(new_primPlusNat1(zzz6200), zzz6200)), Succ(zzz6200))
new_primPlusNat2(Succ(zzz900), Succ(zzz9100)) → Succ(Succ(new_primPlusNat2(zzz900, zzz9100)))
new_primPlusNat2(Zero, Succ(zzz9100)) → Succ(zzz9100)
new_primPlusNat2(Zero, Zero) → Zero
new_primPlusNat2(Succ(zzz900), Zero) → Succ(zzz900)
new_primPlusNat1(Zero) → Zero
new_primPlusNat1(Succ(zzz62000)) → Succ(Succ(new_primPlusNat1(zzz62000)))
new_primPlusNat3(zzz90, Succ(zzz910)) → Succ(Succ(new_primPlusNat2(zzz90, zzz910)))
new_primPlusNat3(zzz90, Zero) → Succ(zzz90)

The set Q consists of the following terms:

new_primPlusNat2(Zero, Succ(x0))
new_primMulNat0(x0)
new_primPlusNat3(x0, Succ(x1))
new_primPlusNat2(Succ(x0), Succ(x1))
new_primPlusNat3(x0, Zero)
new_primPlusNat1(Zero)
new_primPlusNat2(Zero, Zero)
new_primPlusNat1(Succ(x0))
new_primPlusNat2(Succ(x0), Zero)

We have to consider all minimal (P,Q,R)-chains.
By rewriting [15] the rule new_mkVBalBranch3MkVBalBranch215(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, Succ(zzz660), h) → new_mkVBalBranch3MkVBalBranch19(zzz340, zzz341, zzz34200, zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, new_primPlusNat2(new_primMulNat0(zzz34200), Succ(zzz34200)), h) at position [11,0] we obtained the following new rules:

new_mkVBalBranch3MkVBalBranch215(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, Succ(zzz660), h) → new_mkVBalBranch3MkVBalBranch19(zzz340, zzz341, zzz34200, zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, new_primPlusNat2(new_primPlusNat3(Succ(new_primPlusNat3(new_primPlusNat1(zzz34200), zzz34200)), Succ(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
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                    ↳ DependencyGraphProof
                                      ↳ QDP
                                        ↳ Rewriting
                                          ↳ QDP
                                            ↳ Rewriting
                                              ↳ QDP
                                                ↳ Rewriting
                                                  ↳ QDP
                                                    ↳ Rewriting
                                                      ↳ QDP
                                                        ↳ Rewriting
                                                          ↳ QDP
                                                            ↳ Rewriting
                                                              ↳ QDP
                                                                ↳ Rewriting
                                                                  ↳ QDP
                                                                    ↳ Rewriting
                                                                      ↳ QDP
                                                                        ↳ Rewriting
                                                                          ↳ QDP
                                                                            ↳ Rewriting
                                                                              ↳ QDP
                                                                                ↳ Rewriting
                                                                                  ↳ QDP
                                                                                    ↳ Rewriting
                                                                                      ↳ QDP
                                                                                        ↳ Rewriting
                                                                                          ↳ QDP
                                                                                            ↳ Rewriting
                                                                                              ↳ QDP
                                                                                                ↳ Rewriting
                                                                                                  ↳ QDP
                                                                                                    ↳ Rewriting
                                                                                                      ↳ QDP
                                                                                                        ↳ Rewriting
                                                                                                          ↳ QDP
                                                                                                            ↳ UsableRulesProof
                                                                                                              ↳ QDP
                                                                                                                ↳ QReductionProof
                                                                                                                  ↳ QDP
                                                                                                                    ↳ Rewriting
                                                                                                                      ↳ QDP
                                                                                                                        ↳ Rewriting
                                                                                                                          ↳ QDP
                                                                                                                            ↳ DependencyGraphProof
                                                                                                                              ↳ QDP
                                                                                                                                ↳ Rewriting
                                                                                                                                  ↳ QDP
                                                                                                                                    ↳ Rewriting
                                                                                                                                      ↳ QDP
                                                                                                                                        ↳ DependencyGraphProof
                                                                                                                                          ↳ QDP
                                                                                                                                            ↳ Rewriting
                                                                                                                                              ↳ QDP
                                                                                                                                                ↳ Rewriting
                                                                                                                                                  ↳ QDP
                                                                                                                                                    ↳ Rewriting
                                                                                                                                                      ↳ QDP
                                                                                                                                                        ↳ Rewriting
                                                                                                                                                          ↳ QDP
                                                                                                                                                            ↳ Rewriting
                                                                                                                                                              ↳ QDP
                                                                                                                                                                ↳ Rewriting
                                                                                                                                                                  ↳ QDP
                                                                                                                                                                    ↳ Rewriting
                                                                                                                                                                      ↳ QDP
                                                                                                                                                                        ↳ Rewriting
                                                                                                                                                                          ↳ QDP
                                                                                                                                                                            ↳ Rewriting
                                                                                                                                                                              ↳ QDP
                                                                                                                                                                                ↳ Rewriting
                                                                                                                                                                                  ↳ QDP
                                                                                                                                                                                    ↳ Rewriting
                                                                                                                                                                                      ↳ QDP
                                                                                                                                                                                        ↳ Rewriting
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP

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

new_mkVBalBranch3MkVBalBranch225(zzz498, zzz499, zzz500, zzz501, zzz502, zzz503, zzz504, zzz505, zzz506, zzz507, Zero, Zero, bg) → new_mkVBalBranch3MkVBalBranch230(zzz498, zzz499, zzz500, zzz501, zzz502, zzz503, zzz504, zzz505, zzz506, zzz507, bg)
new_mkVBalBranch3MkVBalBranch18(zzz340, zzz341, zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, Succ(zzz1480), h) → new_mkVBalBranch3MkVBalBranch115(zzz340, zzz341, Zero, zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, Succ(zzz1480), Succ(zzz51200), h)
new_mkVBalBranch3MkVBalBranch215(zzz340, zzz341, Pos(Succ(Succ(zzz342000))), zzz343, zzz344, zzz510, zzz511, Succ(zzz512000), zzz513, zzz514, zzz31, Succ(Succ(zzz6600)), h) → new_mkVBalBranch3MkVBalBranch216(zzz340, zzz341, Succ(zzz342000), zzz343, zzz344, zzz510, zzz511, zzz512000, zzz513, zzz514, zzz31, Succ(Succ(new_primPlusNat2(zzz6600, zzz512000))), zzz342000, h)
new_mkVBalBranch0(zzz31, Branch(zzz510, zzz511, Neg(Zero), zzz513, zzz514), Branch(zzz340, zzz341, Pos(Succ(zzz34200)), zzz343, zzz344), h) → new_mkVBalBranch0(zzz31, Branch(zzz510, zzz511, Neg(Zero), zzz513, zzz514), zzz343, h)
new_mkVBalBranch3MkVBalBranch223(zzz340, zzz341, Neg(Succ(Succ(Succ(zzz3420000)))), zzz343, zzz344, zzz510, zzz511, Zero, zzz513, zzz514, zzz31, Succ(Succ(zzz6700)), h) → new_mkVBalBranch3MkVBalBranch225(zzz340, zzz341, Succ(Succ(zzz3420000)), zzz343, zzz344, zzz510, zzz511, zzz513, zzz514, zzz31, Succ(zzz3420000), Succ(zzz6700), h)
new_mkVBalBranch3MkVBalBranch120(zzz2050, zzz2051, zzz2052, zzz2053, zzz2054, zzz2055, zzz2056, zzz2057, zzz2058, zzz2059, zzz2060, Zero, Succ(zzz20620), be) → new_mkVBalBranch0(zzz2060, zzz2059, Branch(zzz2050, zzz2051, Neg(Succ(zzz2052)), zzz2053, zzz2054), be)
new_mkVBalBranch3MkVBalBranch121(zzz473, zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, zzz481, zzz482, Succ(zzz7390), bh) → new_mkVBalBranch3MkVBalBranch115(zzz473, zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, Zero, zzz480, zzz481, zzz482, Succ(zzz7390), Succ(Zero), bh)
new_mkVBalBranch0(zzz31, Branch(zzz510, zzz511, Pos(Zero), zzz513, zzz514), Branch(zzz340, zzz341, Pos(Succ(zzz34200)), zzz343, zzz344), h) → new_mkVBalBranch0(zzz31, Branch(zzz510, zzz511, Pos(Zero), zzz513, zzz514), zzz343, h)
new_mkVBalBranch0(zzz31, Branch(zzz510, zzz511, Pos(Succ(zzz51200)), zzz513, zzz514), Branch(zzz340, zzz341, zzz342, zzz343, zzz344), h) → new_mkVBalBranch3MkVBalBranch215(zzz340, zzz341, zzz342, zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat3(new_primPlusNat1(zzz51200), zzz51200)), zzz51200))), h)
new_mkVBalBranch3MkVBalBranch223(zzz340, zzz341, Neg(Succ(Succ(Zero))), zzz343, zzz344, zzz510, zzz511, Succ(zzz512000), zzz513, zzz514, zzz31, Succ(Succ(zzz6700)), h) → new_mkVBalBranch3MkVBalBranch224(zzz340, zzz341, Succ(Zero), zzz343, zzz344, zzz510, zzz511, zzz512000, zzz513, zzz514, zzz31, Zero, Succ(Succ(new_primPlusNat2(zzz6700, zzz512000))), h)
new_mkVBalBranch3MkVBalBranch224(zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, zzz1125, zzz1126, zzz1127, zzz1128, zzz1129, Succ(zzz11300), Succ(zzz11310), bd) → new_mkVBalBranch3MkVBalBranch224(zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, zzz1125, zzz1126, zzz1127, zzz1128, zzz1129, zzz11300, zzz11310, bd)
new_mkVBalBranch3MkVBalBranch224(zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, zzz1125, zzz1126, zzz1127, zzz1128, zzz1129, Succ(zzz11300), Zero, bd) → new_mkVBalBranch3MkVBalBranch119(zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, zzz1125, zzz1126, zzz1127, zzz1128, zzz1129, new_primPlusNat2(new_primPlusNat3(Succ(new_primPlusNat3(new_primPlusNat1(zzz1121), zzz1121)), Succ(zzz1121)), Succ(zzz1121)), bd)
new_mkVBalBranch3MkVBalBranch217(zzz473, zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, zzz481, zzz482, Zero, Succ(zzz4840), bh) → new_mkVBalBranch0(zzz482, Branch(zzz478, zzz479, Pos(Succ(Zero)), zzz480, zzz481), zzz476, bh)
new_mkVBalBranch3MkVBalBranch218(zzz461, zzz462, zzz463, zzz464, zzz465, zzz466, zzz467, zzz468, zzz469, zzz470, zzz471, bb) → new_mkVBalBranch3MkVBalBranch110(zzz461, zzz462, zzz463, zzz464, zzz465, zzz466, zzz467, zzz468, zzz469, zzz470, zzz471, new_primPlusNat2(new_primPlusNat3(Succ(new_primPlusNat3(new_primPlusNat1(zzz463), zzz463)), Succ(zzz463)), Succ(zzz463)), bb)
new_mkVBalBranch3MkVBalBranch233(zzz473, zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, zzz481, zzz482, bh) → new_mkVBalBranch3MkVBalBranch121(zzz473, zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, zzz481, zzz482, new_primPlusNat2(new_primPlusNat3(Succ(new_primPlusNat3(new_primPlusNat1(zzz475), zzz475)), Succ(zzz475)), Succ(zzz475)), bh)
new_mkVBalBranch3MkVBalBranch110(zzz461, zzz462, zzz463, zzz464, zzz465, zzz466, zzz467, zzz468, zzz469, zzz470, zzz471, Succ(zzz5800), bb) → new_mkVBalBranch3MkVBalBranch115(zzz461, zzz462, zzz463, zzz464, zzz465, zzz466, zzz467, Succ(zzz468), zzz469, zzz470, zzz471, Succ(zzz5800), Succ(Succ(zzz468)), bb)
new_mkVBalBranch3MkVBalBranch227(zzz486, zzz487, zzz488, zzz489, zzz490, zzz491, zzz492, zzz493, zzz494, zzz495, zzz496, bf) → new_mkVBalBranch0(zzz496, Branch(zzz491, zzz492, Neg(Succ(Succ(zzz493))), zzz494, zzz495), zzz489, bf)
new_mkVBalBranch3MkVBalBranch215(zzz340, zzz341, Pos(Zero), zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, Succ(zzz660), h) → new_mkVBalBranch0(zzz31, zzz514, Branch(zzz340, zzz341, Pos(Zero), zzz343, zzz344), h)
new_mkVBalBranch3MkVBalBranch223(zzz340, zzz341, Neg(Zero), zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, Succ(zzz670), h) → new_mkVBalBranch0(zzz31, Branch(zzz510, zzz511, Neg(Succ(zzz51200)), zzz513, zzz514), zzz343, h)
new_mkVBalBranch3MkVBalBranch216(zzz1105, zzz1106, zzz1107, zzz1108, zzz1109, zzz1110, zzz1111, zzz1112, zzz1113, zzz1114, zzz1115, Zero, Succ(zzz11170), ba) → new_mkVBalBranch0(zzz1115, Branch(zzz1110, zzz1111, Pos(Succ(Succ(zzz1112))), zzz1113, zzz1114), zzz1108, ba)
new_mkVBalBranch3MkVBalBranch115(zzz1986, zzz1987, zzz1988, zzz1989, zzz1990, zzz1991, zzz1992, zzz1993, zzz1994, zzz1995, zzz1996, Zero, Succ(zzz19980), bc) → new_mkVBalBranch0(zzz1996, zzz1995, Branch(zzz1986, zzz1987, Pos(Succ(zzz1988)), zzz1989, zzz1990), bc)
new_mkVBalBranch3MkVBalBranch215(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, Succ(zzz660), h) → new_mkVBalBranch3MkVBalBranch19(zzz340, zzz341, zzz34200, zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, new_primPlusNat2(new_primPlusNat3(Succ(new_primPlusNat3(new_primPlusNat1(zzz34200), zzz34200)), Succ(zzz34200)), Succ(zzz34200)), h)
new_mkVBalBranch3MkVBalBranch122(zzz340, zzz341, zzz34200, zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, h) → new_mkVBalBranch0(zzz31, zzz514, Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), h)
new_mkVBalBranch3MkVBalBranch230(zzz498, zzz499, zzz500, zzz501, zzz502, zzz503, zzz504, zzz505, zzz506, zzz507, bg) → new_mkVBalBranch3MkVBalBranch118(zzz498, zzz499, zzz500, zzz501, zzz502, zzz503, zzz504, zzz505, zzz506, zzz507, new_primPlusNat2(Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat3(new_primPlusNat1(zzz500), zzz500)), zzz500))), Succ(zzz500)), bg)
new_mkVBalBranch3MkVBalBranch217(zzz473, zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, zzz481, zzz482, Succ(zzz4830), Succ(zzz4840), bh) → new_mkVBalBranch3MkVBalBranch217(zzz473, zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, zzz481, zzz482, zzz4830, zzz4840, bh)
new_mkVBalBranch3MkVBalBranch116(zzz340, zzz341, zzz34200, zzz343, zzz344, zzz510, zzz511, zzz513, zzz514, zzz31, Succ(zzz1200), h) → new_mkVBalBranch0(zzz31, zzz514, Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), h)
new_mkVBalBranch3MkVBalBranch110(zzz461, zzz462, zzz463, zzz464, zzz465, zzz466, zzz467, zzz468, zzz469, zzz470, zzz471, Zero, bb) → new_mkVBalBranch3MkVBalBranch115(zzz461, zzz462, zzz463, zzz464, zzz465, zzz466, zzz467, Succ(zzz468), zzz469, zzz470, zzz471, Zero, Succ(Succ(zzz468)), bb)
new_mkVBalBranch3MkVBalBranch225(zzz498, zzz499, zzz500, zzz501, zzz502, zzz503, zzz504, zzz505, zzz506, zzz507, Zero, Succ(zzz5090), bg) → new_mkVBalBranch0(zzz507, Branch(zzz503, zzz504, Neg(Succ(Zero)), zzz505, zzz506), zzz501, bg)
new_mkVBalBranch0(zzz31, Branch(zzz510, zzz511, Neg(Succ(zzz51200)), zzz513, zzz514), Branch(zzz340, zzz341, zzz342, zzz343, zzz344), h) → new_mkVBalBranch3MkVBalBranch223(zzz340, zzz341, zzz342, zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat3(new_primPlusNat1(zzz51200), zzz51200)), zzz51200))), h)
new_mkVBalBranch0(zzz31, Branch(zzz510, zzz511, Neg(Zero), zzz513, zzz514), Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), h) → new_mkVBalBranch3MkVBalBranch117(zzz340, zzz341, zzz34200, zzz343, zzz344, zzz510, zzz511, zzz513, zzz514, zzz31, new_primPlusNat2(new_primPlusNat3(Succ(new_primPlusNat3(new_primPlusNat1(zzz34200), zzz34200)), Succ(zzz34200)), Succ(zzz34200)), h)
new_mkVBalBranch3MkVBalBranch217(zzz473, zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, zzz481, zzz482, Succ(zzz4830), Zero, bh) → new_mkVBalBranch3MkVBalBranch121(zzz473, zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, zzz481, zzz482, new_primPlusNat2(new_primPlusNat3(Succ(new_primPlusNat3(new_primPlusNat1(zzz475), zzz475)), Succ(zzz475)), Succ(zzz475)), bh)
new_mkVBalBranch3MkVBalBranch121(zzz473, zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, zzz481, zzz482, Zero, bh) → new_mkVBalBranch3MkVBalBranch115(zzz473, zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, Zero, zzz480, zzz481, zzz482, Zero, Succ(Zero), bh)
new_mkVBalBranch3MkVBalBranch223(zzz340, zzz341, Neg(Succ(Zero)), zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, Succ(zzz670), h) → new_mkVBalBranch0(zzz31, Branch(zzz510, zzz511, Neg(Succ(zzz51200)), zzz513, zzz514), zzz343, h)
new_mkVBalBranch3MkVBalBranch225(zzz498, zzz499, zzz500, zzz501, zzz502, zzz503, zzz504, zzz505, zzz506, zzz507, Succ(zzz5080), Zero, bg) → new_mkVBalBranch3MkVBalBranch118(zzz498, zzz499, zzz500, zzz501, zzz502, zzz503, zzz504, zzz505, zzz506, zzz507, new_primPlusNat2(new_primPlusNat3(Succ(new_primPlusNat3(new_primPlusNat1(zzz500), zzz500)), Succ(zzz500)), Succ(zzz500)), bg)
new_mkVBalBranch3MkVBalBranch229(zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, zzz1125, zzz1126, zzz1127, zzz1128, zzz1129, bd) → new_mkVBalBranch3MkVBalBranch119(zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, zzz1125, zzz1126, zzz1127, zzz1128, zzz1129, new_primPlusNat2(new_primPlusNat3(Succ(new_primPlusNat3(new_primPlusNat1(zzz1121), zzz1121)), Succ(zzz1121)), Succ(zzz1121)), bd)
new_mkVBalBranch3MkVBalBranch215(zzz340, zzz341, Pos(Succ(Zero)), zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, Succ(zzz660), h) → new_mkVBalBranch3MkVBalBranch18(zzz340, zzz341, zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, new_primPlusNat2(new_primMulNat0(Zero), Succ(Zero)), h)
new_mkVBalBranch0(zzz31, Branch(zzz510, zzz511, Pos(Zero), zzz513, zzz514), Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), h) → new_mkVBalBranch3MkVBalBranch116(zzz340, zzz341, zzz34200, zzz343, zzz344, zzz510, zzz511, zzz513, zzz514, zzz31, new_primPlusNat2(new_primPlusNat3(Succ(new_primPlusNat3(new_primPlusNat1(zzz34200), zzz34200)), Succ(zzz34200)), Succ(zzz34200)), h)
new_mkVBalBranch3MkVBalBranch222(zzz461, zzz462, zzz463, zzz464, zzz465, zzz466, zzz467, zzz468, zzz469, zzz470, zzz471, bb) → new_mkVBalBranch3MkVBalBranch110(zzz461, zzz462, zzz463, zzz464, zzz465, zzz466, zzz467, zzz468, zzz469, zzz470, zzz471, new_primPlusNat2(Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat3(new_primPlusNat1(zzz463), zzz463)), zzz463))), Succ(zzz463)), bb)
new_mkVBalBranch3MkVBalBranch215(zzz340, zzz341, Pos(Succ(Succ(zzz342000))), zzz343, zzz344, zzz510, zzz511, Zero, zzz513, zzz514, zzz31, Succ(Succ(zzz6600)), h) → new_mkVBalBranch3MkVBalBranch217(zzz340, zzz341, Succ(zzz342000), zzz343, zzz344, zzz510, zzz511, zzz513, zzz514, zzz31, Succ(zzz6600), zzz342000, h)
new_mkVBalBranch3MkVBalBranch117(zzz340, zzz341, zzz34200, zzz343, zzz344, zzz510, zzz511, zzz513, zzz514, zzz31, Succ(zzz1240), h) → new_mkVBalBranch0(zzz31, zzz514, Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), h)
new_mkVBalBranch3MkVBalBranch217(zzz473, zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, zzz481, zzz482, Zero, Zero, bh) → new_mkVBalBranch3MkVBalBranch233(zzz473, zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, zzz481, zzz482, bh)
new_mkVBalBranch3MkVBalBranch120(zzz2050, zzz2051, zzz2052, zzz2053, zzz2054, zzz2055, zzz2056, zzz2057, zzz2058, zzz2059, zzz2060, Succ(zzz20610), Succ(zzz20620), be) → new_mkVBalBranch3MkVBalBranch120(zzz2050, zzz2051, zzz2052, zzz2053, zzz2054, zzz2055, zzz2056, zzz2057, zzz2058, zzz2059, zzz2060, zzz20610, zzz20620, be)
new_mkVBalBranch3MkVBalBranch223(zzz340, zzz341, Pos(zzz3420), zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, Succ(zzz670), h) → new_mkVBalBranch0(zzz31, Branch(zzz510, zzz511, Neg(Succ(zzz51200)), zzz513, zzz514), zzz343, h)
new_mkVBalBranch3MkVBalBranch216(zzz1105, zzz1106, zzz1107, zzz1108, zzz1109, zzz1110, zzz1111, zzz1112, zzz1113, zzz1114, zzz1115, Succ(zzz11160), Succ(zzz11170), ba) → new_mkVBalBranch3MkVBalBranch216(zzz1105, zzz1106, zzz1107, zzz1108, zzz1109, zzz1110, zzz1111, zzz1112, zzz1113, zzz1114, zzz1115, zzz11160, zzz11170, ba)
new_mkVBalBranch3MkVBalBranch19(zzz340, zzz341, zzz34200, zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, Zero, h) → new_mkVBalBranch3MkVBalBranch122(zzz340, zzz341, zzz34200, zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, h)
new_mkVBalBranch3MkVBalBranch225(zzz498, zzz499, zzz500, zzz501, zzz502, zzz503, zzz504, zzz505, zzz506, zzz507, Succ(zzz5080), Succ(zzz5090), bg) → new_mkVBalBranch3MkVBalBranch225(zzz498, zzz499, zzz500, zzz501, zzz502, zzz503, zzz504, zzz505, zzz506, zzz507, zzz5080, zzz5090, bg)
new_mkVBalBranch3MkVBalBranch19(zzz340, zzz341, zzz34200, zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, Succ(zzz1410), h) → new_mkVBalBranch0(zzz31, zzz514, Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), h)
new_mkVBalBranch3MkVBalBranch224(zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, zzz1125, zzz1126, zzz1127, zzz1128, zzz1129, Zero, Zero, bd) → new_mkVBalBranch3MkVBalBranch229(zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, zzz1125, zzz1126, zzz1127, zzz1128, zzz1129, bd)
new_mkVBalBranch3MkVBalBranch224(zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, zzz1125, zzz1126, zzz1127, zzz1128, zzz1129, Zero, Succ(zzz11310), bd) → new_mkVBalBranch3MkVBalBranch227(zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, zzz1125, zzz1126, zzz1127, zzz1128, zzz1129, bd)
new_mkVBalBranch3MkVBalBranch223(zzz340, zzz341, Neg(Succ(Succ(Zero))), zzz343, zzz344, zzz510, zzz511, Zero, zzz513, zzz514, zzz31, Succ(Succ(zzz6700)), h) → new_mkVBalBranch3MkVBalBranch225(zzz340, zzz341, Succ(Zero), zzz343, zzz344, zzz510, zzz511, zzz513, zzz514, zzz31, Zero, Succ(zzz6700), h)
new_mkVBalBranch3MkVBalBranch223(zzz340, zzz341, Neg(Succ(Succ(Succ(zzz3420000)))), zzz343, zzz344, zzz510, zzz511, Succ(zzz512000), zzz513, zzz514, zzz31, Succ(Succ(zzz6700)), h) → new_mkVBalBranch3MkVBalBranch224(zzz340, zzz341, Succ(Succ(zzz3420000)), zzz343, zzz344, zzz510, zzz511, zzz512000, zzz513, zzz514, zzz31, Succ(zzz3420000), Succ(Succ(new_primPlusNat2(zzz6700, zzz512000))), h)
new_mkVBalBranch3MkVBalBranch115(zzz1986, zzz1987, zzz1988, zzz1989, zzz1990, zzz1991, zzz1992, zzz1993, zzz1994, zzz1995, zzz1996, Succ(zzz19970), Succ(zzz19980), bc) → new_mkVBalBranch3MkVBalBranch115(zzz1986, zzz1987, zzz1988, zzz1989, zzz1990, zzz1991, zzz1992, zzz1993, zzz1994, zzz1995, zzz1996, zzz19970, zzz19980, bc)
new_mkVBalBranch3MkVBalBranch215(zzz340, zzz341, Neg(Zero), zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, Succ(zzz660), h) → new_mkVBalBranch0(zzz31, zzz514, Branch(zzz340, zzz341, Neg(Zero), zzz343, zzz344), h)
new_mkVBalBranch3MkVBalBranch118(zzz498, zzz499, zzz500, zzz501, zzz502, zzz503, zzz504, zzz505, zzz506, zzz507, Succ(zzz8040), bg) → new_mkVBalBranch3MkVBalBranch120(zzz498, zzz499, zzz500, zzz501, zzz502, zzz503, zzz504, Zero, zzz505, zzz506, zzz507, Succ(Zero), Succ(zzz8040), bg)
new_mkVBalBranch3MkVBalBranch216(zzz1105, zzz1106, zzz1107, zzz1108, zzz1109, zzz1110, zzz1111, zzz1112, zzz1113, zzz1114, zzz1115, Succ(zzz11160), Zero, ba) → new_mkVBalBranch3MkVBalBranch218(zzz1105, zzz1106, zzz1107, zzz1108, zzz1109, zzz1110, zzz1111, zzz1112, zzz1113, zzz1114, zzz1115, ba)
new_mkVBalBranch3MkVBalBranch216(zzz1105, zzz1106, zzz1107, zzz1108, zzz1109, zzz1110, zzz1111, zzz1112, zzz1113, zzz1114, zzz1115, Zero, Zero, ba) → new_mkVBalBranch3MkVBalBranch222(zzz1105, zzz1106, zzz1107, zzz1108, zzz1109, zzz1110, zzz1111, zzz1112, zzz1113, zzz1114, zzz1115, ba)
new_mkVBalBranch3MkVBalBranch119(zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, zzz1125, zzz1126, zzz1127, zzz1128, zzz1129, Succ(zzz12130), bd) → new_mkVBalBranch3MkVBalBranch120(zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, zzz1125, Succ(zzz1126), zzz1127, zzz1128, zzz1129, Succ(Succ(zzz1126)), Succ(zzz12130), bd)
new_mkVBalBranch3MkVBalBranch18(zzz340, zzz341, zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, Zero, h) → new_mkVBalBranch3MkVBalBranch115(zzz340, zzz341, Zero, zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, Zero, Succ(zzz51200), h)

The TRS R consists of the following rules:

new_primMulNat0(zzz6200) → new_primPlusNat3(Succ(new_primPlusNat3(new_primPlusNat1(zzz6200), zzz6200)), Succ(zzz6200))
new_primPlusNat2(Succ(zzz900), Succ(zzz9100)) → Succ(Succ(new_primPlusNat2(zzz900, zzz9100)))
new_primPlusNat2(Zero, Succ(zzz9100)) → Succ(zzz9100)
new_primPlusNat2(Zero, Zero) → Zero
new_primPlusNat2(Succ(zzz900), Zero) → Succ(zzz900)
new_primPlusNat1(Zero) → Zero
new_primPlusNat1(Succ(zzz62000)) → Succ(Succ(new_primPlusNat1(zzz62000)))
new_primPlusNat3(zzz90, Succ(zzz910)) → Succ(Succ(new_primPlusNat2(zzz90, zzz910)))
new_primPlusNat3(zzz90, Zero) → Succ(zzz90)

The set Q consists of the following terms:

new_primPlusNat2(Zero, Succ(x0))
new_primMulNat0(x0)
new_primPlusNat3(x0, Succ(x1))
new_primPlusNat2(Succ(x0), Succ(x1))
new_primPlusNat3(x0, Zero)
new_primPlusNat1(Zero)
new_primPlusNat2(Zero, Zero)
new_primPlusNat1(Succ(x0))
new_primPlusNat2(Succ(x0), Zero)

We have to consider all minimal (P,Q,R)-chains.
By rewriting [15] the rule new_mkVBalBranch3MkVBalBranch215(zzz340, zzz341, Pos(Succ(Zero)), zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, Succ(zzz660), h) → new_mkVBalBranch3MkVBalBranch18(zzz340, zzz341, zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, new_primPlusNat2(new_primMulNat0(Zero), Succ(Zero)), h) at position [10,0] we obtained the following new rules:

new_mkVBalBranch3MkVBalBranch215(zzz340, zzz341, Pos(Succ(Zero)), zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, Succ(zzz660), h) → new_mkVBalBranch3MkVBalBranch18(zzz340, zzz341, zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, new_primPlusNat2(new_primPlusNat3(Succ(new_primPlusNat3(new_primPlusNat1(Zero), Zero)), Succ(Zero)), Succ(Zero)), 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
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                    ↳ DependencyGraphProof
                                      ↳ QDP
                                        ↳ Rewriting
                                          ↳ QDP
                                            ↳ Rewriting
                                              ↳ QDP
                                                ↳ Rewriting
                                                  ↳ QDP
                                                    ↳ Rewriting
                                                      ↳ QDP
                                                        ↳ Rewriting
                                                          ↳ QDP
                                                            ↳ Rewriting
                                                              ↳ QDP
                                                                ↳ Rewriting
                                                                  ↳ QDP
                                                                    ↳ Rewriting
                                                                      ↳ QDP
                                                                        ↳ Rewriting
                                                                          ↳ QDP
                                                                            ↳ Rewriting
                                                                              ↳ QDP
                                                                                ↳ Rewriting
                                                                                  ↳ QDP
                                                                                    ↳ Rewriting
                                                                                      ↳ QDP
                                                                                        ↳ Rewriting
                                                                                          ↳ QDP
                                                                                            ↳ Rewriting
                                                                                              ↳ QDP
                                                                                                ↳ Rewriting
                                                                                                  ↳ QDP
                                                                                                    ↳ Rewriting
                                                                                                      ↳ QDP
                                                                                                        ↳ Rewriting
                                                                                                          ↳ QDP
                                                                                                            ↳ UsableRulesProof
                                                                                                              ↳ QDP
                                                                                                                ↳ QReductionProof
                                                                                                                  ↳ QDP
                                                                                                                    ↳ Rewriting
                                                                                                                      ↳ QDP
                                                                                                                        ↳ Rewriting
                                                                                                                          ↳ QDP
                                                                                                                            ↳ DependencyGraphProof
                                                                                                                              ↳ QDP
                                                                                                                                ↳ Rewriting
                                                                                                                                  ↳ QDP
                                                                                                                                    ↳ Rewriting
                                                                                                                                      ↳ QDP
                                                                                                                                        ↳ DependencyGraphProof
                                                                                                                                          ↳ QDP
                                                                                                                                            ↳ Rewriting
                                                                                                                                              ↳ QDP
                                                                                                                                                ↳ Rewriting
                                                                                                                                                  ↳ QDP
                                                                                                                                                    ↳ Rewriting
                                                                                                                                                      ↳ QDP
                                                                                                                                                        ↳ Rewriting
                                                                                                                                                          ↳ QDP
                                                                                                                                                            ↳ Rewriting
                                                                                                                                                              ↳ QDP
                                                                                                                                                                ↳ Rewriting
                                                                                                                                                                  ↳ QDP
                                                                                                                                                                    ↳ Rewriting
                                                                                                                                                                      ↳ QDP
                                                                                                                                                                        ↳ Rewriting
                                                                                                                                                                          ↳ QDP
                                                                                                                                                                            ↳ Rewriting
                                                                                                                                                                              ↳ QDP
                                                                                                                                                                                ↳ Rewriting
                                                                                                                                                                                  ↳ QDP
                                                                                                                                                                                    ↳ Rewriting
                                                                                                                                                                                      ↳ QDP
                                                                                                                                                                                        ↳ Rewriting
                                                                                                                                                                                          ↳ QDP
                                                                                                                                                                                            ↳ UsableRulesProof
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP

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

new_mkVBalBranch3MkVBalBranch225(zzz498, zzz499, zzz500, zzz501, zzz502, zzz503, zzz504, zzz505, zzz506, zzz507, Zero, Zero, bg) → new_mkVBalBranch3MkVBalBranch230(zzz498, zzz499, zzz500, zzz501, zzz502, zzz503, zzz504, zzz505, zzz506, zzz507, bg)
new_mkVBalBranch3MkVBalBranch18(zzz340, zzz341, zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, Succ(zzz1480), h) → new_mkVBalBranch3MkVBalBranch115(zzz340, zzz341, Zero, zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, Succ(zzz1480), Succ(zzz51200), h)
new_mkVBalBranch0(zzz31, Branch(zzz510, zzz511, Neg(Zero), zzz513, zzz514), Branch(zzz340, zzz341, Pos(Succ(zzz34200)), zzz343, zzz344), h) → new_mkVBalBranch0(zzz31, Branch(zzz510, zzz511, Neg(Zero), zzz513, zzz514), zzz343, h)
new_mkVBalBranch3MkVBalBranch215(zzz340, zzz341, Pos(Succ(Succ(zzz342000))), zzz343, zzz344, zzz510, zzz511, Succ(zzz512000), zzz513, zzz514, zzz31, Succ(Succ(zzz6600)), h) → new_mkVBalBranch3MkVBalBranch216(zzz340, zzz341, Succ(zzz342000), zzz343, zzz344, zzz510, zzz511, zzz512000, zzz513, zzz514, zzz31, Succ(Succ(new_primPlusNat2(zzz6600, zzz512000))), zzz342000, h)
new_mkVBalBranch3MkVBalBranch223(zzz340, zzz341, Neg(Succ(Succ(Succ(zzz3420000)))), zzz343, zzz344, zzz510, zzz511, Zero, zzz513, zzz514, zzz31, Succ(Succ(zzz6700)), h) → new_mkVBalBranch3MkVBalBranch225(zzz340, zzz341, Succ(Succ(zzz3420000)), zzz343, zzz344, zzz510, zzz511, zzz513, zzz514, zzz31, Succ(zzz3420000), Succ(zzz6700), h)
new_mkVBalBranch3MkVBalBranch120(zzz2050, zzz2051, zzz2052, zzz2053, zzz2054, zzz2055, zzz2056, zzz2057, zzz2058, zzz2059, zzz2060, Zero, Succ(zzz20620), be) → new_mkVBalBranch0(zzz2060, zzz2059, Branch(zzz2050, zzz2051, Neg(Succ(zzz2052)), zzz2053, zzz2054), be)
new_mkVBalBranch0(zzz31, Branch(zzz510, zzz511, Pos(Zero), zzz513, zzz514), Branch(zzz340, zzz341, Pos(Succ(zzz34200)), zzz343, zzz344), h) → new_mkVBalBranch0(zzz31, Branch(zzz510, zzz511, Pos(Zero), zzz513, zzz514), zzz343, h)
new_mkVBalBranch3MkVBalBranch121(zzz473, zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, zzz481, zzz482, Succ(zzz7390), bh) → new_mkVBalBranch3MkVBalBranch115(zzz473, zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, Zero, zzz480, zzz481, zzz482, Succ(zzz7390), Succ(Zero), bh)
new_mkVBalBranch0(zzz31, Branch(zzz510, zzz511, Pos(Succ(zzz51200)), zzz513, zzz514), Branch(zzz340, zzz341, zzz342, zzz343, zzz344), h) → new_mkVBalBranch3MkVBalBranch215(zzz340, zzz341, zzz342, zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat3(new_primPlusNat1(zzz51200), zzz51200)), zzz51200))), h)
new_mkVBalBranch3MkVBalBranch223(zzz340, zzz341, Neg(Succ(Succ(Zero))), zzz343, zzz344, zzz510, zzz511, Succ(zzz512000), zzz513, zzz514, zzz31, Succ(Succ(zzz6700)), h) → new_mkVBalBranch3MkVBalBranch224(zzz340, zzz341, Succ(Zero), zzz343, zzz344, zzz510, zzz511, zzz512000, zzz513, zzz514, zzz31, Zero, Succ(Succ(new_primPlusNat2(zzz6700, zzz512000))), h)
new_mkVBalBranch3MkVBalBranch224(zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, zzz1125, zzz1126, zzz1127, zzz1128, zzz1129, Succ(zzz11300), Succ(zzz11310), bd) → new_mkVBalBranch3MkVBalBranch224(zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, zzz1125, zzz1126, zzz1127, zzz1128, zzz1129, zzz11300, zzz11310, bd)
new_mkVBalBranch3MkVBalBranch224(zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, zzz1125, zzz1126, zzz1127, zzz1128, zzz1129, Succ(zzz11300), Zero, bd) → new_mkVBalBranch3MkVBalBranch119(zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, zzz1125, zzz1126, zzz1127, zzz1128, zzz1129, new_primPlusNat2(new_primPlusNat3(Succ(new_primPlusNat3(new_primPlusNat1(zzz1121), zzz1121)), Succ(zzz1121)), Succ(zzz1121)), bd)
new_mkVBalBranch3MkVBalBranch217(zzz473, zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, zzz481, zzz482, Zero, Succ(zzz4840), bh) → new_mkVBalBranch0(zzz482, Branch(zzz478, zzz479, Pos(Succ(Zero)), zzz480, zzz481), zzz476, bh)
new_mkVBalBranch3MkVBalBranch218(zzz461, zzz462, zzz463, zzz464, zzz465, zzz466, zzz467, zzz468, zzz469, zzz470, zzz471, bb) → new_mkVBalBranch3MkVBalBranch110(zzz461, zzz462, zzz463, zzz464, zzz465, zzz466, zzz467, zzz468, zzz469, zzz470, zzz471, new_primPlusNat2(new_primPlusNat3(Succ(new_primPlusNat3(new_primPlusNat1(zzz463), zzz463)), Succ(zzz463)), Succ(zzz463)), bb)
new_mkVBalBranch3MkVBalBranch233(zzz473, zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, zzz481, zzz482, bh) → new_mkVBalBranch3MkVBalBranch121(zzz473, zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, zzz481, zzz482, new_primPlusNat2(new_primPlusNat3(Succ(new_primPlusNat3(new_primPlusNat1(zzz475), zzz475)), Succ(zzz475)), Succ(zzz475)), bh)
new_mkVBalBranch3MkVBalBranch110(zzz461, zzz462, zzz463, zzz464, zzz465, zzz466, zzz467, zzz468, zzz469, zzz470, zzz471, Succ(zzz5800), bb) → new_mkVBalBranch3MkVBalBranch115(zzz461, zzz462, zzz463, zzz464, zzz465, zzz466, zzz467, Succ(zzz468), zzz469, zzz470, zzz471, Succ(zzz5800), Succ(Succ(zzz468)), bb)
new_mkVBalBranch3MkVBalBranch227(zzz486, zzz487, zzz488, zzz489, zzz490, zzz491, zzz492, zzz493, zzz494, zzz495, zzz496, bf) → new_mkVBalBranch0(zzz496, Branch(zzz491, zzz492, Neg(Succ(Succ(zzz493))), zzz494, zzz495), zzz489, bf)
new_mkVBalBranch3MkVBalBranch215(zzz340, zzz341, Pos(Zero), zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, Succ(zzz660), h) → new_mkVBalBranch0(zzz31, zzz514, Branch(zzz340, zzz341, Pos(Zero), zzz343, zzz344), h)
new_mkVBalBranch3MkVBalBranch223(zzz340, zzz341, Neg(Zero), zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, Succ(zzz670), h) → new_mkVBalBranch0(zzz31, Branch(zzz510, zzz511, Neg(Succ(zzz51200)), zzz513, zzz514), zzz343, h)
new_mkVBalBranch3MkVBalBranch216(zzz1105, zzz1106, zzz1107, zzz1108, zzz1109, zzz1110, zzz1111, zzz1112, zzz1113, zzz1114, zzz1115, Zero, Succ(zzz11170), ba) → new_mkVBalBranch0(zzz1115, Branch(zzz1110, zzz1111, Pos(Succ(Succ(zzz1112))), zzz1113, zzz1114), zzz1108, ba)
new_mkVBalBranch3MkVBalBranch115(zzz1986, zzz1987, zzz1988, zzz1989, zzz1990, zzz1991, zzz1992, zzz1993, zzz1994, zzz1995, zzz1996, Zero, Succ(zzz19980), bc) → new_mkVBalBranch0(zzz1996, zzz1995, Branch(zzz1986, zzz1987, Pos(Succ(zzz1988)), zzz1989, zzz1990), bc)
new_mkVBalBranch3MkVBalBranch215(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, Succ(zzz660), h) → new_mkVBalBranch3MkVBalBranch19(zzz340, zzz341, zzz34200, zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, new_primPlusNat2(new_primPlusNat3(Succ(new_primPlusNat3(new_primPlusNat1(zzz34200), zzz34200)), Succ(zzz34200)), Succ(zzz34200)), h)
new_mkVBalBranch3MkVBalBranch215(zzz340, zzz341, Pos(Succ(Zero)), zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, Succ(zzz660), h) → new_mkVBalBranch3MkVBalBranch18(zzz340, zzz341, zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, new_primPlusNat2(new_primPlusNat3(Succ(new_primPlusNat3(new_primPlusNat1(Zero), Zero)), Succ(Zero)), Succ(Zero)), h)
new_mkVBalBranch3MkVBalBranch230(zzz498, zzz499, zzz500, zzz501, zzz502, zzz503, zzz504, zzz505, zzz506, zzz507, bg) → new_mkVBalBranch3MkVBalBranch118(zzz498, zzz499, zzz500, zzz501, zzz502, zzz503, zzz504, zzz505, zzz506, zzz507, new_primPlusNat2(Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat3(new_primPlusNat1(zzz500), zzz500)), zzz500))), Succ(zzz500)), bg)
new_mkVBalBranch3MkVBalBranch122(zzz340, zzz341, zzz34200, zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, h) → new_mkVBalBranch0(zzz31, zzz514, Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), h)
new_mkVBalBranch3MkVBalBranch217(zzz473, zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, zzz481, zzz482, Succ(zzz4830), Succ(zzz4840), bh) → new_mkVBalBranch3MkVBalBranch217(zzz473, zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, zzz481, zzz482, zzz4830, zzz4840, bh)
new_mkVBalBranch3MkVBalBranch116(zzz340, zzz341, zzz34200, zzz343, zzz344, zzz510, zzz511, zzz513, zzz514, zzz31, Succ(zzz1200), h) → new_mkVBalBranch0(zzz31, zzz514, Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), h)
new_mkVBalBranch3MkVBalBranch110(zzz461, zzz462, zzz463, zzz464, zzz465, zzz466, zzz467, zzz468, zzz469, zzz470, zzz471, Zero, bb) → new_mkVBalBranch3MkVBalBranch115(zzz461, zzz462, zzz463, zzz464, zzz465, zzz466, zzz467, Succ(zzz468), zzz469, zzz470, zzz471, Zero, Succ(Succ(zzz468)), bb)
new_mkVBalBranch3MkVBalBranch225(zzz498, zzz499, zzz500, zzz501, zzz502, zzz503, zzz504, zzz505, zzz506, zzz507, Zero, Succ(zzz5090), bg) → new_mkVBalBranch0(zzz507, Branch(zzz503, zzz504, Neg(Succ(Zero)), zzz505, zzz506), zzz501, bg)
new_mkVBalBranch0(zzz31, Branch(zzz510, zzz511, Neg(Succ(zzz51200)), zzz513, zzz514), Branch(zzz340, zzz341, zzz342, zzz343, zzz344), h) → new_mkVBalBranch3MkVBalBranch223(zzz340, zzz341, zzz342, zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat3(new_primPlusNat1(zzz51200), zzz51200)), zzz51200))), h)
new_mkVBalBranch0(zzz31, Branch(zzz510, zzz511, Neg(Zero), zzz513, zzz514), Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), h) → new_mkVBalBranch3MkVBalBranch117(zzz340, zzz341, zzz34200, zzz343, zzz344, zzz510, zzz511, zzz513, zzz514, zzz31, new_primPlusNat2(new_primPlusNat3(Succ(new_primPlusNat3(new_primPlusNat1(zzz34200), zzz34200)), Succ(zzz34200)), Succ(zzz34200)), h)
new_mkVBalBranch3MkVBalBranch217(zzz473, zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, zzz481, zzz482, Succ(zzz4830), Zero, bh) → new_mkVBalBranch3MkVBalBranch121(zzz473, zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, zzz481, zzz482, new_primPlusNat2(new_primPlusNat3(Succ(new_primPlusNat3(new_primPlusNat1(zzz475), zzz475)), Succ(zzz475)), Succ(zzz475)), bh)
new_mkVBalBranch3MkVBalBranch121(zzz473, zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, zzz481, zzz482, Zero, bh) → new_mkVBalBranch3MkVBalBranch115(zzz473, zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, Zero, zzz480, zzz481, zzz482, Zero, Succ(Zero), bh)
new_mkVBalBranch3MkVBalBranch223(zzz340, zzz341, Neg(Succ(Zero)), zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, Succ(zzz670), h) → new_mkVBalBranch0(zzz31, Branch(zzz510, zzz511, Neg(Succ(zzz51200)), zzz513, zzz514), zzz343, h)
new_mkVBalBranch3MkVBalBranch229(zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, zzz1125, zzz1126, zzz1127, zzz1128, zzz1129, bd) → new_mkVBalBranch3MkVBalBranch119(zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, zzz1125, zzz1126, zzz1127, zzz1128, zzz1129, new_primPlusNat2(new_primPlusNat3(Succ(new_primPlusNat3(new_primPlusNat1(zzz1121), zzz1121)), Succ(zzz1121)), Succ(zzz1121)), bd)
new_mkVBalBranch3MkVBalBranch225(zzz498, zzz499, zzz500, zzz501, zzz502, zzz503, zzz504, zzz505, zzz506, zzz507, Succ(zzz5080), Zero, bg) → new_mkVBalBranch3MkVBalBranch118(zzz498, zzz499, zzz500, zzz501, zzz502, zzz503, zzz504, zzz505, zzz506, zzz507, new_primPlusNat2(new_primPlusNat3(Succ(new_primPlusNat3(new_primPlusNat1(zzz500), zzz500)), Succ(zzz500)), Succ(zzz500)), bg)
new_mkVBalBranch0(zzz31, Branch(zzz510, zzz511, Pos(Zero), zzz513, zzz514), Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), h) → new_mkVBalBranch3MkVBalBranch116(zzz340, zzz341, zzz34200, zzz343, zzz344, zzz510, zzz511, zzz513, zzz514, zzz31, new_primPlusNat2(new_primPlusNat3(Succ(new_primPlusNat3(new_primPlusNat1(zzz34200), zzz34200)), Succ(zzz34200)), Succ(zzz34200)), h)
new_mkVBalBranch3MkVBalBranch222(zzz461, zzz462, zzz463, zzz464, zzz465, zzz466, zzz467, zzz468, zzz469, zzz470, zzz471, bb) → new_mkVBalBranch3MkVBalBranch110(zzz461, zzz462, zzz463, zzz464, zzz465, zzz466, zzz467, zzz468, zzz469, zzz470, zzz471, new_primPlusNat2(Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat3(new_primPlusNat1(zzz463), zzz463)), zzz463))), Succ(zzz463)), bb)
new_mkVBalBranch3MkVBalBranch215(zzz340, zzz341, Pos(Succ(Succ(zzz342000))), zzz343, zzz344, zzz510, zzz511, Zero, zzz513, zzz514, zzz31, Succ(Succ(zzz6600)), h) → new_mkVBalBranch3MkVBalBranch217(zzz340, zzz341, Succ(zzz342000), zzz343, zzz344, zzz510, zzz511, zzz513, zzz514, zzz31, Succ(zzz6600), zzz342000, h)
new_mkVBalBranch3MkVBalBranch117(zzz340, zzz341, zzz34200, zzz343, zzz344, zzz510, zzz511, zzz513, zzz514, zzz31, Succ(zzz1240), h) → new_mkVBalBranch0(zzz31, zzz514, Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), h)
new_mkVBalBranch3MkVBalBranch120(zzz2050, zzz2051, zzz2052, zzz2053, zzz2054, zzz2055, zzz2056, zzz2057, zzz2058, zzz2059, zzz2060, Succ(zzz20610), Succ(zzz20620), be) → new_mkVBalBranch3MkVBalBranch120(zzz2050, zzz2051, zzz2052, zzz2053, zzz2054, zzz2055, zzz2056, zzz2057, zzz2058, zzz2059, zzz2060, zzz20610, zzz20620, be)
new_mkVBalBranch3MkVBalBranch217(zzz473, zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, zzz481, zzz482, Zero, Zero, bh) → new_mkVBalBranch3MkVBalBranch233(zzz473, zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, zzz481, zzz482, bh)
new_mkVBalBranch3MkVBalBranch216(zzz1105, zzz1106, zzz1107, zzz1108, zzz1109, zzz1110, zzz1111, zzz1112, zzz1113, zzz1114, zzz1115, Succ(zzz11160), Succ(zzz11170), ba) → new_mkVBalBranch3MkVBalBranch216(zzz1105, zzz1106, zzz1107, zzz1108, zzz1109, zzz1110, zzz1111, zzz1112, zzz1113, zzz1114, zzz1115, zzz11160, zzz11170, ba)
new_mkVBalBranch3MkVBalBranch223(zzz340, zzz341, Pos(zzz3420), zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, Succ(zzz670), h) → new_mkVBalBranch0(zzz31, Branch(zzz510, zzz511, Neg(Succ(zzz51200)), zzz513, zzz514), zzz343, h)
new_mkVBalBranch3MkVBalBranch19(zzz340, zzz341, zzz34200, zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, Zero, h) → new_mkVBalBranch3MkVBalBranch122(zzz340, zzz341, zzz34200, zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, h)
new_mkVBalBranch3MkVBalBranch225(zzz498, zzz499, zzz500, zzz501, zzz502, zzz503, zzz504, zzz505, zzz506, zzz507, Succ(zzz5080), Succ(zzz5090), bg) → new_mkVBalBranch3MkVBalBranch225(zzz498, zzz499, zzz500, zzz501, zzz502, zzz503, zzz504, zzz505, zzz506, zzz507, zzz5080, zzz5090, bg)
new_mkVBalBranch3MkVBalBranch19(zzz340, zzz341, zzz34200, zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, Succ(zzz1410), h) → new_mkVBalBranch0(zzz31, zzz514, Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), h)
new_mkVBalBranch3MkVBalBranch224(zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, zzz1125, zzz1126, zzz1127, zzz1128, zzz1129, Zero, Succ(zzz11310), bd) → new_mkVBalBranch3MkVBalBranch227(zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, zzz1125, zzz1126, zzz1127, zzz1128, zzz1129, bd)
new_mkVBalBranch3MkVBalBranch224(zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, zzz1125, zzz1126, zzz1127, zzz1128, zzz1129, Zero, Zero, bd) → new_mkVBalBranch3MkVBalBranch229(zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, zzz1125, zzz1126, zzz1127, zzz1128, zzz1129, bd)
new_mkVBalBranch3MkVBalBranch223(zzz340, zzz341, Neg(Succ(Succ(Succ(zzz3420000)))), zzz343, zzz344, zzz510, zzz511, Succ(zzz512000), zzz513, zzz514, zzz31, Succ(Succ(zzz6700)), h) → new_mkVBalBranch3MkVBalBranch224(zzz340, zzz341, Succ(Succ(zzz3420000)), zzz343, zzz344, zzz510, zzz511, zzz512000, zzz513, zzz514, zzz31, Succ(zzz3420000), Succ(Succ(new_primPlusNat2(zzz6700, zzz512000))), h)
new_mkVBalBranch3MkVBalBranch223(zzz340, zzz341, Neg(Succ(Succ(Zero))), zzz343, zzz344, zzz510, zzz511, Zero, zzz513, zzz514, zzz31, Succ(Succ(zzz6700)), h) → new_mkVBalBranch3MkVBalBranch225(zzz340, zzz341, Succ(Zero), zzz343, zzz344, zzz510, zzz511, zzz513, zzz514, zzz31, Zero, Succ(zzz6700), h)
new_mkVBalBranch3MkVBalBranch115(zzz1986, zzz1987, zzz1988, zzz1989, zzz1990, zzz1991, zzz1992, zzz1993, zzz1994, zzz1995, zzz1996, Succ(zzz19970), Succ(zzz19980), bc) → new_mkVBalBranch3MkVBalBranch115(zzz1986, zzz1987, zzz1988, zzz1989, zzz1990, zzz1991, zzz1992, zzz1993, zzz1994, zzz1995, zzz1996, zzz19970, zzz19980, bc)
new_mkVBalBranch3MkVBalBranch215(zzz340, zzz341, Neg(Zero), zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, Succ(zzz660), h) → new_mkVBalBranch0(zzz31, zzz514, Branch(zzz340, zzz341, Neg(Zero), zzz343, zzz344), h)
new_mkVBalBranch3MkVBalBranch118(zzz498, zzz499, zzz500, zzz501, zzz502, zzz503, zzz504, zzz505, zzz506, zzz507, Succ(zzz8040), bg) → new_mkVBalBranch3MkVBalBranch120(zzz498, zzz499, zzz500, zzz501, zzz502, zzz503, zzz504, Zero, zzz505, zzz506, zzz507, Succ(Zero), Succ(zzz8040), bg)
new_mkVBalBranch3MkVBalBranch216(zzz1105, zzz1106, zzz1107, zzz1108, zzz1109, zzz1110, zzz1111, zzz1112, zzz1113, zzz1114, zzz1115, Succ(zzz11160), Zero, ba) → new_mkVBalBranch3MkVBalBranch218(zzz1105, zzz1106, zzz1107, zzz1108, zzz1109, zzz1110, zzz1111, zzz1112, zzz1113, zzz1114, zzz1115, ba)
new_mkVBalBranch3MkVBalBranch216(zzz1105, zzz1106, zzz1107, zzz1108, zzz1109, zzz1110, zzz1111, zzz1112, zzz1113, zzz1114, zzz1115, Zero, Zero, ba) → new_mkVBalBranch3MkVBalBranch222(zzz1105, zzz1106, zzz1107, zzz1108, zzz1109, zzz1110, zzz1111, zzz1112, zzz1113, zzz1114, zzz1115, ba)
new_mkVBalBranch3MkVBalBranch18(zzz340, zzz341, zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, Zero, h) → new_mkVBalBranch3MkVBalBranch115(zzz340, zzz341, Zero, zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, Zero, Succ(zzz51200), h)
new_mkVBalBranch3MkVBalBranch119(zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, zzz1125, zzz1126, zzz1127, zzz1128, zzz1129, Succ(zzz12130), bd) → new_mkVBalBranch3MkVBalBranch120(zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, zzz1125, Succ(zzz1126), zzz1127, zzz1128, zzz1129, Succ(Succ(zzz1126)), Succ(zzz12130), bd)

The TRS R consists of the following rules:

new_primMulNat0(zzz6200) → new_primPlusNat3(Succ(new_primPlusNat3(new_primPlusNat1(zzz6200), zzz6200)), Succ(zzz6200))
new_primPlusNat2(Succ(zzz900), Succ(zzz9100)) → Succ(Succ(new_primPlusNat2(zzz900, zzz9100)))
new_primPlusNat2(Zero, Succ(zzz9100)) → Succ(zzz9100)
new_primPlusNat2(Zero, Zero) → Zero
new_primPlusNat2(Succ(zzz900), Zero) → Succ(zzz900)
new_primPlusNat1(Zero) → Zero
new_primPlusNat1(Succ(zzz62000)) → Succ(Succ(new_primPlusNat1(zzz62000)))
new_primPlusNat3(zzz90, Succ(zzz910)) → Succ(Succ(new_primPlusNat2(zzz90, zzz910)))
new_primPlusNat3(zzz90, Zero) → Succ(zzz90)

The set Q consists of the following terms:

new_primPlusNat2(Zero, Succ(x0))
new_primMulNat0(x0)
new_primPlusNat3(x0, Succ(x1))
new_primPlusNat2(Succ(x0), Succ(x1))
new_primPlusNat3(x0, Zero)
new_primPlusNat1(Zero)
new_primPlusNat2(Zero, Zero)
new_primPlusNat1(Succ(x0))
new_primPlusNat2(Succ(x0), Zero)

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

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

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

new_mkVBalBranch3MkVBalBranch225(zzz498, zzz499, zzz500, zzz501, zzz502, zzz503, zzz504, zzz505, zzz506, zzz507, Zero, Zero, bg) → new_mkVBalBranch3MkVBalBranch230(zzz498, zzz499, zzz500, zzz501, zzz502, zzz503, zzz504, zzz505, zzz506, zzz507, bg)
new_mkVBalBranch3MkVBalBranch18(zzz340, zzz341, zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, Succ(zzz1480), h) → new_mkVBalBranch3MkVBalBranch115(zzz340, zzz341, Zero, zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, Succ(zzz1480), Succ(zzz51200), h)
new_mkVBalBranch3MkVBalBranch215(zzz340, zzz341, Pos(Succ(Succ(zzz342000))), zzz343, zzz344, zzz510, zzz511, Succ(zzz512000), zzz513, zzz514, zzz31, Succ(Succ(zzz6600)), h) → new_mkVBalBranch3MkVBalBranch216(zzz340, zzz341, Succ(zzz342000), zzz343, zzz344, zzz510, zzz511, zzz512000, zzz513, zzz514, zzz31, Succ(Succ(new_primPlusNat2(zzz6600, zzz512000))), zzz342000, h)
new_mkVBalBranch0(zzz31, Branch(zzz510, zzz511, Neg(Zero), zzz513, zzz514), Branch(zzz340, zzz341, Pos(Succ(zzz34200)), zzz343, zzz344), h) → new_mkVBalBranch0(zzz31, Branch(zzz510, zzz511, Neg(Zero), zzz513, zzz514), zzz343, h)
new_mkVBalBranch3MkVBalBranch223(zzz340, zzz341, Neg(Succ(Succ(Succ(zzz3420000)))), zzz343, zzz344, zzz510, zzz511, Zero, zzz513, zzz514, zzz31, Succ(Succ(zzz6700)), h) → new_mkVBalBranch3MkVBalBranch225(zzz340, zzz341, Succ(Succ(zzz3420000)), zzz343, zzz344, zzz510, zzz511, zzz513, zzz514, zzz31, Succ(zzz3420000), Succ(zzz6700), h)
new_mkVBalBranch3MkVBalBranch120(zzz2050, zzz2051, zzz2052, zzz2053, zzz2054, zzz2055, zzz2056, zzz2057, zzz2058, zzz2059, zzz2060, Zero, Succ(zzz20620), be) → new_mkVBalBranch0(zzz2060, zzz2059, Branch(zzz2050, zzz2051, Neg(Succ(zzz2052)), zzz2053, zzz2054), be)
new_mkVBalBranch0(zzz31, Branch(zzz510, zzz511, Pos(Zero), zzz513, zzz514), Branch(zzz340, zzz341, Pos(Succ(zzz34200)), zzz343, zzz344), h) → new_mkVBalBranch0(zzz31, Branch(zzz510, zzz511, Pos(Zero), zzz513, zzz514), zzz343, h)
new_mkVBalBranch3MkVBalBranch121(zzz473, zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, zzz481, zzz482, Succ(zzz7390), bh) → new_mkVBalBranch3MkVBalBranch115(zzz473, zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, Zero, zzz480, zzz481, zzz482, Succ(zzz7390), Succ(Zero), bh)
new_mkVBalBranch0(zzz31, Branch(zzz510, zzz511, Pos(Succ(zzz51200)), zzz513, zzz514), Branch(zzz340, zzz341, zzz342, zzz343, zzz344), h) → new_mkVBalBranch3MkVBalBranch215(zzz340, zzz341, zzz342, zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat3(new_primPlusNat1(zzz51200), zzz51200)), zzz51200))), h)
new_mkVBalBranch3MkVBalBranch223(zzz340, zzz341, Neg(Succ(Succ(Zero))), zzz343, zzz344, zzz510, zzz511, Succ(zzz512000), zzz513, zzz514, zzz31, Succ(Succ(zzz6700)), h) → new_mkVBalBranch3MkVBalBranch224(zzz340, zzz341, Succ(Zero), zzz343, zzz344, zzz510, zzz511, zzz512000, zzz513, zzz514, zzz31, Zero, Succ(Succ(new_primPlusNat2(zzz6700, zzz512000))), h)
new_mkVBalBranch3MkVBalBranch224(zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, zzz1125, zzz1126, zzz1127, zzz1128, zzz1129, Succ(zzz11300), Succ(zzz11310), bd) → new_mkVBalBranch3MkVBalBranch224(zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, zzz1125, zzz1126, zzz1127, zzz1128, zzz1129, zzz11300, zzz11310, bd)
new_mkVBalBranch3MkVBalBranch224(zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, zzz1125, zzz1126, zzz1127, zzz1128, zzz1129, Succ(zzz11300), Zero, bd) → new_mkVBalBranch3MkVBalBranch119(zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, zzz1125, zzz1126, zzz1127, zzz1128, zzz1129, new_primPlusNat2(new_primPlusNat3(Succ(new_primPlusNat3(new_primPlusNat1(zzz1121), zzz1121)), Succ(zzz1121)), Succ(zzz1121)), bd)
new_mkVBalBranch3MkVBalBranch217(zzz473, zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, zzz481, zzz482, Zero, Succ(zzz4840), bh) → new_mkVBalBranch0(zzz482, Branch(zzz478, zzz479, Pos(Succ(Zero)), zzz480, zzz481), zzz476, bh)
new_mkVBalBranch3MkVBalBranch218(zzz461, zzz462, zzz463, zzz464, zzz465, zzz466, zzz467, zzz468, zzz469, zzz470, zzz471, bb) → new_mkVBalBranch3MkVBalBranch110(zzz461, zzz462, zzz463, zzz464, zzz465, zzz466, zzz467, zzz468, zzz469, zzz470, zzz471, new_primPlusNat2(new_primPlusNat3(Succ(new_primPlusNat3(new_primPlusNat1(zzz463), zzz463)), Succ(zzz463)), Succ(zzz463)), bb)
new_mkVBalBranch3MkVBalBranch233(zzz473, zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, zzz481, zzz482, bh) → new_mkVBalBranch3MkVBalBranch121(zzz473, zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, zzz481, zzz482, new_primPlusNat2(new_primPlusNat3(Succ(new_primPlusNat3(new_primPlusNat1(zzz475), zzz475)), Succ(zzz475)), Succ(zzz475)), bh)
new_mkVBalBranch3MkVBalBranch110(zzz461, zzz462, zzz463, zzz464, zzz465, zzz466, zzz467, zzz468, zzz469, zzz470, zzz471, Succ(zzz5800), bb) → new_mkVBalBranch3MkVBalBranch115(zzz461, zzz462, zzz463, zzz464, zzz465, zzz466, zzz467, Succ(zzz468), zzz469, zzz470, zzz471, Succ(zzz5800), Succ(Succ(zzz468)), bb)
new_mkVBalBranch3MkVBalBranch227(zzz486, zzz487, zzz488, zzz489, zzz490, zzz491, zzz492, zzz493, zzz494, zzz495, zzz496, bf) → new_mkVBalBranch0(zzz496, Branch(zzz491, zzz492, Neg(Succ(Succ(zzz493))), zzz494, zzz495), zzz489, bf)
new_mkVBalBranch3MkVBalBranch215(zzz340, zzz341, Pos(Zero), zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, Succ(zzz660), h) → new_mkVBalBranch0(zzz31, zzz514, Branch(zzz340, zzz341, Pos(Zero), zzz343, zzz344), h)
new_mkVBalBranch3MkVBalBranch223(zzz340, zzz341, Neg(Zero), zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, Succ(zzz670), h) → new_mkVBalBranch0(zzz31, Branch(zzz510, zzz511, Neg(Succ(zzz51200)), zzz513, zzz514), zzz343, h)
new_mkVBalBranch3MkVBalBranch216(zzz1105, zzz1106, zzz1107, zzz1108, zzz1109, zzz1110, zzz1111, zzz1112, zzz1113, zzz1114, zzz1115, Zero, Succ(zzz11170), ba) → new_mkVBalBranch0(zzz1115, Branch(zzz1110, zzz1111, Pos(Succ(Succ(zzz1112))), zzz1113, zzz1114), zzz1108, ba)
new_mkVBalBranch3MkVBalBranch115(zzz1986, zzz1987, zzz1988, zzz1989, zzz1990, zzz1991, zzz1992, zzz1993, zzz1994, zzz1995, zzz1996, Zero, Succ(zzz19980), bc) → new_mkVBalBranch0(zzz1996, zzz1995, Branch(zzz1986, zzz1987, Pos(Succ(zzz1988)), zzz1989, zzz1990), bc)
new_mkVBalBranch3MkVBalBranch215(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, Succ(zzz660), h) → new_mkVBalBranch3MkVBalBranch19(zzz340, zzz341, zzz34200, zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, new_primPlusNat2(new_primPlusNat3(Succ(new_primPlusNat3(new_primPlusNat1(zzz34200), zzz34200)), Succ(zzz34200)), Succ(zzz34200)), h)
new_mkVBalBranch3MkVBalBranch215(zzz340, zzz341, Pos(Succ(Zero)), zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, Succ(zzz660), h) → new_mkVBalBranch3MkVBalBranch18(zzz340, zzz341, zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, new_primPlusNat2(new_primPlusNat3(Succ(new_primPlusNat3(new_primPlusNat1(Zero), Zero)), Succ(Zero)), Succ(Zero)), h)
new_mkVBalBranch3MkVBalBranch230(zzz498, zzz499, zzz500, zzz501, zzz502, zzz503, zzz504, zzz505, zzz506, zzz507, bg) → new_mkVBalBranch3MkVBalBranch118(zzz498, zzz499, zzz500, zzz501, zzz502, zzz503, zzz504, zzz505, zzz506, zzz507, new_primPlusNat2(Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat3(new_primPlusNat1(zzz500), zzz500)), zzz500))), Succ(zzz500)), bg)
new_mkVBalBranch3MkVBalBranch122(zzz340, zzz341, zzz34200, zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, h) → new_mkVBalBranch0(zzz31, zzz514, Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), h)
new_mkVBalBranch3MkVBalBranch217(zzz473, zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, zzz481, zzz482, Succ(zzz4830), Succ(zzz4840), bh) → new_mkVBalBranch3MkVBalBranch217(zzz473, zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, zzz481, zzz482, zzz4830, zzz4840, bh)
new_mkVBalBranch3MkVBalBranch116(zzz340, zzz341, zzz34200, zzz343, zzz344, zzz510, zzz511, zzz513, zzz514, zzz31, Succ(zzz1200), h) → new_mkVBalBranch0(zzz31, zzz514, Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), h)
new_mkVBalBranch3MkVBalBranch110(zzz461, zzz462, zzz463, zzz464, zzz465, zzz466, zzz467, zzz468, zzz469, zzz470, zzz471, Zero, bb) → new_mkVBalBranch3MkVBalBranch115(zzz461, zzz462, zzz463, zzz464, zzz465, zzz466, zzz467, Succ(zzz468), zzz469, zzz470, zzz471, Zero, Succ(Succ(zzz468)), bb)
new_mkVBalBranch3MkVBalBranch225(zzz498, zzz499, zzz500, zzz501, zzz502, zzz503, zzz504, zzz505, zzz506, zzz507, Zero, Succ(zzz5090), bg) → new_mkVBalBranch0(zzz507, Branch(zzz503, zzz504, Neg(Succ(Zero)), zzz505, zzz506), zzz501, bg)
new_mkVBalBranch0(zzz31, Branch(zzz510, zzz511, Neg(Succ(zzz51200)), zzz513, zzz514), Branch(zzz340, zzz341, zzz342, zzz343, zzz344), h) → new_mkVBalBranch3MkVBalBranch223(zzz340, zzz341, zzz342, zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat3(new_primPlusNat1(zzz51200), zzz51200)), zzz51200))), h)
new_mkVBalBranch0(zzz31, Branch(zzz510, zzz511, Neg(Zero), zzz513, zzz514), Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), h) → new_mkVBalBranch3MkVBalBranch117(zzz340, zzz341, zzz34200, zzz343, zzz344, zzz510, zzz511, zzz513, zzz514, zzz31, new_primPlusNat2(new_primPlusNat3(Succ(new_primPlusNat3(new_primPlusNat1(zzz34200), zzz34200)), Succ(zzz34200)), Succ(zzz34200)), h)
new_mkVBalBranch3MkVBalBranch217(zzz473, zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, zzz481, zzz482, Succ(zzz4830), Zero, bh) → new_mkVBalBranch3MkVBalBranch121(zzz473, zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, zzz481, zzz482, new_primPlusNat2(new_primPlusNat3(Succ(new_primPlusNat3(new_primPlusNat1(zzz475), zzz475)), Succ(zzz475)), Succ(zzz475)), bh)
new_mkVBalBranch3MkVBalBranch121(zzz473, zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, zzz481, zzz482, Zero, bh) → new_mkVBalBranch3MkVBalBranch115(zzz473, zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, Zero, zzz480, zzz481, zzz482, Zero, Succ(Zero), bh)
new_mkVBalBranch3MkVBalBranch223(zzz340, zzz341, Neg(Succ(Zero)), zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, Succ(zzz670), h) → new_mkVBalBranch0(zzz31, Branch(zzz510, zzz511, Neg(Succ(zzz51200)), zzz513, zzz514), zzz343, h)
new_mkVBalBranch3MkVBalBranch229(zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, zzz1125, zzz1126, zzz1127, zzz1128, zzz1129, bd) → new_mkVBalBranch3MkVBalBranch119(zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, zzz1125, zzz1126, zzz1127, zzz1128, zzz1129, new_primPlusNat2(new_primPlusNat3(Succ(new_primPlusNat3(new_primPlusNat1(zzz1121), zzz1121)), Succ(zzz1121)), Succ(zzz1121)), bd)
new_mkVBalBranch3MkVBalBranch225(zzz498, zzz499, zzz500, zzz501, zzz502, zzz503, zzz504, zzz505, zzz506, zzz507, Succ(zzz5080), Zero, bg) → new_mkVBalBranch3MkVBalBranch118(zzz498, zzz499, zzz500, zzz501, zzz502, zzz503, zzz504, zzz505, zzz506, zzz507, new_primPlusNat2(new_primPlusNat3(Succ(new_primPlusNat3(new_primPlusNat1(zzz500), zzz500)), Succ(zzz500)), Succ(zzz500)), bg)
new_mkVBalBranch0(zzz31, Branch(zzz510, zzz511, Pos(Zero), zzz513, zzz514), Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), h) → new_mkVBalBranch3MkVBalBranch116(zzz340, zzz341, zzz34200, zzz343, zzz344, zzz510, zzz511, zzz513, zzz514, zzz31, new_primPlusNat2(new_primPlusNat3(Succ(new_primPlusNat3(new_primPlusNat1(zzz34200), zzz34200)), Succ(zzz34200)), Succ(zzz34200)), h)
new_mkVBalBranch3MkVBalBranch222(zzz461, zzz462, zzz463, zzz464, zzz465, zzz466, zzz467, zzz468, zzz469, zzz470, zzz471, bb) → new_mkVBalBranch3MkVBalBranch110(zzz461, zzz462, zzz463, zzz464, zzz465, zzz466, zzz467, zzz468, zzz469, zzz470, zzz471, new_primPlusNat2(Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat3(new_primPlusNat1(zzz463), zzz463)), zzz463))), Succ(zzz463)), bb)
new_mkVBalBranch3MkVBalBranch215(zzz340, zzz341, Pos(Succ(Succ(zzz342000))), zzz343, zzz344, zzz510, zzz511, Zero, zzz513, zzz514, zzz31, Succ(Succ(zzz6600)), h) → new_mkVBalBranch3MkVBalBranch217(zzz340, zzz341, Succ(zzz342000), zzz343, zzz344, zzz510, zzz511, zzz513, zzz514, zzz31, Succ(zzz6600), zzz342000, h)
new_mkVBalBranch3MkVBalBranch117(zzz340, zzz341, zzz34200, zzz343, zzz344, zzz510, zzz511, zzz513, zzz514, zzz31, Succ(zzz1240), h) → new_mkVBalBranch0(zzz31, zzz514, Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), h)
new_mkVBalBranch3MkVBalBranch120(zzz2050, zzz2051, zzz2052, zzz2053, zzz2054, zzz2055, zzz2056, zzz2057, zzz2058, zzz2059, zzz2060, Succ(zzz20610), Succ(zzz20620), be) → new_mkVBalBranch3MkVBalBranch120(zzz2050, zzz2051, zzz2052, zzz2053, zzz2054, zzz2055, zzz2056, zzz2057, zzz2058, zzz2059, zzz2060, zzz20610, zzz20620, be)
new_mkVBalBranch3MkVBalBranch217(zzz473, zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, zzz481, zzz482, Zero, Zero, bh) → new_mkVBalBranch3MkVBalBranch233(zzz473, zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, zzz481, zzz482, bh)
new_mkVBalBranch3MkVBalBranch216(zzz1105, zzz1106, zzz1107, zzz1108, zzz1109, zzz1110, zzz1111, zzz1112, zzz1113, zzz1114, zzz1115, Succ(zzz11160), Succ(zzz11170), ba) → new_mkVBalBranch3MkVBalBranch216(zzz1105, zzz1106, zzz1107, zzz1108, zzz1109, zzz1110, zzz1111, zzz1112, zzz1113, zzz1114, zzz1115, zzz11160, zzz11170, ba)
new_mkVBalBranch3MkVBalBranch223(zzz340, zzz341, Pos(zzz3420), zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, Succ(zzz670), h) → new_mkVBalBranch0(zzz31, Branch(zzz510, zzz511, Neg(Succ(zzz51200)), zzz513, zzz514), zzz343, h)
new_mkVBalBranch3MkVBalBranch19(zzz340, zzz341, zzz34200, zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, Zero, h) → new_mkVBalBranch3MkVBalBranch122(zzz340, zzz341, zzz34200, zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, h)
new_mkVBalBranch3MkVBalBranch225(zzz498, zzz499, zzz500, zzz501, zzz502, zzz503, zzz504, zzz505, zzz506, zzz507, Succ(zzz5080), Succ(zzz5090), bg) → new_mkVBalBranch3MkVBalBranch225(zzz498, zzz499, zzz500, zzz501, zzz502, zzz503, zzz504, zzz505, zzz506, zzz507, zzz5080, zzz5090, bg)
new_mkVBalBranch3MkVBalBranch19(zzz340, zzz341, zzz34200, zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, Succ(zzz1410), h) → new_mkVBalBranch0(zzz31, zzz514, Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), h)
new_mkVBalBranch3MkVBalBranch224(zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, zzz1125, zzz1126, zzz1127, zzz1128, zzz1129, Zero, Succ(zzz11310), bd) → new_mkVBalBranch3MkVBalBranch227(zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, zzz1125, zzz1126, zzz1127, zzz1128, zzz1129, bd)
new_mkVBalBranch3MkVBalBranch224(zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, zzz1125, zzz1126, zzz1127, zzz1128, zzz1129, Zero, Zero, bd) → new_mkVBalBranch3MkVBalBranch229(zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, zzz1125, zzz1126, zzz1127, zzz1128, zzz1129, bd)
new_mkVBalBranch3MkVBalBranch223(zzz340, zzz341, Neg(Succ(Succ(Succ(zzz3420000)))), zzz343, zzz344, zzz510, zzz511, Succ(zzz512000), zzz513, zzz514, zzz31, Succ(Succ(zzz6700)), h) → new_mkVBalBranch3MkVBalBranch224(zzz340, zzz341, Succ(Succ(zzz3420000)), zzz343, zzz344, zzz510, zzz511, zzz512000, zzz513, zzz514, zzz31, Succ(zzz3420000), Succ(Succ(new_primPlusNat2(zzz6700, zzz512000))), h)
new_mkVBalBranch3MkVBalBranch223(zzz340, zzz341, Neg(Succ(Succ(Zero))), zzz343, zzz344, zzz510, zzz511, Zero, zzz513, zzz514, zzz31, Succ(Succ(zzz6700)), h) → new_mkVBalBranch3MkVBalBranch225(zzz340, zzz341, Succ(Zero), zzz343, zzz344, zzz510, zzz511, zzz513, zzz514, zzz31, Zero, Succ(zzz6700), h)
new_mkVBalBranch3MkVBalBranch115(zzz1986, zzz1987, zzz1988, zzz1989, zzz1990, zzz1991, zzz1992, zzz1993, zzz1994, zzz1995, zzz1996, Succ(zzz19970), Succ(zzz19980), bc) → new_mkVBalBranch3MkVBalBranch115(zzz1986, zzz1987, zzz1988, zzz1989, zzz1990, zzz1991, zzz1992, zzz1993, zzz1994, zzz1995, zzz1996, zzz19970, zzz19980, bc)
new_mkVBalBranch3MkVBalBranch215(zzz340, zzz341, Neg(Zero), zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, Succ(zzz660), h) → new_mkVBalBranch0(zzz31, zzz514, Branch(zzz340, zzz341, Neg(Zero), zzz343, zzz344), h)
new_mkVBalBranch3MkVBalBranch118(zzz498, zzz499, zzz500, zzz501, zzz502, zzz503, zzz504, zzz505, zzz506, zzz507, Succ(zzz8040), bg) → new_mkVBalBranch3MkVBalBranch120(zzz498, zzz499, zzz500, zzz501, zzz502, zzz503, zzz504, Zero, zzz505, zzz506, zzz507, Succ(Zero), Succ(zzz8040), bg)
new_mkVBalBranch3MkVBalBranch216(zzz1105, zzz1106, zzz1107, zzz1108, zzz1109, zzz1110, zzz1111, zzz1112, zzz1113, zzz1114, zzz1115, Succ(zzz11160), Zero, ba) → new_mkVBalBranch3MkVBalBranch218(zzz1105, zzz1106, zzz1107, zzz1108, zzz1109, zzz1110, zzz1111, zzz1112, zzz1113, zzz1114, zzz1115, ba)
new_mkVBalBranch3MkVBalBranch216(zzz1105, zzz1106, zzz1107, zzz1108, zzz1109, zzz1110, zzz1111, zzz1112, zzz1113, zzz1114, zzz1115, Zero, Zero, ba) → new_mkVBalBranch3MkVBalBranch222(zzz1105, zzz1106, zzz1107, zzz1108, zzz1109, zzz1110, zzz1111, zzz1112, zzz1113, zzz1114, zzz1115, ba)
new_mkVBalBranch3MkVBalBranch119(zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, zzz1125, zzz1126, zzz1127, zzz1128, zzz1129, Succ(zzz12130), bd) → new_mkVBalBranch3MkVBalBranch120(zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, zzz1125, Succ(zzz1126), zzz1127, zzz1128, zzz1129, Succ(Succ(zzz1126)), Succ(zzz12130), bd)
new_mkVBalBranch3MkVBalBranch18(zzz340, zzz341, zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, Zero, h) → new_mkVBalBranch3MkVBalBranch115(zzz340, zzz341, Zero, zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, Zero, Succ(zzz51200), h)

The TRS R consists of the following rules:

new_primPlusNat1(Zero) → Zero
new_primPlusNat1(Succ(zzz62000)) → Succ(Succ(new_primPlusNat1(zzz62000)))
new_primPlusNat3(zzz90, Succ(zzz910)) → Succ(Succ(new_primPlusNat2(zzz90, zzz910)))
new_primPlusNat3(zzz90, Zero) → Succ(zzz90)
new_primPlusNat2(Succ(zzz900), Succ(zzz9100)) → Succ(Succ(new_primPlusNat2(zzz900, zzz9100)))
new_primPlusNat2(Zero, Succ(zzz9100)) → Succ(zzz9100)
new_primPlusNat2(Zero, Zero) → Zero
new_primPlusNat2(Succ(zzz900), Zero) → Succ(zzz900)

The set Q consists of the following terms:

new_primPlusNat2(Zero, Succ(x0))
new_primMulNat0(x0)
new_primPlusNat3(x0, Succ(x1))
new_primPlusNat2(Succ(x0), Succ(x1))
new_primPlusNat3(x0, Zero)
new_primPlusNat1(Zero)
new_primPlusNat2(Zero, Zero)
new_primPlusNat1(Succ(x0))
new_primPlusNat2(Succ(x0), Zero)

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

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

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

new_mkVBalBranch3MkVBalBranch225(zzz498, zzz499, zzz500, zzz501, zzz502, zzz503, zzz504, zzz505, zzz506, zzz507, Zero, Zero, bg) → new_mkVBalBranch3MkVBalBranch230(zzz498, zzz499, zzz500, zzz501, zzz502, zzz503, zzz504, zzz505, zzz506, zzz507, bg)
new_mkVBalBranch3MkVBalBranch18(zzz340, zzz341, zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, Succ(zzz1480), h) → new_mkVBalBranch3MkVBalBranch115(zzz340, zzz341, Zero, zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, Succ(zzz1480), Succ(zzz51200), h)
new_mkVBalBranch3MkVBalBranch215(zzz340, zzz341, Pos(Succ(Succ(zzz342000))), zzz343, zzz344, zzz510, zzz511, Succ(zzz512000), zzz513, zzz514, zzz31, Succ(Succ(zzz6600)), h) → new_mkVBalBranch3MkVBalBranch216(zzz340, zzz341, Succ(zzz342000), zzz343, zzz344, zzz510, zzz511, zzz512000, zzz513, zzz514, zzz31, Succ(Succ(new_primPlusNat2(zzz6600, zzz512000))), zzz342000, h)
new_mkVBalBranch0(zzz31, Branch(zzz510, zzz511, Neg(Zero), zzz513, zzz514), Branch(zzz340, zzz341, Pos(Succ(zzz34200)), zzz343, zzz344), h) → new_mkVBalBranch0(zzz31, Branch(zzz510, zzz511, Neg(Zero), zzz513, zzz514), zzz343, h)
new_mkVBalBranch3MkVBalBranch223(zzz340, zzz341, Neg(Succ(Succ(Succ(zzz3420000)))), zzz343, zzz344, zzz510, zzz511, Zero, zzz513, zzz514, zzz31, Succ(Succ(zzz6700)), h) → new_mkVBalBranch3MkVBalBranch225(zzz340, zzz341, Succ(Succ(zzz3420000)), zzz343, zzz344, zzz510, zzz511, zzz513, zzz514, zzz31, Succ(zzz3420000), Succ(zzz6700), h)
new_mkVBalBranch3MkVBalBranch120(zzz2050, zzz2051, zzz2052, zzz2053, zzz2054, zzz2055, zzz2056, zzz2057, zzz2058, zzz2059, zzz2060, Zero, Succ(zzz20620), be) → new_mkVBalBranch0(zzz2060, zzz2059, Branch(zzz2050, zzz2051, Neg(Succ(zzz2052)), zzz2053, zzz2054), be)
new_mkVBalBranch0(zzz31, Branch(zzz510, zzz511, Pos(Zero), zzz513, zzz514), Branch(zzz340, zzz341, Pos(Succ(zzz34200)), zzz343, zzz344), h) → new_mkVBalBranch0(zzz31, Branch(zzz510, zzz511, Pos(Zero), zzz513, zzz514), zzz343, h)
new_mkVBalBranch3MkVBalBranch121(zzz473, zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, zzz481, zzz482, Succ(zzz7390), bh) → new_mkVBalBranch3MkVBalBranch115(zzz473, zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, Zero, zzz480, zzz481, zzz482, Succ(zzz7390), Succ(Zero), bh)
new_mkVBalBranch0(zzz31, Branch(zzz510, zzz511, Pos(Succ(zzz51200)), zzz513, zzz514), Branch(zzz340, zzz341, zzz342, zzz343, zzz344), h) → new_mkVBalBranch3MkVBalBranch215(zzz340, zzz341, zzz342, zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat3(new_primPlusNat1(zzz51200), zzz51200)), zzz51200))), h)
new_mkVBalBranch3MkVBalBranch223(zzz340, zzz341, Neg(Succ(Succ(Zero))), zzz343, zzz344, zzz510, zzz511, Succ(zzz512000), zzz513, zzz514, zzz31, Succ(Succ(zzz6700)), h) → new_mkVBalBranch3MkVBalBranch224(zzz340, zzz341, Succ(Zero), zzz343, zzz344, zzz510, zzz511, zzz512000, zzz513, zzz514, zzz31, Zero, Succ(Succ(new_primPlusNat2(zzz6700, zzz512000))), h)
new_mkVBalBranch3MkVBalBranch224(zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, zzz1125, zzz1126, zzz1127, zzz1128, zzz1129, Succ(zzz11300), Succ(zzz11310), bd) → new_mkVBalBranch3MkVBalBranch224(zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, zzz1125, zzz1126, zzz1127, zzz1128, zzz1129, zzz11300, zzz11310, bd)
new_mkVBalBranch3MkVBalBranch224(zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, zzz1125, zzz1126, zzz1127, zzz1128, zzz1129, Succ(zzz11300), Zero, bd) → new_mkVBalBranch3MkVBalBranch119(zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, zzz1125, zzz1126, zzz1127, zzz1128, zzz1129, new_primPlusNat2(new_primPlusNat3(Succ(new_primPlusNat3(new_primPlusNat1(zzz1121), zzz1121)), Succ(zzz1121)), Succ(zzz1121)), bd)
new_mkVBalBranch3MkVBalBranch217(zzz473, zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, zzz481, zzz482, Zero, Succ(zzz4840), bh) → new_mkVBalBranch0(zzz482, Branch(zzz478, zzz479, Pos(Succ(Zero)), zzz480, zzz481), zzz476, bh)
new_mkVBalBranch3MkVBalBranch218(zzz461, zzz462, zzz463, zzz464, zzz465, zzz466, zzz467, zzz468, zzz469, zzz470, zzz471, bb) → new_mkVBalBranch3MkVBalBranch110(zzz461, zzz462, zzz463, zzz464, zzz465, zzz466, zzz467, zzz468, zzz469, zzz470, zzz471, new_primPlusNat2(new_primPlusNat3(Succ(new_primPlusNat3(new_primPlusNat1(zzz463), zzz463)), Succ(zzz463)), Succ(zzz463)), bb)
new_mkVBalBranch3MkVBalBranch233(zzz473, zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, zzz481, zzz482, bh) → new_mkVBalBranch3MkVBalBranch121(zzz473, zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, zzz481, zzz482, new_primPlusNat2(new_primPlusNat3(Succ(new_primPlusNat3(new_primPlusNat1(zzz475), zzz475)), Succ(zzz475)), Succ(zzz475)), bh)
new_mkVBalBranch3MkVBalBranch110(zzz461, zzz462, zzz463, zzz464, zzz465, zzz466, zzz467, zzz468, zzz469, zzz470, zzz471, Succ(zzz5800), bb) → new_mkVBalBranch3MkVBalBranch115(zzz461, zzz462, zzz463, zzz464, zzz465, zzz466, zzz467, Succ(zzz468), zzz469, zzz470, zzz471, Succ(zzz5800), Succ(Succ(zzz468)), bb)
new_mkVBalBranch3MkVBalBranch227(zzz486, zzz487, zzz488, zzz489, zzz490, zzz491, zzz492, zzz493, zzz494, zzz495, zzz496, bf) → new_mkVBalBranch0(zzz496, Branch(zzz491, zzz492, Neg(Succ(Succ(zzz493))), zzz494, zzz495), zzz489, bf)
new_mkVBalBranch3MkVBalBranch215(zzz340, zzz341, Pos(Zero), zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, Succ(zzz660), h) → new_mkVBalBranch0(zzz31, zzz514, Branch(zzz340, zzz341, Pos(Zero), zzz343, zzz344), h)
new_mkVBalBranch3MkVBalBranch223(zzz340, zzz341, Neg(Zero), zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, Succ(zzz670), h) → new_mkVBalBranch0(zzz31, Branch(zzz510, zzz511, Neg(Succ(zzz51200)), zzz513, zzz514), zzz343, h)
new_mkVBalBranch3MkVBalBranch216(zzz1105, zzz1106, zzz1107, zzz1108, zzz1109, zzz1110, zzz1111, zzz1112, zzz1113, zzz1114, zzz1115, Zero, Succ(zzz11170), ba) → new_mkVBalBranch0(zzz1115, Branch(zzz1110, zzz1111, Pos(Succ(Succ(zzz1112))), zzz1113, zzz1114), zzz1108, ba)
new_mkVBalBranch3MkVBalBranch115(zzz1986, zzz1987, zzz1988, zzz1989, zzz1990, zzz1991, zzz1992, zzz1993, zzz1994, zzz1995, zzz1996, Zero, Succ(zzz19980), bc) → new_mkVBalBranch0(zzz1996, zzz1995, Branch(zzz1986, zzz1987, Pos(Succ(zzz1988)), zzz1989, zzz1990), bc)
new_mkVBalBranch3MkVBalBranch215(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, Succ(zzz660), h) → new_mkVBalBranch3MkVBalBranch19(zzz340, zzz341, zzz34200, zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, new_primPlusNat2(new_primPlusNat3(Succ(new_primPlusNat3(new_primPlusNat1(zzz34200), zzz34200)), Succ(zzz34200)), Succ(zzz34200)), h)
new_mkVBalBranch3MkVBalBranch215(zzz340, zzz341, Pos(Succ(Zero)), zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, Succ(zzz660), h) → new_mkVBalBranch3MkVBalBranch18(zzz340, zzz341, zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, new_primPlusNat2(new_primPlusNat3(Succ(new_primPlusNat3(new_primPlusNat1(Zero), Zero)), Succ(Zero)), Succ(Zero)), h)
new_mkVBalBranch3MkVBalBranch122(zzz340, zzz341, zzz34200, zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, h) → new_mkVBalBranch0(zzz31, zzz514, Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), h)
new_mkVBalBranch3MkVBalBranch230(zzz498, zzz499, zzz500, zzz501, zzz502, zzz503, zzz504, zzz505, zzz506, zzz507, bg) → new_mkVBalBranch3MkVBalBranch118(zzz498, zzz499, zzz500, zzz501, zzz502, zzz503, zzz504, zzz505, zzz506, zzz507, new_primPlusNat2(Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat3(new_primPlusNat1(zzz500), zzz500)), zzz500))), Succ(zzz500)), bg)
new_mkVBalBranch3MkVBalBranch217(zzz473, zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, zzz481, zzz482, Succ(zzz4830), Succ(zzz4840), bh) → new_mkVBalBranch3MkVBalBranch217(zzz473, zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, zzz481, zzz482, zzz4830, zzz4840, bh)
new_mkVBalBranch3MkVBalBranch116(zzz340, zzz341, zzz34200, zzz343, zzz344, zzz510, zzz511, zzz513, zzz514, zzz31, Succ(zzz1200), h) → new_mkVBalBranch0(zzz31, zzz514, Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), h)
new_mkVBalBranch3MkVBalBranch110(zzz461, zzz462, zzz463, zzz464, zzz465, zzz466, zzz467, zzz468, zzz469, zzz470, zzz471, Zero, bb) → new_mkVBalBranch3MkVBalBranch115(zzz461, zzz462, zzz463, zzz464, zzz465, zzz466, zzz467, Succ(zzz468), zzz469, zzz470, zzz471, Zero, Succ(Succ(zzz468)), bb)
new_mkVBalBranch3MkVBalBranch225(zzz498, zzz499, zzz500, zzz501, zzz502, zzz503, zzz504, zzz505, zzz506, zzz507, Zero, Succ(zzz5090), bg) → new_mkVBalBranch0(zzz507, Branch(zzz503, zzz504, Neg(Succ(Zero)), zzz505, zzz506), zzz501, bg)
new_mkVBalBranch0(zzz31, Branch(zzz510, zzz511, Neg(Succ(zzz51200)), zzz513, zzz514), Branch(zzz340, zzz341, zzz342, zzz343, zzz344), h) → new_mkVBalBranch3MkVBalBranch223(zzz340, zzz341, zzz342, zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat3(new_primPlusNat1(zzz51200), zzz51200)), zzz51200))), h)
new_mkVBalBranch0(zzz31, Branch(zzz510, zzz511, Neg(Zero), zzz513, zzz514), Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), h) → new_mkVBalBranch3MkVBalBranch117(zzz340, zzz341, zzz34200, zzz343, zzz344, zzz510, zzz511, zzz513, zzz514, zzz31, new_primPlusNat2(new_primPlusNat3(Succ(new_primPlusNat3(new_primPlusNat1(zzz34200), zzz34200)), Succ(zzz34200)), Succ(zzz34200)), h)
new_mkVBalBranch3MkVBalBranch217(zzz473, zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, zzz481, zzz482, Succ(zzz4830), Zero, bh) → new_mkVBalBranch3MkVBalBranch121(zzz473, zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, zzz481, zzz482, new_primPlusNat2(new_primPlusNat3(Succ(new_primPlusNat3(new_primPlusNat1(zzz475), zzz475)), Succ(zzz475)), Succ(zzz475)), bh)
new_mkVBalBranch3MkVBalBranch121(zzz473, zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, zzz481, zzz482, Zero, bh) → new_mkVBalBranch3MkVBalBranch115(zzz473, zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, Zero, zzz480, zzz481, zzz482, Zero, Succ(Zero), bh)
new_mkVBalBranch3MkVBalBranch223(zzz340, zzz341, Neg(Succ(Zero)), zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, Succ(zzz670), h) → new_mkVBalBranch0(zzz31, Branch(zzz510, zzz511, Neg(Succ(zzz51200)), zzz513, zzz514), zzz343, h)
new_mkVBalBranch3MkVBalBranch229(zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, zzz1125, zzz1126, zzz1127, zzz1128, zzz1129, bd) → new_mkVBalBranch3MkVBalBranch119(zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, zzz1125, zzz1126, zzz1127, zzz1128, zzz1129, new_primPlusNat2(new_primPlusNat3(Succ(new_primPlusNat3(new_primPlusNat1(zzz1121), zzz1121)), Succ(zzz1121)), Succ(zzz1121)), bd)
new_mkVBalBranch3MkVBalBranch225(zzz498, zzz499, zzz500, zzz501, zzz502, zzz503, zzz504, zzz505, zzz506, zzz507, Succ(zzz5080), Zero, bg) → new_mkVBalBranch3MkVBalBranch118(zzz498, zzz499, zzz500, zzz501, zzz502, zzz503, zzz504, zzz505, zzz506, zzz507, new_primPlusNat2(new_primPlusNat3(Succ(new_primPlusNat3(new_primPlusNat1(zzz500), zzz500)), Succ(zzz500)), Succ(zzz500)), bg)
new_mkVBalBranch0(zzz31, Branch(zzz510, zzz511, Pos(Zero), zzz513, zzz514), Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), h) → new_mkVBalBranch3MkVBalBranch116(zzz340, zzz341, zzz34200, zzz343, zzz344, zzz510, zzz511, zzz513, zzz514, zzz31, new_primPlusNat2(new_primPlusNat3(Succ(new_primPlusNat3(new_primPlusNat1(zzz34200), zzz34200)), Succ(zzz34200)), Succ(zzz34200)), h)
new_mkVBalBranch3MkVBalBranch222(zzz461, zzz462, zzz463, zzz464, zzz465, zzz466, zzz467, zzz468, zzz469, zzz470, zzz471, bb) → new_mkVBalBranch3MkVBalBranch110(zzz461, zzz462, zzz463, zzz464, zzz465, zzz466, zzz467, zzz468, zzz469, zzz470, zzz471, new_primPlusNat2(Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat3(new_primPlusNat1(zzz463), zzz463)), zzz463))), Succ(zzz463)), bb)
new_mkVBalBranch3MkVBalBranch215(zzz340, zzz341, Pos(Succ(Succ(zzz342000))), zzz343, zzz344, zzz510, zzz511, Zero, zzz513, zzz514, zzz31, Succ(Succ(zzz6600)), h) → new_mkVBalBranch3MkVBalBranch217(zzz340, zzz341, Succ(zzz342000), zzz343, zzz344, zzz510, zzz511, zzz513, zzz514, zzz31, Succ(zzz6600), zzz342000, h)
new_mkVBalBranch3MkVBalBranch117(zzz340, zzz341, zzz34200, zzz343, zzz344, zzz510, zzz511, zzz513, zzz514, zzz31, Succ(zzz1240), h) → new_mkVBalBranch0(zzz31, zzz514, Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), h)
new_mkVBalBranch3MkVBalBranch120(zzz2050, zzz2051, zzz2052, zzz2053, zzz2054, zzz2055, zzz2056, zzz2057, zzz2058, zzz2059, zzz2060, Succ(zzz20610), Succ(zzz20620), be) → new_mkVBalBranch3MkVBalBranch120(zzz2050, zzz2051, zzz2052, zzz2053, zzz2054, zzz2055, zzz2056, zzz2057, zzz2058, zzz2059, zzz2060, zzz20610, zzz20620, be)
new_mkVBalBranch3MkVBalBranch217(zzz473, zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, zzz481, zzz482, Zero, Zero, bh) → new_mkVBalBranch3MkVBalBranch233(zzz473, zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, zzz481, zzz482, bh)
new_mkVBalBranch3MkVBalBranch216(zzz1105, zzz1106, zzz1107, zzz1108, zzz1109, zzz1110, zzz1111, zzz1112, zzz1113, zzz1114, zzz1115, Succ(zzz11160), Succ(zzz11170), ba) → new_mkVBalBranch3MkVBalBranch216(zzz1105, zzz1106, zzz1107, zzz1108, zzz1109, zzz1110, zzz1111, zzz1112, zzz1113, zzz1114, zzz1115, zzz11160, zzz11170, ba)
new_mkVBalBranch3MkVBalBranch223(zzz340, zzz341, Pos(zzz3420), zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, Succ(zzz670), h) → new_mkVBalBranch0(zzz31, Branch(zzz510, zzz511, Neg(Succ(zzz51200)), zzz513, zzz514), zzz343, h)
new_mkVBalBranch3MkVBalBranch19(zzz340, zzz341, zzz34200, zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, Zero, h) → new_mkVBalBranch3MkVBalBranch122(zzz340, zzz341, zzz34200, zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, h)
new_mkVBalBranch3MkVBalBranch225(zzz498, zzz499, zzz500, zzz501, zzz502, zzz503, zzz504, zzz505, zzz506, zzz507, Succ(zzz5080), Succ(zzz5090), bg) → new_mkVBalBranch3MkVBalBranch225(zzz498, zzz499, zzz500, zzz501, zzz502, zzz503, zzz504, zzz505, zzz506, zzz507, zzz5080, zzz5090, bg)
new_mkVBalBranch3MkVBalBranch19(zzz340, zzz341, zzz34200, zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, Succ(zzz1410), h) → new_mkVBalBranch0(zzz31, zzz514, Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), h)
new_mkVBalBranch3MkVBalBranch224(zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, zzz1125, zzz1126, zzz1127, zzz1128, zzz1129, Zero, Succ(zzz11310), bd) → new_mkVBalBranch3MkVBalBranch227(zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, zzz1125, zzz1126, zzz1127, zzz1128, zzz1129, bd)
new_mkVBalBranch3MkVBalBranch224(zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, zzz1125, zzz1126, zzz1127, zzz1128, zzz1129, Zero, Zero, bd) → new_mkVBalBranch3MkVBalBranch229(zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, zzz1125, zzz1126, zzz1127, zzz1128, zzz1129, bd)
new_mkVBalBranch3MkVBalBranch223(zzz340, zzz341, Neg(Succ(Succ(Zero))), zzz343, zzz344, zzz510, zzz511, Zero, zzz513, zzz514, zzz31, Succ(Succ(zzz6700)), h) → new_mkVBalBranch3MkVBalBranch225(zzz340, zzz341, Succ(Zero), zzz343, zzz344, zzz510, zzz511, zzz513, zzz514, zzz31, Zero, Succ(zzz6700), h)
new_mkVBalBranch3MkVBalBranch223(zzz340, zzz341, Neg(Succ(Succ(Succ(zzz3420000)))), zzz343, zzz344, zzz510, zzz511, Succ(zzz512000), zzz513, zzz514, zzz31, Succ(Succ(zzz6700)), h) → new_mkVBalBranch3MkVBalBranch224(zzz340, zzz341, Succ(Succ(zzz3420000)), zzz343, zzz344, zzz510, zzz511, zzz512000, zzz513, zzz514, zzz31, Succ(zzz3420000), Succ(Succ(new_primPlusNat2(zzz6700, zzz512000))), h)
new_mkVBalBranch3MkVBalBranch115(zzz1986, zzz1987, zzz1988, zzz1989, zzz1990, zzz1991, zzz1992, zzz1993, zzz1994, zzz1995, zzz1996, Succ(zzz19970), Succ(zzz19980), bc) → new_mkVBalBranch3MkVBalBranch115(zzz1986, zzz1987, zzz1988, zzz1989, zzz1990, zzz1991, zzz1992, zzz1993, zzz1994, zzz1995, zzz1996, zzz19970, zzz19980, bc)
new_mkVBalBranch3MkVBalBranch215(zzz340, zzz341, Neg(Zero), zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, Succ(zzz660), h) → new_mkVBalBranch0(zzz31, zzz514, Branch(zzz340, zzz341, Neg(Zero), zzz343, zzz344), h)
new_mkVBalBranch3MkVBalBranch118(zzz498, zzz499, zzz500, zzz501, zzz502, zzz503, zzz504, zzz505, zzz506, zzz507, Succ(zzz8040), bg) → new_mkVBalBranch3MkVBalBranch120(zzz498, zzz499, zzz500, zzz501, zzz502, zzz503, zzz504, Zero, zzz505, zzz506, zzz507, Succ(Zero), Succ(zzz8040), bg)
new_mkVBalBranch3MkVBalBranch216(zzz1105, zzz1106, zzz1107, zzz1108, zzz1109, zzz1110, zzz1111, zzz1112, zzz1113, zzz1114, zzz1115, Succ(zzz11160), Zero, ba) → new_mkVBalBranch3MkVBalBranch218(zzz1105, zzz1106, zzz1107, zzz1108, zzz1109, zzz1110, zzz1111, zzz1112, zzz1113, zzz1114, zzz1115, ba)
new_mkVBalBranch3MkVBalBranch216(zzz1105, zzz1106, zzz1107, zzz1108, zzz1109, zzz1110, zzz1111, zzz1112, zzz1113, zzz1114, zzz1115, Zero, Zero, ba) → new_mkVBalBranch3MkVBalBranch222(zzz1105, zzz1106, zzz1107, zzz1108, zzz1109, zzz1110, zzz1111, zzz1112, zzz1113, zzz1114, zzz1115, ba)
new_mkVBalBranch3MkVBalBranch18(zzz340, zzz341, zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, Zero, h) → new_mkVBalBranch3MkVBalBranch115(zzz340, zzz341, Zero, zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, Zero, Succ(zzz51200), h)
new_mkVBalBranch3MkVBalBranch119(zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, zzz1125, zzz1126, zzz1127, zzz1128, zzz1129, Succ(zzz12130), bd) → new_mkVBalBranch3MkVBalBranch120(zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, zzz1125, Succ(zzz1126), zzz1127, zzz1128, zzz1129, Succ(Succ(zzz1126)), Succ(zzz12130), bd)

The TRS R consists of the following rules:

new_primPlusNat1(Zero) → Zero
new_primPlusNat1(Succ(zzz62000)) → Succ(Succ(new_primPlusNat1(zzz62000)))
new_primPlusNat3(zzz90, Succ(zzz910)) → Succ(Succ(new_primPlusNat2(zzz90, zzz910)))
new_primPlusNat3(zzz90, Zero) → Succ(zzz90)
new_primPlusNat2(Succ(zzz900), Succ(zzz9100)) → Succ(Succ(new_primPlusNat2(zzz900, zzz9100)))
new_primPlusNat2(Zero, Succ(zzz9100)) → Succ(zzz9100)
new_primPlusNat2(Zero, Zero) → Zero
new_primPlusNat2(Succ(zzz900), Zero) → Succ(zzz900)

The set Q consists of the following terms:

new_primPlusNat2(Zero, Succ(x0))
new_primPlusNat3(x0, Succ(x1))
new_primPlusNat2(Succ(x0), Succ(x1))
new_primPlusNat3(x0, Zero)
new_primPlusNat1(Zero)
new_primPlusNat2(Zero, Zero)
new_primPlusNat1(Succ(x0))
new_primPlusNat2(Succ(x0), Zero)

We have to consider all minimal (P,Q,R)-chains.
By rewriting [15] the rule new_mkVBalBranch3MkVBalBranch224(zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, zzz1125, zzz1126, zzz1127, zzz1128, zzz1129, Succ(zzz11300), Zero, bd) → new_mkVBalBranch3MkVBalBranch119(zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, zzz1125, zzz1126, zzz1127, zzz1128, zzz1129, new_primPlusNat2(new_primPlusNat3(Succ(new_primPlusNat3(new_primPlusNat1(zzz1121), zzz1121)), Succ(zzz1121)), Succ(zzz1121)), bd) at position [11,0] we obtained the following new rules:

new_mkVBalBranch3MkVBalBranch224(zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, zzz1125, zzz1126, zzz1127, zzz1128, zzz1129, Succ(zzz11300), Zero, bd) → new_mkVBalBranch3MkVBalBranch119(zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, zzz1125, zzz1126, zzz1127, zzz1128, zzz1129, new_primPlusNat2(Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat3(new_primPlusNat1(zzz1121), zzz1121)), zzz1121))), Succ(zzz1121)), bd)



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

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

new_mkVBalBranch3MkVBalBranch225(zzz498, zzz499, zzz500, zzz501, zzz502, zzz503, zzz504, zzz505, zzz506, zzz507, Zero, Zero, bg) → new_mkVBalBranch3MkVBalBranch230(zzz498, zzz499, zzz500, zzz501, zzz502, zzz503, zzz504, zzz505, zzz506, zzz507, bg)
new_mkVBalBranch3MkVBalBranch18(zzz340, zzz341, zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, Succ(zzz1480), h) → new_mkVBalBranch3MkVBalBranch115(zzz340, zzz341, Zero, zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, Succ(zzz1480), Succ(zzz51200), h)
new_mkVBalBranch0(zzz31, Branch(zzz510, zzz511, Neg(Zero), zzz513, zzz514), Branch(zzz340, zzz341, Pos(Succ(zzz34200)), zzz343, zzz344), h) → new_mkVBalBranch0(zzz31, Branch(zzz510, zzz511, Neg(Zero), zzz513, zzz514), zzz343, h)
new_mkVBalBranch3MkVBalBranch215(zzz340, zzz341, Pos(Succ(Succ(zzz342000))), zzz343, zzz344, zzz510, zzz511, Succ(zzz512000), zzz513, zzz514, zzz31, Succ(Succ(zzz6600)), h) → new_mkVBalBranch3MkVBalBranch216(zzz340, zzz341, Succ(zzz342000), zzz343, zzz344, zzz510, zzz511, zzz512000, zzz513, zzz514, zzz31, Succ(Succ(new_primPlusNat2(zzz6600, zzz512000))), zzz342000, h)
new_mkVBalBranch3MkVBalBranch223(zzz340, zzz341, Neg(Succ(Succ(Succ(zzz3420000)))), zzz343, zzz344, zzz510, zzz511, Zero, zzz513, zzz514, zzz31, Succ(Succ(zzz6700)), h) → new_mkVBalBranch3MkVBalBranch225(zzz340, zzz341, Succ(Succ(zzz3420000)), zzz343, zzz344, zzz510, zzz511, zzz513, zzz514, zzz31, Succ(zzz3420000), Succ(zzz6700), h)
new_mkVBalBranch3MkVBalBranch120(zzz2050, zzz2051, zzz2052, zzz2053, zzz2054, zzz2055, zzz2056, zzz2057, zzz2058, zzz2059, zzz2060, Zero, Succ(zzz20620), be) → new_mkVBalBranch0(zzz2060, zzz2059, Branch(zzz2050, zzz2051, Neg(Succ(zzz2052)), zzz2053, zzz2054), be)
new_mkVBalBranch3MkVBalBranch121(zzz473, zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, zzz481, zzz482, Succ(zzz7390), bh) → new_mkVBalBranch3MkVBalBranch115(zzz473, zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, Zero, zzz480, zzz481, zzz482, Succ(zzz7390), Succ(Zero), bh)
new_mkVBalBranch0(zzz31, Branch(zzz510, zzz511, Pos(Zero), zzz513, zzz514), Branch(zzz340, zzz341, Pos(Succ(zzz34200)), zzz343, zzz344), h) → new_mkVBalBranch0(zzz31, Branch(zzz510, zzz511, Pos(Zero), zzz513, zzz514), zzz343, h)
new_mkVBalBranch0(zzz31, Branch(zzz510, zzz511, Pos(Succ(zzz51200)), zzz513, zzz514), Branch(zzz340, zzz341, zzz342, zzz343, zzz344), h) → new_mkVBalBranch3MkVBalBranch215(zzz340, zzz341, zzz342, zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat3(new_primPlusNat1(zzz51200), zzz51200)), zzz51200))), h)
new_mkVBalBranch3MkVBalBranch223(zzz340, zzz341, Neg(Succ(Succ(Zero))), zzz343, zzz344, zzz510, zzz511, Succ(zzz512000), zzz513, zzz514, zzz31, Succ(Succ(zzz6700)), h) → new_mkVBalBranch3MkVBalBranch224(zzz340, zzz341, Succ(Zero), zzz343, zzz344, zzz510, zzz511, zzz512000, zzz513, zzz514, zzz31, Zero, Succ(Succ(new_primPlusNat2(zzz6700, zzz512000))), h)
new_mkVBalBranch3MkVBalBranch224(zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, zzz1125, zzz1126, zzz1127, zzz1128, zzz1129, Succ(zzz11300), Succ(zzz11310), bd) → new_mkVBalBranch3MkVBalBranch224(zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, zzz1125, zzz1126, zzz1127, zzz1128, zzz1129, zzz11300, zzz11310, bd)
new_mkVBalBranch3MkVBalBranch217(zzz473, zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, zzz481, zzz482, Zero, Succ(zzz4840), bh) → new_mkVBalBranch0(zzz482, Branch(zzz478, zzz479, Pos(Succ(Zero)), zzz480, zzz481), zzz476, bh)
new_mkVBalBranch3MkVBalBranch218(zzz461, zzz462, zzz463, zzz464, zzz465, zzz466, zzz467, zzz468, zzz469, zzz470, zzz471, bb) → new_mkVBalBranch3MkVBalBranch110(zzz461, zzz462, zzz463, zzz464, zzz465, zzz466, zzz467, zzz468, zzz469, zzz470, zzz471, new_primPlusNat2(new_primPlusNat3(Succ(new_primPlusNat3(new_primPlusNat1(zzz463), zzz463)), Succ(zzz463)), Succ(zzz463)), bb)
new_mkVBalBranch3MkVBalBranch233(zzz473, zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, zzz481, zzz482, bh) → new_mkVBalBranch3MkVBalBranch121(zzz473, zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, zzz481, zzz482, new_primPlusNat2(new_primPlusNat3(Succ(new_primPlusNat3(new_primPlusNat1(zzz475), zzz475)), Succ(zzz475)), Succ(zzz475)), bh)
new_mkVBalBranch3MkVBalBranch224(zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, zzz1125, zzz1126, zzz1127, zzz1128, zzz1129, Succ(zzz11300), Zero, bd) → new_mkVBalBranch3MkVBalBranch119(zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, zzz1125, zzz1126, zzz1127, zzz1128, zzz1129, new_primPlusNat2(Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat3(new_primPlusNat1(zzz1121), zzz1121)), zzz1121))), Succ(zzz1121)), bd)
new_mkVBalBranch3MkVBalBranch110(zzz461, zzz462, zzz463, zzz464, zzz465, zzz466, zzz467, zzz468, zzz469, zzz470, zzz471, Succ(zzz5800), bb) → new_mkVBalBranch3MkVBalBranch115(zzz461, zzz462, zzz463, zzz464, zzz465, zzz466, zzz467, Succ(zzz468), zzz469, zzz470, zzz471, Succ(zzz5800), Succ(Succ(zzz468)), bb)
new_mkVBalBranch3MkVBalBranch227(zzz486, zzz487, zzz488, zzz489, zzz490, zzz491, zzz492, zzz493, zzz494, zzz495, zzz496, bf) → new_mkVBalBranch0(zzz496, Branch(zzz491, zzz492, Neg(Succ(Succ(zzz493))), zzz494, zzz495), zzz489, bf)
new_mkVBalBranch3MkVBalBranch215(zzz340, zzz341, Pos(Zero), zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, Succ(zzz660), h) → new_mkVBalBranch0(zzz31, zzz514, Branch(zzz340, zzz341, Pos(Zero), zzz343, zzz344), h)
new_mkVBalBranch3MkVBalBranch223(zzz340, zzz341, Neg(Zero), zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, Succ(zzz670), h) → new_mkVBalBranch0(zzz31, Branch(zzz510, zzz511, Neg(Succ(zzz51200)), zzz513, zzz514), zzz343, h)
new_mkVBalBranch3MkVBalBranch216(zzz1105, zzz1106, zzz1107, zzz1108, zzz1109, zzz1110, zzz1111, zzz1112, zzz1113, zzz1114, zzz1115, Zero, Succ(zzz11170), ba) → new_mkVBalBranch0(zzz1115, Branch(zzz1110, zzz1111, Pos(Succ(Succ(zzz1112))), zzz1113, zzz1114), zzz1108, ba)
new_mkVBalBranch3MkVBalBranch115(zzz1986, zzz1987, zzz1988, zzz1989, zzz1990, zzz1991, zzz1992, zzz1993, zzz1994, zzz1995, zzz1996, Zero, Succ(zzz19980), bc) → new_mkVBalBranch0(zzz1996, zzz1995, Branch(zzz1986, zzz1987, Pos(Succ(zzz1988)), zzz1989, zzz1990), bc)
new_mkVBalBranch3MkVBalBranch215(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, Succ(zzz660), h) → new_mkVBalBranch3MkVBalBranch19(zzz340, zzz341, zzz34200, zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, new_primPlusNat2(new_primPlusNat3(Succ(new_primPlusNat3(new_primPlusNat1(zzz34200), zzz34200)), Succ(zzz34200)), Succ(zzz34200)), h)
new_mkVBalBranch3MkVBalBranch215(zzz340, zzz341, Pos(Succ(Zero)), zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, Succ(zzz660), h) → new_mkVBalBranch3MkVBalBranch18(zzz340, zzz341, zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, new_primPlusNat2(new_primPlusNat3(Succ(new_primPlusNat3(new_primPlusNat1(Zero), Zero)), Succ(Zero)), Succ(Zero)), h)
new_mkVBalBranch3MkVBalBranch230(zzz498, zzz499, zzz500, zzz501, zzz502, zzz503, zzz504, zzz505, zzz506, zzz507, bg) → new_mkVBalBranch3MkVBalBranch118(zzz498, zzz499, zzz500, zzz501, zzz502, zzz503, zzz504, zzz505, zzz506, zzz507, new_primPlusNat2(Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat3(new_primPlusNat1(zzz500), zzz500)), zzz500))), Succ(zzz500)), bg)
new_mkVBalBranch3MkVBalBranch122(zzz340, zzz341, zzz34200, zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, h) → new_mkVBalBranch0(zzz31, zzz514, Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), h)
new_mkVBalBranch3MkVBalBranch217(zzz473, zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, zzz481, zzz482, Succ(zzz4830), Succ(zzz4840), bh) → new_mkVBalBranch3MkVBalBranch217(zzz473, zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, zzz481, zzz482, zzz4830, zzz4840, bh)
new_mkVBalBranch3MkVBalBranch116(zzz340, zzz341, zzz34200, zzz343, zzz344, zzz510, zzz511, zzz513, zzz514, zzz31, Succ(zzz1200), h) → new_mkVBalBranch0(zzz31, zzz514, Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), h)
new_mkVBalBranch3MkVBalBranch110(zzz461, zzz462, zzz463, zzz464, zzz465, zzz466, zzz467, zzz468, zzz469, zzz470, zzz471, Zero, bb) → new_mkVBalBranch3MkVBalBranch115(zzz461, zzz462, zzz463, zzz464, zzz465, zzz466, zzz467, Succ(zzz468), zzz469, zzz470, zzz471, Zero, Succ(Succ(zzz468)), bb)
new_mkVBalBranch3MkVBalBranch225(zzz498, zzz499, zzz500, zzz501, zzz502, zzz503, zzz504, zzz505, zzz506, zzz507, Zero, Succ(zzz5090), bg) → new_mkVBalBranch0(zzz507, Branch(zzz503, zzz504, Neg(Succ(Zero)), zzz505, zzz506), zzz501, bg)
new_mkVBalBranch0(zzz31, Branch(zzz510, zzz511, Neg(Succ(zzz51200)), zzz513, zzz514), Branch(zzz340, zzz341, zzz342, zzz343, zzz344), h) → new_mkVBalBranch3MkVBalBranch223(zzz340, zzz341, zzz342, zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat3(new_primPlusNat1(zzz51200), zzz51200)), zzz51200))), h)
new_mkVBalBranch0(zzz31, Branch(zzz510, zzz511, Neg(Zero), zzz513, zzz514), Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), h) → new_mkVBalBranch3MkVBalBranch117(zzz340, zzz341, zzz34200, zzz343, zzz344, zzz510, zzz511, zzz513, zzz514, zzz31, new_primPlusNat2(new_primPlusNat3(Succ(new_primPlusNat3(new_primPlusNat1(zzz34200), zzz34200)), Succ(zzz34200)), Succ(zzz34200)), h)
new_mkVBalBranch3MkVBalBranch217(zzz473, zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, zzz481, zzz482, Succ(zzz4830), Zero, bh) → new_mkVBalBranch3MkVBalBranch121(zzz473, zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, zzz481, zzz482, new_primPlusNat2(new_primPlusNat3(Succ(new_primPlusNat3(new_primPlusNat1(zzz475), zzz475)), Succ(zzz475)), Succ(zzz475)), bh)
new_mkVBalBranch3MkVBalBranch121(zzz473, zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, zzz481, zzz482, Zero, bh) → new_mkVBalBranch3MkVBalBranch115(zzz473, zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, Zero, zzz480, zzz481, zzz482, Zero, Succ(Zero), bh)
new_mkVBalBranch3MkVBalBranch223(zzz340, zzz341, Neg(Succ(Zero)), zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, Succ(zzz670), h) → new_mkVBalBranch0(zzz31, Branch(zzz510, zzz511, Neg(Succ(zzz51200)), zzz513, zzz514), zzz343, h)
new_mkVBalBranch3MkVBalBranch225(zzz498, zzz499, zzz500, zzz501, zzz502, zzz503, zzz504, zzz505, zzz506, zzz507, Succ(zzz5080), Zero, bg) → new_mkVBalBranch3MkVBalBranch118(zzz498, zzz499, zzz500, zzz501, zzz502, zzz503, zzz504, zzz505, zzz506, zzz507, new_primPlusNat2(new_primPlusNat3(Succ(new_primPlusNat3(new_primPlusNat1(zzz500), zzz500)), Succ(zzz500)), Succ(zzz500)), bg)
new_mkVBalBranch3MkVBalBranch229(zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, zzz1125, zzz1126, zzz1127, zzz1128, zzz1129, bd) → new_mkVBalBranch3MkVBalBranch119(zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, zzz1125, zzz1126, zzz1127, zzz1128, zzz1129, new_primPlusNat2(new_primPlusNat3(Succ(new_primPlusNat3(new_primPlusNat1(zzz1121), zzz1121)), Succ(zzz1121)), Succ(zzz1121)), bd)
new_mkVBalBranch0(zzz31, Branch(zzz510, zzz511, Pos(Zero), zzz513, zzz514), Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), h) → new_mkVBalBranch3MkVBalBranch116(zzz340, zzz341, zzz34200, zzz343, zzz344, zzz510, zzz511, zzz513, zzz514, zzz31, new_primPlusNat2(new_primPlusNat3(Succ(new_primPlusNat3(new_primPlusNat1(zzz34200), zzz34200)), Succ(zzz34200)), Succ(zzz34200)), h)
new_mkVBalBranch3MkVBalBranch222(zzz461, zzz462, zzz463, zzz464, zzz465, zzz466, zzz467, zzz468, zzz469, zzz470, zzz471, bb) → new_mkVBalBranch3MkVBalBranch110(zzz461, zzz462, zzz463, zzz464, zzz465, zzz466, zzz467, zzz468, zzz469, zzz470, zzz471, new_primPlusNat2(Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat3(new_primPlusNat1(zzz463), zzz463)), zzz463))), Succ(zzz463)), bb)
new_mkVBalBranch3MkVBalBranch215(zzz340, zzz341, Pos(Succ(Succ(zzz342000))), zzz343, zzz344, zzz510, zzz511, Zero, zzz513, zzz514, zzz31, Succ(Succ(zzz6600)), h) → new_mkVBalBranch3MkVBalBranch217(zzz340, zzz341, Succ(zzz342000), zzz343, zzz344, zzz510, zzz511, zzz513, zzz514, zzz31, Succ(zzz6600), zzz342000, h)
new_mkVBalBranch3MkVBalBranch117(zzz340, zzz341, zzz34200, zzz343, zzz344, zzz510, zzz511, zzz513, zzz514, zzz31, Succ(zzz1240), h) → new_mkVBalBranch0(zzz31, zzz514, Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), h)
new_mkVBalBranch3MkVBalBranch217(zzz473, zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, zzz481, zzz482, Zero, Zero, bh) → new_mkVBalBranch3MkVBalBranch233(zzz473, zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, zzz481, zzz482, bh)
new_mkVBalBranch3MkVBalBranch120(zzz2050, zzz2051, zzz2052, zzz2053, zzz2054, zzz2055, zzz2056, zzz2057, zzz2058, zzz2059, zzz2060, Succ(zzz20610), Succ(zzz20620), be) → new_mkVBalBranch3MkVBalBranch120(zzz2050, zzz2051, zzz2052, zzz2053, zzz2054, zzz2055, zzz2056, zzz2057, zzz2058, zzz2059, zzz2060, zzz20610, zzz20620, be)
new_mkVBalBranch3MkVBalBranch223(zzz340, zzz341, Pos(zzz3420), zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, Succ(zzz670), h) → new_mkVBalBranch0(zzz31, Branch(zzz510, zzz511, Neg(Succ(zzz51200)), zzz513, zzz514), zzz343, h)
new_mkVBalBranch3MkVBalBranch216(zzz1105, zzz1106, zzz1107, zzz1108, zzz1109, zzz1110, zzz1111, zzz1112, zzz1113, zzz1114, zzz1115, Succ(zzz11160), Succ(zzz11170), ba) → new_mkVBalBranch3MkVBalBranch216(zzz1105, zzz1106, zzz1107, zzz1108, zzz1109, zzz1110, zzz1111, zzz1112, zzz1113, zzz1114, zzz1115, zzz11160, zzz11170, ba)
new_mkVBalBranch3MkVBalBranch19(zzz340, zzz341, zzz34200, zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, Zero, h) → new_mkVBalBranch3MkVBalBranch122(zzz340, zzz341, zzz34200, zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, h)
new_mkVBalBranch3MkVBalBranch225(zzz498, zzz499, zzz500, zzz501, zzz502, zzz503, zzz504, zzz505, zzz506, zzz507, Succ(zzz5080), Succ(zzz5090), bg) → new_mkVBalBranch3MkVBalBranch225(zzz498, zzz499, zzz500, zzz501, zzz502, zzz503, zzz504, zzz505, zzz506, zzz507, zzz5080, zzz5090, bg)
new_mkVBalBranch3MkVBalBranch19(zzz340, zzz341, zzz34200, zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, Succ(zzz1410), h) → new_mkVBalBranch0(zzz31, zzz514, Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), h)
new_mkVBalBranch3MkVBalBranch224(zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, zzz1125, zzz1126, zzz1127, zzz1128, zzz1129, Zero, Zero, bd) → new_mkVBalBranch3MkVBalBranch229(zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, zzz1125, zzz1126, zzz1127, zzz1128, zzz1129, bd)
new_mkVBalBranch3MkVBalBranch224(zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, zzz1125, zzz1126, zzz1127, zzz1128, zzz1129, Zero, Succ(zzz11310), bd) → new_mkVBalBranch3MkVBalBranch227(zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, zzz1125, zzz1126, zzz1127, zzz1128, zzz1129, bd)
new_mkVBalBranch3MkVBalBranch223(zzz340, zzz341, Neg(Succ(Succ(Succ(zzz3420000)))), zzz343, zzz344, zzz510, zzz511, Succ(zzz512000), zzz513, zzz514, zzz31, Succ(Succ(zzz6700)), h) → new_mkVBalBranch3MkVBalBranch224(zzz340, zzz341, Succ(Succ(zzz3420000)), zzz343, zzz344, zzz510, zzz511, zzz512000, zzz513, zzz514, zzz31, Succ(zzz3420000), Succ(Succ(new_primPlusNat2(zzz6700, zzz512000))), h)
new_mkVBalBranch3MkVBalBranch223(zzz340, zzz341, Neg(Succ(Succ(Zero))), zzz343, zzz344, zzz510, zzz511, Zero, zzz513, zzz514, zzz31, Succ(Succ(zzz6700)), h) → new_mkVBalBranch3MkVBalBranch225(zzz340, zzz341, Succ(Zero), zzz343, zzz344, zzz510, zzz511, zzz513, zzz514, zzz31, Zero, Succ(zzz6700), h)
new_mkVBalBranch3MkVBalBranch115(zzz1986, zzz1987, zzz1988, zzz1989, zzz1990, zzz1991, zzz1992, zzz1993, zzz1994, zzz1995, zzz1996, Succ(zzz19970), Succ(zzz19980), bc) → new_mkVBalBranch3MkVBalBranch115(zzz1986, zzz1987, zzz1988, zzz1989, zzz1990, zzz1991, zzz1992, zzz1993, zzz1994, zzz1995, zzz1996, zzz19970, zzz19980, bc)
new_mkVBalBranch3MkVBalBranch215(zzz340, zzz341, Neg(Zero), zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, Succ(zzz660), h) → new_mkVBalBranch0(zzz31, zzz514, Branch(zzz340, zzz341, Neg(Zero), zzz343, zzz344), h)
new_mkVBalBranch3MkVBalBranch118(zzz498, zzz499, zzz500, zzz501, zzz502, zzz503, zzz504, zzz505, zzz506, zzz507, Succ(zzz8040), bg) → new_mkVBalBranch3MkVBalBranch120(zzz498, zzz499, zzz500, zzz501, zzz502, zzz503, zzz504, Zero, zzz505, zzz506, zzz507, Succ(Zero), Succ(zzz8040), bg)
new_mkVBalBranch3MkVBalBranch216(zzz1105, zzz1106, zzz1107, zzz1108, zzz1109, zzz1110, zzz1111, zzz1112, zzz1113, zzz1114, zzz1115, Succ(zzz11160), Zero, ba) → new_mkVBalBranch3MkVBalBranch218(zzz1105, zzz1106, zzz1107, zzz1108, zzz1109, zzz1110, zzz1111, zzz1112, zzz1113, zzz1114, zzz1115, ba)
new_mkVBalBranch3MkVBalBranch216(zzz1105, zzz1106, zzz1107, zzz1108, zzz1109, zzz1110, zzz1111, zzz1112, zzz1113, zzz1114, zzz1115, Zero, Zero, ba) → new_mkVBalBranch3MkVBalBranch222(zzz1105, zzz1106, zzz1107, zzz1108, zzz1109, zzz1110, zzz1111, zzz1112, zzz1113, zzz1114, zzz1115, ba)
new_mkVBalBranch3MkVBalBranch119(zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, zzz1125, zzz1126, zzz1127, zzz1128, zzz1129, Succ(zzz12130), bd) → new_mkVBalBranch3MkVBalBranch120(zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, zzz1125, Succ(zzz1126), zzz1127, zzz1128, zzz1129, Succ(Succ(zzz1126)), Succ(zzz12130), bd)
new_mkVBalBranch3MkVBalBranch18(zzz340, zzz341, zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, Zero, h) → new_mkVBalBranch3MkVBalBranch115(zzz340, zzz341, Zero, zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, Zero, Succ(zzz51200), h)

The TRS R consists of the following rules:

new_primPlusNat1(Zero) → Zero
new_primPlusNat1(Succ(zzz62000)) → Succ(Succ(new_primPlusNat1(zzz62000)))
new_primPlusNat3(zzz90, Succ(zzz910)) → Succ(Succ(new_primPlusNat2(zzz90, zzz910)))
new_primPlusNat3(zzz90, Zero) → Succ(zzz90)
new_primPlusNat2(Succ(zzz900), Succ(zzz9100)) → Succ(Succ(new_primPlusNat2(zzz900, zzz9100)))
new_primPlusNat2(Zero, Succ(zzz9100)) → Succ(zzz9100)
new_primPlusNat2(Zero, Zero) → Zero
new_primPlusNat2(Succ(zzz900), Zero) → Succ(zzz900)

The set Q consists of the following terms:

new_primPlusNat2(Zero, Succ(x0))
new_primPlusNat3(x0, Succ(x1))
new_primPlusNat2(Succ(x0), Succ(x1))
new_primPlusNat3(x0, Zero)
new_primPlusNat1(Zero)
new_primPlusNat2(Zero, Zero)
new_primPlusNat1(Succ(x0))
new_primPlusNat2(Succ(x0), Zero)

We have to consider all minimal (P,Q,R)-chains.
By rewriting [15] the rule new_mkVBalBranch3MkVBalBranch218(zzz461, zzz462, zzz463, zzz464, zzz465, zzz466, zzz467, zzz468, zzz469, zzz470, zzz471, bb) → new_mkVBalBranch3MkVBalBranch110(zzz461, zzz462, zzz463, zzz464, zzz465, zzz466, zzz467, zzz468, zzz469, zzz470, zzz471, new_primPlusNat2(new_primPlusNat3(Succ(new_primPlusNat3(new_primPlusNat1(zzz463), zzz463)), Succ(zzz463)), Succ(zzz463)), bb) at position [11,0] we obtained the following new rules:

new_mkVBalBranch3MkVBalBranch218(zzz461, zzz462, zzz463, zzz464, zzz465, zzz466, zzz467, zzz468, zzz469, zzz470, zzz471, bb) → new_mkVBalBranch3MkVBalBranch110(zzz461, zzz462, zzz463, zzz464, zzz465, zzz466, zzz467, zzz468, zzz469, zzz470, zzz471, new_primPlusNat2(Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat3(new_primPlusNat1(zzz463), zzz463)), zzz463))), Succ(zzz463)), bb)



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

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

new_mkVBalBranch3MkVBalBranch225(zzz498, zzz499, zzz500, zzz501, zzz502, zzz503, zzz504, zzz505, zzz506, zzz507, Zero, Zero, bg) → new_mkVBalBranch3MkVBalBranch230(zzz498, zzz499, zzz500, zzz501, zzz502, zzz503, zzz504, zzz505, zzz506, zzz507, bg)
new_mkVBalBranch3MkVBalBranch18(zzz340, zzz341, zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, Succ(zzz1480), h) → new_mkVBalBranch3MkVBalBranch115(zzz340, zzz341, Zero, zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, Succ(zzz1480), Succ(zzz51200), h)
new_mkVBalBranch3MkVBalBranch215(zzz340, zzz341, Pos(Succ(Succ(zzz342000))), zzz343, zzz344, zzz510, zzz511, Succ(zzz512000), zzz513, zzz514, zzz31, Succ(Succ(zzz6600)), h) → new_mkVBalBranch3MkVBalBranch216(zzz340, zzz341, Succ(zzz342000), zzz343, zzz344, zzz510, zzz511, zzz512000, zzz513, zzz514, zzz31, Succ(Succ(new_primPlusNat2(zzz6600, zzz512000))), zzz342000, h)
new_mkVBalBranch0(zzz31, Branch(zzz510, zzz511, Neg(Zero), zzz513, zzz514), Branch(zzz340, zzz341, Pos(Succ(zzz34200)), zzz343, zzz344), h) → new_mkVBalBranch0(zzz31, Branch(zzz510, zzz511, Neg(Zero), zzz513, zzz514), zzz343, h)
new_mkVBalBranch3MkVBalBranch223(zzz340, zzz341, Neg(Succ(Succ(Succ(zzz3420000)))), zzz343, zzz344, zzz510, zzz511, Zero, zzz513, zzz514, zzz31, Succ(Succ(zzz6700)), h) → new_mkVBalBranch3MkVBalBranch225(zzz340, zzz341, Succ(Succ(zzz3420000)), zzz343, zzz344, zzz510, zzz511, zzz513, zzz514, zzz31, Succ(zzz3420000), Succ(zzz6700), h)
new_mkVBalBranch3MkVBalBranch120(zzz2050, zzz2051, zzz2052, zzz2053, zzz2054, zzz2055, zzz2056, zzz2057, zzz2058, zzz2059, zzz2060, Zero, Succ(zzz20620), be) → new_mkVBalBranch0(zzz2060, zzz2059, Branch(zzz2050, zzz2051, Neg(Succ(zzz2052)), zzz2053, zzz2054), be)
new_mkVBalBranch0(zzz31, Branch(zzz510, zzz511, Pos(Zero), zzz513, zzz514), Branch(zzz340, zzz341, Pos(Succ(zzz34200)), zzz343, zzz344), h) → new_mkVBalBranch0(zzz31, Branch(zzz510, zzz511, Pos(Zero), zzz513, zzz514), zzz343, h)
new_mkVBalBranch3MkVBalBranch121(zzz473, zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, zzz481, zzz482, Succ(zzz7390), bh) → new_mkVBalBranch3MkVBalBranch115(zzz473, zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, Zero, zzz480, zzz481, zzz482, Succ(zzz7390), Succ(Zero), bh)
new_mkVBalBranch0(zzz31, Branch(zzz510, zzz511, Pos(Succ(zzz51200)), zzz513, zzz514), Branch(zzz340, zzz341, zzz342, zzz343, zzz344), h) → new_mkVBalBranch3MkVBalBranch215(zzz340, zzz341, zzz342, zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat3(new_primPlusNat1(zzz51200), zzz51200)), zzz51200))), h)
new_mkVBalBranch3MkVBalBranch223(zzz340, zzz341, Neg(Succ(Succ(Zero))), zzz343, zzz344, zzz510, zzz511, Succ(zzz512000), zzz513, zzz514, zzz31, Succ(Succ(zzz6700)), h) → new_mkVBalBranch3MkVBalBranch224(zzz340, zzz341, Succ(Zero), zzz343, zzz344, zzz510, zzz511, zzz512000, zzz513, zzz514, zzz31, Zero, Succ(Succ(new_primPlusNat2(zzz6700, zzz512000))), h)
new_mkVBalBranch3MkVBalBranch224(zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, zzz1125, zzz1126, zzz1127, zzz1128, zzz1129, Succ(zzz11300), Succ(zzz11310), bd) → new_mkVBalBranch3MkVBalBranch224(zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, zzz1125, zzz1126, zzz1127, zzz1128, zzz1129, zzz11300, zzz11310, bd)
new_mkVBalBranch3MkVBalBranch217(zzz473, zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, zzz481, zzz482, Zero, Succ(zzz4840), bh) → new_mkVBalBranch0(zzz482, Branch(zzz478, zzz479, Pos(Succ(Zero)), zzz480, zzz481), zzz476, bh)
new_mkVBalBranch3MkVBalBranch233(zzz473, zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, zzz481, zzz482, bh) → new_mkVBalBranch3MkVBalBranch121(zzz473, zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, zzz481, zzz482, new_primPlusNat2(new_primPlusNat3(Succ(new_primPlusNat3(new_primPlusNat1(zzz475), zzz475)), Succ(zzz475)), Succ(zzz475)), bh)
new_mkVBalBranch3MkVBalBranch224(zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, zzz1125, zzz1126, zzz1127, zzz1128, zzz1129, Succ(zzz11300), Zero, bd) → new_mkVBalBranch3MkVBalBranch119(zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, zzz1125, zzz1126, zzz1127, zzz1128, zzz1129, new_primPlusNat2(Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat3(new_primPlusNat1(zzz1121), zzz1121)), zzz1121))), Succ(zzz1121)), bd)
new_mkVBalBranch3MkVBalBranch110(zzz461, zzz462, zzz463, zzz464, zzz465, zzz466, zzz467, zzz468, zzz469, zzz470, zzz471, Succ(zzz5800), bb) → new_mkVBalBranch3MkVBalBranch115(zzz461, zzz462, zzz463, zzz464, zzz465, zzz466, zzz467, Succ(zzz468), zzz469, zzz470, zzz471, Succ(zzz5800), Succ(Succ(zzz468)), bb)
new_mkVBalBranch3MkVBalBranch227(zzz486, zzz487, zzz488, zzz489, zzz490, zzz491, zzz492, zzz493, zzz494, zzz495, zzz496, bf) → new_mkVBalBranch0(zzz496, Branch(zzz491, zzz492, Neg(Succ(Succ(zzz493))), zzz494, zzz495), zzz489, bf)
new_mkVBalBranch3MkVBalBranch215(zzz340, zzz341, Pos(Zero), zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, Succ(zzz660), h) → new_mkVBalBranch0(zzz31, zzz514, Branch(zzz340, zzz341, Pos(Zero), zzz343, zzz344), h)
new_mkVBalBranch3MkVBalBranch223(zzz340, zzz341, Neg(Zero), zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, Succ(zzz670), h) → new_mkVBalBranch0(zzz31, Branch(zzz510, zzz511, Neg(Succ(zzz51200)), zzz513, zzz514), zzz343, h)
new_mkVBalBranch3MkVBalBranch216(zzz1105, zzz1106, zzz1107, zzz1108, zzz1109, zzz1110, zzz1111, zzz1112, zzz1113, zzz1114, zzz1115, Zero, Succ(zzz11170), ba) → new_mkVBalBranch0(zzz1115, Branch(zzz1110, zzz1111, Pos(Succ(Succ(zzz1112))), zzz1113, zzz1114), zzz1108, ba)
new_mkVBalBranch3MkVBalBranch115(zzz1986, zzz1987, zzz1988, zzz1989, zzz1990, zzz1991, zzz1992, zzz1993, zzz1994, zzz1995, zzz1996, Zero, Succ(zzz19980), bc) → new_mkVBalBranch0(zzz1996, zzz1995, Branch(zzz1986, zzz1987, Pos(Succ(zzz1988)), zzz1989, zzz1990), bc)
new_mkVBalBranch3MkVBalBranch215(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, Succ(zzz660), h) → new_mkVBalBranch3MkVBalBranch19(zzz340, zzz341, zzz34200, zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, new_primPlusNat2(new_primPlusNat3(Succ(new_primPlusNat3(new_primPlusNat1(zzz34200), zzz34200)), Succ(zzz34200)), Succ(zzz34200)), h)
new_mkVBalBranch3MkVBalBranch215(zzz340, zzz341, Pos(Succ(Zero)), zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, Succ(zzz660), h) → new_mkVBalBranch3MkVBalBranch18(zzz340, zzz341, zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, new_primPlusNat2(new_primPlusNat3(Succ(new_primPlusNat3(new_primPlusNat1(Zero), Zero)), Succ(Zero)), Succ(Zero)), h)
new_mkVBalBranch3MkVBalBranch122(zzz340, zzz341, zzz34200, zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, h) → new_mkVBalBranch0(zzz31, zzz514, Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), h)
new_mkVBalBranch3MkVBalBranch230(zzz498, zzz499, zzz500, zzz501, zzz502, zzz503, zzz504, zzz505, zzz506, zzz507, bg) → new_mkVBalBranch3MkVBalBranch118(zzz498, zzz499, zzz500, zzz501, zzz502, zzz503, zzz504, zzz505, zzz506, zzz507, new_primPlusNat2(Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat3(new_primPlusNat1(zzz500), zzz500)), zzz500))), Succ(zzz500)), bg)
new_mkVBalBranch3MkVBalBranch217(zzz473, zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, zzz481, zzz482, Succ(zzz4830), Succ(zzz4840), bh) → new_mkVBalBranch3MkVBalBranch217(zzz473, zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, zzz481, zzz482, zzz4830, zzz4840, bh)
new_mkVBalBranch3MkVBalBranch116(zzz340, zzz341, zzz34200, zzz343, zzz344, zzz510, zzz511, zzz513, zzz514, zzz31, Succ(zzz1200), h) → new_mkVBalBranch0(zzz31, zzz514, Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), h)
new_mkVBalBranch3MkVBalBranch110(zzz461, zzz462, zzz463, zzz464, zzz465, zzz466, zzz467, zzz468, zzz469, zzz470, zzz471, Zero, bb) → new_mkVBalBranch3MkVBalBranch115(zzz461, zzz462, zzz463, zzz464, zzz465, zzz466, zzz467, Succ(zzz468), zzz469, zzz470, zzz471, Zero, Succ(Succ(zzz468)), bb)
new_mkVBalBranch3MkVBalBranch225(zzz498, zzz499, zzz500, zzz501, zzz502, zzz503, zzz504, zzz505, zzz506, zzz507, Zero, Succ(zzz5090), bg) → new_mkVBalBranch0(zzz507, Branch(zzz503, zzz504, Neg(Succ(Zero)), zzz505, zzz506), zzz501, bg)
new_mkVBalBranch0(zzz31, Branch(zzz510, zzz511, Neg(Succ(zzz51200)), zzz513, zzz514), Branch(zzz340, zzz341, zzz342, zzz343, zzz344), h) → new_mkVBalBranch3MkVBalBranch223(zzz340, zzz341, zzz342, zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat3(new_primPlusNat1(zzz51200), zzz51200)), zzz51200))), h)
new_mkVBalBranch0(zzz31, Branch(zzz510, zzz511, Neg(Zero), zzz513, zzz514), Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), h) → new_mkVBalBranch3MkVBalBranch117(zzz340, zzz341, zzz34200, zzz343, zzz344, zzz510, zzz511, zzz513, zzz514, zzz31, new_primPlusNat2(new_primPlusNat3(Succ(new_primPlusNat3(new_primPlusNat1(zzz34200), zzz34200)), Succ(zzz34200)), Succ(zzz34200)), h)
new_mkVBalBranch3MkVBalBranch217(zzz473, zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, zzz481, zzz482, Succ(zzz4830), Zero, bh) → new_mkVBalBranch3MkVBalBranch121(zzz473, zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, zzz481, zzz482, new_primPlusNat2(new_primPlusNat3(Succ(new_primPlusNat3(new_primPlusNat1(zzz475), zzz475)), Succ(zzz475)), Succ(zzz475)), bh)
new_mkVBalBranch3MkVBalBranch121(zzz473, zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, zzz481, zzz482, Zero, bh) → new_mkVBalBranch3MkVBalBranch115(zzz473, zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, Zero, zzz480, zzz481, zzz482, Zero, Succ(Zero), bh)
new_mkVBalBranch3MkVBalBranch223(zzz340, zzz341, Neg(Succ(Zero)), zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, Succ(zzz670), h) → new_mkVBalBranch0(zzz31, Branch(zzz510, zzz511, Neg(Succ(zzz51200)), zzz513, zzz514), zzz343, h)
new_mkVBalBranch3MkVBalBranch229(zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, zzz1125, zzz1126, zzz1127, zzz1128, zzz1129, bd) → new_mkVBalBranch3MkVBalBranch119(zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, zzz1125, zzz1126, zzz1127, zzz1128, zzz1129, new_primPlusNat2(new_primPlusNat3(Succ(new_primPlusNat3(new_primPlusNat1(zzz1121), zzz1121)), Succ(zzz1121)), Succ(zzz1121)), bd)
new_mkVBalBranch3MkVBalBranch225(zzz498, zzz499, zzz500, zzz501, zzz502, zzz503, zzz504, zzz505, zzz506, zzz507, Succ(zzz5080), Zero, bg) → new_mkVBalBranch3MkVBalBranch118(zzz498, zzz499, zzz500, zzz501, zzz502, zzz503, zzz504, zzz505, zzz506, zzz507, new_primPlusNat2(new_primPlusNat3(Succ(new_primPlusNat3(new_primPlusNat1(zzz500), zzz500)), Succ(zzz500)), Succ(zzz500)), bg)
new_mkVBalBranch3MkVBalBranch218(zzz461, zzz462, zzz463, zzz464, zzz465, zzz466, zzz467, zzz468, zzz469, zzz470, zzz471, bb) → new_mkVBalBranch3MkVBalBranch110(zzz461, zzz462, zzz463, zzz464, zzz465, zzz466, zzz467, zzz468, zzz469, zzz470, zzz471, new_primPlusNat2(Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat3(new_primPlusNat1(zzz463), zzz463)), zzz463))), Succ(zzz463)), bb)
new_mkVBalBranch0(zzz31, Branch(zzz510, zzz511, Pos(Zero), zzz513, zzz514), Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), h) → new_mkVBalBranch3MkVBalBranch116(zzz340, zzz341, zzz34200, zzz343, zzz344, zzz510, zzz511, zzz513, zzz514, zzz31, new_primPlusNat2(new_primPlusNat3(Succ(new_primPlusNat3(new_primPlusNat1(zzz34200), zzz34200)), Succ(zzz34200)), Succ(zzz34200)), h)
new_mkVBalBranch3MkVBalBranch222(zzz461, zzz462, zzz463, zzz464, zzz465, zzz466, zzz467, zzz468, zzz469, zzz470, zzz471, bb) → new_mkVBalBranch3MkVBalBranch110(zzz461, zzz462, zzz463, zzz464, zzz465, zzz466, zzz467, zzz468, zzz469, zzz470, zzz471, new_primPlusNat2(Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat3(new_primPlusNat1(zzz463), zzz463)), zzz463))), Succ(zzz463)), bb)
new_mkVBalBranch3MkVBalBranch215(zzz340, zzz341, Pos(Succ(Succ(zzz342000))), zzz343, zzz344, zzz510, zzz511, Zero, zzz513, zzz514, zzz31, Succ(Succ(zzz6600)), h) → new_mkVBalBranch3MkVBalBranch217(zzz340, zzz341, Succ(zzz342000), zzz343, zzz344, zzz510, zzz511, zzz513, zzz514, zzz31, Succ(zzz6600), zzz342000, h)
new_mkVBalBranch3MkVBalBranch117(zzz340, zzz341, zzz34200, zzz343, zzz344, zzz510, zzz511, zzz513, zzz514, zzz31, Succ(zzz1240), h) → new_mkVBalBranch0(zzz31, zzz514, Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), h)
new_mkVBalBranch3MkVBalBranch120(zzz2050, zzz2051, zzz2052, zzz2053, zzz2054, zzz2055, zzz2056, zzz2057, zzz2058, zzz2059, zzz2060, Succ(zzz20610), Succ(zzz20620), be) → new_mkVBalBranch3MkVBalBranch120(zzz2050, zzz2051, zzz2052, zzz2053, zzz2054, zzz2055, zzz2056, zzz2057, zzz2058, zzz2059, zzz2060, zzz20610, zzz20620, be)
new_mkVBalBranch3MkVBalBranch217(zzz473, zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, zzz481, zzz482, Zero, Zero, bh) → new_mkVBalBranch3MkVBalBranch233(zzz473, zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, zzz481, zzz482, bh)
new_mkVBalBranch3MkVBalBranch216(zzz1105, zzz1106, zzz1107, zzz1108, zzz1109, zzz1110, zzz1111, zzz1112, zzz1113, zzz1114, zzz1115, Succ(zzz11160), Succ(zzz11170), ba) → new_mkVBalBranch3MkVBalBranch216(zzz1105, zzz1106, zzz1107, zzz1108, zzz1109, zzz1110, zzz1111, zzz1112, zzz1113, zzz1114, zzz1115, zzz11160, zzz11170, ba)
new_mkVBalBranch3MkVBalBranch223(zzz340, zzz341, Pos(zzz3420), zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, Succ(zzz670), h) → new_mkVBalBranch0(zzz31, Branch(zzz510, zzz511, Neg(Succ(zzz51200)), zzz513, zzz514), zzz343, h)
new_mkVBalBranch3MkVBalBranch19(zzz340, zzz341, zzz34200, zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, Zero, h) → new_mkVBalBranch3MkVBalBranch122(zzz340, zzz341, zzz34200, zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, h)
new_mkVBalBranch3MkVBalBranch225(zzz498, zzz499, zzz500, zzz501, zzz502, zzz503, zzz504, zzz505, zzz506, zzz507, Succ(zzz5080), Succ(zzz5090), bg) → new_mkVBalBranch3MkVBalBranch225(zzz498, zzz499, zzz500, zzz501, zzz502, zzz503, zzz504, zzz505, zzz506, zzz507, zzz5080, zzz5090, bg)
new_mkVBalBranch3MkVBalBranch19(zzz340, zzz341, zzz34200, zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, Succ(zzz1410), h) → new_mkVBalBranch0(zzz31, zzz514, Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), h)
new_mkVBalBranch3MkVBalBranch224(zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, zzz1125, zzz1126, zzz1127, zzz1128, zzz1129, Zero, Succ(zzz11310), bd) → new_mkVBalBranch3MkVBalBranch227(zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, zzz1125, zzz1126, zzz1127, zzz1128, zzz1129, bd)
new_mkVBalBranch3MkVBalBranch224(zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, zzz1125, zzz1126, zzz1127, zzz1128, zzz1129, Zero, Zero, bd) → new_mkVBalBranch3MkVBalBranch229(zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, zzz1125, zzz1126, zzz1127, zzz1128, zzz1129, bd)
new_mkVBalBranch3MkVBalBranch223(zzz340, zzz341, Neg(Succ(Succ(Zero))), zzz343, zzz344, zzz510, zzz511, Zero, zzz513, zzz514, zzz31, Succ(Succ(zzz6700)), h) → new_mkVBalBranch3MkVBalBranch225(zzz340, zzz341, Succ(Zero), zzz343, zzz344, zzz510, zzz511, zzz513, zzz514, zzz31, Zero, Succ(zzz6700), h)
new_mkVBalBranch3MkVBalBranch223(zzz340, zzz341, Neg(Succ(Succ(Succ(zzz3420000)))), zzz343, zzz344, zzz510, zzz511, Succ(zzz512000), zzz513, zzz514, zzz31, Succ(Succ(zzz6700)), h) → new_mkVBalBranch3MkVBalBranch224(zzz340, zzz341, Succ(Succ(zzz3420000)), zzz343, zzz344, zzz510, zzz511, zzz512000, zzz513, zzz514, zzz31, Succ(zzz3420000), Succ(Succ(new_primPlusNat2(zzz6700, zzz512000))), h)
new_mkVBalBranch3MkVBalBranch115(zzz1986, zzz1987, zzz1988, zzz1989, zzz1990, zzz1991, zzz1992, zzz1993, zzz1994, zzz1995, zzz1996, Succ(zzz19970), Succ(zzz19980), bc) → new_mkVBalBranch3MkVBalBranch115(zzz1986, zzz1987, zzz1988, zzz1989, zzz1990, zzz1991, zzz1992, zzz1993, zzz1994, zzz1995, zzz1996, zzz19970, zzz19980, bc)
new_mkVBalBranch3MkVBalBranch215(zzz340, zzz341, Neg(Zero), zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, Succ(zzz660), h) → new_mkVBalBranch0(zzz31, zzz514, Branch(zzz340, zzz341, Neg(Zero), zzz343, zzz344), h)
new_mkVBalBranch3MkVBalBranch118(zzz498, zzz499, zzz500, zzz501, zzz502, zzz503, zzz504, zzz505, zzz506, zzz507, Succ(zzz8040), bg) → new_mkVBalBranch3MkVBalBranch120(zzz498, zzz499, zzz500, zzz501, zzz502, zzz503, zzz504, Zero, zzz505, zzz506, zzz507, Succ(Zero), Succ(zzz8040), bg)
new_mkVBalBranch3MkVBalBranch216(zzz1105, zzz1106, zzz1107, zzz1108, zzz1109, zzz1110, zzz1111, zzz1112, zzz1113, zzz1114, zzz1115, Succ(zzz11160), Zero, ba) → new_mkVBalBranch3MkVBalBranch218(zzz1105, zzz1106, zzz1107, zzz1108, zzz1109, zzz1110, zzz1111, zzz1112, zzz1113, zzz1114, zzz1115, ba)
new_mkVBalBranch3MkVBalBranch216(zzz1105, zzz1106, zzz1107, zzz1108, zzz1109, zzz1110, zzz1111, zzz1112, zzz1113, zzz1114, zzz1115, Zero, Zero, ba) → new_mkVBalBranch3MkVBalBranch222(zzz1105, zzz1106, zzz1107, zzz1108, zzz1109, zzz1110, zzz1111, zzz1112, zzz1113, zzz1114, zzz1115, ba)
new_mkVBalBranch3MkVBalBranch18(zzz340, zzz341, zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, Zero, h) → new_mkVBalBranch3MkVBalBranch115(zzz340, zzz341, Zero, zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, Zero, Succ(zzz51200), h)
new_mkVBalBranch3MkVBalBranch119(zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, zzz1125, zzz1126, zzz1127, zzz1128, zzz1129, Succ(zzz12130), bd) → new_mkVBalBranch3MkVBalBranch120(zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, zzz1125, Succ(zzz1126), zzz1127, zzz1128, zzz1129, Succ(Succ(zzz1126)), Succ(zzz12130), bd)

The TRS R consists of the following rules:

new_primPlusNat1(Zero) → Zero
new_primPlusNat1(Succ(zzz62000)) → Succ(Succ(new_primPlusNat1(zzz62000)))
new_primPlusNat3(zzz90, Succ(zzz910)) → Succ(Succ(new_primPlusNat2(zzz90, zzz910)))
new_primPlusNat3(zzz90, Zero) → Succ(zzz90)
new_primPlusNat2(Succ(zzz900), Succ(zzz9100)) → Succ(Succ(new_primPlusNat2(zzz900, zzz9100)))
new_primPlusNat2(Zero, Succ(zzz9100)) → Succ(zzz9100)
new_primPlusNat2(Zero, Zero) → Zero
new_primPlusNat2(Succ(zzz900), Zero) → Succ(zzz900)

The set Q consists of the following terms:

new_primPlusNat2(Zero, Succ(x0))
new_primPlusNat3(x0, Succ(x1))
new_primPlusNat2(Succ(x0), Succ(x1))
new_primPlusNat3(x0, Zero)
new_primPlusNat1(Zero)
new_primPlusNat2(Zero, Zero)
new_primPlusNat1(Succ(x0))
new_primPlusNat2(Succ(x0), Zero)

We have to consider all minimal (P,Q,R)-chains.
By rewriting [15] the rule new_mkVBalBranch3MkVBalBranch233(zzz473, zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, zzz481, zzz482, bh) → new_mkVBalBranch3MkVBalBranch121(zzz473, zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, zzz481, zzz482, new_primPlusNat2(new_primPlusNat3(Succ(new_primPlusNat3(new_primPlusNat1(zzz475), zzz475)), Succ(zzz475)), Succ(zzz475)), bh) at position [10,0] we obtained the following new rules:

new_mkVBalBranch3MkVBalBranch233(zzz473, zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, zzz481, zzz482, bh) → new_mkVBalBranch3MkVBalBranch121(zzz473, zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, zzz481, zzz482, new_primPlusNat2(Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat3(new_primPlusNat1(zzz475), zzz475)), zzz475))), Succ(zzz475)), bh)



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

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

new_mkVBalBranch3MkVBalBranch225(zzz498, zzz499, zzz500, zzz501, zzz502, zzz503, zzz504, zzz505, zzz506, zzz507, Zero, Zero, bg) → new_mkVBalBranch3MkVBalBranch230(zzz498, zzz499, zzz500, zzz501, zzz502, zzz503, zzz504, zzz505, zzz506, zzz507, bg)
new_mkVBalBranch3MkVBalBranch18(zzz340, zzz341, zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, Succ(zzz1480), h) → new_mkVBalBranch3MkVBalBranch115(zzz340, zzz341, Zero, zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, Succ(zzz1480), Succ(zzz51200), h)
new_mkVBalBranch0(zzz31, Branch(zzz510, zzz511, Neg(Zero), zzz513, zzz514), Branch(zzz340, zzz341, Pos(Succ(zzz34200)), zzz343, zzz344), h) → new_mkVBalBranch0(zzz31, Branch(zzz510, zzz511, Neg(Zero), zzz513, zzz514), zzz343, h)
new_mkVBalBranch3MkVBalBranch215(zzz340, zzz341, Pos(Succ(Succ(zzz342000))), zzz343, zzz344, zzz510, zzz511, Succ(zzz512000), zzz513, zzz514, zzz31, Succ(Succ(zzz6600)), h) → new_mkVBalBranch3MkVBalBranch216(zzz340, zzz341, Succ(zzz342000), zzz343, zzz344, zzz510, zzz511, zzz512000, zzz513, zzz514, zzz31, Succ(Succ(new_primPlusNat2(zzz6600, zzz512000))), zzz342000, h)
new_mkVBalBranch3MkVBalBranch223(zzz340, zzz341, Neg(Succ(Succ(Succ(zzz3420000)))), zzz343, zzz344, zzz510, zzz511, Zero, zzz513, zzz514, zzz31, Succ(Succ(zzz6700)), h) → new_mkVBalBranch3MkVBalBranch225(zzz340, zzz341, Succ(Succ(zzz3420000)), zzz343, zzz344, zzz510, zzz511, zzz513, zzz514, zzz31, Succ(zzz3420000), Succ(zzz6700), h)
new_mkVBalBranch3MkVBalBranch120(zzz2050, zzz2051, zzz2052, zzz2053, zzz2054, zzz2055, zzz2056, zzz2057, zzz2058, zzz2059, zzz2060, Zero, Succ(zzz20620), be) → new_mkVBalBranch0(zzz2060, zzz2059, Branch(zzz2050, zzz2051, Neg(Succ(zzz2052)), zzz2053, zzz2054), be)
new_mkVBalBranch3MkVBalBranch121(zzz473, zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, zzz481, zzz482, Succ(zzz7390), bh) → new_mkVBalBranch3MkVBalBranch115(zzz473, zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, Zero, zzz480, zzz481, zzz482, Succ(zzz7390), Succ(Zero), bh)
new_mkVBalBranch0(zzz31, Branch(zzz510, zzz511, Pos(Zero), zzz513, zzz514), Branch(zzz340, zzz341, Pos(Succ(zzz34200)), zzz343, zzz344), h) → new_mkVBalBranch0(zzz31, Branch(zzz510, zzz511, Pos(Zero), zzz513, zzz514), zzz343, h)
new_mkVBalBranch0(zzz31, Branch(zzz510, zzz511, Pos(Succ(zzz51200)), zzz513, zzz514), Branch(zzz340, zzz341, zzz342, zzz343, zzz344), h) → new_mkVBalBranch3MkVBalBranch215(zzz340, zzz341, zzz342, zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat3(new_primPlusNat1(zzz51200), zzz51200)), zzz51200))), h)
new_mkVBalBranch3MkVBalBranch223(zzz340, zzz341, Neg(Succ(Succ(Zero))), zzz343, zzz344, zzz510, zzz511, Succ(zzz512000), zzz513, zzz514, zzz31, Succ(Succ(zzz6700)), h) → new_mkVBalBranch3MkVBalBranch224(zzz340, zzz341, Succ(Zero), zzz343, zzz344, zzz510, zzz511, zzz512000, zzz513, zzz514, zzz31, Zero, Succ(Succ(new_primPlusNat2(zzz6700, zzz512000))), h)
new_mkVBalBranch3MkVBalBranch224(zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, zzz1125, zzz1126, zzz1127, zzz1128, zzz1129, Succ(zzz11300), Succ(zzz11310), bd) → new_mkVBalBranch3MkVBalBranch224(zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, zzz1125, zzz1126, zzz1127, zzz1128, zzz1129, zzz11300, zzz11310, bd)
new_mkVBalBranch3MkVBalBranch217(zzz473, zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, zzz481, zzz482, Zero, Succ(zzz4840), bh) → new_mkVBalBranch0(zzz482, Branch(zzz478, zzz479, Pos(Succ(Zero)), zzz480, zzz481), zzz476, bh)
new_mkVBalBranch3MkVBalBranch224(zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, zzz1125, zzz1126, zzz1127, zzz1128, zzz1129, Succ(zzz11300), Zero, bd) → new_mkVBalBranch3MkVBalBranch119(zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, zzz1125, zzz1126, zzz1127, zzz1128, zzz1129, new_primPlusNat2(Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat3(new_primPlusNat1(zzz1121), zzz1121)), zzz1121))), Succ(zzz1121)), bd)
new_mkVBalBranch3MkVBalBranch110(zzz461, zzz462, zzz463, zzz464, zzz465, zzz466, zzz467, zzz468, zzz469, zzz470, zzz471, Succ(zzz5800), bb) → new_mkVBalBranch3MkVBalBranch115(zzz461, zzz462, zzz463, zzz464, zzz465, zzz466, zzz467, Succ(zzz468), zzz469, zzz470, zzz471, Succ(zzz5800), Succ(Succ(zzz468)), bb)
new_mkVBalBranch3MkVBalBranch227(zzz486, zzz487, zzz488, zzz489, zzz490, zzz491, zzz492, zzz493, zzz494, zzz495, zzz496, bf) → new_mkVBalBranch0(zzz496, Branch(zzz491, zzz492, Neg(Succ(Succ(zzz493))), zzz494, zzz495), zzz489, bf)
new_mkVBalBranch3MkVBalBranch215(zzz340, zzz341, Pos(Zero), zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, Succ(zzz660), h) → new_mkVBalBranch0(zzz31, zzz514, Branch(zzz340, zzz341, Pos(Zero), zzz343, zzz344), h)
new_mkVBalBranch3MkVBalBranch223(zzz340, zzz341, Neg(Zero), zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, Succ(zzz670), h) → new_mkVBalBranch0(zzz31, Branch(zzz510, zzz511, Neg(Succ(zzz51200)), zzz513, zzz514), zzz343, h)
new_mkVBalBranch3MkVBalBranch216(zzz1105, zzz1106, zzz1107, zzz1108, zzz1109, zzz1110, zzz1111, zzz1112, zzz1113, zzz1114, zzz1115, Zero, Succ(zzz11170), ba) → new_mkVBalBranch0(zzz1115, Branch(zzz1110, zzz1111, Pos(Succ(Succ(zzz1112))), zzz1113, zzz1114), zzz1108, ba)
new_mkVBalBranch3MkVBalBranch115(zzz1986, zzz1987, zzz1988, zzz1989, zzz1990, zzz1991, zzz1992, zzz1993, zzz1994, zzz1995, zzz1996, Zero, Succ(zzz19980), bc) → new_mkVBalBranch0(zzz1996, zzz1995, Branch(zzz1986, zzz1987, Pos(Succ(zzz1988)), zzz1989, zzz1990), bc)
new_mkVBalBranch3MkVBalBranch233(zzz473, zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, zzz481, zzz482, bh) → new_mkVBalBranch3MkVBalBranch121(zzz473, zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, zzz481, zzz482, new_primPlusNat2(Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat3(new_primPlusNat1(zzz475), zzz475)), zzz475))), Succ(zzz475)), bh)
new_mkVBalBranch3MkVBalBranch215(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, Succ(zzz660), h) → new_mkVBalBranch3MkVBalBranch19(zzz340, zzz341, zzz34200, zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, new_primPlusNat2(new_primPlusNat3(Succ(new_primPlusNat3(new_primPlusNat1(zzz34200), zzz34200)), Succ(zzz34200)), Succ(zzz34200)), h)
new_mkVBalBranch3MkVBalBranch215(zzz340, zzz341, Pos(Succ(Zero)), zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, Succ(zzz660), h) → new_mkVBalBranch3MkVBalBranch18(zzz340, zzz341, zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, new_primPlusNat2(new_primPlusNat3(Succ(new_primPlusNat3(new_primPlusNat1(Zero), Zero)), Succ(Zero)), Succ(Zero)), h)
new_mkVBalBranch3MkVBalBranch230(zzz498, zzz499, zzz500, zzz501, zzz502, zzz503, zzz504, zzz505, zzz506, zzz507, bg) → new_mkVBalBranch3MkVBalBranch118(zzz498, zzz499, zzz500, zzz501, zzz502, zzz503, zzz504, zzz505, zzz506, zzz507, new_primPlusNat2(Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat3(new_primPlusNat1(zzz500), zzz500)), zzz500))), Succ(zzz500)), bg)
new_mkVBalBranch3MkVBalBranch122(zzz340, zzz341, zzz34200, zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, h) → new_mkVBalBranch0(zzz31, zzz514, Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), h)
new_mkVBalBranch3MkVBalBranch217(zzz473, zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, zzz481, zzz482, Succ(zzz4830), Succ(zzz4840), bh) → new_mkVBalBranch3MkVBalBranch217(zzz473, zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, zzz481, zzz482, zzz4830, zzz4840, bh)
new_mkVBalBranch3MkVBalBranch116(zzz340, zzz341, zzz34200, zzz343, zzz344, zzz510, zzz511, zzz513, zzz514, zzz31, Succ(zzz1200), h) → new_mkVBalBranch0(zzz31, zzz514, Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), h)
new_mkVBalBranch3MkVBalBranch110(zzz461, zzz462, zzz463, zzz464, zzz465, zzz466, zzz467, zzz468, zzz469, zzz470, zzz471, Zero, bb) → new_mkVBalBranch3MkVBalBranch115(zzz461, zzz462, zzz463, zzz464, zzz465, zzz466, zzz467, Succ(zzz468), zzz469, zzz470, zzz471, Zero, Succ(Succ(zzz468)), bb)
new_mkVBalBranch3MkVBalBranch225(zzz498, zzz499, zzz500, zzz501, zzz502, zzz503, zzz504, zzz505, zzz506, zzz507, Zero, Succ(zzz5090), bg) → new_mkVBalBranch0(zzz507, Branch(zzz503, zzz504, Neg(Succ(Zero)), zzz505, zzz506), zzz501, bg)
new_mkVBalBranch0(zzz31, Branch(zzz510, zzz511, Neg(Succ(zzz51200)), zzz513, zzz514), Branch(zzz340, zzz341, zzz342, zzz343, zzz344), h) → new_mkVBalBranch3MkVBalBranch223(zzz340, zzz341, zzz342, zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat3(new_primPlusNat1(zzz51200), zzz51200)), zzz51200))), h)
new_mkVBalBranch0(zzz31, Branch(zzz510, zzz511, Neg(Zero), zzz513, zzz514), Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), h) → new_mkVBalBranch3MkVBalBranch117(zzz340, zzz341, zzz34200, zzz343, zzz344, zzz510, zzz511, zzz513, zzz514, zzz31, new_primPlusNat2(new_primPlusNat3(Succ(new_primPlusNat3(new_primPlusNat1(zzz34200), zzz34200)), Succ(zzz34200)), Succ(zzz34200)), h)
new_mkVBalBranch3MkVBalBranch217(zzz473, zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, zzz481, zzz482, Succ(zzz4830), Zero, bh) → new_mkVBalBranch3MkVBalBranch121(zzz473, zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, zzz481, zzz482, new_primPlusNat2(new_primPlusNat3(Succ(new_primPlusNat3(new_primPlusNat1(zzz475), zzz475)), Succ(zzz475)), Succ(zzz475)), bh)
new_mkVBalBranch3MkVBalBranch121(zzz473, zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, zzz481, zzz482, Zero, bh) → new_mkVBalBranch3MkVBalBranch115(zzz473, zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, Zero, zzz480, zzz481, zzz482, Zero, Succ(Zero), bh)
new_mkVBalBranch3MkVBalBranch223(zzz340, zzz341, Neg(Succ(Zero)), zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, Succ(zzz670), h) → new_mkVBalBranch0(zzz31, Branch(zzz510, zzz511, Neg(Succ(zzz51200)), zzz513, zzz514), zzz343, h)
new_mkVBalBranch3MkVBalBranch225(zzz498, zzz499, zzz500, zzz501, zzz502, zzz503, zzz504, zzz505, zzz506, zzz507, Succ(zzz5080), Zero, bg) → new_mkVBalBranch3MkVBalBranch118(zzz498, zzz499, zzz500, zzz501, zzz502, zzz503, zzz504, zzz505, zzz506, zzz507, new_primPlusNat2(new_primPlusNat3(Succ(new_primPlusNat3(new_primPlusNat1(zzz500), zzz500)), Succ(zzz500)), Succ(zzz500)), bg)
new_mkVBalBranch3MkVBalBranch229(zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, zzz1125, zzz1126, zzz1127, zzz1128, zzz1129, bd) → new_mkVBalBranch3MkVBalBranch119(zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, zzz1125, zzz1126, zzz1127, zzz1128, zzz1129, new_primPlusNat2(new_primPlusNat3(Succ(new_primPlusNat3(new_primPlusNat1(zzz1121), zzz1121)), Succ(zzz1121)), Succ(zzz1121)), bd)
new_mkVBalBranch3MkVBalBranch218(zzz461, zzz462, zzz463, zzz464, zzz465, zzz466, zzz467, zzz468, zzz469, zzz470, zzz471, bb) → new_mkVBalBranch3MkVBalBranch110(zzz461, zzz462, zzz463, zzz464, zzz465, zzz466, zzz467, zzz468, zzz469, zzz470, zzz471, new_primPlusNat2(Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat3(new_primPlusNat1(zzz463), zzz463)), zzz463))), Succ(zzz463)), bb)
new_mkVBalBranch0(zzz31, Branch(zzz510, zzz511, Pos(Zero), zzz513, zzz514), Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), h) → new_mkVBalBranch3MkVBalBranch116(zzz340, zzz341, zzz34200, zzz343, zzz344, zzz510, zzz511, zzz513, zzz514, zzz31, new_primPlusNat2(new_primPlusNat3(Succ(new_primPlusNat3(new_primPlusNat1(zzz34200), zzz34200)), Succ(zzz34200)), Succ(zzz34200)), h)
new_mkVBalBranch3MkVBalBranch222(zzz461, zzz462, zzz463, zzz464, zzz465, zzz466, zzz467, zzz468, zzz469, zzz470, zzz471, bb) → new_mkVBalBranch3MkVBalBranch110(zzz461, zzz462, zzz463, zzz464, zzz465, zzz466, zzz467, zzz468, zzz469, zzz470, zzz471, new_primPlusNat2(Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat3(new_primPlusNat1(zzz463), zzz463)), zzz463))), Succ(zzz463)), bb)
new_mkVBalBranch3MkVBalBranch215(zzz340, zzz341, Pos(Succ(Succ(zzz342000))), zzz343, zzz344, zzz510, zzz511, Zero, zzz513, zzz514, zzz31, Succ(Succ(zzz6600)), h) → new_mkVBalBranch3MkVBalBranch217(zzz340, zzz341, Succ(zzz342000), zzz343, zzz344, zzz510, zzz511, zzz513, zzz514, zzz31, Succ(zzz6600), zzz342000, h)
new_mkVBalBranch3MkVBalBranch117(zzz340, zzz341, zzz34200, zzz343, zzz344, zzz510, zzz511, zzz513, zzz514, zzz31, Succ(zzz1240), h) → new_mkVBalBranch0(zzz31, zzz514, Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), h)
new_mkVBalBranch3MkVBalBranch217(zzz473, zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, zzz481, zzz482, Zero, Zero, bh) → new_mkVBalBranch3MkVBalBranch233(zzz473, zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, zzz481, zzz482, bh)
new_mkVBalBranch3MkVBalBranch120(zzz2050, zzz2051, zzz2052, zzz2053, zzz2054, zzz2055, zzz2056, zzz2057, zzz2058, zzz2059, zzz2060, Succ(zzz20610), Succ(zzz20620), be) → new_mkVBalBranch3MkVBalBranch120(zzz2050, zzz2051, zzz2052, zzz2053, zzz2054, zzz2055, zzz2056, zzz2057, zzz2058, zzz2059, zzz2060, zzz20610, zzz20620, be)
new_mkVBalBranch3MkVBalBranch223(zzz340, zzz341, Pos(zzz3420), zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, Succ(zzz670), h) → new_mkVBalBranch0(zzz31, Branch(zzz510, zzz511, Neg(Succ(zzz51200)), zzz513, zzz514), zzz343, h)
new_mkVBalBranch3MkVBalBranch216(zzz1105, zzz1106, zzz1107, zzz1108, zzz1109, zzz1110, zzz1111, zzz1112, zzz1113, zzz1114, zzz1115, Succ(zzz11160), Succ(zzz11170), ba) → new_mkVBalBranch3MkVBalBranch216(zzz1105, zzz1106, zzz1107, zzz1108, zzz1109, zzz1110, zzz1111, zzz1112, zzz1113, zzz1114, zzz1115, zzz11160, zzz11170, ba)
new_mkVBalBranch3MkVBalBranch19(zzz340, zzz341, zzz34200, zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, Zero, h) → new_mkVBalBranch3MkVBalBranch122(zzz340, zzz341, zzz34200, zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, h)
new_mkVBalBranch3MkVBalBranch225(zzz498, zzz499, zzz500, zzz501, zzz502, zzz503, zzz504, zzz505, zzz506, zzz507, Succ(zzz5080), Succ(zzz5090), bg) → new_mkVBalBranch3MkVBalBranch225(zzz498, zzz499, zzz500, zzz501, zzz502, zzz503, zzz504, zzz505, zzz506, zzz507, zzz5080, zzz5090, bg)
new_mkVBalBranch3MkVBalBranch19(zzz340, zzz341, zzz34200, zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, Succ(zzz1410), h) → new_mkVBalBranch0(zzz31, zzz514, Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), h)
new_mkVBalBranch3MkVBalBranch224(zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, zzz1125, zzz1126, zzz1127, zzz1128, zzz1129, Zero, Zero, bd) → new_mkVBalBranch3MkVBalBranch229(zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, zzz1125, zzz1126, zzz1127, zzz1128, zzz1129, bd)
new_mkVBalBranch3MkVBalBranch224(zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, zzz1125, zzz1126, zzz1127, zzz1128, zzz1129, Zero, Succ(zzz11310), bd) → new_mkVBalBranch3MkVBalBranch227(zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, zzz1125, zzz1126, zzz1127, zzz1128, zzz1129, bd)
new_mkVBalBranch3MkVBalBranch223(zzz340, zzz341, Neg(Succ(Succ(Succ(zzz3420000)))), zzz343, zzz344, zzz510, zzz511, Succ(zzz512000), zzz513, zzz514, zzz31, Succ(Succ(zzz6700)), h) → new_mkVBalBranch3MkVBalBranch224(zzz340, zzz341, Succ(Succ(zzz3420000)), zzz343, zzz344, zzz510, zzz511, zzz512000, zzz513, zzz514, zzz31, Succ(zzz3420000), Succ(Succ(new_primPlusNat2(zzz6700, zzz512000))), h)
new_mkVBalBranch3MkVBalBranch223(zzz340, zzz341, Neg(Succ(Succ(Zero))), zzz343, zzz344, zzz510, zzz511, Zero, zzz513, zzz514, zzz31, Succ(Succ(zzz6700)), h) → new_mkVBalBranch3MkVBalBranch225(zzz340, zzz341, Succ(Zero), zzz343, zzz344, zzz510, zzz511, zzz513, zzz514, zzz31, Zero, Succ(zzz6700), h)
new_mkVBalBranch3MkVBalBranch115(zzz1986, zzz1987, zzz1988, zzz1989, zzz1990, zzz1991, zzz1992, zzz1993, zzz1994, zzz1995, zzz1996, Succ(zzz19970), Succ(zzz19980), bc) → new_mkVBalBranch3MkVBalBranch115(zzz1986, zzz1987, zzz1988, zzz1989, zzz1990, zzz1991, zzz1992, zzz1993, zzz1994, zzz1995, zzz1996, zzz19970, zzz19980, bc)
new_mkVBalBranch3MkVBalBranch215(zzz340, zzz341, Neg(Zero), zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, Succ(zzz660), h) → new_mkVBalBranch0(zzz31, zzz514, Branch(zzz340, zzz341, Neg(Zero), zzz343, zzz344), h)
new_mkVBalBranch3MkVBalBranch118(zzz498, zzz499, zzz500, zzz501, zzz502, zzz503, zzz504, zzz505, zzz506, zzz507, Succ(zzz8040), bg) → new_mkVBalBranch3MkVBalBranch120(zzz498, zzz499, zzz500, zzz501, zzz502, zzz503, zzz504, Zero, zzz505, zzz506, zzz507, Succ(Zero), Succ(zzz8040), bg)
new_mkVBalBranch3MkVBalBranch216(zzz1105, zzz1106, zzz1107, zzz1108, zzz1109, zzz1110, zzz1111, zzz1112, zzz1113, zzz1114, zzz1115, Succ(zzz11160), Zero, ba) → new_mkVBalBranch3MkVBalBranch218(zzz1105, zzz1106, zzz1107, zzz1108, zzz1109, zzz1110, zzz1111, zzz1112, zzz1113, zzz1114, zzz1115, ba)
new_mkVBalBranch3MkVBalBranch216(zzz1105, zzz1106, zzz1107, zzz1108, zzz1109, zzz1110, zzz1111, zzz1112, zzz1113, zzz1114, zzz1115, Zero, Zero, ba) → new_mkVBalBranch3MkVBalBranch222(zzz1105, zzz1106, zzz1107, zzz1108, zzz1109, zzz1110, zzz1111, zzz1112, zzz1113, zzz1114, zzz1115, ba)
new_mkVBalBranch3MkVBalBranch119(zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, zzz1125, zzz1126, zzz1127, zzz1128, zzz1129, Succ(zzz12130), bd) → new_mkVBalBranch3MkVBalBranch120(zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, zzz1125, Succ(zzz1126), zzz1127, zzz1128, zzz1129, Succ(Succ(zzz1126)), Succ(zzz12130), bd)
new_mkVBalBranch3MkVBalBranch18(zzz340, zzz341, zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, Zero, h) → new_mkVBalBranch3MkVBalBranch115(zzz340, zzz341, Zero, zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, Zero, Succ(zzz51200), h)

The TRS R consists of the following rules:

new_primPlusNat1(Zero) → Zero
new_primPlusNat1(Succ(zzz62000)) → Succ(Succ(new_primPlusNat1(zzz62000)))
new_primPlusNat3(zzz90, Succ(zzz910)) → Succ(Succ(new_primPlusNat2(zzz90, zzz910)))
new_primPlusNat3(zzz90, Zero) → Succ(zzz90)
new_primPlusNat2(Succ(zzz900), Succ(zzz9100)) → Succ(Succ(new_primPlusNat2(zzz900, zzz9100)))
new_primPlusNat2(Zero, Succ(zzz9100)) → Succ(zzz9100)
new_primPlusNat2(Zero, Zero) → Zero
new_primPlusNat2(Succ(zzz900), Zero) → Succ(zzz900)

The set Q consists of the following terms:

new_primPlusNat2(Zero, Succ(x0))
new_primPlusNat3(x0, Succ(x1))
new_primPlusNat2(Succ(x0), Succ(x1))
new_primPlusNat3(x0, Zero)
new_primPlusNat1(Zero)
new_primPlusNat2(Zero, Zero)
new_primPlusNat1(Succ(x0))
new_primPlusNat2(Succ(x0), Zero)

We have to consider all minimal (P,Q,R)-chains.
By rewriting [15] the rule new_mkVBalBranch3MkVBalBranch215(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, Succ(zzz660), h) → new_mkVBalBranch3MkVBalBranch19(zzz340, zzz341, zzz34200, zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, new_primPlusNat2(new_primPlusNat3(Succ(new_primPlusNat3(new_primPlusNat1(zzz34200), zzz34200)), Succ(zzz34200)), Succ(zzz34200)), h) at position [11,0] we obtained the following new rules:

new_mkVBalBranch3MkVBalBranch215(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, Succ(zzz660), h) → new_mkVBalBranch3MkVBalBranch19(zzz340, zzz341, zzz34200, zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, new_primPlusNat2(Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat3(new_primPlusNat1(zzz34200), zzz34200)), 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
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                    ↳ DependencyGraphProof
                                      ↳ QDP
                                        ↳ Rewriting
                                          ↳ QDP
                                            ↳ Rewriting
                                              ↳ QDP
                                                ↳ Rewriting
                                                  ↳ QDP
                                                    ↳ Rewriting
                                                      ↳ QDP
                                                        ↳ Rewriting
                                                          ↳ QDP
                                                            ↳ Rewriting
                                                              ↳ QDP
                                                                ↳ Rewriting
                                                                  ↳ QDP
                                                                    ↳ Rewriting
                                                                      ↳ QDP
                                                                        ↳ Rewriting
                                                                          ↳ QDP
                                                                            ↳ Rewriting
                                                                              ↳ QDP
                                                                                ↳ Rewriting
                                                                                  ↳ QDP
                                                                                    ↳ Rewriting
                                                                                      ↳ QDP
                                                                                        ↳ Rewriting
                                                                                          ↳ QDP
                                                                                            ↳ Rewriting
                                                                                              ↳ QDP
                                                                                                ↳ Rewriting
                                                                                                  ↳ QDP
                                                                                                    ↳ Rewriting
                                                                                                      ↳ QDP
                                                                                                        ↳ Rewriting
                                                                                                          ↳ QDP
                                                                                                            ↳ UsableRulesProof
                                                                                                              ↳ QDP
                                                                                                                ↳ QReductionProof
                                                                                                                  ↳ QDP
                                                                                                                    ↳ Rewriting
                                                                                                                      ↳ QDP
                                                                                                                        ↳ Rewriting
                                                                                                                          ↳ QDP
                                                                                                                            ↳ DependencyGraphProof
                                                                                                                              ↳ QDP
                                                                                                                                ↳ Rewriting
                                                                                                                                  ↳ QDP
                                                                                                                                    ↳ Rewriting
                                                                                                                                      ↳ QDP
                                                                                                                                        ↳ DependencyGraphProof
                                                                                                                                          ↳ QDP
                                                                                                                                            ↳ Rewriting
                                                                                                                                              ↳ QDP
                                                                                                                                                ↳ Rewriting
                                                                                                                                                  ↳ QDP
                                                                                                                                                    ↳ Rewriting
                                                                                                                                                      ↳ QDP
                                                                                                                                                        ↳ Rewriting
                                                                                                                                                          ↳ QDP
                                                                                                                                                            ↳ Rewriting
                                                                                                                                                              ↳ QDP
                                                                                                                                                                ↳ Rewriting
                                                                                                                                                                  ↳ QDP
                                                                                                                                                                    ↳ Rewriting
                                                                                                                                                                      ↳ QDP
                                                                                                                                                                        ↳ Rewriting
                                                                                                                                                                          ↳ QDP
                                                                                                                                                                            ↳ Rewriting
                                                                                                                                                                              ↳ QDP
                                                                                                                                                                                ↳ Rewriting
                                                                                                                                                                                  ↳ QDP
                                                                                                                                                                                    ↳ Rewriting
                                                                                                                                                                                      ↳ QDP
                                                                                                                                                                                        ↳ Rewriting
                                                                                                                                                                                          ↳ QDP
                                                                                                                                                                                            ↳ UsableRulesProof
                                                                                                                                                                                              ↳ QDP
                                                                                                                                                                                                ↳ QReductionProof
                                                                                                                                                                                                  ↳ QDP
                                                                                                                                                                                                    ↳ Rewriting
                                                                                                                                                                                                      ↳ QDP
                                                                                                                                                                                                        ↳ Rewriting
                                                                                                                                                                                                          ↳ QDP
                                                                                                                                                                                                            ↳ Rewriting
                                                                                                                                                                                                              ↳ QDP
                                                                                                                                                                                                                ↳ Rewriting
                                                                                                                                                                                                                  ↳ QDP
                                                                                                                                                                                                                    ↳ Rewriting
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP

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

new_mkVBalBranch3MkVBalBranch225(zzz498, zzz499, zzz500, zzz501, zzz502, zzz503, zzz504, zzz505, zzz506, zzz507, Zero, Zero, bg) → new_mkVBalBranch3MkVBalBranch230(zzz498, zzz499, zzz500, zzz501, zzz502, zzz503, zzz504, zzz505, zzz506, zzz507, bg)
new_mkVBalBranch3MkVBalBranch18(zzz340, zzz341, zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, Succ(zzz1480), h) → new_mkVBalBranch3MkVBalBranch115(zzz340, zzz341, Zero, zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, Succ(zzz1480), Succ(zzz51200), h)
new_mkVBalBranch3MkVBalBranch215(zzz340, zzz341, Pos(Succ(Succ(zzz342000))), zzz343, zzz344, zzz510, zzz511, Succ(zzz512000), zzz513, zzz514, zzz31, Succ(Succ(zzz6600)), h) → new_mkVBalBranch3MkVBalBranch216(zzz340, zzz341, Succ(zzz342000), zzz343, zzz344, zzz510, zzz511, zzz512000, zzz513, zzz514, zzz31, Succ(Succ(new_primPlusNat2(zzz6600, zzz512000))), zzz342000, h)
new_mkVBalBranch0(zzz31, Branch(zzz510, zzz511, Neg(Zero), zzz513, zzz514), Branch(zzz340, zzz341, Pos(Succ(zzz34200)), zzz343, zzz344), h) → new_mkVBalBranch0(zzz31, Branch(zzz510, zzz511, Neg(Zero), zzz513, zzz514), zzz343, h)
new_mkVBalBranch3MkVBalBranch223(zzz340, zzz341, Neg(Succ(Succ(Succ(zzz3420000)))), zzz343, zzz344, zzz510, zzz511, Zero, zzz513, zzz514, zzz31, Succ(Succ(zzz6700)), h) → new_mkVBalBranch3MkVBalBranch225(zzz340, zzz341, Succ(Succ(zzz3420000)), zzz343, zzz344, zzz510, zzz511, zzz513, zzz514, zzz31, Succ(zzz3420000), Succ(zzz6700), h)
new_mkVBalBranch3MkVBalBranch120(zzz2050, zzz2051, zzz2052, zzz2053, zzz2054, zzz2055, zzz2056, zzz2057, zzz2058, zzz2059, zzz2060, Zero, Succ(zzz20620), be) → new_mkVBalBranch0(zzz2060, zzz2059, Branch(zzz2050, zzz2051, Neg(Succ(zzz2052)), zzz2053, zzz2054), be)
new_mkVBalBranch3MkVBalBranch215(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, Succ(zzz660), h) → new_mkVBalBranch3MkVBalBranch19(zzz340, zzz341, zzz34200, zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, new_primPlusNat2(Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat3(new_primPlusNat1(zzz34200), zzz34200)), zzz34200))), Succ(zzz34200)), h)
new_mkVBalBranch0(zzz31, Branch(zzz510, zzz511, Pos(Zero), zzz513, zzz514), Branch(zzz340, zzz341, Pos(Succ(zzz34200)), zzz343, zzz344), h) → new_mkVBalBranch0(zzz31, Branch(zzz510, zzz511, Pos(Zero), zzz513, zzz514), zzz343, h)
new_mkVBalBranch3MkVBalBranch121(zzz473, zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, zzz481, zzz482, Succ(zzz7390), bh) → new_mkVBalBranch3MkVBalBranch115(zzz473, zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, Zero, zzz480, zzz481, zzz482, Succ(zzz7390), Succ(Zero), bh)
new_mkVBalBranch0(zzz31, Branch(zzz510, zzz511, Pos(Succ(zzz51200)), zzz513, zzz514), Branch(zzz340, zzz341, zzz342, zzz343, zzz344), h) → new_mkVBalBranch3MkVBalBranch215(zzz340, zzz341, zzz342, zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat3(new_primPlusNat1(zzz51200), zzz51200)), zzz51200))), h)
new_mkVBalBranch3MkVBalBranch223(zzz340, zzz341, Neg(Succ(Succ(Zero))), zzz343, zzz344, zzz510, zzz511, Succ(zzz512000), zzz513, zzz514, zzz31, Succ(Succ(zzz6700)), h) → new_mkVBalBranch3MkVBalBranch224(zzz340, zzz341, Succ(Zero), zzz343, zzz344, zzz510, zzz511, zzz512000, zzz513, zzz514, zzz31, Zero, Succ(Succ(new_primPlusNat2(zzz6700, zzz512000))), h)
new_mkVBalBranch3MkVBalBranch224(zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, zzz1125, zzz1126, zzz1127, zzz1128, zzz1129, Succ(zzz11300), Succ(zzz11310), bd) → new_mkVBalBranch3MkVBalBranch224(zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, zzz1125, zzz1126, zzz1127, zzz1128, zzz1129, zzz11300, zzz11310, bd)
new_mkVBalBranch3MkVBalBranch217(zzz473, zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, zzz481, zzz482, Zero, Succ(zzz4840), bh) → new_mkVBalBranch0(zzz482, Branch(zzz478, zzz479, Pos(Succ(Zero)), zzz480, zzz481), zzz476, bh)
new_mkVBalBranch3MkVBalBranch224(zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, zzz1125, zzz1126, zzz1127, zzz1128, zzz1129, Succ(zzz11300), Zero, bd) → new_mkVBalBranch3MkVBalBranch119(zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, zzz1125, zzz1126, zzz1127, zzz1128, zzz1129, new_primPlusNat2(Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat3(new_primPlusNat1(zzz1121), zzz1121)), zzz1121))), Succ(zzz1121)), bd)
new_mkVBalBranch3MkVBalBranch110(zzz461, zzz462, zzz463, zzz464, zzz465, zzz466, zzz467, zzz468, zzz469, zzz470, zzz471, Succ(zzz5800), bb) → new_mkVBalBranch3MkVBalBranch115(zzz461, zzz462, zzz463, zzz464, zzz465, zzz466, zzz467, Succ(zzz468), zzz469, zzz470, zzz471, Succ(zzz5800), Succ(Succ(zzz468)), bb)
new_mkVBalBranch3MkVBalBranch227(zzz486, zzz487, zzz488, zzz489, zzz490, zzz491, zzz492, zzz493, zzz494, zzz495, zzz496, bf) → new_mkVBalBranch0(zzz496, Branch(zzz491, zzz492, Neg(Succ(Succ(zzz493))), zzz494, zzz495), zzz489, bf)
new_mkVBalBranch3MkVBalBranch215(zzz340, zzz341, Pos(Zero), zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, Succ(zzz660), h) → new_mkVBalBranch0(zzz31, zzz514, Branch(zzz340, zzz341, Pos(Zero), zzz343, zzz344), h)
new_mkVBalBranch3MkVBalBranch223(zzz340, zzz341, Neg(Zero), zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, Succ(zzz670), h) → new_mkVBalBranch0(zzz31, Branch(zzz510, zzz511, Neg(Succ(zzz51200)), zzz513, zzz514), zzz343, h)
new_mkVBalBranch3MkVBalBranch216(zzz1105, zzz1106, zzz1107, zzz1108, zzz1109, zzz1110, zzz1111, zzz1112, zzz1113, zzz1114, zzz1115, Zero, Succ(zzz11170), ba) → new_mkVBalBranch0(zzz1115, Branch(zzz1110, zzz1111, Pos(Succ(Succ(zzz1112))), zzz1113, zzz1114), zzz1108, ba)
new_mkVBalBranch3MkVBalBranch115(zzz1986, zzz1987, zzz1988, zzz1989, zzz1990, zzz1991, zzz1992, zzz1993, zzz1994, zzz1995, zzz1996, Zero, Succ(zzz19980), bc) → new_mkVBalBranch0(zzz1996, zzz1995, Branch(zzz1986, zzz1987, Pos(Succ(zzz1988)), zzz1989, zzz1990), bc)
new_mkVBalBranch3MkVBalBranch233(zzz473, zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, zzz481, zzz482, bh) → new_mkVBalBranch3MkVBalBranch121(zzz473, zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, zzz481, zzz482, new_primPlusNat2(Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat3(new_primPlusNat1(zzz475), zzz475)), zzz475))), Succ(zzz475)), bh)
new_mkVBalBranch3MkVBalBranch215(zzz340, zzz341, Pos(Succ(Zero)), zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, Succ(zzz660), h) → new_mkVBalBranch3MkVBalBranch18(zzz340, zzz341, zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, new_primPlusNat2(new_primPlusNat3(Succ(new_primPlusNat3(new_primPlusNat1(Zero), Zero)), Succ(Zero)), Succ(Zero)), h)
new_mkVBalBranch3MkVBalBranch122(zzz340, zzz341, zzz34200, zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, h) → new_mkVBalBranch0(zzz31, zzz514, Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), h)
new_mkVBalBranch3MkVBalBranch230(zzz498, zzz499, zzz500, zzz501, zzz502, zzz503, zzz504, zzz505, zzz506, zzz507, bg) → new_mkVBalBranch3MkVBalBranch118(zzz498, zzz499, zzz500, zzz501, zzz502, zzz503, zzz504, zzz505, zzz506, zzz507, new_primPlusNat2(Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat3(new_primPlusNat1(zzz500), zzz500)), zzz500))), Succ(zzz500)), bg)
new_mkVBalBranch3MkVBalBranch217(zzz473, zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, zzz481, zzz482, Succ(zzz4830), Succ(zzz4840), bh) → new_mkVBalBranch3MkVBalBranch217(zzz473, zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, zzz481, zzz482, zzz4830, zzz4840, bh)
new_mkVBalBranch3MkVBalBranch116(zzz340, zzz341, zzz34200, zzz343, zzz344, zzz510, zzz511, zzz513, zzz514, zzz31, Succ(zzz1200), h) → new_mkVBalBranch0(zzz31, zzz514, Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), h)
new_mkVBalBranch3MkVBalBranch110(zzz461, zzz462, zzz463, zzz464, zzz465, zzz466, zzz467, zzz468, zzz469, zzz470, zzz471, Zero, bb) → new_mkVBalBranch3MkVBalBranch115(zzz461, zzz462, zzz463, zzz464, zzz465, zzz466, zzz467, Succ(zzz468), zzz469, zzz470, zzz471, Zero, Succ(Succ(zzz468)), bb)
new_mkVBalBranch3MkVBalBranch225(zzz498, zzz499, zzz500, zzz501, zzz502, zzz503, zzz504, zzz505, zzz506, zzz507, Zero, Succ(zzz5090), bg) → new_mkVBalBranch0(zzz507, Branch(zzz503, zzz504, Neg(Succ(Zero)), zzz505, zzz506), zzz501, bg)
new_mkVBalBranch0(zzz31, Branch(zzz510, zzz511, Neg(Succ(zzz51200)), zzz513, zzz514), Branch(zzz340, zzz341, zzz342, zzz343, zzz344), h) → new_mkVBalBranch3MkVBalBranch223(zzz340, zzz341, zzz342, zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat3(new_primPlusNat1(zzz51200), zzz51200)), zzz51200))), h)
new_mkVBalBranch0(zzz31, Branch(zzz510, zzz511, Neg(Zero), zzz513, zzz514), Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), h) → new_mkVBalBranch3MkVBalBranch117(zzz340, zzz341, zzz34200, zzz343, zzz344, zzz510, zzz511, zzz513, zzz514, zzz31, new_primPlusNat2(new_primPlusNat3(Succ(new_primPlusNat3(new_primPlusNat1(zzz34200), zzz34200)), Succ(zzz34200)), Succ(zzz34200)), h)
new_mkVBalBranch3MkVBalBranch217(zzz473, zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, zzz481, zzz482, Succ(zzz4830), Zero, bh) → new_mkVBalBranch3MkVBalBranch121(zzz473, zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, zzz481, zzz482, new_primPlusNat2(new_primPlusNat3(Succ(new_primPlusNat3(new_primPlusNat1(zzz475), zzz475)), Succ(zzz475)), Succ(zzz475)), bh)
new_mkVBalBranch3MkVBalBranch121(zzz473, zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, zzz481, zzz482, Zero, bh) → new_mkVBalBranch3MkVBalBranch115(zzz473, zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, Zero, zzz480, zzz481, zzz482, Zero, Succ(Zero), bh)
new_mkVBalBranch3MkVBalBranch223(zzz340, zzz341, Neg(Succ(Zero)), zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, Succ(zzz670), h) → new_mkVBalBranch0(zzz31, Branch(zzz510, zzz511, Neg(Succ(zzz51200)), zzz513, zzz514), zzz343, h)
new_mkVBalBranch3MkVBalBranch229(zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, zzz1125, zzz1126, zzz1127, zzz1128, zzz1129, bd) → new_mkVBalBranch3MkVBalBranch119(zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, zzz1125, zzz1126, zzz1127, zzz1128, zzz1129, new_primPlusNat2(new_primPlusNat3(Succ(new_primPlusNat3(new_primPlusNat1(zzz1121), zzz1121)), Succ(zzz1121)), Succ(zzz1121)), bd)
new_mkVBalBranch3MkVBalBranch225(zzz498, zzz499, zzz500, zzz501, zzz502, zzz503, zzz504, zzz505, zzz506, zzz507, Succ(zzz5080), Zero, bg) → new_mkVBalBranch3MkVBalBranch118(zzz498, zzz499, zzz500, zzz501, zzz502, zzz503, zzz504, zzz505, zzz506, zzz507, new_primPlusNat2(new_primPlusNat3(Succ(new_primPlusNat3(new_primPlusNat1(zzz500), zzz500)), Succ(zzz500)), Succ(zzz500)), bg)
new_mkVBalBranch3MkVBalBranch218(zzz461, zzz462, zzz463, zzz464, zzz465, zzz466, zzz467, zzz468, zzz469, zzz470, zzz471, bb) → new_mkVBalBranch3MkVBalBranch110(zzz461, zzz462, zzz463, zzz464, zzz465, zzz466, zzz467, zzz468, zzz469, zzz470, zzz471, new_primPlusNat2(Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat3(new_primPlusNat1(zzz463), zzz463)), zzz463))), Succ(zzz463)), bb)
new_mkVBalBranch0(zzz31, Branch(zzz510, zzz511, Pos(Zero), zzz513, zzz514), Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), h) → new_mkVBalBranch3MkVBalBranch116(zzz340, zzz341, zzz34200, zzz343, zzz344, zzz510, zzz511, zzz513, zzz514, zzz31, new_primPlusNat2(new_primPlusNat3(Succ(new_primPlusNat3(new_primPlusNat1(zzz34200), zzz34200)), Succ(zzz34200)), Succ(zzz34200)), h)
new_mkVBalBranch3MkVBalBranch222(zzz461, zzz462, zzz463, zzz464, zzz465, zzz466, zzz467, zzz468, zzz469, zzz470, zzz471, bb) → new_mkVBalBranch3MkVBalBranch110(zzz461, zzz462, zzz463, zzz464, zzz465, zzz466, zzz467, zzz468, zzz469, zzz470, zzz471, new_primPlusNat2(Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat3(new_primPlusNat1(zzz463), zzz463)), zzz463))), Succ(zzz463)), bb)
new_mkVBalBranch3MkVBalBranch215(zzz340, zzz341, Pos(Succ(Succ(zzz342000))), zzz343, zzz344, zzz510, zzz511, Zero, zzz513, zzz514, zzz31, Succ(Succ(zzz6600)), h) → new_mkVBalBranch3MkVBalBranch217(zzz340, zzz341, Succ(zzz342000), zzz343, zzz344, zzz510, zzz511, zzz513, zzz514, zzz31, Succ(zzz6600), zzz342000, h)
new_mkVBalBranch3MkVBalBranch117(zzz340, zzz341, zzz34200, zzz343, zzz344, zzz510, zzz511, zzz513, zzz514, zzz31, Succ(zzz1240), h) → new_mkVBalBranch0(zzz31, zzz514, Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), h)
new_mkVBalBranch3MkVBalBranch120(zzz2050, zzz2051, zzz2052, zzz2053, zzz2054, zzz2055, zzz2056, zzz2057, zzz2058, zzz2059, zzz2060, Succ(zzz20610), Succ(zzz20620), be) → new_mkVBalBranch3MkVBalBranch120(zzz2050, zzz2051, zzz2052, zzz2053, zzz2054, zzz2055, zzz2056, zzz2057, zzz2058, zzz2059, zzz2060, zzz20610, zzz20620, be)
new_mkVBalBranch3MkVBalBranch217(zzz473, zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, zzz481, zzz482, Zero, Zero, bh) → new_mkVBalBranch3MkVBalBranch233(zzz473, zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, zzz481, zzz482, bh)
new_mkVBalBranch3MkVBalBranch216(zzz1105, zzz1106, zzz1107, zzz1108, zzz1109, zzz1110, zzz1111, zzz1112, zzz1113, zzz1114, zzz1115, Succ(zzz11160), Succ(zzz11170), ba) → new_mkVBalBranch3MkVBalBranch216(zzz1105, zzz1106, zzz1107, zzz1108, zzz1109, zzz1110, zzz1111, zzz1112, zzz1113, zzz1114, zzz1115, zzz11160, zzz11170, ba)
new_mkVBalBranch3MkVBalBranch223(zzz340, zzz341, Pos(zzz3420), zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, Succ(zzz670), h) → new_mkVBalBranch0(zzz31, Branch(zzz510, zzz511, Neg(Succ(zzz51200)), zzz513, zzz514), zzz343, h)
new_mkVBalBranch3MkVBalBranch19(zzz340, zzz341, zzz34200, zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, Zero, h) → new_mkVBalBranch3MkVBalBranch122(zzz340, zzz341, zzz34200, zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, h)
new_mkVBalBranch3MkVBalBranch225(zzz498, zzz499, zzz500, zzz501, zzz502, zzz503, zzz504, zzz505, zzz506, zzz507, Succ(zzz5080), Succ(zzz5090), bg) → new_mkVBalBranch3MkVBalBranch225(zzz498, zzz499, zzz500, zzz501, zzz502, zzz503, zzz504, zzz505, zzz506, zzz507, zzz5080, zzz5090, bg)
new_mkVBalBranch3MkVBalBranch19(zzz340, zzz341, zzz34200, zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, Succ(zzz1410), h) → new_mkVBalBranch0(zzz31, zzz514, Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), h)
new_mkVBalBranch3MkVBalBranch224(zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, zzz1125, zzz1126, zzz1127, zzz1128, zzz1129, Zero, Succ(zzz11310), bd) → new_mkVBalBranch3MkVBalBranch227(zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, zzz1125, zzz1126, zzz1127, zzz1128, zzz1129, bd)
new_mkVBalBranch3MkVBalBranch224(zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, zzz1125, zzz1126, zzz1127, zzz1128, zzz1129, Zero, Zero, bd) → new_mkVBalBranch3MkVBalBranch229(zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, zzz1125, zzz1126, zzz1127, zzz1128, zzz1129, bd)
new_mkVBalBranch3MkVBalBranch223(zzz340, zzz341, Neg(Succ(Succ(Zero))), zzz343, zzz344, zzz510, zzz511, Zero, zzz513, zzz514, zzz31, Succ(Succ(zzz6700)), h) → new_mkVBalBranch3MkVBalBranch225(zzz340, zzz341, Succ(Zero), zzz343, zzz344, zzz510, zzz511, zzz513, zzz514, zzz31, Zero, Succ(zzz6700), h)
new_mkVBalBranch3MkVBalBranch223(zzz340, zzz341, Neg(Succ(Succ(Succ(zzz3420000)))), zzz343, zzz344, zzz510, zzz511, Succ(zzz512000), zzz513, zzz514, zzz31, Succ(Succ(zzz6700)), h) → new_mkVBalBranch3MkVBalBranch224(zzz340, zzz341, Succ(Succ(zzz3420000)), zzz343, zzz344, zzz510, zzz511, zzz512000, zzz513, zzz514, zzz31, Succ(zzz3420000), Succ(Succ(new_primPlusNat2(zzz6700, zzz512000))), h)
new_mkVBalBranch3MkVBalBranch115(zzz1986, zzz1987, zzz1988, zzz1989, zzz1990, zzz1991, zzz1992, zzz1993, zzz1994, zzz1995, zzz1996, Succ(zzz19970), Succ(zzz19980), bc) → new_mkVBalBranch3MkVBalBranch115(zzz1986, zzz1987, zzz1988, zzz1989, zzz1990, zzz1991, zzz1992, zzz1993, zzz1994, zzz1995, zzz1996, zzz19970, zzz19980, bc)
new_mkVBalBranch3MkVBalBranch215(zzz340, zzz341, Neg(Zero), zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, Succ(zzz660), h) → new_mkVBalBranch0(zzz31, zzz514, Branch(zzz340, zzz341, Neg(Zero), zzz343, zzz344), h)
new_mkVBalBranch3MkVBalBranch118(zzz498, zzz499, zzz500, zzz501, zzz502, zzz503, zzz504, zzz505, zzz506, zzz507, Succ(zzz8040), bg) → new_mkVBalBranch3MkVBalBranch120(zzz498, zzz499, zzz500, zzz501, zzz502, zzz503, zzz504, Zero, zzz505, zzz506, zzz507, Succ(Zero), Succ(zzz8040), bg)
new_mkVBalBranch3MkVBalBranch216(zzz1105, zzz1106, zzz1107, zzz1108, zzz1109, zzz1110, zzz1111, zzz1112, zzz1113, zzz1114, zzz1115, Succ(zzz11160), Zero, ba) → new_mkVBalBranch3MkVBalBranch218(zzz1105, zzz1106, zzz1107, zzz1108, zzz1109, zzz1110, zzz1111, zzz1112, zzz1113, zzz1114, zzz1115, ba)
new_mkVBalBranch3MkVBalBranch216(zzz1105, zzz1106, zzz1107, zzz1108, zzz1109, zzz1110, zzz1111, zzz1112, zzz1113, zzz1114, zzz1115, Zero, Zero, ba) → new_mkVBalBranch3MkVBalBranch222(zzz1105, zzz1106, zzz1107, zzz1108, zzz1109, zzz1110, zzz1111, zzz1112, zzz1113, zzz1114, zzz1115, ba)
new_mkVBalBranch3MkVBalBranch18(zzz340, zzz341, zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, Zero, h) → new_mkVBalBranch3MkVBalBranch115(zzz340, zzz341, Zero, zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, Zero, Succ(zzz51200), h)
new_mkVBalBranch3MkVBalBranch119(zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, zzz1125, zzz1126, zzz1127, zzz1128, zzz1129, Succ(zzz12130), bd) → new_mkVBalBranch3MkVBalBranch120(zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, zzz1125, Succ(zzz1126), zzz1127, zzz1128, zzz1129, Succ(Succ(zzz1126)), Succ(zzz12130), bd)

The TRS R consists of the following rules:

new_primPlusNat1(Zero) → Zero
new_primPlusNat1(Succ(zzz62000)) → Succ(Succ(new_primPlusNat1(zzz62000)))
new_primPlusNat3(zzz90, Succ(zzz910)) → Succ(Succ(new_primPlusNat2(zzz90, zzz910)))
new_primPlusNat3(zzz90, Zero) → Succ(zzz90)
new_primPlusNat2(Succ(zzz900), Succ(zzz9100)) → Succ(Succ(new_primPlusNat2(zzz900, zzz9100)))
new_primPlusNat2(Zero, Succ(zzz9100)) → Succ(zzz9100)
new_primPlusNat2(Zero, Zero) → Zero
new_primPlusNat2(Succ(zzz900), Zero) → Succ(zzz900)

The set Q consists of the following terms:

new_primPlusNat2(Zero, Succ(x0))
new_primPlusNat3(x0, Succ(x1))
new_primPlusNat2(Succ(x0), Succ(x1))
new_primPlusNat3(x0, Zero)
new_primPlusNat1(Zero)
new_primPlusNat2(Zero, Zero)
new_primPlusNat1(Succ(x0))
new_primPlusNat2(Succ(x0), Zero)

We have to consider all minimal (P,Q,R)-chains.
By rewriting [15] the rule new_mkVBalBranch3MkVBalBranch215(zzz340, zzz341, Pos(Succ(Zero)), zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, Succ(zzz660), h) → new_mkVBalBranch3MkVBalBranch18(zzz340, zzz341, zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, new_primPlusNat2(new_primPlusNat3(Succ(new_primPlusNat3(new_primPlusNat1(Zero), Zero)), Succ(Zero)), Succ(Zero)), h) at position [10,0] we obtained the following new rules:

new_mkVBalBranch3MkVBalBranch215(zzz340, zzz341, Pos(Succ(Zero)), zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, Succ(zzz660), h) → new_mkVBalBranch3MkVBalBranch18(zzz340, zzz341, zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, new_primPlusNat2(Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat3(new_primPlusNat1(Zero), Zero)), Zero))), Succ(Zero)), 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
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                    ↳ DependencyGraphProof
                                      ↳ QDP
                                        ↳ Rewriting
                                          ↳ QDP
                                            ↳ Rewriting
                                              ↳ QDP
                                                ↳ Rewriting
                                                  ↳ QDP
                                                    ↳ Rewriting
                                                      ↳ QDP
                                                        ↳ Rewriting
                                                          ↳ QDP
                                                            ↳ Rewriting
                                                              ↳ QDP
                                                                ↳ Rewriting
                                                                  ↳ QDP
                                                                    ↳ Rewriting
                                                                      ↳ QDP
                                                                        ↳ Rewriting
                                                                          ↳ QDP
                                                                            ↳ Rewriting
                                                                              ↳ QDP
                                                                                ↳ Rewriting
                                                                                  ↳ QDP
                                                                                    ↳ Rewriting
                                                                                      ↳ QDP
                                                                                        ↳ Rewriting
                                                                                          ↳ QDP
                                                                                            ↳ Rewriting
                                                                                              ↳ QDP
                                                                                                ↳ Rewriting
                                                                                                  ↳ QDP
                                                                                                    ↳ Rewriting
                                                                                                      ↳ QDP
                                                                                                        ↳ Rewriting
                                                                                                          ↳ QDP
                                                                                                            ↳ UsableRulesProof
                                                                                                              ↳ QDP
                                                                                                                ↳ QReductionProof
                                                                                                                  ↳ QDP
                                                                                                                    ↳ Rewriting
                                                                                                                      ↳ QDP
                                                                                                                        ↳ Rewriting
                                                                                                                          ↳ QDP
                                                                                                                            ↳ DependencyGraphProof
                                                                                                                              ↳ QDP
                                                                                                                                ↳ Rewriting
                                                                                                                                  ↳ QDP
                                                                                                                                    ↳ Rewriting
                                                                                                                                      ↳ QDP
                                                                                                                                        ↳ DependencyGraphProof
                                                                                                                                          ↳ QDP
                                                                                                                                            ↳ Rewriting
                                                                                                                                              ↳ QDP
                                                                                                                                                ↳ Rewriting
                                                                                                                                                  ↳ QDP
                                                                                                                                                    ↳ Rewriting
                                                                                                                                                      ↳ QDP
                                                                                                                                                        ↳ Rewriting
                                                                                                                                                          ↳ QDP
                                                                                                                                                            ↳ Rewriting
                                                                                                                                                              ↳ QDP
                                                                                                                                                                ↳ Rewriting
                                                                                                                                                                  ↳ QDP
                                                                                                                                                                    ↳ Rewriting
                                                                                                                                                                      ↳ QDP
                                                                                                                                                                        ↳ Rewriting
                                                                                                                                                                          ↳ QDP
                                                                                                                                                                            ↳ Rewriting
                                                                                                                                                                              ↳ QDP
                                                                                                                                                                                ↳ Rewriting
                                                                                                                                                                                  ↳ QDP
                                                                                                                                                                                    ↳ Rewriting
                                                                                                                                                                                      ↳ QDP
                                                                                                                                                                                        ↳ Rewriting
                                                                                                                                                                                          ↳ QDP
                                                                                                                                                                                            ↳ UsableRulesProof
                                                                                                                                                                                              ↳ QDP
                                                                                                                                                                                                ↳ QReductionProof
                                                                                                                                                                                                  ↳ QDP
                                                                                                                                                                                                    ↳ Rewriting
                                                                                                                                                                                                      ↳ QDP
                                                                                                                                                                                                        ↳ Rewriting
                                                                                                                                                                                                          ↳ QDP
                                                                                                                                                                                                            ↳ Rewriting
                                                                                                                                                                                                              ↳ QDP
                                                                                                                                                                                                                ↳ Rewriting
                                                                                                                                                                                                                  ↳ QDP
                                                                                                                                                                                                                    ↳ Rewriting
                                                                                                                                                                                                                      ↳ QDP
                                                                                                                                                                                                                        ↳ Rewriting
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP

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

new_mkVBalBranch3MkVBalBranch225(zzz498, zzz499, zzz500, zzz501, zzz502, zzz503, zzz504, zzz505, zzz506, zzz507, Zero, Zero, bg) → new_mkVBalBranch3MkVBalBranch230(zzz498, zzz499, zzz500, zzz501, zzz502, zzz503, zzz504, zzz505, zzz506, zzz507, bg)
new_mkVBalBranch3MkVBalBranch18(zzz340, zzz341, zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, Succ(zzz1480), h) → new_mkVBalBranch3MkVBalBranch115(zzz340, zzz341, Zero, zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, Succ(zzz1480), Succ(zzz51200), h)
new_mkVBalBranch0(zzz31, Branch(zzz510, zzz511, Neg(Zero), zzz513, zzz514), Branch(zzz340, zzz341, Pos(Succ(zzz34200)), zzz343, zzz344), h) → new_mkVBalBranch0(zzz31, Branch(zzz510, zzz511, Neg(Zero), zzz513, zzz514), zzz343, h)
new_mkVBalBranch3MkVBalBranch215(zzz340, zzz341, Pos(Succ(Succ(zzz342000))), zzz343, zzz344, zzz510, zzz511, Succ(zzz512000), zzz513, zzz514, zzz31, Succ(Succ(zzz6600)), h) → new_mkVBalBranch3MkVBalBranch216(zzz340, zzz341, Succ(zzz342000), zzz343, zzz344, zzz510, zzz511, zzz512000, zzz513, zzz514, zzz31, Succ(Succ(new_primPlusNat2(zzz6600, zzz512000))), zzz342000, h)
new_mkVBalBranch3MkVBalBranch223(zzz340, zzz341, Neg(Succ(Succ(Succ(zzz3420000)))), zzz343, zzz344, zzz510, zzz511, Zero, zzz513, zzz514, zzz31, Succ(Succ(zzz6700)), h) → new_mkVBalBranch3MkVBalBranch225(zzz340, zzz341, Succ(Succ(zzz3420000)), zzz343, zzz344, zzz510, zzz511, zzz513, zzz514, zzz31, Succ(zzz3420000), Succ(zzz6700), h)
new_mkVBalBranch3MkVBalBranch120(zzz2050, zzz2051, zzz2052, zzz2053, zzz2054, zzz2055, zzz2056, zzz2057, zzz2058, zzz2059, zzz2060, Zero, Succ(zzz20620), be) → new_mkVBalBranch0(zzz2060, zzz2059, Branch(zzz2050, zzz2051, Neg(Succ(zzz2052)), zzz2053, zzz2054), be)
new_mkVBalBranch3MkVBalBranch121(zzz473, zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, zzz481, zzz482, Succ(zzz7390), bh) → new_mkVBalBranch3MkVBalBranch115(zzz473, zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, Zero, zzz480, zzz481, zzz482, Succ(zzz7390), Succ(Zero), bh)
new_mkVBalBranch0(zzz31, Branch(zzz510, zzz511, Pos(Zero), zzz513, zzz514), Branch(zzz340, zzz341, Pos(Succ(zzz34200)), zzz343, zzz344), h) → new_mkVBalBranch0(zzz31, Branch(zzz510, zzz511, Pos(Zero), zzz513, zzz514), zzz343, h)
new_mkVBalBranch3MkVBalBranch215(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, Succ(zzz660), h) → new_mkVBalBranch3MkVBalBranch19(zzz340, zzz341, zzz34200, zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, new_primPlusNat2(Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat3(new_primPlusNat1(zzz34200), zzz34200)), zzz34200))), Succ(zzz34200)), h)
new_mkVBalBranch0(zzz31, Branch(zzz510, zzz511, Pos(Succ(zzz51200)), zzz513, zzz514), Branch(zzz340, zzz341, zzz342, zzz343, zzz344), h) → new_mkVBalBranch3MkVBalBranch215(zzz340, zzz341, zzz342, zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat3(new_primPlusNat1(zzz51200), zzz51200)), zzz51200))), h)
new_mkVBalBranch3MkVBalBranch223(zzz340, zzz341, Neg(Succ(Succ(Zero))), zzz343, zzz344, zzz510, zzz511, Succ(zzz512000), zzz513, zzz514, zzz31, Succ(Succ(zzz6700)), h) → new_mkVBalBranch3MkVBalBranch224(zzz340, zzz341, Succ(Zero), zzz343, zzz344, zzz510, zzz511, zzz512000, zzz513, zzz514, zzz31, Zero, Succ(Succ(new_primPlusNat2(zzz6700, zzz512000))), h)
new_mkVBalBranch3MkVBalBranch224(zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, zzz1125, zzz1126, zzz1127, zzz1128, zzz1129, Succ(zzz11300), Succ(zzz11310), bd) → new_mkVBalBranch3MkVBalBranch224(zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, zzz1125, zzz1126, zzz1127, zzz1128, zzz1129, zzz11300, zzz11310, bd)
new_mkVBalBranch3MkVBalBranch217(zzz473, zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, zzz481, zzz482, Zero, Succ(zzz4840), bh) → new_mkVBalBranch0(zzz482, Branch(zzz478, zzz479, Pos(Succ(Zero)), zzz480, zzz481), zzz476, bh)
new_mkVBalBranch3MkVBalBranch224(zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, zzz1125, zzz1126, zzz1127, zzz1128, zzz1129, Succ(zzz11300), Zero, bd) → new_mkVBalBranch3MkVBalBranch119(zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, zzz1125, zzz1126, zzz1127, zzz1128, zzz1129, new_primPlusNat2(Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat3(new_primPlusNat1(zzz1121), zzz1121)), zzz1121))), Succ(zzz1121)), bd)
new_mkVBalBranch3MkVBalBranch110(zzz461, zzz462, zzz463, zzz464, zzz465, zzz466, zzz467, zzz468, zzz469, zzz470, zzz471, Succ(zzz5800), bb) → new_mkVBalBranch3MkVBalBranch115(zzz461, zzz462, zzz463, zzz464, zzz465, zzz466, zzz467, Succ(zzz468), zzz469, zzz470, zzz471, Succ(zzz5800), Succ(Succ(zzz468)), bb)
new_mkVBalBranch3MkVBalBranch227(zzz486, zzz487, zzz488, zzz489, zzz490, zzz491, zzz492, zzz493, zzz494, zzz495, zzz496, bf) → new_mkVBalBranch0(zzz496, Branch(zzz491, zzz492, Neg(Succ(Succ(zzz493))), zzz494, zzz495), zzz489, bf)
new_mkVBalBranch3MkVBalBranch215(zzz340, zzz341, Pos(Zero), zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, Succ(zzz660), h) → new_mkVBalBranch0(zzz31, zzz514, Branch(zzz340, zzz341, Pos(Zero), zzz343, zzz344), h)
new_mkVBalBranch3MkVBalBranch223(zzz340, zzz341, Neg(Zero), zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, Succ(zzz670), h) → new_mkVBalBranch0(zzz31, Branch(zzz510, zzz511, Neg(Succ(zzz51200)), zzz513, zzz514), zzz343, h)
new_mkVBalBranch3MkVBalBranch216(zzz1105, zzz1106, zzz1107, zzz1108, zzz1109, zzz1110, zzz1111, zzz1112, zzz1113, zzz1114, zzz1115, Zero, Succ(zzz11170), ba) → new_mkVBalBranch0(zzz1115, Branch(zzz1110, zzz1111, Pos(Succ(Succ(zzz1112))), zzz1113, zzz1114), zzz1108, ba)
new_mkVBalBranch3MkVBalBranch115(zzz1986, zzz1987, zzz1988, zzz1989, zzz1990, zzz1991, zzz1992, zzz1993, zzz1994, zzz1995, zzz1996, Zero, Succ(zzz19980), bc) → new_mkVBalBranch0(zzz1996, zzz1995, Branch(zzz1986, zzz1987, Pos(Succ(zzz1988)), zzz1989, zzz1990), bc)
new_mkVBalBranch3MkVBalBranch233(zzz473, zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, zzz481, zzz482, bh) → new_mkVBalBranch3MkVBalBranch121(zzz473, zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, zzz481, zzz482, new_primPlusNat2(Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat3(new_primPlusNat1(zzz475), zzz475)), zzz475))), Succ(zzz475)), bh)
new_mkVBalBranch3MkVBalBranch215(zzz340, zzz341, Pos(Succ(Zero)), zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, Succ(zzz660), h) → new_mkVBalBranch3MkVBalBranch18(zzz340, zzz341, zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, new_primPlusNat2(Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat3(new_primPlusNat1(Zero), Zero)), Zero))), Succ(Zero)), h)
new_mkVBalBranch3MkVBalBranch230(zzz498, zzz499, zzz500, zzz501, zzz502, zzz503, zzz504, zzz505, zzz506, zzz507, bg) → new_mkVBalBranch3MkVBalBranch118(zzz498, zzz499, zzz500, zzz501, zzz502, zzz503, zzz504, zzz505, zzz506, zzz507, new_primPlusNat2(Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat3(new_primPlusNat1(zzz500), zzz500)), zzz500))), Succ(zzz500)), bg)
new_mkVBalBranch3MkVBalBranch122(zzz340, zzz341, zzz34200, zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, h) → new_mkVBalBranch0(zzz31, zzz514, Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), h)
new_mkVBalBranch3MkVBalBranch217(zzz473, zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, zzz481, zzz482, Succ(zzz4830), Succ(zzz4840), bh) → new_mkVBalBranch3MkVBalBranch217(zzz473, zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, zzz481, zzz482, zzz4830, zzz4840, bh)
new_mkVBalBranch3MkVBalBranch116(zzz340, zzz341, zzz34200, zzz343, zzz344, zzz510, zzz511, zzz513, zzz514, zzz31, Succ(zzz1200), h) → new_mkVBalBranch0(zzz31, zzz514, Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), h)
new_mkVBalBranch3MkVBalBranch110(zzz461, zzz462, zzz463, zzz464, zzz465, zzz466, zzz467, zzz468, zzz469, zzz470, zzz471, Zero, bb) → new_mkVBalBranch3MkVBalBranch115(zzz461, zzz462, zzz463, zzz464, zzz465, zzz466, zzz467, Succ(zzz468), zzz469, zzz470, zzz471, Zero, Succ(Succ(zzz468)), bb)
new_mkVBalBranch3MkVBalBranch225(zzz498, zzz499, zzz500, zzz501, zzz502, zzz503, zzz504, zzz505, zzz506, zzz507, Zero, Succ(zzz5090), bg) → new_mkVBalBranch0(zzz507, Branch(zzz503, zzz504, Neg(Succ(Zero)), zzz505, zzz506), zzz501, bg)
new_mkVBalBranch0(zzz31, Branch(zzz510, zzz511, Neg(Succ(zzz51200)), zzz513, zzz514), Branch(zzz340, zzz341, zzz342, zzz343, zzz344), h) → new_mkVBalBranch3MkVBalBranch223(zzz340, zzz341, zzz342, zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat3(new_primPlusNat1(zzz51200), zzz51200)), zzz51200))), h)
new_mkVBalBranch0(zzz31, Branch(zzz510, zzz511, Neg(Zero), zzz513, zzz514), Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), h) → new_mkVBalBranch3MkVBalBranch117(zzz340, zzz341, zzz34200, zzz343, zzz344, zzz510, zzz511, zzz513, zzz514, zzz31, new_primPlusNat2(new_primPlusNat3(Succ(new_primPlusNat3(new_primPlusNat1(zzz34200), zzz34200)), Succ(zzz34200)), Succ(zzz34200)), h)
new_mkVBalBranch3MkVBalBranch217(zzz473, zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, zzz481, zzz482, Succ(zzz4830), Zero, bh) → new_mkVBalBranch3MkVBalBranch121(zzz473, zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, zzz481, zzz482, new_primPlusNat2(new_primPlusNat3(Succ(new_primPlusNat3(new_primPlusNat1(zzz475), zzz475)), Succ(zzz475)), Succ(zzz475)), bh)
new_mkVBalBranch3MkVBalBranch121(zzz473, zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, zzz481, zzz482, Zero, bh) → new_mkVBalBranch3MkVBalBranch115(zzz473, zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, Zero, zzz480, zzz481, zzz482, Zero, Succ(Zero), bh)
new_mkVBalBranch3MkVBalBranch223(zzz340, zzz341, Neg(Succ(Zero)), zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, Succ(zzz670), h) → new_mkVBalBranch0(zzz31, Branch(zzz510, zzz511, Neg(Succ(zzz51200)), zzz513, zzz514), zzz343, h)
new_mkVBalBranch3MkVBalBranch225(zzz498, zzz499, zzz500, zzz501, zzz502, zzz503, zzz504, zzz505, zzz506, zzz507, Succ(zzz5080), Zero, bg) → new_mkVBalBranch3MkVBalBranch118(zzz498, zzz499, zzz500, zzz501, zzz502, zzz503, zzz504, zzz505, zzz506, zzz507, new_primPlusNat2(new_primPlusNat3(Succ(new_primPlusNat3(new_primPlusNat1(zzz500), zzz500)), Succ(zzz500)), Succ(zzz500)), bg)
new_mkVBalBranch3MkVBalBranch229(zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, zzz1125, zzz1126, zzz1127, zzz1128, zzz1129, bd) → new_mkVBalBranch3MkVBalBranch119(zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, zzz1125, zzz1126, zzz1127, zzz1128, zzz1129, new_primPlusNat2(new_primPlusNat3(Succ(new_primPlusNat3(new_primPlusNat1(zzz1121), zzz1121)), Succ(zzz1121)), Succ(zzz1121)), bd)
new_mkVBalBranch3MkVBalBranch218(zzz461, zzz462, zzz463, zzz464, zzz465, zzz466, zzz467, zzz468, zzz469, zzz470, zzz471, bb) → new_mkVBalBranch3MkVBalBranch110(zzz461, zzz462, zzz463, zzz464, zzz465, zzz466, zzz467, zzz468, zzz469, zzz470, zzz471, new_primPlusNat2(Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat3(new_primPlusNat1(zzz463), zzz463)), zzz463))), Succ(zzz463)), bb)
new_mkVBalBranch0(zzz31, Branch(zzz510, zzz511, Pos(Zero), zzz513, zzz514), Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), h) → new_mkVBalBranch3MkVBalBranch116(zzz340, zzz341, zzz34200, zzz343, zzz344, zzz510, zzz511, zzz513, zzz514, zzz31, new_primPlusNat2(new_primPlusNat3(Succ(new_primPlusNat3(new_primPlusNat1(zzz34200), zzz34200)), Succ(zzz34200)), Succ(zzz34200)), h)
new_mkVBalBranch3MkVBalBranch222(zzz461, zzz462, zzz463, zzz464, zzz465, zzz466, zzz467, zzz468, zzz469, zzz470, zzz471, bb) → new_mkVBalBranch3MkVBalBranch110(zzz461, zzz462, zzz463, zzz464, zzz465, zzz466, zzz467, zzz468, zzz469, zzz470, zzz471, new_primPlusNat2(Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat3(new_primPlusNat1(zzz463), zzz463)), zzz463))), Succ(zzz463)), bb)
new_mkVBalBranch3MkVBalBranch215(zzz340, zzz341, Pos(Succ(Succ(zzz342000))), zzz343, zzz344, zzz510, zzz511, Zero, zzz513, zzz514, zzz31, Succ(Succ(zzz6600)), h) → new_mkVBalBranch3MkVBalBranch217(zzz340, zzz341, Succ(zzz342000), zzz343, zzz344, zzz510, zzz511, zzz513, zzz514, zzz31, Succ(zzz6600), zzz342000, h)
new_mkVBalBranch3MkVBalBranch117(zzz340, zzz341, zzz34200, zzz343, zzz344, zzz510, zzz511, zzz513, zzz514, zzz31, Succ(zzz1240), h) → new_mkVBalBranch0(zzz31, zzz514, Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), h)
new_mkVBalBranch3MkVBalBranch217(zzz473, zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, zzz481, zzz482, Zero, Zero, bh) → new_mkVBalBranch3MkVBalBranch233(zzz473, zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, zzz481, zzz482, bh)
new_mkVBalBranch3MkVBalBranch120(zzz2050, zzz2051, zzz2052, zzz2053, zzz2054, zzz2055, zzz2056, zzz2057, zzz2058, zzz2059, zzz2060, Succ(zzz20610), Succ(zzz20620), be) → new_mkVBalBranch3MkVBalBranch120(zzz2050, zzz2051, zzz2052, zzz2053, zzz2054, zzz2055, zzz2056, zzz2057, zzz2058, zzz2059, zzz2060, zzz20610, zzz20620, be)
new_mkVBalBranch3MkVBalBranch223(zzz340, zzz341, Pos(zzz3420), zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, Succ(zzz670), h) → new_mkVBalBranch0(zzz31, Branch(zzz510, zzz511, Neg(Succ(zzz51200)), zzz513, zzz514), zzz343, h)
new_mkVBalBranch3MkVBalBranch216(zzz1105, zzz1106, zzz1107, zzz1108, zzz1109, zzz1110, zzz1111, zzz1112, zzz1113, zzz1114, zzz1115, Succ(zzz11160), Succ(zzz11170), ba) → new_mkVBalBranch3MkVBalBranch216(zzz1105, zzz1106, zzz1107, zzz1108, zzz1109, zzz1110, zzz1111, zzz1112, zzz1113, zzz1114, zzz1115, zzz11160, zzz11170, ba)
new_mkVBalBranch3MkVBalBranch19(zzz340, zzz341, zzz34200, zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, Zero, h) → new_mkVBalBranch3MkVBalBranch122(zzz340, zzz341, zzz34200, zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, h)
new_mkVBalBranch3MkVBalBranch225(zzz498, zzz499, zzz500, zzz501, zzz502, zzz503, zzz504, zzz505, zzz506, zzz507, Succ(zzz5080), Succ(zzz5090), bg) → new_mkVBalBranch3MkVBalBranch225(zzz498, zzz499, zzz500, zzz501, zzz502, zzz503, zzz504, zzz505, zzz506, zzz507, zzz5080, zzz5090, bg)
new_mkVBalBranch3MkVBalBranch19(zzz340, zzz341, zzz34200, zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, Succ(zzz1410), h) → new_mkVBalBranch0(zzz31, zzz514, Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), h)
new_mkVBalBranch3MkVBalBranch224(zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, zzz1125, zzz1126, zzz1127, zzz1128, zzz1129, Zero, Zero, bd) → new_mkVBalBranch3MkVBalBranch229(zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, zzz1125, zzz1126, zzz1127, zzz1128, zzz1129, bd)
new_mkVBalBranch3MkVBalBranch224(zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, zzz1125, zzz1126, zzz1127, zzz1128, zzz1129, Zero, Succ(zzz11310), bd) → new_mkVBalBranch3MkVBalBranch227(zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, zzz1125, zzz1126, zzz1127, zzz1128, zzz1129, bd)
new_mkVBalBranch3MkVBalBranch223(zzz340, zzz341, Neg(Succ(Succ(Succ(zzz3420000)))), zzz343, zzz344, zzz510, zzz511, Succ(zzz512000), zzz513, zzz514, zzz31, Succ(Succ(zzz6700)), h) → new_mkVBalBranch3MkVBalBranch224(zzz340, zzz341, Succ(Succ(zzz3420000)), zzz343, zzz344, zzz510, zzz511, zzz512000, zzz513, zzz514, zzz31, Succ(zzz3420000), Succ(Succ(new_primPlusNat2(zzz6700, zzz512000))), h)
new_mkVBalBranch3MkVBalBranch223(zzz340, zzz341, Neg(Succ(Succ(Zero))), zzz343, zzz344, zzz510, zzz511, Zero, zzz513, zzz514, zzz31, Succ(Succ(zzz6700)), h) → new_mkVBalBranch3MkVBalBranch225(zzz340, zzz341, Succ(Zero), zzz343, zzz344, zzz510, zzz511, zzz513, zzz514, zzz31, Zero, Succ(zzz6700), h)
new_mkVBalBranch3MkVBalBranch115(zzz1986, zzz1987, zzz1988, zzz1989, zzz1990, zzz1991, zzz1992, zzz1993, zzz1994, zzz1995, zzz1996, Succ(zzz19970), Succ(zzz19980), bc) → new_mkVBalBranch3MkVBalBranch115(zzz1986, zzz1987, zzz1988, zzz1989, zzz1990, zzz1991, zzz1992, zzz1993, zzz1994, zzz1995, zzz1996, zzz19970, zzz19980, bc)
new_mkVBalBranch3MkVBalBranch215(zzz340, zzz341, Neg(Zero), zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, Succ(zzz660), h) → new_mkVBalBranch0(zzz31, zzz514, Branch(zzz340, zzz341, Neg(Zero), zzz343, zzz344), h)
new_mkVBalBranch3MkVBalBranch118(zzz498, zzz499, zzz500, zzz501, zzz502, zzz503, zzz504, zzz505, zzz506, zzz507, Succ(zzz8040), bg) → new_mkVBalBranch3MkVBalBranch120(zzz498, zzz499, zzz500, zzz501, zzz502, zzz503, zzz504, Zero, zzz505, zzz506, zzz507, Succ(Zero), Succ(zzz8040), bg)
new_mkVBalBranch3MkVBalBranch216(zzz1105, zzz1106, zzz1107, zzz1108, zzz1109, zzz1110, zzz1111, zzz1112, zzz1113, zzz1114, zzz1115, Succ(zzz11160), Zero, ba) → new_mkVBalBranch3MkVBalBranch218(zzz1105, zzz1106, zzz1107, zzz1108, zzz1109, zzz1110, zzz1111, zzz1112, zzz1113, zzz1114, zzz1115, ba)
new_mkVBalBranch3MkVBalBranch216(zzz1105, zzz1106, zzz1107, zzz1108, zzz1109, zzz1110, zzz1111, zzz1112, zzz1113, zzz1114, zzz1115, Zero, Zero, ba) → new_mkVBalBranch3MkVBalBranch222(zzz1105, zzz1106, zzz1107, zzz1108, zzz1109, zzz1110, zzz1111, zzz1112, zzz1113, zzz1114, zzz1115, ba)
new_mkVBalBranch3MkVBalBranch119(zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, zzz1125, zzz1126, zzz1127, zzz1128, zzz1129, Succ(zzz12130), bd) → new_mkVBalBranch3MkVBalBranch120(zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, zzz1125, Succ(zzz1126), zzz1127, zzz1128, zzz1129, Succ(Succ(zzz1126)), Succ(zzz12130), bd)
new_mkVBalBranch3MkVBalBranch18(zzz340, zzz341, zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, Zero, h) → new_mkVBalBranch3MkVBalBranch115(zzz340, zzz341, Zero, zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, Zero, Succ(zzz51200), h)

The TRS R consists of the following rules:

new_primPlusNat1(Zero) → Zero
new_primPlusNat1(Succ(zzz62000)) → Succ(Succ(new_primPlusNat1(zzz62000)))
new_primPlusNat3(zzz90, Succ(zzz910)) → Succ(Succ(new_primPlusNat2(zzz90, zzz910)))
new_primPlusNat3(zzz90, Zero) → Succ(zzz90)
new_primPlusNat2(Succ(zzz900), Succ(zzz9100)) → Succ(Succ(new_primPlusNat2(zzz900, zzz9100)))
new_primPlusNat2(Zero, Succ(zzz9100)) → Succ(zzz9100)
new_primPlusNat2(Zero, Zero) → Zero
new_primPlusNat2(Succ(zzz900), Zero) → Succ(zzz900)

The set Q consists of the following terms:

new_primPlusNat2(Zero, Succ(x0))
new_primPlusNat3(x0, Succ(x1))
new_primPlusNat2(Succ(x0), Succ(x1))
new_primPlusNat3(x0, Zero)
new_primPlusNat1(Zero)
new_primPlusNat2(Zero, Zero)
new_primPlusNat1(Succ(x0))
new_primPlusNat2(Succ(x0), Zero)

We have to consider all minimal (P,Q,R)-chains.
By rewriting [15] the rule new_mkVBalBranch3MkVBalBranch230(zzz498, zzz499, zzz500, zzz501, zzz502, zzz503, zzz504, zzz505, zzz506, zzz507, bg) → new_mkVBalBranch3MkVBalBranch118(zzz498, zzz499, zzz500, zzz501, zzz502, zzz503, zzz504, zzz505, zzz506, zzz507, new_primPlusNat2(Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat3(new_primPlusNat1(zzz500), zzz500)), zzz500))), Succ(zzz500)), bg) at position [10] we obtained the following new rules:

new_mkVBalBranch3MkVBalBranch230(zzz498, zzz499, zzz500, zzz501, zzz502, zzz503, zzz504, zzz505, zzz506, zzz507, bg) → new_mkVBalBranch3MkVBalBranch118(zzz498, zzz499, zzz500, zzz501, zzz502, zzz503, zzz504, zzz505, zzz506, zzz507, Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat2(Succ(new_primPlusNat3(new_primPlusNat1(zzz500), zzz500)), zzz500)), zzz500))), bg)



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

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

new_mkVBalBranch3MkVBalBranch225(zzz498, zzz499, zzz500, zzz501, zzz502, zzz503, zzz504, zzz505, zzz506, zzz507, Zero, Zero, bg) → new_mkVBalBranch3MkVBalBranch230(zzz498, zzz499, zzz500, zzz501, zzz502, zzz503, zzz504, zzz505, zzz506, zzz507, bg)
new_mkVBalBranch3MkVBalBranch18(zzz340, zzz341, zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, Succ(zzz1480), h) → new_mkVBalBranch3MkVBalBranch115(zzz340, zzz341, Zero, zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, Succ(zzz1480), Succ(zzz51200), h)
new_mkVBalBranch3MkVBalBranch215(zzz340, zzz341, Pos(Succ(Succ(zzz342000))), zzz343, zzz344, zzz510, zzz511, Succ(zzz512000), zzz513, zzz514, zzz31, Succ(Succ(zzz6600)), h) → new_mkVBalBranch3MkVBalBranch216(zzz340, zzz341, Succ(zzz342000), zzz343, zzz344, zzz510, zzz511, zzz512000, zzz513, zzz514, zzz31, Succ(Succ(new_primPlusNat2(zzz6600, zzz512000))), zzz342000, h)
new_mkVBalBranch0(zzz31, Branch(zzz510, zzz511, Neg(Zero), zzz513, zzz514), Branch(zzz340, zzz341, Pos(Succ(zzz34200)), zzz343, zzz344), h) → new_mkVBalBranch0(zzz31, Branch(zzz510, zzz511, Neg(Zero), zzz513, zzz514), zzz343, h)
new_mkVBalBranch3MkVBalBranch223(zzz340, zzz341, Neg(Succ(Succ(Succ(zzz3420000)))), zzz343, zzz344, zzz510, zzz511, Zero, zzz513, zzz514, zzz31, Succ(Succ(zzz6700)), h) → new_mkVBalBranch3MkVBalBranch225(zzz340, zzz341, Succ(Succ(zzz3420000)), zzz343, zzz344, zzz510, zzz511, zzz513, zzz514, zzz31, Succ(zzz3420000), Succ(zzz6700), h)
new_mkVBalBranch3MkVBalBranch120(zzz2050, zzz2051, zzz2052, zzz2053, zzz2054, zzz2055, zzz2056, zzz2057, zzz2058, zzz2059, zzz2060, Zero, Succ(zzz20620), be) → new_mkVBalBranch0(zzz2060, zzz2059, Branch(zzz2050, zzz2051, Neg(Succ(zzz2052)), zzz2053, zzz2054), be)
new_mkVBalBranch3MkVBalBranch215(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, Succ(zzz660), h) → new_mkVBalBranch3MkVBalBranch19(zzz340, zzz341, zzz34200, zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, new_primPlusNat2(Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat3(new_primPlusNat1(zzz34200), zzz34200)), zzz34200))), Succ(zzz34200)), h)
new_mkVBalBranch0(zzz31, Branch(zzz510, zzz511, Pos(Zero), zzz513, zzz514), Branch(zzz340, zzz341, Pos(Succ(zzz34200)), zzz343, zzz344), h) → new_mkVBalBranch0(zzz31, Branch(zzz510, zzz511, Pos(Zero), zzz513, zzz514), zzz343, h)
new_mkVBalBranch3MkVBalBranch121(zzz473, zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, zzz481, zzz482, Succ(zzz7390), bh) → new_mkVBalBranch3MkVBalBranch115(zzz473, zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, Zero, zzz480, zzz481, zzz482, Succ(zzz7390), Succ(Zero), bh)
new_mkVBalBranch0(zzz31, Branch(zzz510, zzz511, Pos(Succ(zzz51200)), zzz513, zzz514), Branch(zzz340, zzz341, zzz342, zzz343, zzz344), h) → new_mkVBalBranch3MkVBalBranch215(zzz340, zzz341, zzz342, zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat3(new_primPlusNat1(zzz51200), zzz51200)), zzz51200))), h)
new_mkVBalBranch3MkVBalBranch230(zzz498, zzz499, zzz500, zzz501, zzz502, zzz503, zzz504, zzz505, zzz506, zzz507, bg) → new_mkVBalBranch3MkVBalBranch118(zzz498, zzz499, zzz500, zzz501, zzz502, zzz503, zzz504, zzz505, zzz506, zzz507, Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat2(Succ(new_primPlusNat3(new_primPlusNat1(zzz500), zzz500)), zzz500)), zzz500))), bg)
new_mkVBalBranch3MkVBalBranch223(zzz340, zzz341, Neg(Succ(Succ(Zero))), zzz343, zzz344, zzz510, zzz511, Succ(zzz512000), zzz513, zzz514, zzz31, Succ(Succ(zzz6700)), h) → new_mkVBalBranch3MkVBalBranch224(zzz340, zzz341, Succ(Zero), zzz343, zzz344, zzz510, zzz511, zzz512000, zzz513, zzz514, zzz31, Zero, Succ(Succ(new_primPlusNat2(zzz6700, zzz512000))), h)
new_mkVBalBranch3MkVBalBranch224(zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, zzz1125, zzz1126, zzz1127, zzz1128, zzz1129, Succ(zzz11300), Succ(zzz11310), bd) → new_mkVBalBranch3MkVBalBranch224(zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, zzz1125, zzz1126, zzz1127, zzz1128, zzz1129, zzz11300, zzz11310, bd)
new_mkVBalBranch3MkVBalBranch217(zzz473, zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, zzz481, zzz482, Zero, Succ(zzz4840), bh) → new_mkVBalBranch0(zzz482, Branch(zzz478, zzz479, Pos(Succ(Zero)), zzz480, zzz481), zzz476, bh)
new_mkVBalBranch3MkVBalBranch224(zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, zzz1125, zzz1126, zzz1127, zzz1128, zzz1129, Succ(zzz11300), Zero, bd) → new_mkVBalBranch3MkVBalBranch119(zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, zzz1125, zzz1126, zzz1127, zzz1128, zzz1129, new_primPlusNat2(Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat3(new_primPlusNat1(zzz1121), zzz1121)), zzz1121))), Succ(zzz1121)), bd)
new_mkVBalBranch3MkVBalBranch110(zzz461, zzz462, zzz463, zzz464, zzz465, zzz466, zzz467, zzz468, zzz469, zzz470, zzz471, Succ(zzz5800), bb) → new_mkVBalBranch3MkVBalBranch115(zzz461, zzz462, zzz463, zzz464, zzz465, zzz466, zzz467, Succ(zzz468), zzz469, zzz470, zzz471, Succ(zzz5800), Succ(Succ(zzz468)), bb)
new_mkVBalBranch3MkVBalBranch227(zzz486, zzz487, zzz488, zzz489, zzz490, zzz491, zzz492, zzz493, zzz494, zzz495, zzz496, bf) → new_mkVBalBranch0(zzz496, Branch(zzz491, zzz492, Neg(Succ(Succ(zzz493))), zzz494, zzz495), zzz489, bf)
new_mkVBalBranch3MkVBalBranch215(zzz340, zzz341, Pos(Zero), zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, Succ(zzz660), h) → new_mkVBalBranch0(zzz31, zzz514, Branch(zzz340, zzz341, Pos(Zero), zzz343, zzz344), h)
new_mkVBalBranch3MkVBalBranch223(zzz340, zzz341, Neg(Zero), zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, Succ(zzz670), h) → new_mkVBalBranch0(zzz31, Branch(zzz510, zzz511, Neg(Succ(zzz51200)), zzz513, zzz514), zzz343, h)
new_mkVBalBranch3MkVBalBranch216(zzz1105, zzz1106, zzz1107, zzz1108, zzz1109, zzz1110, zzz1111, zzz1112, zzz1113, zzz1114, zzz1115, Zero, Succ(zzz11170), ba) → new_mkVBalBranch0(zzz1115, Branch(zzz1110, zzz1111, Pos(Succ(Succ(zzz1112))), zzz1113, zzz1114), zzz1108, ba)
new_mkVBalBranch3MkVBalBranch115(zzz1986, zzz1987, zzz1988, zzz1989, zzz1990, zzz1991, zzz1992, zzz1993, zzz1994, zzz1995, zzz1996, Zero, Succ(zzz19980), bc) → new_mkVBalBranch0(zzz1996, zzz1995, Branch(zzz1986, zzz1987, Pos(Succ(zzz1988)), zzz1989, zzz1990), bc)
new_mkVBalBranch3MkVBalBranch233(zzz473, zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, zzz481, zzz482, bh) → new_mkVBalBranch3MkVBalBranch121(zzz473, zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, zzz481, zzz482, new_primPlusNat2(Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat3(new_primPlusNat1(zzz475), zzz475)), zzz475))), Succ(zzz475)), bh)
new_mkVBalBranch3MkVBalBranch215(zzz340, zzz341, Pos(Succ(Zero)), zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, Succ(zzz660), h) → new_mkVBalBranch3MkVBalBranch18(zzz340, zzz341, zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, new_primPlusNat2(Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat3(new_primPlusNat1(Zero), Zero)), Zero))), Succ(Zero)), h)
new_mkVBalBranch3MkVBalBranch122(zzz340, zzz341, zzz34200, zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, h) → new_mkVBalBranch0(zzz31, zzz514, Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), h)
new_mkVBalBranch3MkVBalBranch217(zzz473, zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, zzz481, zzz482, Succ(zzz4830), Succ(zzz4840), bh) → new_mkVBalBranch3MkVBalBranch217(zzz473, zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, zzz481, zzz482, zzz4830, zzz4840, bh)
new_mkVBalBranch3MkVBalBranch116(zzz340, zzz341, zzz34200, zzz343, zzz344, zzz510, zzz511, zzz513, zzz514, zzz31, Succ(zzz1200), h) → new_mkVBalBranch0(zzz31, zzz514, Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), h)
new_mkVBalBranch3MkVBalBranch110(zzz461, zzz462, zzz463, zzz464, zzz465, zzz466, zzz467, zzz468, zzz469, zzz470, zzz471, Zero, bb) → new_mkVBalBranch3MkVBalBranch115(zzz461, zzz462, zzz463, zzz464, zzz465, zzz466, zzz467, Succ(zzz468), zzz469, zzz470, zzz471, Zero, Succ(Succ(zzz468)), bb)
new_mkVBalBranch3MkVBalBranch225(zzz498, zzz499, zzz500, zzz501, zzz502, zzz503, zzz504, zzz505, zzz506, zzz507, Zero, Succ(zzz5090), bg) → new_mkVBalBranch0(zzz507, Branch(zzz503, zzz504, Neg(Succ(Zero)), zzz505, zzz506), zzz501, bg)
new_mkVBalBranch0(zzz31, Branch(zzz510, zzz511, Neg(Succ(zzz51200)), zzz513, zzz514), Branch(zzz340, zzz341, zzz342, zzz343, zzz344), h) → new_mkVBalBranch3MkVBalBranch223(zzz340, zzz341, zzz342, zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat3(new_primPlusNat1(zzz51200), zzz51200)), zzz51200))), h)
new_mkVBalBranch0(zzz31, Branch(zzz510, zzz511, Neg(Zero), zzz513, zzz514), Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), h) → new_mkVBalBranch3MkVBalBranch117(zzz340, zzz341, zzz34200, zzz343, zzz344, zzz510, zzz511, zzz513, zzz514, zzz31, new_primPlusNat2(new_primPlusNat3(Succ(new_primPlusNat3(new_primPlusNat1(zzz34200), zzz34200)), Succ(zzz34200)), Succ(zzz34200)), h)
new_mkVBalBranch3MkVBalBranch217(zzz473, zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, zzz481, zzz482, Succ(zzz4830), Zero, bh) → new_mkVBalBranch3MkVBalBranch121(zzz473, zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, zzz481, zzz482, new_primPlusNat2(new_primPlusNat3(Succ(new_primPlusNat3(new_primPlusNat1(zzz475), zzz475)), Succ(zzz475)), Succ(zzz475)), bh)
new_mkVBalBranch3MkVBalBranch121(zzz473, zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, zzz481, zzz482, Zero, bh) → new_mkVBalBranch3MkVBalBranch115(zzz473, zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, Zero, zzz480, zzz481, zzz482, Zero, Succ(Zero), bh)
new_mkVBalBranch3MkVBalBranch223(zzz340, zzz341, Neg(Succ(Zero)), zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, Succ(zzz670), h) → new_mkVBalBranch0(zzz31, Branch(zzz510, zzz511, Neg(Succ(zzz51200)), zzz513, zzz514), zzz343, h)
new_mkVBalBranch3MkVBalBranch229(zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, zzz1125, zzz1126, zzz1127, zzz1128, zzz1129, bd) → new_mkVBalBranch3MkVBalBranch119(zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, zzz1125, zzz1126, zzz1127, zzz1128, zzz1129, new_primPlusNat2(new_primPlusNat3(Succ(new_primPlusNat3(new_primPlusNat1(zzz1121), zzz1121)), Succ(zzz1121)), Succ(zzz1121)), bd)
new_mkVBalBranch3MkVBalBranch225(zzz498, zzz499, zzz500, zzz501, zzz502, zzz503, zzz504, zzz505, zzz506, zzz507, Succ(zzz5080), Zero, bg) → new_mkVBalBranch3MkVBalBranch118(zzz498, zzz499, zzz500, zzz501, zzz502, zzz503, zzz504, zzz505, zzz506, zzz507, new_primPlusNat2(new_primPlusNat3(Succ(new_primPlusNat3(new_primPlusNat1(zzz500), zzz500)), Succ(zzz500)), Succ(zzz500)), bg)
new_mkVBalBranch3MkVBalBranch218(zzz461, zzz462, zzz463, zzz464, zzz465, zzz466, zzz467, zzz468, zzz469, zzz470, zzz471, bb) → new_mkVBalBranch3MkVBalBranch110(zzz461, zzz462, zzz463, zzz464, zzz465, zzz466, zzz467, zzz468, zzz469, zzz470, zzz471, new_primPlusNat2(Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat3(new_primPlusNat1(zzz463), zzz463)), zzz463))), Succ(zzz463)), bb)
new_mkVBalBranch0(zzz31, Branch(zzz510, zzz511, Pos(Zero), zzz513, zzz514), Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), h) → new_mkVBalBranch3MkVBalBranch116(zzz340, zzz341, zzz34200, zzz343, zzz344, zzz510, zzz511, zzz513, zzz514, zzz31, new_primPlusNat2(new_primPlusNat3(Succ(new_primPlusNat3(new_primPlusNat1(zzz34200), zzz34200)), Succ(zzz34200)), Succ(zzz34200)), h)
new_mkVBalBranch3MkVBalBranch222(zzz461, zzz462, zzz463, zzz464, zzz465, zzz466, zzz467, zzz468, zzz469, zzz470, zzz471, bb) → new_mkVBalBranch3MkVBalBranch110(zzz461, zzz462, zzz463, zzz464, zzz465, zzz466, zzz467, zzz468, zzz469, zzz470, zzz471, new_primPlusNat2(Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat3(new_primPlusNat1(zzz463), zzz463)), zzz463))), Succ(zzz463)), bb)
new_mkVBalBranch3MkVBalBranch215(zzz340, zzz341, Pos(Succ(Succ(zzz342000))), zzz343, zzz344, zzz510, zzz511, Zero, zzz513, zzz514, zzz31, Succ(Succ(zzz6600)), h) → new_mkVBalBranch3MkVBalBranch217(zzz340, zzz341, Succ(zzz342000), zzz343, zzz344, zzz510, zzz511, zzz513, zzz514, zzz31, Succ(zzz6600), zzz342000, h)
new_mkVBalBranch3MkVBalBranch117(zzz340, zzz341, zzz34200, zzz343, zzz344, zzz510, zzz511, zzz513, zzz514, zzz31, Succ(zzz1240), h) → new_mkVBalBranch0(zzz31, zzz514, Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), h)
new_mkVBalBranch3MkVBalBranch120(zzz2050, zzz2051, zzz2052, zzz2053, zzz2054, zzz2055, zzz2056, zzz2057, zzz2058, zzz2059, zzz2060, Succ(zzz20610), Succ(zzz20620), be) → new_mkVBalBranch3MkVBalBranch120(zzz2050, zzz2051, zzz2052, zzz2053, zzz2054, zzz2055, zzz2056, zzz2057, zzz2058, zzz2059, zzz2060, zzz20610, zzz20620, be)
new_mkVBalBranch3MkVBalBranch217(zzz473, zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, zzz481, zzz482, Zero, Zero, bh) → new_mkVBalBranch3MkVBalBranch233(zzz473, zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, zzz481, zzz482, bh)
new_mkVBalBranch3MkVBalBranch216(zzz1105, zzz1106, zzz1107, zzz1108, zzz1109, zzz1110, zzz1111, zzz1112, zzz1113, zzz1114, zzz1115, Succ(zzz11160), Succ(zzz11170), ba) → new_mkVBalBranch3MkVBalBranch216(zzz1105, zzz1106, zzz1107, zzz1108, zzz1109, zzz1110, zzz1111, zzz1112, zzz1113, zzz1114, zzz1115, zzz11160, zzz11170, ba)
new_mkVBalBranch3MkVBalBranch223(zzz340, zzz341, Pos(zzz3420), zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, Succ(zzz670), h) → new_mkVBalBranch0(zzz31, Branch(zzz510, zzz511, Neg(Succ(zzz51200)), zzz513, zzz514), zzz343, h)
new_mkVBalBranch3MkVBalBranch19(zzz340, zzz341, zzz34200, zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, Zero, h) → new_mkVBalBranch3MkVBalBranch122(zzz340, zzz341, zzz34200, zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, h)
new_mkVBalBranch3MkVBalBranch225(zzz498, zzz499, zzz500, zzz501, zzz502, zzz503, zzz504, zzz505, zzz506, zzz507, Succ(zzz5080), Succ(zzz5090), bg) → new_mkVBalBranch3MkVBalBranch225(zzz498, zzz499, zzz500, zzz501, zzz502, zzz503, zzz504, zzz505, zzz506, zzz507, zzz5080, zzz5090, bg)
new_mkVBalBranch3MkVBalBranch19(zzz340, zzz341, zzz34200, zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, Succ(zzz1410), h) → new_mkVBalBranch0(zzz31, zzz514, Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), h)
new_mkVBalBranch3MkVBalBranch224(zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, zzz1125, zzz1126, zzz1127, zzz1128, zzz1129, Zero, Succ(zzz11310), bd) → new_mkVBalBranch3MkVBalBranch227(zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, zzz1125, zzz1126, zzz1127, zzz1128, zzz1129, bd)
new_mkVBalBranch3MkVBalBranch224(zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, zzz1125, zzz1126, zzz1127, zzz1128, zzz1129, Zero, Zero, bd) → new_mkVBalBranch3MkVBalBranch229(zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, zzz1125, zzz1126, zzz1127, zzz1128, zzz1129, bd)
new_mkVBalBranch3MkVBalBranch223(zzz340, zzz341, Neg(Succ(Succ(Zero))), zzz343, zzz344, zzz510, zzz511, Zero, zzz513, zzz514, zzz31, Succ(Succ(zzz6700)), h) → new_mkVBalBranch3MkVBalBranch225(zzz340, zzz341, Succ(Zero), zzz343, zzz344, zzz510, zzz511, zzz513, zzz514, zzz31, Zero, Succ(zzz6700), h)
new_mkVBalBranch3MkVBalBranch223(zzz340, zzz341, Neg(Succ(Succ(Succ(zzz3420000)))), zzz343, zzz344, zzz510, zzz511, Succ(zzz512000), zzz513, zzz514, zzz31, Succ(Succ(zzz6700)), h) → new_mkVBalBranch3MkVBalBranch224(zzz340, zzz341, Succ(Succ(zzz3420000)), zzz343, zzz344, zzz510, zzz511, zzz512000, zzz513, zzz514, zzz31, Succ(zzz3420000), Succ(Succ(new_primPlusNat2(zzz6700, zzz512000))), h)
new_mkVBalBranch3MkVBalBranch115(zzz1986, zzz1987, zzz1988, zzz1989, zzz1990, zzz1991, zzz1992, zzz1993, zzz1994, zzz1995, zzz1996, Succ(zzz19970), Succ(zzz19980), bc) → new_mkVBalBranch3MkVBalBranch115(zzz1986, zzz1987, zzz1988, zzz1989, zzz1990, zzz1991, zzz1992, zzz1993, zzz1994, zzz1995, zzz1996, zzz19970, zzz19980, bc)
new_mkVBalBranch3MkVBalBranch215(zzz340, zzz341, Neg(Zero), zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, Succ(zzz660), h) → new_mkVBalBranch0(zzz31, zzz514, Branch(zzz340, zzz341, Neg(Zero), zzz343, zzz344), h)
new_mkVBalBranch3MkVBalBranch118(zzz498, zzz499, zzz500, zzz501, zzz502, zzz503, zzz504, zzz505, zzz506, zzz507, Succ(zzz8040), bg) → new_mkVBalBranch3MkVBalBranch120(zzz498, zzz499, zzz500, zzz501, zzz502, zzz503, zzz504, Zero, zzz505, zzz506, zzz507, Succ(Zero), Succ(zzz8040), bg)
new_mkVBalBranch3MkVBalBranch216(zzz1105, zzz1106, zzz1107, zzz1108, zzz1109, zzz1110, zzz1111, zzz1112, zzz1113, zzz1114, zzz1115, Succ(zzz11160), Zero, ba) → new_mkVBalBranch3MkVBalBranch218(zzz1105, zzz1106, zzz1107, zzz1108, zzz1109, zzz1110, zzz1111, zzz1112, zzz1113, zzz1114, zzz1115, ba)
new_mkVBalBranch3MkVBalBranch216(zzz1105, zzz1106, zzz1107, zzz1108, zzz1109, zzz1110, zzz1111, zzz1112, zzz1113, zzz1114, zzz1115, Zero, Zero, ba) → new_mkVBalBranch3MkVBalBranch222(zzz1105, zzz1106, zzz1107, zzz1108, zzz1109, zzz1110, zzz1111, zzz1112, zzz1113, zzz1114, zzz1115, ba)
new_mkVBalBranch3MkVBalBranch18(zzz340, zzz341, zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, Zero, h) → new_mkVBalBranch3MkVBalBranch115(zzz340, zzz341, Zero, zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, Zero, Succ(zzz51200), h)
new_mkVBalBranch3MkVBalBranch119(zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, zzz1125, zzz1126, zzz1127, zzz1128, zzz1129, Succ(zzz12130), bd) → new_mkVBalBranch3MkVBalBranch120(zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, zzz1125, Succ(zzz1126), zzz1127, zzz1128, zzz1129, Succ(Succ(zzz1126)), Succ(zzz12130), bd)

The TRS R consists of the following rules:

new_primPlusNat1(Zero) → Zero
new_primPlusNat1(Succ(zzz62000)) → Succ(Succ(new_primPlusNat1(zzz62000)))
new_primPlusNat3(zzz90, Succ(zzz910)) → Succ(Succ(new_primPlusNat2(zzz90, zzz910)))
new_primPlusNat3(zzz90, Zero) → Succ(zzz90)
new_primPlusNat2(Succ(zzz900), Succ(zzz9100)) → Succ(Succ(new_primPlusNat2(zzz900, zzz9100)))
new_primPlusNat2(Zero, Succ(zzz9100)) → Succ(zzz9100)
new_primPlusNat2(Zero, Zero) → Zero
new_primPlusNat2(Succ(zzz900), Zero) → Succ(zzz900)

The set Q consists of the following terms:

new_primPlusNat2(Zero, Succ(x0))
new_primPlusNat3(x0, Succ(x1))
new_primPlusNat2(Succ(x0), Succ(x1))
new_primPlusNat3(x0, Zero)
new_primPlusNat1(Zero)
new_primPlusNat2(Zero, Zero)
new_primPlusNat1(Succ(x0))
new_primPlusNat2(Succ(x0), Zero)

We have to consider all minimal (P,Q,R)-chains.
By rewriting [15] the rule new_mkVBalBranch0(zzz31, Branch(zzz510, zzz511, Neg(Zero), zzz513, zzz514), Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), h) → new_mkVBalBranch3MkVBalBranch117(zzz340, zzz341, zzz34200, zzz343, zzz344, zzz510, zzz511, zzz513, zzz514, zzz31, new_primPlusNat2(new_primPlusNat3(Succ(new_primPlusNat3(new_primPlusNat1(zzz34200), zzz34200)), Succ(zzz34200)), Succ(zzz34200)), h) at position [10,0] we obtained the following new rules:

new_mkVBalBranch0(zzz31, Branch(zzz510, zzz511, Neg(Zero), zzz513, zzz514), Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), h) → new_mkVBalBranch3MkVBalBranch117(zzz340, zzz341, zzz34200, zzz343, zzz344, zzz510, zzz511, zzz513, zzz514, zzz31, new_primPlusNat2(Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat3(new_primPlusNat1(zzz34200), zzz34200)), 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
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                    ↳ DependencyGraphProof
                                      ↳ QDP
                                        ↳ Rewriting
                                          ↳ QDP
                                            ↳ Rewriting
                                              ↳ QDP
                                                ↳ Rewriting
                                                  ↳ QDP
                                                    ↳ Rewriting
                                                      ↳ QDP
                                                        ↳ Rewriting
                                                          ↳ QDP
                                                            ↳ Rewriting
                                                              ↳ QDP
                                                                ↳ Rewriting
                                                                  ↳ QDP
                                                                    ↳ Rewriting
                                                                      ↳ QDP
                                                                        ↳ Rewriting
                                                                          ↳ QDP
                                                                            ↳ Rewriting
                                                                              ↳ QDP
                                                                                ↳ Rewriting
                                                                                  ↳ QDP
                                                                                    ↳ Rewriting
                                                                                      ↳ QDP
                                                                                        ↳ Rewriting
                                                                                          ↳ QDP
                                                                                            ↳ Rewriting
                                                                                              ↳ QDP
                                                                                                ↳ Rewriting
                                                                                                  ↳ QDP
                                                                                                    ↳ Rewriting
                                                                                                      ↳ QDP
                                                                                                        ↳ Rewriting
                                                                                                          ↳ QDP
                                                                                                            ↳ UsableRulesProof
                                                                                                              ↳ QDP
                                                                                                                ↳ QReductionProof
                                                                                                                  ↳ QDP
                                                                                                                    ↳ Rewriting
                                                                                                                      ↳ QDP
                                                                                                                        ↳ Rewriting
                                                                                                                          ↳ QDP
                                                                                                                            ↳ DependencyGraphProof
                                                                                                                              ↳ QDP
                                                                                                                                ↳ Rewriting
                                                                                                                                  ↳ QDP
                                                                                                                                    ↳ Rewriting
                                                                                                                                      ↳ QDP
                                                                                                                                        ↳ DependencyGraphProof
                                                                                                                                          ↳ QDP
                                                                                                                                            ↳ Rewriting
                                                                                                                                              ↳ QDP
                                                                                                                                                ↳ Rewriting
                                                                                                                                                  ↳ QDP
                                                                                                                                                    ↳ Rewriting
                                                                                                                                                      ↳ QDP
                                                                                                                                                        ↳ Rewriting
                                                                                                                                                          ↳ QDP
                                                                                                                                                            ↳ Rewriting
                                                                                                                                                              ↳ QDP
                                                                                                                                                                ↳ Rewriting
                                                                                                                                                                  ↳ QDP
                                                                                                                                                                    ↳ Rewriting
                                                                                                                                                                      ↳ QDP
                                                                                                                                                                        ↳ Rewriting
                                                                                                                                                                          ↳ QDP
                                                                                                                                                                            ↳ Rewriting
                                                                                                                                                                              ↳ QDP
                                                                                                                                                                                ↳ Rewriting
                                                                                                                                                                                  ↳ QDP
                                                                                                                                                                                    ↳ Rewriting
                                                                                                                                                                                      ↳ QDP
                                                                                                                                                                                        ↳ Rewriting
                                                                                                                                                                                          ↳ QDP
                                                                                                                                                                                            ↳ UsableRulesProof
                                                                                                                                                                                              ↳ QDP
                                                                                                                                                                                                ↳ QReductionProof
                                                                                                                                                                                                  ↳ QDP
                                                                                                                                                                                                    ↳ Rewriting
                                                                                                                                                                                                      ↳ QDP
                                                                                                                                                                                                        ↳ Rewriting
                                                                                                                                                                                                          ↳ QDP
                                                                                                                                                                                                            ↳ Rewriting
                                                                                                                                                                                                              ↳ QDP
                                                                                                                                                                                                                ↳ Rewriting
                                                                                                                                                                                                                  ↳ QDP
                                                                                                                                                                                                                    ↳ Rewriting
                                                                                                                                                                                                                      ↳ QDP
                                                                                                                                                                                                                        ↳ Rewriting
                                                                                                                                                                                                                          ↳ QDP
                                                                                                                                                                                                                            ↳ Rewriting
                                                                                                                                                                                                                              ↳ QDP
                                                                                                                                                                                                                                ↳ Rewriting
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP

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

new_mkVBalBranch3MkVBalBranch225(zzz498, zzz499, zzz500, zzz501, zzz502, zzz503, zzz504, zzz505, zzz506, zzz507, Zero, Zero, bg) → new_mkVBalBranch3MkVBalBranch230(zzz498, zzz499, zzz500, zzz501, zzz502, zzz503, zzz504, zzz505, zzz506, zzz507, bg)
new_mkVBalBranch3MkVBalBranch18(zzz340, zzz341, zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, Succ(zzz1480), h) → new_mkVBalBranch3MkVBalBranch115(zzz340, zzz341, Zero, zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, Succ(zzz1480), Succ(zzz51200), h)
new_mkVBalBranch0(zzz31, Branch(zzz510, zzz511, Neg(Zero), zzz513, zzz514), Branch(zzz340, zzz341, Pos(Succ(zzz34200)), zzz343, zzz344), h) → new_mkVBalBranch0(zzz31, Branch(zzz510, zzz511, Neg(Zero), zzz513, zzz514), zzz343, h)
new_mkVBalBranch3MkVBalBranch215(zzz340, zzz341, Pos(Succ(Succ(zzz342000))), zzz343, zzz344, zzz510, zzz511, Succ(zzz512000), zzz513, zzz514, zzz31, Succ(Succ(zzz6600)), h) → new_mkVBalBranch3MkVBalBranch216(zzz340, zzz341, Succ(zzz342000), zzz343, zzz344, zzz510, zzz511, zzz512000, zzz513, zzz514, zzz31, Succ(Succ(new_primPlusNat2(zzz6600, zzz512000))), zzz342000, h)
new_mkVBalBranch3MkVBalBranch223(zzz340, zzz341, Neg(Succ(Succ(Succ(zzz3420000)))), zzz343, zzz344, zzz510, zzz511, Zero, zzz513, zzz514, zzz31, Succ(Succ(zzz6700)), h) → new_mkVBalBranch3MkVBalBranch225(zzz340, zzz341, Succ(Succ(zzz3420000)), zzz343, zzz344, zzz510, zzz511, zzz513, zzz514, zzz31, Succ(zzz3420000), Succ(zzz6700), h)
new_mkVBalBranch3MkVBalBranch120(zzz2050, zzz2051, zzz2052, zzz2053, zzz2054, zzz2055, zzz2056, zzz2057, zzz2058, zzz2059, zzz2060, Zero, Succ(zzz20620), be) → new_mkVBalBranch0(zzz2060, zzz2059, Branch(zzz2050, zzz2051, Neg(Succ(zzz2052)), zzz2053, zzz2054), be)
new_mkVBalBranch3MkVBalBranch121(zzz473, zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, zzz481, zzz482, Succ(zzz7390), bh) → new_mkVBalBranch3MkVBalBranch115(zzz473, zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, Zero, zzz480, zzz481, zzz482, Succ(zzz7390), Succ(Zero), bh)
new_mkVBalBranch0(zzz31, Branch(zzz510, zzz511, Pos(Zero), zzz513, zzz514), Branch(zzz340, zzz341, Pos(Succ(zzz34200)), zzz343, zzz344), h) → new_mkVBalBranch0(zzz31, Branch(zzz510, zzz511, Pos(Zero), zzz513, zzz514), zzz343, h)
new_mkVBalBranch3MkVBalBranch215(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, Succ(zzz660), h) → new_mkVBalBranch3MkVBalBranch19(zzz340, zzz341, zzz34200, zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, new_primPlusNat2(Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat3(new_primPlusNat1(zzz34200), zzz34200)), zzz34200))), Succ(zzz34200)), h)
new_mkVBalBranch0(zzz31, Branch(zzz510, zzz511, Pos(Succ(zzz51200)), zzz513, zzz514), Branch(zzz340, zzz341, zzz342, zzz343, zzz344), h) → new_mkVBalBranch3MkVBalBranch215(zzz340, zzz341, zzz342, zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat3(new_primPlusNat1(zzz51200), zzz51200)), zzz51200))), h)
new_mkVBalBranch3MkVBalBranch223(zzz340, zzz341, Neg(Succ(Succ(Zero))), zzz343, zzz344, zzz510, zzz511, Succ(zzz512000), zzz513, zzz514, zzz31, Succ(Succ(zzz6700)), h) → new_mkVBalBranch3MkVBalBranch224(zzz340, zzz341, Succ(Zero), zzz343, zzz344, zzz510, zzz511, zzz512000, zzz513, zzz514, zzz31, Zero, Succ(Succ(new_primPlusNat2(zzz6700, zzz512000))), h)
new_mkVBalBranch3MkVBalBranch230(zzz498, zzz499, zzz500, zzz501, zzz502, zzz503, zzz504, zzz505, zzz506, zzz507, bg) → new_mkVBalBranch3MkVBalBranch118(zzz498, zzz499, zzz500, zzz501, zzz502, zzz503, zzz504, zzz505, zzz506, zzz507, Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat2(Succ(new_primPlusNat3(new_primPlusNat1(zzz500), zzz500)), zzz500)), zzz500))), bg)
new_mkVBalBranch3MkVBalBranch224(zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, zzz1125, zzz1126, zzz1127, zzz1128, zzz1129, Succ(zzz11300), Succ(zzz11310), bd) → new_mkVBalBranch3MkVBalBranch224(zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, zzz1125, zzz1126, zzz1127, zzz1128, zzz1129, zzz11300, zzz11310, bd)
new_mkVBalBranch3MkVBalBranch217(zzz473, zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, zzz481, zzz482, Zero, Succ(zzz4840), bh) → new_mkVBalBranch0(zzz482, Branch(zzz478, zzz479, Pos(Succ(Zero)), zzz480, zzz481), zzz476, bh)
new_mkVBalBranch3MkVBalBranch224(zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, zzz1125, zzz1126, zzz1127, zzz1128, zzz1129, Succ(zzz11300), Zero, bd) → new_mkVBalBranch3MkVBalBranch119(zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, zzz1125, zzz1126, zzz1127, zzz1128, zzz1129, new_primPlusNat2(Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat3(new_primPlusNat1(zzz1121), zzz1121)), zzz1121))), Succ(zzz1121)), bd)
new_mkVBalBranch3MkVBalBranch110(zzz461, zzz462, zzz463, zzz464, zzz465, zzz466, zzz467, zzz468, zzz469, zzz470, zzz471, Succ(zzz5800), bb) → new_mkVBalBranch3MkVBalBranch115(zzz461, zzz462, zzz463, zzz464, zzz465, zzz466, zzz467, Succ(zzz468), zzz469, zzz470, zzz471, Succ(zzz5800), Succ(Succ(zzz468)), bb)
new_mkVBalBranch3MkVBalBranch227(zzz486, zzz487, zzz488, zzz489, zzz490, zzz491, zzz492, zzz493, zzz494, zzz495, zzz496, bf) → new_mkVBalBranch0(zzz496, Branch(zzz491, zzz492, Neg(Succ(Succ(zzz493))), zzz494, zzz495), zzz489, bf)
new_mkVBalBranch3MkVBalBranch215(zzz340, zzz341, Pos(Zero), zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, Succ(zzz660), h) → new_mkVBalBranch0(zzz31, zzz514, Branch(zzz340, zzz341, Pos(Zero), zzz343, zzz344), h)
new_mkVBalBranch3MkVBalBranch223(zzz340, zzz341, Neg(Zero), zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, Succ(zzz670), h) → new_mkVBalBranch0(zzz31, Branch(zzz510, zzz511, Neg(Succ(zzz51200)), zzz513, zzz514), zzz343, h)
new_mkVBalBranch3MkVBalBranch216(zzz1105, zzz1106, zzz1107, zzz1108, zzz1109, zzz1110, zzz1111, zzz1112, zzz1113, zzz1114, zzz1115, Zero, Succ(zzz11170), ba) → new_mkVBalBranch0(zzz1115, Branch(zzz1110, zzz1111, Pos(Succ(Succ(zzz1112))), zzz1113, zzz1114), zzz1108, ba)
new_mkVBalBranch3MkVBalBranch115(zzz1986, zzz1987, zzz1988, zzz1989, zzz1990, zzz1991, zzz1992, zzz1993, zzz1994, zzz1995, zzz1996, Zero, Succ(zzz19980), bc) → new_mkVBalBranch0(zzz1996, zzz1995, Branch(zzz1986, zzz1987, Pos(Succ(zzz1988)), zzz1989, zzz1990), bc)
new_mkVBalBranch3MkVBalBranch233(zzz473, zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, zzz481, zzz482, bh) → new_mkVBalBranch3MkVBalBranch121(zzz473, zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, zzz481, zzz482, new_primPlusNat2(Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat3(new_primPlusNat1(zzz475), zzz475)), zzz475))), Succ(zzz475)), bh)
new_mkVBalBranch3MkVBalBranch215(zzz340, zzz341, Pos(Succ(Zero)), zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, Succ(zzz660), h) → new_mkVBalBranch3MkVBalBranch18(zzz340, zzz341, zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, new_primPlusNat2(Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat3(new_primPlusNat1(Zero), Zero)), Zero))), Succ(Zero)), h)
new_mkVBalBranch3MkVBalBranch122(zzz340, zzz341, zzz34200, zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, h) → new_mkVBalBranch0(zzz31, zzz514, Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), h)
new_mkVBalBranch3MkVBalBranch217(zzz473, zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, zzz481, zzz482, Succ(zzz4830), Succ(zzz4840), bh) → new_mkVBalBranch3MkVBalBranch217(zzz473, zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, zzz481, zzz482, zzz4830, zzz4840, bh)
new_mkVBalBranch3MkVBalBranch116(zzz340, zzz341, zzz34200, zzz343, zzz344, zzz510, zzz511, zzz513, zzz514, zzz31, Succ(zzz1200), h) → new_mkVBalBranch0(zzz31, zzz514, Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), h)
new_mkVBalBranch3MkVBalBranch110(zzz461, zzz462, zzz463, zzz464, zzz465, zzz466, zzz467, zzz468, zzz469, zzz470, zzz471, Zero, bb) → new_mkVBalBranch3MkVBalBranch115(zzz461, zzz462, zzz463, zzz464, zzz465, zzz466, zzz467, Succ(zzz468), zzz469, zzz470, zzz471, Zero, Succ(Succ(zzz468)), bb)
new_mkVBalBranch3MkVBalBranch225(zzz498, zzz499, zzz500, zzz501, zzz502, zzz503, zzz504, zzz505, zzz506, zzz507, Zero, Succ(zzz5090), bg) → new_mkVBalBranch0(zzz507, Branch(zzz503, zzz504, Neg(Succ(Zero)), zzz505, zzz506), zzz501, bg)
new_mkVBalBranch0(zzz31, Branch(zzz510, zzz511, Neg(Succ(zzz51200)), zzz513, zzz514), Branch(zzz340, zzz341, zzz342, zzz343, zzz344), h) → new_mkVBalBranch3MkVBalBranch223(zzz340, zzz341, zzz342, zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat3(new_primPlusNat1(zzz51200), zzz51200)), zzz51200))), h)
new_mkVBalBranch3MkVBalBranch217(zzz473, zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, zzz481, zzz482, Succ(zzz4830), Zero, bh) → new_mkVBalBranch3MkVBalBranch121(zzz473, zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, zzz481, zzz482, new_primPlusNat2(new_primPlusNat3(Succ(new_primPlusNat3(new_primPlusNat1(zzz475), zzz475)), Succ(zzz475)), Succ(zzz475)), bh)
new_mkVBalBranch3MkVBalBranch121(zzz473, zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, zzz481, zzz482, Zero, bh) → new_mkVBalBranch3MkVBalBranch115(zzz473, zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, Zero, zzz480, zzz481, zzz482, Zero, Succ(Zero), bh)
new_mkVBalBranch3MkVBalBranch223(zzz340, zzz341, Neg(Succ(Zero)), zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, Succ(zzz670), h) → new_mkVBalBranch0(zzz31, Branch(zzz510, zzz511, Neg(Succ(zzz51200)), zzz513, zzz514), zzz343, h)
new_mkVBalBranch3MkVBalBranch225(zzz498, zzz499, zzz500, zzz501, zzz502, zzz503, zzz504, zzz505, zzz506, zzz507, Succ(zzz5080), Zero, bg) → new_mkVBalBranch3MkVBalBranch118(zzz498, zzz499, zzz500, zzz501, zzz502, zzz503, zzz504, zzz505, zzz506, zzz507, new_primPlusNat2(new_primPlusNat3(Succ(new_primPlusNat3(new_primPlusNat1(zzz500), zzz500)), Succ(zzz500)), Succ(zzz500)), bg)
new_mkVBalBranch3MkVBalBranch229(zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, zzz1125, zzz1126, zzz1127, zzz1128, zzz1129, bd) → new_mkVBalBranch3MkVBalBranch119(zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, zzz1125, zzz1126, zzz1127, zzz1128, zzz1129, new_primPlusNat2(new_primPlusNat3(Succ(new_primPlusNat3(new_primPlusNat1(zzz1121), zzz1121)), Succ(zzz1121)), Succ(zzz1121)), bd)
new_mkVBalBranch3MkVBalBranch218(zzz461, zzz462, zzz463, zzz464, zzz465, zzz466, zzz467, zzz468, zzz469, zzz470, zzz471, bb) → new_mkVBalBranch3MkVBalBranch110(zzz461, zzz462, zzz463, zzz464, zzz465, zzz466, zzz467, zzz468, zzz469, zzz470, zzz471, new_primPlusNat2(Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat3(new_primPlusNat1(zzz463), zzz463)), zzz463))), Succ(zzz463)), bb)
new_mkVBalBranch0(zzz31, Branch(zzz510, zzz511, Pos(Zero), zzz513, zzz514), Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), h) → new_mkVBalBranch3MkVBalBranch116(zzz340, zzz341, zzz34200, zzz343, zzz344, zzz510, zzz511, zzz513, zzz514, zzz31, new_primPlusNat2(new_primPlusNat3(Succ(new_primPlusNat3(new_primPlusNat1(zzz34200), zzz34200)), Succ(zzz34200)), Succ(zzz34200)), h)
new_mkVBalBranch3MkVBalBranch222(zzz461, zzz462, zzz463, zzz464, zzz465, zzz466, zzz467, zzz468, zzz469, zzz470, zzz471, bb) → new_mkVBalBranch3MkVBalBranch110(zzz461, zzz462, zzz463, zzz464, zzz465, zzz466, zzz467, zzz468, zzz469, zzz470, zzz471, new_primPlusNat2(Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat3(new_primPlusNat1(zzz463), zzz463)), zzz463))), Succ(zzz463)), bb)
new_mkVBalBranch3MkVBalBranch215(zzz340, zzz341, Pos(Succ(Succ(zzz342000))), zzz343, zzz344, zzz510, zzz511, Zero, zzz513, zzz514, zzz31, Succ(Succ(zzz6600)), h) → new_mkVBalBranch3MkVBalBranch217(zzz340, zzz341, Succ(zzz342000), zzz343, zzz344, zzz510, zzz511, zzz513, zzz514, zzz31, Succ(zzz6600), zzz342000, h)
new_mkVBalBranch3MkVBalBranch117(zzz340, zzz341, zzz34200, zzz343, zzz344, zzz510, zzz511, zzz513, zzz514, zzz31, Succ(zzz1240), h) → new_mkVBalBranch0(zzz31, zzz514, Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), h)
new_mkVBalBranch3MkVBalBranch217(zzz473, zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, zzz481, zzz482, Zero, Zero, bh) → new_mkVBalBranch3MkVBalBranch233(zzz473, zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, zzz481, zzz482, bh)
new_mkVBalBranch3MkVBalBranch120(zzz2050, zzz2051, zzz2052, zzz2053, zzz2054, zzz2055, zzz2056, zzz2057, zzz2058, zzz2059, zzz2060, Succ(zzz20610), Succ(zzz20620), be) → new_mkVBalBranch3MkVBalBranch120(zzz2050, zzz2051, zzz2052, zzz2053, zzz2054, zzz2055, zzz2056, zzz2057, zzz2058, zzz2059, zzz2060, zzz20610, zzz20620, be)
new_mkVBalBranch3MkVBalBranch223(zzz340, zzz341, Pos(zzz3420), zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, Succ(zzz670), h) → new_mkVBalBranch0(zzz31, Branch(zzz510, zzz511, Neg(Succ(zzz51200)), zzz513, zzz514), zzz343, h)
new_mkVBalBranch3MkVBalBranch216(zzz1105, zzz1106, zzz1107, zzz1108, zzz1109, zzz1110, zzz1111, zzz1112, zzz1113, zzz1114, zzz1115, Succ(zzz11160), Succ(zzz11170), ba) → new_mkVBalBranch3MkVBalBranch216(zzz1105, zzz1106, zzz1107, zzz1108, zzz1109, zzz1110, zzz1111, zzz1112, zzz1113, zzz1114, zzz1115, zzz11160, zzz11170, ba)
new_mkVBalBranch0(zzz31, Branch(zzz510, zzz511, Neg(Zero), zzz513, zzz514), Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), h) → new_mkVBalBranch3MkVBalBranch117(zzz340, zzz341, zzz34200, zzz343, zzz344, zzz510, zzz511, zzz513, zzz514, zzz31, new_primPlusNat2(Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat3(new_primPlusNat1(zzz34200), zzz34200)), zzz34200))), Succ(zzz34200)), h)
new_mkVBalBranch3MkVBalBranch19(zzz340, zzz341, zzz34200, zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, Zero, h) → new_mkVBalBranch3MkVBalBranch122(zzz340, zzz341, zzz34200, zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, h)
new_mkVBalBranch3MkVBalBranch225(zzz498, zzz499, zzz500, zzz501, zzz502, zzz503, zzz504, zzz505, zzz506, zzz507, Succ(zzz5080), Succ(zzz5090), bg) → new_mkVBalBranch3MkVBalBranch225(zzz498, zzz499, zzz500, zzz501, zzz502, zzz503, zzz504, zzz505, zzz506, zzz507, zzz5080, zzz5090, bg)
new_mkVBalBranch3MkVBalBranch19(zzz340, zzz341, zzz34200, zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, Succ(zzz1410), h) → new_mkVBalBranch0(zzz31, zzz514, Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), h)
new_mkVBalBranch3MkVBalBranch224(zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, zzz1125, zzz1126, zzz1127, zzz1128, zzz1129, Zero, Zero, bd) → new_mkVBalBranch3MkVBalBranch229(zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, zzz1125, zzz1126, zzz1127, zzz1128, zzz1129, bd)
new_mkVBalBranch3MkVBalBranch224(zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, zzz1125, zzz1126, zzz1127, zzz1128, zzz1129, Zero, Succ(zzz11310), bd) → new_mkVBalBranch3MkVBalBranch227(zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, zzz1125, zzz1126, zzz1127, zzz1128, zzz1129, bd)
new_mkVBalBranch3MkVBalBranch223(zzz340, zzz341, Neg(Succ(Succ(Succ(zzz3420000)))), zzz343, zzz344, zzz510, zzz511, Succ(zzz512000), zzz513, zzz514, zzz31, Succ(Succ(zzz6700)), h) → new_mkVBalBranch3MkVBalBranch224(zzz340, zzz341, Succ(Succ(zzz3420000)), zzz343, zzz344, zzz510, zzz511, zzz512000, zzz513, zzz514, zzz31, Succ(zzz3420000), Succ(Succ(new_primPlusNat2(zzz6700, zzz512000))), h)
new_mkVBalBranch3MkVBalBranch223(zzz340, zzz341, Neg(Succ(Succ(Zero))), zzz343, zzz344, zzz510, zzz511, Zero, zzz513, zzz514, zzz31, Succ(Succ(zzz6700)), h) → new_mkVBalBranch3MkVBalBranch225(zzz340, zzz341, Succ(Zero), zzz343, zzz344, zzz510, zzz511, zzz513, zzz514, zzz31, Zero, Succ(zzz6700), h)
new_mkVBalBranch3MkVBalBranch115(zzz1986, zzz1987, zzz1988, zzz1989, zzz1990, zzz1991, zzz1992, zzz1993, zzz1994, zzz1995, zzz1996, Succ(zzz19970), Succ(zzz19980), bc) → new_mkVBalBranch3MkVBalBranch115(zzz1986, zzz1987, zzz1988, zzz1989, zzz1990, zzz1991, zzz1992, zzz1993, zzz1994, zzz1995, zzz1996, zzz19970, zzz19980, bc)
new_mkVBalBranch3MkVBalBranch215(zzz340, zzz341, Neg(Zero), zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, Succ(zzz660), h) → new_mkVBalBranch0(zzz31, zzz514, Branch(zzz340, zzz341, Neg(Zero), zzz343, zzz344), h)
new_mkVBalBranch3MkVBalBranch118(zzz498, zzz499, zzz500, zzz501, zzz502, zzz503, zzz504, zzz505, zzz506, zzz507, Succ(zzz8040), bg) → new_mkVBalBranch3MkVBalBranch120(zzz498, zzz499, zzz500, zzz501, zzz502, zzz503, zzz504, Zero, zzz505, zzz506, zzz507, Succ(Zero), Succ(zzz8040), bg)
new_mkVBalBranch3MkVBalBranch216(zzz1105, zzz1106, zzz1107, zzz1108, zzz1109, zzz1110, zzz1111, zzz1112, zzz1113, zzz1114, zzz1115, Succ(zzz11160), Zero, ba) → new_mkVBalBranch3MkVBalBranch218(zzz1105, zzz1106, zzz1107, zzz1108, zzz1109, zzz1110, zzz1111, zzz1112, zzz1113, zzz1114, zzz1115, ba)
new_mkVBalBranch3MkVBalBranch216(zzz1105, zzz1106, zzz1107, zzz1108, zzz1109, zzz1110, zzz1111, zzz1112, zzz1113, zzz1114, zzz1115, Zero, Zero, ba) → new_mkVBalBranch3MkVBalBranch222(zzz1105, zzz1106, zzz1107, zzz1108, zzz1109, zzz1110, zzz1111, zzz1112, zzz1113, zzz1114, zzz1115, ba)
new_mkVBalBranch3MkVBalBranch119(zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, zzz1125, zzz1126, zzz1127, zzz1128, zzz1129, Succ(zzz12130), bd) → new_mkVBalBranch3MkVBalBranch120(zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, zzz1125, Succ(zzz1126), zzz1127, zzz1128, zzz1129, Succ(Succ(zzz1126)), Succ(zzz12130), bd)
new_mkVBalBranch3MkVBalBranch18(zzz340, zzz341, zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, Zero, h) → new_mkVBalBranch3MkVBalBranch115(zzz340, zzz341, Zero, zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, Zero, Succ(zzz51200), h)

The TRS R consists of the following rules:

new_primPlusNat1(Zero) → Zero
new_primPlusNat1(Succ(zzz62000)) → Succ(Succ(new_primPlusNat1(zzz62000)))
new_primPlusNat3(zzz90, Succ(zzz910)) → Succ(Succ(new_primPlusNat2(zzz90, zzz910)))
new_primPlusNat3(zzz90, Zero) → Succ(zzz90)
new_primPlusNat2(Succ(zzz900), Succ(zzz9100)) → Succ(Succ(new_primPlusNat2(zzz900, zzz9100)))
new_primPlusNat2(Zero, Succ(zzz9100)) → Succ(zzz9100)
new_primPlusNat2(Zero, Zero) → Zero
new_primPlusNat2(Succ(zzz900), Zero) → Succ(zzz900)

The set Q consists of the following terms:

new_primPlusNat2(Zero, Succ(x0))
new_primPlusNat3(x0, Succ(x1))
new_primPlusNat2(Succ(x0), Succ(x1))
new_primPlusNat3(x0, Zero)
new_primPlusNat1(Zero)
new_primPlusNat2(Zero, Zero)
new_primPlusNat1(Succ(x0))
new_primPlusNat2(Succ(x0), Zero)

We have to consider all minimal (P,Q,R)-chains.
By rewriting [15] the rule new_mkVBalBranch3MkVBalBranch217(zzz473, zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, zzz481, zzz482, Succ(zzz4830), Zero, bh) → new_mkVBalBranch3MkVBalBranch121(zzz473, zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, zzz481, zzz482, new_primPlusNat2(new_primPlusNat3(Succ(new_primPlusNat3(new_primPlusNat1(zzz475), zzz475)), Succ(zzz475)), Succ(zzz475)), bh) at position [10,0] we obtained the following new rules:

new_mkVBalBranch3MkVBalBranch217(zzz473, zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, zzz481, zzz482, Succ(zzz4830), Zero, bh) → new_mkVBalBranch3MkVBalBranch121(zzz473, zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, zzz481, zzz482, new_primPlusNat2(Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat3(new_primPlusNat1(zzz475), zzz475)), zzz475))), Succ(zzz475)), bh)



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

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

new_mkVBalBranch3MkVBalBranch225(zzz498, zzz499, zzz500, zzz501, zzz502, zzz503, zzz504, zzz505, zzz506, zzz507, Zero, Zero, bg) → new_mkVBalBranch3MkVBalBranch230(zzz498, zzz499, zzz500, zzz501, zzz502, zzz503, zzz504, zzz505, zzz506, zzz507, bg)
new_mkVBalBranch3MkVBalBranch18(zzz340, zzz341, zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, Succ(zzz1480), h) → new_mkVBalBranch3MkVBalBranch115(zzz340, zzz341, Zero, zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, Succ(zzz1480), Succ(zzz51200), h)
new_mkVBalBranch3MkVBalBranch215(zzz340, zzz341, Pos(Succ(Succ(zzz342000))), zzz343, zzz344, zzz510, zzz511, Succ(zzz512000), zzz513, zzz514, zzz31, Succ(Succ(zzz6600)), h) → new_mkVBalBranch3MkVBalBranch216(zzz340, zzz341, Succ(zzz342000), zzz343, zzz344, zzz510, zzz511, zzz512000, zzz513, zzz514, zzz31, Succ(Succ(new_primPlusNat2(zzz6600, zzz512000))), zzz342000, h)
new_mkVBalBranch0(zzz31, Branch(zzz510, zzz511, Neg(Zero), zzz513, zzz514), Branch(zzz340, zzz341, Pos(Succ(zzz34200)), zzz343, zzz344), h) → new_mkVBalBranch0(zzz31, Branch(zzz510, zzz511, Neg(Zero), zzz513, zzz514), zzz343, h)
new_mkVBalBranch3MkVBalBranch223(zzz340, zzz341, Neg(Succ(Succ(Succ(zzz3420000)))), zzz343, zzz344, zzz510, zzz511, Zero, zzz513, zzz514, zzz31, Succ(Succ(zzz6700)), h) → new_mkVBalBranch3MkVBalBranch225(zzz340, zzz341, Succ(Succ(zzz3420000)), zzz343, zzz344, zzz510, zzz511, zzz513, zzz514, zzz31, Succ(zzz3420000), Succ(zzz6700), h)
new_mkVBalBranch3MkVBalBranch120(zzz2050, zzz2051, zzz2052, zzz2053, zzz2054, zzz2055, zzz2056, zzz2057, zzz2058, zzz2059, zzz2060, Zero, Succ(zzz20620), be) → new_mkVBalBranch0(zzz2060, zzz2059, Branch(zzz2050, zzz2051, Neg(Succ(zzz2052)), zzz2053, zzz2054), be)
new_mkVBalBranch3MkVBalBranch215(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, Succ(zzz660), h) → new_mkVBalBranch3MkVBalBranch19(zzz340, zzz341, zzz34200, zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, new_primPlusNat2(Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat3(new_primPlusNat1(zzz34200), zzz34200)), zzz34200))), Succ(zzz34200)), h)
new_mkVBalBranch0(zzz31, Branch(zzz510, zzz511, Pos(Zero), zzz513, zzz514), Branch(zzz340, zzz341, Pos(Succ(zzz34200)), zzz343, zzz344), h) → new_mkVBalBranch0(zzz31, Branch(zzz510, zzz511, Pos(Zero), zzz513, zzz514), zzz343, h)
new_mkVBalBranch3MkVBalBranch121(zzz473, zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, zzz481, zzz482, Succ(zzz7390), bh) → new_mkVBalBranch3MkVBalBranch115(zzz473, zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, Zero, zzz480, zzz481, zzz482, Succ(zzz7390), Succ(Zero), bh)
new_mkVBalBranch0(zzz31, Branch(zzz510, zzz511, Pos(Succ(zzz51200)), zzz513, zzz514), Branch(zzz340, zzz341, zzz342, zzz343, zzz344), h) → new_mkVBalBranch3MkVBalBranch215(zzz340, zzz341, zzz342, zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat3(new_primPlusNat1(zzz51200), zzz51200)), zzz51200))), h)
new_mkVBalBranch3MkVBalBranch217(zzz473, zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, zzz481, zzz482, Succ(zzz4830), Zero, bh) → new_mkVBalBranch3MkVBalBranch121(zzz473, zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, zzz481, zzz482, new_primPlusNat2(Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat3(new_primPlusNat1(zzz475), zzz475)), zzz475))), Succ(zzz475)), bh)
new_mkVBalBranch3MkVBalBranch230(zzz498, zzz499, zzz500, zzz501, zzz502, zzz503, zzz504, zzz505, zzz506, zzz507, bg) → new_mkVBalBranch3MkVBalBranch118(zzz498, zzz499, zzz500, zzz501, zzz502, zzz503, zzz504, zzz505, zzz506, zzz507, Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat2(Succ(new_primPlusNat3(new_primPlusNat1(zzz500), zzz500)), zzz500)), zzz500))), bg)
new_mkVBalBranch3MkVBalBranch223(zzz340, zzz341, Neg(Succ(Succ(Zero))), zzz343, zzz344, zzz510, zzz511, Succ(zzz512000), zzz513, zzz514, zzz31, Succ(Succ(zzz6700)), h) → new_mkVBalBranch3MkVBalBranch224(zzz340, zzz341, Succ(Zero), zzz343, zzz344, zzz510, zzz511, zzz512000, zzz513, zzz514, zzz31, Zero, Succ(Succ(new_primPlusNat2(zzz6700, zzz512000))), h)
new_mkVBalBranch3MkVBalBranch224(zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, zzz1125, zzz1126, zzz1127, zzz1128, zzz1129, Succ(zzz11300), Succ(zzz11310), bd) → new_mkVBalBranch3MkVBalBranch224(zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, zzz1125, zzz1126, zzz1127, zzz1128, zzz1129, zzz11300, zzz11310, bd)
new_mkVBalBranch3MkVBalBranch217(zzz473, zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, zzz481, zzz482, Zero, Succ(zzz4840), bh) → new_mkVBalBranch0(zzz482, Branch(zzz478, zzz479, Pos(Succ(Zero)), zzz480, zzz481), zzz476, bh)
new_mkVBalBranch3MkVBalBranch224(zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, zzz1125, zzz1126, zzz1127, zzz1128, zzz1129, Succ(zzz11300), Zero, bd) → new_mkVBalBranch3MkVBalBranch119(zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, zzz1125, zzz1126, zzz1127, zzz1128, zzz1129, new_primPlusNat2(Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat3(new_primPlusNat1(zzz1121), zzz1121)), zzz1121))), Succ(zzz1121)), bd)
new_mkVBalBranch3MkVBalBranch110(zzz461, zzz462, zzz463, zzz464, zzz465, zzz466, zzz467, zzz468, zzz469, zzz470, zzz471, Succ(zzz5800), bb) → new_mkVBalBranch3MkVBalBranch115(zzz461, zzz462, zzz463, zzz464, zzz465, zzz466, zzz467, Succ(zzz468), zzz469, zzz470, zzz471, Succ(zzz5800), Succ(Succ(zzz468)), bb)
new_mkVBalBranch3MkVBalBranch227(zzz486, zzz487, zzz488, zzz489, zzz490, zzz491, zzz492, zzz493, zzz494, zzz495, zzz496, bf) → new_mkVBalBranch0(zzz496, Branch(zzz491, zzz492, Neg(Succ(Succ(zzz493))), zzz494, zzz495), zzz489, bf)
new_mkVBalBranch3MkVBalBranch215(zzz340, zzz341, Pos(Zero), zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, Succ(zzz660), h) → new_mkVBalBranch0(zzz31, zzz514, Branch(zzz340, zzz341, Pos(Zero), zzz343, zzz344), h)
new_mkVBalBranch3MkVBalBranch223(zzz340, zzz341, Neg(Zero), zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, Succ(zzz670), h) → new_mkVBalBranch0(zzz31, Branch(zzz510, zzz511, Neg(Succ(zzz51200)), zzz513, zzz514), zzz343, h)
new_mkVBalBranch3MkVBalBranch216(zzz1105, zzz1106, zzz1107, zzz1108, zzz1109, zzz1110, zzz1111, zzz1112, zzz1113, zzz1114, zzz1115, Zero, Succ(zzz11170), ba) → new_mkVBalBranch0(zzz1115, Branch(zzz1110, zzz1111, Pos(Succ(Succ(zzz1112))), zzz1113, zzz1114), zzz1108, ba)
new_mkVBalBranch3MkVBalBranch115(zzz1986, zzz1987, zzz1988, zzz1989, zzz1990, zzz1991, zzz1992, zzz1993, zzz1994, zzz1995, zzz1996, Zero, Succ(zzz19980), bc) → new_mkVBalBranch0(zzz1996, zzz1995, Branch(zzz1986, zzz1987, Pos(Succ(zzz1988)), zzz1989, zzz1990), bc)
new_mkVBalBranch3MkVBalBranch233(zzz473, zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, zzz481, zzz482, bh) → new_mkVBalBranch3MkVBalBranch121(zzz473, zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, zzz481, zzz482, new_primPlusNat2(Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat3(new_primPlusNat1(zzz475), zzz475)), zzz475))), Succ(zzz475)), bh)
new_mkVBalBranch3MkVBalBranch215(zzz340, zzz341, Pos(Succ(Zero)), zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, Succ(zzz660), h) → new_mkVBalBranch3MkVBalBranch18(zzz340, zzz341, zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, new_primPlusNat2(Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat3(new_primPlusNat1(Zero), Zero)), Zero))), Succ(Zero)), h)
new_mkVBalBranch3MkVBalBranch122(zzz340, zzz341, zzz34200, zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, h) → new_mkVBalBranch0(zzz31, zzz514, Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), h)
new_mkVBalBranch3MkVBalBranch217(zzz473, zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, zzz481, zzz482, Succ(zzz4830), Succ(zzz4840), bh) → new_mkVBalBranch3MkVBalBranch217(zzz473, zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, zzz481, zzz482, zzz4830, zzz4840, bh)
new_mkVBalBranch3MkVBalBranch116(zzz340, zzz341, zzz34200, zzz343, zzz344, zzz510, zzz511, zzz513, zzz514, zzz31, Succ(zzz1200), h) → new_mkVBalBranch0(zzz31, zzz514, Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), h)
new_mkVBalBranch3MkVBalBranch110(zzz461, zzz462, zzz463, zzz464, zzz465, zzz466, zzz467, zzz468, zzz469, zzz470, zzz471, Zero, bb) → new_mkVBalBranch3MkVBalBranch115(zzz461, zzz462, zzz463, zzz464, zzz465, zzz466, zzz467, Succ(zzz468), zzz469, zzz470, zzz471, Zero, Succ(Succ(zzz468)), bb)
new_mkVBalBranch3MkVBalBranch225(zzz498, zzz499, zzz500, zzz501, zzz502, zzz503, zzz504, zzz505, zzz506, zzz507, Zero, Succ(zzz5090), bg) → new_mkVBalBranch0(zzz507, Branch(zzz503, zzz504, Neg(Succ(Zero)), zzz505, zzz506), zzz501, bg)
new_mkVBalBranch0(zzz31, Branch(zzz510, zzz511, Neg(Succ(zzz51200)), zzz513, zzz514), Branch(zzz340, zzz341, zzz342, zzz343, zzz344), h) → new_mkVBalBranch3MkVBalBranch223(zzz340, zzz341, zzz342, zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat3(new_primPlusNat1(zzz51200), zzz51200)), zzz51200))), h)
new_mkVBalBranch3MkVBalBranch121(zzz473, zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, zzz481, zzz482, Zero, bh) → new_mkVBalBranch3MkVBalBranch115(zzz473, zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, Zero, zzz480, zzz481, zzz482, Zero, Succ(Zero), bh)
new_mkVBalBranch3MkVBalBranch223(zzz340, zzz341, Neg(Succ(Zero)), zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, Succ(zzz670), h) → new_mkVBalBranch0(zzz31, Branch(zzz510, zzz511, Neg(Succ(zzz51200)), zzz513, zzz514), zzz343, h)
new_mkVBalBranch3MkVBalBranch229(zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, zzz1125, zzz1126, zzz1127, zzz1128, zzz1129, bd) → new_mkVBalBranch3MkVBalBranch119(zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, zzz1125, zzz1126, zzz1127, zzz1128, zzz1129, new_primPlusNat2(new_primPlusNat3(Succ(new_primPlusNat3(new_primPlusNat1(zzz1121), zzz1121)), Succ(zzz1121)), Succ(zzz1121)), bd)
new_mkVBalBranch3MkVBalBranch225(zzz498, zzz499, zzz500, zzz501, zzz502, zzz503, zzz504, zzz505, zzz506, zzz507, Succ(zzz5080), Zero, bg) → new_mkVBalBranch3MkVBalBranch118(zzz498, zzz499, zzz500, zzz501, zzz502, zzz503, zzz504, zzz505, zzz506, zzz507, new_primPlusNat2(new_primPlusNat3(Succ(new_primPlusNat3(new_primPlusNat1(zzz500), zzz500)), Succ(zzz500)), Succ(zzz500)), bg)
new_mkVBalBranch3MkVBalBranch218(zzz461, zzz462, zzz463, zzz464, zzz465, zzz466, zzz467, zzz468, zzz469, zzz470, zzz471, bb) → new_mkVBalBranch3MkVBalBranch110(zzz461, zzz462, zzz463, zzz464, zzz465, zzz466, zzz467, zzz468, zzz469, zzz470, zzz471, new_primPlusNat2(Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat3(new_primPlusNat1(zzz463), zzz463)), zzz463))), Succ(zzz463)), bb)
new_mkVBalBranch0(zzz31, Branch(zzz510, zzz511, Pos(Zero), zzz513, zzz514), Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), h) → new_mkVBalBranch3MkVBalBranch116(zzz340, zzz341, zzz34200, zzz343, zzz344, zzz510, zzz511, zzz513, zzz514, zzz31, new_primPlusNat2(new_primPlusNat3(Succ(new_primPlusNat3(new_primPlusNat1(zzz34200), zzz34200)), Succ(zzz34200)), Succ(zzz34200)), h)
new_mkVBalBranch3MkVBalBranch222(zzz461, zzz462, zzz463, zzz464, zzz465, zzz466, zzz467, zzz468, zzz469, zzz470, zzz471, bb) → new_mkVBalBranch3MkVBalBranch110(zzz461, zzz462, zzz463, zzz464, zzz465, zzz466, zzz467, zzz468, zzz469, zzz470, zzz471, new_primPlusNat2(Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat3(new_primPlusNat1(zzz463), zzz463)), zzz463))), Succ(zzz463)), bb)
new_mkVBalBranch3MkVBalBranch215(zzz340, zzz341, Pos(Succ(Succ(zzz342000))), zzz343, zzz344, zzz510, zzz511, Zero, zzz513, zzz514, zzz31, Succ(Succ(zzz6600)), h) → new_mkVBalBranch3MkVBalBranch217(zzz340, zzz341, Succ(zzz342000), zzz343, zzz344, zzz510, zzz511, zzz513, zzz514, zzz31, Succ(zzz6600), zzz342000, h)
new_mkVBalBranch3MkVBalBranch117(zzz340, zzz341, zzz34200, zzz343, zzz344, zzz510, zzz511, zzz513, zzz514, zzz31, Succ(zzz1240), h) → new_mkVBalBranch0(zzz31, zzz514, Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), h)
new_mkVBalBranch3MkVBalBranch120(zzz2050, zzz2051, zzz2052, zzz2053, zzz2054, zzz2055, zzz2056, zzz2057, zzz2058, zzz2059, zzz2060, Succ(zzz20610), Succ(zzz20620), be) → new_mkVBalBranch3MkVBalBranch120(zzz2050, zzz2051, zzz2052, zzz2053, zzz2054, zzz2055, zzz2056, zzz2057, zzz2058, zzz2059, zzz2060, zzz20610, zzz20620, be)
new_mkVBalBranch3MkVBalBranch217(zzz473, zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, zzz481, zzz482, Zero, Zero, bh) → new_mkVBalBranch3MkVBalBranch233(zzz473, zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, zzz481, zzz482, bh)
new_mkVBalBranch3MkVBalBranch216(zzz1105, zzz1106, zzz1107, zzz1108, zzz1109, zzz1110, zzz1111, zzz1112, zzz1113, zzz1114, zzz1115, Succ(zzz11160), Succ(zzz11170), ba) → new_mkVBalBranch3MkVBalBranch216(zzz1105, zzz1106, zzz1107, zzz1108, zzz1109, zzz1110, zzz1111, zzz1112, zzz1113, zzz1114, zzz1115, zzz11160, zzz11170, ba)
new_mkVBalBranch3MkVBalBranch223(zzz340, zzz341, Pos(zzz3420), zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, Succ(zzz670), h) → new_mkVBalBranch0(zzz31, Branch(zzz510, zzz511, Neg(Succ(zzz51200)), zzz513, zzz514), zzz343, h)
new_mkVBalBranch0(zzz31, Branch(zzz510, zzz511, Neg(Zero), zzz513, zzz514), Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), h) → new_mkVBalBranch3MkVBalBranch117(zzz340, zzz341, zzz34200, zzz343, zzz344, zzz510, zzz511, zzz513, zzz514, zzz31, new_primPlusNat2(Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat3(new_primPlusNat1(zzz34200), zzz34200)), zzz34200))), Succ(zzz34200)), h)
new_mkVBalBranch3MkVBalBranch19(zzz340, zzz341, zzz34200, zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, Zero, h) → new_mkVBalBranch3MkVBalBranch122(zzz340, zzz341, zzz34200, zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, h)
new_mkVBalBranch3MkVBalBranch225(zzz498, zzz499, zzz500, zzz501, zzz502, zzz503, zzz504, zzz505, zzz506, zzz507, Succ(zzz5080), Succ(zzz5090), bg) → new_mkVBalBranch3MkVBalBranch225(zzz498, zzz499, zzz500, zzz501, zzz502, zzz503, zzz504, zzz505, zzz506, zzz507, zzz5080, zzz5090, bg)
new_mkVBalBranch3MkVBalBranch19(zzz340, zzz341, zzz34200, zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, Succ(zzz1410), h) → new_mkVBalBranch0(zzz31, zzz514, Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), h)
new_mkVBalBranch3MkVBalBranch224(zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, zzz1125, zzz1126, zzz1127, zzz1128, zzz1129, Zero, Succ(zzz11310), bd) → new_mkVBalBranch3MkVBalBranch227(zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, zzz1125, zzz1126, zzz1127, zzz1128, zzz1129, bd)
new_mkVBalBranch3MkVBalBranch224(zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, zzz1125, zzz1126, zzz1127, zzz1128, zzz1129, Zero, Zero, bd) → new_mkVBalBranch3MkVBalBranch229(zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, zzz1125, zzz1126, zzz1127, zzz1128, zzz1129, bd)
new_mkVBalBranch3MkVBalBranch223(zzz340, zzz341, Neg(Succ(Succ(Zero))), zzz343, zzz344, zzz510, zzz511, Zero, zzz513, zzz514, zzz31, Succ(Succ(zzz6700)), h) → new_mkVBalBranch3MkVBalBranch225(zzz340, zzz341, Succ(Zero), zzz343, zzz344, zzz510, zzz511, zzz513, zzz514, zzz31, Zero, Succ(zzz6700), h)
new_mkVBalBranch3MkVBalBranch223(zzz340, zzz341, Neg(Succ(Succ(Succ(zzz3420000)))), zzz343, zzz344, zzz510, zzz511, Succ(zzz512000), zzz513, zzz514, zzz31, Succ(Succ(zzz6700)), h) → new_mkVBalBranch3MkVBalBranch224(zzz340, zzz341, Succ(Succ(zzz3420000)), zzz343, zzz344, zzz510, zzz511, zzz512000, zzz513, zzz514, zzz31, Succ(zzz3420000), Succ(Succ(new_primPlusNat2(zzz6700, zzz512000))), h)
new_mkVBalBranch3MkVBalBranch115(zzz1986, zzz1987, zzz1988, zzz1989, zzz1990, zzz1991, zzz1992, zzz1993, zzz1994, zzz1995, zzz1996, Succ(zzz19970), Succ(zzz19980), bc) → new_mkVBalBranch3MkVBalBranch115(zzz1986, zzz1987, zzz1988, zzz1989, zzz1990, zzz1991, zzz1992, zzz1993, zzz1994, zzz1995, zzz1996, zzz19970, zzz19980, bc)
new_mkVBalBranch3MkVBalBranch215(zzz340, zzz341, Neg(Zero), zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, Succ(zzz660), h) → new_mkVBalBranch0(zzz31, zzz514, Branch(zzz340, zzz341, Neg(Zero), zzz343, zzz344), h)
new_mkVBalBranch3MkVBalBranch118(zzz498, zzz499, zzz500, zzz501, zzz502, zzz503, zzz504, zzz505, zzz506, zzz507, Succ(zzz8040), bg) → new_mkVBalBranch3MkVBalBranch120(zzz498, zzz499, zzz500, zzz501, zzz502, zzz503, zzz504, Zero, zzz505, zzz506, zzz507, Succ(Zero), Succ(zzz8040), bg)
new_mkVBalBranch3MkVBalBranch216(zzz1105, zzz1106, zzz1107, zzz1108, zzz1109, zzz1110, zzz1111, zzz1112, zzz1113, zzz1114, zzz1115, Succ(zzz11160), Zero, ba) → new_mkVBalBranch3MkVBalBranch218(zzz1105, zzz1106, zzz1107, zzz1108, zzz1109, zzz1110, zzz1111, zzz1112, zzz1113, zzz1114, zzz1115, ba)
new_mkVBalBranch3MkVBalBranch216(zzz1105, zzz1106, zzz1107, zzz1108, zzz1109, zzz1110, zzz1111, zzz1112, zzz1113, zzz1114, zzz1115, Zero, Zero, ba) → new_mkVBalBranch3MkVBalBranch222(zzz1105, zzz1106, zzz1107, zzz1108, zzz1109, zzz1110, zzz1111, zzz1112, zzz1113, zzz1114, zzz1115, ba)
new_mkVBalBranch3MkVBalBranch18(zzz340, zzz341, zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, Zero, h) → new_mkVBalBranch3MkVBalBranch115(zzz340, zzz341, Zero, zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, Zero, Succ(zzz51200), h)
new_mkVBalBranch3MkVBalBranch119(zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, zzz1125, zzz1126, zzz1127, zzz1128, zzz1129, Succ(zzz12130), bd) → new_mkVBalBranch3MkVBalBranch120(zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, zzz1125, Succ(zzz1126), zzz1127, zzz1128, zzz1129, Succ(Succ(zzz1126)), Succ(zzz12130), bd)

The TRS R consists of the following rules:

new_primPlusNat1(Zero) → Zero
new_primPlusNat1(Succ(zzz62000)) → Succ(Succ(new_primPlusNat1(zzz62000)))
new_primPlusNat3(zzz90, Succ(zzz910)) → Succ(Succ(new_primPlusNat2(zzz90, zzz910)))
new_primPlusNat3(zzz90, Zero) → Succ(zzz90)
new_primPlusNat2(Succ(zzz900), Succ(zzz9100)) → Succ(Succ(new_primPlusNat2(zzz900, zzz9100)))
new_primPlusNat2(Zero, Succ(zzz9100)) → Succ(zzz9100)
new_primPlusNat2(Zero, Zero) → Zero
new_primPlusNat2(Succ(zzz900), Zero) → Succ(zzz900)

The set Q consists of the following terms:

new_primPlusNat2(Zero, Succ(x0))
new_primPlusNat3(x0, Succ(x1))
new_primPlusNat2(Succ(x0), Succ(x1))
new_primPlusNat3(x0, Zero)
new_primPlusNat1(Zero)
new_primPlusNat2(Zero, Zero)
new_primPlusNat1(Succ(x0))
new_primPlusNat2(Succ(x0), Zero)

We have to consider all minimal (P,Q,R)-chains.
By rewriting [15] the rule new_mkVBalBranch3MkVBalBranch229(zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, zzz1125, zzz1126, zzz1127, zzz1128, zzz1129, bd) → new_mkVBalBranch3MkVBalBranch119(zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, zzz1125, zzz1126, zzz1127, zzz1128, zzz1129, new_primPlusNat2(new_primPlusNat3(Succ(new_primPlusNat3(new_primPlusNat1(zzz1121), zzz1121)), Succ(zzz1121)), Succ(zzz1121)), bd) at position [11,0] we obtained the following new rules:

new_mkVBalBranch3MkVBalBranch229(zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, zzz1125, zzz1126, zzz1127, zzz1128, zzz1129, bd) → new_mkVBalBranch3MkVBalBranch119(zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, zzz1125, zzz1126, zzz1127, zzz1128, zzz1129, new_primPlusNat2(Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat3(new_primPlusNat1(zzz1121), zzz1121)), zzz1121))), Succ(zzz1121)), bd)



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

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

new_mkVBalBranch3MkVBalBranch225(zzz498, zzz499, zzz500, zzz501, zzz502, zzz503, zzz504, zzz505, zzz506, zzz507, Zero, Zero, bg) → new_mkVBalBranch3MkVBalBranch230(zzz498, zzz499, zzz500, zzz501, zzz502, zzz503, zzz504, zzz505, zzz506, zzz507, bg)
new_mkVBalBranch3MkVBalBranch18(zzz340, zzz341, zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, Succ(zzz1480), h) → new_mkVBalBranch3MkVBalBranch115(zzz340, zzz341, Zero, zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, Succ(zzz1480), Succ(zzz51200), h)
new_mkVBalBranch0(zzz31, Branch(zzz510, zzz511, Neg(Zero), zzz513, zzz514), Branch(zzz340, zzz341, Pos(Succ(zzz34200)), zzz343, zzz344), h) → new_mkVBalBranch0(zzz31, Branch(zzz510, zzz511, Neg(Zero), zzz513, zzz514), zzz343, h)
new_mkVBalBranch3MkVBalBranch215(zzz340, zzz341, Pos(Succ(Succ(zzz342000))), zzz343, zzz344, zzz510, zzz511, Succ(zzz512000), zzz513, zzz514, zzz31, Succ(Succ(zzz6600)), h) → new_mkVBalBranch3MkVBalBranch216(zzz340, zzz341, Succ(zzz342000), zzz343, zzz344, zzz510, zzz511, zzz512000, zzz513, zzz514, zzz31, Succ(Succ(new_primPlusNat2(zzz6600, zzz512000))), zzz342000, h)
new_mkVBalBranch3MkVBalBranch223(zzz340, zzz341, Neg(Succ(Succ(Succ(zzz3420000)))), zzz343, zzz344, zzz510, zzz511, Zero, zzz513, zzz514, zzz31, Succ(Succ(zzz6700)), h) → new_mkVBalBranch3MkVBalBranch225(zzz340, zzz341, Succ(Succ(zzz3420000)), zzz343, zzz344, zzz510, zzz511, zzz513, zzz514, zzz31, Succ(zzz3420000), Succ(zzz6700), h)
new_mkVBalBranch3MkVBalBranch120(zzz2050, zzz2051, zzz2052, zzz2053, zzz2054, zzz2055, zzz2056, zzz2057, zzz2058, zzz2059, zzz2060, Zero, Succ(zzz20620), be) → new_mkVBalBranch0(zzz2060, zzz2059, Branch(zzz2050, zzz2051, Neg(Succ(zzz2052)), zzz2053, zzz2054), be)
new_mkVBalBranch3MkVBalBranch121(zzz473, zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, zzz481, zzz482, Succ(zzz7390), bh) → new_mkVBalBranch3MkVBalBranch115(zzz473, zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, Zero, zzz480, zzz481, zzz482, Succ(zzz7390), Succ(Zero), bh)
new_mkVBalBranch0(zzz31, Branch(zzz510, zzz511, Pos(Zero), zzz513, zzz514), Branch(zzz340, zzz341, Pos(Succ(zzz34200)), zzz343, zzz344), h) → new_mkVBalBranch0(zzz31, Branch(zzz510, zzz511, Pos(Zero), zzz513, zzz514), zzz343, h)
new_mkVBalBranch3MkVBalBranch215(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, Succ(zzz660), h) → new_mkVBalBranch3MkVBalBranch19(zzz340, zzz341, zzz34200, zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, new_primPlusNat2(Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat3(new_primPlusNat1(zzz34200), zzz34200)), zzz34200))), Succ(zzz34200)), h)
new_mkVBalBranch0(zzz31, Branch(zzz510, zzz511, Pos(Succ(zzz51200)), zzz513, zzz514), Branch(zzz340, zzz341, zzz342, zzz343, zzz344), h) → new_mkVBalBranch3MkVBalBranch215(zzz340, zzz341, zzz342, zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat3(new_primPlusNat1(zzz51200), zzz51200)), zzz51200))), h)
new_mkVBalBranch3MkVBalBranch223(zzz340, zzz341, Neg(Succ(Succ(Zero))), zzz343, zzz344, zzz510, zzz511, Succ(zzz512000), zzz513, zzz514, zzz31, Succ(Succ(zzz6700)), h) → new_mkVBalBranch3MkVBalBranch224(zzz340, zzz341, Succ(Zero), zzz343, zzz344, zzz510, zzz511, zzz512000, zzz513, zzz514, zzz31, Zero, Succ(Succ(new_primPlusNat2(zzz6700, zzz512000))), h)
new_mkVBalBranch3MkVBalBranch230(zzz498, zzz499, zzz500, zzz501, zzz502, zzz503, zzz504, zzz505, zzz506, zzz507, bg) → new_mkVBalBranch3MkVBalBranch118(zzz498, zzz499, zzz500, zzz501, zzz502, zzz503, zzz504, zzz505, zzz506, zzz507, Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat2(Succ(new_primPlusNat3(new_primPlusNat1(zzz500), zzz500)), zzz500)), zzz500))), bg)
new_mkVBalBranch3MkVBalBranch217(zzz473, zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, zzz481, zzz482, Succ(zzz4830), Zero, bh) → new_mkVBalBranch3MkVBalBranch121(zzz473, zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, zzz481, zzz482, new_primPlusNat2(Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat3(new_primPlusNat1(zzz475), zzz475)), zzz475))), Succ(zzz475)), bh)
new_mkVBalBranch3MkVBalBranch224(zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, zzz1125, zzz1126, zzz1127, zzz1128, zzz1129, Succ(zzz11300), Succ(zzz11310), bd) → new_mkVBalBranch3MkVBalBranch224(zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, zzz1125, zzz1126, zzz1127, zzz1128, zzz1129, zzz11300, zzz11310, bd)
new_mkVBalBranch3MkVBalBranch217(zzz473, zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, zzz481, zzz482, Zero, Succ(zzz4840), bh) → new_mkVBalBranch0(zzz482, Branch(zzz478, zzz479, Pos(Succ(Zero)), zzz480, zzz481), zzz476, bh)
new_mkVBalBranch3MkVBalBranch224(zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, zzz1125, zzz1126, zzz1127, zzz1128, zzz1129, Succ(zzz11300), Zero, bd) → new_mkVBalBranch3MkVBalBranch119(zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, zzz1125, zzz1126, zzz1127, zzz1128, zzz1129, new_primPlusNat2(Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat3(new_primPlusNat1(zzz1121), zzz1121)), zzz1121))), Succ(zzz1121)), bd)
new_mkVBalBranch3MkVBalBranch110(zzz461, zzz462, zzz463, zzz464, zzz465, zzz466, zzz467, zzz468, zzz469, zzz470, zzz471, Succ(zzz5800), bb) → new_mkVBalBranch3MkVBalBranch115(zzz461, zzz462, zzz463, zzz464, zzz465, zzz466, zzz467, Succ(zzz468), zzz469, zzz470, zzz471, Succ(zzz5800), Succ(Succ(zzz468)), bb)
new_mkVBalBranch3MkVBalBranch227(zzz486, zzz487, zzz488, zzz489, zzz490, zzz491, zzz492, zzz493, zzz494, zzz495, zzz496, bf) → new_mkVBalBranch0(zzz496, Branch(zzz491, zzz492, Neg(Succ(Succ(zzz493))), zzz494, zzz495), zzz489, bf)
new_mkVBalBranch3MkVBalBranch215(zzz340, zzz341, Pos(Zero), zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, Succ(zzz660), h) → new_mkVBalBranch0(zzz31, zzz514, Branch(zzz340, zzz341, Pos(Zero), zzz343, zzz344), h)
new_mkVBalBranch3MkVBalBranch223(zzz340, zzz341, Neg(Zero), zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, Succ(zzz670), h) → new_mkVBalBranch0(zzz31, Branch(zzz510, zzz511, Neg(Succ(zzz51200)), zzz513, zzz514), zzz343, h)
new_mkVBalBranch3MkVBalBranch216(zzz1105, zzz1106, zzz1107, zzz1108, zzz1109, zzz1110, zzz1111, zzz1112, zzz1113, zzz1114, zzz1115, Zero, Succ(zzz11170), ba) → new_mkVBalBranch0(zzz1115, Branch(zzz1110, zzz1111, Pos(Succ(Succ(zzz1112))), zzz1113, zzz1114), zzz1108, ba)
new_mkVBalBranch3MkVBalBranch115(zzz1986, zzz1987, zzz1988, zzz1989, zzz1990, zzz1991, zzz1992, zzz1993, zzz1994, zzz1995, zzz1996, Zero, Succ(zzz19980), bc) → new_mkVBalBranch0(zzz1996, zzz1995, Branch(zzz1986, zzz1987, Pos(Succ(zzz1988)), zzz1989, zzz1990), bc)
new_mkVBalBranch3MkVBalBranch233(zzz473, zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, zzz481, zzz482, bh) → new_mkVBalBranch3MkVBalBranch121(zzz473, zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, zzz481, zzz482, new_primPlusNat2(Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat3(new_primPlusNat1(zzz475), zzz475)), zzz475))), Succ(zzz475)), bh)
new_mkVBalBranch3MkVBalBranch215(zzz340, zzz341, Pos(Succ(Zero)), zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, Succ(zzz660), h) → new_mkVBalBranch3MkVBalBranch18(zzz340, zzz341, zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, new_primPlusNat2(Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat3(new_primPlusNat1(Zero), Zero)), Zero))), Succ(Zero)), h)
new_mkVBalBranch3MkVBalBranch122(zzz340, zzz341, zzz34200, zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, h) → new_mkVBalBranch0(zzz31, zzz514, Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), h)
new_mkVBalBranch3MkVBalBranch217(zzz473, zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, zzz481, zzz482, Succ(zzz4830), Succ(zzz4840), bh) → new_mkVBalBranch3MkVBalBranch217(zzz473, zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, zzz481, zzz482, zzz4830, zzz4840, bh)
new_mkVBalBranch3MkVBalBranch116(zzz340, zzz341, zzz34200, zzz343, zzz344, zzz510, zzz511, zzz513, zzz514, zzz31, Succ(zzz1200), h) → new_mkVBalBranch0(zzz31, zzz514, Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), h)
new_mkVBalBranch3MkVBalBranch110(zzz461, zzz462, zzz463, zzz464, zzz465, zzz466, zzz467, zzz468, zzz469, zzz470, zzz471, Zero, bb) → new_mkVBalBranch3MkVBalBranch115(zzz461, zzz462, zzz463, zzz464, zzz465, zzz466, zzz467, Succ(zzz468), zzz469, zzz470, zzz471, Zero, Succ(Succ(zzz468)), bb)
new_mkVBalBranch3MkVBalBranch225(zzz498, zzz499, zzz500, zzz501, zzz502, zzz503, zzz504, zzz505, zzz506, zzz507, Zero, Succ(zzz5090), bg) → new_mkVBalBranch0(zzz507, Branch(zzz503, zzz504, Neg(Succ(Zero)), zzz505, zzz506), zzz501, bg)
new_mkVBalBranch0(zzz31, Branch(zzz510, zzz511, Neg(Succ(zzz51200)), zzz513, zzz514), Branch(zzz340, zzz341, zzz342, zzz343, zzz344), h) → new_mkVBalBranch3MkVBalBranch223(zzz340, zzz341, zzz342, zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat3(new_primPlusNat1(zzz51200), zzz51200)), zzz51200))), h)
new_mkVBalBranch3MkVBalBranch121(zzz473, zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, zzz481, zzz482, Zero, bh) → new_mkVBalBranch3MkVBalBranch115(zzz473, zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, Zero, zzz480, zzz481, zzz482, Zero, Succ(Zero), bh)
new_mkVBalBranch3MkVBalBranch223(zzz340, zzz341, Neg(Succ(Zero)), zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, Succ(zzz670), h) → new_mkVBalBranch0(zzz31, Branch(zzz510, zzz511, Neg(Succ(zzz51200)), zzz513, zzz514), zzz343, h)
new_mkVBalBranch3MkVBalBranch225(zzz498, zzz499, zzz500, zzz501, zzz502, zzz503, zzz504, zzz505, zzz506, zzz507, Succ(zzz5080), Zero, bg) → new_mkVBalBranch3MkVBalBranch118(zzz498, zzz499, zzz500, zzz501, zzz502, zzz503, zzz504, zzz505, zzz506, zzz507, new_primPlusNat2(new_primPlusNat3(Succ(new_primPlusNat3(new_primPlusNat1(zzz500), zzz500)), Succ(zzz500)), Succ(zzz500)), bg)
new_mkVBalBranch3MkVBalBranch218(zzz461, zzz462, zzz463, zzz464, zzz465, zzz466, zzz467, zzz468, zzz469, zzz470, zzz471, bb) → new_mkVBalBranch3MkVBalBranch110(zzz461, zzz462, zzz463, zzz464, zzz465, zzz466, zzz467, zzz468, zzz469, zzz470, zzz471, new_primPlusNat2(Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat3(new_primPlusNat1(zzz463), zzz463)), zzz463))), Succ(zzz463)), bb)
new_mkVBalBranch0(zzz31, Branch(zzz510, zzz511, Pos(Zero), zzz513, zzz514), Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), h) → new_mkVBalBranch3MkVBalBranch116(zzz340, zzz341, zzz34200, zzz343, zzz344, zzz510, zzz511, zzz513, zzz514, zzz31, new_primPlusNat2(new_primPlusNat3(Succ(new_primPlusNat3(new_primPlusNat1(zzz34200), zzz34200)), Succ(zzz34200)), Succ(zzz34200)), h)
new_mkVBalBranch3MkVBalBranch222(zzz461, zzz462, zzz463, zzz464, zzz465, zzz466, zzz467, zzz468, zzz469, zzz470, zzz471, bb) → new_mkVBalBranch3MkVBalBranch110(zzz461, zzz462, zzz463, zzz464, zzz465, zzz466, zzz467, zzz468, zzz469, zzz470, zzz471, new_primPlusNat2(Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat3(new_primPlusNat1(zzz463), zzz463)), zzz463))), Succ(zzz463)), bb)
new_mkVBalBranch3MkVBalBranch215(zzz340, zzz341, Pos(Succ(Succ(zzz342000))), zzz343, zzz344, zzz510, zzz511, Zero, zzz513, zzz514, zzz31, Succ(Succ(zzz6600)), h) → new_mkVBalBranch3MkVBalBranch217(zzz340, zzz341, Succ(zzz342000), zzz343, zzz344, zzz510, zzz511, zzz513, zzz514, zzz31, Succ(zzz6600), zzz342000, h)
new_mkVBalBranch3MkVBalBranch117(zzz340, zzz341, zzz34200, zzz343, zzz344, zzz510, zzz511, zzz513, zzz514, zzz31, Succ(zzz1240), h) → new_mkVBalBranch0(zzz31, zzz514, Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), h)
new_mkVBalBranch3MkVBalBranch217(zzz473, zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, zzz481, zzz482, Zero, Zero, bh) → new_mkVBalBranch3MkVBalBranch233(zzz473, zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, zzz481, zzz482, bh)
new_mkVBalBranch3MkVBalBranch120(zzz2050, zzz2051, zzz2052, zzz2053, zzz2054, zzz2055, zzz2056, zzz2057, zzz2058, zzz2059, zzz2060, Succ(zzz20610), Succ(zzz20620), be) → new_mkVBalBranch3MkVBalBranch120(zzz2050, zzz2051, zzz2052, zzz2053, zzz2054, zzz2055, zzz2056, zzz2057, zzz2058, zzz2059, zzz2060, zzz20610, zzz20620, be)
new_mkVBalBranch3MkVBalBranch223(zzz340, zzz341, Pos(zzz3420), zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, Succ(zzz670), h) → new_mkVBalBranch0(zzz31, Branch(zzz510, zzz511, Neg(Succ(zzz51200)), zzz513, zzz514), zzz343, h)
new_mkVBalBranch3MkVBalBranch216(zzz1105, zzz1106, zzz1107, zzz1108, zzz1109, zzz1110, zzz1111, zzz1112, zzz1113, zzz1114, zzz1115, Succ(zzz11160), Succ(zzz11170), ba) → new_mkVBalBranch3MkVBalBranch216(zzz1105, zzz1106, zzz1107, zzz1108, zzz1109, zzz1110, zzz1111, zzz1112, zzz1113, zzz1114, zzz1115, zzz11160, zzz11170, ba)
new_mkVBalBranch0(zzz31, Branch(zzz510, zzz511, Neg(Zero), zzz513, zzz514), Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), h) → new_mkVBalBranch3MkVBalBranch117(zzz340, zzz341, zzz34200, zzz343, zzz344, zzz510, zzz511, zzz513, zzz514, zzz31, new_primPlusNat2(Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat3(new_primPlusNat1(zzz34200), zzz34200)), zzz34200))), Succ(zzz34200)), h)
new_mkVBalBranch3MkVBalBranch19(zzz340, zzz341, zzz34200, zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, Zero, h) → new_mkVBalBranch3MkVBalBranch122(zzz340, zzz341, zzz34200, zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, h)
new_mkVBalBranch3MkVBalBranch225(zzz498, zzz499, zzz500, zzz501, zzz502, zzz503, zzz504, zzz505, zzz506, zzz507, Succ(zzz5080), Succ(zzz5090), bg) → new_mkVBalBranch3MkVBalBranch225(zzz498, zzz499, zzz500, zzz501, zzz502, zzz503, zzz504, zzz505, zzz506, zzz507, zzz5080, zzz5090, bg)
new_mkVBalBranch3MkVBalBranch19(zzz340, zzz341, zzz34200, zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, Succ(zzz1410), h) → new_mkVBalBranch0(zzz31, zzz514, Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), h)
new_mkVBalBranch3MkVBalBranch224(zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, zzz1125, zzz1126, zzz1127, zzz1128, zzz1129, Zero, Zero, bd) → new_mkVBalBranch3MkVBalBranch229(zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, zzz1125, zzz1126, zzz1127, zzz1128, zzz1129, bd)
new_mkVBalBranch3MkVBalBranch224(zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, zzz1125, zzz1126, zzz1127, zzz1128, zzz1129, Zero, Succ(zzz11310), bd) → new_mkVBalBranch3MkVBalBranch227(zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, zzz1125, zzz1126, zzz1127, zzz1128, zzz1129, bd)
new_mkVBalBranch3MkVBalBranch223(zzz340, zzz341, Neg(Succ(Succ(Succ(zzz3420000)))), zzz343, zzz344, zzz510, zzz511, Succ(zzz512000), zzz513, zzz514, zzz31, Succ(Succ(zzz6700)), h) → new_mkVBalBranch3MkVBalBranch224(zzz340, zzz341, Succ(Succ(zzz3420000)), zzz343, zzz344, zzz510, zzz511, zzz512000, zzz513, zzz514, zzz31, Succ(zzz3420000), Succ(Succ(new_primPlusNat2(zzz6700, zzz512000))), h)
new_mkVBalBranch3MkVBalBranch223(zzz340, zzz341, Neg(Succ(Succ(Zero))), zzz343, zzz344, zzz510, zzz511, Zero, zzz513, zzz514, zzz31, Succ(Succ(zzz6700)), h) → new_mkVBalBranch3MkVBalBranch225(zzz340, zzz341, Succ(Zero), zzz343, zzz344, zzz510, zzz511, zzz513, zzz514, zzz31, Zero, Succ(zzz6700), h)
new_mkVBalBranch3MkVBalBranch115(zzz1986, zzz1987, zzz1988, zzz1989, zzz1990, zzz1991, zzz1992, zzz1993, zzz1994, zzz1995, zzz1996, Succ(zzz19970), Succ(zzz19980), bc) → new_mkVBalBranch3MkVBalBranch115(zzz1986, zzz1987, zzz1988, zzz1989, zzz1990, zzz1991, zzz1992, zzz1993, zzz1994, zzz1995, zzz1996, zzz19970, zzz19980, bc)
new_mkVBalBranch3MkVBalBranch229(zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, zzz1125, zzz1126, zzz1127, zzz1128, zzz1129, bd) → new_mkVBalBranch3MkVBalBranch119(zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, zzz1125, zzz1126, zzz1127, zzz1128, zzz1129, new_primPlusNat2(Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat3(new_primPlusNat1(zzz1121), zzz1121)), zzz1121))), Succ(zzz1121)), bd)
new_mkVBalBranch3MkVBalBranch215(zzz340, zzz341, Neg(Zero), zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, Succ(zzz660), h) → new_mkVBalBranch0(zzz31, zzz514, Branch(zzz340, zzz341, Neg(Zero), zzz343, zzz344), h)
new_mkVBalBranch3MkVBalBranch118(zzz498, zzz499, zzz500, zzz501, zzz502, zzz503, zzz504, zzz505, zzz506, zzz507, Succ(zzz8040), bg) → new_mkVBalBranch3MkVBalBranch120(zzz498, zzz499, zzz500, zzz501, zzz502, zzz503, zzz504, Zero, zzz505, zzz506, zzz507, Succ(Zero), Succ(zzz8040), bg)
new_mkVBalBranch3MkVBalBranch216(zzz1105, zzz1106, zzz1107, zzz1108, zzz1109, zzz1110, zzz1111, zzz1112, zzz1113, zzz1114, zzz1115, Succ(zzz11160), Zero, ba) → new_mkVBalBranch3MkVBalBranch218(zzz1105, zzz1106, zzz1107, zzz1108, zzz1109, zzz1110, zzz1111, zzz1112, zzz1113, zzz1114, zzz1115, ba)
new_mkVBalBranch3MkVBalBranch216(zzz1105, zzz1106, zzz1107, zzz1108, zzz1109, zzz1110, zzz1111, zzz1112, zzz1113, zzz1114, zzz1115, Zero, Zero, ba) → new_mkVBalBranch3MkVBalBranch222(zzz1105, zzz1106, zzz1107, zzz1108, zzz1109, zzz1110, zzz1111, zzz1112, zzz1113, zzz1114, zzz1115, ba)
new_mkVBalBranch3MkVBalBranch119(zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, zzz1125, zzz1126, zzz1127, zzz1128, zzz1129, Succ(zzz12130), bd) → new_mkVBalBranch3MkVBalBranch120(zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, zzz1125, Succ(zzz1126), zzz1127, zzz1128, zzz1129, Succ(Succ(zzz1126)), Succ(zzz12130), bd)
new_mkVBalBranch3MkVBalBranch18(zzz340, zzz341, zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, Zero, h) → new_mkVBalBranch3MkVBalBranch115(zzz340, zzz341, Zero, zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, Zero, Succ(zzz51200), h)

The TRS R consists of the following rules:

new_primPlusNat1(Zero) → Zero
new_primPlusNat1(Succ(zzz62000)) → Succ(Succ(new_primPlusNat1(zzz62000)))
new_primPlusNat3(zzz90, Succ(zzz910)) → Succ(Succ(new_primPlusNat2(zzz90, zzz910)))
new_primPlusNat3(zzz90, Zero) → Succ(zzz90)
new_primPlusNat2(Succ(zzz900), Succ(zzz9100)) → Succ(Succ(new_primPlusNat2(zzz900, zzz9100)))
new_primPlusNat2(Zero, Succ(zzz9100)) → Succ(zzz9100)
new_primPlusNat2(Zero, Zero) → Zero
new_primPlusNat2(Succ(zzz900), Zero) → Succ(zzz900)

The set Q consists of the following terms:

new_primPlusNat2(Zero, Succ(x0))
new_primPlusNat3(x0, Succ(x1))
new_primPlusNat2(Succ(x0), Succ(x1))
new_primPlusNat3(x0, Zero)
new_primPlusNat1(Zero)
new_primPlusNat2(Zero, Zero)
new_primPlusNat1(Succ(x0))
new_primPlusNat2(Succ(x0), Zero)

We have to consider all minimal (P,Q,R)-chains.
By rewriting [15] the rule new_mkVBalBranch3MkVBalBranch225(zzz498, zzz499, zzz500, zzz501, zzz502, zzz503, zzz504, zzz505, zzz506, zzz507, Succ(zzz5080), Zero, bg) → new_mkVBalBranch3MkVBalBranch118(zzz498, zzz499, zzz500, zzz501, zzz502, zzz503, zzz504, zzz505, zzz506, zzz507, new_primPlusNat2(new_primPlusNat3(Succ(new_primPlusNat3(new_primPlusNat1(zzz500), zzz500)), Succ(zzz500)), Succ(zzz500)), bg) at position [10,0] we obtained the following new rules:

new_mkVBalBranch3MkVBalBranch225(zzz498, zzz499, zzz500, zzz501, zzz502, zzz503, zzz504, zzz505, zzz506, zzz507, Succ(zzz5080), Zero, bg) → new_mkVBalBranch3MkVBalBranch118(zzz498, zzz499, zzz500, zzz501, zzz502, zzz503, zzz504, zzz505, zzz506, zzz507, new_primPlusNat2(Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat3(new_primPlusNat1(zzz500), zzz500)), zzz500))), Succ(zzz500)), bg)



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

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

new_mkVBalBranch3MkVBalBranch225(zzz498, zzz499, zzz500, zzz501, zzz502, zzz503, zzz504, zzz505, zzz506, zzz507, Zero, Zero, bg) → new_mkVBalBranch3MkVBalBranch230(zzz498, zzz499, zzz500, zzz501, zzz502, zzz503, zzz504, zzz505, zzz506, zzz507, bg)
new_mkVBalBranch3MkVBalBranch18(zzz340, zzz341, zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, Succ(zzz1480), h) → new_mkVBalBranch3MkVBalBranch115(zzz340, zzz341, Zero, zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, Succ(zzz1480), Succ(zzz51200), h)
new_mkVBalBranch3MkVBalBranch215(zzz340, zzz341, Pos(Succ(Succ(zzz342000))), zzz343, zzz344, zzz510, zzz511, Succ(zzz512000), zzz513, zzz514, zzz31, Succ(Succ(zzz6600)), h) → new_mkVBalBranch3MkVBalBranch216(zzz340, zzz341, Succ(zzz342000), zzz343, zzz344, zzz510, zzz511, zzz512000, zzz513, zzz514, zzz31, Succ(Succ(new_primPlusNat2(zzz6600, zzz512000))), zzz342000, h)
new_mkVBalBranch0(zzz31, Branch(zzz510, zzz511, Neg(Zero), zzz513, zzz514), Branch(zzz340, zzz341, Pos(Succ(zzz34200)), zzz343, zzz344), h) → new_mkVBalBranch0(zzz31, Branch(zzz510, zzz511, Neg(Zero), zzz513, zzz514), zzz343, h)
new_mkVBalBranch3MkVBalBranch223(zzz340, zzz341, Neg(Succ(Succ(Succ(zzz3420000)))), zzz343, zzz344, zzz510, zzz511, Zero, zzz513, zzz514, zzz31, Succ(Succ(zzz6700)), h) → new_mkVBalBranch3MkVBalBranch225(zzz340, zzz341, Succ(Succ(zzz3420000)), zzz343, zzz344, zzz510, zzz511, zzz513, zzz514, zzz31, Succ(zzz3420000), Succ(zzz6700), h)
new_mkVBalBranch3MkVBalBranch120(zzz2050, zzz2051, zzz2052, zzz2053, zzz2054, zzz2055, zzz2056, zzz2057, zzz2058, zzz2059, zzz2060, Zero, Succ(zzz20620), be) → new_mkVBalBranch0(zzz2060, zzz2059, Branch(zzz2050, zzz2051, Neg(Succ(zzz2052)), zzz2053, zzz2054), be)
new_mkVBalBranch3MkVBalBranch215(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, Succ(zzz660), h) → new_mkVBalBranch3MkVBalBranch19(zzz340, zzz341, zzz34200, zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, new_primPlusNat2(Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat3(new_primPlusNat1(zzz34200), zzz34200)), zzz34200))), Succ(zzz34200)), h)
new_mkVBalBranch0(zzz31, Branch(zzz510, zzz511, Pos(Zero), zzz513, zzz514), Branch(zzz340, zzz341, Pos(Succ(zzz34200)), zzz343, zzz344), h) → new_mkVBalBranch0(zzz31, Branch(zzz510, zzz511, Pos(Zero), zzz513, zzz514), zzz343, h)
new_mkVBalBranch3MkVBalBranch121(zzz473, zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, zzz481, zzz482, Succ(zzz7390), bh) → new_mkVBalBranch3MkVBalBranch115(zzz473, zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, Zero, zzz480, zzz481, zzz482, Succ(zzz7390), Succ(Zero), bh)
new_mkVBalBranch0(zzz31, Branch(zzz510, zzz511, Pos(Succ(zzz51200)), zzz513, zzz514), Branch(zzz340, zzz341, zzz342, zzz343, zzz344), h) → new_mkVBalBranch3MkVBalBranch215(zzz340, zzz341, zzz342, zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat3(new_primPlusNat1(zzz51200), zzz51200)), zzz51200))), h)
new_mkVBalBranch3MkVBalBranch217(zzz473, zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, zzz481, zzz482, Succ(zzz4830), Zero, bh) → new_mkVBalBranch3MkVBalBranch121(zzz473, zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, zzz481, zzz482, new_primPlusNat2(Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat3(new_primPlusNat1(zzz475), zzz475)), zzz475))), Succ(zzz475)), bh)
new_mkVBalBranch3MkVBalBranch230(zzz498, zzz499, zzz500, zzz501, zzz502, zzz503, zzz504, zzz505, zzz506, zzz507, bg) → new_mkVBalBranch3MkVBalBranch118(zzz498, zzz499, zzz500, zzz501, zzz502, zzz503, zzz504, zzz505, zzz506, zzz507, Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat2(Succ(new_primPlusNat3(new_primPlusNat1(zzz500), zzz500)), zzz500)), zzz500))), bg)
new_mkVBalBranch3MkVBalBranch223(zzz340, zzz341, Neg(Succ(Succ(Zero))), zzz343, zzz344, zzz510, zzz511, Succ(zzz512000), zzz513, zzz514, zzz31, Succ(Succ(zzz6700)), h) → new_mkVBalBranch3MkVBalBranch224(zzz340, zzz341, Succ(Zero), zzz343, zzz344, zzz510, zzz511, zzz512000, zzz513, zzz514, zzz31, Zero, Succ(Succ(new_primPlusNat2(zzz6700, zzz512000))), h)
new_mkVBalBranch3MkVBalBranch224(zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, zzz1125, zzz1126, zzz1127, zzz1128, zzz1129, Succ(zzz11300), Succ(zzz11310), bd) → new_mkVBalBranch3MkVBalBranch224(zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, zzz1125, zzz1126, zzz1127, zzz1128, zzz1129, zzz11300, zzz11310, bd)
new_mkVBalBranch3MkVBalBranch217(zzz473, zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, zzz481, zzz482, Zero, Succ(zzz4840), bh) → new_mkVBalBranch0(zzz482, Branch(zzz478, zzz479, Pos(Succ(Zero)), zzz480, zzz481), zzz476, bh)
new_mkVBalBranch3MkVBalBranch224(zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, zzz1125, zzz1126, zzz1127, zzz1128, zzz1129, Succ(zzz11300), Zero, bd) → new_mkVBalBranch3MkVBalBranch119(zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, zzz1125, zzz1126, zzz1127, zzz1128, zzz1129, new_primPlusNat2(Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat3(new_primPlusNat1(zzz1121), zzz1121)), zzz1121))), Succ(zzz1121)), bd)
new_mkVBalBranch3MkVBalBranch110(zzz461, zzz462, zzz463, zzz464, zzz465, zzz466, zzz467, zzz468, zzz469, zzz470, zzz471, Succ(zzz5800), bb) → new_mkVBalBranch3MkVBalBranch115(zzz461, zzz462, zzz463, zzz464, zzz465, zzz466, zzz467, Succ(zzz468), zzz469, zzz470, zzz471, Succ(zzz5800), Succ(Succ(zzz468)), bb)
new_mkVBalBranch3MkVBalBranch227(zzz486, zzz487, zzz488, zzz489, zzz490, zzz491, zzz492, zzz493, zzz494, zzz495, zzz496, bf) → new_mkVBalBranch0(zzz496, Branch(zzz491, zzz492, Neg(Succ(Succ(zzz493))), zzz494, zzz495), zzz489, bf)
new_mkVBalBranch3MkVBalBranch215(zzz340, zzz341, Pos(Zero), zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, Succ(zzz660), h) → new_mkVBalBranch0(zzz31, zzz514, Branch(zzz340, zzz341, Pos(Zero), zzz343, zzz344), h)
new_mkVBalBranch3MkVBalBranch223(zzz340, zzz341, Neg(Zero), zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, Succ(zzz670), h) → new_mkVBalBranch0(zzz31, Branch(zzz510, zzz511, Neg(Succ(zzz51200)), zzz513, zzz514), zzz343, h)
new_mkVBalBranch3MkVBalBranch216(zzz1105, zzz1106, zzz1107, zzz1108, zzz1109, zzz1110, zzz1111, zzz1112, zzz1113, zzz1114, zzz1115, Zero, Succ(zzz11170), ba) → new_mkVBalBranch0(zzz1115, Branch(zzz1110, zzz1111, Pos(Succ(Succ(zzz1112))), zzz1113, zzz1114), zzz1108, ba)
new_mkVBalBranch3MkVBalBranch115(zzz1986, zzz1987, zzz1988, zzz1989, zzz1990, zzz1991, zzz1992, zzz1993, zzz1994, zzz1995, zzz1996, Zero, Succ(zzz19980), bc) → new_mkVBalBranch0(zzz1996, zzz1995, Branch(zzz1986, zzz1987, Pos(Succ(zzz1988)), zzz1989, zzz1990), bc)
new_mkVBalBranch3MkVBalBranch233(zzz473, zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, zzz481, zzz482, bh) → new_mkVBalBranch3MkVBalBranch121(zzz473, zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, zzz481, zzz482, new_primPlusNat2(Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat3(new_primPlusNat1(zzz475), zzz475)), zzz475))), Succ(zzz475)), bh)
new_mkVBalBranch3MkVBalBranch215(zzz340, zzz341, Pos(Succ(Zero)), zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, Succ(zzz660), h) → new_mkVBalBranch3MkVBalBranch18(zzz340, zzz341, zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, new_primPlusNat2(Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat3(new_primPlusNat1(Zero), Zero)), Zero))), Succ(Zero)), h)
new_mkVBalBranch3MkVBalBranch122(zzz340, zzz341, zzz34200, zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, h) → new_mkVBalBranch0(zzz31, zzz514, Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), h)
new_mkVBalBranch3MkVBalBranch217(zzz473, zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, zzz481, zzz482, Succ(zzz4830), Succ(zzz4840), bh) → new_mkVBalBranch3MkVBalBranch217(zzz473, zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, zzz481, zzz482, zzz4830, zzz4840, bh)
new_mkVBalBranch3MkVBalBranch116(zzz340, zzz341, zzz34200, zzz343, zzz344, zzz510, zzz511, zzz513, zzz514, zzz31, Succ(zzz1200), h) → new_mkVBalBranch0(zzz31, zzz514, Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), h)
new_mkVBalBranch3MkVBalBranch110(zzz461, zzz462, zzz463, zzz464, zzz465, zzz466, zzz467, zzz468, zzz469, zzz470, zzz471, Zero, bb) → new_mkVBalBranch3MkVBalBranch115(zzz461, zzz462, zzz463, zzz464, zzz465, zzz466, zzz467, Succ(zzz468), zzz469, zzz470, zzz471, Zero, Succ(Succ(zzz468)), bb)
new_mkVBalBranch3MkVBalBranch225(zzz498, zzz499, zzz500, zzz501, zzz502, zzz503, zzz504, zzz505, zzz506, zzz507, Zero, Succ(zzz5090), bg) → new_mkVBalBranch0(zzz507, Branch(zzz503, zzz504, Neg(Succ(Zero)), zzz505, zzz506), zzz501, bg)
new_mkVBalBranch0(zzz31, Branch(zzz510, zzz511, Neg(Succ(zzz51200)), zzz513, zzz514), Branch(zzz340, zzz341, zzz342, zzz343, zzz344), h) → new_mkVBalBranch3MkVBalBranch223(zzz340, zzz341, zzz342, zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat3(new_primPlusNat1(zzz51200), zzz51200)), zzz51200))), h)
new_mkVBalBranch3MkVBalBranch121(zzz473, zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, zzz481, zzz482, Zero, bh) → new_mkVBalBranch3MkVBalBranch115(zzz473, zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, Zero, zzz480, zzz481, zzz482, Zero, Succ(Zero), bh)
new_mkVBalBranch3MkVBalBranch223(zzz340, zzz341, Neg(Succ(Zero)), zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, Succ(zzz670), h) → new_mkVBalBranch0(zzz31, Branch(zzz510, zzz511, Neg(Succ(zzz51200)), zzz513, zzz514), zzz343, h)
new_mkVBalBranch3MkVBalBranch225(zzz498, zzz499, zzz500, zzz501, zzz502, zzz503, zzz504, zzz505, zzz506, zzz507, Succ(zzz5080), Zero, bg) → new_mkVBalBranch3MkVBalBranch118(zzz498, zzz499, zzz500, zzz501, zzz502, zzz503, zzz504, zzz505, zzz506, zzz507, new_primPlusNat2(Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat3(new_primPlusNat1(zzz500), zzz500)), zzz500))), Succ(zzz500)), bg)
new_mkVBalBranch3MkVBalBranch218(zzz461, zzz462, zzz463, zzz464, zzz465, zzz466, zzz467, zzz468, zzz469, zzz470, zzz471, bb) → new_mkVBalBranch3MkVBalBranch110(zzz461, zzz462, zzz463, zzz464, zzz465, zzz466, zzz467, zzz468, zzz469, zzz470, zzz471, new_primPlusNat2(Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat3(new_primPlusNat1(zzz463), zzz463)), zzz463))), Succ(zzz463)), bb)
new_mkVBalBranch0(zzz31, Branch(zzz510, zzz511, Pos(Zero), zzz513, zzz514), Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), h) → new_mkVBalBranch3MkVBalBranch116(zzz340, zzz341, zzz34200, zzz343, zzz344, zzz510, zzz511, zzz513, zzz514, zzz31, new_primPlusNat2(new_primPlusNat3(Succ(new_primPlusNat3(new_primPlusNat1(zzz34200), zzz34200)), Succ(zzz34200)), Succ(zzz34200)), h)
new_mkVBalBranch3MkVBalBranch222(zzz461, zzz462, zzz463, zzz464, zzz465, zzz466, zzz467, zzz468, zzz469, zzz470, zzz471, bb) → new_mkVBalBranch3MkVBalBranch110(zzz461, zzz462, zzz463, zzz464, zzz465, zzz466, zzz467, zzz468, zzz469, zzz470, zzz471, new_primPlusNat2(Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat3(new_primPlusNat1(zzz463), zzz463)), zzz463))), Succ(zzz463)), bb)
new_mkVBalBranch3MkVBalBranch215(zzz340, zzz341, Pos(Succ(Succ(zzz342000))), zzz343, zzz344, zzz510, zzz511, Zero, zzz513, zzz514, zzz31, Succ(Succ(zzz6600)), h) → new_mkVBalBranch3MkVBalBranch217(zzz340, zzz341, Succ(zzz342000), zzz343, zzz344, zzz510, zzz511, zzz513, zzz514, zzz31, Succ(zzz6600), zzz342000, h)
new_mkVBalBranch3MkVBalBranch117(zzz340, zzz341, zzz34200, zzz343, zzz344, zzz510, zzz511, zzz513, zzz514, zzz31, Succ(zzz1240), h) → new_mkVBalBranch0(zzz31, zzz514, Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), h)
new_mkVBalBranch3MkVBalBranch120(zzz2050, zzz2051, zzz2052, zzz2053, zzz2054, zzz2055, zzz2056, zzz2057, zzz2058, zzz2059, zzz2060, Succ(zzz20610), Succ(zzz20620), be) → new_mkVBalBranch3MkVBalBranch120(zzz2050, zzz2051, zzz2052, zzz2053, zzz2054, zzz2055, zzz2056, zzz2057, zzz2058, zzz2059, zzz2060, zzz20610, zzz20620, be)
new_mkVBalBranch3MkVBalBranch217(zzz473, zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, zzz481, zzz482, Zero, Zero, bh) → new_mkVBalBranch3MkVBalBranch233(zzz473, zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, zzz481, zzz482, bh)
new_mkVBalBranch3MkVBalBranch216(zzz1105, zzz1106, zzz1107, zzz1108, zzz1109, zzz1110, zzz1111, zzz1112, zzz1113, zzz1114, zzz1115, Succ(zzz11160), Succ(zzz11170), ba) → new_mkVBalBranch3MkVBalBranch216(zzz1105, zzz1106, zzz1107, zzz1108, zzz1109, zzz1110, zzz1111, zzz1112, zzz1113, zzz1114, zzz1115, zzz11160, zzz11170, ba)
new_mkVBalBranch3MkVBalBranch223(zzz340, zzz341, Pos(zzz3420), zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, Succ(zzz670), h) → new_mkVBalBranch0(zzz31, Branch(zzz510, zzz511, Neg(Succ(zzz51200)), zzz513, zzz514), zzz343, h)
new_mkVBalBranch0(zzz31, Branch(zzz510, zzz511, Neg(Zero), zzz513, zzz514), Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), h) → new_mkVBalBranch3MkVBalBranch117(zzz340, zzz341, zzz34200, zzz343, zzz344, zzz510, zzz511, zzz513, zzz514, zzz31, new_primPlusNat2(Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat3(new_primPlusNat1(zzz34200), zzz34200)), zzz34200))), Succ(zzz34200)), h)
new_mkVBalBranch3MkVBalBranch19(zzz340, zzz341, zzz34200, zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, Zero, h) → new_mkVBalBranch3MkVBalBranch122(zzz340, zzz341, zzz34200, zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, h)
new_mkVBalBranch3MkVBalBranch225(zzz498, zzz499, zzz500, zzz501, zzz502, zzz503, zzz504, zzz505, zzz506, zzz507, Succ(zzz5080), Succ(zzz5090), bg) → new_mkVBalBranch3MkVBalBranch225(zzz498, zzz499, zzz500, zzz501, zzz502, zzz503, zzz504, zzz505, zzz506, zzz507, zzz5080, zzz5090, bg)
new_mkVBalBranch3MkVBalBranch19(zzz340, zzz341, zzz34200, zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, Succ(zzz1410), h) → new_mkVBalBranch0(zzz31, zzz514, Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), h)
new_mkVBalBranch3MkVBalBranch224(zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, zzz1125, zzz1126, zzz1127, zzz1128, zzz1129, Zero, Succ(zzz11310), bd) → new_mkVBalBranch3MkVBalBranch227(zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, zzz1125, zzz1126, zzz1127, zzz1128, zzz1129, bd)
new_mkVBalBranch3MkVBalBranch224(zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, zzz1125, zzz1126, zzz1127, zzz1128, zzz1129, Zero, Zero, bd) → new_mkVBalBranch3MkVBalBranch229(zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, zzz1125, zzz1126, zzz1127, zzz1128, zzz1129, bd)
new_mkVBalBranch3MkVBalBranch223(zzz340, zzz341, Neg(Succ(Succ(Zero))), zzz343, zzz344, zzz510, zzz511, Zero, zzz513, zzz514, zzz31, Succ(Succ(zzz6700)), h) → new_mkVBalBranch3MkVBalBranch225(zzz340, zzz341, Succ(Zero), zzz343, zzz344, zzz510, zzz511, zzz513, zzz514, zzz31, Zero, Succ(zzz6700), h)
new_mkVBalBranch3MkVBalBranch223(zzz340, zzz341, Neg(Succ(Succ(Succ(zzz3420000)))), zzz343, zzz344, zzz510, zzz511, Succ(zzz512000), zzz513, zzz514, zzz31, Succ(Succ(zzz6700)), h) → new_mkVBalBranch3MkVBalBranch224(zzz340, zzz341, Succ(Succ(zzz3420000)), zzz343, zzz344, zzz510, zzz511, zzz512000, zzz513, zzz514, zzz31, Succ(zzz3420000), Succ(Succ(new_primPlusNat2(zzz6700, zzz512000))), h)
new_mkVBalBranch3MkVBalBranch115(zzz1986, zzz1987, zzz1988, zzz1989, zzz1990, zzz1991, zzz1992, zzz1993, zzz1994, zzz1995, zzz1996, Succ(zzz19970), Succ(zzz19980), bc) → new_mkVBalBranch3MkVBalBranch115(zzz1986, zzz1987, zzz1988, zzz1989, zzz1990, zzz1991, zzz1992, zzz1993, zzz1994, zzz1995, zzz1996, zzz19970, zzz19980, bc)
new_mkVBalBranch3MkVBalBranch215(zzz340, zzz341, Neg(Zero), zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, Succ(zzz660), h) → new_mkVBalBranch0(zzz31, zzz514, Branch(zzz340, zzz341, Neg(Zero), zzz343, zzz344), h)
new_mkVBalBranch3MkVBalBranch229(zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, zzz1125, zzz1126, zzz1127, zzz1128, zzz1129, bd) → new_mkVBalBranch3MkVBalBranch119(zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, zzz1125, zzz1126, zzz1127, zzz1128, zzz1129, new_primPlusNat2(Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat3(new_primPlusNat1(zzz1121), zzz1121)), zzz1121))), Succ(zzz1121)), bd)
new_mkVBalBranch3MkVBalBranch118(zzz498, zzz499, zzz500, zzz501, zzz502, zzz503, zzz504, zzz505, zzz506, zzz507, Succ(zzz8040), bg) → new_mkVBalBranch3MkVBalBranch120(zzz498, zzz499, zzz500, zzz501, zzz502, zzz503, zzz504, Zero, zzz505, zzz506, zzz507, Succ(Zero), Succ(zzz8040), bg)
new_mkVBalBranch3MkVBalBranch216(zzz1105, zzz1106, zzz1107, zzz1108, zzz1109, zzz1110, zzz1111, zzz1112, zzz1113, zzz1114, zzz1115, Succ(zzz11160), Zero, ba) → new_mkVBalBranch3MkVBalBranch218(zzz1105, zzz1106, zzz1107, zzz1108, zzz1109, zzz1110, zzz1111, zzz1112, zzz1113, zzz1114, zzz1115, ba)
new_mkVBalBranch3MkVBalBranch216(zzz1105, zzz1106, zzz1107, zzz1108, zzz1109, zzz1110, zzz1111, zzz1112, zzz1113, zzz1114, zzz1115, Zero, Zero, ba) → new_mkVBalBranch3MkVBalBranch222(zzz1105, zzz1106, zzz1107, zzz1108, zzz1109, zzz1110, zzz1111, zzz1112, zzz1113, zzz1114, zzz1115, ba)
new_mkVBalBranch3MkVBalBranch18(zzz340, zzz341, zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, Zero, h) → new_mkVBalBranch3MkVBalBranch115(zzz340, zzz341, Zero, zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, Zero, Succ(zzz51200), h)
new_mkVBalBranch3MkVBalBranch119(zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, zzz1125, zzz1126, zzz1127, zzz1128, zzz1129, Succ(zzz12130), bd) → new_mkVBalBranch3MkVBalBranch120(zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, zzz1125, Succ(zzz1126), zzz1127, zzz1128, zzz1129, Succ(Succ(zzz1126)), Succ(zzz12130), bd)

The TRS R consists of the following rules:

new_primPlusNat1(Zero) → Zero
new_primPlusNat1(Succ(zzz62000)) → Succ(Succ(new_primPlusNat1(zzz62000)))
new_primPlusNat3(zzz90, Succ(zzz910)) → Succ(Succ(new_primPlusNat2(zzz90, zzz910)))
new_primPlusNat3(zzz90, Zero) → Succ(zzz90)
new_primPlusNat2(Succ(zzz900), Succ(zzz9100)) → Succ(Succ(new_primPlusNat2(zzz900, zzz9100)))
new_primPlusNat2(Zero, Succ(zzz9100)) → Succ(zzz9100)
new_primPlusNat2(Zero, Zero) → Zero
new_primPlusNat2(Succ(zzz900), Zero) → Succ(zzz900)

The set Q consists of the following terms:

new_primPlusNat2(Zero, Succ(x0))
new_primPlusNat3(x0, Succ(x1))
new_primPlusNat2(Succ(x0), Succ(x1))
new_primPlusNat3(x0, Zero)
new_primPlusNat1(Zero)
new_primPlusNat2(Zero, Zero)
new_primPlusNat1(Succ(x0))
new_primPlusNat2(Succ(x0), Zero)

We have to consider all minimal (P,Q,R)-chains.
By rewriting [15] the rule new_mkVBalBranch0(zzz31, Branch(zzz510, zzz511, Pos(Zero), zzz513, zzz514), Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), h) → new_mkVBalBranch3MkVBalBranch116(zzz340, zzz341, zzz34200, zzz343, zzz344, zzz510, zzz511, zzz513, zzz514, zzz31, new_primPlusNat2(new_primPlusNat3(Succ(new_primPlusNat3(new_primPlusNat1(zzz34200), zzz34200)), Succ(zzz34200)), Succ(zzz34200)), h) at position [10,0] we obtained the following new rules:

new_mkVBalBranch0(zzz31, Branch(zzz510, zzz511, Pos(Zero), zzz513, zzz514), Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), h) → new_mkVBalBranch3MkVBalBranch116(zzz340, zzz341, zzz34200, zzz343, zzz344, zzz510, zzz511, zzz513, zzz514, zzz31, new_primPlusNat2(Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat3(new_primPlusNat1(zzz34200), zzz34200)), 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
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                    ↳ DependencyGraphProof
                                      ↳ QDP
                                        ↳ Rewriting
                                          ↳ QDP
                                            ↳ Rewriting
                                              ↳ QDP
                                                ↳ Rewriting
                                                  ↳ QDP
                                                    ↳ Rewriting
                                                      ↳ QDP
                                                        ↳ Rewriting
                                                          ↳ QDP
                                                            ↳ Rewriting
                                                              ↳ QDP
                                                                ↳ Rewriting
                                                                  ↳ QDP
                                                                    ↳ Rewriting
                                                                      ↳ QDP
                                                                        ↳ Rewriting
                                                                          ↳ QDP
                                                                            ↳ Rewriting
                                                                              ↳ QDP
                                                                                ↳ Rewriting
                                                                                  ↳ QDP
                                                                                    ↳ Rewriting
                                                                                      ↳ QDP
                                                                                        ↳ Rewriting
                                                                                          ↳ QDP
                                                                                            ↳ Rewriting
                                                                                              ↳ QDP
                                                                                                ↳ Rewriting
                                                                                                  ↳ QDP
                                                                                                    ↳ Rewriting
                                                                                                      ↳ QDP
                                                                                                        ↳ Rewriting
                                                                                                          ↳ QDP
                                                                                                            ↳ UsableRulesProof
                                                                                                              ↳ QDP
                                                                                                                ↳ QReductionProof
                                                                                                                  ↳ QDP
                                                                                                                    ↳ Rewriting
                                                                                                                      ↳ QDP
                                                                                                                        ↳ Rewriting
                                                                                                                          ↳ QDP
                                                                                                                            ↳ DependencyGraphProof
                                                                                                                              ↳ QDP
                                                                                                                                ↳ Rewriting
                                                                                                                                  ↳ QDP
                                                                                                                                    ↳ Rewriting
                                                                                                                                      ↳ QDP
                                                                                                                                        ↳ DependencyGraphProof
                                                                                                                                          ↳ QDP
                                                                                                                                            ↳ Rewriting
                                                                                                                                              ↳ QDP
                                                                                                                                                ↳ Rewriting
                                                                                                                                                  ↳ QDP
                                                                                                                                                    ↳ Rewriting
                                                                                                                                                      ↳ QDP
                                                                                                                                                        ↳ Rewriting
                                                                                                                                                          ↳ QDP
                                                                                                                                                            ↳ Rewriting
                                                                                                                                                              ↳ QDP
                                                                                                                                                                ↳ Rewriting
                                                                                                                                                                  ↳ QDP
                                                                                                                                                                    ↳ Rewriting
                                                                                                                                                                      ↳ QDP
                                                                                                                                                                        ↳ Rewriting
                                                                                                                                                                          ↳ QDP
                                                                                                                                                                            ↳ Rewriting
                                                                                                                                                                              ↳ QDP
                                                                                                                                                                                ↳ Rewriting
                                                                                                                                                                                  ↳ QDP
                                                                                                                                                                                    ↳ Rewriting
                                                                                                                                                                                      ↳ QDP
                                                                                                                                                                                        ↳ Rewriting
                                                                                                                                                                                          ↳ QDP
                                                                                                                                                                                            ↳ UsableRulesProof
                                                                                                                                                                                              ↳ QDP
                                                                                                                                                                                                ↳ QReductionProof
                                                                                                                                                                                                  ↳ QDP
                                                                                                                                                                                                    ↳ Rewriting
                                                                                                                                                                                                      ↳ QDP
                                                                                                                                                                                                        ↳ Rewriting
                                                                                                                                                                                                          ↳ QDP
                                                                                                                                                                                                            ↳ Rewriting
                                                                                                                                                                                                              ↳ QDP
                                                                                                                                                                                                                ↳ Rewriting
                                                                                                                                                                                                                  ↳ QDP
                                                                                                                                                                                                                    ↳ Rewriting
                                                                                                                                                                                                                      ↳ QDP
                                                                                                                                                                                                                        ↳ Rewriting
                                                                                                                                                                                                                          ↳ QDP
                                                                                                                                                                                                                            ↳ Rewriting
                                                                                                                                                                                                                              ↳ QDP
                                                                                                                                                                                                                                ↳ Rewriting
                                                                                                                                                                                                                                  ↳ QDP
                                                                                                                                                                                                                                    ↳ Rewriting
                                                                                                                                                                                                                                      ↳ QDP
                                                                                                                                                                                                                                        ↳ Rewriting
                                                                                                                                                                                                                                          ↳ QDP
                                                                                                                                                                                                                                            ↳ Rewriting
                                                                                                                                                                                                                                              ↳ QDP
                                                                                                                                                                                                                                                ↳ Rewriting
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP

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

new_mkVBalBranch3MkVBalBranch225(zzz498, zzz499, zzz500, zzz501, zzz502, zzz503, zzz504, zzz505, zzz506, zzz507, Zero, Zero, bg) → new_mkVBalBranch3MkVBalBranch230(zzz498, zzz499, zzz500, zzz501, zzz502, zzz503, zzz504, zzz505, zzz506, zzz507, bg)
new_mkVBalBranch3MkVBalBranch18(zzz340, zzz341, zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, Succ(zzz1480), h) → new_mkVBalBranch3MkVBalBranch115(zzz340, zzz341, Zero, zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, Succ(zzz1480), Succ(zzz51200), h)
new_mkVBalBranch0(zzz31, Branch(zzz510, zzz511, Neg(Zero), zzz513, zzz514), Branch(zzz340, zzz341, Pos(Succ(zzz34200)), zzz343, zzz344), h) → new_mkVBalBranch0(zzz31, Branch(zzz510, zzz511, Neg(Zero), zzz513, zzz514), zzz343, h)
new_mkVBalBranch3MkVBalBranch215(zzz340, zzz341, Pos(Succ(Succ(zzz342000))), zzz343, zzz344, zzz510, zzz511, Succ(zzz512000), zzz513, zzz514, zzz31, Succ(Succ(zzz6600)), h) → new_mkVBalBranch3MkVBalBranch216(zzz340, zzz341, Succ(zzz342000), zzz343, zzz344, zzz510, zzz511, zzz512000, zzz513, zzz514, zzz31, Succ(Succ(new_primPlusNat2(zzz6600, zzz512000))), zzz342000, h)
new_mkVBalBranch3MkVBalBranch223(zzz340, zzz341, Neg(Succ(Succ(Succ(zzz3420000)))), zzz343, zzz344, zzz510, zzz511, Zero, zzz513, zzz514, zzz31, Succ(Succ(zzz6700)), h) → new_mkVBalBranch3MkVBalBranch225(zzz340, zzz341, Succ(Succ(zzz3420000)), zzz343, zzz344, zzz510, zzz511, zzz513, zzz514, zzz31, Succ(zzz3420000), Succ(zzz6700), h)
new_mkVBalBranch3MkVBalBranch120(zzz2050, zzz2051, zzz2052, zzz2053, zzz2054, zzz2055, zzz2056, zzz2057, zzz2058, zzz2059, zzz2060, Zero, Succ(zzz20620), be) → new_mkVBalBranch0(zzz2060, zzz2059, Branch(zzz2050, zzz2051, Neg(Succ(zzz2052)), zzz2053, zzz2054), be)
new_mkVBalBranch3MkVBalBranch121(zzz473, zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, zzz481, zzz482, Succ(zzz7390), bh) → new_mkVBalBranch3MkVBalBranch115(zzz473, zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, Zero, zzz480, zzz481, zzz482, Succ(zzz7390), Succ(Zero), bh)
new_mkVBalBranch0(zzz31, Branch(zzz510, zzz511, Pos(Zero), zzz513, zzz514), Branch(zzz340, zzz341, Pos(Succ(zzz34200)), zzz343, zzz344), h) → new_mkVBalBranch0(zzz31, Branch(zzz510, zzz511, Pos(Zero), zzz513, zzz514), zzz343, h)
new_mkVBalBranch3MkVBalBranch215(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, Succ(zzz660), h) → new_mkVBalBranch3MkVBalBranch19(zzz340, zzz341, zzz34200, zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, new_primPlusNat2(Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat3(new_primPlusNat1(zzz34200), zzz34200)), zzz34200))), Succ(zzz34200)), h)
new_mkVBalBranch0(zzz31, Branch(zzz510, zzz511, Pos(Succ(zzz51200)), zzz513, zzz514), Branch(zzz340, zzz341, zzz342, zzz343, zzz344), h) → new_mkVBalBranch3MkVBalBranch215(zzz340, zzz341, zzz342, zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat3(new_primPlusNat1(zzz51200), zzz51200)), zzz51200))), h)
new_mkVBalBranch3MkVBalBranch223(zzz340, zzz341, Neg(Succ(Succ(Zero))), zzz343, zzz344, zzz510, zzz511, Succ(zzz512000), zzz513, zzz514, zzz31, Succ(Succ(zzz6700)), h) → new_mkVBalBranch3MkVBalBranch224(zzz340, zzz341, Succ(Zero), zzz343, zzz344, zzz510, zzz511, zzz512000, zzz513, zzz514, zzz31, Zero, Succ(Succ(new_primPlusNat2(zzz6700, zzz512000))), h)
new_mkVBalBranch3MkVBalBranch230(zzz498, zzz499, zzz500, zzz501, zzz502, zzz503, zzz504, zzz505, zzz506, zzz507, bg) → new_mkVBalBranch3MkVBalBranch118(zzz498, zzz499, zzz500, zzz501, zzz502, zzz503, zzz504, zzz505, zzz506, zzz507, Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat2(Succ(new_primPlusNat3(new_primPlusNat1(zzz500), zzz500)), zzz500)), zzz500))), bg)
new_mkVBalBranch3MkVBalBranch217(zzz473, zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, zzz481, zzz482, Succ(zzz4830), Zero, bh) → new_mkVBalBranch3MkVBalBranch121(zzz473, zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, zzz481, zzz482, new_primPlusNat2(Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat3(new_primPlusNat1(zzz475), zzz475)), zzz475))), Succ(zzz475)), bh)
new_mkVBalBranch3MkVBalBranch224(zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, zzz1125, zzz1126, zzz1127, zzz1128, zzz1129, Succ(zzz11300), Succ(zzz11310), bd) → new_mkVBalBranch3MkVBalBranch224(zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, zzz1125, zzz1126, zzz1127, zzz1128, zzz1129, zzz11300, zzz11310, bd)
new_mkVBalBranch3MkVBalBranch217(zzz473, zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, zzz481, zzz482, Zero, Succ(zzz4840), bh) → new_mkVBalBranch0(zzz482, Branch(zzz478, zzz479, Pos(Succ(Zero)), zzz480, zzz481), zzz476, bh)
new_mkVBalBranch3MkVBalBranch224(zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, zzz1125, zzz1126, zzz1127, zzz1128, zzz1129, Succ(zzz11300), Zero, bd) → new_mkVBalBranch3MkVBalBranch119(zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, zzz1125, zzz1126, zzz1127, zzz1128, zzz1129, new_primPlusNat2(Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat3(new_primPlusNat1(zzz1121), zzz1121)), zzz1121))), Succ(zzz1121)), bd)
new_mkVBalBranch3MkVBalBranch110(zzz461, zzz462, zzz463, zzz464, zzz465, zzz466, zzz467, zzz468, zzz469, zzz470, zzz471, Succ(zzz5800), bb) → new_mkVBalBranch3MkVBalBranch115(zzz461, zzz462, zzz463, zzz464, zzz465, zzz466, zzz467, Succ(zzz468), zzz469, zzz470, zzz471, Succ(zzz5800), Succ(Succ(zzz468)), bb)
new_mkVBalBranch3MkVBalBranch227(zzz486, zzz487, zzz488, zzz489, zzz490, zzz491, zzz492, zzz493, zzz494, zzz495, zzz496, bf) → new_mkVBalBranch0(zzz496, Branch(zzz491, zzz492, Neg(Succ(Succ(zzz493))), zzz494, zzz495), zzz489, bf)
new_mkVBalBranch3MkVBalBranch215(zzz340, zzz341, Pos(Zero), zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, Succ(zzz660), h) → new_mkVBalBranch0(zzz31, zzz514, Branch(zzz340, zzz341, Pos(Zero), zzz343, zzz344), h)
new_mkVBalBranch3MkVBalBranch223(zzz340, zzz341, Neg(Zero), zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, Succ(zzz670), h) → new_mkVBalBranch0(zzz31, Branch(zzz510, zzz511, Neg(Succ(zzz51200)), zzz513, zzz514), zzz343, h)
new_mkVBalBranch3MkVBalBranch216(zzz1105, zzz1106, zzz1107, zzz1108, zzz1109, zzz1110, zzz1111, zzz1112, zzz1113, zzz1114, zzz1115, Zero, Succ(zzz11170), ba) → new_mkVBalBranch0(zzz1115, Branch(zzz1110, zzz1111, Pos(Succ(Succ(zzz1112))), zzz1113, zzz1114), zzz1108, ba)
new_mkVBalBranch3MkVBalBranch115(zzz1986, zzz1987, zzz1988, zzz1989, zzz1990, zzz1991, zzz1992, zzz1993, zzz1994, zzz1995, zzz1996, Zero, Succ(zzz19980), bc) → new_mkVBalBranch0(zzz1996, zzz1995, Branch(zzz1986, zzz1987, Pos(Succ(zzz1988)), zzz1989, zzz1990), bc)
new_mkVBalBranch3MkVBalBranch233(zzz473, zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, zzz481, zzz482, bh) → new_mkVBalBranch3MkVBalBranch121(zzz473, zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, zzz481, zzz482, new_primPlusNat2(Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat3(new_primPlusNat1(zzz475), zzz475)), zzz475))), Succ(zzz475)), bh)
new_mkVBalBranch3MkVBalBranch215(zzz340, zzz341, Pos(Succ(Zero)), zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, Succ(zzz660), h) → new_mkVBalBranch3MkVBalBranch18(zzz340, zzz341, zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, new_primPlusNat2(Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat3(new_primPlusNat1(Zero), Zero)), Zero))), Succ(Zero)), h)
new_mkVBalBranch3MkVBalBranch122(zzz340, zzz341, zzz34200, zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, h) → new_mkVBalBranch0(zzz31, zzz514, Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), h)
new_mkVBalBranch3MkVBalBranch217(zzz473, zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, zzz481, zzz482, Succ(zzz4830), Succ(zzz4840), bh) → new_mkVBalBranch3MkVBalBranch217(zzz473, zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, zzz481, zzz482, zzz4830, zzz4840, bh)
new_mkVBalBranch3MkVBalBranch116(zzz340, zzz341, zzz34200, zzz343, zzz344, zzz510, zzz511, zzz513, zzz514, zzz31, Succ(zzz1200), h) → new_mkVBalBranch0(zzz31, zzz514, Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), h)
new_mkVBalBranch3MkVBalBranch110(zzz461, zzz462, zzz463, zzz464, zzz465, zzz466, zzz467, zzz468, zzz469, zzz470, zzz471, Zero, bb) → new_mkVBalBranch3MkVBalBranch115(zzz461, zzz462, zzz463, zzz464, zzz465, zzz466, zzz467, Succ(zzz468), zzz469, zzz470, zzz471, Zero, Succ(Succ(zzz468)), bb)
new_mkVBalBranch3MkVBalBranch225(zzz498, zzz499, zzz500, zzz501, zzz502, zzz503, zzz504, zzz505, zzz506, zzz507, Zero, Succ(zzz5090), bg) → new_mkVBalBranch0(zzz507, Branch(zzz503, zzz504, Neg(Succ(Zero)), zzz505, zzz506), zzz501, bg)
new_mkVBalBranch0(zzz31, Branch(zzz510, zzz511, Neg(Succ(zzz51200)), zzz513, zzz514), Branch(zzz340, zzz341, zzz342, zzz343, zzz344), h) → new_mkVBalBranch3MkVBalBranch223(zzz340, zzz341, zzz342, zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat3(new_primPlusNat1(zzz51200), zzz51200)), zzz51200))), h)
new_mkVBalBranch3MkVBalBranch121(zzz473, zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, zzz481, zzz482, Zero, bh) → new_mkVBalBranch3MkVBalBranch115(zzz473, zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, Zero, zzz480, zzz481, zzz482, Zero, Succ(Zero), bh)
new_mkVBalBranch3MkVBalBranch223(zzz340, zzz341, Neg(Succ(Zero)), zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, Succ(zzz670), h) → new_mkVBalBranch0(zzz31, Branch(zzz510, zzz511, Neg(Succ(zzz51200)), zzz513, zzz514), zzz343, h)
new_mkVBalBranch3MkVBalBranch225(zzz498, zzz499, zzz500, zzz501, zzz502, zzz503, zzz504, zzz505, zzz506, zzz507, Succ(zzz5080), Zero, bg) → new_mkVBalBranch3MkVBalBranch118(zzz498, zzz499, zzz500, zzz501, zzz502, zzz503, zzz504, zzz505, zzz506, zzz507, new_primPlusNat2(Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat3(new_primPlusNat1(zzz500), zzz500)), zzz500))), Succ(zzz500)), bg)
new_mkVBalBranch3MkVBalBranch218(zzz461, zzz462, zzz463, zzz464, zzz465, zzz466, zzz467, zzz468, zzz469, zzz470, zzz471, bb) → new_mkVBalBranch3MkVBalBranch110(zzz461, zzz462, zzz463, zzz464, zzz465, zzz466, zzz467, zzz468, zzz469, zzz470, zzz471, new_primPlusNat2(Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat3(new_primPlusNat1(zzz463), zzz463)), zzz463))), Succ(zzz463)), bb)
new_mkVBalBranch0(zzz31, Branch(zzz510, zzz511, Pos(Zero), zzz513, zzz514), Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), h) → new_mkVBalBranch3MkVBalBranch116(zzz340, zzz341, zzz34200, zzz343, zzz344, zzz510, zzz511, zzz513, zzz514, zzz31, new_primPlusNat2(Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat3(new_primPlusNat1(zzz34200), zzz34200)), zzz34200))), Succ(zzz34200)), h)
new_mkVBalBranch3MkVBalBranch222(zzz461, zzz462, zzz463, zzz464, zzz465, zzz466, zzz467, zzz468, zzz469, zzz470, zzz471, bb) → new_mkVBalBranch3MkVBalBranch110(zzz461, zzz462, zzz463, zzz464, zzz465, zzz466, zzz467, zzz468, zzz469, zzz470, zzz471, new_primPlusNat2(Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat3(new_primPlusNat1(zzz463), zzz463)), zzz463))), Succ(zzz463)), bb)
new_mkVBalBranch3MkVBalBranch215(zzz340, zzz341, Pos(Succ(Succ(zzz342000))), zzz343, zzz344, zzz510, zzz511, Zero, zzz513, zzz514, zzz31, Succ(Succ(zzz6600)), h) → new_mkVBalBranch3MkVBalBranch217(zzz340, zzz341, Succ(zzz342000), zzz343, zzz344, zzz510, zzz511, zzz513, zzz514, zzz31, Succ(zzz6600), zzz342000, h)
new_mkVBalBranch3MkVBalBranch117(zzz340, zzz341, zzz34200, zzz343, zzz344, zzz510, zzz511, zzz513, zzz514, zzz31, Succ(zzz1240), h) → new_mkVBalBranch0(zzz31, zzz514, Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), h)
new_mkVBalBranch3MkVBalBranch217(zzz473, zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, zzz481, zzz482, Zero, Zero, bh) → new_mkVBalBranch3MkVBalBranch233(zzz473, zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, zzz481, zzz482, bh)
new_mkVBalBranch3MkVBalBranch120(zzz2050, zzz2051, zzz2052, zzz2053, zzz2054, zzz2055, zzz2056, zzz2057, zzz2058, zzz2059, zzz2060, Succ(zzz20610), Succ(zzz20620), be) → new_mkVBalBranch3MkVBalBranch120(zzz2050, zzz2051, zzz2052, zzz2053, zzz2054, zzz2055, zzz2056, zzz2057, zzz2058, zzz2059, zzz2060, zzz20610, zzz20620, be)
new_mkVBalBranch3MkVBalBranch223(zzz340, zzz341, Pos(zzz3420), zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, Succ(zzz670), h) → new_mkVBalBranch0(zzz31, Branch(zzz510, zzz511, Neg(Succ(zzz51200)), zzz513, zzz514), zzz343, h)
new_mkVBalBranch3MkVBalBranch216(zzz1105, zzz1106, zzz1107, zzz1108, zzz1109, zzz1110, zzz1111, zzz1112, zzz1113, zzz1114, zzz1115, Succ(zzz11160), Succ(zzz11170), ba) → new_mkVBalBranch3MkVBalBranch216(zzz1105, zzz1106, zzz1107, zzz1108, zzz1109, zzz1110, zzz1111, zzz1112, zzz1113, zzz1114, zzz1115, zzz11160, zzz11170, ba)
new_mkVBalBranch0(zzz31, Branch(zzz510, zzz511, Neg(Zero), zzz513, zzz514), Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), h) → new_mkVBalBranch3MkVBalBranch117(zzz340, zzz341, zzz34200, zzz343, zzz344, zzz510, zzz511, zzz513, zzz514, zzz31, new_primPlusNat2(Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat3(new_primPlusNat1(zzz34200), zzz34200)), zzz34200))), Succ(zzz34200)), h)
new_mkVBalBranch3MkVBalBranch19(zzz340, zzz341, zzz34200, zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, Zero, h) → new_mkVBalBranch3MkVBalBranch122(zzz340, zzz341, zzz34200, zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, h)
new_mkVBalBranch3MkVBalBranch225(zzz498, zzz499, zzz500, zzz501, zzz502, zzz503, zzz504, zzz505, zzz506, zzz507, Succ(zzz5080), Succ(zzz5090), bg) → new_mkVBalBranch3MkVBalBranch225(zzz498, zzz499, zzz500, zzz501, zzz502, zzz503, zzz504, zzz505, zzz506, zzz507, zzz5080, zzz5090, bg)
new_mkVBalBranch3MkVBalBranch19(zzz340, zzz341, zzz34200, zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, Succ(zzz1410), h) → new_mkVBalBranch0(zzz31, zzz514, Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), h)
new_mkVBalBranch3MkVBalBranch224(zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, zzz1125, zzz1126, zzz1127, zzz1128, zzz1129, Zero, Zero, bd) → new_mkVBalBranch3MkVBalBranch229(zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, zzz1125, zzz1126, zzz1127, zzz1128, zzz1129, bd)
new_mkVBalBranch3MkVBalBranch224(zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, zzz1125, zzz1126, zzz1127, zzz1128, zzz1129, Zero, Succ(zzz11310), bd) → new_mkVBalBranch3MkVBalBranch227(zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, zzz1125, zzz1126, zzz1127, zzz1128, zzz1129, bd)
new_mkVBalBranch3MkVBalBranch223(zzz340, zzz341, Neg(Succ(Succ(Succ(zzz3420000)))), zzz343, zzz344, zzz510, zzz511, Succ(zzz512000), zzz513, zzz514, zzz31, Succ(Succ(zzz6700)), h) → new_mkVBalBranch3MkVBalBranch224(zzz340, zzz341, Succ(Succ(zzz3420000)), zzz343, zzz344, zzz510, zzz511, zzz512000, zzz513, zzz514, zzz31, Succ(zzz3420000), Succ(Succ(new_primPlusNat2(zzz6700, zzz512000))), h)
new_mkVBalBranch3MkVBalBranch223(zzz340, zzz341, Neg(Succ(Succ(Zero))), zzz343, zzz344, zzz510, zzz511, Zero, zzz513, zzz514, zzz31, Succ(Succ(zzz6700)), h) → new_mkVBalBranch3MkVBalBranch225(zzz340, zzz341, Succ(Zero), zzz343, zzz344, zzz510, zzz511, zzz513, zzz514, zzz31, Zero, Succ(zzz6700), h)
new_mkVBalBranch3MkVBalBranch115(zzz1986, zzz1987, zzz1988, zzz1989, zzz1990, zzz1991, zzz1992, zzz1993, zzz1994, zzz1995, zzz1996, Succ(zzz19970), Succ(zzz19980), bc) → new_mkVBalBranch3MkVBalBranch115(zzz1986, zzz1987, zzz1988, zzz1989, zzz1990, zzz1991, zzz1992, zzz1993, zzz1994, zzz1995, zzz1996, zzz19970, zzz19980, bc)
new_mkVBalBranch3MkVBalBranch229(zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, zzz1125, zzz1126, zzz1127, zzz1128, zzz1129, bd) → new_mkVBalBranch3MkVBalBranch119(zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, zzz1125, zzz1126, zzz1127, zzz1128, zzz1129, new_primPlusNat2(Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat3(new_primPlusNat1(zzz1121), zzz1121)), zzz1121))), Succ(zzz1121)), bd)
new_mkVBalBranch3MkVBalBranch215(zzz340, zzz341, Neg(Zero), zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, Succ(zzz660), h) → new_mkVBalBranch0(zzz31, zzz514, Branch(zzz340, zzz341, Neg(Zero), zzz343, zzz344), h)
new_mkVBalBranch3MkVBalBranch118(zzz498, zzz499, zzz500, zzz501, zzz502, zzz503, zzz504, zzz505, zzz506, zzz507, Succ(zzz8040), bg) → new_mkVBalBranch3MkVBalBranch120(zzz498, zzz499, zzz500, zzz501, zzz502, zzz503, zzz504, Zero, zzz505, zzz506, zzz507, Succ(Zero), Succ(zzz8040), bg)
new_mkVBalBranch3MkVBalBranch216(zzz1105, zzz1106, zzz1107, zzz1108, zzz1109, zzz1110, zzz1111, zzz1112, zzz1113, zzz1114, zzz1115, Succ(zzz11160), Zero, ba) → new_mkVBalBranch3MkVBalBranch218(zzz1105, zzz1106, zzz1107, zzz1108, zzz1109, zzz1110, zzz1111, zzz1112, zzz1113, zzz1114, zzz1115, ba)
new_mkVBalBranch3MkVBalBranch216(zzz1105, zzz1106, zzz1107, zzz1108, zzz1109, zzz1110, zzz1111, zzz1112, zzz1113, zzz1114, zzz1115, Zero, Zero, ba) → new_mkVBalBranch3MkVBalBranch222(zzz1105, zzz1106, zzz1107, zzz1108, zzz1109, zzz1110, zzz1111, zzz1112, zzz1113, zzz1114, zzz1115, ba)
new_mkVBalBranch3MkVBalBranch119(zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, zzz1125, zzz1126, zzz1127, zzz1128, zzz1129, Succ(zzz12130), bd) → new_mkVBalBranch3MkVBalBranch120(zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, zzz1125, Succ(zzz1126), zzz1127, zzz1128, zzz1129, Succ(Succ(zzz1126)), Succ(zzz12130), bd)
new_mkVBalBranch3MkVBalBranch18(zzz340, zzz341, zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, Zero, h) → new_mkVBalBranch3MkVBalBranch115(zzz340, zzz341, Zero, zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, Zero, Succ(zzz51200), h)

The TRS R consists of the following rules:

new_primPlusNat1(Zero) → Zero
new_primPlusNat1(Succ(zzz62000)) → Succ(Succ(new_primPlusNat1(zzz62000)))
new_primPlusNat3(zzz90, Succ(zzz910)) → Succ(Succ(new_primPlusNat2(zzz90, zzz910)))
new_primPlusNat3(zzz90, Zero) → Succ(zzz90)
new_primPlusNat2(Succ(zzz900), Succ(zzz9100)) → Succ(Succ(new_primPlusNat2(zzz900, zzz9100)))
new_primPlusNat2(Zero, Succ(zzz9100)) → Succ(zzz9100)
new_primPlusNat2(Zero, Zero) → Zero
new_primPlusNat2(Succ(zzz900), Zero) → Succ(zzz900)

The set Q consists of the following terms:

new_primPlusNat2(Zero, Succ(x0))
new_primPlusNat3(x0, Succ(x1))
new_primPlusNat2(Succ(x0), Succ(x1))
new_primPlusNat3(x0, Zero)
new_primPlusNat1(Zero)
new_primPlusNat2(Zero, Zero)
new_primPlusNat1(Succ(x0))
new_primPlusNat2(Succ(x0), Zero)

We have to consider all minimal (P,Q,R)-chains.
By rewriting [15] the rule new_mkVBalBranch3MkVBalBranch222(zzz461, zzz462, zzz463, zzz464, zzz465, zzz466, zzz467, zzz468, zzz469, zzz470, zzz471, bb) → new_mkVBalBranch3MkVBalBranch110(zzz461, zzz462, zzz463, zzz464, zzz465, zzz466, zzz467, zzz468, zzz469, zzz470, zzz471, new_primPlusNat2(Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat3(new_primPlusNat1(zzz463), zzz463)), zzz463))), Succ(zzz463)), bb) at position [11] we obtained the following new rules:

new_mkVBalBranch3MkVBalBranch222(zzz461, zzz462, zzz463, zzz464, zzz465, zzz466, zzz467, zzz468, zzz469, zzz470, zzz471, bb) → new_mkVBalBranch3MkVBalBranch110(zzz461, zzz462, zzz463, zzz464, zzz465, zzz466, zzz467, zzz468, zzz469, zzz470, zzz471, Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat2(Succ(new_primPlusNat3(new_primPlusNat1(zzz463), zzz463)), zzz463)), zzz463))), bb)



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

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

new_mkVBalBranch3MkVBalBranch225(zzz498, zzz499, zzz500, zzz501, zzz502, zzz503, zzz504, zzz505, zzz506, zzz507, Zero, Zero, bg) → new_mkVBalBranch3MkVBalBranch230(zzz498, zzz499, zzz500, zzz501, zzz502, zzz503, zzz504, zzz505, zzz506, zzz507, bg)
new_mkVBalBranch3MkVBalBranch18(zzz340, zzz341, zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, Succ(zzz1480), h) → new_mkVBalBranch3MkVBalBranch115(zzz340, zzz341, Zero, zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, Succ(zzz1480), Succ(zzz51200), h)
new_mkVBalBranch3MkVBalBranch215(zzz340, zzz341, Pos(Succ(Succ(zzz342000))), zzz343, zzz344, zzz510, zzz511, Succ(zzz512000), zzz513, zzz514, zzz31, Succ(Succ(zzz6600)), h) → new_mkVBalBranch3MkVBalBranch216(zzz340, zzz341, Succ(zzz342000), zzz343, zzz344, zzz510, zzz511, zzz512000, zzz513, zzz514, zzz31, Succ(Succ(new_primPlusNat2(zzz6600, zzz512000))), zzz342000, h)
new_mkVBalBranch0(zzz31, Branch(zzz510, zzz511, Neg(Zero), zzz513, zzz514), Branch(zzz340, zzz341, Pos(Succ(zzz34200)), zzz343, zzz344), h) → new_mkVBalBranch0(zzz31, Branch(zzz510, zzz511, Neg(Zero), zzz513, zzz514), zzz343, h)
new_mkVBalBranch3MkVBalBranch223(zzz340, zzz341, Neg(Succ(Succ(Succ(zzz3420000)))), zzz343, zzz344, zzz510, zzz511, Zero, zzz513, zzz514, zzz31, Succ(Succ(zzz6700)), h) → new_mkVBalBranch3MkVBalBranch225(zzz340, zzz341, Succ(Succ(zzz3420000)), zzz343, zzz344, zzz510, zzz511, zzz513, zzz514, zzz31, Succ(zzz3420000), Succ(zzz6700), h)
new_mkVBalBranch3MkVBalBranch120(zzz2050, zzz2051, zzz2052, zzz2053, zzz2054, zzz2055, zzz2056, zzz2057, zzz2058, zzz2059, zzz2060, Zero, Succ(zzz20620), be) → new_mkVBalBranch0(zzz2060, zzz2059, Branch(zzz2050, zzz2051, Neg(Succ(zzz2052)), zzz2053, zzz2054), be)
new_mkVBalBranch3MkVBalBranch215(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, Succ(zzz660), h) → new_mkVBalBranch3MkVBalBranch19(zzz340, zzz341, zzz34200, zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, new_primPlusNat2(Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat3(new_primPlusNat1(zzz34200), zzz34200)), zzz34200))), Succ(zzz34200)), h)
new_mkVBalBranch0(zzz31, Branch(zzz510, zzz511, Pos(Zero), zzz513, zzz514), Branch(zzz340, zzz341, Pos(Succ(zzz34200)), zzz343, zzz344), h) → new_mkVBalBranch0(zzz31, Branch(zzz510, zzz511, Pos(Zero), zzz513, zzz514), zzz343, h)
new_mkVBalBranch3MkVBalBranch121(zzz473, zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, zzz481, zzz482, Succ(zzz7390), bh) → new_mkVBalBranch3MkVBalBranch115(zzz473, zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, Zero, zzz480, zzz481, zzz482, Succ(zzz7390), Succ(Zero), bh)
new_mkVBalBranch0(zzz31, Branch(zzz510, zzz511, Pos(Succ(zzz51200)), zzz513, zzz514), Branch(zzz340, zzz341, zzz342, zzz343, zzz344), h) → new_mkVBalBranch3MkVBalBranch215(zzz340, zzz341, zzz342, zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat3(new_primPlusNat1(zzz51200), zzz51200)), zzz51200))), h)
new_mkVBalBranch3MkVBalBranch217(zzz473, zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, zzz481, zzz482, Succ(zzz4830), Zero, bh) → new_mkVBalBranch3MkVBalBranch121(zzz473, zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, zzz481, zzz482, new_primPlusNat2(Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat3(new_primPlusNat1(zzz475), zzz475)), zzz475))), Succ(zzz475)), bh)
new_mkVBalBranch3MkVBalBranch230(zzz498, zzz499, zzz500, zzz501, zzz502, zzz503, zzz504, zzz505, zzz506, zzz507, bg) → new_mkVBalBranch3MkVBalBranch118(zzz498, zzz499, zzz500, zzz501, zzz502, zzz503, zzz504, zzz505, zzz506, zzz507, Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat2(Succ(new_primPlusNat3(new_primPlusNat1(zzz500), zzz500)), zzz500)), zzz500))), bg)
new_mkVBalBranch3MkVBalBranch223(zzz340, zzz341, Neg(Succ(Succ(Zero))), zzz343, zzz344, zzz510, zzz511, Succ(zzz512000), zzz513, zzz514, zzz31, Succ(Succ(zzz6700)), h) → new_mkVBalBranch3MkVBalBranch224(zzz340, zzz341, Succ(Zero), zzz343, zzz344, zzz510, zzz511, zzz512000, zzz513, zzz514, zzz31, Zero, Succ(Succ(new_primPlusNat2(zzz6700, zzz512000))), h)
new_mkVBalBranch3MkVBalBranch224(zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, zzz1125, zzz1126, zzz1127, zzz1128, zzz1129, Succ(zzz11300), Succ(zzz11310), bd) → new_mkVBalBranch3MkVBalBranch224(zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, zzz1125, zzz1126, zzz1127, zzz1128, zzz1129, zzz11300, zzz11310, bd)
new_mkVBalBranch3MkVBalBranch217(zzz473, zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, zzz481, zzz482, Zero, Succ(zzz4840), bh) → new_mkVBalBranch0(zzz482, Branch(zzz478, zzz479, Pos(Succ(Zero)), zzz480, zzz481), zzz476, bh)
new_mkVBalBranch3MkVBalBranch224(zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, zzz1125, zzz1126, zzz1127, zzz1128, zzz1129, Succ(zzz11300), Zero, bd) → new_mkVBalBranch3MkVBalBranch119(zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, zzz1125, zzz1126, zzz1127, zzz1128, zzz1129, new_primPlusNat2(Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat3(new_primPlusNat1(zzz1121), zzz1121)), zzz1121))), Succ(zzz1121)), bd)
new_mkVBalBranch3MkVBalBranch110(zzz461, zzz462, zzz463, zzz464, zzz465, zzz466, zzz467, zzz468, zzz469, zzz470, zzz471, Succ(zzz5800), bb) → new_mkVBalBranch3MkVBalBranch115(zzz461, zzz462, zzz463, zzz464, zzz465, zzz466, zzz467, Succ(zzz468), zzz469, zzz470, zzz471, Succ(zzz5800), Succ(Succ(zzz468)), bb)
new_mkVBalBranch3MkVBalBranch227(zzz486, zzz487, zzz488, zzz489, zzz490, zzz491, zzz492, zzz493, zzz494, zzz495, zzz496, bf) → new_mkVBalBranch0(zzz496, Branch(zzz491, zzz492, Neg(Succ(Succ(zzz493))), zzz494, zzz495), zzz489, bf)
new_mkVBalBranch3MkVBalBranch215(zzz340, zzz341, Pos(Zero), zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, Succ(zzz660), h) → new_mkVBalBranch0(zzz31, zzz514, Branch(zzz340, zzz341, Pos(Zero), zzz343, zzz344), h)
new_mkVBalBranch3MkVBalBranch223(zzz340, zzz341, Neg(Zero), zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, Succ(zzz670), h) → new_mkVBalBranch0(zzz31, Branch(zzz510, zzz511, Neg(Succ(zzz51200)), zzz513, zzz514), zzz343, h)
new_mkVBalBranch3MkVBalBranch216(zzz1105, zzz1106, zzz1107, zzz1108, zzz1109, zzz1110, zzz1111, zzz1112, zzz1113, zzz1114, zzz1115, Zero, Succ(zzz11170), ba) → new_mkVBalBranch0(zzz1115, Branch(zzz1110, zzz1111, Pos(Succ(Succ(zzz1112))), zzz1113, zzz1114), zzz1108, ba)
new_mkVBalBranch3MkVBalBranch115(zzz1986, zzz1987, zzz1988, zzz1989, zzz1990, zzz1991, zzz1992, zzz1993, zzz1994, zzz1995, zzz1996, Zero, Succ(zzz19980), bc) → new_mkVBalBranch0(zzz1996, zzz1995, Branch(zzz1986, zzz1987, Pos(Succ(zzz1988)), zzz1989, zzz1990), bc)
new_mkVBalBranch3MkVBalBranch233(zzz473, zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, zzz481, zzz482, bh) → new_mkVBalBranch3MkVBalBranch121(zzz473, zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, zzz481, zzz482, new_primPlusNat2(Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat3(new_primPlusNat1(zzz475), zzz475)), zzz475))), Succ(zzz475)), bh)
new_mkVBalBranch3MkVBalBranch215(zzz340, zzz341, Pos(Succ(Zero)), zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, Succ(zzz660), h) → new_mkVBalBranch3MkVBalBranch18(zzz340, zzz341, zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, new_primPlusNat2(Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat3(new_primPlusNat1(Zero), Zero)), Zero))), Succ(Zero)), h)
new_mkVBalBranch3MkVBalBranch122(zzz340, zzz341, zzz34200, zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, h) → new_mkVBalBranch0(zzz31, zzz514, Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), h)
new_mkVBalBranch3MkVBalBranch217(zzz473, zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, zzz481, zzz482, Succ(zzz4830), Succ(zzz4840), bh) → new_mkVBalBranch3MkVBalBranch217(zzz473, zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, zzz481, zzz482, zzz4830, zzz4840, bh)
new_mkVBalBranch3MkVBalBranch116(zzz340, zzz341, zzz34200, zzz343, zzz344, zzz510, zzz511, zzz513, zzz514, zzz31, Succ(zzz1200), h) → new_mkVBalBranch0(zzz31, zzz514, Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), h)
new_mkVBalBranch3MkVBalBranch110(zzz461, zzz462, zzz463, zzz464, zzz465, zzz466, zzz467, zzz468, zzz469, zzz470, zzz471, Zero, bb) → new_mkVBalBranch3MkVBalBranch115(zzz461, zzz462, zzz463, zzz464, zzz465, zzz466, zzz467, Succ(zzz468), zzz469, zzz470, zzz471, Zero, Succ(Succ(zzz468)), bb)
new_mkVBalBranch3MkVBalBranch225(zzz498, zzz499, zzz500, zzz501, zzz502, zzz503, zzz504, zzz505, zzz506, zzz507, Zero, Succ(zzz5090), bg) → new_mkVBalBranch0(zzz507, Branch(zzz503, zzz504, Neg(Succ(Zero)), zzz505, zzz506), zzz501, bg)
new_mkVBalBranch0(zzz31, Branch(zzz510, zzz511, Neg(Succ(zzz51200)), zzz513, zzz514), Branch(zzz340, zzz341, zzz342, zzz343, zzz344), h) → new_mkVBalBranch3MkVBalBranch223(zzz340, zzz341, zzz342, zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat3(new_primPlusNat1(zzz51200), zzz51200)), zzz51200))), h)
new_mkVBalBranch3MkVBalBranch121(zzz473, zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, zzz481, zzz482, Zero, bh) → new_mkVBalBranch3MkVBalBranch115(zzz473, zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, Zero, zzz480, zzz481, zzz482, Zero, Succ(Zero), bh)
new_mkVBalBranch3MkVBalBranch223(zzz340, zzz341, Neg(Succ(Zero)), zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, Succ(zzz670), h) → new_mkVBalBranch0(zzz31, Branch(zzz510, zzz511, Neg(Succ(zzz51200)), zzz513, zzz514), zzz343, h)
new_mkVBalBranch3MkVBalBranch225(zzz498, zzz499, zzz500, zzz501, zzz502, zzz503, zzz504, zzz505, zzz506, zzz507, Succ(zzz5080), Zero, bg) → new_mkVBalBranch3MkVBalBranch118(zzz498, zzz499, zzz500, zzz501, zzz502, zzz503, zzz504, zzz505, zzz506, zzz507, new_primPlusNat2(Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat3(new_primPlusNat1(zzz500), zzz500)), zzz500))), Succ(zzz500)), bg)
new_mkVBalBranch3MkVBalBranch218(zzz461, zzz462, zzz463, zzz464, zzz465, zzz466, zzz467, zzz468, zzz469, zzz470, zzz471, bb) → new_mkVBalBranch3MkVBalBranch110(zzz461, zzz462, zzz463, zzz464, zzz465, zzz466, zzz467, zzz468, zzz469, zzz470, zzz471, new_primPlusNat2(Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat3(new_primPlusNat1(zzz463), zzz463)), zzz463))), Succ(zzz463)), bb)
new_mkVBalBranch0(zzz31, Branch(zzz510, zzz511, Pos(Zero), zzz513, zzz514), Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), h) → new_mkVBalBranch3MkVBalBranch116(zzz340, zzz341, zzz34200, zzz343, zzz344, zzz510, zzz511, zzz513, zzz514, zzz31, new_primPlusNat2(Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat3(new_primPlusNat1(zzz34200), zzz34200)), zzz34200))), Succ(zzz34200)), h)
new_mkVBalBranch3MkVBalBranch215(zzz340, zzz341, Pos(Succ(Succ(zzz342000))), zzz343, zzz344, zzz510, zzz511, Zero, zzz513, zzz514, zzz31, Succ(Succ(zzz6600)), h) → new_mkVBalBranch3MkVBalBranch217(zzz340, zzz341, Succ(zzz342000), zzz343, zzz344, zzz510, zzz511, zzz513, zzz514, zzz31, Succ(zzz6600), zzz342000, h)
new_mkVBalBranch3MkVBalBranch117(zzz340, zzz341, zzz34200, zzz343, zzz344, zzz510, zzz511, zzz513, zzz514, zzz31, Succ(zzz1240), h) → new_mkVBalBranch0(zzz31, zzz514, Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), h)
new_mkVBalBranch3MkVBalBranch120(zzz2050, zzz2051, zzz2052, zzz2053, zzz2054, zzz2055, zzz2056, zzz2057, zzz2058, zzz2059, zzz2060, Succ(zzz20610), Succ(zzz20620), be) → new_mkVBalBranch3MkVBalBranch120(zzz2050, zzz2051, zzz2052, zzz2053, zzz2054, zzz2055, zzz2056, zzz2057, zzz2058, zzz2059, zzz2060, zzz20610, zzz20620, be)
new_mkVBalBranch3MkVBalBranch217(zzz473, zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, zzz481, zzz482, Zero, Zero, bh) → new_mkVBalBranch3MkVBalBranch233(zzz473, zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, zzz481, zzz482, bh)
new_mkVBalBranch3MkVBalBranch216(zzz1105, zzz1106, zzz1107, zzz1108, zzz1109, zzz1110, zzz1111, zzz1112, zzz1113, zzz1114, zzz1115, Succ(zzz11160), Succ(zzz11170), ba) → new_mkVBalBranch3MkVBalBranch216(zzz1105, zzz1106, zzz1107, zzz1108, zzz1109, zzz1110, zzz1111, zzz1112, zzz1113, zzz1114, zzz1115, zzz11160, zzz11170, ba)
new_mkVBalBranch3MkVBalBranch223(zzz340, zzz341, Pos(zzz3420), zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, Succ(zzz670), h) → new_mkVBalBranch0(zzz31, Branch(zzz510, zzz511, Neg(Succ(zzz51200)), zzz513, zzz514), zzz343, h)
new_mkVBalBranch0(zzz31, Branch(zzz510, zzz511, Neg(Zero), zzz513, zzz514), Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), h) → new_mkVBalBranch3MkVBalBranch117(zzz340, zzz341, zzz34200, zzz343, zzz344, zzz510, zzz511, zzz513, zzz514, zzz31, new_primPlusNat2(Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat3(new_primPlusNat1(zzz34200), zzz34200)), zzz34200))), Succ(zzz34200)), h)
new_mkVBalBranch3MkVBalBranch19(zzz340, zzz341, zzz34200, zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, Zero, h) → new_mkVBalBranch3MkVBalBranch122(zzz340, zzz341, zzz34200, zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, h)
new_mkVBalBranch3MkVBalBranch225(zzz498, zzz499, zzz500, zzz501, zzz502, zzz503, zzz504, zzz505, zzz506, zzz507, Succ(zzz5080), Succ(zzz5090), bg) → new_mkVBalBranch3MkVBalBranch225(zzz498, zzz499, zzz500, zzz501, zzz502, zzz503, zzz504, zzz505, zzz506, zzz507, zzz5080, zzz5090, bg)
new_mkVBalBranch3MkVBalBranch19(zzz340, zzz341, zzz34200, zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, Succ(zzz1410), h) → new_mkVBalBranch0(zzz31, zzz514, Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), h)
new_mkVBalBranch3MkVBalBranch224(zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, zzz1125, zzz1126, zzz1127, zzz1128, zzz1129, Zero, Succ(zzz11310), bd) → new_mkVBalBranch3MkVBalBranch227(zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, zzz1125, zzz1126, zzz1127, zzz1128, zzz1129, bd)
new_mkVBalBranch3MkVBalBranch224(zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, zzz1125, zzz1126, zzz1127, zzz1128, zzz1129, Zero, Zero, bd) → new_mkVBalBranch3MkVBalBranch229(zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, zzz1125, zzz1126, zzz1127, zzz1128, zzz1129, bd)
new_mkVBalBranch3MkVBalBranch223(zzz340, zzz341, Neg(Succ(Succ(Zero))), zzz343, zzz344, zzz510, zzz511, Zero, zzz513, zzz514, zzz31, Succ(Succ(zzz6700)), h) → new_mkVBalBranch3MkVBalBranch225(zzz340, zzz341, Succ(Zero), zzz343, zzz344, zzz510, zzz511, zzz513, zzz514, zzz31, Zero, Succ(zzz6700), h)
new_mkVBalBranch3MkVBalBranch223(zzz340, zzz341, Neg(Succ(Succ(Succ(zzz3420000)))), zzz343, zzz344, zzz510, zzz511, Succ(zzz512000), zzz513, zzz514, zzz31, Succ(Succ(zzz6700)), h) → new_mkVBalBranch3MkVBalBranch224(zzz340, zzz341, Succ(Succ(zzz3420000)), zzz343, zzz344, zzz510, zzz511, zzz512000, zzz513, zzz514, zzz31, Succ(zzz3420000), Succ(Succ(new_primPlusNat2(zzz6700, zzz512000))), h)
new_mkVBalBranch3MkVBalBranch115(zzz1986, zzz1987, zzz1988, zzz1989, zzz1990, zzz1991, zzz1992, zzz1993, zzz1994, zzz1995, zzz1996, Succ(zzz19970), Succ(zzz19980), bc) → new_mkVBalBranch3MkVBalBranch115(zzz1986, zzz1987, zzz1988, zzz1989, zzz1990, zzz1991, zzz1992, zzz1993, zzz1994, zzz1995, zzz1996, zzz19970, zzz19980, bc)
new_mkVBalBranch3MkVBalBranch215(zzz340, zzz341, Neg(Zero), zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, Succ(zzz660), h) → new_mkVBalBranch0(zzz31, zzz514, Branch(zzz340, zzz341, Neg(Zero), zzz343, zzz344), h)
new_mkVBalBranch3MkVBalBranch229(zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, zzz1125, zzz1126, zzz1127, zzz1128, zzz1129, bd) → new_mkVBalBranch3MkVBalBranch119(zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, zzz1125, zzz1126, zzz1127, zzz1128, zzz1129, new_primPlusNat2(Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat3(new_primPlusNat1(zzz1121), zzz1121)), zzz1121))), Succ(zzz1121)), bd)
new_mkVBalBranch3MkVBalBranch222(zzz461, zzz462, zzz463, zzz464, zzz465, zzz466, zzz467, zzz468, zzz469, zzz470, zzz471, bb) → new_mkVBalBranch3MkVBalBranch110(zzz461, zzz462, zzz463, zzz464, zzz465, zzz466, zzz467, zzz468, zzz469, zzz470, zzz471, Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat2(Succ(new_primPlusNat3(new_primPlusNat1(zzz463), zzz463)), zzz463)), zzz463))), bb)
new_mkVBalBranch3MkVBalBranch118(zzz498, zzz499, zzz500, zzz501, zzz502, zzz503, zzz504, zzz505, zzz506, zzz507, Succ(zzz8040), bg) → new_mkVBalBranch3MkVBalBranch120(zzz498, zzz499, zzz500, zzz501, zzz502, zzz503, zzz504, Zero, zzz505, zzz506, zzz507, Succ(Zero), Succ(zzz8040), bg)
new_mkVBalBranch3MkVBalBranch216(zzz1105, zzz1106, zzz1107, zzz1108, zzz1109, zzz1110, zzz1111, zzz1112, zzz1113, zzz1114, zzz1115, Succ(zzz11160), Zero, ba) → new_mkVBalBranch3MkVBalBranch218(zzz1105, zzz1106, zzz1107, zzz1108, zzz1109, zzz1110, zzz1111, zzz1112, zzz1113, zzz1114, zzz1115, ba)
new_mkVBalBranch3MkVBalBranch216(zzz1105, zzz1106, zzz1107, zzz1108, zzz1109, zzz1110, zzz1111, zzz1112, zzz1113, zzz1114, zzz1115, Zero, Zero, ba) → new_mkVBalBranch3MkVBalBranch222(zzz1105, zzz1106, zzz1107, zzz1108, zzz1109, zzz1110, zzz1111, zzz1112, zzz1113, zzz1114, zzz1115, ba)
new_mkVBalBranch3MkVBalBranch18(zzz340, zzz341, zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, Zero, h) → new_mkVBalBranch3MkVBalBranch115(zzz340, zzz341, Zero, zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, Zero, Succ(zzz51200), h)
new_mkVBalBranch3MkVBalBranch119(zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, zzz1125, zzz1126, zzz1127, zzz1128, zzz1129, Succ(zzz12130), bd) → new_mkVBalBranch3MkVBalBranch120(zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, zzz1125, Succ(zzz1126), zzz1127, zzz1128, zzz1129, Succ(Succ(zzz1126)), Succ(zzz12130), bd)

The TRS R consists of the following rules:

new_primPlusNat1(Zero) → Zero
new_primPlusNat1(Succ(zzz62000)) → Succ(Succ(new_primPlusNat1(zzz62000)))
new_primPlusNat3(zzz90, Succ(zzz910)) → Succ(Succ(new_primPlusNat2(zzz90, zzz910)))
new_primPlusNat3(zzz90, Zero) → Succ(zzz90)
new_primPlusNat2(Succ(zzz900), Succ(zzz9100)) → Succ(Succ(new_primPlusNat2(zzz900, zzz9100)))
new_primPlusNat2(Zero, Succ(zzz9100)) → Succ(zzz9100)
new_primPlusNat2(Zero, Zero) → Zero
new_primPlusNat2(Succ(zzz900), Zero) → Succ(zzz900)

The set Q consists of the following terms:

new_primPlusNat2(Zero, Succ(x0))
new_primPlusNat3(x0, Succ(x1))
new_primPlusNat2(Succ(x0), Succ(x1))
new_primPlusNat3(x0, Zero)
new_primPlusNat1(Zero)
new_primPlusNat2(Zero, Zero)
new_primPlusNat1(Succ(x0))
new_primPlusNat2(Succ(x0), Zero)

We have to consider all minimal (P,Q,R)-chains.
By rewriting [15] the rule new_mkVBalBranch3MkVBalBranch224(zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, zzz1125, zzz1126, zzz1127, zzz1128, zzz1129, Succ(zzz11300), Zero, bd) → new_mkVBalBranch3MkVBalBranch119(zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, zzz1125, zzz1126, zzz1127, zzz1128, zzz1129, new_primPlusNat2(Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat3(new_primPlusNat1(zzz1121), zzz1121)), zzz1121))), Succ(zzz1121)), bd) at position [11] we obtained the following new rules:

new_mkVBalBranch3MkVBalBranch224(zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, zzz1125, zzz1126, zzz1127, zzz1128, zzz1129, Succ(zzz11300), Zero, bd) → new_mkVBalBranch3MkVBalBranch119(zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, zzz1125, zzz1126, zzz1127, zzz1128, zzz1129, Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat2(Succ(new_primPlusNat3(new_primPlusNat1(zzz1121), zzz1121)), zzz1121)), zzz1121))), bd)



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

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

new_mkVBalBranch3MkVBalBranch225(zzz498, zzz499, zzz500, zzz501, zzz502, zzz503, zzz504, zzz505, zzz506, zzz507, Zero, Zero, bg) → new_mkVBalBranch3MkVBalBranch230(zzz498, zzz499, zzz500, zzz501, zzz502, zzz503, zzz504, zzz505, zzz506, zzz507, bg)
new_mkVBalBranch3MkVBalBranch18(zzz340, zzz341, zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, Succ(zzz1480), h) → new_mkVBalBranch3MkVBalBranch115(zzz340, zzz341, Zero, zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, Succ(zzz1480), Succ(zzz51200), h)
new_mkVBalBranch0(zzz31, Branch(zzz510, zzz511, Neg(Zero), zzz513, zzz514), Branch(zzz340, zzz341, Pos(Succ(zzz34200)), zzz343, zzz344), h) → new_mkVBalBranch0(zzz31, Branch(zzz510, zzz511, Neg(Zero), zzz513, zzz514), zzz343, h)
new_mkVBalBranch3MkVBalBranch215(zzz340, zzz341, Pos(Succ(Succ(zzz342000))), zzz343, zzz344, zzz510, zzz511, Succ(zzz512000), zzz513, zzz514, zzz31, Succ(Succ(zzz6600)), h) → new_mkVBalBranch3MkVBalBranch216(zzz340, zzz341, Succ(zzz342000), zzz343, zzz344, zzz510, zzz511, zzz512000, zzz513, zzz514, zzz31, Succ(Succ(new_primPlusNat2(zzz6600, zzz512000))), zzz342000, h)
new_mkVBalBranch3MkVBalBranch223(zzz340, zzz341, Neg(Succ(Succ(Succ(zzz3420000)))), zzz343, zzz344, zzz510, zzz511, Zero, zzz513, zzz514, zzz31, Succ(Succ(zzz6700)), h) → new_mkVBalBranch3MkVBalBranch225(zzz340, zzz341, Succ(Succ(zzz3420000)), zzz343, zzz344, zzz510, zzz511, zzz513, zzz514, zzz31, Succ(zzz3420000), Succ(zzz6700), h)
new_mkVBalBranch3MkVBalBranch120(zzz2050, zzz2051, zzz2052, zzz2053, zzz2054, zzz2055, zzz2056, zzz2057, zzz2058, zzz2059, zzz2060, Zero, Succ(zzz20620), be) → new_mkVBalBranch0(zzz2060, zzz2059, Branch(zzz2050, zzz2051, Neg(Succ(zzz2052)), zzz2053, zzz2054), be)
new_mkVBalBranch3MkVBalBranch121(zzz473, zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, zzz481, zzz482, Succ(zzz7390), bh) → new_mkVBalBranch3MkVBalBranch115(zzz473, zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, Zero, zzz480, zzz481, zzz482, Succ(zzz7390), Succ(Zero), bh)
new_mkVBalBranch0(zzz31, Branch(zzz510, zzz511, Pos(Zero), zzz513, zzz514), Branch(zzz340, zzz341, Pos(Succ(zzz34200)), zzz343, zzz344), h) → new_mkVBalBranch0(zzz31, Branch(zzz510, zzz511, Pos(Zero), zzz513, zzz514), zzz343, h)
new_mkVBalBranch3MkVBalBranch215(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, Succ(zzz660), h) → new_mkVBalBranch3MkVBalBranch19(zzz340, zzz341, zzz34200, zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, new_primPlusNat2(Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat3(new_primPlusNat1(zzz34200), zzz34200)), zzz34200))), Succ(zzz34200)), h)
new_mkVBalBranch0(zzz31, Branch(zzz510, zzz511, Pos(Succ(zzz51200)), zzz513, zzz514), Branch(zzz340, zzz341, zzz342, zzz343, zzz344), h) → new_mkVBalBranch3MkVBalBranch215(zzz340, zzz341, zzz342, zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat3(new_primPlusNat1(zzz51200), zzz51200)), zzz51200))), h)
new_mkVBalBranch3MkVBalBranch223(zzz340, zzz341, Neg(Succ(Succ(Zero))), zzz343, zzz344, zzz510, zzz511, Succ(zzz512000), zzz513, zzz514, zzz31, Succ(Succ(zzz6700)), h) → new_mkVBalBranch3MkVBalBranch224(zzz340, zzz341, Succ(Zero), zzz343, zzz344, zzz510, zzz511, zzz512000, zzz513, zzz514, zzz31, Zero, Succ(Succ(new_primPlusNat2(zzz6700, zzz512000))), h)
new_mkVBalBranch3MkVBalBranch230(zzz498, zzz499, zzz500, zzz501, zzz502, zzz503, zzz504, zzz505, zzz506, zzz507, bg) → new_mkVBalBranch3MkVBalBranch118(zzz498, zzz499, zzz500, zzz501, zzz502, zzz503, zzz504, zzz505, zzz506, zzz507, Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat2(Succ(new_primPlusNat3(new_primPlusNat1(zzz500), zzz500)), zzz500)), zzz500))), bg)
new_mkVBalBranch3MkVBalBranch217(zzz473, zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, zzz481, zzz482, Succ(zzz4830), Zero, bh) → new_mkVBalBranch3MkVBalBranch121(zzz473, zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, zzz481, zzz482, new_primPlusNat2(Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat3(new_primPlusNat1(zzz475), zzz475)), zzz475))), Succ(zzz475)), bh)
new_mkVBalBranch3MkVBalBranch224(zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, zzz1125, zzz1126, zzz1127, zzz1128, zzz1129, Succ(zzz11300), Succ(zzz11310), bd) → new_mkVBalBranch3MkVBalBranch224(zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, zzz1125, zzz1126, zzz1127, zzz1128, zzz1129, zzz11300, zzz11310, bd)
new_mkVBalBranch3MkVBalBranch217(zzz473, zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, zzz481, zzz482, Zero, Succ(zzz4840), bh) → new_mkVBalBranch0(zzz482, Branch(zzz478, zzz479, Pos(Succ(Zero)), zzz480, zzz481), zzz476, bh)
new_mkVBalBranch3MkVBalBranch110(zzz461, zzz462, zzz463, zzz464, zzz465, zzz466, zzz467, zzz468, zzz469, zzz470, zzz471, Succ(zzz5800), bb) → new_mkVBalBranch3MkVBalBranch115(zzz461, zzz462, zzz463, zzz464, zzz465, zzz466, zzz467, Succ(zzz468), zzz469, zzz470, zzz471, Succ(zzz5800), Succ(Succ(zzz468)), bb)
new_mkVBalBranch3MkVBalBranch227(zzz486, zzz487, zzz488, zzz489, zzz490, zzz491, zzz492, zzz493, zzz494, zzz495, zzz496, bf) → new_mkVBalBranch0(zzz496, Branch(zzz491, zzz492, Neg(Succ(Succ(zzz493))), zzz494, zzz495), zzz489, bf)
new_mkVBalBranch3MkVBalBranch215(zzz340, zzz341, Pos(Zero), zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, Succ(zzz660), h) → new_mkVBalBranch0(zzz31, zzz514, Branch(zzz340, zzz341, Pos(Zero), zzz343, zzz344), h)
new_mkVBalBranch3MkVBalBranch223(zzz340, zzz341, Neg(Zero), zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, Succ(zzz670), h) → new_mkVBalBranch0(zzz31, Branch(zzz510, zzz511, Neg(Succ(zzz51200)), zzz513, zzz514), zzz343, h)
new_mkVBalBranch3MkVBalBranch216(zzz1105, zzz1106, zzz1107, zzz1108, zzz1109, zzz1110, zzz1111, zzz1112, zzz1113, zzz1114, zzz1115, Zero, Succ(zzz11170), ba) → new_mkVBalBranch0(zzz1115, Branch(zzz1110, zzz1111, Pos(Succ(Succ(zzz1112))), zzz1113, zzz1114), zzz1108, ba)
new_mkVBalBranch3MkVBalBranch115(zzz1986, zzz1987, zzz1988, zzz1989, zzz1990, zzz1991, zzz1992, zzz1993, zzz1994, zzz1995, zzz1996, Zero, Succ(zzz19980), bc) → new_mkVBalBranch0(zzz1996, zzz1995, Branch(zzz1986, zzz1987, Pos(Succ(zzz1988)), zzz1989, zzz1990), bc)
new_mkVBalBranch3MkVBalBranch233(zzz473, zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, zzz481, zzz482, bh) → new_mkVBalBranch3MkVBalBranch121(zzz473, zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, zzz481, zzz482, new_primPlusNat2(Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat3(new_primPlusNat1(zzz475), zzz475)), zzz475))), Succ(zzz475)), bh)
new_mkVBalBranch3MkVBalBranch215(zzz340, zzz341, Pos(Succ(Zero)), zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, Succ(zzz660), h) → new_mkVBalBranch3MkVBalBranch18(zzz340, zzz341, zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, new_primPlusNat2(Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat3(new_primPlusNat1(Zero), Zero)), Zero))), Succ(Zero)), h)
new_mkVBalBranch3MkVBalBranch122(zzz340, zzz341, zzz34200, zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, h) → new_mkVBalBranch0(zzz31, zzz514, Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), h)
new_mkVBalBranch3MkVBalBranch217(zzz473, zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, zzz481, zzz482, Succ(zzz4830), Succ(zzz4840), bh) → new_mkVBalBranch3MkVBalBranch217(zzz473, zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, zzz481, zzz482, zzz4830, zzz4840, bh)
new_mkVBalBranch3MkVBalBranch116(zzz340, zzz341, zzz34200, zzz343, zzz344, zzz510, zzz511, zzz513, zzz514, zzz31, Succ(zzz1200), h) → new_mkVBalBranch0(zzz31, zzz514, Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), h)
new_mkVBalBranch3MkVBalBranch110(zzz461, zzz462, zzz463, zzz464, zzz465, zzz466, zzz467, zzz468, zzz469, zzz470, zzz471, Zero, bb) → new_mkVBalBranch3MkVBalBranch115(zzz461, zzz462, zzz463, zzz464, zzz465, zzz466, zzz467, Succ(zzz468), zzz469, zzz470, zzz471, Zero, Succ(Succ(zzz468)), bb)
new_mkVBalBranch3MkVBalBranch225(zzz498, zzz499, zzz500, zzz501, zzz502, zzz503, zzz504, zzz505, zzz506, zzz507, Zero, Succ(zzz5090), bg) → new_mkVBalBranch0(zzz507, Branch(zzz503, zzz504, Neg(Succ(Zero)), zzz505, zzz506), zzz501, bg)
new_mkVBalBranch0(zzz31, Branch(zzz510, zzz511, Neg(Succ(zzz51200)), zzz513, zzz514), Branch(zzz340, zzz341, zzz342, zzz343, zzz344), h) → new_mkVBalBranch3MkVBalBranch223(zzz340, zzz341, zzz342, zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat3(new_primPlusNat1(zzz51200), zzz51200)), zzz51200))), h)
new_mkVBalBranch3MkVBalBranch121(zzz473, zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, zzz481, zzz482, Zero, bh) → new_mkVBalBranch3MkVBalBranch115(zzz473, zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, Zero, zzz480, zzz481, zzz482, Zero, Succ(Zero), bh)
new_mkVBalBranch3MkVBalBranch223(zzz340, zzz341, Neg(Succ(Zero)), zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, Succ(zzz670), h) → new_mkVBalBranch0(zzz31, Branch(zzz510, zzz511, Neg(Succ(zzz51200)), zzz513, zzz514), zzz343, h)
new_mkVBalBranch3MkVBalBranch225(zzz498, zzz499, zzz500, zzz501, zzz502, zzz503, zzz504, zzz505, zzz506, zzz507, Succ(zzz5080), Zero, bg) → new_mkVBalBranch3MkVBalBranch118(zzz498, zzz499, zzz500, zzz501, zzz502, zzz503, zzz504, zzz505, zzz506, zzz507, new_primPlusNat2(Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat3(new_primPlusNat1(zzz500), zzz500)), zzz500))), Succ(zzz500)), bg)
new_mkVBalBranch3MkVBalBranch218(zzz461, zzz462, zzz463, zzz464, zzz465, zzz466, zzz467, zzz468, zzz469, zzz470, zzz471, bb) → new_mkVBalBranch3MkVBalBranch110(zzz461, zzz462, zzz463, zzz464, zzz465, zzz466, zzz467, zzz468, zzz469, zzz470, zzz471, new_primPlusNat2(Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat3(new_primPlusNat1(zzz463), zzz463)), zzz463))), Succ(zzz463)), bb)
new_mkVBalBranch0(zzz31, Branch(zzz510, zzz511, Pos(Zero), zzz513, zzz514), Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), h) → new_mkVBalBranch3MkVBalBranch116(zzz340, zzz341, zzz34200, zzz343, zzz344, zzz510, zzz511, zzz513, zzz514, zzz31, new_primPlusNat2(Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat3(new_primPlusNat1(zzz34200), zzz34200)), zzz34200))), Succ(zzz34200)), h)
new_mkVBalBranch3MkVBalBranch215(zzz340, zzz341, Pos(Succ(Succ(zzz342000))), zzz343, zzz344, zzz510, zzz511, Zero, zzz513, zzz514, zzz31, Succ(Succ(zzz6600)), h) → new_mkVBalBranch3MkVBalBranch217(zzz340, zzz341, Succ(zzz342000), zzz343, zzz344, zzz510, zzz511, zzz513, zzz514, zzz31, Succ(zzz6600), zzz342000, h)
new_mkVBalBranch3MkVBalBranch117(zzz340, zzz341, zzz34200, zzz343, zzz344, zzz510, zzz511, zzz513, zzz514, zzz31, Succ(zzz1240), h) → new_mkVBalBranch0(zzz31, zzz514, Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), h)
new_mkVBalBranch3MkVBalBranch217(zzz473, zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, zzz481, zzz482, Zero, Zero, bh) → new_mkVBalBranch3MkVBalBranch233(zzz473, zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, zzz481, zzz482, bh)
new_mkVBalBranch3MkVBalBranch120(zzz2050, zzz2051, zzz2052, zzz2053, zzz2054, zzz2055, zzz2056, zzz2057, zzz2058, zzz2059, zzz2060, Succ(zzz20610), Succ(zzz20620), be) → new_mkVBalBranch3MkVBalBranch120(zzz2050, zzz2051, zzz2052, zzz2053, zzz2054, zzz2055, zzz2056, zzz2057, zzz2058, zzz2059, zzz2060, zzz20610, zzz20620, be)
new_mkVBalBranch3MkVBalBranch223(zzz340, zzz341, Pos(zzz3420), zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, Succ(zzz670), h) → new_mkVBalBranch0(zzz31, Branch(zzz510, zzz511, Neg(Succ(zzz51200)), zzz513, zzz514), zzz343, h)
new_mkVBalBranch3MkVBalBranch216(zzz1105, zzz1106, zzz1107, zzz1108, zzz1109, zzz1110, zzz1111, zzz1112, zzz1113, zzz1114, zzz1115, Succ(zzz11160), Succ(zzz11170), ba) → new_mkVBalBranch3MkVBalBranch216(zzz1105, zzz1106, zzz1107, zzz1108, zzz1109, zzz1110, zzz1111, zzz1112, zzz1113, zzz1114, zzz1115, zzz11160, zzz11170, ba)
new_mkVBalBranch0(zzz31, Branch(zzz510, zzz511, Neg(Zero), zzz513, zzz514), Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), h) → new_mkVBalBranch3MkVBalBranch117(zzz340, zzz341, zzz34200, zzz343, zzz344, zzz510, zzz511, zzz513, zzz514, zzz31, new_primPlusNat2(Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat3(new_primPlusNat1(zzz34200), zzz34200)), zzz34200))), Succ(zzz34200)), h)
new_mkVBalBranch3MkVBalBranch19(zzz340, zzz341, zzz34200, zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, Zero, h) → new_mkVBalBranch3MkVBalBranch122(zzz340, zzz341, zzz34200, zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, h)
new_mkVBalBranch3MkVBalBranch225(zzz498, zzz499, zzz500, zzz501, zzz502, zzz503, zzz504, zzz505, zzz506, zzz507, Succ(zzz5080), Succ(zzz5090), bg) → new_mkVBalBranch3MkVBalBranch225(zzz498, zzz499, zzz500, zzz501, zzz502, zzz503, zzz504, zzz505, zzz506, zzz507, zzz5080, zzz5090, bg)
new_mkVBalBranch3MkVBalBranch19(zzz340, zzz341, zzz34200, zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, Succ(zzz1410), h) → new_mkVBalBranch0(zzz31, zzz514, Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), h)
new_mkVBalBranch3MkVBalBranch224(zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, zzz1125, zzz1126, zzz1127, zzz1128, zzz1129, Zero, Zero, bd) → new_mkVBalBranch3MkVBalBranch229(zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, zzz1125, zzz1126, zzz1127, zzz1128, zzz1129, bd)
new_mkVBalBranch3MkVBalBranch224(zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, zzz1125, zzz1126, zzz1127, zzz1128, zzz1129, Zero, Succ(zzz11310), bd) → new_mkVBalBranch3MkVBalBranch227(zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, zzz1125, zzz1126, zzz1127, zzz1128, zzz1129, bd)
new_mkVBalBranch3MkVBalBranch223(zzz340, zzz341, Neg(Succ(Succ(Succ(zzz3420000)))), zzz343, zzz344, zzz510, zzz511, Succ(zzz512000), zzz513, zzz514, zzz31, Succ(Succ(zzz6700)), h) → new_mkVBalBranch3MkVBalBranch224(zzz340, zzz341, Succ(Succ(zzz3420000)), zzz343, zzz344, zzz510, zzz511, zzz512000, zzz513, zzz514, zzz31, Succ(zzz3420000), Succ(Succ(new_primPlusNat2(zzz6700, zzz512000))), h)
new_mkVBalBranch3MkVBalBranch223(zzz340, zzz341, Neg(Succ(Succ(Zero))), zzz343, zzz344, zzz510, zzz511, Zero, zzz513, zzz514, zzz31, Succ(Succ(zzz6700)), h) → new_mkVBalBranch3MkVBalBranch225(zzz340, zzz341, Succ(Zero), zzz343, zzz344, zzz510, zzz511, zzz513, zzz514, zzz31, Zero, Succ(zzz6700), h)
new_mkVBalBranch3MkVBalBranch115(zzz1986, zzz1987, zzz1988, zzz1989, zzz1990, zzz1991, zzz1992, zzz1993, zzz1994, zzz1995, zzz1996, Succ(zzz19970), Succ(zzz19980), bc) → new_mkVBalBranch3MkVBalBranch115(zzz1986, zzz1987, zzz1988, zzz1989, zzz1990, zzz1991, zzz1992, zzz1993, zzz1994, zzz1995, zzz1996, zzz19970, zzz19980, bc)
new_mkVBalBranch3MkVBalBranch229(zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, zzz1125, zzz1126, zzz1127, zzz1128, zzz1129, bd) → new_mkVBalBranch3MkVBalBranch119(zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, zzz1125, zzz1126, zzz1127, zzz1128, zzz1129, new_primPlusNat2(Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat3(new_primPlusNat1(zzz1121), zzz1121)), zzz1121))), Succ(zzz1121)), bd)
new_mkVBalBranch3MkVBalBranch215(zzz340, zzz341, Neg(Zero), zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, Succ(zzz660), h) → new_mkVBalBranch0(zzz31, zzz514, Branch(zzz340, zzz341, Neg(Zero), zzz343, zzz344), h)
new_mkVBalBranch3MkVBalBranch224(zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, zzz1125, zzz1126, zzz1127, zzz1128, zzz1129, Succ(zzz11300), Zero, bd) → new_mkVBalBranch3MkVBalBranch119(zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, zzz1125, zzz1126, zzz1127, zzz1128, zzz1129, Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat2(Succ(new_primPlusNat3(new_primPlusNat1(zzz1121), zzz1121)), zzz1121)), zzz1121))), bd)
new_mkVBalBranch3MkVBalBranch118(zzz498, zzz499, zzz500, zzz501, zzz502, zzz503, zzz504, zzz505, zzz506, zzz507, Succ(zzz8040), bg) → new_mkVBalBranch3MkVBalBranch120(zzz498, zzz499, zzz500, zzz501, zzz502, zzz503, zzz504, Zero, zzz505, zzz506, zzz507, Succ(Zero), Succ(zzz8040), bg)
new_mkVBalBranch3MkVBalBranch222(zzz461, zzz462, zzz463, zzz464, zzz465, zzz466, zzz467, zzz468, zzz469, zzz470, zzz471, bb) → new_mkVBalBranch3MkVBalBranch110(zzz461, zzz462, zzz463, zzz464, zzz465, zzz466, zzz467, zzz468, zzz469, zzz470, zzz471, Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat2(Succ(new_primPlusNat3(new_primPlusNat1(zzz463), zzz463)), zzz463)), zzz463))), bb)
new_mkVBalBranch3MkVBalBranch216(zzz1105, zzz1106, zzz1107, zzz1108, zzz1109, zzz1110, zzz1111, zzz1112, zzz1113, zzz1114, zzz1115, Succ(zzz11160), Zero, ba) → new_mkVBalBranch3MkVBalBranch218(zzz1105, zzz1106, zzz1107, zzz1108, zzz1109, zzz1110, zzz1111, zzz1112, zzz1113, zzz1114, zzz1115, ba)
new_mkVBalBranch3MkVBalBranch216(zzz1105, zzz1106, zzz1107, zzz1108, zzz1109, zzz1110, zzz1111, zzz1112, zzz1113, zzz1114, zzz1115, Zero, Zero, ba) → new_mkVBalBranch3MkVBalBranch222(zzz1105, zzz1106, zzz1107, zzz1108, zzz1109, zzz1110, zzz1111, zzz1112, zzz1113, zzz1114, zzz1115, ba)
new_mkVBalBranch3MkVBalBranch119(zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, zzz1125, zzz1126, zzz1127, zzz1128, zzz1129, Succ(zzz12130), bd) → new_mkVBalBranch3MkVBalBranch120(zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, zzz1125, Succ(zzz1126), zzz1127, zzz1128, zzz1129, Succ(Succ(zzz1126)), Succ(zzz12130), bd)
new_mkVBalBranch3MkVBalBranch18(zzz340, zzz341, zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, Zero, h) → new_mkVBalBranch3MkVBalBranch115(zzz340, zzz341, Zero, zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, Zero, Succ(zzz51200), h)

The TRS R consists of the following rules:

new_primPlusNat1(Zero) → Zero
new_primPlusNat1(Succ(zzz62000)) → Succ(Succ(new_primPlusNat1(zzz62000)))
new_primPlusNat3(zzz90, Succ(zzz910)) → Succ(Succ(new_primPlusNat2(zzz90, zzz910)))
new_primPlusNat3(zzz90, Zero) → Succ(zzz90)
new_primPlusNat2(Succ(zzz900), Succ(zzz9100)) → Succ(Succ(new_primPlusNat2(zzz900, zzz9100)))
new_primPlusNat2(Zero, Succ(zzz9100)) → Succ(zzz9100)
new_primPlusNat2(Zero, Zero) → Zero
new_primPlusNat2(Succ(zzz900), Zero) → Succ(zzz900)

The set Q consists of the following terms:

new_primPlusNat2(Zero, Succ(x0))
new_primPlusNat3(x0, Succ(x1))
new_primPlusNat2(Succ(x0), Succ(x1))
new_primPlusNat3(x0, Zero)
new_primPlusNat1(Zero)
new_primPlusNat2(Zero, Zero)
new_primPlusNat1(Succ(x0))
new_primPlusNat2(Succ(x0), Zero)

We have to consider all minimal (P,Q,R)-chains.
By rewriting [15] the rule new_mkVBalBranch3MkVBalBranch218(zzz461, zzz462, zzz463, zzz464, zzz465, zzz466, zzz467, zzz468, zzz469, zzz470, zzz471, bb) → new_mkVBalBranch3MkVBalBranch110(zzz461, zzz462, zzz463, zzz464, zzz465, zzz466, zzz467, zzz468, zzz469, zzz470, zzz471, new_primPlusNat2(Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat3(new_primPlusNat1(zzz463), zzz463)), zzz463))), Succ(zzz463)), bb) at position [11] we obtained the following new rules:

new_mkVBalBranch3MkVBalBranch218(zzz461, zzz462, zzz463, zzz464, zzz465, zzz466, zzz467, zzz468, zzz469, zzz470, zzz471, bb) → new_mkVBalBranch3MkVBalBranch110(zzz461, zzz462, zzz463, zzz464, zzz465, zzz466, zzz467, zzz468, zzz469, zzz470, zzz471, Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat2(Succ(new_primPlusNat3(new_primPlusNat1(zzz463), zzz463)), zzz463)), zzz463))), bb)



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

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

new_mkVBalBranch3MkVBalBranch225(zzz498, zzz499, zzz500, zzz501, zzz502, zzz503, zzz504, zzz505, zzz506, zzz507, Zero, Zero, bg) → new_mkVBalBranch3MkVBalBranch230(zzz498, zzz499, zzz500, zzz501, zzz502, zzz503, zzz504, zzz505, zzz506, zzz507, bg)
new_mkVBalBranch3MkVBalBranch18(zzz340, zzz341, zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, Succ(zzz1480), h) → new_mkVBalBranch3MkVBalBranch115(zzz340, zzz341, Zero, zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, Succ(zzz1480), Succ(zzz51200), h)
new_mkVBalBranch3MkVBalBranch215(zzz340, zzz341, Pos(Succ(Succ(zzz342000))), zzz343, zzz344, zzz510, zzz511, Succ(zzz512000), zzz513, zzz514, zzz31, Succ(Succ(zzz6600)), h) → new_mkVBalBranch3MkVBalBranch216(zzz340, zzz341, Succ(zzz342000), zzz343, zzz344, zzz510, zzz511, zzz512000, zzz513, zzz514, zzz31, Succ(Succ(new_primPlusNat2(zzz6600, zzz512000))), zzz342000, h)
new_mkVBalBranch0(zzz31, Branch(zzz510, zzz511, Neg(Zero), zzz513, zzz514), Branch(zzz340, zzz341, Pos(Succ(zzz34200)), zzz343, zzz344), h) → new_mkVBalBranch0(zzz31, Branch(zzz510, zzz511, Neg(Zero), zzz513, zzz514), zzz343, h)
new_mkVBalBranch3MkVBalBranch223(zzz340, zzz341, Neg(Succ(Succ(Succ(zzz3420000)))), zzz343, zzz344, zzz510, zzz511, Zero, zzz513, zzz514, zzz31, Succ(Succ(zzz6700)), h) → new_mkVBalBranch3MkVBalBranch225(zzz340, zzz341, Succ(Succ(zzz3420000)), zzz343, zzz344, zzz510, zzz511, zzz513, zzz514, zzz31, Succ(zzz3420000), Succ(zzz6700), h)
new_mkVBalBranch3MkVBalBranch120(zzz2050, zzz2051, zzz2052, zzz2053, zzz2054, zzz2055, zzz2056, zzz2057, zzz2058, zzz2059, zzz2060, Zero, Succ(zzz20620), be) → new_mkVBalBranch0(zzz2060, zzz2059, Branch(zzz2050, zzz2051, Neg(Succ(zzz2052)), zzz2053, zzz2054), be)
new_mkVBalBranch3MkVBalBranch215(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, Succ(zzz660), h) → new_mkVBalBranch3MkVBalBranch19(zzz340, zzz341, zzz34200, zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, new_primPlusNat2(Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat3(new_primPlusNat1(zzz34200), zzz34200)), zzz34200))), Succ(zzz34200)), h)
new_mkVBalBranch0(zzz31, Branch(zzz510, zzz511, Pos(Zero), zzz513, zzz514), Branch(zzz340, zzz341, Pos(Succ(zzz34200)), zzz343, zzz344), h) → new_mkVBalBranch0(zzz31, Branch(zzz510, zzz511, Pos(Zero), zzz513, zzz514), zzz343, h)
new_mkVBalBranch3MkVBalBranch121(zzz473, zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, zzz481, zzz482, Succ(zzz7390), bh) → new_mkVBalBranch3MkVBalBranch115(zzz473, zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, Zero, zzz480, zzz481, zzz482, Succ(zzz7390), Succ(Zero), bh)
new_mkVBalBranch0(zzz31, Branch(zzz510, zzz511, Pos(Succ(zzz51200)), zzz513, zzz514), Branch(zzz340, zzz341, zzz342, zzz343, zzz344), h) → new_mkVBalBranch3MkVBalBranch215(zzz340, zzz341, zzz342, zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat3(new_primPlusNat1(zzz51200), zzz51200)), zzz51200))), h)
new_mkVBalBranch3MkVBalBranch217(zzz473, zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, zzz481, zzz482, Succ(zzz4830), Zero, bh) → new_mkVBalBranch3MkVBalBranch121(zzz473, zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, zzz481, zzz482, new_primPlusNat2(Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat3(new_primPlusNat1(zzz475), zzz475)), zzz475))), Succ(zzz475)), bh)
new_mkVBalBranch3MkVBalBranch230(zzz498, zzz499, zzz500, zzz501, zzz502, zzz503, zzz504, zzz505, zzz506, zzz507, bg) → new_mkVBalBranch3MkVBalBranch118(zzz498, zzz499, zzz500, zzz501, zzz502, zzz503, zzz504, zzz505, zzz506, zzz507, Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat2(Succ(new_primPlusNat3(new_primPlusNat1(zzz500), zzz500)), zzz500)), zzz500))), bg)
new_mkVBalBranch3MkVBalBranch223(zzz340, zzz341, Neg(Succ(Succ(Zero))), zzz343, zzz344, zzz510, zzz511, Succ(zzz512000), zzz513, zzz514, zzz31, Succ(Succ(zzz6700)), h) → new_mkVBalBranch3MkVBalBranch224(zzz340, zzz341, Succ(Zero), zzz343, zzz344, zzz510, zzz511, zzz512000, zzz513, zzz514, zzz31, Zero, Succ(Succ(new_primPlusNat2(zzz6700, zzz512000))), h)
new_mkVBalBranch3MkVBalBranch224(zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, zzz1125, zzz1126, zzz1127, zzz1128, zzz1129, Succ(zzz11300), Succ(zzz11310), bd) → new_mkVBalBranch3MkVBalBranch224(zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, zzz1125, zzz1126, zzz1127, zzz1128, zzz1129, zzz11300, zzz11310, bd)
new_mkVBalBranch3MkVBalBranch217(zzz473, zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, zzz481, zzz482, Zero, Succ(zzz4840), bh) → new_mkVBalBranch0(zzz482, Branch(zzz478, zzz479, Pos(Succ(Zero)), zzz480, zzz481), zzz476, bh)
new_mkVBalBranch3MkVBalBranch218(zzz461, zzz462, zzz463, zzz464, zzz465, zzz466, zzz467, zzz468, zzz469, zzz470, zzz471, bb) → new_mkVBalBranch3MkVBalBranch110(zzz461, zzz462, zzz463, zzz464, zzz465, zzz466, zzz467, zzz468, zzz469, zzz470, zzz471, Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat2(Succ(new_primPlusNat3(new_primPlusNat1(zzz463), zzz463)), zzz463)), zzz463))), bb)
new_mkVBalBranch3MkVBalBranch110(zzz461, zzz462, zzz463, zzz464, zzz465, zzz466, zzz467, zzz468, zzz469, zzz470, zzz471, Succ(zzz5800), bb) → new_mkVBalBranch3MkVBalBranch115(zzz461, zzz462, zzz463, zzz464, zzz465, zzz466, zzz467, Succ(zzz468), zzz469, zzz470, zzz471, Succ(zzz5800), Succ(Succ(zzz468)), bb)
new_mkVBalBranch3MkVBalBranch227(zzz486, zzz487, zzz488, zzz489, zzz490, zzz491, zzz492, zzz493, zzz494, zzz495, zzz496, bf) → new_mkVBalBranch0(zzz496, Branch(zzz491, zzz492, Neg(Succ(Succ(zzz493))), zzz494, zzz495), zzz489, bf)
new_mkVBalBranch3MkVBalBranch215(zzz340, zzz341, Pos(Zero), zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, Succ(zzz660), h) → new_mkVBalBranch0(zzz31, zzz514, Branch(zzz340, zzz341, Pos(Zero), zzz343, zzz344), h)
new_mkVBalBranch3MkVBalBranch223(zzz340, zzz341, Neg(Zero), zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, Succ(zzz670), h) → new_mkVBalBranch0(zzz31, Branch(zzz510, zzz511, Neg(Succ(zzz51200)), zzz513, zzz514), zzz343, h)
new_mkVBalBranch3MkVBalBranch216(zzz1105, zzz1106, zzz1107, zzz1108, zzz1109, zzz1110, zzz1111, zzz1112, zzz1113, zzz1114, zzz1115, Zero, Succ(zzz11170), ba) → new_mkVBalBranch0(zzz1115, Branch(zzz1110, zzz1111, Pos(Succ(Succ(zzz1112))), zzz1113, zzz1114), zzz1108, ba)
new_mkVBalBranch3MkVBalBranch115(zzz1986, zzz1987, zzz1988, zzz1989, zzz1990, zzz1991, zzz1992, zzz1993, zzz1994, zzz1995, zzz1996, Zero, Succ(zzz19980), bc) → new_mkVBalBranch0(zzz1996, zzz1995, Branch(zzz1986, zzz1987, Pos(Succ(zzz1988)), zzz1989, zzz1990), bc)
new_mkVBalBranch3MkVBalBranch233(zzz473, zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, zzz481, zzz482, bh) → new_mkVBalBranch3MkVBalBranch121(zzz473, zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, zzz481, zzz482, new_primPlusNat2(Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat3(new_primPlusNat1(zzz475), zzz475)), zzz475))), Succ(zzz475)), bh)
new_mkVBalBranch3MkVBalBranch215(zzz340, zzz341, Pos(Succ(Zero)), zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, Succ(zzz660), h) → new_mkVBalBranch3MkVBalBranch18(zzz340, zzz341, zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, new_primPlusNat2(Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat3(new_primPlusNat1(Zero), Zero)), Zero))), Succ(Zero)), h)
new_mkVBalBranch3MkVBalBranch122(zzz340, zzz341, zzz34200, zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, h) → new_mkVBalBranch0(zzz31, zzz514, Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), h)
new_mkVBalBranch3MkVBalBranch217(zzz473, zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, zzz481, zzz482, Succ(zzz4830), Succ(zzz4840), bh) → new_mkVBalBranch3MkVBalBranch217(zzz473, zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, zzz481, zzz482, zzz4830, zzz4840, bh)
new_mkVBalBranch3MkVBalBranch116(zzz340, zzz341, zzz34200, zzz343, zzz344, zzz510, zzz511, zzz513, zzz514, zzz31, Succ(zzz1200), h) → new_mkVBalBranch0(zzz31, zzz514, Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), h)
new_mkVBalBranch3MkVBalBranch110(zzz461, zzz462, zzz463, zzz464, zzz465, zzz466, zzz467, zzz468, zzz469, zzz470, zzz471, Zero, bb) → new_mkVBalBranch3MkVBalBranch115(zzz461, zzz462, zzz463, zzz464, zzz465, zzz466, zzz467, Succ(zzz468), zzz469, zzz470, zzz471, Zero, Succ(Succ(zzz468)), bb)
new_mkVBalBranch3MkVBalBranch225(zzz498, zzz499, zzz500, zzz501, zzz502, zzz503, zzz504, zzz505, zzz506, zzz507, Zero, Succ(zzz5090), bg) → new_mkVBalBranch0(zzz507, Branch(zzz503, zzz504, Neg(Succ(Zero)), zzz505, zzz506), zzz501, bg)
new_mkVBalBranch0(zzz31, Branch(zzz510, zzz511, Neg(Succ(zzz51200)), zzz513, zzz514), Branch(zzz340, zzz341, zzz342, zzz343, zzz344), h) → new_mkVBalBranch3MkVBalBranch223(zzz340, zzz341, zzz342, zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat3(new_primPlusNat1(zzz51200), zzz51200)), zzz51200))), h)
new_mkVBalBranch3MkVBalBranch121(zzz473, zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, zzz481, zzz482, Zero, bh) → new_mkVBalBranch3MkVBalBranch115(zzz473, zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, Zero, zzz480, zzz481, zzz482, Zero, Succ(Zero), bh)
new_mkVBalBranch3MkVBalBranch223(zzz340, zzz341, Neg(Succ(Zero)), zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, Succ(zzz670), h) → new_mkVBalBranch0(zzz31, Branch(zzz510, zzz511, Neg(Succ(zzz51200)), zzz513, zzz514), zzz343, h)
new_mkVBalBranch3MkVBalBranch225(zzz498, zzz499, zzz500, zzz501, zzz502, zzz503, zzz504, zzz505, zzz506, zzz507, Succ(zzz5080), Zero, bg) → new_mkVBalBranch3MkVBalBranch118(zzz498, zzz499, zzz500, zzz501, zzz502, zzz503, zzz504, zzz505, zzz506, zzz507, new_primPlusNat2(Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat3(new_primPlusNat1(zzz500), zzz500)), zzz500))), Succ(zzz500)), bg)
new_mkVBalBranch0(zzz31, Branch(zzz510, zzz511, Pos(Zero), zzz513, zzz514), Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), h) → new_mkVBalBranch3MkVBalBranch116(zzz340, zzz341, zzz34200, zzz343, zzz344, zzz510, zzz511, zzz513, zzz514, zzz31, new_primPlusNat2(Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat3(new_primPlusNat1(zzz34200), zzz34200)), zzz34200))), Succ(zzz34200)), h)
new_mkVBalBranch3MkVBalBranch215(zzz340, zzz341, Pos(Succ(Succ(zzz342000))), zzz343, zzz344, zzz510, zzz511, Zero, zzz513, zzz514, zzz31, Succ(Succ(zzz6600)), h) → new_mkVBalBranch3MkVBalBranch217(zzz340, zzz341, Succ(zzz342000), zzz343, zzz344, zzz510, zzz511, zzz513, zzz514, zzz31, Succ(zzz6600), zzz342000, h)
new_mkVBalBranch3MkVBalBranch117(zzz340, zzz341, zzz34200, zzz343, zzz344, zzz510, zzz511, zzz513, zzz514, zzz31, Succ(zzz1240), h) → new_mkVBalBranch0(zzz31, zzz514, Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), h)
new_mkVBalBranch3MkVBalBranch120(zzz2050, zzz2051, zzz2052, zzz2053, zzz2054, zzz2055, zzz2056, zzz2057, zzz2058, zzz2059, zzz2060, Succ(zzz20610), Succ(zzz20620), be) → new_mkVBalBranch3MkVBalBranch120(zzz2050, zzz2051, zzz2052, zzz2053, zzz2054, zzz2055, zzz2056, zzz2057, zzz2058, zzz2059, zzz2060, zzz20610, zzz20620, be)
new_mkVBalBranch3MkVBalBranch217(zzz473, zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, zzz481, zzz482, Zero, Zero, bh) → new_mkVBalBranch3MkVBalBranch233(zzz473, zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, zzz481, zzz482, bh)
new_mkVBalBranch3MkVBalBranch216(zzz1105, zzz1106, zzz1107, zzz1108, zzz1109, zzz1110, zzz1111, zzz1112, zzz1113, zzz1114, zzz1115, Succ(zzz11160), Succ(zzz11170), ba) → new_mkVBalBranch3MkVBalBranch216(zzz1105, zzz1106, zzz1107, zzz1108, zzz1109, zzz1110, zzz1111, zzz1112, zzz1113, zzz1114, zzz1115, zzz11160, zzz11170, ba)
new_mkVBalBranch3MkVBalBranch223(zzz340, zzz341, Pos(zzz3420), zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, Succ(zzz670), h) → new_mkVBalBranch0(zzz31, Branch(zzz510, zzz511, Neg(Succ(zzz51200)), zzz513, zzz514), zzz343, h)
new_mkVBalBranch0(zzz31, Branch(zzz510, zzz511, Neg(Zero), zzz513, zzz514), Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), h) → new_mkVBalBranch3MkVBalBranch117(zzz340, zzz341, zzz34200, zzz343, zzz344, zzz510, zzz511, zzz513, zzz514, zzz31, new_primPlusNat2(Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat3(new_primPlusNat1(zzz34200), zzz34200)), zzz34200))), Succ(zzz34200)), h)
new_mkVBalBranch3MkVBalBranch19(zzz340, zzz341, zzz34200, zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, Zero, h) → new_mkVBalBranch3MkVBalBranch122(zzz340, zzz341, zzz34200, zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, h)
new_mkVBalBranch3MkVBalBranch225(zzz498, zzz499, zzz500, zzz501, zzz502, zzz503, zzz504, zzz505, zzz506, zzz507, Succ(zzz5080), Succ(zzz5090), bg) → new_mkVBalBranch3MkVBalBranch225(zzz498, zzz499, zzz500, zzz501, zzz502, zzz503, zzz504, zzz505, zzz506, zzz507, zzz5080, zzz5090, bg)
new_mkVBalBranch3MkVBalBranch19(zzz340, zzz341, zzz34200, zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, Succ(zzz1410), h) → new_mkVBalBranch0(zzz31, zzz514, Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), h)
new_mkVBalBranch3MkVBalBranch224(zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, zzz1125, zzz1126, zzz1127, zzz1128, zzz1129, Zero, Succ(zzz11310), bd) → new_mkVBalBranch3MkVBalBranch227(zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, zzz1125, zzz1126, zzz1127, zzz1128, zzz1129, bd)
new_mkVBalBranch3MkVBalBranch224(zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, zzz1125, zzz1126, zzz1127, zzz1128, zzz1129, Zero, Zero, bd) → new_mkVBalBranch3MkVBalBranch229(zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, zzz1125, zzz1126, zzz1127, zzz1128, zzz1129, bd)
new_mkVBalBranch3MkVBalBranch223(zzz340, zzz341, Neg(Succ(Succ(Zero))), zzz343, zzz344, zzz510, zzz511, Zero, zzz513, zzz514, zzz31, Succ(Succ(zzz6700)), h) → new_mkVBalBranch3MkVBalBranch225(zzz340, zzz341, Succ(Zero), zzz343, zzz344, zzz510, zzz511, zzz513, zzz514, zzz31, Zero, Succ(zzz6700), h)
new_mkVBalBranch3MkVBalBranch223(zzz340, zzz341, Neg(Succ(Succ(Succ(zzz3420000)))), zzz343, zzz344, zzz510, zzz511, Succ(zzz512000), zzz513, zzz514, zzz31, Succ(Succ(zzz6700)), h) → new_mkVBalBranch3MkVBalBranch224(zzz340, zzz341, Succ(Succ(zzz3420000)), zzz343, zzz344, zzz510, zzz511, zzz512000, zzz513, zzz514, zzz31, Succ(zzz3420000), Succ(Succ(new_primPlusNat2(zzz6700, zzz512000))), h)
new_mkVBalBranch3MkVBalBranch115(zzz1986, zzz1987, zzz1988, zzz1989, zzz1990, zzz1991, zzz1992, zzz1993, zzz1994, zzz1995, zzz1996, Succ(zzz19970), Succ(zzz19980), bc) → new_mkVBalBranch3MkVBalBranch115(zzz1986, zzz1987, zzz1988, zzz1989, zzz1990, zzz1991, zzz1992, zzz1993, zzz1994, zzz1995, zzz1996, zzz19970, zzz19980, bc)
new_mkVBalBranch3MkVBalBranch215(zzz340, zzz341, Neg(Zero), zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, Succ(zzz660), h) → new_mkVBalBranch0(zzz31, zzz514, Branch(zzz340, zzz341, Neg(Zero), zzz343, zzz344), h)
new_mkVBalBranch3MkVBalBranch229(zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, zzz1125, zzz1126, zzz1127, zzz1128, zzz1129, bd) → new_mkVBalBranch3MkVBalBranch119(zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, zzz1125, zzz1126, zzz1127, zzz1128, zzz1129, new_primPlusNat2(Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat3(new_primPlusNat1(zzz1121), zzz1121)), zzz1121))), Succ(zzz1121)), bd)
new_mkVBalBranch3MkVBalBranch224(zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, zzz1125, zzz1126, zzz1127, zzz1128, zzz1129, Succ(zzz11300), Zero, bd) → new_mkVBalBranch3MkVBalBranch119(zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, zzz1125, zzz1126, zzz1127, zzz1128, zzz1129, Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat2(Succ(new_primPlusNat3(new_primPlusNat1(zzz1121), zzz1121)), zzz1121)), zzz1121))), bd)
new_mkVBalBranch3MkVBalBranch222(zzz461, zzz462, zzz463, zzz464, zzz465, zzz466, zzz467, zzz468, zzz469, zzz470, zzz471, bb) → new_mkVBalBranch3MkVBalBranch110(zzz461, zzz462, zzz463, zzz464, zzz465, zzz466, zzz467, zzz468, zzz469, zzz470, zzz471, Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat2(Succ(new_primPlusNat3(new_primPlusNat1(zzz463), zzz463)), zzz463)), zzz463))), bb)
new_mkVBalBranch3MkVBalBranch118(zzz498, zzz499, zzz500, zzz501, zzz502, zzz503, zzz504, zzz505, zzz506, zzz507, Succ(zzz8040), bg) → new_mkVBalBranch3MkVBalBranch120(zzz498, zzz499, zzz500, zzz501, zzz502, zzz503, zzz504, Zero, zzz505, zzz506, zzz507, Succ(Zero), Succ(zzz8040), bg)
new_mkVBalBranch3MkVBalBranch216(zzz1105, zzz1106, zzz1107, zzz1108, zzz1109, zzz1110, zzz1111, zzz1112, zzz1113, zzz1114, zzz1115, Succ(zzz11160), Zero, ba) → new_mkVBalBranch3MkVBalBranch218(zzz1105, zzz1106, zzz1107, zzz1108, zzz1109, zzz1110, zzz1111, zzz1112, zzz1113, zzz1114, zzz1115, ba)
new_mkVBalBranch3MkVBalBranch216(zzz1105, zzz1106, zzz1107, zzz1108, zzz1109, zzz1110, zzz1111, zzz1112, zzz1113, zzz1114, zzz1115, Zero, Zero, ba) → new_mkVBalBranch3MkVBalBranch222(zzz1105, zzz1106, zzz1107, zzz1108, zzz1109, zzz1110, zzz1111, zzz1112, zzz1113, zzz1114, zzz1115, ba)
new_mkVBalBranch3MkVBalBranch18(zzz340, zzz341, zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, Zero, h) → new_mkVBalBranch3MkVBalBranch115(zzz340, zzz341, Zero, zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, Zero, Succ(zzz51200), h)
new_mkVBalBranch3MkVBalBranch119(zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, zzz1125, zzz1126, zzz1127, zzz1128, zzz1129, Succ(zzz12130), bd) → new_mkVBalBranch3MkVBalBranch120(zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, zzz1125, Succ(zzz1126), zzz1127, zzz1128, zzz1129, Succ(Succ(zzz1126)), Succ(zzz12130), bd)

The TRS R consists of the following rules:

new_primPlusNat1(Zero) → Zero
new_primPlusNat1(Succ(zzz62000)) → Succ(Succ(new_primPlusNat1(zzz62000)))
new_primPlusNat3(zzz90, Succ(zzz910)) → Succ(Succ(new_primPlusNat2(zzz90, zzz910)))
new_primPlusNat3(zzz90, Zero) → Succ(zzz90)
new_primPlusNat2(Succ(zzz900), Succ(zzz9100)) → Succ(Succ(new_primPlusNat2(zzz900, zzz9100)))
new_primPlusNat2(Zero, Succ(zzz9100)) → Succ(zzz9100)
new_primPlusNat2(Zero, Zero) → Zero
new_primPlusNat2(Succ(zzz900), Zero) → Succ(zzz900)

The set Q consists of the following terms:

new_primPlusNat2(Zero, Succ(x0))
new_primPlusNat3(x0, Succ(x1))
new_primPlusNat2(Succ(x0), Succ(x1))
new_primPlusNat3(x0, Zero)
new_primPlusNat1(Zero)
new_primPlusNat2(Zero, Zero)
new_primPlusNat1(Succ(x0))
new_primPlusNat2(Succ(x0), Zero)

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

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

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

new_mkVBalBranch3MkVBalBranch225(zzz498, zzz499, zzz500, zzz501, zzz502, zzz503, zzz504, zzz505, zzz506, zzz507, Zero, Zero, bg) → new_mkVBalBranch3MkVBalBranch230(zzz498, zzz499, zzz500, zzz501, zzz502, zzz503, zzz504, zzz505, zzz506, zzz507, bg)
new_mkVBalBranch3MkVBalBranch18(zzz340, zzz341, zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, Succ(zzz1480), h) → new_mkVBalBranch3MkVBalBranch115(zzz340, zzz341, Zero, zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, Succ(zzz1480), Succ(zzz51200), h)
new_mkVBalBranch0(zzz31, Branch(zzz510, zzz511, Neg(Zero), zzz513, zzz514), Branch(zzz340, zzz341, Pos(Succ(zzz34200)), zzz343, zzz344), h) → new_mkVBalBranch0(zzz31, Branch(zzz510, zzz511, Neg(Zero), zzz513, zzz514), zzz343, h)
new_mkVBalBranch3MkVBalBranch215(zzz340, zzz341, Pos(Succ(Succ(zzz342000))), zzz343, zzz344, zzz510, zzz511, Succ(zzz512000), zzz513, zzz514, zzz31, Succ(Succ(zzz6600)), h) → new_mkVBalBranch3MkVBalBranch216(zzz340, zzz341, Succ(zzz342000), zzz343, zzz344, zzz510, zzz511, zzz512000, zzz513, zzz514, zzz31, Succ(Succ(new_primPlusNat2(zzz6600, zzz512000))), zzz342000, h)
new_mkVBalBranch3MkVBalBranch223(zzz340, zzz341, Neg(Succ(Succ(Succ(zzz3420000)))), zzz343, zzz344, zzz510, zzz511, Zero, zzz513, zzz514, zzz31, Succ(Succ(zzz6700)), h) → new_mkVBalBranch3MkVBalBranch225(zzz340, zzz341, Succ(Succ(zzz3420000)), zzz343, zzz344, zzz510, zzz511, zzz513, zzz514, zzz31, Succ(zzz3420000), Succ(zzz6700), h)
new_mkVBalBranch3MkVBalBranch120(zzz2050, zzz2051, zzz2052, zzz2053, zzz2054, zzz2055, zzz2056, zzz2057, zzz2058, zzz2059, zzz2060, Zero, Succ(zzz20620), be) → new_mkVBalBranch0(zzz2060, zzz2059, Branch(zzz2050, zzz2051, Neg(Succ(zzz2052)), zzz2053, zzz2054), be)
new_mkVBalBranch3MkVBalBranch215(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, Succ(zzz660), h) → new_mkVBalBranch3MkVBalBranch19(zzz340, zzz341, zzz34200, zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, new_primPlusNat2(Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat3(new_primPlusNat1(zzz34200), zzz34200)), zzz34200))), Succ(zzz34200)), h)
new_mkVBalBranch0(zzz31, Branch(zzz510, zzz511, Pos(Zero), zzz513, zzz514), Branch(zzz340, zzz341, Pos(Succ(zzz34200)), zzz343, zzz344), h) → new_mkVBalBranch0(zzz31, Branch(zzz510, zzz511, Pos(Zero), zzz513, zzz514), zzz343, h)
new_mkVBalBranch3MkVBalBranch121(zzz473, zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, zzz481, zzz482, Succ(zzz7390), bh) → new_mkVBalBranch3MkVBalBranch115(zzz473, zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, Zero, zzz480, zzz481, zzz482, Succ(zzz7390), Succ(Zero), bh)
new_mkVBalBranch0(zzz31, Branch(zzz510, zzz511, Pos(Succ(zzz51200)), zzz513, zzz514), Branch(zzz340, zzz341, zzz342, zzz343, zzz344), h) → new_mkVBalBranch3MkVBalBranch215(zzz340, zzz341, zzz342, zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat3(new_primPlusNat1(zzz51200), zzz51200)), zzz51200))), h)
new_mkVBalBranch3MkVBalBranch223(zzz340, zzz341, Neg(Succ(Succ(Zero))), zzz343, zzz344, zzz510, zzz511, Succ(zzz512000), zzz513, zzz514, zzz31, Succ(Succ(zzz6700)), h) → new_mkVBalBranch3MkVBalBranch224(zzz340, zzz341, Succ(Zero), zzz343, zzz344, zzz510, zzz511, zzz512000, zzz513, zzz514, zzz31, Zero, Succ(Succ(new_primPlusNat2(zzz6700, zzz512000))), h)
new_mkVBalBranch3MkVBalBranch230(zzz498, zzz499, zzz500, zzz501, zzz502, zzz503, zzz504, zzz505, zzz506, zzz507, bg) → new_mkVBalBranch3MkVBalBranch118(zzz498, zzz499, zzz500, zzz501, zzz502, zzz503, zzz504, zzz505, zzz506, zzz507, Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat2(Succ(new_primPlusNat3(new_primPlusNat1(zzz500), zzz500)), zzz500)), zzz500))), bg)
new_mkVBalBranch3MkVBalBranch217(zzz473, zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, zzz481, zzz482, Succ(zzz4830), Zero, bh) → new_mkVBalBranch3MkVBalBranch121(zzz473, zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, zzz481, zzz482, new_primPlusNat2(Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat3(new_primPlusNat1(zzz475), zzz475)), zzz475))), Succ(zzz475)), bh)
new_mkVBalBranch3MkVBalBranch224(zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, zzz1125, zzz1126, zzz1127, zzz1128, zzz1129, Succ(zzz11300), Succ(zzz11310), bd) → new_mkVBalBranch3MkVBalBranch224(zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, zzz1125, zzz1126, zzz1127, zzz1128, zzz1129, zzz11300, zzz11310, bd)
new_mkVBalBranch3MkVBalBranch217(zzz473, zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, zzz481, zzz482, Zero, Succ(zzz4840), bh) → new_mkVBalBranch0(zzz482, Branch(zzz478, zzz479, Pos(Succ(Zero)), zzz480, zzz481), zzz476, bh)
new_mkVBalBranch3MkVBalBranch218(zzz461, zzz462, zzz463, zzz464, zzz465, zzz466, zzz467, zzz468, zzz469, zzz470, zzz471, bb) → new_mkVBalBranch3MkVBalBranch110(zzz461, zzz462, zzz463, zzz464, zzz465, zzz466, zzz467, zzz468, zzz469, zzz470, zzz471, Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat2(Succ(new_primPlusNat3(new_primPlusNat1(zzz463), zzz463)), zzz463)), zzz463))), bb)
new_mkVBalBranch3MkVBalBranch110(zzz461, zzz462, zzz463, zzz464, zzz465, zzz466, zzz467, zzz468, zzz469, zzz470, zzz471, Succ(zzz5800), bb) → new_mkVBalBranch3MkVBalBranch115(zzz461, zzz462, zzz463, zzz464, zzz465, zzz466, zzz467, Succ(zzz468), zzz469, zzz470, zzz471, Succ(zzz5800), Succ(Succ(zzz468)), bb)
new_mkVBalBranch3MkVBalBranch227(zzz486, zzz487, zzz488, zzz489, zzz490, zzz491, zzz492, zzz493, zzz494, zzz495, zzz496, bf) → new_mkVBalBranch0(zzz496, Branch(zzz491, zzz492, Neg(Succ(Succ(zzz493))), zzz494, zzz495), zzz489, bf)
new_mkVBalBranch3MkVBalBranch215(zzz340, zzz341, Pos(Zero), zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, Succ(zzz660), h) → new_mkVBalBranch0(zzz31, zzz514, Branch(zzz340, zzz341, Pos(Zero), zzz343, zzz344), h)
new_mkVBalBranch3MkVBalBranch223(zzz340, zzz341, Neg(Zero), zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, Succ(zzz670), h) → new_mkVBalBranch0(zzz31, Branch(zzz510, zzz511, Neg(Succ(zzz51200)), zzz513, zzz514), zzz343, h)
new_mkVBalBranch3MkVBalBranch216(zzz1105, zzz1106, zzz1107, zzz1108, zzz1109, zzz1110, zzz1111, zzz1112, zzz1113, zzz1114, zzz1115, Zero, Succ(zzz11170), ba) → new_mkVBalBranch0(zzz1115, Branch(zzz1110, zzz1111, Pos(Succ(Succ(zzz1112))), zzz1113, zzz1114), zzz1108, ba)
new_mkVBalBranch3MkVBalBranch115(zzz1986, zzz1987, zzz1988, zzz1989, zzz1990, zzz1991, zzz1992, zzz1993, zzz1994, zzz1995, zzz1996, Zero, Succ(zzz19980), bc) → new_mkVBalBranch0(zzz1996, zzz1995, Branch(zzz1986, zzz1987, Pos(Succ(zzz1988)), zzz1989, zzz1990), bc)
new_mkVBalBranch3MkVBalBranch233(zzz473, zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, zzz481, zzz482, bh) → new_mkVBalBranch3MkVBalBranch121(zzz473, zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, zzz481, zzz482, new_primPlusNat2(Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat3(new_primPlusNat1(zzz475), zzz475)), zzz475))), Succ(zzz475)), bh)
new_mkVBalBranch3MkVBalBranch215(zzz340, zzz341, Pos(Succ(Zero)), zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, Succ(zzz660), h) → new_mkVBalBranch3MkVBalBranch18(zzz340, zzz341, zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, new_primPlusNat2(Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat3(new_primPlusNat1(Zero), Zero)), Zero))), Succ(Zero)), h)
new_mkVBalBranch3MkVBalBranch122(zzz340, zzz341, zzz34200, zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, h) → new_mkVBalBranch0(zzz31, zzz514, Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), h)
new_mkVBalBranch3MkVBalBranch217(zzz473, zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, zzz481, zzz482, Succ(zzz4830), Succ(zzz4840), bh) → new_mkVBalBranch3MkVBalBranch217(zzz473, zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, zzz481, zzz482, zzz4830, zzz4840, bh)
new_mkVBalBranch3MkVBalBranch116(zzz340, zzz341, zzz34200, zzz343, zzz344, zzz510, zzz511, zzz513, zzz514, zzz31, Succ(zzz1200), h) → new_mkVBalBranch0(zzz31, zzz514, Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), h)
new_mkVBalBranch3MkVBalBranch225(zzz498, zzz499, zzz500, zzz501, zzz502, zzz503, zzz504, zzz505, zzz506, zzz507, Zero, Succ(zzz5090), bg) → new_mkVBalBranch0(zzz507, Branch(zzz503, zzz504, Neg(Succ(Zero)), zzz505, zzz506), zzz501, bg)
new_mkVBalBranch0(zzz31, Branch(zzz510, zzz511, Neg(Succ(zzz51200)), zzz513, zzz514), Branch(zzz340, zzz341, zzz342, zzz343, zzz344), h) → new_mkVBalBranch3MkVBalBranch223(zzz340, zzz341, zzz342, zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat3(new_primPlusNat1(zzz51200), zzz51200)), zzz51200))), h)
new_mkVBalBranch3MkVBalBranch121(zzz473, zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, zzz481, zzz482, Zero, bh) → new_mkVBalBranch3MkVBalBranch115(zzz473, zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, Zero, zzz480, zzz481, zzz482, Zero, Succ(Zero), bh)
new_mkVBalBranch3MkVBalBranch223(zzz340, zzz341, Neg(Succ(Zero)), zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, Succ(zzz670), h) → new_mkVBalBranch0(zzz31, Branch(zzz510, zzz511, Neg(Succ(zzz51200)), zzz513, zzz514), zzz343, h)
new_mkVBalBranch3MkVBalBranch225(zzz498, zzz499, zzz500, zzz501, zzz502, zzz503, zzz504, zzz505, zzz506, zzz507, Succ(zzz5080), Zero, bg) → new_mkVBalBranch3MkVBalBranch118(zzz498, zzz499, zzz500, zzz501, zzz502, zzz503, zzz504, zzz505, zzz506, zzz507, new_primPlusNat2(Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat3(new_primPlusNat1(zzz500), zzz500)), zzz500))), Succ(zzz500)), bg)
new_mkVBalBranch0(zzz31, Branch(zzz510, zzz511, Pos(Zero), zzz513, zzz514), Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), h) → new_mkVBalBranch3MkVBalBranch116(zzz340, zzz341, zzz34200, zzz343, zzz344, zzz510, zzz511, zzz513, zzz514, zzz31, new_primPlusNat2(Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat3(new_primPlusNat1(zzz34200), zzz34200)), zzz34200))), Succ(zzz34200)), h)
new_mkVBalBranch3MkVBalBranch215(zzz340, zzz341, Pos(Succ(Succ(zzz342000))), zzz343, zzz344, zzz510, zzz511, Zero, zzz513, zzz514, zzz31, Succ(Succ(zzz6600)), h) → new_mkVBalBranch3MkVBalBranch217(zzz340, zzz341, Succ(zzz342000), zzz343, zzz344, zzz510, zzz511, zzz513, zzz514, zzz31, Succ(zzz6600), zzz342000, h)
new_mkVBalBranch3MkVBalBranch117(zzz340, zzz341, zzz34200, zzz343, zzz344, zzz510, zzz511, zzz513, zzz514, zzz31, Succ(zzz1240), h) → new_mkVBalBranch0(zzz31, zzz514, Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), h)
new_mkVBalBranch3MkVBalBranch120(zzz2050, zzz2051, zzz2052, zzz2053, zzz2054, zzz2055, zzz2056, zzz2057, zzz2058, zzz2059, zzz2060, Succ(zzz20610), Succ(zzz20620), be) → new_mkVBalBranch3MkVBalBranch120(zzz2050, zzz2051, zzz2052, zzz2053, zzz2054, zzz2055, zzz2056, zzz2057, zzz2058, zzz2059, zzz2060, zzz20610, zzz20620, be)
new_mkVBalBranch3MkVBalBranch217(zzz473, zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, zzz481, zzz482, Zero, Zero, bh) → new_mkVBalBranch3MkVBalBranch233(zzz473, zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, zzz481, zzz482, bh)
new_mkVBalBranch3MkVBalBranch216(zzz1105, zzz1106, zzz1107, zzz1108, zzz1109, zzz1110, zzz1111, zzz1112, zzz1113, zzz1114, zzz1115, Succ(zzz11160), Succ(zzz11170), ba) → new_mkVBalBranch3MkVBalBranch216(zzz1105, zzz1106, zzz1107, zzz1108, zzz1109, zzz1110, zzz1111, zzz1112, zzz1113, zzz1114, zzz1115, zzz11160, zzz11170, ba)
new_mkVBalBranch3MkVBalBranch223(zzz340, zzz341, Pos(zzz3420), zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, Succ(zzz670), h) → new_mkVBalBranch0(zzz31, Branch(zzz510, zzz511, Neg(Succ(zzz51200)), zzz513, zzz514), zzz343, h)
new_mkVBalBranch0(zzz31, Branch(zzz510, zzz511, Neg(Zero), zzz513, zzz514), Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), h) → new_mkVBalBranch3MkVBalBranch117(zzz340, zzz341, zzz34200, zzz343, zzz344, zzz510, zzz511, zzz513, zzz514, zzz31, new_primPlusNat2(Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat3(new_primPlusNat1(zzz34200), zzz34200)), zzz34200))), Succ(zzz34200)), h)
new_mkVBalBranch3MkVBalBranch19(zzz340, zzz341, zzz34200, zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, Zero, h) → new_mkVBalBranch3MkVBalBranch122(zzz340, zzz341, zzz34200, zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, h)
new_mkVBalBranch3MkVBalBranch225(zzz498, zzz499, zzz500, zzz501, zzz502, zzz503, zzz504, zzz505, zzz506, zzz507, Succ(zzz5080), Succ(zzz5090), bg) → new_mkVBalBranch3MkVBalBranch225(zzz498, zzz499, zzz500, zzz501, zzz502, zzz503, zzz504, zzz505, zzz506, zzz507, zzz5080, zzz5090, bg)
new_mkVBalBranch3MkVBalBranch19(zzz340, zzz341, zzz34200, zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, Succ(zzz1410), h) → new_mkVBalBranch0(zzz31, zzz514, Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), h)
new_mkVBalBranch3MkVBalBranch224(zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, zzz1125, zzz1126, zzz1127, zzz1128, zzz1129, Zero, Succ(zzz11310), bd) → new_mkVBalBranch3MkVBalBranch227(zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, zzz1125, zzz1126, zzz1127, zzz1128, zzz1129, bd)
new_mkVBalBranch3MkVBalBranch224(zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, zzz1125, zzz1126, zzz1127, zzz1128, zzz1129, Zero, Zero, bd) → new_mkVBalBranch3MkVBalBranch229(zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, zzz1125, zzz1126, zzz1127, zzz1128, zzz1129, bd)
new_mkVBalBranch3MkVBalBranch223(zzz340, zzz341, Neg(Succ(Succ(Succ(zzz3420000)))), zzz343, zzz344, zzz510, zzz511, Succ(zzz512000), zzz513, zzz514, zzz31, Succ(Succ(zzz6700)), h) → new_mkVBalBranch3MkVBalBranch224(zzz340, zzz341, Succ(Succ(zzz3420000)), zzz343, zzz344, zzz510, zzz511, zzz512000, zzz513, zzz514, zzz31, Succ(zzz3420000), Succ(Succ(new_primPlusNat2(zzz6700, zzz512000))), h)
new_mkVBalBranch3MkVBalBranch223(zzz340, zzz341, Neg(Succ(Succ(Zero))), zzz343, zzz344, zzz510, zzz511, Zero, zzz513, zzz514, zzz31, Succ(Succ(zzz6700)), h) → new_mkVBalBranch3MkVBalBranch225(zzz340, zzz341, Succ(Zero), zzz343, zzz344, zzz510, zzz511, zzz513, zzz514, zzz31, Zero, Succ(zzz6700), h)
new_mkVBalBranch3MkVBalBranch115(zzz1986, zzz1987, zzz1988, zzz1989, zzz1990, zzz1991, zzz1992, zzz1993, zzz1994, zzz1995, zzz1996, Succ(zzz19970), Succ(zzz19980), bc) → new_mkVBalBranch3MkVBalBranch115(zzz1986, zzz1987, zzz1988, zzz1989, zzz1990, zzz1991, zzz1992, zzz1993, zzz1994, zzz1995, zzz1996, zzz19970, zzz19980, bc)
new_mkVBalBranch3MkVBalBranch215(zzz340, zzz341, Neg(Zero), zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, Succ(zzz660), h) → new_mkVBalBranch0(zzz31, zzz514, Branch(zzz340, zzz341, Neg(Zero), zzz343, zzz344), h)
new_mkVBalBranch3MkVBalBranch229(zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, zzz1125, zzz1126, zzz1127, zzz1128, zzz1129, bd) → new_mkVBalBranch3MkVBalBranch119(zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, zzz1125, zzz1126, zzz1127, zzz1128, zzz1129, new_primPlusNat2(Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat3(new_primPlusNat1(zzz1121), zzz1121)), zzz1121))), Succ(zzz1121)), bd)
new_mkVBalBranch3MkVBalBranch224(zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, zzz1125, zzz1126, zzz1127, zzz1128, zzz1129, Succ(zzz11300), Zero, bd) → new_mkVBalBranch3MkVBalBranch119(zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, zzz1125, zzz1126, zzz1127, zzz1128, zzz1129, Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat2(Succ(new_primPlusNat3(new_primPlusNat1(zzz1121), zzz1121)), zzz1121)), zzz1121))), bd)
new_mkVBalBranch3MkVBalBranch118(zzz498, zzz499, zzz500, zzz501, zzz502, zzz503, zzz504, zzz505, zzz506, zzz507, Succ(zzz8040), bg) → new_mkVBalBranch3MkVBalBranch120(zzz498, zzz499, zzz500, zzz501, zzz502, zzz503, zzz504, Zero, zzz505, zzz506, zzz507, Succ(Zero), Succ(zzz8040), bg)
new_mkVBalBranch3MkVBalBranch222(zzz461, zzz462, zzz463, zzz464, zzz465, zzz466, zzz467, zzz468, zzz469, zzz470, zzz471, bb) → new_mkVBalBranch3MkVBalBranch110(zzz461, zzz462, zzz463, zzz464, zzz465, zzz466, zzz467, zzz468, zzz469, zzz470, zzz471, Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat2(Succ(new_primPlusNat3(new_primPlusNat1(zzz463), zzz463)), zzz463)), zzz463))), bb)
new_mkVBalBranch3MkVBalBranch216(zzz1105, zzz1106, zzz1107, zzz1108, zzz1109, zzz1110, zzz1111, zzz1112, zzz1113, zzz1114, zzz1115, Succ(zzz11160), Zero, ba) → new_mkVBalBranch3MkVBalBranch218(zzz1105, zzz1106, zzz1107, zzz1108, zzz1109, zzz1110, zzz1111, zzz1112, zzz1113, zzz1114, zzz1115, ba)
new_mkVBalBranch3MkVBalBranch216(zzz1105, zzz1106, zzz1107, zzz1108, zzz1109, zzz1110, zzz1111, zzz1112, zzz1113, zzz1114, zzz1115, Zero, Zero, ba) → new_mkVBalBranch3MkVBalBranch222(zzz1105, zzz1106, zzz1107, zzz1108, zzz1109, zzz1110, zzz1111, zzz1112, zzz1113, zzz1114, zzz1115, ba)
new_mkVBalBranch3MkVBalBranch18(zzz340, zzz341, zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, Zero, h) → new_mkVBalBranch3MkVBalBranch115(zzz340, zzz341, Zero, zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, Zero, Succ(zzz51200), h)
new_mkVBalBranch3MkVBalBranch119(zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, zzz1125, zzz1126, zzz1127, zzz1128, zzz1129, Succ(zzz12130), bd) → new_mkVBalBranch3MkVBalBranch120(zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, zzz1125, Succ(zzz1126), zzz1127, zzz1128, zzz1129, Succ(Succ(zzz1126)), Succ(zzz12130), bd)

The TRS R consists of the following rules:

new_primPlusNat1(Zero) → Zero
new_primPlusNat1(Succ(zzz62000)) → Succ(Succ(new_primPlusNat1(zzz62000)))
new_primPlusNat3(zzz90, Succ(zzz910)) → Succ(Succ(new_primPlusNat2(zzz90, zzz910)))
new_primPlusNat3(zzz90, Zero) → Succ(zzz90)
new_primPlusNat2(Succ(zzz900), Succ(zzz9100)) → Succ(Succ(new_primPlusNat2(zzz900, zzz9100)))
new_primPlusNat2(Zero, Succ(zzz9100)) → Succ(zzz9100)
new_primPlusNat2(Zero, Zero) → Zero
new_primPlusNat2(Succ(zzz900), Zero) → Succ(zzz900)

The set Q consists of the following terms:

new_primPlusNat2(Zero, Succ(x0))
new_primPlusNat3(x0, Succ(x1))
new_primPlusNat2(Succ(x0), Succ(x1))
new_primPlusNat3(x0, Zero)
new_primPlusNat1(Zero)
new_primPlusNat2(Zero, Zero)
new_primPlusNat1(Succ(x0))
new_primPlusNat2(Succ(x0), Zero)

We have to consider all minimal (P,Q,R)-chains.
By rewriting [15] the rule new_mkVBalBranch0(zzz31, Branch(zzz510, zzz511, Neg(Zero), zzz513, zzz514), Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), h) → new_mkVBalBranch3MkVBalBranch117(zzz340, zzz341, zzz34200, zzz343, zzz344, zzz510, zzz511, zzz513, zzz514, zzz31, new_primPlusNat2(Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat3(new_primPlusNat1(zzz34200), zzz34200)), zzz34200))), Succ(zzz34200)), h) at position [10] we obtained the following new rules:

new_mkVBalBranch0(zzz31, Branch(zzz510, zzz511, Neg(Zero), zzz513, zzz514), Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), h) → new_mkVBalBranch3MkVBalBranch117(zzz340, zzz341, zzz34200, zzz343, zzz344, zzz510, zzz511, zzz513, zzz514, zzz31, Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat2(Succ(new_primPlusNat3(new_primPlusNat1(zzz34200), zzz34200)), 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
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                    ↳ DependencyGraphProof
                                      ↳ QDP
                                        ↳ Rewriting
                                          ↳ QDP
                                            ↳ Rewriting
                                              ↳ QDP
                                                ↳ Rewriting
                                                  ↳ QDP
                                                    ↳ Rewriting
                                                      ↳ QDP
                                                        ↳ Rewriting
                                                          ↳ QDP
                                                            ↳ Rewriting
                                                              ↳ QDP
                                                                ↳ Rewriting
                                                                  ↳ QDP
                                                                    ↳ Rewriting
                                                                      ↳ QDP
                                                                        ↳ Rewriting
                                                                          ↳ QDP
                                                                            ↳ Rewriting
                                                                              ↳ QDP
                                                                                ↳ Rewriting
                                                                                  ↳ QDP
                                                                                    ↳ Rewriting
                                                                                      ↳ QDP
                                                                                        ↳ Rewriting
                                                                                          ↳ QDP
                                                                                            ↳ Rewriting
                                                                                              ↳ QDP
                                                                                                ↳ Rewriting
                                                                                                  ↳ QDP
                                                                                                    ↳ Rewriting
                                                                                                      ↳ QDP
                                                                                                        ↳ Rewriting
                                                                                                          ↳ QDP
                                                                                                            ↳ UsableRulesProof
                                                                                                              ↳ QDP
                                                                                                                ↳ QReductionProof
                                                                                                                  ↳ QDP
                                                                                                                    ↳ Rewriting
                                                                                                                      ↳ QDP
                                                                                                                        ↳ Rewriting
                                                                                                                          ↳ QDP
                                                                                                                            ↳ DependencyGraphProof
                                                                                                                              ↳ QDP
                                                                                                                                ↳ Rewriting
                                                                                                                                  ↳ QDP
                                                                                                                                    ↳ Rewriting
                                                                                                                                      ↳ QDP
                                                                                                                                        ↳ DependencyGraphProof
                                                                                                                                          ↳ QDP
                                                                                                                                            ↳ Rewriting
                                                                                                                                              ↳ QDP
                                                                                                                                                ↳ Rewriting
                                                                                                                                                  ↳ QDP
                                                                                                                                                    ↳ Rewriting
                                                                                                                                                      ↳ QDP
                                                                                                                                                        ↳ Rewriting
                                                                                                                                                          ↳ QDP
                                                                                                                                                            ↳ Rewriting
                                                                                                                                                              ↳ QDP
                                                                                                                                                                ↳ Rewriting
                                                                                                                                                                  ↳ QDP
                                                                                                                                                                    ↳ Rewriting
                                                                                                                                                                      ↳ QDP
                                                                                                                                                                        ↳ Rewriting
                                                                                                                                                                          ↳ QDP
                                                                                                                                                                            ↳ Rewriting
                                                                                                                                                                              ↳ QDP
                                                                                                                                                                                ↳ Rewriting
                                                                                                                                                                                  ↳ QDP
                                                                                                                                                                                    ↳ Rewriting
                                                                                                                                                                                      ↳ QDP
                                                                                                                                                                                        ↳ Rewriting
                                                                                                                                                                                          ↳ QDP
                                                                                                                                                                                            ↳ UsableRulesProof
                                                                                                                                                                                              ↳ QDP
                                                                                                                                                                                                ↳ QReductionProof
                                                                                                                                                                                                  ↳ QDP
                                                                                                                                                                                                    ↳ Rewriting
                                                                                                                                                                                                      ↳ QDP
                                                                                                                                                                                                        ↳ Rewriting
                                                                                                                                                                                                          ↳ QDP
                                                                                                                                                                                                            ↳ Rewriting
                                                                                                                                                                                                              ↳ QDP
                                                                                                                                                                                                                ↳ Rewriting
                                                                                                                                                                                                                  ↳ QDP
                                                                                                                                                                                                                    ↳ Rewriting
                                                                                                                                                                                                                      ↳ QDP
                                                                                                                                                                                                                        ↳ Rewriting
                                                                                                                                                                                                                          ↳ QDP
                                                                                                                                                                                                                            ↳ Rewriting
                                                                                                                                                                                                                              ↳ QDP
                                                                                                                                                                                                                                ↳ Rewriting
                                                                                                                                                                                                                                  ↳ QDP
                                                                                                                                                                                                                                    ↳ Rewriting
                                                                                                                                                                                                                                      ↳ QDP
                                                                                                                                                                                                                                        ↳ Rewriting
                                                                                                                                                                                                                                          ↳ QDP
                                                                                                                                                                                                                                            ↳ Rewriting
                                                                                                                                                                                                                                              ↳ QDP
                                                                                                                                                                                                                                                ↳ Rewriting
                                                                                                                                                                                                                                                  ↳ QDP
                                                                                                                                                                                                                                                    ↳ Rewriting
                                                                                                                                                                                                                                                      ↳ QDP
                                                                                                                                                                                                                                                        ↳ Rewriting
                                                                                                                                                                                                                                                          ↳ QDP
                                                                                                                                                                                                                                                            ↳ DependencyGraphProof
                                                                                                                                                                                                                                                              ↳ QDP
                                                                                                                                                                                                                                                                ↳ Rewriting
                                                                                                                                                                                                                                                                  ↳ QDP
                                                                                                                                                                                                                                                                    ↳ Rewriting
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP

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

new_mkVBalBranch3MkVBalBranch225(zzz498, zzz499, zzz500, zzz501, zzz502, zzz503, zzz504, zzz505, zzz506, zzz507, Zero, Zero, bg) → new_mkVBalBranch3MkVBalBranch230(zzz498, zzz499, zzz500, zzz501, zzz502, zzz503, zzz504, zzz505, zzz506, zzz507, bg)
new_mkVBalBranch3MkVBalBranch18(zzz340, zzz341, zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, Succ(zzz1480), h) → new_mkVBalBranch3MkVBalBranch115(zzz340, zzz341, Zero, zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, Succ(zzz1480), Succ(zzz51200), h)
new_mkVBalBranch3MkVBalBranch215(zzz340, zzz341, Pos(Succ(Succ(zzz342000))), zzz343, zzz344, zzz510, zzz511, Succ(zzz512000), zzz513, zzz514, zzz31, Succ(Succ(zzz6600)), h) → new_mkVBalBranch3MkVBalBranch216(zzz340, zzz341, Succ(zzz342000), zzz343, zzz344, zzz510, zzz511, zzz512000, zzz513, zzz514, zzz31, Succ(Succ(new_primPlusNat2(zzz6600, zzz512000))), zzz342000, h)
new_mkVBalBranch0(zzz31, Branch(zzz510, zzz511, Neg(Zero), zzz513, zzz514), Branch(zzz340, zzz341, Pos(Succ(zzz34200)), zzz343, zzz344), h) → new_mkVBalBranch0(zzz31, Branch(zzz510, zzz511, Neg(Zero), zzz513, zzz514), zzz343, h)
new_mkVBalBranch3MkVBalBranch223(zzz340, zzz341, Neg(Succ(Succ(Succ(zzz3420000)))), zzz343, zzz344, zzz510, zzz511, Zero, zzz513, zzz514, zzz31, Succ(Succ(zzz6700)), h) → new_mkVBalBranch3MkVBalBranch225(zzz340, zzz341, Succ(Succ(zzz3420000)), zzz343, zzz344, zzz510, zzz511, zzz513, zzz514, zzz31, Succ(zzz3420000), Succ(zzz6700), h)
new_mkVBalBranch3MkVBalBranch120(zzz2050, zzz2051, zzz2052, zzz2053, zzz2054, zzz2055, zzz2056, zzz2057, zzz2058, zzz2059, zzz2060, Zero, Succ(zzz20620), be) → new_mkVBalBranch0(zzz2060, zzz2059, Branch(zzz2050, zzz2051, Neg(Succ(zzz2052)), zzz2053, zzz2054), be)
new_mkVBalBranch3MkVBalBranch121(zzz473, zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, zzz481, zzz482, Succ(zzz7390), bh) → new_mkVBalBranch3MkVBalBranch115(zzz473, zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, Zero, zzz480, zzz481, zzz482, Succ(zzz7390), Succ(Zero), bh)
new_mkVBalBranch0(zzz31, Branch(zzz510, zzz511, Pos(Zero), zzz513, zzz514), Branch(zzz340, zzz341, Pos(Succ(zzz34200)), zzz343, zzz344), h) → new_mkVBalBranch0(zzz31, Branch(zzz510, zzz511, Pos(Zero), zzz513, zzz514), zzz343, h)
new_mkVBalBranch3MkVBalBranch215(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, Succ(zzz660), h) → new_mkVBalBranch3MkVBalBranch19(zzz340, zzz341, zzz34200, zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, new_primPlusNat2(Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat3(new_primPlusNat1(zzz34200), zzz34200)), zzz34200))), Succ(zzz34200)), h)
new_mkVBalBranch0(zzz31, Branch(zzz510, zzz511, Pos(Succ(zzz51200)), zzz513, zzz514), Branch(zzz340, zzz341, zzz342, zzz343, zzz344), h) → new_mkVBalBranch3MkVBalBranch215(zzz340, zzz341, zzz342, zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat3(new_primPlusNat1(zzz51200), zzz51200)), zzz51200))), h)
new_mkVBalBranch3MkVBalBranch217(zzz473, zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, zzz481, zzz482, Succ(zzz4830), Zero, bh) → new_mkVBalBranch3MkVBalBranch121(zzz473, zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, zzz481, zzz482, new_primPlusNat2(Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat3(new_primPlusNat1(zzz475), zzz475)), zzz475))), Succ(zzz475)), bh)
new_mkVBalBranch3MkVBalBranch230(zzz498, zzz499, zzz500, zzz501, zzz502, zzz503, zzz504, zzz505, zzz506, zzz507, bg) → new_mkVBalBranch3MkVBalBranch118(zzz498, zzz499, zzz500, zzz501, zzz502, zzz503, zzz504, zzz505, zzz506, zzz507, Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat2(Succ(new_primPlusNat3(new_primPlusNat1(zzz500), zzz500)), zzz500)), zzz500))), bg)
new_mkVBalBranch3MkVBalBranch223(zzz340, zzz341, Neg(Succ(Succ(Zero))), zzz343, zzz344, zzz510, zzz511, Succ(zzz512000), zzz513, zzz514, zzz31, Succ(Succ(zzz6700)), h) → new_mkVBalBranch3MkVBalBranch224(zzz340, zzz341, Succ(Zero), zzz343, zzz344, zzz510, zzz511, zzz512000, zzz513, zzz514, zzz31, Zero, Succ(Succ(new_primPlusNat2(zzz6700, zzz512000))), h)
new_mkVBalBranch0(zzz31, Branch(zzz510, zzz511, Neg(Zero), zzz513, zzz514), Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), h) → new_mkVBalBranch3MkVBalBranch117(zzz340, zzz341, zzz34200, zzz343, zzz344, zzz510, zzz511, zzz513, zzz514, zzz31, Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat2(Succ(new_primPlusNat3(new_primPlusNat1(zzz34200), zzz34200)), zzz34200)), zzz34200))), h)
new_mkVBalBranch3MkVBalBranch224(zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, zzz1125, zzz1126, zzz1127, zzz1128, zzz1129, Succ(zzz11300), Succ(zzz11310), bd) → new_mkVBalBranch3MkVBalBranch224(zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, zzz1125, zzz1126, zzz1127, zzz1128, zzz1129, zzz11300, zzz11310, bd)
new_mkVBalBranch3MkVBalBranch217(zzz473, zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, zzz481, zzz482, Zero, Succ(zzz4840), bh) → new_mkVBalBranch0(zzz482, Branch(zzz478, zzz479, Pos(Succ(Zero)), zzz480, zzz481), zzz476, bh)
new_mkVBalBranch3MkVBalBranch218(zzz461, zzz462, zzz463, zzz464, zzz465, zzz466, zzz467, zzz468, zzz469, zzz470, zzz471, bb) → new_mkVBalBranch3MkVBalBranch110(zzz461, zzz462, zzz463, zzz464, zzz465, zzz466, zzz467, zzz468, zzz469, zzz470, zzz471, Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat2(Succ(new_primPlusNat3(new_primPlusNat1(zzz463), zzz463)), zzz463)), zzz463))), bb)
new_mkVBalBranch3MkVBalBranch110(zzz461, zzz462, zzz463, zzz464, zzz465, zzz466, zzz467, zzz468, zzz469, zzz470, zzz471, Succ(zzz5800), bb) → new_mkVBalBranch3MkVBalBranch115(zzz461, zzz462, zzz463, zzz464, zzz465, zzz466, zzz467, Succ(zzz468), zzz469, zzz470, zzz471, Succ(zzz5800), Succ(Succ(zzz468)), bb)
new_mkVBalBranch3MkVBalBranch227(zzz486, zzz487, zzz488, zzz489, zzz490, zzz491, zzz492, zzz493, zzz494, zzz495, zzz496, bf) → new_mkVBalBranch0(zzz496, Branch(zzz491, zzz492, Neg(Succ(Succ(zzz493))), zzz494, zzz495), zzz489, bf)
new_mkVBalBranch3MkVBalBranch215(zzz340, zzz341, Pos(Zero), zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, Succ(zzz660), h) → new_mkVBalBranch0(zzz31, zzz514, Branch(zzz340, zzz341, Pos(Zero), zzz343, zzz344), h)
new_mkVBalBranch3MkVBalBranch223(zzz340, zzz341, Neg(Zero), zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, Succ(zzz670), h) → new_mkVBalBranch0(zzz31, Branch(zzz510, zzz511, Neg(Succ(zzz51200)), zzz513, zzz514), zzz343, h)
new_mkVBalBranch3MkVBalBranch216(zzz1105, zzz1106, zzz1107, zzz1108, zzz1109, zzz1110, zzz1111, zzz1112, zzz1113, zzz1114, zzz1115, Zero, Succ(zzz11170), ba) → new_mkVBalBranch0(zzz1115, Branch(zzz1110, zzz1111, Pos(Succ(Succ(zzz1112))), zzz1113, zzz1114), zzz1108, ba)
new_mkVBalBranch3MkVBalBranch115(zzz1986, zzz1987, zzz1988, zzz1989, zzz1990, zzz1991, zzz1992, zzz1993, zzz1994, zzz1995, zzz1996, Zero, Succ(zzz19980), bc) → new_mkVBalBranch0(zzz1996, zzz1995, Branch(zzz1986, zzz1987, Pos(Succ(zzz1988)), zzz1989, zzz1990), bc)
new_mkVBalBranch3MkVBalBranch233(zzz473, zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, zzz481, zzz482, bh) → new_mkVBalBranch3MkVBalBranch121(zzz473, zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, zzz481, zzz482, new_primPlusNat2(Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat3(new_primPlusNat1(zzz475), zzz475)), zzz475))), Succ(zzz475)), bh)
new_mkVBalBranch3MkVBalBranch215(zzz340, zzz341, Pos(Succ(Zero)), zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, Succ(zzz660), h) → new_mkVBalBranch3MkVBalBranch18(zzz340, zzz341, zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, new_primPlusNat2(Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat3(new_primPlusNat1(Zero), Zero)), Zero))), Succ(Zero)), h)
new_mkVBalBranch3MkVBalBranch122(zzz340, zzz341, zzz34200, zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, h) → new_mkVBalBranch0(zzz31, zzz514, Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), h)
new_mkVBalBranch3MkVBalBranch217(zzz473, zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, zzz481, zzz482, Succ(zzz4830), Succ(zzz4840), bh) → new_mkVBalBranch3MkVBalBranch217(zzz473, zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, zzz481, zzz482, zzz4830, zzz4840, bh)
new_mkVBalBranch3MkVBalBranch116(zzz340, zzz341, zzz34200, zzz343, zzz344, zzz510, zzz511, zzz513, zzz514, zzz31, Succ(zzz1200), h) → new_mkVBalBranch0(zzz31, zzz514, Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), h)
new_mkVBalBranch3MkVBalBranch225(zzz498, zzz499, zzz500, zzz501, zzz502, zzz503, zzz504, zzz505, zzz506, zzz507, Zero, Succ(zzz5090), bg) → new_mkVBalBranch0(zzz507, Branch(zzz503, zzz504, Neg(Succ(Zero)), zzz505, zzz506), zzz501, bg)
new_mkVBalBranch0(zzz31, Branch(zzz510, zzz511, Neg(Succ(zzz51200)), zzz513, zzz514), Branch(zzz340, zzz341, zzz342, zzz343, zzz344), h) → new_mkVBalBranch3MkVBalBranch223(zzz340, zzz341, zzz342, zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat3(new_primPlusNat1(zzz51200), zzz51200)), zzz51200))), h)
new_mkVBalBranch3MkVBalBranch121(zzz473, zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, zzz481, zzz482, Zero, bh) → new_mkVBalBranch3MkVBalBranch115(zzz473, zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, Zero, zzz480, zzz481, zzz482, Zero, Succ(Zero), bh)
new_mkVBalBranch3MkVBalBranch223(zzz340, zzz341, Neg(Succ(Zero)), zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, Succ(zzz670), h) → new_mkVBalBranch0(zzz31, Branch(zzz510, zzz511, Neg(Succ(zzz51200)), zzz513, zzz514), zzz343, h)
new_mkVBalBranch3MkVBalBranch225(zzz498, zzz499, zzz500, zzz501, zzz502, zzz503, zzz504, zzz505, zzz506, zzz507, Succ(zzz5080), Zero, bg) → new_mkVBalBranch3MkVBalBranch118(zzz498, zzz499, zzz500, zzz501, zzz502, zzz503, zzz504, zzz505, zzz506, zzz507, new_primPlusNat2(Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat3(new_primPlusNat1(zzz500), zzz500)), zzz500))), Succ(zzz500)), bg)
new_mkVBalBranch0(zzz31, Branch(zzz510, zzz511, Pos(Zero), zzz513, zzz514), Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), h) → new_mkVBalBranch3MkVBalBranch116(zzz340, zzz341, zzz34200, zzz343, zzz344, zzz510, zzz511, zzz513, zzz514, zzz31, new_primPlusNat2(Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat3(new_primPlusNat1(zzz34200), zzz34200)), zzz34200))), Succ(zzz34200)), h)
new_mkVBalBranch3MkVBalBranch215(zzz340, zzz341, Pos(Succ(Succ(zzz342000))), zzz343, zzz344, zzz510, zzz511, Zero, zzz513, zzz514, zzz31, Succ(Succ(zzz6600)), h) → new_mkVBalBranch3MkVBalBranch217(zzz340, zzz341, Succ(zzz342000), zzz343, zzz344, zzz510, zzz511, zzz513, zzz514, zzz31, Succ(zzz6600), zzz342000, h)
new_mkVBalBranch3MkVBalBranch117(zzz340, zzz341, zzz34200, zzz343, zzz344, zzz510, zzz511, zzz513, zzz514, zzz31, Succ(zzz1240), h) → new_mkVBalBranch0(zzz31, zzz514, Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), h)
new_mkVBalBranch3MkVBalBranch217(zzz473, zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, zzz481, zzz482, Zero, Zero, bh) → new_mkVBalBranch3MkVBalBranch233(zzz473, zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, zzz481, zzz482, bh)
new_mkVBalBranch3MkVBalBranch120(zzz2050, zzz2051, zzz2052, zzz2053, zzz2054, zzz2055, zzz2056, zzz2057, zzz2058, zzz2059, zzz2060, Succ(zzz20610), Succ(zzz20620), be) → new_mkVBalBranch3MkVBalBranch120(zzz2050, zzz2051, zzz2052, zzz2053, zzz2054, zzz2055, zzz2056, zzz2057, zzz2058, zzz2059, zzz2060, zzz20610, zzz20620, be)
new_mkVBalBranch3MkVBalBranch223(zzz340, zzz341, Pos(zzz3420), zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, Succ(zzz670), h) → new_mkVBalBranch0(zzz31, Branch(zzz510, zzz511, Neg(Succ(zzz51200)), zzz513, zzz514), zzz343, h)
new_mkVBalBranch3MkVBalBranch216(zzz1105, zzz1106, zzz1107, zzz1108, zzz1109, zzz1110, zzz1111, zzz1112, zzz1113, zzz1114, zzz1115, Succ(zzz11160), Succ(zzz11170), ba) → new_mkVBalBranch3MkVBalBranch216(zzz1105, zzz1106, zzz1107, zzz1108, zzz1109, zzz1110, zzz1111, zzz1112, zzz1113, zzz1114, zzz1115, zzz11160, zzz11170, ba)
new_mkVBalBranch3MkVBalBranch19(zzz340, zzz341, zzz34200, zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, Zero, h) → new_mkVBalBranch3MkVBalBranch122(zzz340, zzz341, zzz34200, zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, h)
new_mkVBalBranch3MkVBalBranch225(zzz498, zzz499, zzz500, zzz501, zzz502, zzz503, zzz504, zzz505, zzz506, zzz507, Succ(zzz5080), Succ(zzz5090), bg) → new_mkVBalBranch3MkVBalBranch225(zzz498, zzz499, zzz500, zzz501, zzz502, zzz503, zzz504, zzz505, zzz506, zzz507, zzz5080, zzz5090, bg)
new_mkVBalBranch3MkVBalBranch19(zzz340, zzz341, zzz34200, zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, Succ(zzz1410), h) → new_mkVBalBranch0(zzz31, zzz514, Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), h)
new_mkVBalBranch3MkVBalBranch224(zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, zzz1125, zzz1126, zzz1127, zzz1128, zzz1129, Zero, Zero, bd) → new_mkVBalBranch3MkVBalBranch229(zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, zzz1125, zzz1126, zzz1127, zzz1128, zzz1129, bd)
new_mkVBalBranch3MkVBalBranch224(zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, zzz1125, zzz1126, zzz1127, zzz1128, zzz1129, Zero, Succ(zzz11310), bd) → new_mkVBalBranch3MkVBalBranch227(zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, zzz1125, zzz1126, zzz1127, zzz1128, zzz1129, bd)
new_mkVBalBranch3MkVBalBranch223(zzz340, zzz341, Neg(Succ(Succ(Zero))), zzz343, zzz344, zzz510, zzz511, Zero, zzz513, zzz514, zzz31, Succ(Succ(zzz6700)), h) → new_mkVBalBranch3MkVBalBranch225(zzz340, zzz341, Succ(Zero), zzz343, zzz344, zzz510, zzz511, zzz513, zzz514, zzz31, Zero, Succ(zzz6700), h)
new_mkVBalBranch3MkVBalBranch223(zzz340, zzz341, Neg(Succ(Succ(Succ(zzz3420000)))), zzz343, zzz344, zzz510, zzz511, Succ(zzz512000), zzz513, zzz514, zzz31, Succ(Succ(zzz6700)), h) → new_mkVBalBranch3MkVBalBranch224(zzz340, zzz341, Succ(Succ(zzz3420000)), zzz343, zzz344, zzz510, zzz511, zzz512000, zzz513, zzz514, zzz31, Succ(zzz3420000), Succ(Succ(new_primPlusNat2(zzz6700, zzz512000))), h)
new_mkVBalBranch3MkVBalBranch115(zzz1986, zzz1987, zzz1988, zzz1989, zzz1990, zzz1991, zzz1992, zzz1993, zzz1994, zzz1995, zzz1996, Succ(zzz19970), Succ(zzz19980), bc) → new_mkVBalBranch3MkVBalBranch115(zzz1986, zzz1987, zzz1988, zzz1989, zzz1990, zzz1991, zzz1992, zzz1993, zzz1994, zzz1995, zzz1996, zzz19970, zzz19980, bc)
new_mkVBalBranch3MkVBalBranch229(zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, zzz1125, zzz1126, zzz1127, zzz1128, zzz1129, bd) → new_mkVBalBranch3MkVBalBranch119(zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, zzz1125, zzz1126, zzz1127, zzz1128, zzz1129, new_primPlusNat2(Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat3(new_primPlusNat1(zzz1121), zzz1121)), zzz1121))), Succ(zzz1121)), bd)
new_mkVBalBranch3MkVBalBranch215(zzz340, zzz341, Neg(Zero), zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, Succ(zzz660), h) → new_mkVBalBranch0(zzz31, zzz514, Branch(zzz340, zzz341, Neg(Zero), zzz343, zzz344), h)
new_mkVBalBranch3MkVBalBranch224(zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, zzz1125, zzz1126, zzz1127, zzz1128, zzz1129, Succ(zzz11300), Zero, bd) → new_mkVBalBranch3MkVBalBranch119(zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, zzz1125, zzz1126, zzz1127, zzz1128, zzz1129, Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat2(Succ(new_primPlusNat3(new_primPlusNat1(zzz1121), zzz1121)), zzz1121)), zzz1121))), bd)
new_mkVBalBranch3MkVBalBranch222(zzz461, zzz462, zzz463, zzz464, zzz465, zzz466, zzz467, zzz468, zzz469, zzz470, zzz471, bb) → new_mkVBalBranch3MkVBalBranch110(zzz461, zzz462, zzz463, zzz464, zzz465, zzz466, zzz467, zzz468, zzz469, zzz470, zzz471, Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat2(Succ(new_primPlusNat3(new_primPlusNat1(zzz463), zzz463)), zzz463)), zzz463))), bb)
new_mkVBalBranch3MkVBalBranch118(zzz498, zzz499, zzz500, zzz501, zzz502, zzz503, zzz504, zzz505, zzz506, zzz507, Succ(zzz8040), bg) → new_mkVBalBranch3MkVBalBranch120(zzz498, zzz499, zzz500, zzz501, zzz502, zzz503, zzz504, Zero, zzz505, zzz506, zzz507, Succ(Zero), Succ(zzz8040), bg)
new_mkVBalBranch3MkVBalBranch216(zzz1105, zzz1106, zzz1107, zzz1108, zzz1109, zzz1110, zzz1111, zzz1112, zzz1113, zzz1114, zzz1115, Succ(zzz11160), Zero, ba) → new_mkVBalBranch3MkVBalBranch218(zzz1105, zzz1106, zzz1107, zzz1108, zzz1109, zzz1110, zzz1111, zzz1112, zzz1113, zzz1114, zzz1115, ba)
new_mkVBalBranch3MkVBalBranch216(zzz1105, zzz1106, zzz1107, zzz1108, zzz1109, zzz1110, zzz1111, zzz1112, zzz1113, zzz1114, zzz1115, Zero, Zero, ba) → new_mkVBalBranch3MkVBalBranch222(zzz1105, zzz1106, zzz1107, zzz1108, zzz1109, zzz1110, zzz1111, zzz1112, zzz1113, zzz1114, zzz1115, ba)
new_mkVBalBranch3MkVBalBranch119(zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, zzz1125, zzz1126, zzz1127, zzz1128, zzz1129, Succ(zzz12130), bd) → new_mkVBalBranch3MkVBalBranch120(zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, zzz1125, Succ(zzz1126), zzz1127, zzz1128, zzz1129, Succ(Succ(zzz1126)), Succ(zzz12130), bd)
new_mkVBalBranch3MkVBalBranch18(zzz340, zzz341, zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, Zero, h) → new_mkVBalBranch3MkVBalBranch115(zzz340, zzz341, Zero, zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, Zero, Succ(zzz51200), h)

The TRS R consists of the following rules:

new_primPlusNat1(Zero) → Zero
new_primPlusNat1(Succ(zzz62000)) → Succ(Succ(new_primPlusNat1(zzz62000)))
new_primPlusNat3(zzz90, Succ(zzz910)) → Succ(Succ(new_primPlusNat2(zzz90, zzz910)))
new_primPlusNat3(zzz90, Zero) → Succ(zzz90)
new_primPlusNat2(Succ(zzz900), Succ(zzz9100)) → Succ(Succ(new_primPlusNat2(zzz900, zzz9100)))
new_primPlusNat2(Zero, Succ(zzz9100)) → Succ(zzz9100)
new_primPlusNat2(Zero, Zero) → Zero
new_primPlusNat2(Succ(zzz900), Zero) → Succ(zzz900)

The set Q consists of the following terms:

new_primPlusNat2(Zero, Succ(x0))
new_primPlusNat3(x0, Succ(x1))
new_primPlusNat2(Succ(x0), Succ(x1))
new_primPlusNat3(x0, Zero)
new_primPlusNat1(Zero)
new_primPlusNat2(Zero, Zero)
new_primPlusNat1(Succ(x0))
new_primPlusNat2(Succ(x0), Zero)

We have to consider all minimal (P,Q,R)-chains.
By rewriting [15] the rule new_mkVBalBranch3MkVBalBranch225(zzz498, zzz499, zzz500, zzz501, zzz502, zzz503, zzz504, zzz505, zzz506, zzz507, Succ(zzz5080), Zero, bg) → new_mkVBalBranch3MkVBalBranch118(zzz498, zzz499, zzz500, zzz501, zzz502, zzz503, zzz504, zzz505, zzz506, zzz507, new_primPlusNat2(Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat3(new_primPlusNat1(zzz500), zzz500)), zzz500))), Succ(zzz500)), bg) at position [10] we obtained the following new rules:

new_mkVBalBranch3MkVBalBranch225(zzz498, zzz499, zzz500, zzz501, zzz502, zzz503, zzz504, zzz505, zzz506, zzz507, Succ(zzz5080), Zero, bg) → new_mkVBalBranch3MkVBalBranch118(zzz498, zzz499, zzz500, zzz501, zzz502, zzz503, zzz504, zzz505, zzz506, zzz507, Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat2(Succ(new_primPlusNat3(new_primPlusNat1(zzz500), zzz500)), zzz500)), zzz500))), bg)



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

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

new_mkVBalBranch3MkVBalBranch225(zzz498, zzz499, zzz500, zzz501, zzz502, zzz503, zzz504, zzz505, zzz506, zzz507, Zero, Zero, bg) → new_mkVBalBranch3MkVBalBranch230(zzz498, zzz499, zzz500, zzz501, zzz502, zzz503, zzz504, zzz505, zzz506, zzz507, bg)
new_mkVBalBranch3MkVBalBranch18(zzz340, zzz341, zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, Succ(zzz1480), h) → new_mkVBalBranch3MkVBalBranch115(zzz340, zzz341, Zero, zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, Succ(zzz1480), Succ(zzz51200), h)
new_mkVBalBranch0(zzz31, Branch(zzz510, zzz511, Neg(Zero), zzz513, zzz514), Branch(zzz340, zzz341, Pos(Succ(zzz34200)), zzz343, zzz344), h) → new_mkVBalBranch0(zzz31, Branch(zzz510, zzz511, Neg(Zero), zzz513, zzz514), zzz343, h)
new_mkVBalBranch3MkVBalBranch215(zzz340, zzz341, Pos(Succ(Succ(zzz342000))), zzz343, zzz344, zzz510, zzz511, Succ(zzz512000), zzz513, zzz514, zzz31, Succ(Succ(zzz6600)), h) → new_mkVBalBranch3MkVBalBranch216(zzz340, zzz341, Succ(zzz342000), zzz343, zzz344, zzz510, zzz511, zzz512000, zzz513, zzz514, zzz31, Succ(Succ(new_primPlusNat2(zzz6600, zzz512000))), zzz342000, h)
new_mkVBalBranch3MkVBalBranch223(zzz340, zzz341, Neg(Succ(Succ(Succ(zzz3420000)))), zzz343, zzz344, zzz510, zzz511, Zero, zzz513, zzz514, zzz31, Succ(Succ(zzz6700)), h) → new_mkVBalBranch3MkVBalBranch225(zzz340, zzz341, Succ(Succ(zzz3420000)), zzz343, zzz344, zzz510, zzz511, zzz513, zzz514, zzz31, Succ(zzz3420000), Succ(zzz6700), h)
new_mkVBalBranch3MkVBalBranch120(zzz2050, zzz2051, zzz2052, zzz2053, zzz2054, zzz2055, zzz2056, zzz2057, zzz2058, zzz2059, zzz2060, Zero, Succ(zzz20620), be) → new_mkVBalBranch0(zzz2060, zzz2059, Branch(zzz2050, zzz2051, Neg(Succ(zzz2052)), zzz2053, zzz2054), be)
new_mkVBalBranch3MkVBalBranch215(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, Succ(zzz660), h) → new_mkVBalBranch3MkVBalBranch19(zzz340, zzz341, zzz34200, zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, new_primPlusNat2(Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat3(new_primPlusNat1(zzz34200), zzz34200)), zzz34200))), Succ(zzz34200)), h)
new_mkVBalBranch0(zzz31, Branch(zzz510, zzz511, Pos(Zero), zzz513, zzz514), Branch(zzz340, zzz341, Pos(Succ(zzz34200)), zzz343, zzz344), h) → new_mkVBalBranch0(zzz31, Branch(zzz510, zzz511, Pos(Zero), zzz513, zzz514), zzz343, h)
new_mkVBalBranch3MkVBalBranch121(zzz473, zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, zzz481, zzz482, Succ(zzz7390), bh) → new_mkVBalBranch3MkVBalBranch115(zzz473, zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, Zero, zzz480, zzz481, zzz482, Succ(zzz7390), Succ(Zero), bh)
new_mkVBalBranch0(zzz31, Branch(zzz510, zzz511, Pos(Succ(zzz51200)), zzz513, zzz514), Branch(zzz340, zzz341, zzz342, zzz343, zzz344), h) → new_mkVBalBranch3MkVBalBranch215(zzz340, zzz341, zzz342, zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat3(new_primPlusNat1(zzz51200), zzz51200)), zzz51200))), h)
new_mkVBalBranch3MkVBalBranch223(zzz340, zzz341, Neg(Succ(Succ(Zero))), zzz343, zzz344, zzz510, zzz511, Succ(zzz512000), zzz513, zzz514, zzz31, Succ(Succ(zzz6700)), h) → new_mkVBalBranch3MkVBalBranch224(zzz340, zzz341, Succ(Zero), zzz343, zzz344, zzz510, zzz511, zzz512000, zzz513, zzz514, zzz31, Zero, Succ(Succ(new_primPlusNat2(zzz6700, zzz512000))), h)
new_mkVBalBranch3MkVBalBranch230(zzz498, zzz499, zzz500, zzz501, zzz502, zzz503, zzz504, zzz505, zzz506, zzz507, bg) → new_mkVBalBranch3MkVBalBranch118(zzz498, zzz499, zzz500, zzz501, zzz502, zzz503, zzz504, zzz505, zzz506, zzz507, Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat2(Succ(new_primPlusNat3(new_primPlusNat1(zzz500), zzz500)), zzz500)), zzz500))), bg)
new_mkVBalBranch3MkVBalBranch217(zzz473, zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, zzz481, zzz482, Succ(zzz4830), Zero, bh) → new_mkVBalBranch3MkVBalBranch121(zzz473, zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, zzz481, zzz482, new_primPlusNat2(Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat3(new_primPlusNat1(zzz475), zzz475)), zzz475))), Succ(zzz475)), bh)
new_mkVBalBranch0(zzz31, Branch(zzz510, zzz511, Neg(Zero), zzz513, zzz514), Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), h) → new_mkVBalBranch3MkVBalBranch117(zzz340, zzz341, zzz34200, zzz343, zzz344, zzz510, zzz511, zzz513, zzz514, zzz31, Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat2(Succ(new_primPlusNat3(new_primPlusNat1(zzz34200), zzz34200)), zzz34200)), zzz34200))), h)
new_mkVBalBranch3MkVBalBranch224(zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, zzz1125, zzz1126, zzz1127, zzz1128, zzz1129, Succ(zzz11300), Succ(zzz11310), bd) → new_mkVBalBranch3MkVBalBranch224(zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, zzz1125, zzz1126, zzz1127, zzz1128, zzz1129, zzz11300, zzz11310, bd)
new_mkVBalBranch3MkVBalBranch217(zzz473, zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, zzz481, zzz482, Zero, Succ(zzz4840), bh) → new_mkVBalBranch0(zzz482, Branch(zzz478, zzz479, Pos(Succ(Zero)), zzz480, zzz481), zzz476, bh)
new_mkVBalBranch3MkVBalBranch218(zzz461, zzz462, zzz463, zzz464, zzz465, zzz466, zzz467, zzz468, zzz469, zzz470, zzz471, bb) → new_mkVBalBranch3MkVBalBranch110(zzz461, zzz462, zzz463, zzz464, zzz465, zzz466, zzz467, zzz468, zzz469, zzz470, zzz471, Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat2(Succ(new_primPlusNat3(new_primPlusNat1(zzz463), zzz463)), zzz463)), zzz463))), bb)
new_mkVBalBranch3MkVBalBranch110(zzz461, zzz462, zzz463, zzz464, zzz465, zzz466, zzz467, zzz468, zzz469, zzz470, zzz471, Succ(zzz5800), bb) → new_mkVBalBranch3MkVBalBranch115(zzz461, zzz462, zzz463, zzz464, zzz465, zzz466, zzz467, Succ(zzz468), zzz469, zzz470, zzz471, Succ(zzz5800), Succ(Succ(zzz468)), bb)
new_mkVBalBranch3MkVBalBranch227(zzz486, zzz487, zzz488, zzz489, zzz490, zzz491, zzz492, zzz493, zzz494, zzz495, zzz496, bf) → new_mkVBalBranch0(zzz496, Branch(zzz491, zzz492, Neg(Succ(Succ(zzz493))), zzz494, zzz495), zzz489, bf)
new_mkVBalBranch3MkVBalBranch215(zzz340, zzz341, Pos(Zero), zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, Succ(zzz660), h) → new_mkVBalBranch0(zzz31, zzz514, Branch(zzz340, zzz341, Pos(Zero), zzz343, zzz344), h)
new_mkVBalBranch3MkVBalBranch223(zzz340, zzz341, Neg(Zero), zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, Succ(zzz670), h) → new_mkVBalBranch0(zzz31, Branch(zzz510, zzz511, Neg(Succ(zzz51200)), zzz513, zzz514), zzz343, h)
new_mkVBalBranch3MkVBalBranch216(zzz1105, zzz1106, zzz1107, zzz1108, zzz1109, zzz1110, zzz1111, zzz1112, zzz1113, zzz1114, zzz1115, Zero, Succ(zzz11170), ba) → new_mkVBalBranch0(zzz1115, Branch(zzz1110, zzz1111, Pos(Succ(Succ(zzz1112))), zzz1113, zzz1114), zzz1108, ba)
new_mkVBalBranch3MkVBalBranch115(zzz1986, zzz1987, zzz1988, zzz1989, zzz1990, zzz1991, zzz1992, zzz1993, zzz1994, zzz1995, zzz1996, Zero, Succ(zzz19980), bc) → new_mkVBalBranch0(zzz1996, zzz1995, Branch(zzz1986, zzz1987, Pos(Succ(zzz1988)), zzz1989, zzz1990), bc)
new_mkVBalBranch3MkVBalBranch233(zzz473, zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, zzz481, zzz482, bh) → new_mkVBalBranch3MkVBalBranch121(zzz473, zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, zzz481, zzz482, new_primPlusNat2(Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat3(new_primPlusNat1(zzz475), zzz475)), zzz475))), Succ(zzz475)), bh)
new_mkVBalBranch3MkVBalBranch215(zzz340, zzz341, Pos(Succ(Zero)), zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, Succ(zzz660), h) → new_mkVBalBranch3MkVBalBranch18(zzz340, zzz341, zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, new_primPlusNat2(Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat3(new_primPlusNat1(Zero), Zero)), Zero))), Succ(Zero)), h)
new_mkVBalBranch3MkVBalBranch122(zzz340, zzz341, zzz34200, zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, h) → new_mkVBalBranch0(zzz31, zzz514, Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), h)
new_mkVBalBranch3MkVBalBranch217(zzz473, zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, zzz481, zzz482, Succ(zzz4830), Succ(zzz4840), bh) → new_mkVBalBranch3MkVBalBranch217(zzz473, zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, zzz481, zzz482, zzz4830, zzz4840, bh)
new_mkVBalBranch3MkVBalBranch116(zzz340, zzz341, zzz34200, zzz343, zzz344, zzz510, zzz511, zzz513, zzz514, zzz31, Succ(zzz1200), h) → new_mkVBalBranch0(zzz31, zzz514, Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), h)
new_mkVBalBranch3MkVBalBranch225(zzz498, zzz499, zzz500, zzz501, zzz502, zzz503, zzz504, zzz505, zzz506, zzz507, Zero, Succ(zzz5090), bg) → new_mkVBalBranch0(zzz507, Branch(zzz503, zzz504, Neg(Succ(Zero)), zzz505, zzz506), zzz501, bg)
new_mkVBalBranch0(zzz31, Branch(zzz510, zzz511, Neg(Succ(zzz51200)), zzz513, zzz514), Branch(zzz340, zzz341, zzz342, zzz343, zzz344), h) → new_mkVBalBranch3MkVBalBranch223(zzz340, zzz341, zzz342, zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat3(new_primPlusNat1(zzz51200), zzz51200)), zzz51200))), h)
new_mkVBalBranch3MkVBalBranch121(zzz473, zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, zzz481, zzz482, Zero, bh) → new_mkVBalBranch3MkVBalBranch115(zzz473, zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, Zero, zzz480, zzz481, zzz482, Zero, Succ(Zero), bh)
new_mkVBalBranch3MkVBalBranch223(zzz340, zzz341, Neg(Succ(Zero)), zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, Succ(zzz670), h) → new_mkVBalBranch0(zzz31, Branch(zzz510, zzz511, Neg(Succ(zzz51200)), zzz513, zzz514), zzz343, h)
new_mkVBalBranch0(zzz31, Branch(zzz510, zzz511, Pos(Zero), zzz513, zzz514), Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), h) → new_mkVBalBranch3MkVBalBranch116(zzz340, zzz341, zzz34200, zzz343, zzz344, zzz510, zzz511, zzz513, zzz514, zzz31, new_primPlusNat2(Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat3(new_primPlusNat1(zzz34200), zzz34200)), zzz34200))), Succ(zzz34200)), h)
new_mkVBalBranch3MkVBalBranch215(zzz340, zzz341, Pos(Succ(Succ(zzz342000))), zzz343, zzz344, zzz510, zzz511, Zero, zzz513, zzz514, zzz31, Succ(Succ(zzz6600)), h) → new_mkVBalBranch3MkVBalBranch217(zzz340, zzz341, Succ(zzz342000), zzz343, zzz344, zzz510, zzz511, zzz513, zzz514, zzz31, Succ(zzz6600), zzz342000, h)
new_mkVBalBranch3MkVBalBranch117(zzz340, zzz341, zzz34200, zzz343, zzz344, zzz510, zzz511, zzz513, zzz514, zzz31, Succ(zzz1240), h) → new_mkVBalBranch0(zzz31, zzz514, Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), h)
new_mkVBalBranch3MkVBalBranch120(zzz2050, zzz2051, zzz2052, zzz2053, zzz2054, zzz2055, zzz2056, zzz2057, zzz2058, zzz2059, zzz2060, Succ(zzz20610), Succ(zzz20620), be) → new_mkVBalBranch3MkVBalBranch120(zzz2050, zzz2051, zzz2052, zzz2053, zzz2054, zzz2055, zzz2056, zzz2057, zzz2058, zzz2059, zzz2060, zzz20610, zzz20620, be)
new_mkVBalBranch3MkVBalBranch217(zzz473, zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, zzz481, zzz482, Zero, Zero, bh) → new_mkVBalBranch3MkVBalBranch233(zzz473, zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, zzz481, zzz482, bh)
new_mkVBalBranch3MkVBalBranch216(zzz1105, zzz1106, zzz1107, zzz1108, zzz1109, zzz1110, zzz1111, zzz1112, zzz1113, zzz1114, zzz1115, Succ(zzz11160), Succ(zzz11170), ba) → new_mkVBalBranch3MkVBalBranch216(zzz1105, zzz1106, zzz1107, zzz1108, zzz1109, zzz1110, zzz1111, zzz1112, zzz1113, zzz1114, zzz1115, zzz11160, zzz11170, ba)
new_mkVBalBranch3MkVBalBranch223(zzz340, zzz341, Pos(zzz3420), zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, Succ(zzz670), h) → new_mkVBalBranch0(zzz31, Branch(zzz510, zzz511, Neg(Succ(zzz51200)), zzz513, zzz514), zzz343, h)
new_mkVBalBranch3MkVBalBranch19(zzz340, zzz341, zzz34200, zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, Zero, h) → new_mkVBalBranch3MkVBalBranch122(zzz340, zzz341, zzz34200, zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, h)
new_mkVBalBranch3MkVBalBranch225(zzz498, zzz499, zzz500, zzz501, zzz502, zzz503, zzz504, zzz505, zzz506, zzz507, Succ(zzz5080), Succ(zzz5090), bg) → new_mkVBalBranch3MkVBalBranch225(zzz498, zzz499, zzz500, zzz501, zzz502, zzz503, zzz504, zzz505, zzz506, zzz507, zzz5080, zzz5090, bg)
new_mkVBalBranch3MkVBalBranch19(zzz340, zzz341, zzz34200, zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, Succ(zzz1410), h) → new_mkVBalBranch0(zzz31, zzz514, Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), h)
new_mkVBalBranch3MkVBalBranch224(zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, zzz1125, zzz1126, zzz1127, zzz1128, zzz1129, Zero, Succ(zzz11310), bd) → new_mkVBalBranch3MkVBalBranch227(zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, zzz1125, zzz1126, zzz1127, zzz1128, zzz1129, bd)
new_mkVBalBranch3MkVBalBranch224(zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, zzz1125, zzz1126, zzz1127, zzz1128, zzz1129, Zero, Zero, bd) → new_mkVBalBranch3MkVBalBranch229(zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, zzz1125, zzz1126, zzz1127, zzz1128, zzz1129, bd)
new_mkVBalBranch3MkVBalBranch225(zzz498, zzz499, zzz500, zzz501, zzz502, zzz503, zzz504, zzz505, zzz506, zzz507, Succ(zzz5080), Zero, bg) → new_mkVBalBranch3MkVBalBranch118(zzz498, zzz499, zzz500, zzz501, zzz502, zzz503, zzz504, zzz505, zzz506, zzz507, Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat2(Succ(new_primPlusNat3(new_primPlusNat1(zzz500), zzz500)), zzz500)), zzz500))), bg)
new_mkVBalBranch3MkVBalBranch223(zzz340, zzz341, Neg(Succ(Succ(Succ(zzz3420000)))), zzz343, zzz344, zzz510, zzz511, Succ(zzz512000), zzz513, zzz514, zzz31, Succ(Succ(zzz6700)), h) → new_mkVBalBranch3MkVBalBranch224(zzz340, zzz341, Succ(Succ(zzz3420000)), zzz343, zzz344, zzz510, zzz511, zzz512000, zzz513, zzz514, zzz31, Succ(zzz3420000), Succ(Succ(new_primPlusNat2(zzz6700, zzz512000))), h)
new_mkVBalBranch3MkVBalBranch223(zzz340, zzz341, Neg(Succ(Succ(Zero))), zzz343, zzz344, zzz510, zzz511, Zero, zzz513, zzz514, zzz31, Succ(Succ(zzz6700)), h) → new_mkVBalBranch3MkVBalBranch225(zzz340, zzz341, Succ(Zero), zzz343, zzz344, zzz510, zzz511, zzz513, zzz514, zzz31, Zero, Succ(zzz6700), h)
new_mkVBalBranch3MkVBalBranch115(zzz1986, zzz1987, zzz1988, zzz1989, zzz1990, zzz1991, zzz1992, zzz1993, zzz1994, zzz1995, zzz1996, Succ(zzz19970), Succ(zzz19980), bc) → new_mkVBalBranch3MkVBalBranch115(zzz1986, zzz1987, zzz1988, zzz1989, zzz1990, zzz1991, zzz1992, zzz1993, zzz1994, zzz1995, zzz1996, zzz19970, zzz19980, bc)
new_mkVBalBranch3MkVBalBranch215(zzz340, zzz341, Neg(Zero), zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, Succ(zzz660), h) → new_mkVBalBranch0(zzz31, zzz514, Branch(zzz340, zzz341, Neg(Zero), zzz343, zzz344), h)
new_mkVBalBranch3MkVBalBranch229(zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, zzz1125, zzz1126, zzz1127, zzz1128, zzz1129, bd) → new_mkVBalBranch3MkVBalBranch119(zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, zzz1125, zzz1126, zzz1127, zzz1128, zzz1129, new_primPlusNat2(Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat3(new_primPlusNat1(zzz1121), zzz1121)), zzz1121))), Succ(zzz1121)), bd)
new_mkVBalBranch3MkVBalBranch224(zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, zzz1125, zzz1126, zzz1127, zzz1128, zzz1129, Succ(zzz11300), Zero, bd) → new_mkVBalBranch3MkVBalBranch119(zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, zzz1125, zzz1126, zzz1127, zzz1128, zzz1129, Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat2(Succ(new_primPlusNat3(new_primPlusNat1(zzz1121), zzz1121)), zzz1121)), zzz1121))), bd)
new_mkVBalBranch3MkVBalBranch118(zzz498, zzz499, zzz500, zzz501, zzz502, zzz503, zzz504, zzz505, zzz506, zzz507, Succ(zzz8040), bg) → new_mkVBalBranch3MkVBalBranch120(zzz498, zzz499, zzz500, zzz501, zzz502, zzz503, zzz504, Zero, zzz505, zzz506, zzz507, Succ(Zero), Succ(zzz8040), bg)
new_mkVBalBranch3MkVBalBranch222(zzz461, zzz462, zzz463, zzz464, zzz465, zzz466, zzz467, zzz468, zzz469, zzz470, zzz471, bb) → new_mkVBalBranch3MkVBalBranch110(zzz461, zzz462, zzz463, zzz464, zzz465, zzz466, zzz467, zzz468, zzz469, zzz470, zzz471, Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat2(Succ(new_primPlusNat3(new_primPlusNat1(zzz463), zzz463)), zzz463)), zzz463))), bb)
new_mkVBalBranch3MkVBalBranch216(zzz1105, zzz1106, zzz1107, zzz1108, zzz1109, zzz1110, zzz1111, zzz1112, zzz1113, zzz1114, zzz1115, Succ(zzz11160), Zero, ba) → new_mkVBalBranch3MkVBalBranch218(zzz1105, zzz1106, zzz1107, zzz1108, zzz1109, zzz1110, zzz1111, zzz1112, zzz1113, zzz1114, zzz1115, ba)
new_mkVBalBranch3MkVBalBranch216(zzz1105, zzz1106, zzz1107, zzz1108, zzz1109, zzz1110, zzz1111, zzz1112, zzz1113, zzz1114, zzz1115, Zero, Zero, ba) → new_mkVBalBranch3MkVBalBranch222(zzz1105, zzz1106, zzz1107, zzz1108, zzz1109, zzz1110, zzz1111, zzz1112, zzz1113, zzz1114, zzz1115, ba)
new_mkVBalBranch3MkVBalBranch18(zzz340, zzz341, zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, Zero, h) → new_mkVBalBranch3MkVBalBranch115(zzz340, zzz341, Zero, zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, Zero, Succ(zzz51200), h)
new_mkVBalBranch3MkVBalBranch119(zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, zzz1125, zzz1126, zzz1127, zzz1128, zzz1129, Succ(zzz12130), bd) → new_mkVBalBranch3MkVBalBranch120(zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, zzz1125, Succ(zzz1126), zzz1127, zzz1128, zzz1129, Succ(Succ(zzz1126)), Succ(zzz12130), bd)

The TRS R consists of the following rules:

new_primPlusNat1(Zero) → Zero
new_primPlusNat1(Succ(zzz62000)) → Succ(Succ(new_primPlusNat1(zzz62000)))
new_primPlusNat3(zzz90, Succ(zzz910)) → Succ(Succ(new_primPlusNat2(zzz90, zzz910)))
new_primPlusNat3(zzz90, Zero) → Succ(zzz90)
new_primPlusNat2(Succ(zzz900), Succ(zzz9100)) → Succ(Succ(new_primPlusNat2(zzz900, zzz9100)))
new_primPlusNat2(Zero, Succ(zzz9100)) → Succ(zzz9100)
new_primPlusNat2(Zero, Zero) → Zero
new_primPlusNat2(Succ(zzz900), Zero) → Succ(zzz900)

The set Q consists of the following terms:

new_primPlusNat2(Zero, Succ(x0))
new_primPlusNat3(x0, Succ(x1))
new_primPlusNat2(Succ(x0), Succ(x1))
new_primPlusNat3(x0, Zero)
new_primPlusNat1(Zero)
new_primPlusNat2(Zero, Zero)
new_primPlusNat1(Succ(x0))
new_primPlusNat2(Succ(x0), Zero)

We have to consider all minimal (P,Q,R)-chains.
By rewriting [15] the rule new_mkVBalBranch3MkVBalBranch229(zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, zzz1125, zzz1126, zzz1127, zzz1128, zzz1129, bd) → new_mkVBalBranch3MkVBalBranch119(zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, zzz1125, zzz1126, zzz1127, zzz1128, zzz1129, new_primPlusNat2(Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat3(new_primPlusNat1(zzz1121), zzz1121)), zzz1121))), Succ(zzz1121)), bd) at position [11] we obtained the following new rules:

new_mkVBalBranch3MkVBalBranch229(zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, zzz1125, zzz1126, zzz1127, zzz1128, zzz1129, bd) → new_mkVBalBranch3MkVBalBranch119(zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, zzz1125, zzz1126, zzz1127, zzz1128, zzz1129, Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat2(Succ(new_primPlusNat3(new_primPlusNat1(zzz1121), zzz1121)), zzz1121)), zzz1121))), bd)



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

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

new_mkVBalBranch3MkVBalBranch225(zzz498, zzz499, zzz500, zzz501, zzz502, zzz503, zzz504, zzz505, zzz506, zzz507, Zero, Zero, bg) → new_mkVBalBranch3MkVBalBranch230(zzz498, zzz499, zzz500, zzz501, zzz502, zzz503, zzz504, zzz505, zzz506, zzz507, bg)
new_mkVBalBranch3MkVBalBranch18(zzz340, zzz341, zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, Succ(zzz1480), h) → new_mkVBalBranch3MkVBalBranch115(zzz340, zzz341, Zero, zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, Succ(zzz1480), Succ(zzz51200), h)
new_mkVBalBranch3MkVBalBranch215(zzz340, zzz341, Pos(Succ(Succ(zzz342000))), zzz343, zzz344, zzz510, zzz511, Succ(zzz512000), zzz513, zzz514, zzz31, Succ(Succ(zzz6600)), h) → new_mkVBalBranch3MkVBalBranch216(zzz340, zzz341, Succ(zzz342000), zzz343, zzz344, zzz510, zzz511, zzz512000, zzz513, zzz514, zzz31, Succ(Succ(new_primPlusNat2(zzz6600, zzz512000))), zzz342000, h)
new_mkVBalBranch0(zzz31, Branch(zzz510, zzz511, Neg(Zero), zzz513, zzz514), Branch(zzz340, zzz341, Pos(Succ(zzz34200)), zzz343, zzz344), h) → new_mkVBalBranch0(zzz31, Branch(zzz510, zzz511, Neg(Zero), zzz513, zzz514), zzz343, h)
new_mkVBalBranch3MkVBalBranch223(zzz340, zzz341, Neg(Succ(Succ(Succ(zzz3420000)))), zzz343, zzz344, zzz510, zzz511, Zero, zzz513, zzz514, zzz31, Succ(Succ(zzz6700)), h) → new_mkVBalBranch3MkVBalBranch225(zzz340, zzz341, Succ(Succ(zzz3420000)), zzz343, zzz344, zzz510, zzz511, zzz513, zzz514, zzz31, Succ(zzz3420000), Succ(zzz6700), h)
new_mkVBalBranch3MkVBalBranch120(zzz2050, zzz2051, zzz2052, zzz2053, zzz2054, zzz2055, zzz2056, zzz2057, zzz2058, zzz2059, zzz2060, Zero, Succ(zzz20620), be) → new_mkVBalBranch0(zzz2060, zzz2059, Branch(zzz2050, zzz2051, Neg(Succ(zzz2052)), zzz2053, zzz2054), be)
new_mkVBalBranch3MkVBalBranch121(zzz473, zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, zzz481, zzz482, Succ(zzz7390), bh) → new_mkVBalBranch3MkVBalBranch115(zzz473, zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, Zero, zzz480, zzz481, zzz482, Succ(zzz7390), Succ(Zero), bh)
new_mkVBalBranch0(zzz31, Branch(zzz510, zzz511, Pos(Zero), zzz513, zzz514), Branch(zzz340, zzz341, Pos(Succ(zzz34200)), zzz343, zzz344), h) → new_mkVBalBranch0(zzz31, Branch(zzz510, zzz511, Pos(Zero), zzz513, zzz514), zzz343, h)
new_mkVBalBranch3MkVBalBranch215(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, Succ(zzz660), h) → new_mkVBalBranch3MkVBalBranch19(zzz340, zzz341, zzz34200, zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, new_primPlusNat2(Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat3(new_primPlusNat1(zzz34200), zzz34200)), zzz34200))), Succ(zzz34200)), h)
new_mkVBalBranch0(zzz31, Branch(zzz510, zzz511, Pos(Succ(zzz51200)), zzz513, zzz514), Branch(zzz340, zzz341, zzz342, zzz343, zzz344), h) → new_mkVBalBranch3MkVBalBranch215(zzz340, zzz341, zzz342, zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat3(new_primPlusNat1(zzz51200), zzz51200)), zzz51200))), h)
new_mkVBalBranch3MkVBalBranch217(zzz473, zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, zzz481, zzz482, Succ(zzz4830), Zero, bh) → new_mkVBalBranch3MkVBalBranch121(zzz473, zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, zzz481, zzz482, new_primPlusNat2(Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat3(new_primPlusNat1(zzz475), zzz475)), zzz475))), Succ(zzz475)), bh)
new_mkVBalBranch3MkVBalBranch230(zzz498, zzz499, zzz500, zzz501, zzz502, zzz503, zzz504, zzz505, zzz506, zzz507, bg) → new_mkVBalBranch3MkVBalBranch118(zzz498, zzz499, zzz500, zzz501, zzz502, zzz503, zzz504, zzz505, zzz506, zzz507, Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat2(Succ(new_primPlusNat3(new_primPlusNat1(zzz500), zzz500)), zzz500)), zzz500))), bg)
new_mkVBalBranch3MkVBalBranch223(zzz340, zzz341, Neg(Succ(Succ(Zero))), zzz343, zzz344, zzz510, zzz511, Succ(zzz512000), zzz513, zzz514, zzz31, Succ(Succ(zzz6700)), h) → new_mkVBalBranch3MkVBalBranch224(zzz340, zzz341, Succ(Zero), zzz343, zzz344, zzz510, zzz511, zzz512000, zzz513, zzz514, zzz31, Zero, Succ(Succ(new_primPlusNat2(zzz6700, zzz512000))), h)
new_mkVBalBranch0(zzz31, Branch(zzz510, zzz511, Neg(Zero), zzz513, zzz514), Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), h) → new_mkVBalBranch3MkVBalBranch117(zzz340, zzz341, zzz34200, zzz343, zzz344, zzz510, zzz511, zzz513, zzz514, zzz31, Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat2(Succ(new_primPlusNat3(new_primPlusNat1(zzz34200), zzz34200)), zzz34200)), zzz34200))), h)
new_mkVBalBranch3MkVBalBranch224(zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, zzz1125, zzz1126, zzz1127, zzz1128, zzz1129, Succ(zzz11300), Succ(zzz11310), bd) → new_mkVBalBranch3MkVBalBranch224(zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, zzz1125, zzz1126, zzz1127, zzz1128, zzz1129, zzz11300, zzz11310, bd)
new_mkVBalBranch3MkVBalBranch229(zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, zzz1125, zzz1126, zzz1127, zzz1128, zzz1129, bd) → new_mkVBalBranch3MkVBalBranch119(zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, zzz1125, zzz1126, zzz1127, zzz1128, zzz1129, Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat2(Succ(new_primPlusNat3(new_primPlusNat1(zzz1121), zzz1121)), zzz1121)), zzz1121))), bd)
new_mkVBalBranch3MkVBalBranch217(zzz473, zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, zzz481, zzz482, Zero, Succ(zzz4840), bh) → new_mkVBalBranch0(zzz482, Branch(zzz478, zzz479, Pos(Succ(Zero)), zzz480, zzz481), zzz476, bh)
new_mkVBalBranch3MkVBalBranch218(zzz461, zzz462, zzz463, zzz464, zzz465, zzz466, zzz467, zzz468, zzz469, zzz470, zzz471, bb) → new_mkVBalBranch3MkVBalBranch110(zzz461, zzz462, zzz463, zzz464, zzz465, zzz466, zzz467, zzz468, zzz469, zzz470, zzz471, Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat2(Succ(new_primPlusNat3(new_primPlusNat1(zzz463), zzz463)), zzz463)), zzz463))), bb)
new_mkVBalBranch3MkVBalBranch110(zzz461, zzz462, zzz463, zzz464, zzz465, zzz466, zzz467, zzz468, zzz469, zzz470, zzz471, Succ(zzz5800), bb) → new_mkVBalBranch3MkVBalBranch115(zzz461, zzz462, zzz463, zzz464, zzz465, zzz466, zzz467, Succ(zzz468), zzz469, zzz470, zzz471, Succ(zzz5800), Succ(Succ(zzz468)), bb)
new_mkVBalBranch3MkVBalBranch227(zzz486, zzz487, zzz488, zzz489, zzz490, zzz491, zzz492, zzz493, zzz494, zzz495, zzz496, bf) → new_mkVBalBranch0(zzz496, Branch(zzz491, zzz492, Neg(Succ(Succ(zzz493))), zzz494, zzz495), zzz489, bf)
new_mkVBalBranch3MkVBalBranch215(zzz340, zzz341, Pos(Zero), zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, Succ(zzz660), h) → new_mkVBalBranch0(zzz31, zzz514, Branch(zzz340, zzz341, Pos(Zero), zzz343, zzz344), h)
new_mkVBalBranch3MkVBalBranch223(zzz340, zzz341, Neg(Zero), zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, Succ(zzz670), h) → new_mkVBalBranch0(zzz31, Branch(zzz510, zzz511, Neg(Succ(zzz51200)), zzz513, zzz514), zzz343, h)
new_mkVBalBranch3MkVBalBranch216(zzz1105, zzz1106, zzz1107, zzz1108, zzz1109, zzz1110, zzz1111, zzz1112, zzz1113, zzz1114, zzz1115, Zero, Succ(zzz11170), ba) → new_mkVBalBranch0(zzz1115, Branch(zzz1110, zzz1111, Pos(Succ(Succ(zzz1112))), zzz1113, zzz1114), zzz1108, ba)
new_mkVBalBranch3MkVBalBranch115(zzz1986, zzz1987, zzz1988, zzz1989, zzz1990, zzz1991, zzz1992, zzz1993, zzz1994, zzz1995, zzz1996, Zero, Succ(zzz19980), bc) → new_mkVBalBranch0(zzz1996, zzz1995, Branch(zzz1986, zzz1987, Pos(Succ(zzz1988)), zzz1989, zzz1990), bc)
new_mkVBalBranch3MkVBalBranch233(zzz473, zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, zzz481, zzz482, bh) → new_mkVBalBranch3MkVBalBranch121(zzz473, zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, zzz481, zzz482, new_primPlusNat2(Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat3(new_primPlusNat1(zzz475), zzz475)), zzz475))), Succ(zzz475)), bh)
new_mkVBalBranch3MkVBalBranch215(zzz340, zzz341, Pos(Succ(Zero)), zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, Succ(zzz660), h) → new_mkVBalBranch3MkVBalBranch18(zzz340, zzz341, zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, new_primPlusNat2(Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat3(new_primPlusNat1(Zero), Zero)), Zero))), Succ(Zero)), h)
new_mkVBalBranch3MkVBalBranch122(zzz340, zzz341, zzz34200, zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, h) → new_mkVBalBranch0(zzz31, zzz514, Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), h)
new_mkVBalBranch3MkVBalBranch217(zzz473, zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, zzz481, zzz482, Succ(zzz4830), Succ(zzz4840), bh) → new_mkVBalBranch3MkVBalBranch217(zzz473, zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, zzz481, zzz482, zzz4830, zzz4840, bh)
new_mkVBalBranch3MkVBalBranch116(zzz340, zzz341, zzz34200, zzz343, zzz344, zzz510, zzz511, zzz513, zzz514, zzz31, Succ(zzz1200), h) → new_mkVBalBranch0(zzz31, zzz514, Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), h)
new_mkVBalBranch3MkVBalBranch225(zzz498, zzz499, zzz500, zzz501, zzz502, zzz503, zzz504, zzz505, zzz506, zzz507, Zero, Succ(zzz5090), bg) → new_mkVBalBranch0(zzz507, Branch(zzz503, zzz504, Neg(Succ(Zero)), zzz505, zzz506), zzz501, bg)
new_mkVBalBranch0(zzz31, Branch(zzz510, zzz511, Neg(Succ(zzz51200)), zzz513, zzz514), Branch(zzz340, zzz341, zzz342, zzz343, zzz344), h) → new_mkVBalBranch3MkVBalBranch223(zzz340, zzz341, zzz342, zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat3(new_primPlusNat1(zzz51200), zzz51200)), zzz51200))), h)
new_mkVBalBranch3MkVBalBranch121(zzz473, zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, zzz481, zzz482, Zero, bh) → new_mkVBalBranch3MkVBalBranch115(zzz473, zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, Zero, zzz480, zzz481, zzz482, Zero, Succ(Zero), bh)
new_mkVBalBranch3MkVBalBranch223(zzz340, zzz341, Neg(Succ(Zero)), zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, Succ(zzz670), h) → new_mkVBalBranch0(zzz31, Branch(zzz510, zzz511, Neg(Succ(zzz51200)), zzz513, zzz514), zzz343, h)
new_mkVBalBranch0(zzz31, Branch(zzz510, zzz511, Pos(Zero), zzz513, zzz514), Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), h) → new_mkVBalBranch3MkVBalBranch116(zzz340, zzz341, zzz34200, zzz343, zzz344, zzz510, zzz511, zzz513, zzz514, zzz31, new_primPlusNat2(Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat3(new_primPlusNat1(zzz34200), zzz34200)), zzz34200))), Succ(zzz34200)), h)
new_mkVBalBranch3MkVBalBranch215(zzz340, zzz341, Pos(Succ(Succ(zzz342000))), zzz343, zzz344, zzz510, zzz511, Zero, zzz513, zzz514, zzz31, Succ(Succ(zzz6600)), h) → new_mkVBalBranch3MkVBalBranch217(zzz340, zzz341, Succ(zzz342000), zzz343, zzz344, zzz510, zzz511, zzz513, zzz514, zzz31, Succ(zzz6600), zzz342000, h)
new_mkVBalBranch3MkVBalBranch117(zzz340, zzz341, zzz34200, zzz343, zzz344, zzz510, zzz511, zzz513, zzz514, zzz31, Succ(zzz1240), h) → new_mkVBalBranch0(zzz31, zzz514, Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), h)
new_mkVBalBranch3MkVBalBranch217(zzz473, zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, zzz481, zzz482, Zero, Zero, bh) → new_mkVBalBranch3MkVBalBranch233(zzz473, zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, zzz481, zzz482, bh)
new_mkVBalBranch3MkVBalBranch120(zzz2050, zzz2051, zzz2052, zzz2053, zzz2054, zzz2055, zzz2056, zzz2057, zzz2058, zzz2059, zzz2060, Succ(zzz20610), Succ(zzz20620), be) → new_mkVBalBranch3MkVBalBranch120(zzz2050, zzz2051, zzz2052, zzz2053, zzz2054, zzz2055, zzz2056, zzz2057, zzz2058, zzz2059, zzz2060, zzz20610, zzz20620, be)
new_mkVBalBranch3MkVBalBranch223(zzz340, zzz341, Pos(zzz3420), zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, Succ(zzz670), h) → new_mkVBalBranch0(zzz31, Branch(zzz510, zzz511, Neg(Succ(zzz51200)), zzz513, zzz514), zzz343, h)
new_mkVBalBranch3MkVBalBranch216(zzz1105, zzz1106, zzz1107, zzz1108, zzz1109, zzz1110, zzz1111, zzz1112, zzz1113, zzz1114, zzz1115, Succ(zzz11160), Succ(zzz11170), ba) → new_mkVBalBranch3MkVBalBranch216(zzz1105, zzz1106, zzz1107, zzz1108, zzz1109, zzz1110, zzz1111, zzz1112, zzz1113, zzz1114, zzz1115, zzz11160, zzz11170, ba)
new_mkVBalBranch3MkVBalBranch19(zzz340, zzz341, zzz34200, zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, Zero, h) → new_mkVBalBranch3MkVBalBranch122(zzz340, zzz341, zzz34200, zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, h)
new_mkVBalBranch3MkVBalBranch225(zzz498, zzz499, zzz500, zzz501, zzz502, zzz503, zzz504, zzz505, zzz506, zzz507, Succ(zzz5080), Succ(zzz5090), bg) → new_mkVBalBranch3MkVBalBranch225(zzz498, zzz499, zzz500, zzz501, zzz502, zzz503, zzz504, zzz505, zzz506, zzz507, zzz5080, zzz5090, bg)
new_mkVBalBranch3MkVBalBranch19(zzz340, zzz341, zzz34200, zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, Succ(zzz1410), h) → new_mkVBalBranch0(zzz31, zzz514, Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), h)
new_mkVBalBranch3MkVBalBranch224(zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, zzz1125, zzz1126, zzz1127, zzz1128, zzz1129, Zero, Zero, bd) → new_mkVBalBranch3MkVBalBranch229(zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, zzz1125, zzz1126, zzz1127, zzz1128, zzz1129, bd)
new_mkVBalBranch3MkVBalBranch224(zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, zzz1125, zzz1126, zzz1127, zzz1128, zzz1129, Zero, Succ(zzz11310), bd) → new_mkVBalBranch3MkVBalBranch227(zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, zzz1125, zzz1126, zzz1127, zzz1128, zzz1129, bd)
new_mkVBalBranch3MkVBalBranch223(zzz340, zzz341, Neg(Succ(Succ(Zero))), zzz343, zzz344, zzz510, zzz511, Zero, zzz513, zzz514, zzz31, Succ(Succ(zzz6700)), h) → new_mkVBalBranch3MkVBalBranch225(zzz340, zzz341, Succ(Zero), zzz343, zzz344, zzz510, zzz511, zzz513, zzz514, zzz31, Zero, Succ(zzz6700), h)
new_mkVBalBranch3MkVBalBranch223(zzz340, zzz341, Neg(Succ(Succ(Succ(zzz3420000)))), zzz343, zzz344, zzz510, zzz511, Succ(zzz512000), zzz513, zzz514, zzz31, Succ(Succ(zzz6700)), h) → new_mkVBalBranch3MkVBalBranch224(zzz340, zzz341, Succ(Succ(zzz3420000)), zzz343, zzz344, zzz510, zzz511, zzz512000, zzz513, zzz514, zzz31, Succ(zzz3420000), Succ(Succ(new_primPlusNat2(zzz6700, zzz512000))), h)
new_mkVBalBranch3MkVBalBranch225(zzz498, zzz499, zzz500, zzz501, zzz502, zzz503, zzz504, zzz505, zzz506, zzz507, Succ(zzz5080), Zero, bg) → new_mkVBalBranch3MkVBalBranch118(zzz498, zzz499, zzz500, zzz501, zzz502, zzz503, zzz504, zzz505, zzz506, zzz507, Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat2(Succ(new_primPlusNat3(new_primPlusNat1(zzz500), zzz500)), zzz500)), zzz500))), bg)
new_mkVBalBranch3MkVBalBranch115(zzz1986, zzz1987, zzz1988, zzz1989, zzz1990, zzz1991, zzz1992, zzz1993, zzz1994, zzz1995, zzz1996, Succ(zzz19970), Succ(zzz19980), bc) → new_mkVBalBranch3MkVBalBranch115(zzz1986, zzz1987, zzz1988, zzz1989, zzz1990, zzz1991, zzz1992, zzz1993, zzz1994, zzz1995, zzz1996, zzz19970, zzz19980, bc)
new_mkVBalBranch3MkVBalBranch215(zzz340, zzz341, Neg(Zero), zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, Succ(zzz660), h) → new_mkVBalBranch0(zzz31, zzz514, Branch(zzz340, zzz341, Neg(Zero), zzz343, zzz344), h)
new_mkVBalBranch3MkVBalBranch224(zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, zzz1125, zzz1126, zzz1127, zzz1128, zzz1129, Succ(zzz11300), Zero, bd) → new_mkVBalBranch3MkVBalBranch119(zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, zzz1125, zzz1126, zzz1127, zzz1128, zzz1129, Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat2(Succ(new_primPlusNat3(new_primPlusNat1(zzz1121), zzz1121)), zzz1121)), zzz1121))), bd)
new_mkVBalBranch3MkVBalBranch222(zzz461, zzz462, zzz463, zzz464, zzz465, zzz466, zzz467, zzz468, zzz469, zzz470, zzz471, bb) → new_mkVBalBranch3MkVBalBranch110(zzz461, zzz462, zzz463, zzz464, zzz465, zzz466, zzz467, zzz468, zzz469, zzz470, zzz471, Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat2(Succ(new_primPlusNat3(new_primPlusNat1(zzz463), zzz463)), zzz463)), zzz463))), bb)
new_mkVBalBranch3MkVBalBranch118(zzz498, zzz499, zzz500, zzz501, zzz502, zzz503, zzz504, zzz505, zzz506, zzz507, Succ(zzz8040), bg) → new_mkVBalBranch3MkVBalBranch120(zzz498, zzz499, zzz500, zzz501, zzz502, zzz503, zzz504, Zero, zzz505, zzz506, zzz507, Succ(Zero), Succ(zzz8040), bg)
new_mkVBalBranch3MkVBalBranch216(zzz1105, zzz1106, zzz1107, zzz1108, zzz1109, zzz1110, zzz1111, zzz1112, zzz1113, zzz1114, zzz1115, Succ(zzz11160), Zero, ba) → new_mkVBalBranch3MkVBalBranch218(zzz1105, zzz1106, zzz1107, zzz1108, zzz1109, zzz1110, zzz1111, zzz1112, zzz1113, zzz1114, zzz1115, ba)
new_mkVBalBranch3MkVBalBranch216(zzz1105, zzz1106, zzz1107, zzz1108, zzz1109, zzz1110, zzz1111, zzz1112, zzz1113, zzz1114, zzz1115, Zero, Zero, ba) → new_mkVBalBranch3MkVBalBranch222(zzz1105, zzz1106, zzz1107, zzz1108, zzz1109, zzz1110, zzz1111, zzz1112, zzz1113, zzz1114, zzz1115, ba)
new_mkVBalBranch3MkVBalBranch119(zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, zzz1125, zzz1126, zzz1127, zzz1128, zzz1129, Succ(zzz12130), bd) → new_mkVBalBranch3MkVBalBranch120(zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, zzz1125, Succ(zzz1126), zzz1127, zzz1128, zzz1129, Succ(Succ(zzz1126)), Succ(zzz12130), bd)
new_mkVBalBranch3MkVBalBranch18(zzz340, zzz341, zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, Zero, h) → new_mkVBalBranch3MkVBalBranch115(zzz340, zzz341, Zero, zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, Zero, Succ(zzz51200), h)

The TRS R consists of the following rules:

new_primPlusNat1(Zero) → Zero
new_primPlusNat1(Succ(zzz62000)) → Succ(Succ(new_primPlusNat1(zzz62000)))
new_primPlusNat3(zzz90, Succ(zzz910)) → Succ(Succ(new_primPlusNat2(zzz90, zzz910)))
new_primPlusNat3(zzz90, Zero) → Succ(zzz90)
new_primPlusNat2(Succ(zzz900), Succ(zzz9100)) → Succ(Succ(new_primPlusNat2(zzz900, zzz9100)))
new_primPlusNat2(Zero, Succ(zzz9100)) → Succ(zzz9100)
new_primPlusNat2(Zero, Zero) → Zero
new_primPlusNat2(Succ(zzz900), Zero) → Succ(zzz900)

The set Q consists of the following terms:

new_primPlusNat2(Zero, Succ(x0))
new_primPlusNat3(x0, Succ(x1))
new_primPlusNat2(Succ(x0), Succ(x1))
new_primPlusNat3(x0, Zero)
new_primPlusNat1(Zero)
new_primPlusNat2(Zero, Zero)
new_primPlusNat1(Succ(x0))
new_primPlusNat2(Succ(x0), Zero)

We have to consider all minimal (P,Q,R)-chains.
By rewriting [15] the rule new_mkVBalBranch0(zzz31, Branch(zzz510, zzz511, Pos(Zero), zzz513, zzz514), Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), h) → new_mkVBalBranch3MkVBalBranch116(zzz340, zzz341, zzz34200, zzz343, zzz344, zzz510, zzz511, zzz513, zzz514, zzz31, new_primPlusNat2(Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat3(new_primPlusNat1(zzz34200), zzz34200)), zzz34200))), Succ(zzz34200)), h) at position [10] we obtained the following new rules:

new_mkVBalBranch0(zzz31, Branch(zzz510, zzz511, Pos(Zero), zzz513, zzz514), Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), h) → new_mkVBalBranch3MkVBalBranch116(zzz340, zzz341, zzz34200, zzz343, zzz344, zzz510, zzz511, zzz513, zzz514, zzz31, Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat2(Succ(new_primPlusNat3(new_primPlusNat1(zzz34200), zzz34200)), 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
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                    ↳ DependencyGraphProof
                                      ↳ QDP
                                        ↳ Rewriting
                                          ↳ QDP
                                            ↳ Rewriting
                                              ↳ QDP
                                                ↳ Rewriting
                                                  ↳ QDP
                                                    ↳ Rewriting
                                                      ↳ QDP
                                                        ↳ Rewriting
                                                          ↳ QDP
                                                            ↳ Rewriting
                                                              ↳ QDP
                                                                ↳ Rewriting
                                                                  ↳ QDP
                                                                    ↳ Rewriting
                                                                      ↳ QDP
                                                                        ↳ Rewriting
                                                                          ↳ QDP
                                                                            ↳ Rewriting
                                                                              ↳ QDP
                                                                                ↳ Rewriting
                                                                                  ↳ QDP
                                                                                    ↳ Rewriting
                                                                                      ↳ QDP
                                                                                        ↳ Rewriting
                                                                                          ↳ QDP
                                                                                            ↳ Rewriting
                                                                                              ↳ QDP
                                                                                                ↳ Rewriting
                                                                                                  ↳ QDP
                                                                                                    ↳ Rewriting
                                                                                                      ↳ QDP
                                                                                                        ↳ Rewriting
                                                                                                          ↳ QDP
                                                                                                            ↳ UsableRulesProof
                                                                                                              ↳ QDP
                                                                                                                ↳ QReductionProof
                                                                                                                  ↳ QDP
                                                                                                                    ↳ Rewriting
                                                                                                                      ↳ QDP
                                                                                                                        ↳ Rewriting
                                                                                                                          ↳ QDP
                                                                                                                            ↳ DependencyGraphProof
                                                                                                                              ↳ QDP
                                                                                                                                ↳ Rewriting
                                                                                                                                  ↳ QDP
                                                                                                                                    ↳ Rewriting
                                                                                                                                      ↳ QDP
                                                                                                                                        ↳ DependencyGraphProof
                                                                                                                                          ↳ QDP
                                                                                                                                            ↳ Rewriting
                                                                                                                                              ↳ QDP
                                                                                                                                                ↳ Rewriting
                                                                                                                                                  ↳ QDP
                                                                                                                                                    ↳ Rewriting
                                                                                                                                                      ↳ QDP
                                                                                                                                                        ↳ Rewriting
                                                                                                                                                          ↳ QDP
                                                                                                                                                            ↳ Rewriting
                                                                                                                                                              ↳ QDP
                                                                                                                                                                ↳ Rewriting
                                                                                                                                                                  ↳ QDP
                                                                                                                                                                    ↳ Rewriting
                                                                                                                                                                      ↳ QDP
                                                                                                                                                                        ↳ Rewriting
                                                                                                                                                                          ↳ QDP
                                                                                                                                                                            ↳ Rewriting
                                                                                                                                                                              ↳ QDP
                                                                                                                                                                                ↳ Rewriting
                                                                                                                                                                                  ↳ QDP
                                                                                                                                                                                    ↳ Rewriting
                                                                                                                                                                                      ↳ QDP
                                                                                                                                                                                        ↳ Rewriting
                                                                                                                                                                                          ↳ QDP
                                                                                                                                                                                            ↳ UsableRulesProof
                                                                                                                                                                                              ↳ QDP
                                                                                                                                                                                                ↳ QReductionProof
                                                                                                                                                                                                  ↳ QDP
                                                                                                                                                                                                    ↳ Rewriting
                                                                                                                                                                                                      ↳ QDP
                                                                                                                                                                                                        ↳ Rewriting
                                                                                                                                                                                                          ↳ QDP
                                                                                                                                                                                                            ↳ Rewriting
                                                                                                                                                                                                              ↳ QDP
                                                                                                                                                                                                                ↳ Rewriting
                                                                                                                                                                                                                  ↳ QDP
                                                                                                                                                                                                                    ↳ Rewriting
                                                                                                                                                                                                                      ↳ QDP
                                                                                                                                                                                                                        ↳ Rewriting
                                                                                                                                                                                                                          ↳ QDP
                                                                                                                                                                                                                            ↳ Rewriting
                                                                                                                                                                                                                              ↳ QDP
                                                                                                                                                                                                                                ↳ Rewriting
                                                                                                                                                                                                                                  ↳ QDP
                                                                                                                                                                                                                                    ↳ Rewriting
                                                                                                                                                                                                                                      ↳ QDP
                                                                                                                                                                                                                                        ↳ Rewriting
                                                                                                                                                                                                                                          ↳ QDP
                                                                                                                                                                                                                                            ↳ Rewriting
                                                                                                                                                                                                                                              ↳ QDP
                                                                                                                                                                                                                                                ↳ Rewriting
                                                                                                                                                                                                                                                  ↳ QDP
                                                                                                                                                                                                                                                    ↳ Rewriting
                                                                                                                                                                                                                                                      ↳ QDP
                                                                                                                                                                                                                                                        ↳ Rewriting
                                                                                                                                                                                                                                                          ↳ QDP
                                                                                                                                                                                                                                                            ↳ DependencyGraphProof
                                                                                                                                                                                                                                                              ↳ QDP
                                                                                                                                                                                                                                                                ↳ Rewriting
                                                                                                                                                                                                                                                                  ↳ QDP
                                                                                                                                                                                                                                                                    ↳ Rewriting
                                                                                                                                                                                                                                                                      ↳ QDP
                                                                                                                                                                                                                                                                        ↳ Rewriting
                                                                                                                                                                                                                                                                          ↳ QDP
                                                                                                                                                                                                                                                                            ↳ Rewriting
                                                                                                                                                                                                                                                                              ↳ QDP
                                                                                                                                                                                                                                                                                ↳ Rewriting
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP

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

new_mkVBalBranch3MkVBalBranch225(zzz498, zzz499, zzz500, zzz501, zzz502, zzz503, zzz504, zzz505, zzz506, zzz507, Zero, Zero, bg) → new_mkVBalBranch3MkVBalBranch230(zzz498, zzz499, zzz500, zzz501, zzz502, zzz503, zzz504, zzz505, zzz506, zzz507, bg)
new_mkVBalBranch3MkVBalBranch18(zzz340, zzz341, zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, Succ(zzz1480), h) → new_mkVBalBranch3MkVBalBranch115(zzz340, zzz341, Zero, zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, Succ(zzz1480), Succ(zzz51200), h)
new_mkVBalBranch0(zzz31, Branch(zzz510, zzz511, Neg(Zero), zzz513, zzz514), Branch(zzz340, zzz341, Pos(Succ(zzz34200)), zzz343, zzz344), h) → new_mkVBalBranch0(zzz31, Branch(zzz510, zzz511, Neg(Zero), zzz513, zzz514), zzz343, h)
new_mkVBalBranch3MkVBalBranch215(zzz340, zzz341, Pos(Succ(Succ(zzz342000))), zzz343, zzz344, zzz510, zzz511, Succ(zzz512000), zzz513, zzz514, zzz31, Succ(Succ(zzz6600)), h) → new_mkVBalBranch3MkVBalBranch216(zzz340, zzz341, Succ(zzz342000), zzz343, zzz344, zzz510, zzz511, zzz512000, zzz513, zzz514, zzz31, Succ(Succ(new_primPlusNat2(zzz6600, zzz512000))), zzz342000, h)
new_mkVBalBranch3MkVBalBranch223(zzz340, zzz341, Neg(Succ(Succ(Succ(zzz3420000)))), zzz343, zzz344, zzz510, zzz511, Zero, zzz513, zzz514, zzz31, Succ(Succ(zzz6700)), h) → new_mkVBalBranch3MkVBalBranch225(zzz340, zzz341, Succ(Succ(zzz3420000)), zzz343, zzz344, zzz510, zzz511, zzz513, zzz514, zzz31, Succ(zzz3420000), Succ(zzz6700), h)
new_mkVBalBranch3MkVBalBranch120(zzz2050, zzz2051, zzz2052, zzz2053, zzz2054, zzz2055, zzz2056, zzz2057, zzz2058, zzz2059, zzz2060, Zero, Succ(zzz20620), be) → new_mkVBalBranch0(zzz2060, zzz2059, Branch(zzz2050, zzz2051, Neg(Succ(zzz2052)), zzz2053, zzz2054), be)
new_mkVBalBranch3MkVBalBranch215(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, Succ(zzz660), h) → new_mkVBalBranch3MkVBalBranch19(zzz340, zzz341, zzz34200, zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, new_primPlusNat2(Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat3(new_primPlusNat1(zzz34200), zzz34200)), zzz34200))), Succ(zzz34200)), h)
new_mkVBalBranch0(zzz31, Branch(zzz510, zzz511, Pos(Zero), zzz513, zzz514), Branch(zzz340, zzz341, Pos(Succ(zzz34200)), zzz343, zzz344), h) → new_mkVBalBranch0(zzz31, Branch(zzz510, zzz511, Pos(Zero), zzz513, zzz514), zzz343, h)
new_mkVBalBranch3MkVBalBranch121(zzz473, zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, zzz481, zzz482, Succ(zzz7390), bh) → new_mkVBalBranch3MkVBalBranch115(zzz473, zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, Zero, zzz480, zzz481, zzz482, Succ(zzz7390), Succ(Zero), bh)
new_mkVBalBranch0(zzz31, Branch(zzz510, zzz511, Pos(Succ(zzz51200)), zzz513, zzz514), Branch(zzz340, zzz341, zzz342, zzz343, zzz344), h) → new_mkVBalBranch3MkVBalBranch215(zzz340, zzz341, zzz342, zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat3(new_primPlusNat1(zzz51200), zzz51200)), zzz51200))), h)
new_mkVBalBranch3MkVBalBranch223(zzz340, zzz341, Neg(Succ(Succ(Zero))), zzz343, zzz344, zzz510, zzz511, Succ(zzz512000), zzz513, zzz514, zzz31, Succ(Succ(zzz6700)), h) → new_mkVBalBranch3MkVBalBranch224(zzz340, zzz341, Succ(Zero), zzz343, zzz344, zzz510, zzz511, zzz512000, zzz513, zzz514, zzz31, Zero, Succ(Succ(new_primPlusNat2(zzz6700, zzz512000))), h)
new_mkVBalBranch3MkVBalBranch230(zzz498, zzz499, zzz500, zzz501, zzz502, zzz503, zzz504, zzz505, zzz506, zzz507, bg) → new_mkVBalBranch3MkVBalBranch118(zzz498, zzz499, zzz500, zzz501, zzz502, zzz503, zzz504, zzz505, zzz506, zzz507, Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat2(Succ(new_primPlusNat3(new_primPlusNat1(zzz500), zzz500)), zzz500)), zzz500))), bg)
new_mkVBalBranch3MkVBalBranch217(zzz473, zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, zzz481, zzz482, Succ(zzz4830), Zero, bh) → new_mkVBalBranch3MkVBalBranch121(zzz473, zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, zzz481, zzz482, new_primPlusNat2(Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat3(new_primPlusNat1(zzz475), zzz475)), zzz475))), Succ(zzz475)), bh)
new_mkVBalBranch0(zzz31, Branch(zzz510, zzz511, Pos(Zero), zzz513, zzz514), Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), h) → new_mkVBalBranch3MkVBalBranch116(zzz340, zzz341, zzz34200, zzz343, zzz344, zzz510, zzz511, zzz513, zzz514, zzz31, Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat2(Succ(new_primPlusNat3(new_primPlusNat1(zzz34200), zzz34200)), zzz34200)), zzz34200))), h)
new_mkVBalBranch0(zzz31, Branch(zzz510, zzz511, Neg(Zero), zzz513, zzz514), Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), h) → new_mkVBalBranch3MkVBalBranch117(zzz340, zzz341, zzz34200, zzz343, zzz344, zzz510, zzz511, zzz513, zzz514, zzz31, Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat2(Succ(new_primPlusNat3(new_primPlusNat1(zzz34200), zzz34200)), zzz34200)), zzz34200))), h)
new_mkVBalBranch3MkVBalBranch224(zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, zzz1125, zzz1126, zzz1127, zzz1128, zzz1129, Succ(zzz11300), Succ(zzz11310), bd) → new_mkVBalBranch3MkVBalBranch224(zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, zzz1125, zzz1126, zzz1127, zzz1128, zzz1129, zzz11300, zzz11310, bd)
new_mkVBalBranch3MkVBalBranch229(zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, zzz1125, zzz1126, zzz1127, zzz1128, zzz1129, bd) → new_mkVBalBranch3MkVBalBranch119(zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, zzz1125, zzz1126, zzz1127, zzz1128, zzz1129, Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat2(Succ(new_primPlusNat3(new_primPlusNat1(zzz1121), zzz1121)), zzz1121)), zzz1121))), bd)
new_mkVBalBranch3MkVBalBranch217(zzz473, zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, zzz481, zzz482, Zero, Succ(zzz4840), bh) → new_mkVBalBranch0(zzz482, Branch(zzz478, zzz479, Pos(Succ(Zero)), zzz480, zzz481), zzz476, bh)
new_mkVBalBranch3MkVBalBranch218(zzz461, zzz462, zzz463, zzz464, zzz465, zzz466, zzz467, zzz468, zzz469, zzz470, zzz471, bb) → new_mkVBalBranch3MkVBalBranch110(zzz461, zzz462, zzz463, zzz464, zzz465, zzz466, zzz467, zzz468, zzz469, zzz470, zzz471, Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat2(Succ(new_primPlusNat3(new_primPlusNat1(zzz463), zzz463)), zzz463)), zzz463))), bb)
new_mkVBalBranch3MkVBalBranch110(zzz461, zzz462, zzz463, zzz464, zzz465, zzz466, zzz467, zzz468, zzz469, zzz470, zzz471, Succ(zzz5800), bb) → new_mkVBalBranch3MkVBalBranch115(zzz461, zzz462, zzz463, zzz464, zzz465, zzz466, zzz467, Succ(zzz468), zzz469, zzz470, zzz471, Succ(zzz5800), Succ(Succ(zzz468)), bb)
new_mkVBalBranch3MkVBalBranch227(zzz486, zzz487, zzz488, zzz489, zzz490, zzz491, zzz492, zzz493, zzz494, zzz495, zzz496, bf) → new_mkVBalBranch0(zzz496, Branch(zzz491, zzz492, Neg(Succ(Succ(zzz493))), zzz494, zzz495), zzz489, bf)
new_mkVBalBranch3MkVBalBranch215(zzz340, zzz341, Pos(Zero), zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, Succ(zzz660), h) → new_mkVBalBranch0(zzz31, zzz514, Branch(zzz340, zzz341, Pos(Zero), zzz343, zzz344), h)
new_mkVBalBranch3MkVBalBranch223(zzz340, zzz341, Neg(Zero), zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, Succ(zzz670), h) → new_mkVBalBranch0(zzz31, Branch(zzz510, zzz511, Neg(Succ(zzz51200)), zzz513, zzz514), zzz343, h)
new_mkVBalBranch3MkVBalBranch216(zzz1105, zzz1106, zzz1107, zzz1108, zzz1109, zzz1110, zzz1111, zzz1112, zzz1113, zzz1114, zzz1115, Zero, Succ(zzz11170), ba) → new_mkVBalBranch0(zzz1115, Branch(zzz1110, zzz1111, Pos(Succ(Succ(zzz1112))), zzz1113, zzz1114), zzz1108, ba)
new_mkVBalBranch3MkVBalBranch115(zzz1986, zzz1987, zzz1988, zzz1989, zzz1990, zzz1991, zzz1992, zzz1993, zzz1994, zzz1995, zzz1996, Zero, Succ(zzz19980), bc) → new_mkVBalBranch0(zzz1996, zzz1995, Branch(zzz1986, zzz1987, Pos(Succ(zzz1988)), zzz1989, zzz1990), bc)
new_mkVBalBranch3MkVBalBranch233(zzz473, zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, zzz481, zzz482, bh) → new_mkVBalBranch3MkVBalBranch121(zzz473, zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, zzz481, zzz482, new_primPlusNat2(Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat3(new_primPlusNat1(zzz475), zzz475)), zzz475))), Succ(zzz475)), bh)
new_mkVBalBranch3MkVBalBranch215(zzz340, zzz341, Pos(Succ(Zero)), zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, Succ(zzz660), h) → new_mkVBalBranch3MkVBalBranch18(zzz340, zzz341, zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, new_primPlusNat2(Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat3(new_primPlusNat1(Zero), Zero)), Zero))), Succ(Zero)), h)
new_mkVBalBranch3MkVBalBranch122(zzz340, zzz341, zzz34200, zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, h) → new_mkVBalBranch0(zzz31, zzz514, Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), h)
new_mkVBalBranch3MkVBalBranch217(zzz473, zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, zzz481, zzz482, Succ(zzz4830), Succ(zzz4840), bh) → new_mkVBalBranch3MkVBalBranch217(zzz473, zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, zzz481, zzz482, zzz4830, zzz4840, bh)
new_mkVBalBranch3MkVBalBranch116(zzz340, zzz341, zzz34200, zzz343, zzz344, zzz510, zzz511, zzz513, zzz514, zzz31, Succ(zzz1200), h) → new_mkVBalBranch0(zzz31, zzz514, Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), h)
new_mkVBalBranch3MkVBalBranch225(zzz498, zzz499, zzz500, zzz501, zzz502, zzz503, zzz504, zzz505, zzz506, zzz507, Zero, Succ(zzz5090), bg) → new_mkVBalBranch0(zzz507, Branch(zzz503, zzz504, Neg(Succ(Zero)), zzz505, zzz506), zzz501, bg)
new_mkVBalBranch0(zzz31, Branch(zzz510, zzz511, Neg(Succ(zzz51200)), zzz513, zzz514), Branch(zzz340, zzz341, zzz342, zzz343, zzz344), h) → new_mkVBalBranch3MkVBalBranch223(zzz340, zzz341, zzz342, zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat3(new_primPlusNat1(zzz51200), zzz51200)), zzz51200))), h)
new_mkVBalBranch3MkVBalBranch121(zzz473, zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, zzz481, zzz482, Zero, bh) → new_mkVBalBranch3MkVBalBranch115(zzz473, zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, Zero, zzz480, zzz481, zzz482, Zero, Succ(Zero), bh)
new_mkVBalBranch3MkVBalBranch223(zzz340, zzz341, Neg(Succ(Zero)), zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, Succ(zzz670), h) → new_mkVBalBranch0(zzz31, Branch(zzz510, zzz511, Neg(Succ(zzz51200)), zzz513, zzz514), zzz343, h)
new_mkVBalBranch3MkVBalBranch215(zzz340, zzz341, Pos(Succ(Succ(zzz342000))), zzz343, zzz344, zzz510, zzz511, Zero, zzz513, zzz514, zzz31, Succ(Succ(zzz6600)), h) → new_mkVBalBranch3MkVBalBranch217(zzz340, zzz341, Succ(zzz342000), zzz343, zzz344, zzz510, zzz511, zzz513, zzz514, zzz31, Succ(zzz6600), zzz342000, h)
new_mkVBalBranch3MkVBalBranch117(zzz340, zzz341, zzz34200, zzz343, zzz344, zzz510, zzz511, zzz513, zzz514, zzz31, Succ(zzz1240), h) → new_mkVBalBranch0(zzz31, zzz514, Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), h)
new_mkVBalBranch3MkVBalBranch120(zzz2050, zzz2051, zzz2052, zzz2053, zzz2054, zzz2055, zzz2056, zzz2057, zzz2058, zzz2059, zzz2060, Succ(zzz20610), Succ(zzz20620), be) → new_mkVBalBranch3MkVBalBranch120(zzz2050, zzz2051, zzz2052, zzz2053, zzz2054, zzz2055, zzz2056, zzz2057, zzz2058, zzz2059, zzz2060, zzz20610, zzz20620, be)
new_mkVBalBranch3MkVBalBranch217(zzz473, zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, zzz481, zzz482, Zero, Zero, bh) → new_mkVBalBranch3MkVBalBranch233(zzz473, zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, zzz481, zzz482, bh)
new_mkVBalBranch3MkVBalBranch216(zzz1105, zzz1106, zzz1107, zzz1108, zzz1109, zzz1110, zzz1111, zzz1112, zzz1113, zzz1114, zzz1115, Succ(zzz11160), Succ(zzz11170), ba) → new_mkVBalBranch3MkVBalBranch216(zzz1105, zzz1106, zzz1107, zzz1108, zzz1109, zzz1110, zzz1111, zzz1112, zzz1113, zzz1114, zzz1115, zzz11160, zzz11170, ba)
new_mkVBalBranch3MkVBalBranch223(zzz340, zzz341, Pos(zzz3420), zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, Succ(zzz670), h) → new_mkVBalBranch0(zzz31, Branch(zzz510, zzz511, Neg(Succ(zzz51200)), zzz513, zzz514), zzz343, h)
new_mkVBalBranch3MkVBalBranch19(zzz340, zzz341, zzz34200, zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, Zero, h) → new_mkVBalBranch3MkVBalBranch122(zzz340, zzz341, zzz34200, zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, h)
new_mkVBalBranch3MkVBalBranch225(zzz498, zzz499, zzz500, zzz501, zzz502, zzz503, zzz504, zzz505, zzz506, zzz507, Succ(zzz5080), Succ(zzz5090), bg) → new_mkVBalBranch3MkVBalBranch225(zzz498, zzz499, zzz500, zzz501, zzz502, zzz503, zzz504, zzz505, zzz506, zzz507, zzz5080, zzz5090, bg)
new_mkVBalBranch3MkVBalBranch19(zzz340, zzz341, zzz34200, zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, Succ(zzz1410), h) → new_mkVBalBranch0(zzz31, zzz514, Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), h)
new_mkVBalBranch3MkVBalBranch224(zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, zzz1125, zzz1126, zzz1127, zzz1128, zzz1129, Zero, Succ(zzz11310), bd) → new_mkVBalBranch3MkVBalBranch227(zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, zzz1125, zzz1126, zzz1127, zzz1128, zzz1129, bd)
new_mkVBalBranch3MkVBalBranch224(zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, zzz1125, zzz1126, zzz1127, zzz1128, zzz1129, Zero, Zero, bd) → new_mkVBalBranch3MkVBalBranch229(zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, zzz1125, zzz1126, zzz1127, zzz1128, zzz1129, bd)
new_mkVBalBranch3MkVBalBranch225(zzz498, zzz499, zzz500, zzz501, zzz502, zzz503, zzz504, zzz505, zzz506, zzz507, Succ(zzz5080), Zero, bg) → new_mkVBalBranch3MkVBalBranch118(zzz498, zzz499, zzz500, zzz501, zzz502, zzz503, zzz504, zzz505, zzz506, zzz507, Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat2(Succ(new_primPlusNat3(new_primPlusNat1(zzz500), zzz500)), zzz500)), zzz500))), bg)
new_mkVBalBranch3MkVBalBranch223(zzz340, zzz341, Neg(Succ(Succ(Succ(zzz3420000)))), zzz343, zzz344, zzz510, zzz511, Succ(zzz512000), zzz513, zzz514, zzz31, Succ(Succ(zzz6700)), h) → new_mkVBalBranch3MkVBalBranch224(zzz340, zzz341, Succ(Succ(zzz3420000)), zzz343, zzz344, zzz510, zzz511, zzz512000, zzz513, zzz514, zzz31, Succ(zzz3420000), Succ(Succ(new_primPlusNat2(zzz6700, zzz512000))), h)
new_mkVBalBranch3MkVBalBranch223(zzz340, zzz341, Neg(Succ(Succ(Zero))), zzz343, zzz344, zzz510, zzz511, Zero, zzz513, zzz514, zzz31, Succ(Succ(zzz6700)), h) → new_mkVBalBranch3MkVBalBranch225(zzz340, zzz341, Succ(Zero), zzz343, zzz344, zzz510, zzz511, zzz513, zzz514, zzz31, Zero, Succ(zzz6700), h)
new_mkVBalBranch3MkVBalBranch115(zzz1986, zzz1987, zzz1988, zzz1989, zzz1990, zzz1991, zzz1992, zzz1993, zzz1994, zzz1995, zzz1996, Succ(zzz19970), Succ(zzz19980), bc) → new_mkVBalBranch3MkVBalBranch115(zzz1986, zzz1987, zzz1988, zzz1989, zzz1990, zzz1991, zzz1992, zzz1993, zzz1994, zzz1995, zzz1996, zzz19970, zzz19980, bc)
new_mkVBalBranch3MkVBalBranch215(zzz340, zzz341, Neg(Zero), zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, Succ(zzz660), h) → new_mkVBalBranch0(zzz31, zzz514, Branch(zzz340, zzz341, Neg(Zero), zzz343, zzz344), h)
new_mkVBalBranch3MkVBalBranch224(zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, zzz1125, zzz1126, zzz1127, zzz1128, zzz1129, Succ(zzz11300), Zero, bd) → new_mkVBalBranch3MkVBalBranch119(zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, zzz1125, zzz1126, zzz1127, zzz1128, zzz1129, Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat2(Succ(new_primPlusNat3(new_primPlusNat1(zzz1121), zzz1121)), zzz1121)), zzz1121))), bd)
new_mkVBalBranch3MkVBalBranch118(zzz498, zzz499, zzz500, zzz501, zzz502, zzz503, zzz504, zzz505, zzz506, zzz507, Succ(zzz8040), bg) → new_mkVBalBranch3MkVBalBranch120(zzz498, zzz499, zzz500, zzz501, zzz502, zzz503, zzz504, Zero, zzz505, zzz506, zzz507, Succ(Zero), Succ(zzz8040), bg)
new_mkVBalBranch3MkVBalBranch222(zzz461, zzz462, zzz463, zzz464, zzz465, zzz466, zzz467, zzz468, zzz469, zzz470, zzz471, bb) → new_mkVBalBranch3MkVBalBranch110(zzz461, zzz462, zzz463, zzz464, zzz465, zzz466, zzz467, zzz468, zzz469, zzz470, zzz471, Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat2(Succ(new_primPlusNat3(new_primPlusNat1(zzz463), zzz463)), zzz463)), zzz463))), bb)
new_mkVBalBranch3MkVBalBranch216(zzz1105, zzz1106, zzz1107, zzz1108, zzz1109, zzz1110, zzz1111, zzz1112, zzz1113, zzz1114, zzz1115, Succ(zzz11160), Zero, ba) → new_mkVBalBranch3MkVBalBranch218(zzz1105, zzz1106, zzz1107, zzz1108, zzz1109, zzz1110, zzz1111, zzz1112, zzz1113, zzz1114, zzz1115, ba)
new_mkVBalBranch3MkVBalBranch216(zzz1105, zzz1106, zzz1107, zzz1108, zzz1109, zzz1110, zzz1111, zzz1112, zzz1113, zzz1114, zzz1115, Zero, Zero, ba) → new_mkVBalBranch3MkVBalBranch222(zzz1105, zzz1106, zzz1107, zzz1108, zzz1109, zzz1110, zzz1111, zzz1112, zzz1113, zzz1114, zzz1115, ba)
new_mkVBalBranch3MkVBalBranch18(zzz340, zzz341, zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, Zero, h) → new_mkVBalBranch3MkVBalBranch115(zzz340, zzz341, Zero, zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, Zero, Succ(zzz51200), h)
new_mkVBalBranch3MkVBalBranch119(zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, zzz1125, zzz1126, zzz1127, zzz1128, zzz1129, Succ(zzz12130), bd) → new_mkVBalBranch3MkVBalBranch120(zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, zzz1125, Succ(zzz1126), zzz1127, zzz1128, zzz1129, Succ(Succ(zzz1126)), Succ(zzz12130), bd)

The TRS R consists of the following rules:

new_primPlusNat1(Zero) → Zero
new_primPlusNat1(Succ(zzz62000)) → Succ(Succ(new_primPlusNat1(zzz62000)))
new_primPlusNat3(zzz90, Succ(zzz910)) → Succ(Succ(new_primPlusNat2(zzz90, zzz910)))
new_primPlusNat3(zzz90, Zero) → Succ(zzz90)
new_primPlusNat2(Succ(zzz900), Succ(zzz9100)) → Succ(Succ(new_primPlusNat2(zzz900, zzz9100)))
new_primPlusNat2(Zero, Succ(zzz9100)) → Succ(zzz9100)
new_primPlusNat2(Zero, Zero) → Zero
new_primPlusNat2(Succ(zzz900), Zero) → Succ(zzz900)

The set Q consists of the following terms:

new_primPlusNat2(Zero, Succ(x0))
new_primPlusNat3(x0, Succ(x1))
new_primPlusNat2(Succ(x0), Succ(x1))
new_primPlusNat3(x0, Zero)
new_primPlusNat1(Zero)
new_primPlusNat2(Zero, Zero)
new_primPlusNat1(Succ(x0))
new_primPlusNat2(Succ(x0), Zero)

We have to consider all minimal (P,Q,R)-chains.
By rewriting [15] the rule new_mkVBalBranch3MkVBalBranch233(zzz473, zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, zzz481, zzz482, bh) → new_mkVBalBranch3MkVBalBranch121(zzz473, zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, zzz481, zzz482, new_primPlusNat2(Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat3(new_primPlusNat1(zzz475), zzz475)), zzz475))), Succ(zzz475)), bh) at position [10] we obtained the following new rules:

new_mkVBalBranch3MkVBalBranch233(zzz473, zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, zzz481, zzz482, bh) → new_mkVBalBranch3MkVBalBranch121(zzz473, zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, zzz481, zzz482, Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat2(Succ(new_primPlusNat3(new_primPlusNat1(zzz475), zzz475)), zzz475)), zzz475))), bh)



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

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

new_mkVBalBranch3MkVBalBranch225(zzz498, zzz499, zzz500, zzz501, zzz502, zzz503, zzz504, zzz505, zzz506, zzz507, Zero, Zero, bg) → new_mkVBalBranch3MkVBalBranch230(zzz498, zzz499, zzz500, zzz501, zzz502, zzz503, zzz504, zzz505, zzz506, zzz507, bg)
new_mkVBalBranch3MkVBalBranch18(zzz340, zzz341, zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, Succ(zzz1480), h) → new_mkVBalBranch3MkVBalBranch115(zzz340, zzz341, Zero, zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, Succ(zzz1480), Succ(zzz51200), h)
new_mkVBalBranch3MkVBalBranch215(zzz340, zzz341, Pos(Succ(Succ(zzz342000))), zzz343, zzz344, zzz510, zzz511, Succ(zzz512000), zzz513, zzz514, zzz31, Succ(Succ(zzz6600)), h) → new_mkVBalBranch3MkVBalBranch216(zzz340, zzz341, Succ(zzz342000), zzz343, zzz344, zzz510, zzz511, zzz512000, zzz513, zzz514, zzz31, Succ(Succ(new_primPlusNat2(zzz6600, zzz512000))), zzz342000, h)
new_mkVBalBranch0(zzz31, Branch(zzz510, zzz511, Neg(Zero), zzz513, zzz514), Branch(zzz340, zzz341, Pos(Succ(zzz34200)), zzz343, zzz344), h) → new_mkVBalBranch0(zzz31, Branch(zzz510, zzz511, Neg(Zero), zzz513, zzz514), zzz343, h)
new_mkVBalBranch3MkVBalBranch223(zzz340, zzz341, Neg(Succ(Succ(Succ(zzz3420000)))), zzz343, zzz344, zzz510, zzz511, Zero, zzz513, zzz514, zzz31, Succ(Succ(zzz6700)), h) → new_mkVBalBranch3MkVBalBranch225(zzz340, zzz341, Succ(Succ(zzz3420000)), zzz343, zzz344, zzz510, zzz511, zzz513, zzz514, zzz31, Succ(zzz3420000), Succ(zzz6700), h)
new_mkVBalBranch3MkVBalBranch120(zzz2050, zzz2051, zzz2052, zzz2053, zzz2054, zzz2055, zzz2056, zzz2057, zzz2058, zzz2059, zzz2060, Zero, Succ(zzz20620), be) → new_mkVBalBranch0(zzz2060, zzz2059, Branch(zzz2050, zzz2051, Neg(Succ(zzz2052)), zzz2053, zzz2054), be)
new_mkVBalBranch3MkVBalBranch121(zzz473, zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, zzz481, zzz482, Succ(zzz7390), bh) → new_mkVBalBranch3MkVBalBranch115(zzz473, zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, Zero, zzz480, zzz481, zzz482, Succ(zzz7390), Succ(Zero), bh)
new_mkVBalBranch0(zzz31, Branch(zzz510, zzz511, Pos(Zero), zzz513, zzz514), Branch(zzz340, zzz341, Pos(Succ(zzz34200)), zzz343, zzz344), h) → new_mkVBalBranch0(zzz31, Branch(zzz510, zzz511, Pos(Zero), zzz513, zzz514), zzz343, h)
new_mkVBalBranch3MkVBalBranch215(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, Succ(zzz660), h) → new_mkVBalBranch3MkVBalBranch19(zzz340, zzz341, zzz34200, zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, new_primPlusNat2(Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat3(new_primPlusNat1(zzz34200), zzz34200)), zzz34200))), Succ(zzz34200)), h)
new_mkVBalBranch0(zzz31, Branch(zzz510, zzz511, Pos(Succ(zzz51200)), zzz513, zzz514), Branch(zzz340, zzz341, zzz342, zzz343, zzz344), h) → new_mkVBalBranch3MkVBalBranch215(zzz340, zzz341, zzz342, zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat3(new_primPlusNat1(zzz51200), zzz51200)), zzz51200))), h)
new_mkVBalBranch3MkVBalBranch217(zzz473, zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, zzz481, zzz482, Succ(zzz4830), Zero, bh) → new_mkVBalBranch3MkVBalBranch121(zzz473, zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, zzz481, zzz482, new_primPlusNat2(Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat3(new_primPlusNat1(zzz475), zzz475)), zzz475))), Succ(zzz475)), bh)
new_mkVBalBranch3MkVBalBranch230(zzz498, zzz499, zzz500, zzz501, zzz502, zzz503, zzz504, zzz505, zzz506, zzz507, bg) → new_mkVBalBranch3MkVBalBranch118(zzz498, zzz499, zzz500, zzz501, zzz502, zzz503, zzz504, zzz505, zzz506, zzz507, Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat2(Succ(new_primPlusNat3(new_primPlusNat1(zzz500), zzz500)), zzz500)), zzz500))), bg)
new_mkVBalBranch3MkVBalBranch223(zzz340, zzz341, Neg(Succ(Succ(Zero))), zzz343, zzz344, zzz510, zzz511, Succ(zzz512000), zzz513, zzz514, zzz31, Succ(Succ(zzz6700)), h) → new_mkVBalBranch3MkVBalBranch224(zzz340, zzz341, Succ(Zero), zzz343, zzz344, zzz510, zzz511, zzz512000, zzz513, zzz514, zzz31, Zero, Succ(Succ(new_primPlusNat2(zzz6700, zzz512000))), h)
new_mkVBalBranch0(zzz31, Branch(zzz510, zzz511, Pos(Zero), zzz513, zzz514), Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), h) → new_mkVBalBranch3MkVBalBranch116(zzz340, zzz341, zzz34200, zzz343, zzz344, zzz510, zzz511, zzz513, zzz514, zzz31, Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat2(Succ(new_primPlusNat3(new_primPlusNat1(zzz34200), zzz34200)), zzz34200)), zzz34200))), h)
new_mkVBalBranch0(zzz31, Branch(zzz510, zzz511, Neg(Zero), zzz513, zzz514), Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), h) → new_mkVBalBranch3MkVBalBranch117(zzz340, zzz341, zzz34200, zzz343, zzz344, zzz510, zzz511, zzz513, zzz514, zzz31, Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat2(Succ(new_primPlusNat3(new_primPlusNat1(zzz34200), zzz34200)), zzz34200)), zzz34200))), h)
new_mkVBalBranch3MkVBalBranch224(zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, zzz1125, zzz1126, zzz1127, zzz1128, zzz1129, Succ(zzz11300), Succ(zzz11310), bd) → new_mkVBalBranch3MkVBalBranch224(zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, zzz1125, zzz1126, zzz1127, zzz1128, zzz1129, zzz11300, zzz11310, bd)
new_mkVBalBranch3MkVBalBranch229(zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, zzz1125, zzz1126, zzz1127, zzz1128, zzz1129, bd) → new_mkVBalBranch3MkVBalBranch119(zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, zzz1125, zzz1126, zzz1127, zzz1128, zzz1129, Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat2(Succ(new_primPlusNat3(new_primPlusNat1(zzz1121), zzz1121)), zzz1121)), zzz1121))), bd)
new_mkVBalBranch3MkVBalBranch217(zzz473, zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, zzz481, zzz482, Zero, Succ(zzz4840), bh) → new_mkVBalBranch0(zzz482, Branch(zzz478, zzz479, Pos(Succ(Zero)), zzz480, zzz481), zzz476, bh)
new_mkVBalBranch3MkVBalBranch218(zzz461, zzz462, zzz463, zzz464, zzz465, zzz466, zzz467, zzz468, zzz469, zzz470, zzz471, bb) → new_mkVBalBranch3MkVBalBranch110(zzz461, zzz462, zzz463, zzz464, zzz465, zzz466, zzz467, zzz468, zzz469, zzz470, zzz471, Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat2(Succ(new_primPlusNat3(new_primPlusNat1(zzz463), zzz463)), zzz463)), zzz463))), bb)
new_mkVBalBranch3MkVBalBranch110(zzz461, zzz462, zzz463, zzz464, zzz465, zzz466, zzz467, zzz468, zzz469, zzz470, zzz471, Succ(zzz5800), bb) → new_mkVBalBranch3MkVBalBranch115(zzz461, zzz462, zzz463, zzz464, zzz465, zzz466, zzz467, Succ(zzz468), zzz469, zzz470, zzz471, Succ(zzz5800), Succ(Succ(zzz468)), bb)
new_mkVBalBranch3MkVBalBranch227(zzz486, zzz487, zzz488, zzz489, zzz490, zzz491, zzz492, zzz493, zzz494, zzz495, zzz496, bf) → new_mkVBalBranch0(zzz496, Branch(zzz491, zzz492, Neg(Succ(Succ(zzz493))), zzz494, zzz495), zzz489, bf)
new_mkVBalBranch3MkVBalBranch215(zzz340, zzz341, Pos(Zero), zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, Succ(zzz660), h) → new_mkVBalBranch0(zzz31, zzz514, Branch(zzz340, zzz341, Pos(Zero), zzz343, zzz344), h)
new_mkVBalBranch3MkVBalBranch223(zzz340, zzz341, Neg(Zero), zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, Succ(zzz670), h) → new_mkVBalBranch0(zzz31, Branch(zzz510, zzz511, Neg(Succ(zzz51200)), zzz513, zzz514), zzz343, h)
new_mkVBalBranch3MkVBalBranch216(zzz1105, zzz1106, zzz1107, zzz1108, zzz1109, zzz1110, zzz1111, zzz1112, zzz1113, zzz1114, zzz1115, Zero, Succ(zzz11170), ba) → new_mkVBalBranch0(zzz1115, Branch(zzz1110, zzz1111, Pos(Succ(Succ(zzz1112))), zzz1113, zzz1114), zzz1108, ba)
new_mkVBalBranch3MkVBalBranch115(zzz1986, zzz1987, zzz1988, zzz1989, zzz1990, zzz1991, zzz1992, zzz1993, zzz1994, zzz1995, zzz1996, Zero, Succ(zzz19980), bc) → new_mkVBalBranch0(zzz1996, zzz1995, Branch(zzz1986, zzz1987, Pos(Succ(zzz1988)), zzz1989, zzz1990), bc)
new_mkVBalBranch3MkVBalBranch215(zzz340, zzz341, Pos(Succ(Zero)), zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, Succ(zzz660), h) → new_mkVBalBranch3MkVBalBranch18(zzz340, zzz341, zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, new_primPlusNat2(Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat3(new_primPlusNat1(Zero), Zero)), Zero))), Succ(Zero)), h)
new_mkVBalBranch3MkVBalBranch233(zzz473, zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, zzz481, zzz482, bh) → new_mkVBalBranch3MkVBalBranch121(zzz473, zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, zzz481, zzz482, Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat2(Succ(new_primPlusNat3(new_primPlusNat1(zzz475), zzz475)), zzz475)), zzz475))), bh)
new_mkVBalBranch3MkVBalBranch122(zzz340, zzz341, zzz34200, zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, h) → new_mkVBalBranch0(zzz31, zzz514, Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), h)
new_mkVBalBranch3MkVBalBranch217(zzz473, zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, zzz481, zzz482, Succ(zzz4830), Succ(zzz4840), bh) → new_mkVBalBranch3MkVBalBranch217(zzz473, zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, zzz481, zzz482, zzz4830, zzz4840, bh)
new_mkVBalBranch3MkVBalBranch116(zzz340, zzz341, zzz34200, zzz343, zzz344, zzz510, zzz511, zzz513, zzz514, zzz31, Succ(zzz1200), h) → new_mkVBalBranch0(zzz31, zzz514, Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), h)
new_mkVBalBranch3MkVBalBranch225(zzz498, zzz499, zzz500, zzz501, zzz502, zzz503, zzz504, zzz505, zzz506, zzz507, Zero, Succ(zzz5090), bg) → new_mkVBalBranch0(zzz507, Branch(zzz503, zzz504, Neg(Succ(Zero)), zzz505, zzz506), zzz501, bg)
new_mkVBalBranch0(zzz31, Branch(zzz510, zzz511, Neg(Succ(zzz51200)), zzz513, zzz514), Branch(zzz340, zzz341, zzz342, zzz343, zzz344), h) → new_mkVBalBranch3MkVBalBranch223(zzz340, zzz341, zzz342, zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat3(new_primPlusNat1(zzz51200), zzz51200)), zzz51200))), h)
new_mkVBalBranch3MkVBalBranch121(zzz473, zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, zzz481, zzz482, Zero, bh) → new_mkVBalBranch3MkVBalBranch115(zzz473, zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, Zero, zzz480, zzz481, zzz482, Zero, Succ(Zero), bh)
new_mkVBalBranch3MkVBalBranch223(zzz340, zzz341, Neg(Succ(Zero)), zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, Succ(zzz670), h) → new_mkVBalBranch0(zzz31, Branch(zzz510, zzz511, Neg(Succ(zzz51200)), zzz513, zzz514), zzz343, h)
new_mkVBalBranch3MkVBalBranch215(zzz340, zzz341, Pos(Succ(Succ(zzz342000))), zzz343, zzz344, zzz510, zzz511, Zero, zzz513, zzz514, zzz31, Succ(Succ(zzz6600)), h) → new_mkVBalBranch3MkVBalBranch217(zzz340, zzz341, Succ(zzz342000), zzz343, zzz344, zzz510, zzz511, zzz513, zzz514, zzz31, Succ(zzz6600), zzz342000, h)
new_mkVBalBranch3MkVBalBranch117(zzz340, zzz341, zzz34200, zzz343, zzz344, zzz510, zzz511, zzz513, zzz514, zzz31, Succ(zzz1240), h) → new_mkVBalBranch0(zzz31, zzz514, Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), h)
new_mkVBalBranch3MkVBalBranch217(zzz473, zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, zzz481, zzz482, Zero, Zero, bh) → new_mkVBalBranch3MkVBalBranch233(zzz473, zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, zzz481, zzz482, bh)
new_mkVBalBranch3MkVBalBranch120(zzz2050, zzz2051, zzz2052, zzz2053, zzz2054, zzz2055, zzz2056, zzz2057, zzz2058, zzz2059, zzz2060, Succ(zzz20610), Succ(zzz20620), be) → new_mkVBalBranch3MkVBalBranch120(zzz2050, zzz2051, zzz2052, zzz2053, zzz2054, zzz2055, zzz2056, zzz2057, zzz2058, zzz2059, zzz2060, zzz20610, zzz20620, be)
new_mkVBalBranch3MkVBalBranch223(zzz340, zzz341, Pos(zzz3420), zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, Succ(zzz670), h) → new_mkVBalBranch0(zzz31, Branch(zzz510, zzz511, Neg(Succ(zzz51200)), zzz513, zzz514), zzz343, h)
new_mkVBalBranch3MkVBalBranch216(zzz1105, zzz1106, zzz1107, zzz1108, zzz1109, zzz1110, zzz1111, zzz1112, zzz1113, zzz1114, zzz1115, Succ(zzz11160), Succ(zzz11170), ba) → new_mkVBalBranch3MkVBalBranch216(zzz1105, zzz1106, zzz1107, zzz1108, zzz1109, zzz1110, zzz1111, zzz1112, zzz1113, zzz1114, zzz1115, zzz11160, zzz11170, ba)
new_mkVBalBranch3MkVBalBranch19(zzz340, zzz341, zzz34200, zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, Zero, h) → new_mkVBalBranch3MkVBalBranch122(zzz340, zzz341, zzz34200, zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, h)
new_mkVBalBranch3MkVBalBranch225(zzz498, zzz499, zzz500, zzz501, zzz502, zzz503, zzz504, zzz505, zzz506, zzz507, Succ(zzz5080), Succ(zzz5090), bg) → new_mkVBalBranch3MkVBalBranch225(zzz498, zzz499, zzz500, zzz501, zzz502, zzz503, zzz504, zzz505, zzz506, zzz507, zzz5080, zzz5090, bg)
new_mkVBalBranch3MkVBalBranch19(zzz340, zzz341, zzz34200, zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, Succ(zzz1410), h) → new_mkVBalBranch0(zzz31, zzz514, Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), h)
new_mkVBalBranch3MkVBalBranch224(zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, zzz1125, zzz1126, zzz1127, zzz1128, zzz1129, Zero, Zero, bd) → new_mkVBalBranch3MkVBalBranch229(zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, zzz1125, zzz1126, zzz1127, zzz1128, zzz1129, bd)
new_mkVBalBranch3MkVBalBranch224(zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, zzz1125, zzz1126, zzz1127, zzz1128, zzz1129, Zero, Succ(zzz11310), bd) → new_mkVBalBranch3MkVBalBranch227(zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, zzz1125, zzz1126, zzz1127, zzz1128, zzz1129, bd)
new_mkVBalBranch3MkVBalBranch223(zzz340, zzz341, Neg(Succ(Succ(Zero))), zzz343, zzz344, zzz510, zzz511, Zero, zzz513, zzz514, zzz31, Succ(Succ(zzz6700)), h) → new_mkVBalBranch3MkVBalBranch225(zzz340, zzz341, Succ(Zero), zzz343, zzz344, zzz510, zzz511, zzz513, zzz514, zzz31, Zero, Succ(zzz6700), h)
new_mkVBalBranch3MkVBalBranch223(zzz340, zzz341, Neg(Succ(Succ(Succ(zzz3420000)))), zzz343, zzz344, zzz510, zzz511, Succ(zzz512000), zzz513, zzz514, zzz31, Succ(Succ(zzz6700)), h) → new_mkVBalBranch3MkVBalBranch224(zzz340, zzz341, Succ(Succ(zzz3420000)), zzz343, zzz344, zzz510, zzz511, zzz512000, zzz513, zzz514, zzz31, Succ(zzz3420000), Succ(Succ(new_primPlusNat2(zzz6700, zzz512000))), h)
new_mkVBalBranch3MkVBalBranch225(zzz498, zzz499, zzz500, zzz501, zzz502, zzz503, zzz504, zzz505, zzz506, zzz507, Succ(zzz5080), Zero, bg) → new_mkVBalBranch3MkVBalBranch118(zzz498, zzz499, zzz500, zzz501, zzz502, zzz503, zzz504, zzz505, zzz506, zzz507, Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat2(Succ(new_primPlusNat3(new_primPlusNat1(zzz500), zzz500)), zzz500)), zzz500))), bg)
new_mkVBalBranch3MkVBalBranch115(zzz1986, zzz1987, zzz1988, zzz1989, zzz1990, zzz1991, zzz1992, zzz1993, zzz1994, zzz1995, zzz1996, Succ(zzz19970), Succ(zzz19980), bc) → new_mkVBalBranch3MkVBalBranch115(zzz1986, zzz1987, zzz1988, zzz1989, zzz1990, zzz1991, zzz1992, zzz1993, zzz1994, zzz1995, zzz1996, zzz19970, zzz19980, bc)
new_mkVBalBranch3MkVBalBranch215(zzz340, zzz341, Neg(Zero), zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, Succ(zzz660), h) → new_mkVBalBranch0(zzz31, zzz514, Branch(zzz340, zzz341, Neg(Zero), zzz343, zzz344), h)
new_mkVBalBranch3MkVBalBranch224(zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, zzz1125, zzz1126, zzz1127, zzz1128, zzz1129, Succ(zzz11300), Zero, bd) → new_mkVBalBranch3MkVBalBranch119(zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, zzz1125, zzz1126, zzz1127, zzz1128, zzz1129, Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat2(Succ(new_primPlusNat3(new_primPlusNat1(zzz1121), zzz1121)), zzz1121)), zzz1121))), bd)
new_mkVBalBranch3MkVBalBranch222(zzz461, zzz462, zzz463, zzz464, zzz465, zzz466, zzz467, zzz468, zzz469, zzz470, zzz471, bb) → new_mkVBalBranch3MkVBalBranch110(zzz461, zzz462, zzz463, zzz464, zzz465, zzz466, zzz467, zzz468, zzz469, zzz470, zzz471, Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat2(Succ(new_primPlusNat3(new_primPlusNat1(zzz463), zzz463)), zzz463)), zzz463))), bb)
new_mkVBalBranch3MkVBalBranch118(zzz498, zzz499, zzz500, zzz501, zzz502, zzz503, zzz504, zzz505, zzz506, zzz507, Succ(zzz8040), bg) → new_mkVBalBranch3MkVBalBranch120(zzz498, zzz499, zzz500, zzz501, zzz502, zzz503, zzz504, Zero, zzz505, zzz506, zzz507, Succ(Zero), Succ(zzz8040), bg)
new_mkVBalBranch3MkVBalBranch216(zzz1105, zzz1106, zzz1107, zzz1108, zzz1109, zzz1110, zzz1111, zzz1112, zzz1113, zzz1114, zzz1115, Succ(zzz11160), Zero, ba) → new_mkVBalBranch3MkVBalBranch218(zzz1105, zzz1106, zzz1107, zzz1108, zzz1109, zzz1110, zzz1111, zzz1112, zzz1113, zzz1114, zzz1115, ba)
new_mkVBalBranch3MkVBalBranch216(zzz1105, zzz1106, zzz1107, zzz1108, zzz1109, zzz1110, zzz1111, zzz1112, zzz1113, zzz1114, zzz1115, Zero, Zero, ba) → new_mkVBalBranch3MkVBalBranch222(zzz1105, zzz1106, zzz1107, zzz1108, zzz1109, zzz1110, zzz1111, zzz1112, zzz1113, zzz1114, zzz1115, ba)
new_mkVBalBranch3MkVBalBranch119(zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, zzz1125, zzz1126, zzz1127, zzz1128, zzz1129, Succ(zzz12130), bd) → new_mkVBalBranch3MkVBalBranch120(zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, zzz1125, Succ(zzz1126), zzz1127, zzz1128, zzz1129, Succ(Succ(zzz1126)), Succ(zzz12130), bd)
new_mkVBalBranch3MkVBalBranch18(zzz340, zzz341, zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, Zero, h) → new_mkVBalBranch3MkVBalBranch115(zzz340, zzz341, Zero, zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, Zero, Succ(zzz51200), h)

The TRS R consists of the following rules:

new_primPlusNat1(Zero) → Zero
new_primPlusNat1(Succ(zzz62000)) → Succ(Succ(new_primPlusNat1(zzz62000)))
new_primPlusNat3(zzz90, Succ(zzz910)) → Succ(Succ(new_primPlusNat2(zzz90, zzz910)))
new_primPlusNat3(zzz90, Zero) → Succ(zzz90)
new_primPlusNat2(Succ(zzz900), Succ(zzz9100)) → Succ(Succ(new_primPlusNat2(zzz900, zzz9100)))
new_primPlusNat2(Zero, Succ(zzz9100)) → Succ(zzz9100)
new_primPlusNat2(Zero, Zero) → Zero
new_primPlusNat2(Succ(zzz900), Zero) → Succ(zzz900)

The set Q consists of the following terms:

new_primPlusNat2(Zero, Succ(x0))
new_primPlusNat3(x0, Succ(x1))
new_primPlusNat2(Succ(x0), Succ(x1))
new_primPlusNat3(x0, Zero)
new_primPlusNat1(Zero)
new_primPlusNat2(Zero, Zero)
new_primPlusNat1(Succ(x0))
new_primPlusNat2(Succ(x0), Zero)

We have to consider all minimal (P,Q,R)-chains.
By rewriting [15] the rule new_mkVBalBranch3MkVBalBranch217(zzz473, zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, zzz481, zzz482, Succ(zzz4830), Zero, bh) → new_mkVBalBranch3MkVBalBranch121(zzz473, zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, zzz481, zzz482, new_primPlusNat2(Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat3(new_primPlusNat1(zzz475), zzz475)), zzz475))), Succ(zzz475)), bh) at position [10] we obtained the following new rules:

new_mkVBalBranch3MkVBalBranch217(zzz473, zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, zzz481, zzz482, Succ(zzz4830), Zero, bh) → new_mkVBalBranch3MkVBalBranch121(zzz473, zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, zzz481, zzz482, Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat2(Succ(new_primPlusNat3(new_primPlusNat1(zzz475), zzz475)), zzz475)), zzz475))), bh)



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

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

new_mkVBalBranch3MkVBalBranch225(zzz498, zzz499, zzz500, zzz501, zzz502, zzz503, zzz504, zzz505, zzz506, zzz507, Zero, Zero, bg) → new_mkVBalBranch3MkVBalBranch230(zzz498, zzz499, zzz500, zzz501, zzz502, zzz503, zzz504, zzz505, zzz506, zzz507, bg)
new_mkVBalBranch3MkVBalBranch18(zzz340, zzz341, zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, Succ(zzz1480), h) → new_mkVBalBranch3MkVBalBranch115(zzz340, zzz341, Zero, zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, Succ(zzz1480), Succ(zzz51200), h)
new_mkVBalBranch0(zzz31, Branch(zzz510, zzz511, Neg(Zero), zzz513, zzz514), Branch(zzz340, zzz341, Pos(Succ(zzz34200)), zzz343, zzz344), h) → new_mkVBalBranch0(zzz31, Branch(zzz510, zzz511, Neg(Zero), zzz513, zzz514), zzz343, h)
new_mkVBalBranch3MkVBalBranch215(zzz340, zzz341, Pos(Succ(Succ(zzz342000))), zzz343, zzz344, zzz510, zzz511, Succ(zzz512000), zzz513, zzz514, zzz31, Succ(Succ(zzz6600)), h) → new_mkVBalBranch3MkVBalBranch216(zzz340, zzz341, Succ(zzz342000), zzz343, zzz344, zzz510, zzz511, zzz512000, zzz513, zzz514, zzz31, Succ(Succ(new_primPlusNat2(zzz6600, zzz512000))), zzz342000, h)
new_mkVBalBranch3MkVBalBranch223(zzz340, zzz341, Neg(Succ(Succ(Succ(zzz3420000)))), zzz343, zzz344, zzz510, zzz511, Zero, zzz513, zzz514, zzz31, Succ(Succ(zzz6700)), h) → new_mkVBalBranch3MkVBalBranch225(zzz340, zzz341, Succ(Succ(zzz3420000)), zzz343, zzz344, zzz510, zzz511, zzz513, zzz514, zzz31, Succ(zzz3420000), Succ(zzz6700), h)
new_mkVBalBranch3MkVBalBranch120(zzz2050, zzz2051, zzz2052, zzz2053, zzz2054, zzz2055, zzz2056, zzz2057, zzz2058, zzz2059, zzz2060, Zero, Succ(zzz20620), be) → new_mkVBalBranch0(zzz2060, zzz2059, Branch(zzz2050, zzz2051, Neg(Succ(zzz2052)), zzz2053, zzz2054), be)
new_mkVBalBranch3MkVBalBranch215(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, Succ(zzz660), h) → new_mkVBalBranch3MkVBalBranch19(zzz340, zzz341, zzz34200, zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, new_primPlusNat2(Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat3(new_primPlusNat1(zzz34200), zzz34200)), zzz34200))), Succ(zzz34200)), h)
new_mkVBalBranch0(zzz31, Branch(zzz510, zzz511, Pos(Zero), zzz513, zzz514), Branch(zzz340, zzz341, Pos(Succ(zzz34200)), zzz343, zzz344), h) → new_mkVBalBranch0(zzz31, Branch(zzz510, zzz511, Pos(Zero), zzz513, zzz514), zzz343, h)
new_mkVBalBranch3MkVBalBranch121(zzz473, zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, zzz481, zzz482, Succ(zzz7390), bh) → new_mkVBalBranch3MkVBalBranch115(zzz473, zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, Zero, zzz480, zzz481, zzz482, Succ(zzz7390), Succ(Zero), bh)
new_mkVBalBranch0(zzz31, Branch(zzz510, zzz511, Pos(Succ(zzz51200)), zzz513, zzz514), Branch(zzz340, zzz341, zzz342, zzz343, zzz344), h) → new_mkVBalBranch3MkVBalBranch215(zzz340, zzz341, zzz342, zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat3(new_primPlusNat1(zzz51200), zzz51200)), zzz51200))), h)
new_mkVBalBranch3MkVBalBranch223(zzz340, zzz341, Neg(Succ(Succ(Zero))), zzz343, zzz344, zzz510, zzz511, Succ(zzz512000), zzz513, zzz514, zzz31, Succ(Succ(zzz6700)), h) → new_mkVBalBranch3MkVBalBranch224(zzz340, zzz341, Succ(Zero), zzz343, zzz344, zzz510, zzz511, zzz512000, zzz513, zzz514, zzz31, Zero, Succ(Succ(new_primPlusNat2(zzz6700, zzz512000))), h)
new_mkVBalBranch3MkVBalBranch230(zzz498, zzz499, zzz500, zzz501, zzz502, zzz503, zzz504, zzz505, zzz506, zzz507, bg) → new_mkVBalBranch3MkVBalBranch118(zzz498, zzz499, zzz500, zzz501, zzz502, zzz503, zzz504, zzz505, zzz506, zzz507, Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat2(Succ(new_primPlusNat3(new_primPlusNat1(zzz500), zzz500)), zzz500)), zzz500))), bg)
new_mkVBalBranch0(zzz31, Branch(zzz510, zzz511, Pos(Zero), zzz513, zzz514), Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), h) → new_mkVBalBranch3MkVBalBranch116(zzz340, zzz341, zzz34200, zzz343, zzz344, zzz510, zzz511, zzz513, zzz514, zzz31, Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat2(Succ(new_primPlusNat3(new_primPlusNat1(zzz34200), zzz34200)), zzz34200)), zzz34200))), h)
new_mkVBalBranch0(zzz31, Branch(zzz510, zzz511, Neg(Zero), zzz513, zzz514), Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), h) → new_mkVBalBranch3MkVBalBranch117(zzz340, zzz341, zzz34200, zzz343, zzz344, zzz510, zzz511, zzz513, zzz514, zzz31, Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat2(Succ(new_primPlusNat3(new_primPlusNat1(zzz34200), zzz34200)), zzz34200)), zzz34200))), h)
new_mkVBalBranch3MkVBalBranch224(zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, zzz1125, zzz1126, zzz1127, zzz1128, zzz1129, Succ(zzz11300), Succ(zzz11310), bd) → new_mkVBalBranch3MkVBalBranch224(zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, zzz1125, zzz1126, zzz1127, zzz1128, zzz1129, zzz11300, zzz11310, bd)
new_mkVBalBranch3MkVBalBranch217(zzz473, zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, zzz481, zzz482, Succ(zzz4830), Zero, bh) → new_mkVBalBranch3MkVBalBranch121(zzz473, zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, zzz481, zzz482, Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat2(Succ(new_primPlusNat3(new_primPlusNat1(zzz475), zzz475)), zzz475)), zzz475))), bh)
new_mkVBalBranch3MkVBalBranch229(zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, zzz1125, zzz1126, zzz1127, zzz1128, zzz1129, bd) → new_mkVBalBranch3MkVBalBranch119(zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, zzz1125, zzz1126, zzz1127, zzz1128, zzz1129, Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat2(Succ(new_primPlusNat3(new_primPlusNat1(zzz1121), zzz1121)), zzz1121)), zzz1121))), bd)
new_mkVBalBranch3MkVBalBranch217(zzz473, zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, zzz481, zzz482, Zero, Succ(zzz4840), bh) → new_mkVBalBranch0(zzz482, Branch(zzz478, zzz479, Pos(Succ(Zero)), zzz480, zzz481), zzz476, bh)
new_mkVBalBranch3MkVBalBranch218(zzz461, zzz462, zzz463, zzz464, zzz465, zzz466, zzz467, zzz468, zzz469, zzz470, zzz471, bb) → new_mkVBalBranch3MkVBalBranch110(zzz461, zzz462, zzz463, zzz464, zzz465, zzz466, zzz467, zzz468, zzz469, zzz470, zzz471, Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat2(Succ(new_primPlusNat3(new_primPlusNat1(zzz463), zzz463)), zzz463)), zzz463))), bb)
new_mkVBalBranch3MkVBalBranch110(zzz461, zzz462, zzz463, zzz464, zzz465, zzz466, zzz467, zzz468, zzz469, zzz470, zzz471, Succ(zzz5800), bb) → new_mkVBalBranch3MkVBalBranch115(zzz461, zzz462, zzz463, zzz464, zzz465, zzz466, zzz467, Succ(zzz468), zzz469, zzz470, zzz471, Succ(zzz5800), Succ(Succ(zzz468)), bb)
new_mkVBalBranch3MkVBalBranch227(zzz486, zzz487, zzz488, zzz489, zzz490, zzz491, zzz492, zzz493, zzz494, zzz495, zzz496, bf) → new_mkVBalBranch0(zzz496, Branch(zzz491, zzz492, Neg(Succ(Succ(zzz493))), zzz494, zzz495), zzz489, bf)
new_mkVBalBranch3MkVBalBranch215(zzz340, zzz341, Pos(Zero), zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, Succ(zzz660), h) → new_mkVBalBranch0(zzz31, zzz514, Branch(zzz340, zzz341, Pos(Zero), zzz343, zzz344), h)
new_mkVBalBranch3MkVBalBranch223(zzz340, zzz341, Neg(Zero), zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, Succ(zzz670), h) → new_mkVBalBranch0(zzz31, Branch(zzz510, zzz511, Neg(Succ(zzz51200)), zzz513, zzz514), zzz343, h)
new_mkVBalBranch3MkVBalBranch216(zzz1105, zzz1106, zzz1107, zzz1108, zzz1109, zzz1110, zzz1111, zzz1112, zzz1113, zzz1114, zzz1115, Zero, Succ(zzz11170), ba) → new_mkVBalBranch0(zzz1115, Branch(zzz1110, zzz1111, Pos(Succ(Succ(zzz1112))), zzz1113, zzz1114), zzz1108, ba)
new_mkVBalBranch3MkVBalBranch115(zzz1986, zzz1987, zzz1988, zzz1989, zzz1990, zzz1991, zzz1992, zzz1993, zzz1994, zzz1995, zzz1996, Zero, Succ(zzz19980), bc) → new_mkVBalBranch0(zzz1996, zzz1995, Branch(zzz1986, zzz1987, Pos(Succ(zzz1988)), zzz1989, zzz1990), bc)
new_mkVBalBranch3MkVBalBranch215(zzz340, zzz341, Pos(Succ(Zero)), zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, Succ(zzz660), h) → new_mkVBalBranch3MkVBalBranch18(zzz340, zzz341, zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, new_primPlusNat2(Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat3(new_primPlusNat1(Zero), Zero)), Zero))), Succ(Zero)), h)
new_mkVBalBranch3MkVBalBranch122(zzz340, zzz341, zzz34200, zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, h) → new_mkVBalBranch0(zzz31, zzz514, Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), h)
new_mkVBalBranch3MkVBalBranch233(zzz473, zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, zzz481, zzz482, bh) → new_mkVBalBranch3MkVBalBranch121(zzz473, zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, zzz481, zzz482, Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat2(Succ(new_primPlusNat3(new_primPlusNat1(zzz475), zzz475)), zzz475)), zzz475))), bh)
new_mkVBalBranch3MkVBalBranch217(zzz473, zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, zzz481, zzz482, Succ(zzz4830), Succ(zzz4840), bh) → new_mkVBalBranch3MkVBalBranch217(zzz473, zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, zzz481, zzz482, zzz4830, zzz4840, bh)
new_mkVBalBranch3MkVBalBranch116(zzz340, zzz341, zzz34200, zzz343, zzz344, zzz510, zzz511, zzz513, zzz514, zzz31, Succ(zzz1200), h) → new_mkVBalBranch0(zzz31, zzz514, Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), h)
new_mkVBalBranch3MkVBalBranch225(zzz498, zzz499, zzz500, zzz501, zzz502, zzz503, zzz504, zzz505, zzz506, zzz507, Zero, Succ(zzz5090), bg) → new_mkVBalBranch0(zzz507, Branch(zzz503, zzz504, Neg(Succ(Zero)), zzz505, zzz506), zzz501, bg)
new_mkVBalBranch0(zzz31, Branch(zzz510, zzz511, Neg(Succ(zzz51200)), zzz513, zzz514), Branch(zzz340, zzz341, zzz342, zzz343, zzz344), h) → new_mkVBalBranch3MkVBalBranch223(zzz340, zzz341, zzz342, zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat3(new_primPlusNat1(zzz51200), zzz51200)), zzz51200))), h)
new_mkVBalBranch3MkVBalBranch121(zzz473, zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, zzz481, zzz482, Zero, bh) → new_mkVBalBranch3MkVBalBranch115(zzz473, zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, Zero, zzz480, zzz481, zzz482, Zero, Succ(Zero), bh)
new_mkVBalBranch3MkVBalBranch223(zzz340, zzz341, Neg(Succ(Zero)), zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, Succ(zzz670), h) → new_mkVBalBranch0(zzz31, Branch(zzz510, zzz511, Neg(Succ(zzz51200)), zzz513, zzz514), zzz343, h)
new_mkVBalBranch3MkVBalBranch215(zzz340, zzz341, Pos(Succ(Succ(zzz342000))), zzz343, zzz344, zzz510, zzz511, Zero, zzz513, zzz514, zzz31, Succ(Succ(zzz6600)), h) → new_mkVBalBranch3MkVBalBranch217(zzz340, zzz341, Succ(zzz342000), zzz343, zzz344, zzz510, zzz511, zzz513, zzz514, zzz31, Succ(zzz6600), zzz342000, h)
new_mkVBalBranch3MkVBalBranch117(zzz340, zzz341, zzz34200, zzz343, zzz344, zzz510, zzz511, zzz513, zzz514, zzz31, Succ(zzz1240), h) → new_mkVBalBranch0(zzz31, zzz514, Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), h)
new_mkVBalBranch3MkVBalBranch120(zzz2050, zzz2051, zzz2052, zzz2053, zzz2054, zzz2055, zzz2056, zzz2057, zzz2058, zzz2059, zzz2060, Succ(zzz20610), Succ(zzz20620), be) → new_mkVBalBranch3MkVBalBranch120(zzz2050, zzz2051, zzz2052, zzz2053, zzz2054, zzz2055, zzz2056, zzz2057, zzz2058, zzz2059, zzz2060, zzz20610, zzz20620, be)
new_mkVBalBranch3MkVBalBranch217(zzz473, zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, zzz481, zzz482, Zero, Zero, bh) → new_mkVBalBranch3MkVBalBranch233(zzz473, zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, zzz481, zzz482, bh)
new_mkVBalBranch3MkVBalBranch216(zzz1105, zzz1106, zzz1107, zzz1108, zzz1109, zzz1110, zzz1111, zzz1112, zzz1113, zzz1114, zzz1115, Succ(zzz11160), Succ(zzz11170), ba) → new_mkVBalBranch3MkVBalBranch216(zzz1105, zzz1106, zzz1107, zzz1108, zzz1109, zzz1110, zzz1111, zzz1112, zzz1113, zzz1114, zzz1115, zzz11160, zzz11170, ba)
new_mkVBalBranch3MkVBalBranch223(zzz340, zzz341, Pos(zzz3420), zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, Succ(zzz670), h) → new_mkVBalBranch0(zzz31, Branch(zzz510, zzz511, Neg(Succ(zzz51200)), zzz513, zzz514), zzz343, h)
new_mkVBalBranch3MkVBalBranch19(zzz340, zzz341, zzz34200, zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, Zero, h) → new_mkVBalBranch3MkVBalBranch122(zzz340, zzz341, zzz34200, zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, h)
new_mkVBalBranch3MkVBalBranch225(zzz498, zzz499, zzz500, zzz501, zzz502, zzz503, zzz504, zzz505, zzz506, zzz507, Succ(zzz5080), Succ(zzz5090), bg) → new_mkVBalBranch3MkVBalBranch225(zzz498, zzz499, zzz500, zzz501, zzz502, zzz503, zzz504, zzz505, zzz506, zzz507, zzz5080, zzz5090, bg)
new_mkVBalBranch3MkVBalBranch19(zzz340, zzz341, zzz34200, zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, Succ(zzz1410), h) → new_mkVBalBranch0(zzz31, zzz514, Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), h)
new_mkVBalBranch3MkVBalBranch224(zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, zzz1125, zzz1126, zzz1127, zzz1128, zzz1129, Zero, Succ(zzz11310), bd) → new_mkVBalBranch3MkVBalBranch227(zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, zzz1125, zzz1126, zzz1127, zzz1128, zzz1129, bd)
new_mkVBalBranch3MkVBalBranch224(zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, zzz1125, zzz1126, zzz1127, zzz1128, zzz1129, Zero, Zero, bd) → new_mkVBalBranch3MkVBalBranch229(zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, zzz1125, zzz1126, zzz1127, zzz1128, zzz1129, bd)
new_mkVBalBranch3MkVBalBranch225(zzz498, zzz499, zzz500, zzz501, zzz502, zzz503, zzz504, zzz505, zzz506, zzz507, Succ(zzz5080), Zero, bg) → new_mkVBalBranch3MkVBalBranch118(zzz498, zzz499, zzz500, zzz501, zzz502, zzz503, zzz504, zzz505, zzz506, zzz507, Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat2(Succ(new_primPlusNat3(new_primPlusNat1(zzz500), zzz500)), zzz500)), zzz500))), bg)
new_mkVBalBranch3MkVBalBranch223(zzz340, zzz341, Neg(Succ(Succ(Succ(zzz3420000)))), zzz343, zzz344, zzz510, zzz511, Succ(zzz512000), zzz513, zzz514, zzz31, Succ(Succ(zzz6700)), h) → new_mkVBalBranch3MkVBalBranch224(zzz340, zzz341, Succ(Succ(zzz3420000)), zzz343, zzz344, zzz510, zzz511, zzz512000, zzz513, zzz514, zzz31, Succ(zzz3420000), Succ(Succ(new_primPlusNat2(zzz6700, zzz512000))), h)
new_mkVBalBranch3MkVBalBranch223(zzz340, zzz341, Neg(Succ(Succ(Zero))), zzz343, zzz344, zzz510, zzz511, Zero, zzz513, zzz514, zzz31, Succ(Succ(zzz6700)), h) → new_mkVBalBranch3MkVBalBranch225(zzz340, zzz341, Succ(Zero), zzz343, zzz344, zzz510, zzz511, zzz513, zzz514, zzz31, Zero, Succ(zzz6700), h)
new_mkVBalBranch3MkVBalBranch115(zzz1986, zzz1987, zzz1988, zzz1989, zzz1990, zzz1991, zzz1992, zzz1993, zzz1994, zzz1995, zzz1996, Succ(zzz19970), Succ(zzz19980), bc) → new_mkVBalBranch3MkVBalBranch115(zzz1986, zzz1987, zzz1988, zzz1989, zzz1990, zzz1991, zzz1992, zzz1993, zzz1994, zzz1995, zzz1996, zzz19970, zzz19980, bc)
new_mkVBalBranch3MkVBalBranch215(zzz340, zzz341, Neg(Zero), zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, Succ(zzz660), h) → new_mkVBalBranch0(zzz31, zzz514, Branch(zzz340, zzz341, Neg(Zero), zzz343, zzz344), h)
new_mkVBalBranch3MkVBalBranch224(zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, zzz1125, zzz1126, zzz1127, zzz1128, zzz1129, Succ(zzz11300), Zero, bd) → new_mkVBalBranch3MkVBalBranch119(zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, zzz1125, zzz1126, zzz1127, zzz1128, zzz1129, Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat2(Succ(new_primPlusNat3(new_primPlusNat1(zzz1121), zzz1121)), zzz1121)), zzz1121))), bd)
new_mkVBalBranch3MkVBalBranch118(zzz498, zzz499, zzz500, zzz501, zzz502, zzz503, zzz504, zzz505, zzz506, zzz507, Succ(zzz8040), bg) → new_mkVBalBranch3MkVBalBranch120(zzz498, zzz499, zzz500, zzz501, zzz502, zzz503, zzz504, Zero, zzz505, zzz506, zzz507, Succ(Zero), Succ(zzz8040), bg)
new_mkVBalBranch3MkVBalBranch222(zzz461, zzz462, zzz463, zzz464, zzz465, zzz466, zzz467, zzz468, zzz469, zzz470, zzz471, bb) → new_mkVBalBranch3MkVBalBranch110(zzz461, zzz462, zzz463, zzz464, zzz465, zzz466, zzz467, zzz468, zzz469, zzz470, zzz471, Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat2(Succ(new_primPlusNat3(new_primPlusNat1(zzz463), zzz463)), zzz463)), zzz463))), bb)
new_mkVBalBranch3MkVBalBranch216(zzz1105, zzz1106, zzz1107, zzz1108, zzz1109, zzz1110, zzz1111, zzz1112, zzz1113, zzz1114, zzz1115, Succ(zzz11160), Zero, ba) → new_mkVBalBranch3MkVBalBranch218(zzz1105, zzz1106, zzz1107, zzz1108, zzz1109, zzz1110, zzz1111, zzz1112, zzz1113, zzz1114, zzz1115, ba)
new_mkVBalBranch3MkVBalBranch216(zzz1105, zzz1106, zzz1107, zzz1108, zzz1109, zzz1110, zzz1111, zzz1112, zzz1113, zzz1114, zzz1115, Zero, Zero, ba) → new_mkVBalBranch3MkVBalBranch222(zzz1105, zzz1106, zzz1107, zzz1108, zzz1109, zzz1110, zzz1111, zzz1112, zzz1113, zzz1114, zzz1115, ba)
new_mkVBalBranch3MkVBalBranch18(zzz340, zzz341, zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, Zero, h) → new_mkVBalBranch3MkVBalBranch115(zzz340, zzz341, Zero, zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, Zero, Succ(zzz51200), h)
new_mkVBalBranch3MkVBalBranch119(zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, zzz1125, zzz1126, zzz1127, zzz1128, zzz1129, Succ(zzz12130), bd) → new_mkVBalBranch3MkVBalBranch120(zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, zzz1125, Succ(zzz1126), zzz1127, zzz1128, zzz1129, Succ(Succ(zzz1126)), Succ(zzz12130), bd)

The TRS R consists of the following rules:

new_primPlusNat1(Zero) → Zero
new_primPlusNat1(Succ(zzz62000)) → Succ(Succ(new_primPlusNat1(zzz62000)))
new_primPlusNat3(zzz90, Succ(zzz910)) → Succ(Succ(new_primPlusNat2(zzz90, zzz910)))
new_primPlusNat3(zzz90, Zero) → Succ(zzz90)
new_primPlusNat2(Succ(zzz900), Succ(zzz9100)) → Succ(Succ(new_primPlusNat2(zzz900, zzz9100)))
new_primPlusNat2(Zero, Succ(zzz9100)) → Succ(zzz9100)
new_primPlusNat2(Zero, Zero) → Zero
new_primPlusNat2(Succ(zzz900), Zero) → Succ(zzz900)

The set Q consists of the following terms:

new_primPlusNat2(Zero, Succ(x0))
new_primPlusNat3(x0, Succ(x1))
new_primPlusNat2(Succ(x0), Succ(x1))
new_primPlusNat3(x0, Zero)
new_primPlusNat1(Zero)
new_primPlusNat2(Zero, Zero)
new_primPlusNat1(Succ(x0))
new_primPlusNat2(Succ(x0), Zero)

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

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

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

new_mkVBalBranch3MkVBalBranch225(zzz498, zzz499, zzz500, zzz501, zzz502, zzz503, zzz504, zzz505, zzz506, zzz507, Zero, Zero, bg) → new_mkVBalBranch3MkVBalBranch230(zzz498, zzz499, zzz500, zzz501, zzz502, zzz503, zzz504, zzz505, zzz506, zzz507, bg)
new_mkVBalBranch3MkVBalBranch18(zzz340, zzz341, zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, Succ(zzz1480), h) → new_mkVBalBranch3MkVBalBranch115(zzz340, zzz341, Zero, zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, Succ(zzz1480), Succ(zzz51200), h)
new_mkVBalBranch3MkVBalBranch215(zzz340, zzz341, Pos(Succ(Succ(zzz342000))), zzz343, zzz344, zzz510, zzz511, Succ(zzz512000), zzz513, zzz514, zzz31, Succ(Succ(zzz6600)), h) → new_mkVBalBranch3MkVBalBranch216(zzz340, zzz341, Succ(zzz342000), zzz343, zzz344, zzz510, zzz511, zzz512000, zzz513, zzz514, zzz31, Succ(Succ(new_primPlusNat2(zzz6600, zzz512000))), zzz342000, h)
new_mkVBalBranch0(zzz31, Branch(zzz510, zzz511, Neg(Zero), zzz513, zzz514), Branch(zzz340, zzz341, Pos(Succ(zzz34200)), zzz343, zzz344), h) → new_mkVBalBranch0(zzz31, Branch(zzz510, zzz511, Neg(Zero), zzz513, zzz514), zzz343, h)
new_mkVBalBranch3MkVBalBranch223(zzz340, zzz341, Neg(Succ(Succ(Succ(zzz3420000)))), zzz343, zzz344, zzz510, zzz511, Zero, zzz513, zzz514, zzz31, Succ(Succ(zzz6700)), h) → new_mkVBalBranch3MkVBalBranch225(zzz340, zzz341, Succ(Succ(zzz3420000)), zzz343, zzz344, zzz510, zzz511, zzz513, zzz514, zzz31, Succ(zzz3420000), Succ(zzz6700), h)
new_mkVBalBranch3MkVBalBranch120(zzz2050, zzz2051, zzz2052, zzz2053, zzz2054, zzz2055, zzz2056, zzz2057, zzz2058, zzz2059, zzz2060, Zero, Succ(zzz20620), be) → new_mkVBalBranch0(zzz2060, zzz2059, Branch(zzz2050, zzz2051, Neg(Succ(zzz2052)), zzz2053, zzz2054), be)
new_mkVBalBranch3MkVBalBranch215(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, Succ(zzz660), h) → new_mkVBalBranch3MkVBalBranch19(zzz340, zzz341, zzz34200, zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, new_primPlusNat2(Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat3(new_primPlusNat1(zzz34200), zzz34200)), zzz34200))), Succ(zzz34200)), h)
new_mkVBalBranch0(zzz31, Branch(zzz510, zzz511, Pos(Zero), zzz513, zzz514), Branch(zzz340, zzz341, Pos(Succ(zzz34200)), zzz343, zzz344), h) → new_mkVBalBranch0(zzz31, Branch(zzz510, zzz511, Pos(Zero), zzz513, zzz514), zzz343, h)
new_mkVBalBranch3MkVBalBranch121(zzz473, zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, zzz481, zzz482, Succ(zzz7390), bh) → new_mkVBalBranch3MkVBalBranch115(zzz473, zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, Zero, zzz480, zzz481, zzz482, Succ(zzz7390), Succ(Zero), bh)
new_mkVBalBranch0(zzz31, Branch(zzz510, zzz511, Pos(Succ(zzz51200)), zzz513, zzz514), Branch(zzz340, zzz341, zzz342, zzz343, zzz344), h) → new_mkVBalBranch3MkVBalBranch215(zzz340, zzz341, zzz342, zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat3(new_primPlusNat1(zzz51200), zzz51200)), zzz51200))), h)
new_mkVBalBranch3MkVBalBranch223(zzz340, zzz341, Neg(Succ(Succ(Zero))), zzz343, zzz344, zzz510, zzz511, Succ(zzz512000), zzz513, zzz514, zzz31, Succ(Succ(zzz6700)), h) → new_mkVBalBranch3MkVBalBranch224(zzz340, zzz341, Succ(Zero), zzz343, zzz344, zzz510, zzz511, zzz512000, zzz513, zzz514, zzz31, Zero, Succ(Succ(new_primPlusNat2(zzz6700, zzz512000))), h)
new_mkVBalBranch3MkVBalBranch230(zzz498, zzz499, zzz500, zzz501, zzz502, zzz503, zzz504, zzz505, zzz506, zzz507, bg) → new_mkVBalBranch3MkVBalBranch118(zzz498, zzz499, zzz500, zzz501, zzz502, zzz503, zzz504, zzz505, zzz506, zzz507, Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat2(Succ(new_primPlusNat3(new_primPlusNat1(zzz500), zzz500)), zzz500)), zzz500))), bg)
new_mkVBalBranch0(zzz31, Branch(zzz510, zzz511, Pos(Zero), zzz513, zzz514), Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), h) → new_mkVBalBranch3MkVBalBranch116(zzz340, zzz341, zzz34200, zzz343, zzz344, zzz510, zzz511, zzz513, zzz514, zzz31, Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat2(Succ(new_primPlusNat3(new_primPlusNat1(zzz34200), zzz34200)), zzz34200)), zzz34200))), h)
new_mkVBalBranch0(zzz31, Branch(zzz510, zzz511, Neg(Zero), zzz513, zzz514), Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), h) → new_mkVBalBranch3MkVBalBranch117(zzz340, zzz341, zzz34200, zzz343, zzz344, zzz510, zzz511, zzz513, zzz514, zzz31, Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat2(Succ(new_primPlusNat3(new_primPlusNat1(zzz34200), zzz34200)), zzz34200)), zzz34200))), h)
new_mkVBalBranch3MkVBalBranch224(zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, zzz1125, zzz1126, zzz1127, zzz1128, zzz1129, Succ(zzz11300), Succ(zzz11310), bd) → new_mkVBalBranch3MkVBalBranch224(zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, zzz1125, zzz1126, zzz1127, zzz1128, zzz1129, zzz11300, zzz11310, bd)
new_mkVBalBranch3MkVBalBranch229(zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, zzz1125, zzz1126, zzz1127, zzz1128, zzz1129, bd) → new_mkVBalBranch3MkVBalBranch119(zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, zzz1125, zzz1126, zzz1127, zzz1128, zzz1129, Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat2(Succ(new_primPlusNat3(new_primPlusNat1(zzz1121), zzz1121)), zzz1121)), zzz1121))), bd)
new_mkVBalBranch3MkVBalBranch217(zzz473, zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, zzz481, zzz482, Succ(zzz4830), Zero, bh) → new_mkVBalBranch3MkVBalBranch121(zzz473, zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, zzz481, zzz482, Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat2(Succ(new_primPlusNat3(new_primPlusNat1(zzz475), zzz475)), zzz475)), zzz475))), bh)
new_mkVBalBranch3MkVBalBranch217(zzz473, zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, zzz481, zzz482, Zero, Succ(zzz4840), bh) → new_mkVBalBranch0(zzz482, Branch(zzz478, zzz479, Pos(Succ(Zero)), zzz480, zzz481), zzz476, bh)
new_mkVBalBranch3MkVBalBranch218(zzz461, zzz462, zzz463, zzz464, zzz465, zzz466, zzz467, zzz468, zzz469, zzz470, zzz471, bb) → new_mkVBalBranch3MkVBalBranch110(zzz461, zzz462, zzz463, zzz464, zzz465, zzz466, zzz467, zzz468, zzz469, zzz470, zzz471, Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat2(Succ(new_primPlusNat3(new_primPlusNat1(zzz463), zzz463)), zzz463)), zzz463))), bb)
new_mkVBalBranch3MkVBalBranch110(zzz461, zzz462, zzz463, zzz464, zzz465, zzz466, zzz467, zzz468, zzz469, zzz470, zzz471, Succ(zzz5800), bb) → new_mkVBalBranch3MkVBalBranch115(zzz461, zzz462, zzz463, zzz464, zzz465, zzz466, zzz467, Succ(zzz468), zzz469, zzz470, zzz471, Succ(zzz5800), Succ(Succ(zzz468)), bb)
new_mkVBalBranch3MkVBalBranch227(zzz486, zzz487, zzz488, zzz489, zzz490, zzz491, zzz492, zzz493, zzz494, zzz495, zzz496, bf) → new_mkVBalBranch0(zzz496, Branch(zzz491, zzz492, Neg(Succ(Succ(zzz493))), zzz494, zzz495), zzz489, bf)
new_mkVBalBranch3MkVBalBranch215(zzz340, zzz341, Pos(Zero), zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, Succ(zzz660), h) → new_mkVBalBranch0(zzz31, zzz514, Branch(zzz340, zzz341, Pos(Zero), zzz343, zzz344), h)
new_mkVBalBranch3MkVBalBranch223(zzz340, zzz341, Neg(Zero), zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, Succ(zzz670), h) → new_mkVBalBranch0(zzz31, Branch(zzz510, zzz511, Neg(Succ(zzz51200)), zzz513, zzz514), zzz343, h)
new_mkVBalBranch3MkVBalBranch216(zzz1105, zzz1106, zzz1107, zzz1108, zzz1109, zzz1110, zzz1111, zzz1112, zzz1113, zzz1114, zzz1115, Zero, Succ(zzz11170), ba) → new_mkVBalBranch0(zzz1115, Branch(zzz1110, zzz1111, Pos(Succ(Succ(zzz1112))), zzz1113, zzz1114), zzz1108, ba)
new_mkVBalBranch3MkVBalBranch115(zzz1986, zzz1987, zzz1988, zzz1989, zzz1990, zzz1991, zzz1992, zzz1993, zzz1994, zzz1995, zzz1996, Zero, Succ(zzz19980), bc) → new_mkVBalBranch0(zzz1996, zzz1995, Branch(zzz1986, zzz1987, Pos(Succ(zzz1988)), zzz1989, zzz1990), bc)
new_mkVBalBranch3MkVBalBranch215(zzz340, zzz341, Pos(Succ(Zero)), zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, Succ(zzz660), h) → new_mkVBalBranch3MkVBalBranch18(zzz340, zzz341, zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, new_primPlusNat2(Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat3(new_primPlusNat1(Zero), Zero)), Zero))), Succ(Zero)), h)
new_mkVBalBranch3MkVBalBranch122(zzz340, zzz341, zzz34200, zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, h) → new_mkVBalBranch0(zzz31, zzz514, Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), h)
new_mkVBalBranch3MkVBalBranch233(zzz473, zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, zzz481, zzz482, bh) → new_mkVBalBranch3MkVBalBranch121(zzz473, zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, zzz481, zzz482, Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat2(Succ(new_primPlusNat3(new_primPlusNat1(zzz475), zzz475)), zzz475)), zzz475))), bh)
new_mkVBalBranch3MkVBalBranch217(zzz473, zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, zzz481, zzz482, Succ(zzz4830), Succ(zzz4840), bh) → new_mkVBalBranch3MkVBalBranch217(zzz473, zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, zzz481, zzz482, zzz4830, zzz4840, bh)
new_mkVBalBranch3MkVBalBranch116(zzz340, zzz341, zzz34200, zzz343, zzz344, zzz510, zzz511, zzz513, zzz514, zzz31, Succ(zzz1200), h) → new_mkVBalBranch0(zzz31, zzz514, Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), h)
new_mkVBalBranch3MkVBalBranch225(zzz498, zzz499, zzz500, zzz501, zzz502, zzz503, zzz504, zzz505, zzz506, zzz507, Zero, Succ(zzz5090), bg) → new_mkVBalBranch0(zzz507, Branch(zzz503, zzz504, Neg(Succ(Zero)), zzz505, zzz506), zzz501, bg)
new_mkVBalBranch0(zzz31, Branch(zzz510, zzz511, Neg(Succ(zzz51200)), zzz513, zzz514), Branch(zzz340, zzz341, zzz342, zzz343, zzz344), h) → new_mkVBalBranch3MkVBalBranch223(zzz340, zzz341, zzz342, zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat3(new_primPlusNat1(zzz51200), zzz51200)), zzz51200))), h)
new_mkVBalBranch3MkVBalBranch223(zzz340, zzz341, Neg(Succ(Zero)), zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, Succ(zzz670), h) → new_mkVBalBranch0(zzz31, Branch(zzz510, zzz511, Neg(Succ(zzz51200)), zzz513, zzz514), zzz343, h)
new_mkVBalBranch3MkVBalBranch215(zzz340, zzz341, Pos(Succ(Succ(zzz342000))), zzz343, zzz344, zzz510, zzz511, Zero, zzz513, zzz514, zzz31, Succ(Succ(zzz6600)), h) → new_mkVBalBranch3MkVBalBranch217(zzz340, zzz341, Succ(zzz342000), zzz343, zzz344, zzz510, zzz511, zzz513, zzz514, zzz31, Succ(zzz6600), zzz342000, h)
new_mkVBalBranch3MkVBalBranch117(zzz340, zzz341, zzz34200, zzz343, zzz344, zzz510, zzz511, zzz513, zzz514, zzz31, Succ(zzz1240), h) → new_mkVBalBranch0(zzz31, zzz514, Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), h)
new_mkVBalBranch3MkVBalBranch120(zzz2050, zzz2051, zzz2052, zzz2053, zzz2054, zzz2055, zzz2056, zzz2057, zzz2058, zzz2059, zzz2060, Succ(zzz20610), Succ(zzz20620), be) → new_mkVBalBranch3MkVBalBranch120(zzz2050, zzz2051, zzz2052, zzz2053, zzz2054, zzz2055, zzz2056, zzz2057, zzz2058, zzz2059, zzz2060, zzz20610, zzz20620, be)
new_mkVBalBranch3MkVBalBranch217(zzz473, zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, zzz481, zzz482, Zero, Zero, bh) → new_mkVBalBranch3MkVBalBranch233(zzz473, zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, zzz481, zzz482, bh)
new_mkVBalBranch3MkVBalBranch216(zzz1105, zzz1106, zzz1107, zzz1108, zzz1109, zzz1110, zzz1111, zzz1112, zzz1113, zzz1114, zzz1115, Succ(zzz11160), Succ(zzz11170), ba) → new_mkVBalBranch3MkVBalBranch216(zzz1105, zzz1106, zzz1107, zzz1108, zzz1109, zzz1110, zzz1111, zzz1112, zzz1113, zzz1114, zzz1115, zzz11160, zzz11170, ba)
new_mkVBalBranch3MkVBalBranch223(zzz340, zzz341, Pos(zzz3420), zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, Succ(zzz670), h) → new_mkVBalBranch0(zzz31, Branch(zzz510, zzz511, Neg(Succ(zzz51200)), zzz513, zzz514), zzz343, h)
new_mkVBalBranch3MkVBalBranch19(zzz340, zzz341, zzz34200, zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, Zero, h) → new_mkVBalBranch3MkVBalBranch122(zzz340, zzz341, zzz34200, zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, h)
new_mkVBalBranch3MkVBalBranch225(zzz498, zzz499, zzz500, zzz501, zzz502, zzz503, zzz504, zzz505, zzz506, zzz507, Succ(zzz5080), Succ(zzz5090), bg) → new_mkVBalBranch3MkVBalBranch225(zzz498, zzz499, zzz500, zzz501, zzz502, zzz503, zzz504, zzz505, zzz506, zzz507, zzz5080, zzz5090, bg)
new_mkVBalBranch3MkVBalBranch19(zzz340, zzz341, zzz34200, zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, Succ(zzz1410), h) → new_mkVBalBranch0(zzz31, zzz514, Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), h)
new_mkVBalBranch3MkVBalBranch224(zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, zzz1125, zzz1126, zzz1127, zzz1128, zzz1129, Zero, Succ(zzz11310), bd) → new_mkVBalBranch3MkVBalBranch227(zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, zzz1125, zzz1126, zzz1127, zzz1128, zzz1129, bd)
new_mkVBalBranch3MkVBalBranch224(zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, zzz1125, zzz1126, zzz1127, zzz1128, zzz1129, Zero, Zero, bd) → new_mkVBalBranch3MkVBalBranch229(zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, zzz1125, zzz1126, zzz1127, zzz1128, zzz1129, bd)
new_mkVBalBranch3MkVBalBranch225(zzz498, zzz499, zzz500, zzz501, zzz502, zzz503, zzz504, zzz505, zzz506, zzz507, Succ(zzz5080), Zero, bg) → new_mkVBalBranch3MkVBalBranch118(zzz498, zzz499, zzz500, zzz501, zzz502, zzz503, zzz504, zzz505, zzz506, zzz507, Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat2(Succ(new_primPlusNat3(new_primPlusNat1(zzz500), zzz500)), zzz500)), zzz500))), bg)
new_mkVBalBranch3MkVBalBranch223(zzz340, zzz341, Neg(Succ(Succ(Succ(zzz3420000)))), zzz343, zzz344, zzz510, zzz511, Succ(zzz512000), zzz513, zzz514, zzz31, Succ(Succ(zzz6700)), h) → new_mkVBalBranch3MkVBalBranch224(zzz340, zzz341, Succ(Succ(zzz3420000)), zzz343, zzz344, zzz510, zzz511, zzz512000, zzz513, zzz514, zzz31, Succ(zzz3420000), Succ(Succ(new_primPlusNat2(zzz6700, zzz512000))), h)
new_mkVBalBranch3MkVBalBranch223(zzz340, zzz341, Neg(Succ(Succ(Zero))), zzz343, zzz344, zzz510, zzz511, Zero, zzz513, zzz514, zzz31, Succ(Succ(zzz6700)), h) → new_mkVBalBranch3MkVBalBranch225(zzz340, zzz341, Succ(Zero), zzz343, zzz344, zzz510, zzz511, zzz513, zzz514, zzz31, Zero, Succ(zzz6700), h)
new_mkVBalBranch3MkVBalBranch115(zzz1986, zzz1987, zzz1988, zzz1989, zzz1990, zzz1991, zzz1992, zzz1993, zzz1994, zzz1995, zzz1996, Succ(zzz19970), Succ(zzz19980), bc) → new_mkVBalBranch3MkVBalBranch115(zzz1986, zzz1987, zzz1988, zzz1989, zzz1990, zzz1991, zzz1992, zzz1993, zzz1994, zzz1995, zzz1996, zzz19970, zzz19980, bc)
new_mkVBalBranch3MkVBalBranch215(zzz340, zzz341, Neg(Zero), zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, Succ(zzz660), h) → new_mkVBalBranch0(zzz31, zzz514, Branch(zzz340, zzz341, Neg(Zero), zzz343, zzz344), h)
new_mkVBalBranch3MkVBalBranch224(zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, zzz1125, zzz1126, zzz1127, zzz1128, zzz1129, Succ(zzz11300), Zero, bd) → new_mkVBalBranch3MkVBalBranch119(zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, zzz1125, zzz1126, zzz1127, zzz1128, zzz1129, Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat2(Succ(new_primPlusNat3(new_primPlusNat1(zzz1121), zzz1121)), zzz1121)), zzz1121))), bd)
new_mkVBalBranch3MkVBalBranch118(zzz498, zzz499, zzz500, zzz501, zzz502, zzz503, zzz504, zzz505, zzz506, zzz507, Succ(zzz8040), bg) → new_mkVBalBranch3MkVBalBranch120(zzz498, zzz499, zzz500, zzz501, zzz502, zzz503, zzz504, Zero, zzz505, zzz506, zzz507, Succ(Zero), Succ(zzz8040), bg)
new_mkVBalBranch3MkVBalBranch222(zzz461, zzz462, zzz463, zzz464, zzz465, zzz466, zzz467, zzz468, zzz469, zzz470, zzz471, bb) → new_mkVBalBranch3MkVBalBranch110(zzz461, zzz462, zzz463, zzz464, zzz465, zzz466, zzz467, zzz468, zzz469, zzz470, zzz471, Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat2(Succ(new_primPlusNat3(new_primPlusNat1(zzz463), zzz463)), zzz463)), zzz463))), bb)
new_mkVBalBranch3MkVBalBranch216(zzz1105, zzz1106, zzz1107, zzz1108, zzz1109, zzz1110, zzz1111, zzz1112, zzz1113, zzz1114, zzz1115, Succ(zzz11160), Zero, ba) → new_mkVBalBranch3MkVBalBranch218(zzz1105, zzz1106, zzz1107, zzz1108, zzz1109, zzz1110, zzz1111, zzz1112, zzz1113, zzz1114, zzz1115, ba)
new_mkVBalBranch3MkVBalBranch216(zzz1105, zzz1106, zzz1107, zzz1108, zzz1109, zzz1110, zzz1111, zzz1112, zzz1113, zzz1114, zzz1115, Zero, Zero, ba) → new_mkVBalBranch3MkVBalBranch222(zzz1105, zzz1106, zzz1107, zzz1108, zzz1109, zzz1110, zzz1111, zzz1112, zzz1113, zzz1114, zzz1115, ba)
new_mkVBalBranch3MkVBalBranch18(zzz340, zzz341, zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, Zero, h) → new_mkVBalBranch3MkVBalBranch115(zzz340, zzz341, Zero, zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, Zero, Succ(zzz51200), h)
new_mkVBalBranch3MkVBalBranch119(zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, zzz1125, zzz1126, zzz1127, zzz1128, zzz1129, Succ(zzz12130), bd) → new_mkVBalBranch3MkVBalBranch120(zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, zzz1125, Succ(zzz1126), zzz1127, zzz1128, zzz1129, Succ(Succ(zzz1126)), Succ(zzz12130), bd)

The TRS R consists of the following rules:

new_primPlusNat1(Zero) → Zero
new_primPlusNat1(Succ(zzz62000)) → Succ(Succ(new_primPlusNat1(zzz62000)))
new_primPlusNat3(zzz90, Succ(zzz910)) → Succ(Succ(new_primPlusNat2(zzz90, zzz910)))
new_primPlusNat3(zzz90, Zero) → Succ(zzz90)
new_primPlusNat2(Succ(zzz900), Succ(zzz9100)) → Succ(Succ(new_primPlusNat2(zzz900, zzz9100)))
new_primPlusNat2(Zero, Succ(zzz9100)) → Succ(zzz9100)
new_primPlusNat2(Zero, Zero) → Zero
new_primPlusNat2(Succ(zzz900), Zero) → Succ(zzz900)

The set Q consists of the following terms:

new_primPlusNat2(Zero, Succ(x0))
new_primPlusNat3(x0, Succ(x1))
new_primPlusNat2(Succ(x0), Succ(x1))
new_primPlusNat3(x0, Zero)
new_primPlusNat1(Zero)
new_primPlusNat2(Zero, Zero)
new_primPlusNat1(Succ(x0))
new_primPlusNat2(Succ(x0), Zero)

We have to consider all minimal (P,Q,R)-chains.
By rewriting [15] the rule new_mkVBalBranch3MkVBalBranch215(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, Succ(zzz660), h) → new_mkVBalBranch3MkVBalBranch19(zzz340, zzz341, zzz34200, zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, new_primPlusNat2(Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat3(new_primPlusNat1(zzz34200), zzz34200)), zzz34200))), Succ(zzz34200)), h) at position [11] we obtained the following new rules:

new_mkVBalBranch3MkVBalBranch215(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, Succ(zzz660), h) → new_mkVBalBranch3MkVBalBranch19(zzz340, zzz341, zzz34200, zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat2(Succ(new_primPlusNat3(new_primPlusNat1(zzz34200), zzz34200)), 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
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                    ↳ DependencyGraphProof
                                      ↳ QDP
                                        ↳ Rewriting
                                          ↳ QDP
                                            ↳ Rewriting
                                              ↳ QDP
                                                ↳ Rewriting
                                                  ↳ QDP
                                                    ↳ Rewriting
                                                      ↳ QDP
                                                        ↳ Rewriting
                                                          ↳ QDP
                                                            ↳ Rewriting
                                                              ↳ QDP
                                                                ↳ Rewriting
                                                                  ↳ QDP
                                                                    ↳ Rewriting
                                                                      ↳ QDP
                                                                        ↳ Rewriting
                                                                          ↳ QDP
                                                                            ↳ Rewriting
                                                                              ↳ QDP
                                                                                ↳ Rewriting
                                                                                  ↳ QDP
                                                                                    ↳ Rewriting
                                                                                      ↳ QDP
                                                                                        ↳ Rewriting
                                                                                          ↳ QDP
                                                                                            ↳ Rewriting
                                                                                              ↳ QDP
                                                                                                ↳ Rewriting
                                                                                                  ↳ QDP
                                                                                                    ↳ Rewriting
                                                                                                      ↳ QDP
                                                                                                        ↳ Rewriting
                                                                                                          ↳ QDP
                                                                                                            ↳ UsableRulesProof
                                                                                                              ↳ QDP
                                                                                                                ↳ QReductionProof
                                                                                                                  ↳ QDP
                                                                                                                    ↳ Rewriting
                                                                                                                      ↳ QDP
                                                                                                                        ↳ Rewriting
                                                                                                                          ↳ QDP
                                                                                                                            ↳ DependencyGraphProof
                                                                                                                              ↳ QDP
                                                                                                                                ↳ Rewriting
                                                                                                                                  ↳ QDP
                                                                                                                                    ↳ Rewriting
                                                                                                                                      ↳ QDP
                                                                                                                                        ↳ DependencyGraphProof
                                                                                                                                          ↳ QDP
                                                                                                                                            ↳ Rewriting
                                                                                                                                              ↳ QDP
                                                                                                                                                ↳ Rewriting
                                                                                                                                                  ↳ QDP
                                                                                                                                                    ↳ Rewriting
                                                                                                                                                      ↳ QDP
                                                                                                                                                        ↳ Rewriting
                                                                                                                                                          ↳ QDP
                                                                                                                                                            ↳ Rewriting
                                                                                                                                                              ↳ QDP
                                                                                                                                                                ↳ Rewriting
                                                                                                                                                                  ↳ QDP
                                                                                                                                                                    ↳ Rewriting
                                                                                                                                                                      ↳ QDP
                                                                                                                                                                        ↳ Rewriting
                                                                                                                                                                          ↳ QDP
                                                                                                                                                                            ↳ Rewriting
                                                                                                                                                                              ↳ QDP
                                                                                                                                                                                ↳ Rewriting
                                                                                                                                                                                  ↳ QDP
                                                                                                                                                                                    ↳ Rewriting
                                                                                                                                                                                      ↳ QDP
                                                                                                                                                                                        ↳ Rewriting
                                                                                                                                                                                          ↳ QDP
                                                                                                                                                                                            ↳ UsableRulesProof
                                                                                                                                                                                              ↳ QDP
                                                                                                                                                                                                ↳ QReductionProof
                                                                                                                                                                                                  ↳ QDP
                                                                                                                                                                                                    ↳ Rewriting
                                                                                                                                                                                                      ↳ QDP
                                                                                                                                                                                                        ↳ Rewriting
                                                                                                                                                                                                          ↳ QDP
                                                                                                                                                                                                            ↳ Rewriting
                                                                                                                                                                                                              ↳ QDP
                                                                                                                                                                                                                ↳ Rewriting
                                                                                                                                                                                                                  ↳ QDP
                                                                                                                                                                                                                    ↳ Rewriting
                                                                                                                                                                                                                      ↳ QDP
                                                                                                                                                                                                                        ↳ Rewriting
                                                                                                                                                                                                                          ↳ QDP
                                                                                                                                                                                                                            ↳ Rewriting
                                                                                                                                                                                                                              ↳ QDP
                                                                                                                                                                                                                                ↳ Rewriting
                                                                                                                                                                                                                                  ↳ QDP
                                                                                                                                                                                                                                    ↳ Rewriting
                                                                                                                                                                                                                                      ↳ QDP
                                                                                                                                                                                                                                        ↳ Rewriting
                                                                                                                                                                                                                                          ↳ QDP
                                                                                                                                                                                                                                            ↳ Rewriting
                                                                                                                                                                                                                                              ↳ QDP
                                                                                                                                                                                                                                                ↳ Rewriting
                                                                                                                                                                                                                                                  ↳ QDP
                                                                                                                                                                                                                                                    ↳ Rewriting
                                                                                                                                                                                                                                                      ↳ QDP
                                                                                                                                                                                                                                                        ↳ Rewriting
                                                                                                                                                                                                                                                          ↳ QDP
                                                                                                                                                                                                                                                            ↳ DependencyGraphProof
                                                                                                                                                                                                                                                              ↳ QDP
                                                                                                                                                                                                                                                                ↳ Rewriting
                                                                                                                                                                                                                                                                  ↳ QDP
                                                                                                                                                                                                                                                                    ↳ Rewriting
                                                                                                                                                                                                                                                                      ↳ QDP
                                                                                                                                                                                                                                                                        ↳ Rewriting
                                                                                                                                                                                                                                                                          ↳ QDP
                                                                                                                                                                                                                                                                            ↳ Rewriting
                                                                                                                                                                                                                                                                              ↳ QDP
                                                                                                                                                                                                                                                                                ↳ Rewriting
                                                                                                                                                                                                                                                                                  ↳ QDP
                                                                                                                                                                                                                                                                                    ↳ Rewriting
                                                                                                                                                                                                                                                                                      ↳ QDP
                                                                                                                                                                                                                                                                                        ↳ DependencyGraphProof
                                                                                                                                                                                                                                                                                          ↳ QDP
                                                                                                                                                                                                                                                                                            ↳ Rewriting
                                                                                                                                                                                                                                                                                              ↳ QDP
                                                                                                                                                                                                                                                                                                ↳ DependencyGraphProof
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP

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

new_mkVBalBranch3MkVBalBranch225(zzz498, zzz499, zzz500, zzz501, zzz502, zzz503, zzz504, zzz505, zzz506, zzz507, Zero, Zero, bg) → new_mkVBalBranch3MkVBalBranch230(zzz498, zzz499, zzz500, zzz501, zzz502, zzz503, zzz504, zzz505, zzz506, zzz507, bg)
new_mkVBalBranch3MkVBalBranch18(zzz340, zzz341, zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, Succ(zzz1480), h) → new_mkVBalBranch3MkVBalBranch115(zzz340, zzz341, Zero, zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, Succ(zzz1480), Succ(zzz51200), h)
new_mkVBalBranch0(zzz31, Branch(zzz510, zzz511, Neg(Zero), zzz513, zzz514), Branch(zzz340, zzz341, Pos(Succ(zzz34200)), zzz343, zzz344), h) → new_mkVBalBranch0(zzz31, Branch(zzz510, zzz511, Neg(Zero), zzz513, zzz514), zzz343, h)
new_mkVBalBranch3MkVBalBranch215(zzz340, zzz341, Pos(Succ(Succ(zzz342000))), zzz343, zzz344, zzz510, zzz511, Succ(zzz512000), zzz513, zzz514, zzz31, Succ(Succ(zzz6600)), h) → new_mkVBalBranch3MkVBalBranch216(zzz340, zzz341, Succ(zzz342000), zzz343, zzz344, zzz510, zzz511, zzz512000, zzz513, zzz514, zzz31, Succ(Succ(new_primPlusNat2(zzz6600, zzz512000))), zzz342000, h)
new_mkVBalBranch3MkVBalBranch223(zzz340, zzz341, Neg(Succ(Succ(Succ(zzz3420000)))), zzz343, zzz344, zzz510, zzz511, Zero, zzz513, zzz514, zzz31, Succ(Succ(zzz6700)), h) → new_mkVBalBranch3MkVBalBranch225(zzz340, zzz341, Succ(Succ(zzz3420000)), zzz343, zzz344, zzz510, zzz511, zzz513, zzz514, zzz31, Succ(zzz3420000), Succ(zzz6700), h)
new_mkVBalBranch3MkVBalBranch120(zzz2050, zzz2051, zzz2052, zzz2053, zzz2054, zzz2055, zzz2056, zzz2057, zzz2058, zzz2059, zzz2060, Zero, Succ(zzz20620), be) → new_mkVBalBranch0(zzz2060, zzz2059, Branch(zzz2050, zzz2051, Neg(Succ(zzz2052)), zzz2053, zzz2054), be)
new_mkVBalBranch3MkVBalBranch121(zzz473, zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, zzz481, zzz482, Succ(zzz7390), bh) → new_mkVBalBranch3MkVBalBranch115(zzz473, zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, Zero, zzz480, zzz481, zzz482, Succ(zzz7390), Succ(Zero), bh)
new_mkVBalBranch0(zzz31, Branch(zzz510, zzz511, Pos(Zero), zzz513, zzz514), Branch(zzz340, zzz341, Pos(Succ(zzz34200)), zzz343, zzz344), h) → new_mkVBalBranch0(zzz31, Branch(zzz510, zzz511, Pos(Zero), zzz513, zzz514), zzz343, h)
new_mkVBalBranch0(zzz31, Branch(zzz510, zzz511, Pos(Succ(zzz51200)), zzz513, zzz514), Branch(zzz340, zzz341, zzz342, zzz343, zzz344), h) → new_mkVBalBranch3MkVBalBranch215(zzz340, zzz341, zzz342, zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat3(new_primPlusNat1(zzz51200), zzz51200)), zzz51200))), h)
new_mkVBalBranch3MkVBalBranch215(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, Succ(zzz660), h) → new_mkVBalBranch3MkVBalBranch19(zzz340, zzz341, zzz34200, zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat2(Succ(new_primPlusNat3(new_primPlusNat1(zzz34200), zzz34200)), zzz34200)), zzz34200))), h)
new_mkVBalBranch3MkVBalBranch230(zzz498, zzz499, zzz500, zzz501, zzz502, zzz503, zzz504, zzz505, zzz506, zzz507, bg) → new_mkVBalBranch3MkVBalBranch118(zzz498, zzz499, zzz500, zzz501, zzz502, zzz503, zzz504, zzz505, zzz506, zzz507, Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat2(Succ(new_primPlusNat3(new_primPlusNat1(zzz500), zzz500)), zzz500)), zzz500))), bg)
new_mkVBalBranch3MkVBalBranch223(zzz340, zzz341, Neg(Succ(Succ(Zero))), zzz343, zzz344, zzz510, zzz511, Succ(zzz512000), zzz513, zzz514, zzz31, Succ(Succ(zzz6700)), h) → new_mkVBalBranch3MkVBalBranch224(zzz340, zzz341, Succ(Zero), zzz343, zzz344, zzz510, zzz511, zzz512000, zzz513, zzz514, zzz31, Zero, Succ(Succ(new_primPlusNat2(zzz6700, zzz512000))), h)
new_mkVBalBranch0(zzz31, Branch(zzz510, zzz511, Pos(Zero), zzz513, zzz514), Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), h) → new_mkVBalBranch3MkVBalBranch116(zzz340, zzz341, zzz34200, zzz343, zzz344, zzz510, zzz511, zzz513, zzz514, zzz31, Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat2(Succ(new_primPlusNat3(new_primPlusNat1(zzz34200), zzz34200)), zzz34200)), zzz34200))), h)
new_mkVBalBranch0(zzz31, Branch(zzz510, zzz511, Neg(Zero), zzz513, zzz514), Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), h) → new_mkVBalBranch3MkVBalBranch117(zzz340, zzz341, zzz34200, zzz343, zzz344, zzz510, zzz511, zzz513, zzz514, zzz31, Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat2(Succ(new_primPlusNat3(new_primPlusNat1(zzz34200), zzz34200)), zzz34200)), zzz34200))), h)
new_mkVBalBranch3MkVBalBranch224(zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, zzz1125, zzz1126, zzz1127, zzz1128, zzz1129, Succ(zzz11300), Succ(zzz11310), bd) → new_mkVBalBranch3MkVBalBranch224(zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, zzz1125, zzz1126, zzz1127, zzz1128, zzz1129, zzz11300, zzz11310, bd)
new_mkVBalBranch3MkVBalBranch217(zzz473, zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, zzz481, zzz482, Succ(zzz4830), Zero, bh) → new_mkVBalBranch3MkVBalBranch121(zzz473, zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, zzz481, zzz482, Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat2(Succ(new_primPlusNat3(new_primPlusNat1(zzz475), zzz475)), zzz475)), zzz475))), bh)
new_mkVBalBranch3MkVBalBranch229(zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, zzz1125, zzz1126, zzz1127, zzz1128, zzz1129, bd) → new_mkVBalBranch3MkVBalBranch119(zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, zzz1125, zzz1126, zzz1127, zzz1128, zzz1129, Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat2(Succ(new_primPlusNat3(new_primPlusNat1(zzz1121), zzz1121)), zzz1121)), zzz1121))), bd)
new_mkVBalBranch3MkVBalBranch217(zzz473, zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, zzz481, zzz482, Zero, Succ(zzz4840), bh) → new_mkVBalBranch0(zzz482, Branch(zzz478, zzz479, Pos(Succ(Zero)), zzz480, zzz481), zzz476, bh)
new_mkVBalBranch3MkVBalBranch218(zzz461, zzz462, zzz463, zzz464, zzz465, zzz466, zzz467, zzz468, zzz469, zzz470, zzz471, bb) → new_mkVBalBranch3MkVBalBranch110(zzz461, zzz462, zzz463, zzz464, zzz465, zzz466, zzz467, zzz468, zzz469, zzz470, zzz471, Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat2(Succ(new_primPlusNat3(new_primPlusNat1(zzz463), zzz463)), zzz463)), zzz463))), bb)
new_mkVBalBranch3MkVBalBranch110(zzz461, zzz462, zzz463, zzz464, zzz465, zzz466, zzz467, zzz468, zzz469, zzz470, zzz471, Succ(zzz5800), bb) → new_mkVBalBranch3MkVBalBranch115(zzz461, zzz462, zzz463, zzz464, zzz465, zzz466, zzz467, Succ(zzz468), zzz469, zzz470, zzz471, Succ(zzz5800), Succ(Succ(zzz468)), bb)
new_mkVBalBranch3MkVBalBranch227(zzz486, zzz487, zzz488, zzz489, zzz490, zzz491, zzz492, zzz493, zzz494, zzz495, zzz496, bf) → new_mkVBalBranch0(zzz496, Branch(zzz491, zzz492, Neg(Succ(Succ(zzz493))), zzz494, zzz495), zzz489, bf)
new_mkVBalBranch3MkVBalBranch215(zzz340, zzz341, Pos(Zero), zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, Succ(zzz660), h) → new_mkVBalBranch0(zzz31, zzz514, Branch(zzz340, zzz341, Pos(Zero), zzz343, zzz344), h)
new_mkVBalBranch3MkVBalBranch223(zzz340, zzz341, Neg(Zero), zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, Succ(zzz670), h) → new_mkVBalBranch0(zzz31, Branch(zzz510, zzz511, Neg(Succ(zzz51200)), zzz513, zzz514), zzz343, h)
new_mkVBalBranch3MkVBalBranch216(zzz1105, zzz1106, zzz1107, zzz1108, zzz1109, zzz1110, zzz1111, zzz1112, zzz1113, zzz1114, zzz1115, Zero, Succ(zzz11170), ba) → new_mkVBalBranch0(zzz1115, Branch(zzz1110, zzz1111, Pos(Succ(Succ(zzz1112))), zzz1113, zzz1114), zzz1108, ba)
new_mkVBalBranch3MkVBalBranch115(zzz1986, zzz1987, zzz1988, zzz1989, zzz1990, zzz1991, zzz1992, zzz1993, zzz1994, zzz1995, zzz1996, Zero, Succ(zzz19980), bc) → new_mkVBalBranch0(zzz1996, zzz1995, Branch(zzz1986, zzz1987, Pos(Succ(zzz1988)), zzz1989, zzz1990), bc)
new_mkVBalBranch3MkVBalBranch215(zzz340, zzz341, Pos(Succ(Zero)), zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, Succ(zzz660), h) → new_mkVBalBranch3MkVBalBranch18(zzz340, zzz341, zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, new_primPlusNat2(Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat3(new_primPlusNat1(Zero), Zero)), Zero))), Succ(Zero)), h)
new_mkVBalBranch3MkVBalBranch233(zzz473, zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, zzz481, zzz482, bh) → new_mkVBalBranch3MkVBalBranch121(zzz473, zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, zzz481, zzz482, Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat2(Succ(new_primPlusNat3(new_primPlusNat1(zzz475), zzz475)), zzz475)), zzz475))), bh)
new_mkVBalBranch3MkVBalBranch122(zzz340, zzz341, zzz34200, zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, h) → new_mkVBalBranch0(zzz31, zzz514, Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), h)
new_mkVBalBranch3MkVBalBranch217(zzz473, zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, zzz481, zzz482, Succ(zzz4830), Succ(zzz4840), bh) → new_mkVBalBranch3MkVBalBranch217(zzz473, zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, zzz481, zzz482, zzz4830, zzz4840, bh)
new_mkVBalBranch3MkVBalBranch116(zzz340, zzz341, zzz34200, zzz343, zzz344, zzz510, zzz511, zzz513, zzz514, zzz31, Succ(zzz1200), h) → new_mkVBalBranch0(zzz31, zzz514, Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), h)
new_mkVBalBranch3MkVBalBranch225(zzz498, zzz499, zzz500, zzz501, zzz502, zzz503, zzz504, zzz505, zzz506, zzz507, Zero, Succ(zzz5090), bg) → new_mkVBalBranch0(zzz507, Branch(zzz503, zzz504, Neg(Succ(Zero)), zzz505, zzz506), zzz501, bg)
new_mkVBalBranch0(zzz31, Branch(zzz510, zzz511, Neg(Succ(zzz51200)), zzz513, zzz514), Branch(zzz340, zzz341, zzz342, zzz343, zzz344), h) → new_mkVBalBranch3MkVBalBranch223(zzz340, zzz341, zzz342, zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat3(new_primPlusNat1(zzz51200), zzz51200)), zzz51200))), h)
new_mkVBalBranch3MkVBalBranch223(zzz340, zzz341, Neg(Succ(Zero)), zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, Succ(zzz670), h) → new_mkVBalBranch0(zzz31, Branch(zzz510, zzz511, Neg(Succ(zzz51200)), zzz513, zzz514), zzz343, h)
new_mkVBalBranch3MkVBalBranch215(zzz340, zzz341, Pos(Succ(Succ(zzz342000))), zzz343, zzz344, zzz510, zzz511, Zero, zzz513, zzz514, zzz31, Succ(Succ(zzz6600)), h) → new_mkVBalBranch3MkVBalBranch217(zzz340, zzz341, Succ(zzz342000), zzz343, zzz344, zzz510, zzz511, zzz513, zzz514, zzz31, Succ(zzz6600), zzz342000, h)
new_mkVBalBranch3MkVBalBranch117(zzz340, zzz341, zzz34200, zzz343, zzz344, zzz510, zzz511, zzz513, zzz514, zzz31, Succ(zzz1240), h) → new_mkVBalBranch0(zzz31, zzz514, Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), h)
new_mkVBalBranch3MkVBalBranch217(zzz473, zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, zzz481, zzz482, Zero, Zero, bh) → new_mkVBalBranch3MkVBalBranch233(zzz473, zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, zzz481, zzz482, bh)
new_mkVBalBranch3MkVBalBranch120(zzz2050, zzz2051, zzz2052, zzz2053, zzz2054, zzz2055, zzz2056, zzz2057, zzz2058, zzz2059, zzz2060, Succ(zzz20610), Succ(zzz20620), be) → new_mkVBalBranch3MkVBalBranch120(zzz2050, zzz2051, zzz2052, zzz2053, zzz2054, zzz2055, zzz2056, zzz2057, zzz2058, zzz2059, zzz2060, zzz20610, zzz20620, be)
new_mkVBalBranch3MkVBalBranch223(zzz340, zzz341, Pos(zzz3420), zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, Succ(zzz670), h) → new_mkVBalBranch0(zzz31, Branch(zzz510, zzz511, Neg(Succ(zzz51200)), zzz513, zzz514), zzz343, h)
new_mkVBalBranch3MkVBalBranch216(zzz1105, zzz1106, zzz1107, zzz1108, zzz1109, zzz1110, zzz1111, zzz1112, zzz1113, zzz1114, zzz1115, Succ(zzz11160), Succ(zzz11170), ba) → new_mkVBalBranch3MkVBalBranch216(zzz1105, zzz1106, zzz1107, zzz1108, zzz1109, zzz1110, zzz1111, zzz1112, zzz1113, zzz1114, zzz1115, zzz11160, zzz11170, ba)
new_mkVBalBranch3MkVBalBranch19(zzz340, zzz341, zzz34200, zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, Zero, h) → new_mkVBalBranch3MkVBalBranch122(zzz340, zzz341, zzz34200, zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, h)
new_mkVBalBranch3MkVBalBranch225(zzz498, zzz499, zzz500, zzz501, zzz502, zzz503, zzz504, zzz505, zzz506, zzz507, Succ(zzz5080), Succ(zzz5090), bg) → new_mkVBalBranch3MkVBalBranch225(zzz498, zzz499, zzz500, zzz501, zzz502, zzz503, zzz504, zzz505, zzz506, zzz507, zzz5080, zzz5090, bg)
new_mkVBalBranch3MkVBalBranch19(zzz340, zzz341, zzz34200, zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, Succ(zzz1410), h) → new_mkVBalBranch0(zzz31, zzz514, Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), h)
new_mkVBalBranch3MkVBalBranch224(zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, zzz1125, zzz1126, zzz1127, zzz1128, zzz1129, Zero, Zero, bd) → new_mkVBalBranch3MkVBalBranch229(zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, zzz1125, zzz1126, zzz1127, zzz1128, zzz1129, bd)
new_mkVBalBranch3MkVBalBranch224(zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, zzz1125, zzz1126, zzz1127, zzz1128, zzz1129, Zero, Succ(zzz11310), bd) → new_mkVBalBranch3MkVBalBranch227(zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, zzz1125, zzz1126, zzz1127, zzz1128, zzz1129, bd)
new_mkVBalBranch3MkVBalBranch223(zzz340, zzz341, Neg(Succ(Succ(Zero))), zzz343, zzz344, zzz510, zzz511, Zero, zzz513, zzz514, zzz31, Succ(Succ(zzz6700)), h) → new_mkVBalBranch3MkVBalBranch225(zzz340, zzz341, Succ(Zero), zzz343, zzz344, zzz510, zzz511, zzz513, zzz514, zzz31, Zero, Succ(zzz6700), h)
new_mkVBalBranch3MkVBalBranch223(zzz340, zzz341, Neg(Succ(Succ(Succ(zzz3420000)))), zzz343, zzz344, zzz510, zzz511, Succ(zzz512000), zzz513, zzz514, zzz31, Succ(Succ(zzz6700)), h) → new_mkVBalBranch3MkVBalBranch224(zzz340, zzz341, Succ(Succ(zzz3420000)), zzz343, zzz344, zzz510, zzz511, zzz512000, zzz513, zzz514, zzz31, Succ(zzz3420000), Succ(Succ(new_primPlusNat2(zzz6700, zzz512000))), h)
new_mkVBalBranch3MkVBalBranch225(zzz498, zzz499, zzz500, zzz501, zzz502, zzz503, zzz504, zzz505, zzz506, zzz507, Succ(zzz5080), Zero, bg) → new_mkVBalBranch3MkVBalBranch118(zzz498, zzz499, zzz500, zzz501, zzz502, zzz503, zzz504, zzz505, zzz506, zzz507, Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat2(Succ(new_primPlusNat3(new_primPlusNat1(zzz500), zzz500)), zzz500)), zzz500))), bg)
new_mkVBalBranch3MkVBalBranch115(zzz1986, zzz1987, zzz1988, zzz1989, zzz1990, zzz1991, zzz1992, zzz1993, zzz1994, zzz1995, zzz1996, Succ(zzz19970), Succ(zzz19980), bc) → new_mkVBalBranch3MkVBalBranch115(zzz1986, zzz1987, zzz1988, zzz1989, zzz1990, zzz1991, zzz1992, zzz1993, zzz1994, zzz1995, zzz1996, zzz19970, zzz19980, bc)
new_mkVBalBranch3MkVBalBranch215(zzz340, zzz341, Neg(Zero), zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, Succ(zzz660), h) → new_mkVBalBranch0(zzz31, zzz514, Branch(zzz340, zzz341, Neg(Zero), zzz343, zzz344), h)
new_mkVBalBranch3MkVBalBranch224(zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, zzz1125, zzz1126, zzz1127, zzz1128, zzz1129, Succ(zzz11300), Zero, bd) → new_mkVBalBranch3MkVBalBranch119(zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, zzz1125, zzz1126, zzz1127, zzz1128, zzz1129, Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat2(Succ(new_primPlusNat3(new_primPlusNat1(zzz1121), zzz1121)), zzz1121)), zzz1121))), bd)
new_mkVBalBranch3MkVBalBranch222(zzz461, zzz462, zzz463, zzz464, zzz465, zzz466, zzz467, zzz468, zzz469, zzz470, zzz471, bb) → new_mkVBalBranch3MkVBalBranch110(zzz461, zzz462, zzz463, zzz464, zzz465, zzz466, zzz467, zzz468, zzz469, zzz470, zzz471, Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat2(Succ(new_primPlusNat3(new_primPlusNat1(zzz463), zzz463)), zzz463)), zzz463))), bb)
new_mkVBalBranch3MkVBalBranch118(zzz498, zzz499, zzz500, zzz501, zzz502, zzz503, zzz504, zzz505, zzz506, zzz507, Succ(zzz8040), bg) → new_mkVBalBranch3MkVBalBranch120(zzz498, zzz499, zzz500, zzz501, zzz502, zzz503, zzz504, Zero, zzz505, zzz506, zzz507, Succ(Zero), Succ(zzz8040), bg)
new_mkVBalBranch3MkVBalBranch216(zzz1105, zzz1106, zzz1107, zzz1108, zzz1109, zzz1110, zzz1111, zzz1112, zzz1113, zzz1114, zzz1115, Succ(zzz11160), Zero, ba) → new_mkVBalBranch3MkVBalBranch218(zzz1105, zzz1106, zzz1107, zzz1108, zzz1109, zzz1110, zzz1111, zzz1112, zzz1113, zzz1114, zzz1115, ba)
new_mkVBalBranch3MkVBalBranch216(zzz1105, zzz1106, zzz1107, zzz1108, zzz1109, zzz1110, zzz1111, zzz1112, zzz1113, zzz1114, zzz1115, Zero, Zero, ba) → new_mkVBalBranch3MkVBalBranch222(zzz1105, zzz1106, zzz1107, zzz1108, zzz1109, zzz1110, zzz1111, zzz1112, zzz1113, zzz1114, zzz1115, ba)
new_mkVBalBranch3MkVBalBranch119(zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, zzz1125, zzz1126, zzz1127, zzz1128, zzz1129, Succ(zzz12130), bd) → new_mkVBalBranch3MkVBalBranch120(zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, zzz1125, Succ(zzz1126), zzz1127, zzz1128, zzz1129, Succ(Succ(zzz1126)), Succ(zzz12130), bd)
new_mkVBalBranch3MkVBalBranch18(zzz340, zzz341, zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, Zero, h) → new_mkVBalBranch3MkVBalBranch115(zzz340, zzz341, Zero, zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, Zero, Succ(zzz51200), h)

The TRS R consists of the following rules:

new_primPlusNat1(Zero) → Zero
new_primPlusNat1(Succ(zzz62000)) → Succ(Succ(new_primPlusNat1(zzz62000)))
new_primPlusNat3(zzz90, Succ(zzz910)) → Succ(Succ(new_primPlusNat2(zzz90, zzz910)))
new_primPlusNat3(zzz90, Zero) → Succ(zzz90)
new_primPlusNat2(Succ(zzz900), Succ(zzz9100)) → Succ(Succ(new_primPlusNat2(zzz900, zzz9100)))
new_primPlusNat2(Zero, Succ(zzz9100)) → Succ(zzz9100)
new_primPlusNat2(Zero, Zero) → Zero
new_primPlusNat2(Succ(zzz900), Zero) → Succ(zzz900)

The set Q consists of the following terms:

new_primPlusNat2(Zero, Succ(x0))
new_primPlusNat3(x0, Succ(x1))
new_primPlusNat2(Succ(x0), Succ(x1))
new_primPlusNat3(x0, Zero)
new_primPlusNat1(Zero)
new_primPlusNat2(Zero, Zero)
new_primPlusNat1(Succ(x0))
new_primPlusNat2(Succ(x0), Zero)

We have to consider all minimal (P,Q,R)-chains.
The approximation of the Dependency Graph [15,17,22] contains 1 SCC with 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
                                    ↳ DependencyGraphProof
                                      ↳ QDP
                                        ↳ Rewriting
                                          ↳ QDP
                                            ↳ Rewriting
                                              ↳ QDP
                                                ↳ Rewriting
                                                  ↳ QDP
                                                    ↳ Rewriting
                                                      ↳ QDP
                                                        ↳ Rewriting
                                                          ↳ QDP
                                                            ↳ Rewriting
                                                              ↳ QDP
                                                                ↳ Rewriting
                                                                  ↳ QDP
                                                                    ↳ Rewriting
                                                                      ↳ QDP
                                                                        ↳ Rewriting
                                                                          ↳ QDP
                                                                            ↳ Rewriting
                                                                              ↳ QDP
                                                                                ↳ Rewriting
                                                                                  ↳ QDP
                                                                                    ↳ Rewriting
                                                                                      ↳ QDP
                                                                                        ↳ Rewriting
                                                                                          ↳ QDP
                                                                                            ↳ Rewriting
                                                                                              ↳ QDP
                                                                                                ↳ Rewriting
                                                                                                  ↳ QDP
                                                                                                    ↳ Rewriting
                                                                                                      ↳ QDP
                                                                                                        ↳ Rewriting
                                                                                                          ↳ QDP
                                                                                                            ↳ UsableRulesProof
                                                                                                              ↳ QDP
                                                                                                                ↳ QReductionProof
                                                                                                                  ↳ QDP
                                                                                                                    ↳ Rewriting
                                                                                                                      ↳ QDP
                                                                                                                        ↳ Rewriting
                                                                                                                          ↳ QDP
                                                                                                                            ↳ DependencyGraphProof
                                                                                                                              ↳ QDP
                                                                                                                                ↳ Rewriting
                                                                                                                                  ↳ QDP
                                                                                                                                    ↳ Rewriting
                                                                                                                                      ↳ QDP
                                                                                                                                        ↳ DependencyGraphProof
                                                                                                                                          ↳ QDP
                                                                                                                                            ↳ Rewriting
                                                                                                                                              ↳ QDP
                                                                                                                                                ↳ Rewriting
                                                                                                                                                  ↳ QDP
                                                                                                                                                    ↳ Rewriting
                                                                                                                                                      ↳ QDP
                                                                                                                                                        ↳ Rewriting
                                                                                                                                                          ↳ QDP
                                                                                                                                                            ↳ Rewriting
                                                                                                                                                              ↳ QDP
                                                                                                                                                                ↳ Rewriting
                                                                                                                                                                  ↳ QDP
                                                                                                                                                                    ↳ Rewriting
                                                                                                                                                                      ↳ QDP
                                                                                                                                                                        ↳ Rewriting
                                                                                                                                                                          ↳ QDP
                                                                                                                                                                            ↳ Rewriting
                                                                                                                                                                              ↳ QDP
                                                                                                                                                                                ↳ Rewriting
                                                                                                                                                                                  ↳ QDP
                                                                                                                                                                                    ↳ Rewriting
                                                                                                                                                                                      ↳ QDP
                                                                                                                                                                                        ↳ Rewriting
                                                                                                                                                                                          ↳ QDP
                                                                                                                                                                                            ↳ UsableRulesProof
                                                                                                                                                                                              ↳ QDP
                                                                                                                                                                                                ↳ QReductionProof
                                                                                                                                                                                                  ↳ QDP
                                                                                                                                                                                                    ↳ Rewriting
                                                                                                                                                                                                      ↳ QDP
                                                                                                                                                                                                        ↳ Rewriting
                                                                                                                                                                                                          ↳ QDP
                                                                                                                                                                                                            ↳ Rewriting
                                                                                                                                                                                                              ↳ QDP
                                                                                                                                                                                                                ↳ Rewriting
                                                                                                                                                                                                                  ↳ QDP
                                                                                                                                                                                                                    ↳ Rewriting
                                                                                                                                                                                                                      ↳ QDP
                                                                                                                                                                                                                        ↳ Rewriting
                                                                                                                                                                                                                          ↳ QDP
                                                                                                                                                                                                                            ↳ Rewriting
                                                                                                                                                                                                                              ↳ QDP
                                                                                                                                                                                                                                ↳ Rewriting
                                                                                                                                                                                                                                  ↳ QDP
                                                                                                                                                                                                                                    ↳ Rewriting
                                                                                                                                                                                                                                      ↳ QDP
                                                                                                                                                                                                                                        ↳ Rewriting
                                                                                                                                                                                                                                          ↳ QDP
                                                                                                                                                                                                                                            ↳ Rewriting
                                                                                                                                                                                                                                              ↳ QDP
                                                                                                                                                                                                                                                ↳ Rewriting
                                                                                                                                                                                                                                                  ↳ QDP
                                                                                                                                                                                                                                                    ↳ Rewriting
                                                                                                                                                                                                                                                      ↳ QDP
                                                                                                                                                                                                                                                        ↳ Rewriting
                                                                                                                                                                                                                                                          ↳ QDP
                                                                                                                                                                                                                                                            ↳ DependencyGraphProof
                                                                                                                                                                                                                                                              ↳ QDP
                                                                                                                                                                                                                                                                ↳ Rewriting
                                                                                                                                                                                                                                                                  ↳ QDP
                                                                                                                                                                                                                                                                    ↳ Rewriting
                                                                                                                                                                                                                                                                      ↳ QDP
                                                                                                                                                                                                                                                                        ↳ Rewriting
                                                                                                                                                                                                                                                                          ↳ QDP
                                                                                                                                                                                                                                                                            ↳ Rewriting
                                                                                                                                                                                                                                                                              ↳ QDP
                                                                                                                                                                                                                                                                                ↳ Rewriting
                                                                                                                                                                                                                                                                                  ↳ QDP
                                                                                                                                                                                                                                                                                    ↳ Rewriting
                                                                                                                                                                                                                                                                                      ↳ QDP
                                                                                                                                                                                                                                                                                        ↳ DependencyGraphProof
                                                                                                                                                                                                                                                                                          ↳ QDP
                                                                                                                                                                                                                                                                                            ↳ Rewriting
                                                                                                                                                                                                                                                                                              ↳ QDP
                                                                                                                                                                                                                                                                                                ↳ DependencyGraphProof
                                                                                                                                                                                                                                                                                                  ↳ QDP
                                                                                                                                                                                                                                                                                                    ↳ Rewriting
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP

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

new_mkVBalBranch3MkVBalBranch225(zzz498, zzz499, zzz500, zzz501, zzz502, zzz503, zzz504, zzz505, zzz506, zzz507, Zero, Zero, bg) → new_mkVBalBranch3MkVBalBranch230(zzz498, zzz499, zzz500, zzz501, zzz502, zzz503, zzz504, zzz505, zzz506, zzz507, bg)
new_mkVBalBranch3MkVBalBranch18(zzz340, zzz341, zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, Succ(zzz1480), h) → new_mkVBalBranch3MkVBalBranch115(zzz340, zzz341, Zero, zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, Succ(zzz1480), Succ(zzz51200), h)
new_mkVBalBranch3MkVBalBranch215(zzz340, zzz341, Pos(Succ(Succ(zzz342000))), zzz343, zzz344, zzz510, zzz511, Succ(zzz512000), zzz513, zzz514, zzz31, Succ(Succ(zzz6600)), h) → new_mkVBalBranch3MkVBalBranch216(zzz340, zzz341, Succ(zzz342000), zzz343, zzz344, zzz510, zzz511, zzz512000, zzz513, zzz514, zzz31, Succ(Succ(new_primPlusNat2(zzz6600, zzz512000))), zzz342000, h)
new_mkVBalBranch0(zzz31, Branch(zzz510, zzz511, Neg(Zero), zzz513, zzz514), Branch(zzz340, zzz341, Pos(Succ(zzz34200)), zzz343, zzz344), h) → new_mkVBalBranch0(zzz31, Branch(zzz510, zzz511, Neg(Zero), zzz513, zzz514), zzz343, h)
new_mkVBalBranch3MkVBalBranch223(zzz340, zzz341, Neg(Succ(Succ(Succ(zzz3420000)))), zzz343, zzz344, zzz510, zzz511, Zero, zzz513, zzz514, zzz31, Succ(Succ(zzz6700)), h) → new_mkVBalBranch3MkVBalBranch225(zzz340, zzz341, Succ(Succ(zzz3420000)), zzz343, zzz344, zzz510, zzz511, zzz513, zzz514, zzz31, Succ(zzz3420000), Succ(zzz6700), h)
new_mkVBalBranch3MkVBalBranch120(zzz2050, zzz2051, zzz2052, zzz2053, zzz2054, zzz2055, zzz2056, zzz2057, zzz2058, zzz2059, zzz2060, Zero, Succ(zzz20620), be) → new_mkVBalBranch0(zzz2060, zzz2059, Branch(zzz2050, zzz2051, Neg(Succ(zzz2052)), zzz2053, zzz2054), be)
new_mkVBalBranch0(zzz31, Branch(zzz510, zzz511, Pos(Zero), zzz513, zzz514), Branch(zzz340, zzz341, Pos(Succ(zzz34200)), zzz343, zzz344), h) → new_mkVBalBranch0(zzz31, Branch(zzz510, zzz511, Pos(Zero), zzz513, zzz514), zzz343, h)
new_mkVBalBranch3MkVBalBranch121(zzz473, zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, zzz481, zzz482, Succ(zzz7390), bh) → new_mkVBalBranch3MkVBalBranch115(zzz473, zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, Zero, zzz480, zzz481, zzz482, Succ(zzz7390), Succ(Zero), bh)
new_mkVBalBranch0(zzz31, Branch(zzz510, zzz511, Pos(Succ(zzz51200)), zzz513, zzz514), Branch(zzz340, zzz341, zzz342, zzz343, zzz344), h) → new_mkVBalBranch3MkVBalBranch215(zzz340, zzz341, zzz342, zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat3(new_primPlusNat1(zzz51200), zzz51200)), zzz51200))), h)
new_mkVBalBranch3MkVBalBranch215(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, Succ(zzz660), h) → new_mkVBalBranch3MkVBalBranch19(zzz340, zzz341, zzz34200, zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat2(Succ(new_primPlusNat3(new_primPlusNat1(zzz34200), zzz34200)), zzz34200)), zzz34200))), h)
new_mkVBalBranch3MkVBalBranch223(zzz340, zzz341, Neg(Succ(Succ(Zero))), zzz343, zzz344, zzz510, zzz511, Succ(zzz512000), zzz513, zzz514, zzz31, Succ(Succ(zzz6700)), h) → new_mkVBalBranch3MkVBalBranch224(zzz340, zzz341, Succ(Zero), zzz343, zzz344, zzz510, zzz511, zzz512000, zzz513, zzz514, zzz31, Zero, Succ(Succ(new_primPlusNat2(zzz6700, zzz512000))), h)
new_mkVBalBranch3MkVBalBranch230(zzz498, zzz499, zzz500, zzz501, zzz502, zzz503, zzz504, zzz505, zzz506, zzz507, bg) → new_mkVBalBranch3MkVBalBranch118(zzz498, zzz499, zzz500, zzz501, zzz502, zzz503, zzz504, zzz505, zzz506, zzz507, Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat2(Succ(new_primPlusNat3(new_primPlusNat1(zzz500), zzz500)), zzz500)), zzz500))), bg)
new_mkVBalBranch0(zzz31, Branch(zzz510, zzz511, Pos(Zero), zzz513, zzz514), Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), h) → new_mkVBalBranch3MkVBalBranch116(zzz340, zzz341, zzz34200, zzz343, zzz344, zzz510, zzz511, zzz513, zzz514, zzz31, Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat2(Succ(new_primPlusNat3(new_primPlusNat1(zzz34200), zzz34200)), zzz34200)), zzz34200))), h)
new_mkVBalBranch0(zzz31, Branch(zzz510, zzz511, Neg(Zero), zzz513, zzz514), Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), h) → new_mkVBalBranch3MkVBalBranch117(zzz340, zzz341, zzz34200, zzz343, zzz344, zzz510, zzz511, zzz513, zzz514, zzz31, Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat2(Succ(new_primPlusNat3(new_primPlusNat1(zzz34200), zzz34200)), zzz34200)), zzz34200))), h)
new_mkVBalBranch3MkVBalBranch224(zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, zzz1125, zzz1126, zzz1127, zzz1128, zzz1129, Succ(zzz11300), Succ(zzz11310), bd) → new_mkVBalBranch3MkVBalBranch224(zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, zzz1125, zzz1126, zzz1127, zzz1128, zzz1129, zzz11300, zzz11310, bd)
new_mkVBalBranch3MkVBalBranch229(zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, zzz1125, zzz1126, zzz1127, zzz1128, zzz1129, bd) → new_mkVBalBranch3MkVBalBranch119(zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, zzz1125, zzz1126, zzz1127, zzz1128, zzz1129, Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat2(Succ(new_primPlusNat3(new_primPlusNat1(zzz1121), zzz1121)), zzz1121)), zzz1121))), bd)
new_mkVBalBranch3MkVBalBranch217(zzz473, zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, zzz481, zzz482, Succ(zzz4830), Zero, bh) → new_mkVBalBranch3MkVBalBranch121(zzz473, zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, zzz481, zzz482, Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat2(Succ(new_primPlusNat3(new_primPlusNat1(zzz475), zzz475)), zzz475)), zzz475))), bh)
new_mkVBalBranch3MkVBalBranch217(zzz473, zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, zzz481, zzz482, Zero, Succ(zzz4840), bh) → new_mkVBalBranch0(zzz482, Branch(zzz478, zzz479, Pos(Succ(Zero)), zzz480, zzz481), zzz476, bh)
new_mkVBalBranch3MkVBalBranch218(zzz461, zzz462, zzz463, zzz464, zzz465, zzz466, zzz467, zzz468, zzz469, zzz470, zzz471, bb) → new_mkVBalBranch3MkVBalBranch110(zzz461, zzz462, zzz463, zzz464, zzz465, zzz466, zzz467, zzz468, zzz469, zzz470, zzz471, Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat2(Succ(new_primPlusNat3(new_primPlusNat1(zzz463), zzz463)), zzz463)), zzz463))), bb)
new_mkVBalBranch3MkVBalBranch110(zzz461, zzz462, zzz463, zzz464, zzz465, zzz466, zzz467, zzz468, zzz469, zzz470, zzz471, Succ(zzz5800), bb) → new_mkVBalBranch3MkVBalBranch115(zzz461, zzz462, zzz463, zzz464, zzz465, zzz466, zzz467, Succ(zzz468), zzz469, zzz470, zzz471, Succ(zzz5800), Succ(Succ(zzz468)), bb)
new_mkVBalBranch3MkVBalBranch227(zzz486, zzz487, zzz488, zzz489, zzz490, zzz491, zzz492, zzz493, zzz494, zzz495, zzz496, bf) → new_mkVBalBranch0(zzz496, Branch(zzz491, zzz492, Neg(Succ(Succ(zzz493))), zzz494, zzz495), zzz489, bf)
new_mkVBalBranch3MkVBalBranch215(zzz340, zzz341, Pos(Zero), zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, Succ(zzz660), h) → new_mkVBalBranch0(zzz31, zzz514, Branch(zzz340, zzz341, Pos(Zero), zzz343, zzz344), h)
new_mkVBalBranch3MkVBalBranch223(zzz340, zzz341, Neg(Zero), zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, Succ(zzz670), h) → new_mkVBalBranch0(zzz31, Branch(zzz510, zzz511, Neg(Succ(zzz51200)), zzz513, zzz514), zzz343, h)
new_mkVBalBranch3MkVBalBranch216(zzz1105, zzz1106, zzz1107, zzz1108, zzz1109, zzz1110, zzz1111, zzz1112, zzz1113, zzz1114, zzz1115, Zero, Succ(zzz11170), ba) → new_mkVBalBranch0(zzz1115, Branch(zzz1110, zzz1111, Pos(Succ(Succ(zzz1112))), zzz1113, zzz1114), zzz1108, ba)
new_mkVBalBranch3MkVBalBranch115(zzz1986, zzz1987, zzz1988, zzz1989, zzz1990, zzz1991, zzz1992, zzz1993, zzz1994, zzz1995, zzz1996, Zero, Succ(zzz19980), bc) → new_mkVBalBranch0(zzz1996, zzz1995, Branch(zzz1986, zzz1987, Pos(Succ(zzz1988)), zzz1989, zzz1990), bc)
new_mkVBalBranch3MkVBalBranch215(zzz340, zzz341, Pos(Succ(Zero)), zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, Succ(zzz660), h) → new_mkVBalBranch3MkVBalBranch18(zzz340, zzz341, zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, new_primPlusNat2(Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat3(new_primPlusNat1(Zero), Zero)), Zero))), Succ(Zero)), h)
new_mkVBalBranch3MkVBalBranch233(zzz473, zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, zzz481, zzz482, bh) → new_mkVBalBranch3MkVBalBranch121(zzz473, zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, zzz481, zzz482, Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat2(Succ(new_primPlusNat3(new_primPlusNat1(zzz475), zzz475)), zzz475)), zzz475))), bh)
new_mkVBalBranch3MkVBalBranch217(zzz473, zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, zzz481, zzz482, Succ(zzz4830), Succ(zzz4840), bh) → new_mkVBalBranch3MkVBalBranch217(zzz473, zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, zzz481, zzz482, zzz4830, zzz4840, bh)
new_mkVBalBranch3MkVBalBranch116(zzz340, zzz341, zzz34200, zzz343, zzz344, zzz510, zzz511, zzz513, zzz514, zzz31, Succ(zzz1200), h) → new_mkVBalBranch0(zzz31, zzz514, Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), h)
new_mkVBalBranch3MkVBalBranch225(zzz498, zzz499, zzz500, zzz501, zzz502, zzz503, zzz504, zzz505, zzz506, zzz507, Zero, Succ(zzz5090), bg) → new_mkVBalBranch0(zzz507, Branch(zzz503, zzz504, Neg(Succ(Zero)), zzz505, zzz506), zzz501, bg)
new_mkVBalBranch0(zzz31, Branch(zzz510, zzz511, Neg(Succ(zzz51200)), zzz513, zzz514), Branch(zzz340, zzz341, zzz342, zzz343, zzz344), h) → new_mkVBalBranch3MkVBalBranch223(zzz340, zzz341, zzz342, zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat3(new_primPlusNat1(zzz51200), zzz51200)), zzz51200))), h)
new_mkVBalBranch3MkVBalBranch223(zzz340, zzz341, Neg(Succ(Zero)), zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, Succ(zzz670), h) → new_mkVBalBranch0(zzz31, Branch(zzz510, zzz511, Neg(Succ(zzz51200)), zzz513, zzz514), zzz343, h)
new_mkVBalBranch3MkVBalBranch215(zzz340, zzz341, Pos(Succ(Succ(zzz342000))), zzz343, zzz344, zzz510, zzz511, Zero, zzz513, zzz514, zzz31, Succ(Succ(zzz6600)), h) → new_mkVBalBranch3MkVBalBranch217(zzz340, zzz341, Succ(zzz342000), zzz343, zzz344, zzz510, zzz511, zzz513, zzz514, zzz31, Succ(zzz6600), zzz342000, h)
new_mkVBalBranch3MkVBalBranch117(zzz340, zzz341, zzz34200, zzz343, zzz344, zzz510, zzz511, zzz513, zzz514, zzz31, Succ(zzz1240), h) → new_mkVBalBranch0(zzz31, zzz514, Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), h)
new_mkVBalBranch3MkVBalBranch120(zzz2050, zzz2051, zzz2052, zzz2053, zzz2054, zzz2055, zzz2056, zzz2057, zzz2058, zzz2059, zzz2060, Succ(zzz20610), Succ(zzz20620), be) → new_mkVBalBranch3MkVBalBranch120(zzz2050, zzz2051, zzz2052, zzz2053, zzz2054, zzz2055, zzz2056, zzz2057, zzz2058, zzz2059, zzz2060, zzz20610, zzz20620, be)
new_mkVBalBranch3MkVBalBranch217(zzz473, zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, zzz481, zzz482, Zero, Zero, bh) → new_mkVBalBranch3MkVBalBranch233(zzz473, zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, zzz481, zzz482, bh)
new_mkVBalBranch3MkVBalBranch216(zzz1105, zzz1106, zzz1107, zzz1108, zzz1109, zzz1110, zzz1111, zzz1112, zzz1113, zzz1114, zzz1115, Succ(zzz11160), Succ(zzz11170), ba) → new_mkVBalBranch3MkVBalBranch216(zzz1105, zzz1106, zzz1107, zzz1108, zzz1109, zzz1110, zzz1111, zzz1112, zzz1113, zzz1114, zzz1115, zzz11160, zzz11170, ba)
new_mkVBalBranch3MkVBalBranch223(zzz340, zzz341, Pos(zzz3420), zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, Succ(zzz670), h) → new_mkVBalBranch0(zzz31, Branch(zzz510, zzz511, Neg(Succ(zzz51200)), zzz513, zzz514), zzz343, h)
new_mkVBalBranch3MkVBalBranch225(zzz498, zzz499, zzz500, zzz501, zzz502, zzz503, zzz504, zzz505, zzz506, zzz507, Succ(zzz5080), Succ(zzz5090), bg) → new_mkVBalBranch3MkVBalBranch225(zzz498, zzz499, zzz500, zzz501, zzz502, zzz503, zzz504, zzz505, zzz506, zzz507, zzz5080, zzz5090, bg)
new_mkVBalBranch3MkVBalBranch19(zzz340, zzz341, zzz34200, zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, Succ(zzz1410), h) → new_mkVBalBranch0(zzz31, zzz514, Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), h)
new_mkVBalBranch3MkVBalBranch224(zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, zzz1125, zzz1126, zzz1127, zzz1128, zzz1129, Zero, Succ(zzz11310), bd) → new_mkVBalBranch3MkVBalBranch227(zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, zzz1125, zzz1126, zzz1127, zzz1128, zzz1129, bd)
new_mkVBalBranch3MkVBalBranch224(zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, zzz1125, zzz1126, zzz1127, zzz1128, zzz1129, Zero, Zero, bd) → new_mkVBalBranch3MkVBalBranch229(zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, zzz1125, zzz1126, zzz1127, zzz1128, zzz1129, bd)
new_mkVBalBranch3MkVBalBranch225(zzz498, zzz499, zzz500, zzz501, zzz502, zzz503, zzz504, zzz505, zzz506, zzz507, Succ(zzz5080), Zero, bg) → new_mkVBalBranch3MkVBalBranch118(zzz498, zzz499, zzz500, zzz501, zzz502, zzz503, zzz504, zzz505, zzz506, zzz507, Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat2(Succ(new_primPlusNat3(new_primPlusNat1(zzz500), zzz500)), zzz500)), zzz500))), bg)
new_mkVBalBranch3MkVBalBranch223(zzz340, zzz341, Neg(Succ(Succ(Succ(zzz3420000)))), zzz343, zzz344, zzz510, zzz511, Succ(zzz512000), zzz513, zzz514, zzz31, Succ(Succ(zzz6700)), h) → new_mkVBalBranch3MkVBalBranch224(zzz340, zzz341, Succ(Succ(zzz3420000)), zzz343, zzz344, zzz510, zzz511, zzz512000, zzz513, zzz514, zzz31, Succ(zzz3420000), Succ(Succ(new_primPlusNat2(zzz6700, zzz512000))), h)
new_mkVBalBranch3MkVBalBranch223(zzz340, zzz341, Neg(Succ(Succ(Zero))), zzz343, zzz344, zzz510, zzz511, Zero, zzz513, zzz514, zzz31, Succ(Succ(zzz6700)), h) → new_mkVBalBranch3MkVBalBranch225(zzz340, zzz341, Succ(Zero), zzz343, zzz344, zzz510, zzz511, zzz513, zzz514, zzz31, Zero, Succ(zzz6700), h)
new_mkVBalBranch3MkVBalBranch115(zzz1986, zzz1987, zzz1988, zzz1989, zzz1990, zzz1991, zzz1992, zzz1993, zzz1994, zzz1995, zzz1996, Succ(zzz19970), Succ(zzz19980), bc) → new_mkVBalBranch3MkVBalBranch115(zzz1986, zzz1987, zzz1988, zzz1989, zzz1990, zzz1991, zzz1992, zzz1993, zzz1994, zzz1995, zzz1996, zzz19970, zzz19980, bc)
new_mkVBalBranch3MkVBalBranch215(zzz340, zzz341, Neg(Zero), zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, Succ(zzz660), h) → new_mkVBalBranch0(zzz31, zzz514, Branch(zzz340, zzz341, Neg(Zero), zzz343, zzz344), h)
new_mkVBalBranch3MkVBalBranch224(zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, zzz1125, zzz1126, zzz1127, zzz1128, zzz1129, Succ(zzz11300), Zero, bd) → new_mkVBalBranch3MkVBalBranch119(zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, zzz1125, zzz1126, zzz1127, zzz1128, zzz1129, Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat2(Succ(new_primPlusNat3(new_primPlusNat1(zzz1121), zzz1121)), zzz1121)), zzz1121))), bd)
new_mkVBalBranch3MkVBalBranch118(zzz498, zzz499, zzz500, zzz501, zzz502, zzz503, zzz504, zzz505, zzz506, zzz507, Succ(zzz8040), bg) → new_mkVBalBranch3MkVBalBranch120(zzz498, zzz499, zzz500, zzz501, zzz502, zzz503, zzz504, Zero, zzz505, zzz506, zzz507, Succ(Zero), Succ(zzz8040), bg)
new_mkVBalBranch3MkVBalBranch222(zzz461, zzz462, zzz463, zzz464, zzz465, zzz466, zzz467, zzz468, zzz469, zzz470, zzz471, bb) → new_mkVBalBranch3MkVBalBranch110(zzz461, zzz462, zzz463, zzz464, zzz465, zzz466, zzz467, zzz468, zzz469, zzz470, zzz471, Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat2(Succ(new_primPlusNat3(new_primPlusNat1(zzz463), zzz463)), zzz463)), zzz463))), bb)
new_mkVBalBranch3MkVBalBranch216(zzz1105, zzz1106, zzz1107, zzz1108, zzz1109, zzz1110, zzz1111, zzz1112, zzz1113, zzz1114, zzz1115, Succ(zzz11160), Zero, ba) → new_mkVBalBranch3MkVBalBranch218(zzz1105, zzz1106, zzz1107, zzz1108, zzz1109, zzz1110, zzz1111, zzz1112, zzz1113, zzz1114, zzz1115, ba)
new_mkVBalBranch3MkVBalBranch216(zzz1105, zzz1106, zzz1107, zzz1108, zzz1109, zzz1110, zzz1111, zzz1112, zzz1113, zzz1114, zzz1115, Zero, Zero, ba) → new_mkVBalBranch3MkVBalBranch222(zzz1105, zzz1106, zzz1107, zzz1108, zzz1109, zzz1110, zzz1111, zzz1112, zzz1113, zzz1114, zzz1115, ba)
new_mkVBalBranch3MkVBalBranch18(zzz340, zzz341, zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, Zero, h) → new_mkVBalBranch3MkVBalBranch115(zzz340, zzz341, Zero, zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, Zero, Succ(zzz51200), h)
new_mkVBalBranch3MkVBalBranch119(zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, zzz1125, zzz1126, zzz1127, zzz1128, zzz1129, Succ(zzz12130), bd) → new_mkVBalBranch3MkVBalBranch120(zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, zzz1125, Succ(zzz1126), zzz1127, zzz1128, zzz1129, Succ(Succ(zzz1126)), Succ(zzz12130), bd)

The TRS R consists of the following rules:

new_primPlusNat1(Zero) → Zero
new_primPlusNat1(Succ(zzz62000)) → Succ(Succ(new_primPlusNat1(zzz62000)))
new_primPlusNat3(zzz90, Succ(zzz910)) → Succ(Succ(new_primPlusNat2(zzz90, zzz910)))
new_primPlusNat3(zzz90, Zero) → Succ(zzz90)
new_primPlusNat2(Succ(zzz900), Succ(zzz9100)) → Succ(Succ(new_primPlusNat2(zzz900, zzz9100)))
new_primPlusNat2(Zero, Succ(zzz9100)) → Succ(zzz9100)
new_primPlusNat2(Zero, Zero) → Zero
new_primPlusNat2(Succ(zzz900), Zero) → Succ(zzz900)

The set Q consists of the following terms:

new_primPlusNat2(Zero, Succ(x0))
new_primPlusNat3(x0, Succ(x1))
new_primPlusNat2(Succ(x0), Succ(x1))
new_primPlusNat3(x0, Zero)
new_primPlusNat1(Zero)
new_primPlusNat2(Zero, Zero)
new_primPlusNat1(Succ(x0))
new_primPlusNat2(Succ(x0), Zero)

We have to consider all minimal (P,Q,R)-chains.
By rewriting [15] the rule new_mkVBalBranch3MkVBalBranch215(zzz340, zzz341, Pos(Succ(Zero)), zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, Succ(zzz660), h) → new_mkVBalBranch3MkVBalBranch18(zzz340, zzz341, zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, new_primPlusNat2(Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat3(new_primPlusNat1(Zero), Zero)), Zero))), Succ(Zero)), h) at position [10] we obtained the following new rules:

new_mkVBalBranch3MkVBalBranch215(zzz340, zzz341, Pos(Succ(Zero)), zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, Succ(zzz660), h) → new_mkVBalBranch3MkVBalBranch18(zzz340, zzz341, zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat2(Succ(new_primPlusNat3(new_primPlusNat1(Zero), Zero)), Zero)), Zero))), 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
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                    ↳ DependencyGraphProof
                                      ↳ QDP
                                        ↳ Rewriting
                                          ↳ QDP
                                            ↳ Rewriting
                                              ↳ QDP
                                                ↳ Rewriting
                                                  ↳ QDP
                                                    ↳ Rewriting
                                                      ↳ QDP
                                                        ↳ Rewriting
                                                          ↳ QDP
                                                            ↳ Rewriting
                                                              ↳ QDP
                                                                ↳ Rewriting
                                                                  ↳ QDP
                                                                    ↳ Rewriting
                                                                      ↳ QDP
                                                                        ↳ Rewriting
                                                                          ↳ QDP
                                                                            ↳ Rewriting
                                                                              ↳ QDP
                                                                                ↳ Rewriting
                                                                                  ↳ QDP
                                                                                    ↳ Rewriting
                                                                                      ↳ QDP
                                                                                        ↳ Rewriting
                                                                                          ↳ QDP
                                                                                            ↳ Rewriting
                                                                                              ↳ QDP
                                                                                                ↳ Rewriting
                                                                                                  ↳ QDP
                                                                                                    ↳ Rewriting
                                                                                                      ↳ QDP
                                                                                                        ↳ Rewriting
                                                                                                          ↳ QDP
                                                                                                            ↳ UsableRulesProof
                                                                                                              ↳ QDP
                                                                                                                ↳ QReductionProof
                                                                                                                  ↳ QDP
                                                                                                                    ↳ Rewriting
                                                                                                                      ↳ QDP
                                                                                                                        ↳ Rewriting
                                                                                                                          ↳ QDP
                                                                                                                            ↳ DependencyGraphProof
                                                                                                                              ↳ QDP
                                                                                                                                ↳ Rewriting
                                                                                                                                  ↳ QDP
                                                                                                                                    ↳ Rewriting
                                                                                                                                      ↳ QDP
                                                                                                                                        ↳ DependencyGraphProof
                                                                                                                                          ↳ QDP
                                                                                                                                            ↳ Rewriting
                                                                                                                                              ↳ QDP
                                                                                                                                                ↳ Rewriting
                                                                                                                                                  ↳ QDP
                                                                                                                                                    ↳ Rewriting
                                                                                                                                                      ↳ QDP
                                                                                                                                                        ↳ Rewriting
                                                                                                                                                          ↳ QDP
                                                                                                                                                            ↳ Rewriting
                                                                                                                                                              ↳ QDP
                                                                                                                                                                ↳ Rewriting
                                                                                                                                                                  ↳ QDP
                                                                                                                                                                    ↳ Rewriting
                                                                                                                                                                      ↳ QDP
                                                                                                                                                                        ↳ Rewriting
                                                                                                                                                                          ↳ QDP
                                                                                                                                                                            ↳ Rewriting
                                                                                                                                                                              ↳ QDP
                                                                                                                                                                                ↳ Rewriting
                                                                                                                                                                                  ↳ QDP
                                                                                                                                                                                    ↳ Rewriting
                                                                                                                                                                                      ↳ QDP
                                                                                                                                                                                        ↳ Rewriting
                                                                                                                                                                                          ↳ QDP
                                                                                                                                                                                            ↳ UsableRulesProof
                                                                                                                                                                                              ↳ QDP
                                                                                                                                                                                                ↳ QReductionProof
                                                                                                                                                                                                  ↳ QDP
                                                                                                                                                                                                    ↳ Rewriting
                                                                                                                                                                                                      ↳ QDP
                                                                                                                                                                                                        ↳ Rewriting
                                                                                                                                                                                                          ↳ QDP
                                                                                                                                                                                                            ↳ Rewriting
                                                                                                                                                                                                              ↳ QDP
                                                                                                                                                                                                                ↳ Rewriting
                                                                                                                                                                                                                  ↳ QDP
                                                                                                                                                                                                                    ↳ Rewriting
                                                                                                                                                                                                                      ↳ QDP
                                                                                                                                                                                                                        ↳ Rewriting
                                                                                                                                                                                                                          ↳ QDP
                                                                                                                                                                                                                            ↳ Rewriting
                                                                                                                                                                                                                              ↳ QDP
                                                                                                                                                                                                                                ↳ Rewriting
                                                                                                                                                                                                                                  ↳ QDP
                                                                                                                                                                                                                                    ↳ Rewriting
                                                                                                                                                                                                                                      ↳ QDP
                                                                                                                                                                                                                                        ↳ Rewriting
                                                                                                                                                                                                                                          ↳ QDP
                                                                                                                                                                                                                                            ↳ Rewriting
                                                                                                                                                                                                                                              ↳ QDP
                                                                                                                                                                                                                                                ↳ Rewriting
                                                                                                                                                                                                                                                  ↳ QDP
                                                                                                                                                                                                                                                    ↳ Rewriting
                                                                                                                                                                                                                                                      ↳ QDP
                                                                                                                                                                                                                                                        ↳ Rewriting
                                                                                                                                                                                                                                                          ↳ QDP
                                                                                                                                                                                                                                                            ↳ DependencyGraphProof
                                                                                                                                                                                                                                                              ↳ QDP
                                                                                                                                                                                                                                                                ↳ Rewriting
                                                                                                                                                                                                                                                                  ↳ QDP
                                                                                                                                                                                                                                                                    ↳ Rewriting
                                                                                                                                                                                                                                                                      ↳ QDP
                                                                                                                                                                                                                                                                        ↳ Rewriting
                                                                                                                                                                                                                                                                          ↳ QDP
                                                                                                                                                                                                                                                                            ↳ Rewriting
                                                                                                                                                                                                                                                                              ↳ QDP
                                                                                                                                                                                                                                                                                ↳ Rewriting
                                                                                                                                                                                                                                                                                  ↳ QDP
                                                                                                                                                                                                                                                                                    ↳ Rewriting
                                                                                                                                                                                                                                                                                      ↳ QDP
                                                                                                                                                                                                                                                                                        ↳ DependencyGraphProof
                                                                                                                                                                                                                                                                                          ↳ QDP
                                                                                                                                                                                                                                                                                            ↳ Rewriting
                                                                                                                                                                                                                                                                                              ↳ QDP
                                                                                                                                                                                                                                                                                                ↳ DependencyGraphProof
                                                                                                                                                                                                                                                                                                  ↳ QDP
                                                                                                                                                                                                                                                                                                    ↳ Rewriting
                                                                                                                                                                                                                                                                                                      ↳ QDP
                                                                                                                                                                                                                                                                                                        ↳ DependencyGraphProof
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP

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

new_mkVBalBranch3MkVBalBranch225(zzz498, zzz499, zzz500, zzz501, zzz502, zzz503, zzz504, zzz505, zzz506, zzz507, Zero, Zero, bg) → new_mkVBalBranch3MkVBalBranch230(zzz498, zzz499, zzz500, zzz501, zzz502, zzz503, zzz504, zzz505, zzz506, zzz507, bg)
new_mkVBalBranch3MkVBalBranch18(zzz340, zzz341, zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, Succ(zzz1480), h) → new_mkVBalBranch3MkVBalBranch115(zzz340, zzz341, Zero, zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, Succ(zzz1480), Succ(zzz51200), h)
new_mkVBalBranch0(zzz31, Branch(zzz510, zzz511, Neg(Zero), zzz513, zzz514), Branch(zzz340, zzz341, Pos(Succ(zzz34200)), zzz343, zzz344), h) → new_mkVBalBranch0(zzz31, Branch(zzz510, zzz511, Neg(Zero), zzz513, zzz514), zzz343, h)
new_mkVBalBranch3MkVBalBranch215(zzz340, zzz341, Pos(Succ(Succ(zzz342000))), zzz343, zzz344, zzz510, zzz511, Succ(zzz512000), zzz513, zzz514, zzz31, Succ(Succ(zzz6600)), h) → new_mkVBalBranch3MkVBalBranch216(zzz340, zzz341, Succ(zzz342000), zzz343, zzz344, zzz510, zzz511, zzz512000, zzz513, zzz514, zzz31, Succ(Succ(new_primPlusNat2(zzz6600, zzz512000))), zzz342000, h)
new_mkVBalBranch3MkVBalBranch223(zzz340, zzz341, Neg(Succ(Succ(Succ(zzz3420000)))), zzz343, zzz344, zzz510, zzz511, Zero, zzz513, zzz514, zzz31, Succ(Succ(zzz6700)), h) → new_mkVBalBranch3MkVBalBranch225(zzz340, zzz341, Succ(Succ(zzz3420000)), zzz343, zzz344, zzz510, zzz511, zzz513, zzz514, zzz31, Succ(zzz3420000), Succ(zzz6700), h)
new_mkVBalBranch3MkVBalBranch120(zzz2050, zzz2051, zzz2052, zzz2053, zzz2054, zzz2055, zzz2056, zzz2057, zzz2058, zzz2059, zzz2060, Zero, Succ(zzz20620), be) → new_mkVBalBranch0(zzz2060, zzz2059, Branch(zzz2050, zzz2051, Neg(Succ(zzz2052)), zzz2053, zzz2054), be)
new_mkVBalBranch3MkVBalBranch121(zzz473, zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, zzz481, zzz482, Succ(zzz7390), bh) → new_mkVBalBranch3MkVBalBranch115(zzz473, zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, Zero, zzz480, zzz481, zzz482, Succ(zzz7390), Succ(Zero), bh)
new_mkVBalBranch0(zzz31, Branch(zzz510, zzz511, Pos(Zero), zzz513, zzz514), Branch(zzz340, zzz341, Pos(Succ(zzz34200)), zzz343, zzz344), h) → new_mkVBalBranch0(zzz31, Branch(zzz510, zzz511, Pos(Zero), zzz513, zzz514), zzz343, h)
new_mkVBalBranch0(zzz31, Branch(zzz510, zzz511, Pos(Succ(zzz51200)), zzz513, zzz514), Branch(zzz340, zzz341, zzz342, zzz343, zzz344), h) → new_mkVBalBranch3MkVBalBranch215(zzz340, zzz341, zzz342, zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat3(new_primPlusNat1(zzz51200), zzz51200)), zzz51200))), h)
new_mkVBalBranch3MkVBalBranch215(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, Succ(zzz660), h) → new_mkVBalBranch3MkVBalBranch19(zzz340, zzz341, zzz34200, zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat2(Succ(new_primPlusNat3(new_primPlusNat1(zzz34200), zzz34200)), zzz34200)), zzz34200))), h)
new_mkVBalBranch3MkVBalBranch230(zzz498, zzz499, zzz500, zzz501, zzz502, zzz503, zzz504, zzz505, zzz506, zzz507, bg) → new_mkVBalBranch3MkVBalBranch118(zzz498, zzz499, zzz500, zzz501, zzz502, zzz503, zzz504, zzz505, zzz506, zzz507, Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat2(Succ(new_primPlusNat3(new_primPlusNat1(zzz500), zzz500)), zzz500)), zzz500))), bg)
new_mkVBalBranch3MkVBalBranch223(zzz340, zzz341, Neg(Succ(Succ(Zero))), zzz343, zzz344, zzz510, zzz511, Succ(zzz512000), zzz513, zzz514, zzz31, Succ(Succ(zzz6700)), h) → new_mkVBalBranch3MkVBalBranch224(zzz340, zzz341, Succ(Zero), zzz343, zzz344, zzz510, zzz511, zzz512000, zzz513, zzz514, zzz31, Zero, Succ(Succ(new_primPlusNat2(zzz6700, zzz512000))), h)
new_mkVBalBranch0(zzz31, Branch(zzz510, zzz511, Pos(Zero), zzz513, zzz514), Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), h) → new_mkVBalBranch3MkVBalBranch116(zzz340, zzz341, zzz34200, zzz343, zzz344, zzz510, zzz511, zzz513, zzz514, zzz31, Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat2(Succ(new_primPlusNat3(new_primPlusNat1(zzz34200), zzz34200)), zzz34200)), zzz34200))), h)
new_mkVBalBranch0(zzz31, Branch(zzz510, zzz511, Neg(Zero), zzz513, zzz514), Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), h) → new_mkVBalBranch3MkVBalBranch117(zzz340, zzz341, zzz34200, zzz343, zzz344, zzz510, zzz511, zzz513, zzz514, zzz31, Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat2(Succ(new_primPlusNat3(new_primPlusNat1(zzz34200), zzz34200)), zzz34200)), zzz34200))), h)
new_mkVBalBranch3MkVBalBranch224(zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, zzz1125, zzz1126, zzz1127, zzz1128, zzz1129, Succ(zzz11300), Succ(zzz11310), bd) → new_mkVBalBranch3MkVBalBranch224(zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, zzz1125, zzz1126, zzz1127, zzz1128, zzz1129, zzz11300, zzz11310, bd)
new_mkVBalBranch3MkVBalBranch217(zzz473, zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, zzz481, zzz482, Succ(zzz4830), Zero, bh) → new_mkVBalBranch3MkVBalBranch121(zzz473, zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, zzz481, zzz482, Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat2(Succ(new_primPlusNat3(new_primPlusNat1(zzz475), zzz475)), zzz475)), zzz475))), bh)
new_mkVBalBranch3MkVBalBranch229(zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, zzz1125, zzz1126, zzz1127, zzz1128, zzz1129, bd) → new_mkVBalBranch3MkVBalBranch119(zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, zzz1125, zzz1126, zzz1127, zzz1128, zzz1129, Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat2(Succ(new_primPlusNat3(new_primPlusNat1(zzz1121), zzz1121)), zzz1121)), zzz1121))), bd)
new_mkVBalBranch3MkVBalBranch217(zzz473, zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, zzz481, zzz482, Zero, Succ(zzz4840), bh) → new_mkVBalBranch0(zzz482, Branch(zzz478, zzz479, Pos(Succ(Zero)), zzz480, zzz481), zzz476, bh)
new_mkVBalBranch3MkVBalBranch218(zzz461, zzz462, zzz463, zzz464, zzz465, zzz466, zzz467, zzz468, zzz469, zzz470, zzz471, bb) → new_mkVBalBranch3MkVBalBranch110(zzz461, zzz462, zzz463, zzz464, zzz465, zzz466, zzz467, zzz468, zzz469, zzz470, zzz471, Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat2(Succ(new_primPlusNat3(new_primPlusNat1(zzz463), zzz463)), zzz463)), zzz463))), bb)
new_mkVBalBranch3MkVBalBranch110(zzz461, zzz462, zzz463, zzz464, zzz465, zzz466, zzz467, zzz468, zzz469, zzz470, zzz471, Succ(zzz5800), bb) → new_mkVBalBranch3MkVBalBranch115(zzz461, zzz462, zzz463, zzz464, zzz465, zzz466, zzz467, Succ(zzz468), zzz469, zzz470, zzz471, Succ(zzz5800), Succ(Succ(zzz468)), bb)
new_mkVBalBranch3MkVBalBranch227(zzz486, zzz487, zzz488, zzz489, zzz490, zzz491, zzz492, zzz493, zzz494, zzz495, zzz496, bf) → new_mkVBalBranch0(zzz496, Branch(zzz491, zzz492, Neg(Succ(Succ(zzz493))), zzz494, zzz495), zzz489, bf)
new_mkVBalBranch3MkVBalBranch215(zzz340, zzz341, Pos(Zero), zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, Succ(zzz660), h) → new_mkVBalBranch0(zzz31, zzz514, Branch(zzz340, zzz341, Pos(Zero), zzz343, zzz344), h)
new_mkVBalBranch3MkVBalBranch223(zzz340, zzz341, Neg(Zero), zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, Succ(zzz670), h) → new_mkVBalBranch0(zzz31, Branch(zzz510, zzz511, Neg(Succ(zzz51200)), zzz513, zzz514), zzz343, h)
new_mkVBalBranch3MkVBalBranch216(zzz1105, zzz1106, zzz1107, zzz1108, zzz1109, zzz1110, zzz1111, zzz1112, zzz1113, zzz1114, zzz1115, Zero, Succ(zzz11170), ba) → new_mkVBalBranch0(zzz1115, Branch(zzz1110, zzz1111, Pos(Succ(Succ(zzz1112))), zzz1113, zzz1114), zzz1108, ba)
new_mkVBalBranch3MkVBalBranch115(zzz1986, zzz1987, zzz1988, zzz1989, zzz1990, zzz1991, zzz1992, zzz1993, zzz1994, zzz1995, zzz1996, Zero, Succ(zzz19980), bc) → new_mkVBalBranch0(zzz1996, zzz1995, Branch(zzz1986, zzz1987, Pos(Succ(zzz1988)), zzz1989, zzz1990), bc)
new_mkVBalBranch3MkVBalBranch233(zzz473, zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, zzz481, zzz482, bh) → new_mkVBalBranch3MkVBalBranch121(zzz473, zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, zzz481, zzz482, Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat2(Succ(new_primPlusNat3(new_primPlusNat1(zzz475), zzz475)), zzz475)), zzz475))), bh)
new_mkVBalBranch3MkVBalBranch217(zzz473, zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, zzz481, zzz482, Succ(zzz4830), Succ(zzz4840), bh) → new_mkVBalBranch3MkVBalBranch217(zzz473, zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, zzz481, zzz482, zzz4830, zzz4840, bh)
new_mkVBalBranch3MkVBalBranch116(zzz340, zzz341, zzz34200, zzz343, zzz344, zzz510, zzz511, zzz513, zzz514, zzz31, Succ(zzz1200), h) → new_mkVBalBranch0(zzz31, zzz514, Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), h)
new_mkVBalBranch3MkVBalBranch225(zzz498, zzz499, zzz500, zzz501, zzz502, zzz503, zzz504, zzz505, zzz506, zzz507, Zero, Succ(zzz5090), bg) → new_mkVBalBranch0(zzz507, Branch(zzz503, zzz504, Neg(Succ(Zero)), zzz505, zzz506), zzz501, bg)
new_mkVBalBranch0(zzz31, Branch(zzz510, zzz511, Neg(Succ(zzz51200)), zzz513, zzz514), Branch(zzz340, zzz341, zzz342, zzz343, zzz344), h) → new_mkVBalBranch3MkVBalBranch223(zzz340, zzz341, zzz342, zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat3(new_primPlusNat1(zzz51200), zzz51200)), zzz51200))), h)
new_mkVBalBranch3MkVBalBranch223(zzz340, zzz341, Neg(Succ(Zero)), zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, Succ(zzz670), h) → new_mkVBalBranch0(zzz31, Branch(zzz510, zzz511, Neg(Succ(zzz51200)), zzz513, zzz514), zzz343, h)
new_mkVBalBranch3MkVBalBranch215(zzz340, zzz341, Pos(Succ(Succ(zzz342000))), zzz343, zzz344, zzz510, zzz511, Zero, zzz513, zzz514, zzz31, Succ(Succ(zzz6600)), h) → new_mkVBalBranch3MkVBalBranch217(zzz340, zzz341, Succ(zzz342000), zzz343, zzz344, zzz510, zzz511, zzz513, zzz514, zzz31, Succ(zzz6600), zzz342000, h)
new_mkVBalBranch3MkVBalBranch117(zzz340, zzz341, zzz34200, zzz343, zzz344, zzz510, zzz511, zzz513, zzz514, zzz31, Succ(zzz1240), h) → new_mkVBalBranch0(zzz31, zzz514, Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), h)
new_mkVBalBranch3MkVBalBranch217(zzz473, zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, zzz481, zzz482, Zero, Zero, bh) → new_mkVBalBranch3MkVBalBranch233(zzz473, zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, zzz481, zzz482, bh)
new_mkVBalBranch3MkVBalBranch120(zzz2050, zzz2051, zzz2052, zzz2053, zzz2054, zzz2055, zzz2056, zzz2057, zzz2058, zzz2059, zzz2060, Succ(zzz20610), Succ(zzz20620), be) → new_mkVBalBranch3MkVBalBranch120(zzz2050, zzz2051, zzz2052, zzz2053, zzz2054, zzz2055, zzz2056, zzz2057, zzz2058, zzz2059, zzz2060, zzz20610, zzz20620, be)
new_mkVBalBranch3MkVBalBranch223(zzz340, zzz341, Pos(zzz3420), zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, Succ(zzz670), h) → new_mkVBalBranch0(zzz31, Branch(zzz510, zzz511, Neg(Succ(zzz51200)), zzz513, zzz514), zzz343, h)
new_mkVBalBranch3MkVBalBranch216(zzz1105, zzz1106, zzz1107, zzz1108, zzz1109, zzz1110, zzz1111, zzz1112, zzz1113, zzz1114, zzz1115, Succ(zzz11160), Succ(zzz11170), ba) → new_mkVBalBranch3MkVBalBranch216(zzz1105, zzz1106, zzz1107, zzz1108, zzz1109, zzz1110, zzz1111, zzz1112, zzz1113, zzz1114, zzz1115, zzz11160, zzz11170, ba)
new_mkVBalBranch3MkVBalBranch225(zzz498, zzz499, zzz500, zzz501, zzz502, zzz503, zzz504, zzz505, zzz506, zzz507, Succ(zzz5080), Succ(zzz5090), bg) → new_mkVBalBranch3MkVBalBranch225(zzz498, zzz499, zzz500, zzz501, zzz502, zzz503, zzz504, zzz505, zzz506, zzz507, zzz5080, zzz5090, bg)
new_mkVBalBranch3MkVBalBranch19(zzz340, zzz341, zzz34200, zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, Succ(zzz1410), h) → new_mkVBalBranch0(zzz31, zzz514, Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), h)
new_mkVBalBranch3MkVBalBranch224(zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, zzz1125, zzz1126, zzz1127, zzz1128, zzz1129, Zero, Zero, bd) → new_mkVBalBranch3MkVBalBranch229(zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, zzz1125, zzz1126, zzz1127, zzz1128, zzz1129, bd)
new_mkVBalBranch3MkVBalBranch224(zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, zzz1125, zzz1126, zzz1127, zzz1128, zzz1129, Zero, Succ(zzz11310), bd) → new_mkVBalBranch3MkVBalBranch227(zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, zzz1125, zzz1126, zzz1127, zzz1128, zzz1129, bd)
new_mkVBalBranch3MkVBalBranch215(zzz340, zzz341, Pos(Succ(Zero)), zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, Succ(zzz660), h) → new_mkVBalBranch3MkVBalBranch18(zzz340, zzz341, zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat2(Succ(new_primPlusNat3(new_primPlusNat1(Zero), Zero)), Zero)), Zero))), h)
new_mkVBalBranch3MkVBalBranch223(zzz340, zzz341, Neg(Succ(Succ(Zero))), zzz343, zzz344, zzz510, zzz511, Zero, zzz513, zzz514, zzz31, Succ(Succ(zzz6700)), h) → new_mkVBalBranch3MkVBalBranch225(zzz340, zzz341, Succ(Zero), zzz343, zzz344, zzz510, zzz511, zzz513, zzz514, zzz31, Zero, Succ(zzz6700), h)
new_mkVBalBranch3MkVBalBranch223(zzz340, zzz341, Neg(Succ(Succ(Succ(zzz3420000)))), zzz343, zzz344, zzz510, zzz511, Succ(zzz512000), zzz513, zzz514, zzz31, Succ(Succ(zzz6700)), h) → new_mkVBalBranch3MkVBalBranch224(zzz340, zzz341, Succ(Succ(zzz3420000)), zzz343, zzz344, zzz510, zzz511, zzz512000, zzz513, zzz514, zzz31, Succ(zzz3420000), Succ(Succ(new_primPlusNat2(zzz6700, zzz512000))), h)
new_mkVBalBranch3MkVBalBranch225(zzz498, zzz499, zzz500, zzz501, zzz502, zzz503, zzz504, zzz505, zzz506, zzz507, Succ(zzz5080), Zero, bg) → new_mkVBalBranch3MkVBalBranch118(zzz498, zzz499, zzz500, zzz501, zzz502, zzz503, zzz504, zzz505, zzz506, zzz507, Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat2(Succ(new_primPlusNat3(new_primPlusNat1(zzz500), zzz500)), zzz500)), zzz500))), bg)
new_mkVBalBranch3MkVBalBranch115(zzz1986, zzz1987, zzz1988, zzz1989, zzz1990, zzz1991, zzz1992, zzz1993, zzz1994, zzz1995, zzz1996, Succ(zzz19970), Succ(zzz19980), bc) → new_mkVBalBranch3MkVBalBranch115(zzz1986, zzz1987, zzz1988, zzz1989, zzz1990, zzz1991, zzz1992, zzz1993, zzz1994, zzz1995, zzz1996, zzz19970, zzz19980, bc)
new_mkVBalBranch3MkVBalBranch215(zzz340, zzz341, Neg(Zero), zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, Succ(zzz660), h) → new_mkVBalBranch0(zzz31, zzz514, Branch(zzz340, zzz341, Neg(Zero), zzz343, zzz344), h)
new_mkVBalBranch3MkVBalBranch224(zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, zzz1125, zzz1126, zzz1127, zzz1128, zzz1129, Succ(zzz11300), Zero, bd) → new_mkVBalBranch3MkVBalBranch119(zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, zzz1125, zzz1126, zzz1127, zzz1128, zzz1129, Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat2(Succ(new_primPlusNat3(new_primPlusNat1(zzz1121), zzz1121)), zzz1121)), zzz1121))), bd)
new_mkVBalBranch3MkVBalBranch222(zzz461, zzz462, zzz463, zzz464, zzz465, zzz466, zzz467, zzz468, zzz469, zzz470, zzz471, bb) → new_mkVBalBranch3MkVBalBranch110(zzz461, zzz462, zzz463, zzz464, zzz465, zzz466, zzz467, zzz468, zzz469, zzz470, zzz471, Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat2(Succ(new_primPlusNat3(new_primPlusNat1(zzz463), zzz463)), zzz463)), zzz463))), bb)
new_mkVBalBranch3MkVBalBranch118(zzz498, zzz499, zzz500, zzz501, zzz502, zzz503, zzz504, zzz505, zzz506, zzz507, Succ(zzz8040), bg) → new_mkVBalBranch3MkVBalBranch120(zzz498, zzz499, zzz500, zzz501, zzz502, zzz503, zzz504, Zero, zzz505, zzz506, zzz507, Succ(Zero), Succ(zzz8040), bg)
new_mkVBalBranch3MkVBalBranch216(zzz1105, zzz1106, zzz1107, zzz1108, zzz1109, zzz1110, zzz1111, zzz1112, zzz1113, zzz1114, zzz1115, Succ(zzz11160), Zero, ba) → new_mkVBalBranch3MkVBalBranch218(zzz1105, zzz1106, zzz1107, zzz1108, zzz1109, zzz1110, zzz1111, zzz1112, zzz1113, zzz1114, zzz1115, ba)
new_mkVBalBranch3MkVBalBranch216(zzz1105, zzz1106, zzz1107, zzz1108, zzz1109, zzz1110, zzz1111, zzz1112, zzz1113, zzz1114, zzz1115, Zero, Zero, ba) → new_mkVBalBranch3MkVBalBranch222(zzz1105, zzz1106, zzz1107, zzz1108, zzz1109, zzz1110, zzz1111, zzz1112, zzz1113, zzz1114, zzz1115, ba)
new_mkVBalBranch3MkVBalBranch119(zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, zzz1125, zzz1126, zzz1127, zzz1128, zzz1129, Succ(zzz12130), bd) → new_mkVBalBranch3MkVBalBranch120(zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, zzz1125, Succ(zzz1126), zzz1127, zzz1128, zzz1129, Succ(Succ(zzz1126)), Succ(zzz12130), bd)
new_mkVBalBranch3MkVBalBranch18(zzz340, zzz341, zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, Zero, h) → new_mkVBalBranch3MkVBalBranch115(zzz340, zzz341, Zero, zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, Zero, Succ(zzz51200), h)

The TRS R consists of the following rules:

new_primPlusNat1(Zero) → Zero
new_primPlusNat1(Succ(zzz62000)) → Succ(Succ(new_primPlusNat1(zzz62000)))
new_primPlusNat3(zzz90, Succ(zzz910)) → Succ(Succ(new_primPlusNat2(zzz90, zzz910)))
new_primPlusNat3(zzz90, Zero) → Succ(zzz90)
new_primPlusNat2(Succ(zzz900), Succ(zzz9100)) → Succ(Succ(new_primPlusNat2(zzz900, zzz9100)))
new_primPlusNat2(Zero, Succ(zzz9100)) → Succ(zzz9100)
new_primPlusNat2(Zero, Zero) → Zero
new_primPlusNat2(Succ(zzz900), Zero) → Succ(zzz900)

The set Q consists of the following terms:

new_primPlusNat2(Zero, Succ(x0))
new_primPlusNat3(x0, Succ(x1))
new_primPlusNat2(Succ(x0), Succ(x1))
new_primPlusNat3(x0, Zero)
new_primPlusNat1(Zero)
new_primPlusNat2(Zero, Zero)
new_primPlusNat1(Succ(x0))
new_primPlusNat2(Succ(x0), Zero)

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

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

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

new_mkVBalBranch3MkVBalBranch225(zzz498, zzz499, zzz500, zzz501, zzz502, zzz503, zzz504, zzz505, zzz506, zzz507, Zero, Zero, bg) → new_mkVBalBranch3MkVBalBranch230(zzz498, zzz499, zzz500, zzz501, zzz502, zzz503, zzz504, zzz505, zzz506, zzz507, bg)
new_mkVBalBranch3MkVBalBranch18(zzz340, zzz341, zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, Succ(zzz1480), h) → new_mkVBalBranch3MkVBalBranch115(zzz340, zzz341, Zero, zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, Succ(zzz1480), Succ(zzz51200), h)
new_mkVBalBranch3MkVBalBranch215(zzz340, zzz341, Pos(Succ(Succ(zzz342000))), zzz343, zzz344, zzz510, zzz511, Succ(zzz512000), zzz513, zzz514, zzz31, Succ(Succ(zzz6600)), h) → new_mkVBalBranch3MkVBalBranch216(zzz340, zzz341, Succ(zzz342000), zzz343, zzz344, zzz510, zzz511, zzz512000, zzz513, zzz514, zzz31, Succ(Succ(new_primPlusNat2(zzz6600, zzz512000))), zzz342000, h)
new_mkVBalBranch0(zzz31, Branch(zzz510, zzz511, Neg(Zero), zzz513, zzz514), Branch(zzz340, zzz341, Pos(Succ(zzz34200)), zzz343, zzz344), h) → new_mkVBalBranch0(zzz31, Branch(zzz510, zzz511, Neg(Zero), zzz513, zzz514), zzz343, h)
new_mkVBalBranch3MkVBalBranch223(zzz340, zzz341, Neg(Succ(Succ(Succ(zzz3420000)))), zzz343, zzz344, zzz510, zzz511, Zero, zzz513, zzz514, zzz31, Succ(Succ(zzz6700)), h) → new_mkVBalBranch3MkVBalBranch225(zzz340, zzz341, Succ(Succ(zzz3420000)), zzz343, zzz344, zzz510, zzz511, zzz513, zzz514, zzz31, Succ(zzz3420000), Succ(zzz6700), h)
new_mkVBalBranch3MkVBalBranch120(zzz2050, zzz2051, zzz2052, zzz2053, zzz2054, zzz2055, zzz2056, zzz2057, zzz2058, zzz2059, zzz2060, Zero, Succ(zzz20620), be) → new_mkVBalBranch0(zzz2060, zzz2059, Branch(zzz2050, zzz2051, Neg(Succ(zzz2052)), zzz2053, zzz2054), be)
new_mkVBalBranch0(zzz31, Branch(zzz510, zzz511, Pos(Zero), zzz513, zzz514), Branch(zzz340, zzz341, Pos(Succ(zzz34200)), zzz343, zzz344), h) → new_mkVBalBranch0(zzz31, Branch(zzz510, zzz511, Pos(Zero), zzz513, zzz514), zzz343, h)
new_mkVBalBranch3MkVBalBranch121(zzz473, zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, zzz481, zzz482, Succ(zzz7390), bh) → new_mkVBalBranch3MkVBalBranch115(zzz473, zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, Zero, zzz480, zzz481, zzz482, Succ(zzz7390), Succ(Zero), bh)
new_mkVBalBranch0(zzz31, Branch(zzz510, zzz511, Pos(Succ(zzz51200)), zzz513, zzz514), Branch(zzz340, zzz341, zzz342, zzz343, zzz344), h) → new_mkVBalBranch3MkVBalBranch215(zzz340, zzz341, zzz342, zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat3(new_primPlusNat1(zzz51200), zzz51200)), zzz51200))), h)
new_mkVBalBranch3MkVBalBranch215(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, Succ(zzz660), h) → new_mkVBalBranch3MkVBalBranch19(zzz340, zzz341, zzz34200, zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat2(Succ(new_primPlusNat3(new_primPlusNat1(zzz34200), zzz34200)), zzz34200)), zzz34200))), h)
new_mkVBalBranch3MkVBalBranch223(zzz340, zzz341, Neg(Succ(Succ(Zero))), zzz343, zzz344, zzz510, zzz511, Succ(zzz512000), zzz513, zzz514, zzz31, Succ(Succ(zzz6700)), h) → new_mkVBalBranch3MkVBalBranch224(zzz340, zzz341, Succ(Zero), zzz343, zzz344, zzz510, zzz511, zzz512000, zzz513, zzz514, zzz31, Zero, Succ(Succ(new_primPlusNat2(zzz6700, zzz512000))), h)
new_mkVBalBranch3MkVBalBranch230(zzz498, zzz499, zzz500, zzz501, zzz502, zzz503, zzz504, zzz505, zzz506, zzz507, bg) → new_mkVBalBranch3MkVBalBranch118(zzz498, zzz499, zzz500, zzz501, zzz502, zzz503, zzz504, zzz505, zzz506, zzz507, Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat2(Succ(new_primPlusNat3(new_primPlusNat1(zzz500), zzz500)), zzz500)), zzz500))), bg)
new_mkVBalBranch0(zzz31, Branch(zzz510, zzz511, Pos(Zero), zzz513, zzz514), Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), h) → new_mkVBalBranch3MkVBalBranch116(zzz340, zzz341, zzz34200, zzz343, zzz344, zzz510, zzz511, zzz513, zzz514, zzz31, Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat2(Succ(new_primPlusNat3(new_primPlusNat1(zzz34200), zzz34200)), zzz34200)), zzz34200))), h)
new_mkVBalBranch0(zzz31, Branch(zzz510, zzz511, Neg(Zero), zzz513, zzz514), Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), h) → new_mkVBalBranch3MkVBalBranch117(zzz340, zzz341, zzz34200, zzz343, zzz344, zzz510, zzz511, zzz513, zzz514, zzz31, Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat2(Succ(new_primPlusNat3(new_primPlusNat1(zzz34200), zzz34200)), zzz34200)), zzz34200))), h)
new_mkVBalBranch3MkVBalBranch224(zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, zzz1125, zzz1126, zzz1127, zzz1128, zzz1129, Succ(zzz11300), Succ(zzz11310), bd) → new_mkVBalBranch3MkVBalBranch224(zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, zzz1125, zzz1126, zzz1127, zzz1128, zzz1129, zzz11300, zzz11310, bd)
new_mkVBalBranch3MkVBalBranch229(zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, zzz1125, zzz1126, zzz1127, zzz1128, zzz1129, bd) → new_mkVBalBranch3MkVBalBranch119(zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, zzz1125, zzz1126, zzz1127, zzz1128, zzz1129, Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat2(Succ(new_primPlusNat3(new_primPlusNat1(zzz1121), zzz1121)), zzz1121)), zzz1121))), bd)
new_mkVBalBranch3MkVBalBranch217(zzz473, zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, zzz481, zzz482, Succ(zzz4830), Zero, bh) → new_mkVBalBranch3MkVBalBranch121(zzz473, zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, zzz481, zzz482, Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat2(Succ(new_primPlusNat3(new_primPlusNat1(zzz475), zzz475)), zzz475)), zzz475))), bh)
new_mkVBalBranch3MkVBalBranch217(zzz473, zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, zzz481, zzz482, Zero, Succ(zzz4840), bh) → new_mkVBalBranch0(zzz482, Branch(zzz478, zzz479, Pos(Succ(Zero)), zzz480, zzz481), zzz476, bh)
new_mkVBalBranch3MkVBalBranch218(zzz461, zzz462, zzz463, zzz464, zzz465, zzz466, zzz467, zzz468, zzz469, zzz470, zzz471, bb) → new_mkVBalBranch3MkVBalBranch110(zzz461, zzz462, zzz463, zzz464, zzz465, zzz466, zzz467, zzz468, zzz469, zzz470, zzz471, Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat2(Succ(new_primPlusNat3(new_primPlusNat1(zzz463), zzz463)), zzz463)), zzz463))), bb)
new_mkVBalBranch3MkVBalBranch110(zzz461, zzz462, zzz463, zzz464, zzz465, zzz466, zzz467, zzz468, zzz469, zzz470, zzz471, Succ(zzz5800), bb) → new_mkVBalBranch3MkVBalBranch115(zzz461, zzz462, zzz463, zzz464, zzz465, zzz466, zzz467, Succ(zzz468), zzz469, zzz470, zzz471, Succ(zzz5800), Succ(Succ(zzz468)), bb)
new_mkVBalBranch3MkVBalBranch227(zzz486, zzz487, zzz488, zzz489, zzz490, zzz491, zzz492, zzz493, zzz494, zzz495, zzz496, bf) → new_mkVBalBranch0(zzz496, Branch(zzz491, zzz492, Neg(Succ(Succ(zzz493))), zzz494, zzz495), zzz489, bf)
new_mkVBalBranch3MkVBalBranch215(zzz340, zzz341, Pos(Zero), zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, Succ(zzz660), h) → new_mkVBalBranch0(zzz31, zzz514, Branch(zzz340, zzz341, Pos(Zero), zzz343, zzz344), h)
new_mkVBalBranch3MkVBalBranch223(zzz340, zzz341, Neg(Zero), zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, Succ(zzz670), h) → new_mkVBalBranch0(zzz31, Branch(zzz510, zzz511, Neg(Succ(zzz51200)), zzz513, zzz514), zzz343, h)
new_mkVBalBranch3MkVBalBranch216(zzz1105, zzz1106, zzz1107, zzz1108, zzz1109, zzz1110, zzz1111, zzz1112, zzz1113, zzz1114, zzz1115, Zero, Succ(zzz11170), ba) → new_mkVBalBranch0(zzz1115, Branch(zzz1110, zzz1111, Pos(Succ(Succ(zzz1112))), zzz1113, zzz1114), zzz1108, ba)
new_mkVBalBranch3MkVBalBranch115(zzz1986, zzz1987, zzz1988, zzz1989, zzz1990, zzz1991, zzz1992, zzz1993, zzz1994, zzz1995, zzz1996, Zero, Succ(zzz19980), bc) → new_mkVBalBranch0(zzz1996, zzz1995, Branch(zzz1986, zzz1987, Pos(Succ(zzz1988)), zzz1989, zzz1990), bc)
new_mkVBalBranch3MkVBalBranch233(zzz473, zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, zzz481, zzz482, bh) → new_mkVBalBranch3MkVBalBranch121(zzz473, zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, zzz481, zzz482, Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat2(Succ(new_primPlusNat3(new_primPlusNat1(zzz475), zzz475)), zzz475)), zzz475))), bh)
new_mkVBalBranch3MkVBalBranch217(zzz473, zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, zzz481, zzz482, Succ(zzz4830), Succ(zzz4840), bh) → new_mkVBalBranch3MkVBalBranch217(zzz473, zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, zzz481, zzz482, zzz4830, zzz4840, bh)
new_mkVBalBranch3MkVBalBranch116(zzz340, zzz341, zzz34200, zzz343, zzz344, zzz510, zzz511, zzz513, zzz514, zzz31, Succ(zzz1200), h) → new_mkVBalBranch0(zzz31, zzz514, Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), h)
new_mkVBalBranch3MkVBalBranch225(zzz498, zzz499, zzz500, zzz501, zzz502, zzz503, zzz504, zzz505, zzz506, zzz507, Zero, Succ(zzz5090), bg) → new_mkVBalBranch0(zzz507, Branch(zzz503, zzz504, Neg(Succ(Zero)), zzz505, zzz506), zzz501, bg)
new_mkVBalBranch0(zzz31, Branch(zzz510, zzz511, Neg(Succ(zzz51200)), zzz513, zzz514), Branch(zzz340, zzz341, zzz342, zzz343, zzz344), h) → new_mkVBalBranch3MkVBalBranch223(zzz340, zzz341, zzz342, zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat3(new_primPlusNat1(zzz51200), zzz51200)), zzz51200))), h)
new_mkVBalBranch3MkVBalBranch223(zzz340, zzz341, Neg(Succ(Zero)), zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, Succ(zzz670), h) → new_mkVBalBranch0(zzz31, Branch(zzz510, zzz511, Neg(Succ(zzz51200)), zzz513, zzz514), zzz343, h)
new_mkVBalBranch3MkVBalBranch215(zzz340, zzz341, Pos(Succ(Succ(zzz342000))), zzz343, zzz344, zzz510, zzz511, Zero, zzz513, zzz514, zzz31, Succ(Succ(zzz6600)), h) → new_mkVBalBranch3MkVBalBranch217(zzz340, zzz341, Succ(zzz342000), zzz343, zzz344, zzz510, zzz511, zzz513, zzz514, zzz31, Succ(zzz6600), zzz342000, h)
new_mkVBalBranch3MkVBalBranch117(zzz340, zzz341, zzz34200, zzz343, zzz344, zzz510, zzz511, zzz513, zzz514, zzz31, Succ(zzz1240), h) → new_mkVBalBranch0(zzz31, zzz514, Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), h)
new_mkVBalBranch3MkVBalBranch120(zzz2050, zzz2051, zzz2052, zzz2053, zzz2054, zzz2055, zzz2056, zzz2057, zzz2058, zzz2059, zzz2060, Succ(zzz20610), Succ(zzz20620), be) → new_mkVBalBranch3MkVBalBranch120(zzz2050, zzz2051, zzz2052, zzz2053, zzz2054, zzz2055, zzz2056, zzz2057, zzz2058, zzz2059, zzz2060, zzz20610, zzz20620, be)
new_mkVBalBranch3MkVBalBranch217(zzz473, zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, zzz481, zzz482, Zero, Zero, bh) → new_mkVBalBranch3MkVBalBranch233(zzz473, zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, zzz481, zzz482, bh)
new_mkVBalBranch3MkVBalBranch216(zzz1105, zzz1106, zzz1107, zzz1108, zzz1109, zzz1110, zzz1111, zzz1112, zzz1113, zzz1114, zzz1115, Succ(zzz11160), Succ(zzz11170), ba) → new_mkVBalBranch3MkVBalBranch216(zzz1105, zzz1106, zzz1107, zzz1108, zzz1109, zzz1110, zzz1111, zzz1112, zzz1113, zzz1114, zzz1115, zzz11160, zzz11170, ba)
new_mkVBalBranch3MkVBalBranch223(zzz340, zzz341, Pos(zzz3420), zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, Succ(zzz670), h) → new_mkVBalBranch0(zzz31, Branch(zzz510, zzz511, Neg(Succ(zzz51200)), zzz513, zzz514), zzz343, h)
new_mkVBalBranch3MkVBalBranch225(zzz498, zzz499, zzz500, zzz501, zzz502, zzz503, zzz504, zzz505, zzz506, zzz507, Succ(zzz5080), Succ(zzz5090), bg) → new_mkVBalBranch3MkVBalBranch225(zzz498, zzz499, zzz500, zzz501, zzz502, zzz503, zzz504, zzz505, zzz506, zzz507, zzz5080, zzz5090, bg)
new_mkVBalBranch3MkVBalBranch19(zzz340, zzz341, zzz34200, zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, Succ(zzz1410), h) → new_mkVBalBranch0(zzz31, zzz514, Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), h)
new_mkVBalBranch3MkVBalBranch224(zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, zzz1125, zzz1126, zzz1127, zzz1128, zzz1129, Zero, Succ(zzz11310), bd) → new_mkVBalBranch3MkVBalBranch227(zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, zzz1125, zzz1126, zzz1127, zzz1128, zzz1129, bd)
new_mkVBalBranch3MkVBalBranch224(zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, zzz1125, zzz1126, zzz1127, zzz1128, zzz1129, Zero, Zero, bd) → new_mkVBalBranch3MkVBalBranch229(zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, zzz1125, zzz1126, zzz1127, zzz1128, zzz1129, bd)
new_mkVBalBranch3MkVBalBranch215(zzz340, zzz341, Pos(Succ(Zero)), zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, Succ(zzz660), h) → new_mkVBalBranch3MkVBalBranch18(zzz340, zzz341, zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat2(Succ(new_primPlusNat3(new_primPlusNat1(Zero), Zero)), Zero)), Zero))), h)
new_mkVBalBranch3MkVBalBranch225(zzz498, zzz499, zzz500, zzz501, zzz502, zzz503, zzz504, zzz505, zzz506, zzz507, Succ(zzz5080), Zero, bg) → new_mkVBalBranch3MkVBalBranch118(zzz498, zzz499, zzz500, zzz501, zzz502, zzz503, zzz504, zzz505, zzz506, zzz507, Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat2(Succ(new_primPlusNat3(new_primPlusNat1(zzz500), zzz500)), zzz500)), zzz500))), bg)
new_mkVBalBranch3MkVBalBranch223(zzz340, zzz341, Neg(Succ(Succ(Succ(zzz3420000)))), zzz343, zzz344, zzz510, zzz511, Succ(zzz512000), zzz513, zzz514, zzz31, Succ(Succ(zzz6700)), h) → new_mkVBalBranch3MkVBalBranch224(zzz340, zzz341, Succ(Succ(zzz3420000)), zzz343, zzz344, zzz510, zzz511, zzz512000, zzz513, zzz514, zzz31, Succ(zzz3420000), Succ(Succ(new_primPlusNat2(zzz6700, zzz512000))), h)
new_mkVBalBranch3MkVBalBranch223(zzz340, zzz341, Neg(Succ(Succ(Zero))), zzz343, zzz344, zzz510, zzz511, Zero, zzz513, zzz514, zzz31, Succ(Succ(zzz6700)), h) → new_mkVBalBranch3MkVBalBranch225(zzz340, zzz341, Succ(Zero), zzz343, zzz344, zzz510, zzz511, zzz513, zzz514, zzz31, Zero, Succ(zzz6700), h)
new_mkVBalBranch3MkVBalBranch115(zzz1986, zzz1987, zzz1988, zzz1989, zzz1990, zzz1991, zzz1992, zzz1993, zzz1994, zzz1995, zzz1996, Succ(zzz19970), Succ(zzz19980), bc) → new_mkVBalBranch3MkVBalBranch115(zzz1986, zzz1987, zzz1988, zzz1989, zzz1990, zzz1991, zzz1992, zzz1993, zzz1994, zzz1995, zzz1996, zzz19970, zzz19980, bc)
new_mkVBalBranch3MkVBalBranch215(zzz340, zzz341, Neg(Zero), zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, Succ(zzz660), h) → new_mkVBalBranch0(zzz31, zzz514, Branch(zzz340, zzz341, Neg(Zero), zzz343, zzz344), h)
new_mkVBalBranch3MkVBalBranch224(zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, zzz1125, zzz1126, zzz1127, zzz1128, zzz1129, Succ(zzz11300), Zero, bd) → new_mkVBalBranch3MkVBalBranch119(zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, zzz1125, zzz1126, zzz1127, zzz1128, zzz1129, Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat2(Succ(new_primPlusNat3(new_primPlusNat1(zzz1121), zzz1121)), zzz1121)), zzz1121))), bd)
new_mkVBalBranch3MkVBalBranch118(zzz498, zzz499, zzz500, zzz501, zzz502, zzz503, zzz504, zzz505, zzz506, zzz507, Succ(zzz8040), bg) → new_mkVBalBranch3MkVBalBranch120(zzz498, zzz499, zzz500, zzz501, zzz502, zzz503, zzz504, Zero, zzz505, zzz506, zzz507, Succ(Zero), Succ(zzz8040), bg)
new_mkVBalBranch3MkVBalBranch222(zzz461, zzz462, zzz463, zzz464, zzz465, zzz466, zzz467, zzz468, zzz469, zzz470, zzz471, bb) → new_mkVBalBranch3MkVBalBranch110(zzz461, zzz462, zzz463, zzz464, zzz465, zzz466, zzz467, zzz468, zzz469, zzz470, zzz471, Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat2(Succ(new_primPlusNat3(new_primPlusNat1(zzz463), zzz463)), zzz463)), zzz463))), bb)
new_mkVBalBranch3MkVBalBranch216(zzz1105, zzz1106, zzz1107, zzz1108, zzz1109, zzz1110, zzz1111, zzz1112, zzz1113, zzz1114, zzz1115, Succ(zzz11160), Zero, ba) → new_mkVBalBranch3MkVBalBranch218(zzz1105, zzz1106, zzz1107, zzz1108, zzz1109, zzz1110, zzz1111, zzz1112, zzz1113, zzz1114, zzz1115, ba)
new_mkVBalBranch3MkVBalBranch216(zzz1105, zzz1106, zzz1107, zzz1108, zzz1109, zzz1110, zzz1111, zzz1112, zzz1113, zzz1114, zzz1115, Zero, Zero, ba) → new_mkVBalBranch3MkVBalBranch222(zzz1105, zzz1106, zzz1107, zzz1108, zzz1109, zzz1110, zzz1111, zzz1112, zzz1113, zzz1114, zzz1115, ba)
new_mkVBalBranch3MkVBalBranch119(zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, zzz1125, zzz1126, zzz1127, zzz1128, zzz1129, Succ(zzz12130), bd) → new_mkVBalBranch3MkVBalBranch120(zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, zzz1125, Succ(zzz1126), zzz1127, zzz1128, zzz1129, Succ(Succ(zzz1126)), Succ(zzz12130), bd)

The TRS R consists of the following rules:

new_primPlusNat1(Zero) → Zero
new_primPlusNat1(Succ(zzz62000)) → Succ(Succ(new_primPlusNat1(zzz62000)))
new_primPlusNat3(zzz90, Succ(zzz910)) → Succ(Succ(new_primPlusNat2(zzz90, zzz910)))
new_primPlusNat3(zzz90, Zero) → Succ(zzz90)
new_primPlusNat2(Succ(zzz900), Succ(zzz9100)) → Succ(Succ(new_primPlusNat2(zzz900, zzz9100)))
new_primPlusNat2(Zero, Succ(zzz9100)) → Succ(zzz9100)
new_primPlusNat2(Zero, Zero) → Zero
new_primPlusNat2(Succ(zzz900), Zero) → Succ(zzz900)

The set Q consists of the following terms:

new_primPlusNat2(Zero, Succ(x0))
new_primPlusNat3(x0, Succ(x1))
new_primPlusNat2(Succ(x0), Succ(x1))
new_primPlusNat3(x0, Zero)
new_primPlusNat1(Zero)
new_primPlusNat2(Zero, Zero)
new_primPlusNat1(Succ(x0))
new_primPlusNat2(Succ(x0), Zero)

We have to consider all minimal (P,Q,R)-chains.
By rewriting [15] the rule new_mkVBalBranch3MkVBalBranch215(zzz340, zzz341, Pos(Succ(Zero)), zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, Succ(zzz660), h) → new_mkVBalBranch3MkVBalBranch18(zzz340, zzz341, zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat2(Succ(new_primPlusNat3(new_primPlusNat1(Zero), Zero)), Zero)), Zero))), h) at position [10,0,0] we obtained the following new rules:

new_mkVBalBranch3MkVBalBranch215(zzz340, zzz341, Pos(Succ(Zero)), zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, Succ(zzz660), h) → new_mkVBalBranch3MkVBalBranch18(zzz340, zzz341, zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, Succ(Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat3(new_primPlusNat1(Zero), Zero)), Zero)))), 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
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                    ↳ DependencyGraphProof
                                      ↳ QDP
                                        ↳ Rewriting
                                          ↳ QDP
                                            ↳ Rewriting
                                              ↳ QDP
                                                ↳ Rewriting
                                                  ↳ QDP
                                                    ↳ Rewriting
                                                      ↳ QDP
                                                        ↳ Rewriting
                                                          ↳ QDP
                                                            ↳ Rewriting
                                                              ↳ QDP
                                                                ↳ Rewriting
                                                                  ↳ QDP
                                                                    ↳ Rewriting
                                                                      ↳ QDP
                                                                        ↳ Rewriting
                                                                          ↳ QDP
                                                                            ↳ Rewriting
                                                                              ↳ QDP
                                                                                ↳ Rewriting
                                                                                  ↳ QDP
                                                                                    ↳ Rewriting
                                                                                      ↳ QDP
                                                                                        ↳ Rewriting
                                                                                          ↳ QDP
                                                                                            ↳ Rewriting
                                                                                              ↳ QDP
                                                                                                ↳ Rewriting
                                                                                                  ↳ QDP
                                                                                                    ↳ Rewriting
                                                                                                      ↳ QDP
                                                                                                        ↳ Rewriting
                                                                                                          ↳ QDP
                                                                                                            ↳ UsableRulesProof
                                                                                                              ↳ QDP
                                                                                                                ↳ QReductionProof
                                                                                                                  ↳ QDP
                                                                                                                    ↳ Rewriting
                                                                                                                      ↳ QDP
                                                                                                                        ↳ Rewriting
                                                                                                                          ↳ QDP
                                                                                                                            ↳ DependencyGraphProof
                                                                                                                              ↳ QDP
                                                                                                                                ↳ Rewriting
                                                                                                                                  ↳ QDP
                                                                                                                                    ↳ Rewriting
                                                                                                                                      ↳ QDP
                                                                                                                                        ↳ DependencyGraphProof
                                                                                                                                          ↳ QDP
                                                                                                                                            ↳ Rewriting
                                                                                                                                              ↳ QDP
                                                                                                                                                ↳ Rewriting
                                                                                                                                                  ↳ QDP
                                                                                                                                                    ↳ Rewriting
                                                                                                                                                      ↳ QDP
                                                                                                                                                        ↳ Rewriting
                                                                                                                                                          ↳ QDP
                                                                                                                                                            ↳ Rewriting
                                                                                                                                                              ↳ QDP
                                                                                                                                                                ↳ Rewriting
                                                                                                                                                                  ↳ QDP
                                                                                                                                                                    ↳ Rewriting
                                                                                                                                                                      ↳ QDP
                                                                                                                                                                        ↳ Rewriting
                                                                                                                                                                          ↳ QDP
                                                                                                                                                                            ↳ Rewriting
                                                                                                                                                                              ↳ QDP
                                                                                                                                                                                ↳ Rewriting
                                                                                                                                                                                  ↳ QDP
                                                                                                                                                                                    ↳ Rewriting
                                                                                                                                                                                      ↳ QDP
                                                                                                                                                                                        ↳ Rewriting
                                                                                                                                                                                          ↳ QDP
                                                                                                                                                                                            ↳ UsableRulesProof
                                                                                                                                                                                              ↳ QDP
                                                                                                                                                                                                ↳ QReductionProof
                                                                                                                                                                                                  ↳ QDP
                                                                                                                                                                                                    ↳ Rewriting
                                                                                                                                                                                                      ↳ QDP
                                                                                                                                                                                                        ↳ Rewriting
                                                                                                                                                                                                          ↳ QDP
                                                                                                                                                                                                            ↳ Rewriting
                                                                                                                                                                                                              ↳ QDP
                                                                                                                                                                                                                ↳ Rewriting
                                                                                                                                                                                                                  ↳ QDP
                                                                                                                                                                                                                    ↳ Rewriting
                                                                                                                                                                                                                      ↳ QDP
                                                                                                                                                                                                                        ↳ Rewriting
                                                                                                                                                                                                                          ↳ QDP
                                                                                                                                                                                                                            ↳ Rewriting
                                                                                                                                                                                                                              ↳ QDP
                                                                                                                                                                                                                                ↳ Rewriting
                                                                                                                                                                                                                                  ↳ QDP
                                                                                                                                                                                                                                    ↳ Rewriting
                                                                                                                                                                                                                                      ↳ QDP
                                                                                                                                                                                                                                        ↳ Rewriting
                                                                                                                                                                                                                                          ↳ QDP
                                                                                                                                                                                                                                            ↳ Rewriting
                                                                                                                                                                                                                                              ↳ QDP
                                                                                                                                                                                                                                                ↳ Rewriting
                                                                                                                                                                                                                                                  ↳ QDP
                                                                                                                                                                                                                                                    ↳ Rewriting
                                                                                                                                                                                                                                                      ↳ QDP
                                                                                                                                                                                                                                                        ↳ Rewriting
                                                                                                                                                                                                                                                          ↳ QDP
                                                                                                                                                                                                                                                            ↳ DependencyGraphProof
                                                                                                                                                                                                                                                              ↳ QDP
                                                                                                                                                                                                                                                                ↳ Rewriting
                                                                                                                                                                                                                                                                  ↳ QDP
                                                                                                                                                                                                                                                                    ↳ Rewriting
                                                                                                                                                                                                                                                                      ↳ QDP
                                                                                                                                                                                                                                                                        ↳ Rewriting
                                                                                                                                                                                                                                                                          ↳ QDP
                                                                                                                                                                                                                                                                            ↳ Rewriting
                                                                                                                                                                                                                                                                              ↳ QDP
                                                                                                                                                                                                                                                                                ↳ Rewriting
                                                                                                                                                                                                                                                                                  ↳ QDP
                                                                                                                                                                                                                                                                                    ↳ Rewriting
                                                                                                                                                                                                                                                                                      ↳ QDP
                                                                                                                                                                                                                                                                                        ↳ DependencyGraphProof
                                                                                                                                                                                                                                                                                          ↳ QDP
                                                                                                                                                                                                                                                                                            ↳ Rewriting
                                                                                                                                                                                                                                                                                              ↳ QDP
                                                                                                                                                                                                                                                                                                ↳ DependencyGraphProof
                                                                                                                                                                                                                                                                                                  ↳ QDP
                                                                                                                                                                                                                                                                                                    ↳ Rewriting
                                                                                                                                                                                                                                                                                                      ↳ QDP
                                                                                                                                                                                                                                                                                                        ↳ DependencyGraphProof
                                                                                                                                                                                                                                                                                                          ↳ QDP
                                                                                                                                                                                                                                                                                                            ↳ Rewriting
                                                                                                                                                                                                                                                                                                              ↳ QDP
                                                                                                                                                                                                                                                                                                                ↳ Rewriting
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP

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

new_mkVBalBranch3MkVBalBranch225(zzz498, zzz499, zzz500, zzz501, zzz502, zzz503, zzz504, zzz505, zzz506, zzz507, Zero, Zero, bg) → new_mkVBalBranch3MkVBalBranch230(zzz498, zzz499, zzz500, zzz501, zzz502, zzz503, zzz504, zzz505, zzz506, zzz507, bg)
new_mkVBalBranch3MkVBalBranch18(zzz340, zzz341, zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, Succ(zzz1480), h) → new_mkVBalBranch3MkVBalBranch115(zzz340, zzz341, Zero, zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, Succ(zzz1480), Succ(zzz51200), h)
new_mkVBalBranch0(zzz31, Branch(zzz510, zzz511, Neg(Zero), zzz513, zzz514), Branch(zzz340, zzz341, Pos(Succ(zzz34200)), zzz343, zzz344), h) → new_mkVBalBranch0(zzz31, Branch(zzz510, zzz511, Neg(Zero), zzz513, zzz514), zzz343, h)
new_mkVBalBranch3MkVBalBranch215(zzz340, zzz341, Pos(Succ(Succ(zzz342000))), zzz343, zzz344, zzz510, zzz511, Succ(zzz512000), zzz513, zzz514, zzz31, Succ(Succ(zzz6600)), h) → new_mkVBalBranch3MkVBalBranch216(zzz340, zzz341, Succ(zzz342000), zzz343, zzz344, zzz510, zzz511, zzz512000, zzz513, zzz514, zzz31, Succ(Succ(new_primPlusNat2(zzz6600, zzz512000))), zzz342000, h)
new_mkVBalBranch3MkVBalBranch223(zzz340, zzz341, Neg(Succ(Succ(Succ(zzz3420000)))), zzz343, zzz344, zzz510, zzz511, Zero, zzz513, zzz514, zzz31, Succ(Succ(zzz6700)), h) → new_mkVBalBranch3MkVBalBranch225(zzz340, zzz341, Succ(Succ(zzz3420000)), zzz343, zzz344, zzz510, zzz511, zzz513, zzz514, zzz31, Succ(zzz3420000), Succ(zzz6700), h)
new_mkVBalBranch3MkVBalBranch120(zzz2050, zzz2051, zzz2052, zzz2053, zzz2054, zzz2055, zzz2056, zzz2057, zzz2058, zzz2059, zzz2060, Zero, Succ(zzz20620), be) → new_mkVBalBranch0(zzz2060, zzz2059, Branch(zzz2050, zzz2051, Neg(Succ(zzz2052)), zzz2053, zzz2054), be)
new_mkVBalBranch3MkVBalBranch121(zzz473, zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, zzz481, zzz482, Succ(zzz7390), bh) → new_mkVBalBranch3MkVBalBranch115(zzz473, zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, Zero, zzz480, zzz481, zzz482, Succ(zzz7390), Succ(Zero), bh)
new_mkVBalBranch0(zzz31, Branch(zzz510, zzz511, Pos(Zero), zzz513, zzz514), Branch(zzz340, zzz341, Pos(Succ(zzz34200)), zzz343, zzz344), h) → new_mkVBalBranch0(zzz31, Branch(zzz510, zzz511, Pos(Zero), zzz513, zzz514), zzz343, h)
new_mkVBalBranch0(zzz31, Branch(zzz510, zzz511, Pos(Succ(zzz51200)), zzz513, zzz514), Branch(zzz340, zzz341, zzz342, zzz343, zzz344), h) → new_mkVBalBranch3MkVBalBranch215(zzz340, zzz341, zzz342, zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat3(new_primPlusNat1(zzz51200), zzz51200)), zzz51200))), h)
new_mkVBalBranch3MkVBalBranch215(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, Succ(zzz660), h) → new_mkVBalBranch3MkVBalBranch19(zzz340, zzz341, zzz34200, zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat2(Succ(new_primPlusNat3(new_primPlusNat1(zzz34200), zzz34200)), zzz34200)), zzz34200))), h)
new_mkVBalBranch3MkVBalBranch230(zzz498, zzz499, zzz500, zzz501, zzz502, zzz503, zzz504, zzz505, zzz506, zzz507, bg) → new_mkVBalBranch3MkVBalBranch118(zzz498, zzz499, zzz500, zzz501, zzz502, zzz503, zzz504, zzz505, zzz506, zzz507, Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat2(Succ(new_primPlusNat3(new_primPlusNat1(zzz500), zzz500)), zzz500)), zzz500))), bg)
new_mkVBalBranch3MkVBalBranch223(zzz340, zzz341, Neg(Succ(Succ(Zero))), zzz343, zzz344, zzz510, zzz511, Succ(zzz512000), zzz513, zzz514, zzz31, Succ(Succ(zzz6700)), h) → new_mkVBalBranch3MkVBalBranch224(zzz340, zzz341, Succ(Zero), zzz343, zzz344, zzz510, zzz511, zzz512000, zzz513, zzz514, zzz31, Zero, Succ(Succ(new_primPlusNat2(zzz6700, zzz512000))), h)
new_mkVBalBranch0(zzz31, Branch(zzz510, zzz511, Pos(Zero), zzz513, zzz514), Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), h) → new_mkVBalBranch3MkVBalBranch116(zzz340, zzz341, zzz34200, zzz343, zzz344, zzz510, zzz511, zzz513, zzz514, zzz31, Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat2(Succ(new_primPlusNat3(new_primPlusNat1(zzz34200), zzz34200)), zzz34200)), zzz34200))), h)
new_mkVBalBranch0(zzz31, Branch(zzz510, zzz511, Neg(Zero), zzz513, zzz514), Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), h) → new_mkVBalBranch3MkVBalBranch117(zzz340, zzz341, zzz34200, zzz343, zzz344, zzz510, zzz511, zzz513, zzz514, zzz31, Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat2(Succ(new_primPlusNat3(new_primPlusNat1(zzz34200), zzz34200)), zzz34200)), zzz34200))), h)
new_mkVBalBranch3MkVBalBranch224(zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, zzz1125, zzz1126, zzz1127, zzz1128, zzz1129, Succ(zzz11300), Succ(zzz11310), bd) → new_mkVBalBranch3MkVBalBranch224(zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, zzz1125, zzz1126, zzz1127, zzz1128, zzz1129, zzz11300, zzz11310, bd)
new_mkVBalBranch3MkVBalBranch217(zzz473, zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, zzz481, zzz482, Succ(zzz4830), Zero, bh) → new_mkVBalBranch3MkVBalBranch121(zzz473, zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, zzz481, zzz482, Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat2(Succ(new_primPlusNat3(new_primPlusNat1(zzz475), zzz475)), zzz475)), zzz475))), bh)
new_mkVBalBranch3MkVBalBranch229(zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, zzz1125, zzz1126, zzz1127, zzz1128, zzz1129, bd) → new_mkVBalBranch3MkVBalBranch119(zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, zzz1125, zzz1126, zzz1127, zzz1128, zzz1129, Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat2(Succ(new_primPlusNat3(new_primPlusNat1(zzz1121), zzz1121)), zzz1121)), zzz1121))), bd)
new_mkVBalBranch3MkVBalBranch217(zzz473, zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, zzz481, zzz482, Zero, Succ(zzz4840), bh) → new_mkVBalBranch0(zzz482, Branch(zzz478, zzz479, Pos(Succ(Zero)), zzz480, zzz481), zzz476, bh)
new_mkVBalBranch3MkVBalBranch218(zzz461, zzz462, zzz463, zzz464, zzz465, zzz466, zzz467, zzz468, zzz469, zzz470, zzz471, bb) → new_mkVBalBranch3MkVBalBranch110(zzz461, zzz462, zzz463, zzz464, zzz465, zzz466, zzz467, zzz468, zzz469, zzz470, zzz471, Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat2(Succ(new_primPlusNat3(new_primPlusNat1(zzz463), zzz463)), zzz463)), zzz463))), bb)
new_mkVBalBranch3MkVBalBranch110(zzz461, zzz462, zzz463, zzz464, zzz465, zzz466, zzz467, zzz468, zzz469, zzz470, zzz471, Succ(zzz5800), bb) → new_mkVBalBranch3MkVBalBranch115(zzz461, zzz462, zzz463, zzz464, zzz465, zzz466, zzz467, Succ(zzz468), zzz469, zzz470, zzz471, Succ(zzz5800), Succ(Succ(zzz468)), bb)
new_mkVBalBranch3MkVBalBranch227(zzz486, zzz487, zzz488, zzz489, zzz490, zzz491, zzz492, zzz493, zzz494, zzz495, zzz496, bf) → new_mkVBalBranch0(zzz496, Branch(zzz491, zzz492, Neg(Succ(Succ(zzz493))), zzz494, zzz495), zzz489, bf)
new_mkVBalBranch3MkVBalBranch215(zzz340, zzz341, Pos(Zero), zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, Succ(zzz660), h) → new_mkVBalBranch0(zzz31, zzz514, Branch(zzz340, zzz341, Pos(Zero), zzz343, zzz344), h)
new_mkVBalBranch3MkVBalBranch223(zzz340, zzz341, Neg(Zero), zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, Succ(zzz670), h) → new_mkVBalBranch0(zzz31, Branch(zzz510, zzz511, Neg(Succ(zzz51200)), zzz513, zzz514), zzz343, h)
new_mkVBalBranch3MkVBalBranch216(zzz1105, zzz1106, zzz1107, zzz1108, zzz1109, zzz1110, zzz1111, zzz1112, zzz1113, zzz1114, zzz1115, Zero, Succ(zzz11170), ba) → new_mkVBalBranch0(zzz1115, Branch(zzz1110, zzz1111, Pos(Succ(Succ(zzz1112))), zzz1113, zzz1114), zzz1108, ba)
new_mkVBalBranch3MkVBalBranch115(zzz1986, zzz1987, zzz1988, zzz1989, zzz1990, zzz1991, zzz1992, zzz1993, zzz1994, zzz1995, zzz1996, Zero, Succ(zzz19980), bc) → new_mkVBalBranch0(zzz1996, zzz1995, Branch(zzz1986, zzz1987, Pos(Succ(zzz1988)), zzz1989, zzz1990), bc)
new_mkVBalBranch3MkVBalBranch233(zzz473, zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, zzz481, zzz482, bh) → new_mkVBalBranch3MkVBalBranch121(zzz473, zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, zzz481, zzz482, Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat2(Succ(new_primPlusNat3(new_primPlusNat1(zzz475), zzz475)), zzz475)), zzz475))), bh)
new_mkVBalBranch3MkVBalBranch217(zzz473, zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, zzz481, zzz482, Succ(zzz4830), Succ(zzz4840), bh) → new_mkVBalBranch3MkVBalBranch217(zzz473, zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, zzz481, zzz482, zzz4830, zzz4840, bh)
new_mkVBalBranch3MkVBalBranch116(zzz340, zzz341, zzz34200, zzz343, zzz344, zzz510, zzz511, zzz513, zzz514, zzz31, Succ(zzz1200), h) → new_mkVBalBranch0(zzz31, zzz514, Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), h)
new_mkVBalBranch3MkVBalBranch225(zzz498, zzz499, zzz500, zzz501, zzz502, zzz503, zzz504, zzz505, zzz506, zzz507, Zero, Succ(zzz5090), bg) → new_mkVBalBranch0(zzz507, Branch(zzz503, zzz504, Neg(Succ(Zero)), zzz505, zzz506), zzz501, bg)
new_mkVBalBranch0(zzz31, Branch(zzz510, zzz511, Neg(Succ(zzz51200)), zzz513, zzz514), Branch(zzz340, zzz341, zzz342, zzz343, zzz344), h) → new_mkVBalBranch3MkVBalBranch223(zzz340, zzz341, zzz342, zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat3(new_primPlusNat1(zzz51200), zzz51200)), zzz51200))), h)
new_mkVBalBranch3MkVBalBranch223(zzz340, zzz341, Neg(Succ(Zero)), zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, Succ(zzz670), h) → new_mkVBalBranch0(zzz31, Branch(zzz510, zzz511, Neg(Succ(zzz51200)), zzz513, zzz514), zzz343, h)
new_mkVBalBranch3MkVBalBranch215(zzz340, zzz341, Pos(Succ(Succ(zzz342000))), zzz343, zzz344, zzz510, zzz511, Zero, zzz513, zzz514, zzz31, Succ(Succ(zzz6600)), h) → new_mkVBalBranch3MkVBalBranch217(zzz340, zzz341, Succ(zzz342000), zzz343, zzz344, zzz510, zzz511, zzz513, zzz514, zzz31, Succ(zzz6600), zzz342000, h)
new_mkVBalBranch3MkVBalBranch117(zzz340, zzz341, zzz34200, zzz343, zzz344, zzz510, zzz511, zzz513, zzz514, zzz31, Succ(zzz1240), h) → new_mkVBalBranch0(zzz31, zzz514, Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), h)
new_mkVBalBranch3MkVBalBranch215(zzz340, zzz341, Pos(Succ(Zero)), zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, Succ(zzz660), h) → new_mkVBalBranch3MkVBalBranch18(zzz340, zzz341, zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, Succ(Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat3(new_primPlusNat1(Zero), Zero)), Zero)))), h)
new_mkVBalBranch3MkVBalBranch217(zzz473, zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, zzz481, zzz482, Zero, Zero, bh) → new_mkVBalBranch3MkVBalBranch233(zzz473, zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, zzz481, zzz482, bh)
new_mkVBalBranch3MkVBalBranch120(zzz2050, zzz2051, zzz2052, zzz2053, zzz2054, zzz2055, zzz2056, zzz2057, zzz2058, zzz2059, zzz2060, Succ(zzz20610), Succ(zzz20620), be) → new_mkVBalBranch3MkVBalBranch120(zzz2050, zzz2051, zzz2052, zzz2053, zzz2054, zzz2055, zzz2056, zzz2057, zzz2058, zzz2059, zzz2060, zzz20610, zzz20620, be)
new_mkVBalBranch3MkVBalBranch223(zzz340, zzz341, Pos(zzz3420), zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, Succ(zzz670), h) → new_mkVBalBranch0(zzz31, Branch(zzz510, zzz511, Neg(Succ(zzz51200)), zzz513, zzz514), zzz343, h)
new_mkVBalBranch3MkVBalBranch216(zzz1105, zzz1106, zzz1107, zzz1108, zzz1109, zzz1110, zzz1111, zzz1112, zzz1113, zzz1114, zzz1115, Succ(zzz11160), Succ(zzz11170), ba) → new_mkVBalBranch3MkVBalBranch216(zzz1105, zzz1106, zzz1107, zzz1108, zzz1109, zzz1110, zzz1111, zzz1112, zzz1113, zzz1114, zzz1115, zzz11160, zzz11170, ba)
new_mkVBalBranch3MkVBalBranch225(zzz498, zzz499, zzz500, zzz501, zzz502, zzz503, zzz504, zzz505, zzz506, zzz507, Succ(zzz5080), Succ(zzz5090), bg) → new_mkVBalBranch3MkVBalBranch225(zzz498, zzz499, zzz500, zzz501, zzz502, zzz503, zzz504, zzz505, zzz506, zzz507, zzz5080, zzz5090, bg)
new_mkVBalBranch3MkVBalBranch19(zzz340, zzz341, zzz34200, zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, Succ(zzz1410), h) → new_mkVBalBranch0(zzz31, zzz514, Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), h)
new_mkVBalBranch3MkVBalBranch224(zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, zzz1125, zzz1126, zzz1127, zzz1128, zzz1129, Zero, Zero, bd) → new_mkVBalBranch3MkVBalBranch229(zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, zzz1125, zzz1126, zzz1127, zzz1128, zzz1129, bd)
new_mkVBalBranch3MkVBalBranch224(zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, zzz1125, zzz1126, zzz1127, zzz1128, zzz1129, Zero, Succ(zzz11310), bd) → new_mkVBalBranch3MkVBalBranch227(zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, zzz1125, zzz1126, zzz1127, zzz1128, zzz1129, bd)
new_mkVBalBranch3MkVBalBranch223(zzz340, zzz341, Neg(Succ(Succ(Zero))), zzz343, zzz344, zzz510, zzz511, Zero, zzz513, zzz514, zzz31, Succ(Succ(zzz6700)), h) → new_mkVBalBranch3MkVBalBranch225(zzz340, zzz341, Succ(Zero), zzz343, zzz344, zzz510, zzz511, zzz513, zzz514, zzz31, Zero, Succ(zzz6700), h)
new_mkVBalBranch3MkVBalBranch223(zzz340, zzz341, Neg(Succ(Succ(Succ(zzz3420000)))), zzz343, zzz344, zzz510, zzz511, Succ(zzz512000), zzz513, zzz514, zzz31, Succ(Succ(zzz6700)), h) → new_mkVBalBranch3MkVBalBranch224(zzz340, zzz341, Succ(Succ(zzz3420000)), zzz343, zzz344, zzz510, zzz511, zzz512000, zzz513, zzz514, zzz31, Succ(zzz3420000), Succ(Succ(new_primPlusNat2(zzz6700, zzz512000))), h)
new_mkVBalBranch3MkVBalBranch225(zzz498, zzz499, zzz500, zzz501, zzz502, zzz503, zzz504, zzz505, zzz506, zzz507, Succ(zzz5080), Zero, bg) → new_mkVBalBranch3MkVBalBranch118(zzz498, zzz499, zzz500, zzz501, zzz502, zzz503, zzz504, zzz505, zzz506, zzz507, Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat2(Succ(new_primPlusNat3(new_primPlusNat1(zzz500), zzz500)), zzz500)), zzz500))), bg)
new_mkVBalBranch3MkVBalBranch115(zzz1986, zzz1987, zzz1988, zzz1989, zzz1990, zzz1991, zzz1992, zzz1993, zzz1994, zzz1995, zzz1996, Succ(zzz19970), Succ(zzz19980), bc) → new_mkVBalBranch3MkVBalBranch115(zzz1986, zzz1987, zzz1988, zzz1989, zzz1990, zzz1991, zzz1992, zzz1993, zzz1994, zzz1995, zzz1996, zzz19970, zzz19980, bc)
new_mkVBalBranch3MkVBalBranch215(zzz340, zzz341, Neg(Zero), zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, Succ(zzz660), h) → new_mkVBalBranch0(zzz31, zzz514, Branch(zzz340, zzz341, Neg(Zero), zzz343, zzz344), h)
new_mkVBalBranch3MkVBalBranch224(zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, zzz1125, zzz1126, zzz1127, zzz1128, zzz1129, Succ(zzz11300), Zero, bd) → new_mkVBalBranch3MkVBalBranch119(zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, zzz1125, zzz1126, zzz1127, zzz1128, zzz1129, Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat2(Succ(new_primPlusNat3(new_primPlusNat1(zzz1121), zzz1121)), zzz1121)), zzz1121))), bd)
new_mkVBalBranch3MkVBalBranch222(zzz461, zzz462, zzz463, zzz464, zzz465, zzz466, zzz467, zzz468, zzz469, zzz470, zzz471, bb) → new_mkVBalBranch3MkVBalBranch110(zzz461, zzz462, zzz463, zzz464, zzz465, zzz466, zzz467, zzz468, zzz469, zzz470, zzz471, Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat2(Succ(new_primPlusNat3(new_primPlusNat1(zzz463), zzz463)), zzz463)), zzz463))), bb)
new_mkVBalBranch3MkVBalBranch118(zzz498, zzz499, zzz500, zzz501, zzz502, zzz503, zzz504, zzz505, zzz506, zzz507, Succ(zzz8040), bg) → new_mkVBalBranch3MkVBalBranch120(zzz498, zzz499, zzz500, zzz501, zzz502, zzz503, zzz504, Zero, zzz505, zzz506, zzz507, Succ(Zero), Succ(zzz8040), bg)
new_mkVBalBranch3MkVBalBranch216(zzz1105, zzz1106, zzz1107, zzz1108, zzz1109, zzz1110, zzz1111, zzz1112, zzz1113, zzz1114, zzz1115, Succ(zzz11160), Zero, ba) → new_mkVBalBranch3MkVBalBranch218(zzz1105, zzz1106, zzz1107, zzz1108, zzz1109, zzz1110, zzz1111, zzz1112, zzz1113, zzz1114, zzz1115, ba)
new_mkVBalBranch3MkVBalBranch216(zzz1105, zzz1106, zzz1107, zzz1108, zzz1109, zzz1110, zzz1111, zzz1112, zzz1113, zzz1114, zzz1115, Zero, Zero, ba) → new_mkVBalBranch3MkVBalBranch222(zzz1105, zzz1106, zzz1107, zzz1108, zzz1109, zzz1110, zzz1111, zzz1112, zzz1113, zzz1114, zzz1115, ba)
new_mkVBalBranch3MkVBalBranch119(zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, zzz1125, zzz1126, zzz1127, zzz1128, zzz1129, Succ(zzz12130), bd) → new_mkVBalBranch3MkVBalBranch120(zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, zzz1125, Succ(zzz1126), zzz1127, zzz1128, zzz1129, Succ(Succ(zzz1126)), Succ(zzz12130), bd)

The TRS R consists of the following rules:

new_primPlusNat1(Zero) → Zero
new_primPlusNat1(Succ(zzz62000)) → Succ(Succ(new_primPlusNat1(zzz62000)))
new_primPlusNat3(zzz90, Succ(zzz910)) → Succ(Succ(new_primPlusNat2(zzz90, zzz910)))
new_primPlusNat3(zzz90, Zero) → Succ(zzz90)
new_primPlusNat2(Succ(zzz900), Succ(zzz9100)) → Succ(Succ(new_primPlusNat2(zzz900, zzz9100)))
new_primPlusNat2(Zero, Succ(zzz9100)) → Succ(zzz9100)
new_primPlusNat2(Zero, Zero) → Zero
new_primPlusNat2(Succ(zzz900), Zero) → Succ(zzz900)

The set Q consists of the following terms:

new_primPlusNat2(Zero, Succ(x0))
new_primPlusNat3(x0, Succ(x1))
new_primPlusNat2(Succ(x0), Succ(x1))
new_primPlusNat3(x0, Zero)
new_primPlusNat1(Zero)
new_primPlusNat2(Zero, Zero)
new_primPlusNat1(Succ(x0))
new_primPlusNat2(Succ(x0), Zero)

We have to consider all minimal (P,Q,R)-chains.
By rewriting [15] the rule new_mkVBalBranch3MkVBalBranch215(zzz340, zzz341, Pos(Succ(Zero)), zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, Succ(zzz660), h) → new_mkVBalBranch3MkVBalBranch18(zzz340, zzz341, zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, Succ(Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat3(new_primPlusNat1(Zero), Zero)), Zero)))), h) at position [10,0,0,0] we obtained the following new rules:

new_mkVBalBranch3MkVBalBranch215(zzz340, zzz341, Pos(Succ(Zero)), zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, Succ(zzz660), h) → new_mkVBalBranch3MkVBalBranch18(zzz340, zzz341, zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, Succ(Succ(Succ(Succ(new_primPlusNat3(new_primPlusNat1(Zero), Zero))))), 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
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                    ↳ DependencyGraphProof
                                      ↳ QDP
                                        ↳ Rewriting
                                          ↳ QDP
                                            ↳ Rewriting
                                              ↳ QDP
                                                ↳ Rewriting
                                                  ↳ QDP
                                                    ↳ Rewriting
                                                      ↳ QDP
                                                        ↳ Rewriting
                                                          ↳ QDP
                                                            ↳ Rewriting
                                                              ↳ QDP
                                                                ↳ Rewriting
                                                                  ↳ QDP
                                                                    ↳ Rewriting
                                                                      ↳ QDP
                                                                        ↳ Rewriting
                                                                          ↳ QDP
                                                                            ↳ Rewriting
                                                                              ↳ QDP
                                                                                ↳ Rewriting
                                                                                  ↳ QDP
                                                                                    ↳ Rewriting
                                                                                      ↳ QDP
                                                                                        ↳ Rewriting
                                                                                          ↳ QDP
                                                                                            ↳ Rewriting
                                                                                              ↳ QDP
                                                                                                ↳ Rewriting
                                                                                                  ↳ QDP
                                                                                                    ↳ Rewriting
                                                                                                      ↳ QDP
                                                                                                        ↳ Rewriting
                                                                                                          ↳ QDP
                                                                                                            ↳ UsableRulesProof
                                                                                                              ↳ QDP
                                                                                                                ↳ QReductionProof
                                                                                                                  ↳ QDP
                                                                                                                    ↳ Rewriting
                                                                                                                      ↳ QDP
                                                                                                                        ↳ Rewriting
                                                                                                                          ↳ QDP
                                                                                                                            ↳ DependencyGraphProof
                                                                                                                              ↳ QDP
                                                                                                                                ↳ Rewriting
                                                                                                                                  ↳ QDP
                                                                                                                                    ↳ Rewriting
                                                                                                                                      ↳ QDP
                                                                                                                                        ↳ DependencyGraphProof
                                                                                                                                          ↳ QDP
                                                                                                                                            ↳ Rewriting
                                                                                                                                              ↳ QDP
                                                                                                                                                ↳ Rewriting
                                                                                                                                                  ↳ QDP
                                                                                                                                                    ↳ Rewriting
                                                                                                                                                      ↳ QDP
                                                                                                                                                        ↳ Rewriting
                                                                                                                                                          ↳ QDP
                                                                                                                                                            ↳ Rewriting
                                                                                                                                                              ↳ QDP
                                                                                                                                                                ↳ Rewriting
                                                                                                                                                                  ↳ QDP
                                                                                                                                                                    ↳ Rewriting
                                                                                                                                                                      ↳ QDP
                                                                                                                                                                        ↳ Rewriting
                                                                                                                                                                          ↳ QDP
                                                                                                                                                                            ↳ Rewriting
                                                                                                                                                                              ↳ QDP
                                                                                                                                                                                ↳ Rewriting
                                                                                                                                                                                  ↳ QDP
                                                                                                                                                                                    ↳ Rewriting
                                                                                                                                                                                      ↳ QDP
                                                                                                                                                                                        ↳ Rewriting
                                                                                                                                                                                          ↳ QDP
                                                                                                                                                                                            ↳ UsableRulesProof
                                                                                                                                                                                              ↳ QDP
                                                                                                                                                                                                ↳ QReductionProof
                                                                                                                                                                                                  ↳ QDP
                                                                                                                                                                                                    ↳ Rewriting
                                                                                                                                                                                                      ↳ QDP
                                                                                                                                                                                                        ↳ Rewriting
                                                                                                                                                                                                          ↳ QDP
                                                                                                                                                                                                            ↳ Rewriting
                                                                                                                                                                                                              ↳ QDP
                                                                                                                                                                                                                ↳ Rewriting
                                                                                                                                                                                                                  ↳ QDP
                                                                                                                                                                                                                    ↳ Rewriting
                                                                                                                                                                                                                      ↳ QDP
                                                                                                                                                                                                                        ↳ Rewriting
                                                                                                                                                                                                                          ↳ QDP
                                                                                                                                                                                                                            ↳ Rewriting
                                                                                                                                                                                                                              ↳ QDP
                                                                                                                                                                                                                                ↳ Rewriting
                                                                                                                                                                                                                                  ↳ QDP
                                                                                                                                                                                                                                    ↳ Rewriting
                                                                                                                                                                                                                                      ↳ QDP
                                                                                                                                                                                                                                        ↳ Rewriting
                                                                                                                                                                                                                                          ↳ QDP
                                                                                                                                                                                                                                            ↳ Rewriting
                                                                                                                                                                                                                                              ↳ QDP
                                                                                                                                                                                                                                                ↳ Rewriting
                                                                                                                                                                                                                                                  ↳ QDP
                                                                                                                                                                                                                                                    ↳ Rewriting
                                                                                                                                                                                                                                                      ↳ QDP
                                                                                                                                                                                                                                                        ↳ Rewriting
                                                                                                                                                                                                                                                          ↳ QDP
                                                                                                                                                                                                                                                            ↳ DependencyGraphProof
                                                                                                                                                                                                                                                              ↳ QDP
                                                                                                                                                                                                                                                                ↳ Rewriting
                                                                                                                                                                                                                                                                  ↳ QDP
                                                                                                                                                                                                                                                                    ↳ Rewriting
                                                                                                                                                                                                                                                                      ↳ QDP
                                                                                                                                                                                                                                                                        ↳ Rewriting
                                                                                                                                                                                                                                                                          ↳ QDP
                                                                                                                                                                                                                                                                            ↳ Rewriting
                                                                                                                                                                                                                                                                              ↳ QDP
                                                                                                                                                                                                                                                                                ↳ Rewriting
                                                                                                                                                                                                                                                                                  ↳ QDP
                                                                                                                                                                                                                                                                                    ↳ Rewriting
                                                                                                                                                                                                                                                                                      ↳ QDP
                                                                                                                                                                                                                                                                                        ↳ DependencyGraphProof
                                                                                                                                                                                                                                                                                          ↳ QDP
                                                                                                                                                                                                                                                                                            ↳ Rewriting
                                                                                                                                                                                                                                                                                              ↳ QDP
                                                                                                                                                                                                                                                                                                ↳ DependencyGraphProof
                                                                                                                                                                                                                                                                                                  ↳ QDP
                                                                                                                                                                                                                                                                                                    ↳ Rewriting
                                                                                                                                                                                                                                                                                                      ↳ QDP
                                                                                                                                                                                                                                                                                                        ↳ DependencyGraphProof
                                                                                                                                                                                                                                                                                                          ↳ QDP
                                                                                                                                                                                                                                                                                                            ↳ Rewriting
                                                                                                                                                                                                                                                                                                              ↳ QDP
                                                                                                                                                                                                                                                                                                                ↳ Rewriting
                                                                                                                                                                                                                                                                                                                  ↳ QDP
                                                                                                                                                                                                                                                                                                                    ↳ Rewriting
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP

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

new_mkVBalBranch3MkVBalBranch225(zzz498, zzz499, zzz500, zzz501, zzz502, zzz503, zzz504, zzz505, zzz506, zzz507, Zero, Zero, bg) → new_mkVBalBranch3MkVBalBranch230(zzz498, zzz499, zzz500, zzz501, zzz502, zzz503, zzz504, zzz505, zzz506, zzz507, bg)
new_mkVBalBranch3MkVBalBranch18(zzz340, zzz341, zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, Succ(zzz1480), h) → new_mkVBalBranch3MkVBalBranch115(zzz340, zzz341, Zero, zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, Succ(zzz1480), Succ(zzz51200), h)
new_mkVBalBranch3MkVBalBranch215(zzz340, zzz341, Pos(Succ(Succ(zzz342000))), zzz343, zzz344, zzz510, zzz511, Succ(zzz512000), zzz513, zzz514, zzz31, Succ(Succ(zzz6600)), h) → new_mkVBalBranch3MkVBalBranch216(zzz340, zzz341, Succ(zzz342000), zzz343, zzz344, zzz510, zzz511, zzz512000, zzz513, zzz514, zzz31, Succ(Succ(new_primPlusNat2(zzz6600, zzz512000))), zzz342000, h)
new_mkVBalBranch0(zzz31, Branch(zzz510, zzz511, Neg(Zero), zzz513, zzz514), Branch(zzz340, zzz341, Pos(Succ(zzz34200)), zzz343, zzz344), h) → new_mkVBalBranch0(zzz31, Branch(zzz510, zzz511, Neg(Zero), zzz513, zzz514), zzz343, h)
new_mkVBalBranch3MkVBalBranch223(zzz340, zzz341, Neg(Succ(Succ(Succ(zzz3420000)))), zzz343, zzz344, zzz510, zzz511, Zero, zzz513, zzz514, zzz31, Succ(Succ(zzz6700)), h) → new_mkVBalBranch3MkVBalBranch225(zzz340, zzz341, Succ(Succ(zzz3420000)), zzz343, zzz344, zzz510, zzz511, zzz513, zzz514, zzz31, Succ(zzz3420000), Succ(zzz6700), h)
new_mkVBalBranch3MkVBalBranch120(zzz2050, zzz2051, zzz2052, zzz2053, zzz2054, zzz2055, zzz2056, zzz2057, zzz2058, zzz2059, zzz2060, Zero, Succ(zzz20620), be) → new_mkVBalBranch0(zzz2060, zzz2059, Branch(zzz2050, zzz2051, Neg(Succ(zzz2052)), zzz2053, zzz2054), be)
new_mkVBalBranch0(zzz31, Branch(zzz510, zzz511, Pos(Zero), zzz513, zzz514), Branch(zzz340, zzz341, Pos(Succ(zzz34200)), zzz343, zzz344), h) → new_mkVBalBranch0(zzz31, Branch(zzz510, zzz511, Pos(Zero), zzz513, zzz514), zzz343, h)
new_mkVBalBranch3MkVBalBranch121(zzz473, zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, zzz481, zzz482, Succ(zzz7390), bh) → new_mkVBalBranch3MkVBalBranch115(zzz473, zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, Zero, zzz480, zzz481, zzz482, Succ(zzz7390), Succ(Zero), bh)
new_mkVBalBranch0(zzz31, Branch(zzz510, zzz511, Pos(Succ(zzz51200)), zzz513, zzz514), Branch(zzz340, zzz341, zzz342, zzz343, zzz344), h) → new_mkVBalBranch3MkVBalBranch215(zzz340, zzz341, zzz342, zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat3(new_primPlusNat1(zzz51200), zzz51200)), zzz51200))), h)
new_mkVBalBranch3MkVBalBranch215(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, Succ(zzz660), h) → new_mkVBalBranch3MkVBalBranch19(zzz340, zzz341, zzz34200, zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat2(Succ(new_primPlusNat3(new_primPlusNat1(zzz34200), zzz34200)), zzz34200)), zzz34200))), h)
new_mkVBalBranch3MkVBalBranch223(zzz340, zzz341, Neg(Succ(Succ(Zero))), zzz343, zzz344, zzz510, zzz511, Succ(zzz512000), zzz513, zzz514, zzz31, Succ(Succ(zzz6700)), h) → new_mkVBalBranch3MkVBalBranch224(zzz340, zzz341, Succ(Zero), zzz343, zzz344, zzz510, zzz511, zzz512000, zzz513, zzz514, zzz31, Zero, Succ(Succ(new_primPlusNat2(zzz6700, zzz512000))), h)
new_mkVBalBranch3MkVBalBranch230(zzz498, zzz499, zzz500, zzz501, zzz502, zzz503, zzz504, zzz505, zzz506, zzz507, bg) → new_mkVBalBranch3MkVBalBranch118(zzz498, zzz499, zzz500, zzz501, zzz502, zzz503, zzz504, zzz505, zzz506, zzz507, Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat2(Succ(new_primPlusNat3(new_primPlusNat1(zzz500), zzz500)), zzz500)), zzz500))), bg)
new_mkVBalBranch0(zzz31, Branch(zzz510, zzz511, Pos(Zero), zzz513, zzz514), Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), h) → new_mkVBalBranch3MkVBalBranch116(zzz340, zzz341, zzz34200, zzz343, zzz344, zzz510, zzz511, zzz513, zzz514, zzz31, Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat2(Succ(new_primPlusNat3(new_primPlusNat1(zzz34200), zzz34200)), zzz34200)), zzz34200))), h)
new_mkVBalBranch0(zzz31, Branch(zzz510, zzz511, Neg(Zero), zzz513, zzz514), Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), h) → new_mkVBalBranch3MkVBalBranch117(zzz340, zzz341, zzz34200, zzz343, zzz344, zzz510, zzz511, zzz513, zzz514, zzz31, Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat2(Succ(new_primPlusNat3(new_primPlusNat1(zzz34200), zzz34200)), zzz34200)), zzz34200))), h)
new_mkVBalBranch3MkVBalBranch224(zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, zzz1125, zzz1126, zzz1127, zzz1128, zzz1129, Succ(zzz11300), Succ(zzz11310), bd) → new_mkVBalBranch3MkVBalBranch224(zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, zzz1125, zzz1126, zzz1127, zzz1128, zzz1129, zzz11300, zzz11310, bd)
new_mkVBalBranch3MkVBalBranch229(zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, zzz1125, zzz1126, zzz1127, zzz1128, zzz1129, bd) → new_mkVBalBranch3MkVBalBranch119(zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, zzz1125, zzz1126, zzz1127, zzz1128, zzz1129, Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat2(Succ(new_primPlusNat3(new_primPlusNat1(zzz1121), zzz1121)), zzz1121)), zzz1121))), bd)
new_mkVBalBranch3MkVBalBranch217(zzz473, zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, zzz481, zzz482, Succ(zzz4830), Zero, bh) → new_mkVBalBranch3MkVBalBranch121(zzz473, zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, zzz481, zzz482, Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat2(Succ(new_primPlusNat3(new_primPlusNat1(zzz475), zzz475)), zzz475)), zzz475))), bh)
new_mkVBalBranch3MkVBalBranch217(zzz473, zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, zzz481, zzz482, Zero, Succ(zzz4840), bh) → new_mkVBalBranch0(zzz482, Branch(zzz478, zzz479, Pos(Succ(Zero)), zzz480, zzz481), zzz476, bh)
new_mkVBalBranch3MkVBalBranch218(zzz461, zzz462, zzz463, zzz464, zzz465, zzz466, zzz467, zzz468, zzz469, zzz470, zzz471, bb) → new_mkVBalBranch3MkVBalBranch110(zzz461, zzz462, zzz463, zzz464, zzz465, zzz466, zzz467, zzz468, zzz469, zzz470, zzz471, Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat2(Succ(new_primPlusNat3(new_primPlusNat1(zzz463), zzz463)), zzz463)), zzz463))), bb)
new_mkVBalBranch3MkVBalBranch110(zzz461, zzz462, zzz463, zzz464, zzz465, zzz466, zzz467, zzz468, zzz469, zzz470, zzz471, Succ(zzz5800), bb) → new_mkVBalBranch3MkVBalBranch115(zzz461, zzz462, zzz463, zzz464, zzz465, zzz466, zzz467, Succ(zzz468), zzz469, zzz470, zzz471, Succ(zzz5800), Succ(Succ(zzz468)), bb)
new_mkVBalBranch3MkVBalBranch215(zzz340, zzz341, Pos(Succ(Zero)), zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, Succ(zzz660), h) → new_mkVBalBranch3MkVBalBranch18(zzz340, zzz341, zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, Succ(Succ(Succ(Succ(new_primPlusNat3(new_primPlusNat1(Zero), Zero))))), h)
new_mkVBalBranch3MkVBalBranch227(zzz486, zzz487, zzz488, zzz489, zzz490, zzz491, zzz492, zzz493, zzz494, zzz495, zzz496, bf) → new_mkVBalBranch0(zzz496, Branch(zzz491, zzz492, Neg(Succ(Succ(zzz493))), zzz494, zzz495), zzz489, bf)
new_mkVBalBranch3MkVBalBranch215(zzz340, zzz341, Pos(Zero), zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, Succ(zzz660), h) → new_mkVBalBranch0(zzz31, zzz514, Branch(zzz340, zzz341, Pos(Zero), zzz343, zzz344), h)
new_mkVBalBranch3MkVBalBranch223(zzz340, zzz341, Neg(Zero), zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, Succ(zzz670), h) → new_mkVBalBranch0(zzz31, Branch(zzz510, zzz511, Neg(Succ(zzz51200)), zzz513, zzz514), zzz343, h)
new_mkVBalBranch3MkVBalBranch216(zzz1105, zzz1106, zzz1107, zzz1108, zzz1109, zzz1110, zzz1111, zzz1112, zzz1113, zzz1114, zzz1115, Zero, Succ(zzz11170), ba) → new_mkVBalBranch0(zzz1115, Branch(zzz1110, zzz1111, Pos(Succ(Succ(zzz1112))), zzz1113, zzz1114), zzz1108, ba)
new_mkVBalBranch3MkVBalBranch115(zzz1986, zzz1987, zzz1988, zzz1989, zzz1990, zzz1991, zzz1992, zzz1993, zzz1994, zzz1995, zzz1996, Zero, Succ(zzz19980), bc) → new_mkVBalBranch0(zzz1996, zzz1995, Branch(zzz1986, zzz1987, Pos(Succ(zzz1988)), zzz1989, zzz1990), bc)
new_mkVBalBranch3MkVBalBranch233(zzz473, zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, zzz481, zzz482, bh) → new_mkVBalBranch3MkVBalBranch121(zzz473, zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, zzz481, zzz482, Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat2(Succ(new_primPlusNat3(new_primPlusNat1(zzz475), zzz475)), zzz475)), zzz475))), bh)
new_mkVBalBranch3MkVBalBranch217(zzz473, zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, zzz481, zzz482, Succ(zzz4830), Succ(zzz4840), bh) → new_mkVBalBranch3MkVBalBranch217(zzz473, zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, zzz481, zzz482, zzz4830, zzz4840, bh)
new_mkVBalBranch3MkVBalBranch116(zzz340, zzz341, zzz34200, zzz343, zzz344, zzz510, zzz511, zzz513, zzz514, zzz31, Succ(zzz1200), h) → new_mkVBalBranch0(zzz31, zzz514, Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), h)
new_mkVBalBranch3MkVBalBranch225(zzz498, zzz499, zzz500, zzz501, zzz502, zzz503, zzz504, zzz505, zzz506, zzz507, Zero, Succ(zzz5090), bg) → new_mkVBalBranch0(zzz507, Branch(zzz503, zzz504, Neg(Succ(Zero)), zzz505, zzz506), zzz501, bg)
new_mkVBalBranch0(zzz31, Branch(zzz510, zzz511, Neg(Succ(zzz51200)), zzz513, zzz514), Branch(zzz340, zzz341, zzz342, zzz343, zzz344), h) → new_mkVBalBranch3MkVBalBranch223(zzz340, zzz341, zzz342, zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat3(new_primPlusNat1(zzz51200), zzz51200)), zzz51200))), h)
new_mkVBalBranch3MkVBalBranch223(zzz340, zzz341, Neg(Succ(Zero)), zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, Succ(zzz670), h) → new_mkVBalBranch0(zzz31, Branch(zzz510, zzz511, Neg(Succ(zzz51200)), zzz513, zzz514), zzz343, h)
new_mkVBalBranch3MkVBalBranch215(zzz340, zzz341, Pos(Succ(Succ(zzz342000))), zzz343, zzz344, zzz510, zzz511, Zero, zzz513, zzz514, zzz31, Succ(Succ(zzz6600)), h) → new_mkVBalBranch3MkVBalBranch217(zzz340, zzz341, Succ(zzz342000), zzz343, zzz344, zzz510, zzz511, zzz513, zzz514, zzz31, Succ(zzz6600), zzz342000, h)
new_mkVBalBranch3MkVBalBranch117(zzz340, zzz341, zzz34200, zzz343, zzz344, zzz510, zzz511, zzz513, zzz514, zzz31, Succ(zzz1240), h) → new_mkVBalBranch0(zzz31, zzz514, Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), h)
new_mkVBalBranch3MkVBalBranch120(zzz2050, zzz2051, zzz2052, zzz2053, zzz2054, zzz2055, zzz2056, zzz2057, zzz2058, zzz2059, zzz2060, Succ(zzz20610), Succ(zzz20620), be) → new_mkVBalBranch3MkVBalBranch120(zzz2050, zzz2051, zzz2052, zzz2053, zzz2054, zzz2055, zzz2056, zzz2057, zzz2058, zzz2059, zzz2060, zzz20610, zzz20620, be)
new_mkVBalBranch3MkVBalBranch217(zzz473, zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, zzz481, zzz482, Zero, Zero, bh) → new_mkVBalBranch3MkVBalBranch233(zzz473, zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, zzz481, zzz482, bh)
new_mkVBalBranch3MkVBalBranch216(zzz1105, zzz1106, zzz1107, zzz1108, zzz1109, zzz1110, zzz1111, zzz1112, zzz1113, zzz1114, zzz1115, Succ(zzz11160), Succ(zzz11170), ba) → new_mkVBalBranch3MkVBalBranch216(zzz1105, zzz1106, zzz1107, zzz1108, zzz1109, zzz1110, zzz1111, zzz1112, zzz1113, zzz1114, zzz1115, zzz11160, zzz11170, ba)
new_mkVBalBranch3MkVBalBranch223(zzz340, zzz341, Pos(zzz3420), zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, Succ(zzz670), h) → new_mkVBalBranch0(zzz31, Branch(zzz510, zzz511, Neg(Succ(zzz51200)), zzz513, zzz514), zzz343, h)
new_mkVBalBranch3MkVBalBranch225(zzz498, zzz499, zzz500, zzz501, zzz502, zzz503, zzz504, zzz505, zzz506, zzz507, Succ(zzz5080), Succ(zzz5090), bg) → new_mkVBalBranch3MkVBalBranch225(zzz498, zzz499, zzz500, zzz501, zzz502, zzz503, zzz504, zzz505, zzz506, zzz507, zzz5080, zzz5090, bg)
new_mkVBalBranch3MkVBalBranch19(zzz340, zzz341, zzz34200, zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, Succ(zzz1410), h) → new_mkVBalBranch0(zzz31, zzz514, Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), h)
new_mkVBalBranch3MkVBalBranch224(zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, zzz1125, zzz1126, zzz1127, zzz1128, zzz1129, Zero, Succ(zzz11310), bd) → new_mkVBalBranch3MkVBalBranch227(zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, zzz1125, zzz1126, zzz1127, zzz1128, zzz1129, bd)
new_mkVBalBranch3MkVBalBranch224(zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, zzz1125, zzz1126, zzz1127, zzz1128, zzz1129, Zero, Zero, bd) → new_mkVBalBranch3MkVBalBranch229(zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, zzz1125, zzz1126, zzz1127, zzz1128, zzz1129, bd)
new_mkVBalBranch3MkVBalBranch225(zzz498, zzz499, zzz500, zzz501, zzz502, zzz503, zzz504, zzz505, zzz506, zzz507, Succ(zzz5080), Zero, bg) → new_mkVBalBranch3MkVBalBranch118(zzz498, zzz499, zzz500, zzz501, zzz502, zzz503, zzz504, zzz505, zzz506, zzz507, Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat2(Succ(new_primPlusNat3(new_primPlusNat1(zzz500), zzz500)), zzz500)), zzz500))), bg)
new_mkVBalBranch3MkVBalBranch223(zzz340, zzz341, Neg(Succ(Succ(Succ(zzz3420000)))), zzz343, zzz344, zzz510, zzz511, Succ(zzz512000), zzz513, zzz514, zzz31, Succ(Succ(zzz6700)), h) → new_mkVBalBranch3MkVBalBranch224(zzz340, zzz341, Succ(Succ(zzz3420000)), zzz343, zzz344, zzz510, zzz511, zzz512000, zzz513, zzz514, zzz31, Succ(zzz3420000), Succ(Succ(new_primPlusNat2(zzz6700, zzz512000))), h)
new_mkVBalBranch3MkVBalBranch223(zzz340, zzz341, Neg(Succ(Succ(Zero))), zzz343, zzz344, zzz510, zzz511, Zero, zzz513, zzz514, zzz31, Succ(Succ(zzz6700)), h) → new_mkVBalBranch3MkVBalBranch225(zzz340, zzz341, Succ(Zero), zzz343, zzz344, zzz510, zzz511, zzz513, zzz514, zzz31, Zero, Succ(zzz6700), h)
new_mkVBalBranch3MkVBalBranch115(zzz1986, zzz1987, zzz1988, zzz1989, zzz1990, zzz1991, zzz1992, zzz1993, zzz1994, zzz1995, zzz1996, Succ(zzz19970), Succ(zzz19980), bc) → new_mkVBalBranch3MkVBalBranch115(zzz1986, zzz1987, zzz1988, zzz1989, zzz1990, zzz1991, zzz1992, zzz1993, zzz1994, zzz1995, zzz1996, zzz19970, zzz19980, bc)
new_mkVBalBranch3MkVBalBranch215(zzz340, zzz341, Neg(Zero), zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, Succ(zzz660), h) → new_mkVBalBranch0(zzz31, zzz514, Branch(zzz340, zzz341, Neg(Zero), zzz343, zzz344), h)
new_mkVBalBranch3MkVBalBranch224(zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, zzz1125, zzz1126, zzz1127, zzz1128, zzz1129, Succ(zzz11300), Zero, bd) → new_mkVBalBranch3MkVBalBranch119(zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, zzz1125, zzz1126, zzz1127, zzz1128, zzz1129, Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat2(Succ(new_primPlusNat3(new_primPlusNat1(zzz1121), zzz1121)), zzz1121)), zzz1121))), bd)
new_mkVBalBranch3MkVBalBranch118(zzz498, zzz499, zzz500, zzz501, zzz502, zzz503, zzz504, zzz505, zzz506, zzz507, Succ(zzz8040), bg) → new_mkVBalBranch3MkVBalBranch120(zzz498, zzz499, zzz500, zzz501, zzz502, zzz503, zzz504, Zero, zzz505, zzz506, zzz507, Succ(Zero), Succ(zzz8040), bg)
new_mkVBalBranch3MkVBalBranch222(zzz461, zzz462, zzz463, zzz464, zzz465, zzz466, zzz467, zzz468, zzz469, zzz470, zzz471, bb) → new_mkVBalBranch3MkVBalBranch110(zzz461, zzz462, zzz463, zzz464, zzz465, zzz466, zzz467, zzz468, zzz469, zzz470, zzz471, Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat2(Succ(new_primPlusNat3(new_primPlusNat1(zzz463), zzz463)), zzz463)), zzz463))), bb)
new_mkVBalBranch3MkVBalBranch216(zzz1105, zzz1106, zzz1107, zzz1108, zzz1109, zzz1110, zzz1111, zzz1112, zzz1113, zzz1114, zzz1115, Succ(zzz11160), Zero, ba) → new_mkVBalBranch3MkVBalBranch218(zzz1105, zzz1106, zzz1107, zzz1108, zzz1109, zzz1110, zzz1111, zzz1112, zzz1113, zzz1114, zzz1115, ba)
new_mkVBalBranch3MkVBalBranch216(zzz1105, zzz1106, zzz1107, zzz1108, zzz1109, zzz1110, zzz1111, zzz1112, zzz1113, zzz1114, zzz1115, Zero, Zero, ba) → new_mkVBalBranch3MkVBalBranch222(zzz1105, zzz1106, zzz1107, zzz1108, zzz1109, zzz1110, zzz1111, zzz1112, zzz1113, zzz1114, zzz1115, ba)
new_mkVBalBranch3MkVBalBranch119(zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, zzz1125, zzz1126, zzz1127, zzz1128, zzz1129, Succ(zzz12130), bd) → new_mkVBalBranch3MkVBalBranch120(zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, zzz1125, Succ(zzz1126), zzz1127, zzz1128, zzz1129, Succ(Succ(zzz1126)), Succ(zzz12130), bd)

The TRS R consists of the following rules:

new_primPlusNat1(Zero) → Zero
new_primPlusNat1(Succ(zzz62000)) → Succ(Succ(new_primPlusNat1(zzz62000)))
new_primPlusNat3(zzz90, Succ(zzz910)) → Succ(Succ(new_primPlusNat2(zzz90, zzz910)))
new_primPlusNat3(zzz90, Zero) → Succ(zzz90)
new_primPlusNat2(Succ(zzz900), Succ(zzz9100)) → Succ(Succ(new_primPlusNat2(zzz900, zzz9100)))
new_primPlusNat2(Zero, Succ(zzz9100)) → Succ(zzz9100)
new_primPlusNat2(Zero, Zero) → Zero
new_primPlusNat2(Succ(zzz900), Zero) → Succ(zzz900)

The set Q consists of the following terms:

new_primPlusNat2(Zero, Succ(x0))
new_primPlusNat3(x0, Succ(x1))
new_primPlusNat2(Succ(x0), Succ(x1))
new_primPlusNat3(x0, Zero)
new_primPlusNat1(Zero)
new_primPlusNat2(Zero, Zero)
new_primPlusNat1(Succ(x0))
new_primPlusNat2(Succ(x0), Zero)

We have to consider all minimal (P,Q,R)-chains.
By rewriting [15] the rule new_mkVBalBranch3MkVBalBranch215(zzz340, zzz341, Pos(Succ(Zero)), zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, Succ(zzz660), h) → new_mkVBalBranch3MkVBalBranch18(zzz340, zzz341, zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, Succ(Succ(Succ(Succ(new_primPlusNat3(new_primPlusNat1(Zero), Zero))))), h) at position [10,0,0,0,0] we obtained the following new rules:

new_mkVBalBranch3MkVBalBranch215(zzz340, zzz341, Pos(Succ(Zero)), zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, Succ(zzz660), h) → new_mkVBalBranch3MkVBalBranch18(zzz340, zzz341, zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, Succ(Succ(Succ(Succ(Succ(new_primPlusNat1(Zero)))))), 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
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                    ↳ DependencyGraphProof
                                      ↳ QDP
                                        ↳ Rewriting
                                          ↳ QDP
                                            ↳ Rewriting
                                              ↳ QDP
                                                ↳ Rewriting
                                                  ↳ QDP
                                                    ↳ Rewriting
                                                      ↳ QDP
                                                        ↳ Rewriting
                                                          ↳ QDP
                                                            ↳ Rewriting
                                                              ↳ QDP
                                                                ↳ Rewriting
                                                                  ↳ QDP
                                                                    ↳ Rewriting
                                                                      ↳ QDP
                                                                        ↳ Rewriting
                                                                          ↳ QDP
                                                                            ↳ Rewriting
                                                                              ↳ QDP
                                                                                ↳ Rewriting
                                                                                  ↳ QDP
                                                                                    ↳ Rewriting
                                                                                      ↳ QDP
                                                                                        ↳ Rewriting
                                                                                          ↳ QDP
                                                                                            ↳ Rewriting
                                                                                              ↳ QDP
                                                                                                ↳ Rewriting
                                                                                                  ↳ QDP
                                                                                                    ↳ Rewriting
                                                                                                      ↳ QDP
                                                                                                        ↳ Rewriting
                                                                                                          ↳ QDP
                                                                                                            ↳ UsableRulesProof
                                                                                                              ↳ QDP
                                                                                                                ↳ QReductionProof
                                                                                                                  ↳ QDP
                                                                                                                    ↳ Rewriting
                                                                                                                      ↳ QDP
                                                                                                                        ↳ Rewriting
                                                                                                                          ↳ QDP
                                                                                                                            ↳ DependencyGraphProof
                                                                                                                              ↳ QDP
                                                                                                                                ↳ Rewriting
                                                                                                                                  ↳ QDP
                                                                                                                                    ↳ Rewriting
                                                                                                                                      ↳ QDP
                                                                                                                                        ↳ DependencyGraphProof
                                                                                                                                          ↳ QDP
                                                                                                                                            ↳ Rewriting
                                                                                                                                              ↳ QDP
                                                                                                                                                ↳ Rewriting
                                                                                                                                                  ↳ QDP
                                                                                                                                                    ↳ Rewriting
                                                                                                                                                      ↳ QDP
                                                                                                                                                        ↳ Rewriting
                                                                                                                                                          ↳ QDP
                                                                                                                                                            ↳ Rewriting
                                                                                                                                                              ↳ QDP
                                                                                                                                                                ↳ Rewriting
                                                                                                                                                                  ↳ QDP
                                                                                                                                                                    ↳ Rewriting
                                                                                                                                                                      ↳ QDP
                                                                                                                                                                        ↳ Rewriting
                                                                                                                                                                          ↳ QDP
                                                                                                                                                                            ↳ Rewriting
                                                                                                                                                                              ↳ QDP
                                                                                                                                                                                ↳ Rewriting
                                                                                                                                                                                  ↳ QDP
                                                                                                                                                                                    ↳ Rewriting
                                                                                                                                                                                      ↳ QDP
                                                                                                                                                                                        ↳ Rewriting
                                                                                                                                                                                          ↳ QDP
                                                                                                                                                                                            ↳ UsableRulesProof
                                                                                                                                                                                              ↳ QDP
                                                                                                                                                                                                ↳ QReductionProof
                                                                                                                                                                                                  ↳ QDP
                                                                                                                                                                                                    ↳ Rewriting
                                                                                                                                                                                                      ↳ QDP
                                                                                                                                                                                                        ↳ Rewriting
                                                                                                                                                                                                          ↳ QDP
                                                                                                                                                                                                            ↳ Rewriting
                                                                                                                                                                                                              ↳ QDP
                                                                                                                                                                                                                ↳ Rewriting
                                                                                                                                                                                                                  ↳ QDP
                                                                                                                                                                                                                    ↳ Rewriting
                                                                                                                                                                                                                      ↳ QDP
                                                                                                                                                                                                                        ↳ Rewriting
                                                                                                                                                                                                                          ↳ QDP
                                                                                                                                                                                                                            ↳ Rewriting
                                                                                                                                                                                                                              ↳ QDP
                                                                                                                                                                                                                                ↳ Rewriting
                                                                                                                                                                                                                                  ↳ QDP
                                                                                                                                                                                                                                    ↳ Rewriting
                                                                                                                                                                                                                                      ↳ QDP
                                                                                                                                                                                                                                        ↳ Rewriting
                                                                                                                                                                                                                                          ↳ QDP
                                                                                                                                                                                                                                            ↳ Rewriting
                                                                                                                                                                                                                                              ↳ QDP
                                                                                                                                                                                                                                                ↳ Rewriting
                                                                                                                                                                                                                                                  ↳ QDP
                                                                                                                                                                                                                                                    ↳ Rewriting
                                                                                                                                                                                                                                                      ↳ QDP
                                                                                                                                                                                                                                                        ↳ Rewriting
                                                                                                                                                                                                                                                          ↳ QDP
                                                                                                                                                                                                                                                            ↳ DependencyGraphProof
                                                                                                                                                                                                                                                              ↳ QDP
                                                                                                                                                                                                                                                                ↳ Rewriting
                                                                                                                                                                                                                                                                  ↳ QDP
                                                                                                                                                                                                                                                                    ↳ Rewriting
                                                                                                                                                                                                                                                                      ↳ QDP
                                                                                                                                                                                                                                                                        ↳ Rewriting
                                                                                                                                                                                                                                                                          ↳ QDP
                                                                                                                                                                                                                                                                            ↳ Rewriting
                                                                                                                                                                                                                                                                              ↳ QDP
                                                                                                                                                                                                                                                                                ↳ Rewriting
                                                                                                                                                                                                                                                                                  ↳ QDP
                                                                                                                                                                                                                                                                                    ↳ Rewriting
                                                                                                                                                                                                                                                                                      ↳ QDP
                                                                                                                                                                                                                                                                                        ↳ DependencyGraphProof
                                                                                                                                                                                                                                                                                          ↳ QDP
                                                                                                                                                                                                                                                                                            ↳ Rewriting
                                                                                                                                                                                                                                                                                              ↳ QDP
                                                                                                                                                                                                                                                                                                ↳ DependencyGraphProof
                                                                                                                                                                                                                                                                                                  ↳ QDP
                                                                                                                                                                                                                                                                                                    ↳ Rewriting
                                                                                                                                                                                                                                                                                                      ↳ QDP
                                                                                                                                                                                                                                                                                                        ↳ DependencyGraphProof
                                                                                                                                                                                                                                                                                                          ↳ QDP
                                                                                                                                                                                                                                                                                                            ↳ Rewriting
                                                                                                                                                                                                                                                                                                              ↳ QDP
                                                                                                                                                                                                                                                                                                                ↳ Rewriting
                                                                                                                                                                                                                                                                                                                  ↳ QDP
                                                                                                                                                                                                                                                                                                                    ↳ Rewriting
                                                                                                                                                                                                                                                                                                                      ↳ QDP
                                                                                                                                                                                                                                                                                                                        ↳ Rewriting
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP

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

new_mkVBalBranch3MkVBalBranch215(zzz340, zzz341, Pos(Succ(Zero)), zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, Succ(zzz660), h) → new_mkVBalBranch3MkVBalBranch18(zzz340, zzz341, zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, Succ(Succ(Succ(Succ(Succ(new_primPlusNat1(Zero)))))), h)
new_mkVBalBranch3MkVBalBranch225(zzz498, zzz499, zzz500, zzz501, zzz502, zzz503, zzz504, zzz505, zzz506, zzz507, Zero, Zero, bg) → new_mkVBalBranch3MkVBalBranch230(zzz498, zzz499, zzz500, zzz501, zzz502, zzz503, zzz504, zzz505, zzz506, zzz507, bg)
new_mkVBalBranch3MkVBalBranch18(zzz340, zzz341, zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, Succ(zzz1480), h) → new_mkVBalBranch3MkVBalBranch115(zzz340, zzz341, Zero, zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, Succ(zzz1480), Succ(zzz51200), h)
new_mkVBalBranch0(zzz31, Branch(zzz510, zzz511, Neg(Zero), zzz513, zzz514), Branch(zzz340, zzz341, Pos(Succ(zzz34200)), zzz343, zzz344), h) → new_mkVBalBranch0(zzz31, Branch(zzz510, zzz511, Neg(Zero), zzz513, zzz514), zzz343, h)
new_mkVBalBranch3MkVBalBranch215(zzz340, zzz341, Pos(Succ(Succ(zzz342000))), zzz343, zzz344, zzz510, zzz511, Succ(zzz512000), zzz513, zzz514, zzz31, Succ(Succ(zzz6600)), h) → new_mkVBalBranch3MkVBalBranch216(zzz340, zzz341, Succ(zzz342000), zzz343, zzz344, zzz510, zzz511, zzz512000, zzz513, zzz514, zzz31, Succ(Succ(new_primPlusNat2(zzz6600, zzz512000))), zzz342000, h)
new_mkVBalBranch3MkVBalBranch223(zzz340, zzz341, Neg(Succ(Succ(Succ(zzz3420000)))), zzz343, zzz344, zzz510, zzz511, Zero, zzz513, zzz514, zzz31, Succ(Succ(zzz6700)), h) → new_mkVBalBranch3MkVBalBranch225(zzz340, zzz341, Succ(Succ(zzz3420000)), zzz343, zzz344, zzz510, zzz511, zzz513, zzz514, zzz31, Succ(zzz3420000), Succ(zzz6700), h)
new_mkVBalBranch3MkVBalBranch120(zzz2050, zzz2051, zzz2052, zzz2053, zzz2054, zzz2055, zzz2056, zzz2057, zzz2058, zzz2059, zzz2060, Zero, Succ(zzz20620), be) → new_mkVBalBranch0(zzz2060, zzz2059, Branch(zzz2050, zzz2051, Neg(Succ(zzz2052)), zzz2053, zzz2054), be)
new_mkVBalBranch3MkVBalBranch121(zzz473, zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, zzz481, zzz482, Succ(zzz7390), bh) → new_mkVBalBranch3MkVBalBranch115(zzz473, zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, Zero, zzz480, zzz481, zzz482, Succ(zzz7390), Succ(Zero), bh)
new_mkVBalBranch0(zzz31, Branch(zzz510, zzz511, Pos(Zero), zzz513, zzz514), Branch(zzz340, zzz341, Pos(Succ(zzz34200)), zzz343, zzz344), h) → new_mkVBalBranch0(zzz31, Branch(zzz510, zzz511, Pos(Zero), zzz513, zzz514), zzz343, h)
new_mkVBalBranch0(zzz31, Branch(zzz510, zzz511, Pos(Succ(zzz51200)), zzz513, zzz514), Branch(zzz340, zzz341, zzz342, zzz343, zzz344), h) → new_mkVBalBranch3MkVBalBranch215(zzz340, zzz341, zzz342, zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat3(new_primPlusNat1(zzz51200), zzz51200)), zzz51200))), h)
new_mkVBalBranch3MkVBalBranch215(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, Succ(zzz660), h) → new_mkVBalBranch3MkVBalBranch19(zzz340, zzz341, zzz34200, zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat2(Succ(new_primPlusNat3(new_primPlusNat1(zzz34200), zzz34200)), zzz34200)), zzz34200))), h)
new_mkVBalBranch3MkVBalBranch230(zzz498, zzz499, zzz500, zzz501, zzz502, zzz503, zzz504, zzz505, zzz506, zzz507, bg) → new_mkVBalBranch3MkVBalBranch118(zzz498, zzz499, zzz500, zzz501, zzz502, zzz503, zzz504, zzz505, zzz506, zzz507, Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat2(Succ(new_primPlusNat3(new_primPlusNat1(zzz500), zzz500)), zzz500)), zzz500))), bg)
new_mkVBalBranch3MkVBalBranch223(zzz340, zzz341, Neg(Succ(Succ(Zero))), zzz343, zzz344, zzz510, zzz511, Succ(zzz512000), zzz513, zzz514, zzz31, Succ(Succ(zzz6700)), h) → new_mkVBalBranch3MkVBalBranch224(zzz340, zzz341, Succ(Zero), zzz343, zzz344, zzz510, zzz511, zzz512000, zzz513, zzz514, zzz31, Zero, Succ(Succ(new_primPlusNat2(zzz6700, zzz512000))), h)
new_mkVBalBranch0(zzz31, Branch(zzz510, zzz511, Pos(Zero), zzz513, zzz514), Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), h) → new_mkVBalBranch3MkVBalBranch116(zzz340, zzz341, zzz34200, zzz343, zzz344, zzz510, zzz511, zzz513, zzz514, zzz31, Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat2(Succ(new_primPlusNat3(new_primPlusNat1(zzz34200), zzz34200)), zzz34200)), zzz34200))), h)
new_mkVBalBranch0(zzz31, Branch(zzz510, zzz511, Neg(Zero), zzz513, zzz514), Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), h) → new_mkVBalBranch3MkVBalBranch117(zzz340, zzz341, zzz34200, zzz343, zzz344, zzz510, zzz511, zzz513, zzz514, zzz31, Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat2(Succ(new_primPlusNat3(new_primPlusNat1(zzz34200), zzz34200)), zzz34200)), zzz34200))), h)
new_mkVBalBranch3MkVBalBranch224(zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, zzz1125, zzz1126, zzz1127, zzz1128, zzz1129, Succ(zzz11300), Succ(zzz11310), bd) → new_mkVBalBranch3MkVBalBranch224(zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, zzz1125, zzz1126, zzz1127, zzz1128, zzz1129, zzz11300, zzz11310, bd)
new_mkVBalBranch3MkVBalBranch217(zzz473, zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, zzz481, zzz482, Succ(zzz4830), Zero, bh) → new_mkVBalBranch3MkVBalBranch121(zzz473, zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, zzz481, zzz482, Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat2(Succ(new_primPlusNat3(new_primPlusNat1(zzz475), zzz475)), zzz475)), zzz475))), bh)
new_mkVBalBranch3MkVBalBranch229(zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, zzz1125, zzz1126, zzz1127, zzz1128, zzz1129, bd) → new_mkVBalBranch3MkVBalBranch119(zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, zzz1125, zzz1126, zzz1127, zzz1128, zzz1129, Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat2(Succ(new_primPlusNat3(new_primPlusNat1(zzz1121), zzz1121)), zzz1121)), zzz1121))), bd)
new_mkVBalBranch3MkVBalBranch217(zzz473, zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, zzz481, zzz482, Zero, Succ(zzz4840), bh) → new_mkVBalBranch0(zzz482, Branch(zzz478, zzz479, Pos(Succ(Zero)), zzz480, zzz481), zzz476, bh)
new_mkVBalBranch3MkVBalBranch218(zzz461, zzz462, zzz463, zzz464, zzz465, zzz466, zzz467, zzz468, zzz469, zzz470, zzz471, bb) → new_mkVBalBranch3MkVBalBranch110(zzz461, zzz462, zzz463, zzz464, zzz465, zzz466, zzz467, zzz468, zzz469, zzz470, zzz471, Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat2(Succ(new_primPlusNat3(new_primPlusNat1(zzz463), zzz463)), zzz463)), zzz463))), bb)
new_mkVBalBranch3MkVBalBranch110(zzz461, zzz462, zzz463, zzz464, zzz465, zzz466, zzz467, zzz468, zzz469, zzz470, zzz471, Succ(zzz5800), bb) → new_mkVBalBranch3MkVBalBranch115(zzz461, zzz462, zzz463, zzz464, zzz465, zzz466, zzz467, Succ(zzz468), zzz469, zzz470, zzz471, Succ(zzz5800), Succ(Succ(zzz468)), bb)
new_mkVBalBranch3MkVBalBranch227(zzz486, zzz487, zzz488, zzz489, zzz490, zzz491, zzz492, zzz493, zzz494, zzz495, zzz496, bf) → new_mkVBalBranch0(zzz496, Branch(zzz491, zzz492, Neg(Succ(Succ(zzz493))), zzz494, zzz495), zzz489, bf)
new_mkVBalBranch3MkVBalBranch215(zzz340, zzz341, Pos(Zero), zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, Succ(zzz660), h) → new_mkVBalBranch0(zzz31, zzz514, Branch(zzz340, zzz341, Pos(Zero), zzz343, zzz344), h)
new_mkVBalBranch3MkVBalBranch223(zzz340, zzz341, Neg(Zero), zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, Succ(zzz670), h) → new_mkVBalBranch0(zzz31, Branch(zzz510, zzz511, Neg(Succ(zzz51200)), zzz513, zzz514), zzz343, h)
new_mkVBalBranch3MkVBalBranch216(zzz1105, zzz1106, zzz1107, zzz1108, zzz1109, zzz1110, zzz1111, zzz1112, zzz1113, zzz1114, zzz1115, Zero, Succ(zzz11170), ba) → new_mkVBalBranch0(zzz1115, Branch(zzz1110, zzz1111, Pos(Succ(Succ(zzz1112))), zzz1113, zzz1114), zzz1108, ba)
new_mkVBalBranch3MkVBalBranch115(zzz1986, zzz1987, zzz1988, zzz1989, zzz1990, zzz1991, zzz1992, zzz1993, zzz1994, zzz1995, zzz1996, Zero, Succ(zzz19980), bc) → new_mkVBalBranch0(zzz1996, zzz1995, Branch(zzz1986, zzz1987, Pos(Succ(zzz1988)), zzz1989, zzz1990), bc)
new_mkVBalBranch3MkVBalBranch233(zzz473, zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, zzz481, zzz482, bh) → new_mkVBalBranch3MkVBalBranch121(zzz473, zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, zzz481, zzz482, Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat2(Succ(new_primPlusNat3(new_primPlusNat1(zzz475), zzz475)), zzz475)), zzz475))), bh)
new_mkVBalBranch3MkVBalBranch217(zzz473, zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, zzz481, zzz482, Succ(zzz4830), Succ(zzz4840), bh) → new_mkVBalBranch3MkVBalBranch217(zzz473, zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, zzz481, zzz482, zzz4830, zzz4840, bh)
new_mkVBalBranch3MkVBalBranch116(zzz340, zzz341, zzz34200, zzz343, zzz344, zzz510, zzz511, zzz513, zzz514, zzz31, Succ(zzz1200), h) → new_mkVBalBranch0(zzz31, zzz514, Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), h)
new_mkVBalBranch3MkVBalBranch225(zzz498, zzz499, zzz500, zzz501, zzz502, zzz503, zzz504, zzz505, zzz506, zzz507, Zero, Succ(zzz5090), bg) → new_mkVBalBranch0(zzz507, Branch(zzz503, zzz504, Neg(Succ(Zero)), zzz505, zzz506), zzz501, bg)
new_mkVBalBranch0(zzz31, Branch(zzz510, zzz511, Neg(Succ(zzz51200)), zzz513, zzz514), Branch(zzz340, zzz341, zzz342, zzz343, zzz344), h) → new_mkVBalBranch3MkVBalBranch223(zzz340, zzz341, zzz342, zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat3(new_primPlusNat1(zzz51200), zzz51200)), zzz51200))), h)
new_mkVBalBranch3MkVBalBranch223(zzz340, zzz341, Neg(Succ(Zero)), zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, Succ(zzz670), h) → new_mkVBalBranch0(zzz31, Branch(zzz510, zzz511, Neg(Succ(zzz51200)), zzz513, zzz514), zzz343, h)
new_mkVBalBranch3MkVBalBranch215(zzz340, zzz341, Pos(Succ(Succ(zzz342000))), zzz343, zzz344, zzz510, zzz511, Zero, zzz513, zzz514, zzz31, Succ(Succ(zzz6600)), h) → new_mkVBalBranch3MkVBalBranch217(zzz340, zzz341, Succ(zzz342000), zzz343, zzz344, zzz510, zzz511, zzz513, zzz514, zzz31, Succ(zzz6600), zzz342000, h)
new_mkVBalBranch3MkVBalBranch117(zzz340, zzz341, zzz34200, zzz343, zzz344, zzz510, zzz511, zzz513, zzz514, zzz31, Succ(zzz1240), h) → new_mkVBalBranch0(zzz31, zzz514, Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), h)
new_mkVBalBranch3MkVBalBranch217(zzz473, zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, zzz481, zzz482, Zero, Zero, bh) → new_mkVBalBranch3MkVBalBranch233(zzz473, zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, zzz481, zzz482, bh)
new_mkVBalBranch3MkVBalBranch120(zzz2050, zzz2051, zzz2052, zzz2053, zzz2054, zzz2055, zzz2056, zzz2057, zzz2058, zzz2059, zzz2060, Succ(zzz20610), Succ(zzz20620), be) → new_mkVBalBranch3MkVBalBranch120(zzz2050, zzz2051, zzz2052, zzz2053, zzz2054, zzz2055, zzz2056, zzz2057, zzz2058, zzz2059, zzz2060, zzz20610, zzz20620, be)
new_mkVBalBranch3MkVBalBranch223(zzz340, zzz341, Pos(zzz3420), zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, Succ(zzz670), h) → new_mkVBalBranch0(zzz31, Branch(zzz510, zzz511, Neg(Succ(zzz51200)), zzz513, zzz514), zzz343, h)
new_mkVBalBranch3MkVBalBranch216(zzz1105, zzz1106, zzz1107, zzz1108, zzz1109, zzz1110, zzz1111, zzz1112, zzz1113, zzz1114, zzz1115, Succ(zzz11160), Succ(zzz11170), ba) → new_mkVBalBranch3MkVBalBranch216(zzz1105, zzz1106, zzz1107, zzz1108, zzz1109, zzz1110, zzz1111, zzz1112, zzz1113, zzz1114, zzz1115, zzz11160, zzz11170, ba)
new_mkVBalBranch3MkVBalBranch225(zzz498, zzz499, zzz500, zzz501, zzz502, zzz503, zzz504, zzz505, zzz506, zzz507, Succ(zzz5080), Succ(zzz5090), bg) → new_mkVBalBranch3MkVBalBranch225(zzz498, zzz499, zzz500, zzz501, zzz502, zzz503, zzz504, zzz505, zzz506, zzz507, zzz5080, zzz5090, bg)
new_mkVBalBranch3MkVBalBranch19(zzz340, zzz341, zzz34200, zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, Succ(zzz1410), h) → new_mkVBalBranch0(zzz31, zzz514, Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), h)
new_mkVBalBranch3MkVBalBranch224(zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, zzz1125, zzz1126, zzz1127, zzz1128, zzz1129, Zero, Zero, bd) → new_mkVBalBranch3MkVBalBranch229(zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, zzz1125, zzz1126, zzz1127, zzz1128, zzz1129, bd)
new_mkVBalBranch3MkVBalBranch224(zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, zzz1125, zzz1126, zzz1127, zzz1128, zzz1129, Zero, Succ(zzz11310), bd) → new_mkVBalBranch3MkVBalBranch227(zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, zzz1125, zzz1126, zzz1127, zzz1128, zzz1129, bd)
new_mkVBalBranch3MkVBalBranch223(zzz340, zzz341, Neg(Succ(Succ(Zero))), zzz343, zzz344, zzz510, zzz511, Zero, zzz513, zzz514, zzz31, Succ(Succ(zzz6700)), h) → new_mkVBalBranch3MkVBalBranch225(zzz340, zzz341, Succ(Zero), zzz343, zzz344, zzz510, zzz511, zzz513, zzz514, zzz31, Zero, Succ(zzz6700), h)
new_mkVBalBranch3MkVBalBranch223(zzz340, zzz341, Neg(Succ(Succ(Succ(zzz3420000)))), zzz343, zzz344, zzz510, zzz511, Succ(zzz512000), zzz513, zzz514, zzz31, Succ(Succ(zzz6700)), h) → new_mkVBalBranch3MkVBalBranch224(zzz340, zzz341, Succ(Succ(zzz3420000)), zzz343, zzz344, zzz510, zzz511, zzz512000, zzz513, zzz514, zzz31, Succ(zzz3420000), Succ(Succ(new_primPlusNat2(zzz6700, zzz512000))), h)
new_mkVBalBranch3MkVBalBranch225(zzz498, zzz499, zzz500, zzz501, zzz502, zzz503, zzz504, zzz505, zzz506, zzz507, Succ(zzz5080), Zero, bg) → new_mkVBalBranch3MkVBalBranch118(zzz498, zzz499, zzz500, zzz501, zzz502, zzz503, zzz504, zzz505, zzz506, zzz507, Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat2(Succ(new_primPlusNat3(new_primPlusNat1(zzz500), zzz500)), zzz500)), zzz500))), bg)
new_mkVBalBranch3MkVBalBranch115(zzz1986, zzz1987, zzz1988, zzz1989, zzz1990, zzz1991, zzz1992, zzz1993, zzz1994, zzz1995, zzz1996, Succ(zzz19970), Succ(zzz19980), bc) → new_mkVBalBranch3MkVBalBranch115(zzz1986, zzz1987, zzz1988, zzz1989, zzz1990, zzz1991, zzz1992, zzz1993, zzz1994, zzz1995, zzz1996, zzz19970, zzz19980, bc)
new_mkVBalBranch3MkVBalBranch215(zzz340, zzz341, Neg(Zero), zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, Succ(zzz660), h) → new_mkVBalBranch0(zzz31, zzz514, Branch(zzz340, zzz341, Neg(Zero), zzz343, zzz344), h)
new_mkVBalBranch3MkVBalBranch224(zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, zzz1125, zzz1126, zzz1127, zzz1128, zzz1129, Succ(zzz11300), Zero, bd) → new_mkVBalBranch3MkVBalBranch119(zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, zzz1125, zzz1126, zzz1127, zzz1128, zzz1129, Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat2(Succ(new_primPlusNat3(new_primPlusNat1(zzz1121), zzz1121)), zzz1121)), zzz1121))), bd)
new_mkVBalBranch3MkVBalBranch222(zzz461, zzz462, zzz463, zzz464, zzz465, zzz466, zzz467, zzz468, zzz469, zzz470, zzz471, bb) → new_mkVBalBranch3MkVBalBranch110(zzz461, zzz462, zzz463, zzz464, zzz465, zzz466, zzz467, zzz468, zzz469, zzz470, zzz471, Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat2(Succ(new_primPlusNat3(new_primPlusNat1(zzz463), zzz463)), zzz463)), zzz463))), bb)
new_mkVBalBranch3MkVBalBranch118(zzz498, zzz499, zzz500, zzz501, zzz502, zzz503, zzz504, zzz505, zzz506, zzz507, Succ(zzz8040), bg) → new_mkVBalBranch3MkVBalBranch120(zzz498, zzz499, zzz500, zzz501, zzz502, zzz503, zzz504, Zero, zzz505, zzz506, zzz507, Succ(Zero), Succ(zzz8040), bg)
new_mkVBalBranch3MkVBalBranch216(zzz1105, zzz1106, zzz1107, zzz1108, zzz1109, zzz1110, zzz1111, zzz1112, zzz1113, zzz1114, zzz1115, Succ(zzz11160), Zero, ba) → new_mkVBalBranch3MkVBalBranch218(zzz1105, zzz1106, zzz1107, zzz1108, zzz1109, zzz1110, zzz1111, zzz1112, zzz1113, zzz1114, zzz1115, ba)
new_mkVBalBranch3MkVBalBranch216(zzz1105, zzz1106, zzz1107, zzz1108, zzz1109, zzz1110, zzz1111, zzz1112, zzz1113, zzz1114, zzz1115, Zero, Zero, ba) → new_mkVBalBranch3MkVBalBranch222(zzz1105, zzz1106, zzz1107, zzz1108, zzz1109, zzz1110, zzz1111, zzz1112, zzz1113, zzz1114, zzz1115, ba)
new_mkVBalBranch3MkVBalBranch119(zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, zzz1125, zzz1126, zzz1127, zzz1128, zzz1129, Succ(zzz12130), bd) → new_mkVBalBranch3MkVBalBranch120(zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, zzz1125, Succ(zzz1126), zzz1127, zzz1128, zzz1129, Succ(Succ(zzz1126)), Succ(zzz12130), bd)

The TRS R consists of the following rules:

new_primPlusNat1(Zero) → Zero
new_primPlusNat1(Succ(zzz62000)) → Succ(Succ(new_primPlusNat1(zzz62000)))
new_primPlusNat3(zzz90, Succ(zzz910)) → Succ(Succ(new_primPlusNat2(zzz90, zzz910)))
new_primPlusNat3(zzz90, Zero) → Succ(zzz90)
new_primPlusNat2(Succ(zzz900), Succ(zzz9100)) → Succ(Succ(new_primPlusNat2(zzz900, zzz9100)))
new_primPlusNat2(Zero, Succ(zzz9100)) → Succ(zzz9100)
new_primPlusNat2(Zero, Zero) → Zero
new_primPlusNat2(Succ(zzz900), Zero) → Succ(zzz900)

The set Q consists of the following terms:

new_primPlusNat2(Zero, Succ(x0))
new_primPlusNat3(x0, Succ(x1))
new_primPlusNat2(Succ(x0), Succ(x1))
new_primPlusNat3(x0, Zero)
new_primPlusNat1(Zero)
new_primPlusNat2(Zero, Zero)
new_primPlusNat1(Succ(x0))
new_primPlusNat2(Succ(x0), Zero)

We have to consider all minimal (P,Q,R)-chains.
By rewriting [15] the rule new_mkVBalBranch3MkVBalBranch215(zzz340, zzz341, Pos(Succ(Zero)), zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, Succ(zzz660), h) → new_mkVBalBranch3MkVBalBranch18(zzz340, zzz341, zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, Succ(Succ(Succ(Succ(Succ(new_primPlusNat1(Zero)))))), h) at position [10,0,0,0,0,0] we obtained the following new rules:

new_mkVBalBranch3MkVBalBranch215(zzz340, zzz341, Pos(Succ(Zero)), zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, Succ(zzz660), h) → new_mkVBalBranch3MkVBalBranch18(zzz340, zzz341, zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, Succ(Succ(Succ(Succ(Succ(Zero))))), 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
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                    ↳ DependencyGraphProof
                                      ↳ QDP
                                        ↳ Rewriting
                                          ↳ QDP
                                            ↳ Rewriting
                                              ↳ QDP
                                                ↳ Rewriting
                                                  ↳ QDP
                                                    ↳ Rewriting
                                                      ↳ QDP
                                                        ↳ Rewriting
                                                          ↳ QDP
                                                            ↳ Rewriting
                                                              ↳ QDP
                                                                ↳ Rewriting
                                                                  ↳ QDP
                                                                    ↳ Rewriting
                                                                      ↳ QDP
                                                                        ↳ Rewriting
                                                                          ↳ QDP
                                                                            ↳ Rewriting
                                                                              ↳ QDP
                                                                                ↳ Rewriting
                                                                                  ↳ QDP
                                                                                    ↳ Rewriting
                                                                                      ↳ QDP
                                                                                        ↳ Rewriting
                                                                                          ↳ QDP
                                                                                            ↳ Rewriting
                                                                                              ↳ QDP
                                                                                                ↳ Rewriting
                                                                                                  ↳ QDP
                                                                                                    ↳ Rewriting
                                                                                                      ↳ QDP
                                                                                                        ↳ Rewriting
                                                                                                          ↳ QDP
                                                                                                            ↳ UsableRulesProof
                                                                                                              ↳ QDP
                                                                                                                ↳ QReductionProof
                                                                                                                  ↳ QDP
                                                                                                                    ↳ Rewriting
                                                                                                                      ↳ QDP
                                                                                                                        ↳ Rewriting
                                                                                                                          ↳ QDP
                                                                                                                            ↳ DependencyGraphProof
                                                                                                                              ↳ QDP
                                                                                                                                ↳ Rewriting
                                                                                                                                  ↳ QDP
                                                                                                                                    ↳ Rewriting
                                                                                                                                      ↳ QDP
                                                                                                                                        ↳ DependencyGraphProof
                                                                                                                                          ↳ QDP
                                                                                                                                            ↳ Rewriting
                                                                                                                                              ↳ QDP
                                                                                                                                                ↳ Rewriting
                                                                                                                                                  ↳ QDP
                                                                                                                                                    ↳ Rewriting
                                                                                                                                                      ↳ QDP
                                                                                                                                                        ↳ Rewriting
                                                                                                                                                          ↳ QDP
                                                                                                                                                            ↳ Rewriting
                                                                                                                                                              ↳ QDP
                                                                                                                                                                ↳ Rewriting
                                                                                                                                                                  ↳ QDP
                                                                                                                                                                    ↳ Rewriting
                                                                                                                                                                      ↳ QDP
                                                                                                                                                                        ↳ Rewriting
                                                                                                                                                                          ↳ QDP
                                                                                                                                                                            ↳ Rewriting
                                                                                                                                                                              ↳ QDP
                                                                                                                                                                                ↳ Rewriting
                                                                                                                                                                                  ↳ QDP
                                                                                                                                                                                    ↳ Rewriting
                                                                                                                                                                                      ↳ QDP
                                                                                                                                                                                        ↳ Rewriting
                                                                                                                                                                                          ↳ QDP
                                                                                                                                                                                            ↳ UsableRulesProof
                                                                                                                                                                                              ↳ QDP
                                                                                                                                                                                                ↳ QReductionProof
                                                                                                                                                                                                  ↳ QDP
                                                                                                                                                                                                    ↳ Rewriting
                                                                                                                                                                                                      ↳ QDP
                                                                                                                                                                                                        ↳ Rewriting
                                                                                                                                                                                                          ↳ QDP
                                                                                                                                                                                                            ↳ Rewriting
                                                                                                                                                                                                              ↳ QDP
                                                                                                                                                                                                                ↳ Rewriting
                                                                                                                                                                                                                  ↳ QDP
                                                                                                                                                                                                                    ↳ Rewriting
                                                                                                                                                                                                                      ↳ QDP
                                                                                                                                                                                                                        ↳ Rewriting
                                                                                                                                                                                                                          ↳ QDP
                                                                                                                                                                                                                            ↳ Rewriting
                                                                                                                                                                                                                              ↳ QDP
                                                                                                                                                                                                                                ↳ Rewriting
                                                                                                                                                                                                                                  ↳ QDP
                                                                                                                                                                                                                                    ↳ Rewriting
                                                                                                                                                                                                                                      ↳ QDP
                                                                                                                                                                                                                                        ↳ Rewriting
                                                                                                                                                                                                                                          ↳ QDP
                                                                                                                                                                                                                                            ↳ Rewriting
                                                                                                                                                                                                                                              ↳ QDP
                                                                                                                                                                                                                                                ↳ Rewriting
                                                                                                                                                                                                                                                  ↳ QDP
                                                                                                                                                                                                                                                    ↳ Rewriting
                                                                                                                                                                                                                                                      ↳ QDP
                                                                                                                                                                                                                                                        ↳ Rewriting
                                                                                                                                                                                                                                                          ↳ QDP
                                                                                                                                                                                                                                                            ↳ DependencyGraphProof
                                                                                                                                                                                                                                                              ↳ QDP
                                                                                                                                                                                                                                                                ↳ Rewriting
                                                                                                                                                                                                                                                                  ↳ QDP
                                                                                                                                                                                                                                                                    ↳ Rewriting
                                                                                                                                                                                                                                                                      ↳ QDP
                                                                                                                                                                                                                                                                        ↳ Rewriting
                                                                                                                                                                                                                                                                          ↳ QDP
                                                                                                                                                                                                                                                                            ↳ Rewriting
                                                                                                                                                                                                                                                                              ↳ QDP
                                                                                                                                                                                                                                                                                ↳ Rewriting
                                                                                                                                                                                                                                                                                  ↳ QDP
                                                                                                                                                                                                                                                                                    ↳ Rewriting
                                                                                                                                                                                                                                                                                      ↳ QDP
                                                                                                                                                                                                                                                                                        ↳ DependencyGraphProof
                                                                                                                                                                                                                                                                                          ↳ QDP
                                                                                                                                                                                                                                                                                            ↳ Rewriting
                                                                                                                                                                                                                                                                                              ↳ QDP
                                                                                                                                                                                                                                                                                                ↳ DependencyGraphProof
                                                                                                                                                                                                                                                                                                  ↳ QDP
                                                                                                                                                                                                                                                                                                    ↳ Rewriting
                                                                                                                                                                                                                                                                                                      ↳ QDP
                                                                                                                                                                                                                                                                                                        ↳ DependencyGraphProof
                                                                                                                                                                                                                                                                                                          ↳ QDP
                                                                                                                                                                                                                                                                                                            ↳ Rewriting
                                                                                                                                                                                                                                                                                                              ↳ QDP
                                                                                                                                                                                                                                                                                                                ↳ Rewriting
                                                                                                                                                                                                                                                                                                                  ↳ QDP
                                                                                                                                                                                                                                                                                                                    ↳ Rewriting
                                                                                                                                                                                                                                                                                                                      ↳ QDP
                                                                                                                                                                                                                                                                                                                        ↳ Rewriting
                                                                                                                                                                                                                                                                                                                          ↳ QDP
                                                                                                                                                                                                                                                                                                                            ↳ Instantiation
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP

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

new_mkVBalBranch3MkVBalBranch225(zzz498, zzz499, zzz500, zzz501, zzz502, zzz503, zzz504, zzz505, zzz506, zzz507, Zero, Zero, bg) → new_mkVBalBranch3MkVBalBranch230(zzz498, zzz499, zzz500, zzz501, zzz502, zzz503, zzz504, zzz505, zzz506, zzz507, bg)
new_mkVBalBranch3MkVBalBranch18(zzz340, zzz341, zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, Succ(zzz1480), h) → new_mkVBalBranch3MkVBalBranch115(zzz340, zzz341, Zero, zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, Succ(zzz1480), Succ(zzz51200), h)
new_mkVBalBranch3MkVBalBranch215(zzz340, zzz341, Pos(Succ(Succ(zzz342000))), zzz343, zzz344, zzz510, zzz511, Succ(zzz512000), zzz513, zzz514, zzz31, Succ(Succ(zzz6600)), h) → new_mkVBalBranch3MkVBalBranch216(zzz340, zzz341, Succ(zzz342000), zzz343, zzz344, zzz510, zzz511, zzz512000, zzz513, zzz514, zzz31, Succ(Succ(new_primPlusNat2(zzz6600, zzz512000))), zzz342000, h)
new_mkVBalBranch0(zzz31, Branch(zzz510, zzz511, Neg(Zero), zzz513, zzz514), Branch(zzz340, zzz341, Pos(Succ(zzz34200)), zzz343, zzz344), h) → new_mkVBalBranch0(zzz31, Branch(zzz510, zzz511, Neg(Zero), zzz513, zzz514), zzz343, h)
new_mkVBalBranch3MkVBalBranch223(zzz340, zzz341, Neg(Succ(Succ(Succ(zzz3420000)))), zzz343, zzz344, zzz510, zzz511, Zero, zzz513, zzz514, zzz31, Succ(Succ(zzz6700)), h) → new_mkVBalBranch3MkVBalBranch225(zzz340, zzz341, Succ(Succ(zzz3420000)), zzz343, zzz344, zzz510, zzz511, zzz513, zzz514, zzz31, Succ(zzz3420000), Succ(zzz6700), h)
new_mkVBalBranch3MkVBalBranch120(zzz2050, zzz2051, zzz2052, zzz2053, zzz2054, zzz2055, zzz2056, zzz2057, zzz2058, zzz2059, zzz2060, Zero, Succ(zzz20620), be) → new_mkVBalBranch0(zzz2060, zzz2059, Branch(zzz2050, zzz2051, Neg(Succ(zzz2052)), zzz2053, zzz2054), be)
new_mkVBalBranch0(zzz31, Branch(zzz510, zzz511, Pos(Zero), zzz513, zzz514), Branch(zzz340, zzz341, Pos(Succ(zzz34200)), zzz343, zzz344), h) → new_mkVBalBranch0(zzz31, Branch(zzz510, zzz511, Pos(Zero), zzz513, zzz514), zzz343, h)
new_mkVBalBranch3MkVBalBranch121(zzz473, zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, zzz481, zzz482, Succ(zzz7390), bh) → new_mkVBalBranch3MkVBalBranch115(zzz473, zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, Zero, zzz480, zzz481, zzz482, Succ(zzz7390), Succ(Zero), bh)
new_mkVBalBranch0(zzz31, Branch(zzz510, zzz511, Pos(Succ(zzz51200)), zzz513, zzz514), Branch(zzz340, zzz341, zzz342, zzz343, zzz344), h) → new_mkVBalBranch3MkVBalBranch215(zzz340, zzz341, zzz342, zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat3(new_primPlusNat1(zzz51200), zzz51200)), zzz51200))), h)
new_mkVBalBranch3MkVBalBranch215(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, Succ(zzz660), h) → new_mkVBalBranch3MkVBalBranch19(zzz340, zzz341, zzz34200, zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat2(Succ(new_primPlusNat3(new_primPlusNat1(zzz34200), zzz34200)), zzz34200)), zzz34200))), h)
new_mkVBalBranch3MkVBalBranch223(zzz340, zzz341, Neg(Succ(Succ(Zero))), zzz343, zzz344, zzz510, zzz511, Succ(zzz512000), zzz513, zzz514, zzz31, Succ(Succ(zzz6700)), h) → new_mkVBalBranch3MkVBalBranch224(zzz340, zzz341, Succ(Zero), zzz343, zzz344, zzz510, zzz511, zzz512000, zzz513, zzz514, zzz31, Zero, Succ(Succ(new_primPlusNat2(zzz6700, zzz512000))), h)
new_mkVBalBranch3MkVBalBranch230(zzz498, zzz499, zzz500, zzz501, zzz502, zzz503, zzz504, zzz505, zzz506, zzz507, bg) → new_mkVBalBranch3MkVBalBranch118(zzz498, zzz499, zzz500, zzz501, zzz502, zzz503, zzz504, zzz505, zzz506, zzz507, Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat2(Succ(new_primPlusNat3(new_primPlusNat1(zzz500), zzz500)), zzz500)), zzz500))), bg)
new_mkVBalBranch0(zzz31, Branch(zzz510, zzz511, Pos(Zero), zzz513, zzz514), Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), h) → new_mkVBalBranch3MkVBalBranch116(zzz340, zzz341, zzz34200, zzz343, zzz344, zzz510, zzz511, zzz513, zzz514, zzz31, Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat2(Succ(new_primPlusNat3(new_primPlusNat1(zzz34200), zzz34200)), zzz34200)), zzz34200))), h)
new_mkVBalBranch0(zzz31, Branch(zzz510, zzz511, Neg(Zero), zzz513, zzz514), Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), h) → new_mkVBalBranch3MkVBalBranch117(zzz340, zzz341, zzz34200, zzz343, zzz344, zzz510, zzz511, zzz513, zzz514, zzz31, Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat2(Succ(new_primPlusNat3(new_primPlusNat1(zzz34200), zzz34200)), zzz34200)), zzz34200))), h)
new_mkVBalBranch3MkVBalBranch224(zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, zzz1125, zzz1126, zzz1127, zzz1128, zzz1129, Succ(zzz11300), Succ(zzz11310), bd) → new_mkVBalBranch3MkVBalBranch224(zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, zzz1125, zzz1126, zzz1127, zzz1128, zzz1129, zzz11300, zzz11310, bd)
new_mkVBalBranch3MkVBalBranch229(zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, zzz1125, zzz1126, zzz1127, zzz1128, zzz1129, bd) → new_mkVBalBranch3MkVBalBranch119(zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, zzz1125, zzz1126, zzz1127, zzz1128, zzz1129, Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat2(Succ(new_primPlusNat3(new_primPlusNat1(zzz1121), zzz1121)), zzz1121)), zzz1121))), bd)
new_mkVBalBranch3MkVBalBranch217(zzz473, zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, zzz481, zzz482, Succ(zzz4830), Zero, bh) → new_mkVBalBranch3MkVBalBranch121(zzz473, zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, zzz481, zzz482, Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat2(Succ(new_primPlusNat3(new_primPlusNat1(zzz475), zzz475)), zzz475)), zzz475))), bh)
new_mkVBalBranch3MkVBalBranch217(zzz473, zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, zzz481, zzz482, Zero, Succ(zzz4840), bh) → new_mkVBalBranch0(zzz482, Branch(zzz478, zzz479, Pos(Succ(Zero)), zzz480, zzz481), zzz476, bh)
new_mkVBalBranch3MkVBalBranch215(zzz340, zzz341, Pos(Succ(Zero)), zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, Succ(zzz660), h) → new_mkVBalBranch3MkVBalBranch18(zzz340, zzz341, zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, Succ(Succ(Succ(Succ(Succ(Zero))))), h)
new_mkVBalBranch3MkVBalBranch218(zzz461, zzz462, zzz463, zzz464, zzz465, zzz466, zzz467, zzz468, zzz469, zzz470, zzz471, bb) → new_mkVBalBranch3MkVBalBranch110(zzz461, zzz462, zzz463, zzz464, zzz465, zzz466, zzz467, zzz468, zzz469, zzz470, zzz471, Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat2(Succ(new_primPlusNat3(new_primPlusNat1(zzz463), zzz463)), zzz463)), zzz463))), bb)
new_mkVBalBranch3MkVBalBranch110(zzz461, zzz462, zzz463, zzz464, zzz465, zzz466, zzz467, zzz468, zzz469, zzz470, zzz471, Succ(zzz5800), bb) → new_mkVBalBranch3MkVBalBranch115(zzz461, zzz462, zzz463, zzz464, zzz465, zzz466, zzz467, Succ(zzz468), zzz469, zzz470, zzz471, Succ(zzz5800), Succ(Succ(zzz468)), bb)
new_mkVBalBranch3MkVBalBranch227(zzz486, zzz487, zzz488, zzz489, zzz490, zzz491, zzz492, zzz493, zzz494, zzz495, zzz496, bf) → new_mkVBalBranch0(zzz496, Branch(zzz491, zzz492, Neg(Succ(Succ(zzz493))), zzz494, zzz495), zzz489, bf)
new_mkVBalBranch3MkVBalBranch215(zzz340, zzz341, Pos(Zero), zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, Succ(zzz660), h) → new_mkVBalBranch0(zzz31, zzz514, Branch(zzz340, zzz341, Pos(Zero), zzz343, zzz344), h)
new_mkVBalBranch3MkVBalBranch223(zzz340, zzz341, Neg(Zero), zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, Succ(zzz670), h) → new_mkVBalBranch0(zzz31, Branch(zzz510, zzz511, Neg(Succ(zzz51200)), zzz513, zzz514), zzz343, h)
new_mkVBalBranch3MkVBalBranch216(zzz1105, zzz1106, zzz1107, zzz1108, zzz1109, zzz1110, zzz1111, zzz1112, zzz1113, zzz1114, zzz1115, Zero, Succ(zzz11170), ba) → new_mkVBalBranch0(zzz1115, Branch(zzz1110, zzz1111, Pos(Succ(Succ(zzz1112))), zzz1113, zzz1114), zzz1108, ba)
new_mkVBalBranch3MkVBalBranch115(zzz1986, zzz1987, zzz1988, zzz1989, zzz1990, zzz1991, zzz1992, zzz1993, zzz1994, zzz1995, zzz1996, Zero, Succ(zzz19980), bc) → new_mkVBalBranch0(zzz1996, zzz1995, Branch(zzz1986, zzz1987, Pos(Succ(zzz1988)), zzz1989, zzz1990), bc)
new_mkVBalBranch3MkVBalBranch233(zzz473, zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, zzz481, zzz482, bh) → new_mkVBalBranch3MkVBalBranch121(zzz473, zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, zzz481, zzz482, Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat2(Succ(new_primPlusNat3(new_primPlusNat1(zzz475), zzz475)), zzz475)), zzz475))), bh)
new_mkVBalBranch3MkVBalBranch217(zzz473, zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, zzz481, zzz482, Succ(zzz4830), Succ(zzz4840), bh) → new_mkVBalBranch3MkVBalBranch217(zzz473, zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, zzz481, zzz482, zzz4830, zzz4840, bh)
new_mkVBalBranch3MkVBalBranch116(zzz340, zzz341, zzz34200, zzz343, zzz344, zzz510, zzz511, zzz513, zzz514, zzz31, Succ(zzz1200), h) → new_mkVBalBranch0(zzz31, zzz514, Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), h)
new_mkVBalBranch3MkVBalBranch225(zzz498, zzz499, zzz500, zzz501, zzz502, zzz503, zzz504, zzz505, zzz506, zzz507, Zero, Succ(zzz5090), bg) → new_mkVBalBranch0(zzz507, Branch(zzz503, zzz504, Neg(Succ(Zero)), zzz505, zzz506), zzz501, bg)
new_mkVBalBranch0(zzz31, Branch(zzz510, zzz511, Neg(Succ(zzz51200)), zzz513, zzz514), Branch(zzz340, zzz341, zzz342, zzz343, zzz344), h) → new_mkVBalBranch3MkVBalBranch223(zzz340, zzz341, zzz342, zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat3(new_primPlusNat1(zzz51200), zzz51200)), zzz51200))), h)
new_mkVBalBranch3MkVBalBranch223(zzz340, zzz341, Neg(Succ(Zero)), zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, Succ(zzz670), h) → new_mkVBalBranch0(zzz31, Branch(zzz510, zzz511, Neg(Succ(zzz51200)), zzz513, zzz514), zzz343, h)
new_mkVBalBranch3MkVBalBranch215(zzz340, zzz341, Pos(Succ(Succ(zzz342000))), zzz343, zzz344, zzz510, zzz511, Zero, zzz513, zzz514, zzz31, Succ(Succ(zzz6600)), h) → new_mkVBalBranch3MkVBalBranch217(zzz340, zzz341, Succ(zzz342000), zzz343, zzz344, zzz510, zzz511, zzz513, zzz514, zzz31, Succ(zzz6600), zzz342000, h)
new_mkVBalBranch3MkVBalBranch117(zzz340, zzz341, zzz34200, zzz343, zzz344, zzz510, zzz511, zzz513, zzz514, zzz31, Succ(zzz1240), h) → new_mkVBalBranch0(zzz31, zzz514, Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), h)
new_mkVBalBranch3MkVBalBranch120(zzz2050, zzz2051, zzz2052, zzz2053, zzz2054, zzz2055, zzz2056, zzz2057, zzz2058, zzz2059, zzz2060, Succ(zzz20610), Succ(zzz20620), be) → new_mkVBalBranch3MkVBalBranch120(zzz2050, zzz2051, zzz2052, zzz2053, zzz2054, zzz2055, zzz2056, zzz2057, zzz2058, zzz2059, zzz2060, zzz20610, zzz20620, be)
new_mkVBalBranch3MkVBalBranch217(zzz473, zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, zzz481, zzz482, Zero, Zero, bh) → new_mkVBalBranch3MkVBalBranch233(zzz473, zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, zzz481, zzz482, bh)
new_mkVBalBranch3MkVBalBranch216(zzz1105, zzz1106, zzz1107, zzz1108, zzz1109, zzz1110, zzz1111, zzz1112, zzz1113, zzz1114, zzz1115, Succ(zzz11160), Succ(zzz11170), ba) → new_mkVBalBranch3MkVBalBranch216(zzz1105, zzz1106, zzz1107, zzz1108, zzz1109, zzz1110, zzz1111, zzz1112, zzz1113, zzz1114, zzz1115, zzz11160, zzz11170, ba)
new_mkVBalBranch3MkVBalBranch223(zzz340, zzz341, Pos(zzz3420), zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, Succ(zzz670), h) → new_mkVBalBranch0(zzz31, Branch(zzz510, zzz511, Neg(Succ(zzz51200)), zzz513, zzz514), zzz343, h)
new_mkVBalBranch3MkVBalBranch225(zzz498, zzz499, zzz500, zzz501, zzz502, zzz503, zzz504, zzz505, zzz506, zzz507, Succ(zzz5080), Succ(zzz5090), bg) → new_mkVBalBranch3MkVBalBranch225(zzz498, zzz499, zzz500, zzz501, zzz502, zzz503, zzz504, zzz505, zzz506, zzz507, zzz5080, zzz5090, bg)
new_mkVBalBranch3MkVBalBranch19(zzz340, zzz341, zzz34200, zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, Succ(zzz1410), h) → new_mkVBalBranch0(zzz31, zzz514, Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), h)
new_mkVBalBranch3MkVBalBranch224(zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, zzz1125, zzz1126, zzz1127, zzz1128, zzz1129, Zero, Succ(zzz11310), bd) → new_mkVBalBranch3MkVBalBranch227(zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, zzz1125, zzz1126, zzz1127, zzz1128, zzz1129, bd)
new_mkVBalBranch3MkVBalBranch224(zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, zzz1125, zzz1126, zzz1127, zzz1128, zzz1129, Zero, Zero, bd) → new_mkVBalBranch3MkVBalBranch229(zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, zzz1125, zzz1126, zzz1127, zzz1128, zzz1129, bd)
new_mkVBalBranch3MkVBalBranch225(zzz498, zzz499, zzz500, zzz501, zzz502, zzz503, zzz504, zzz505, zzz506, zzz507, Succ(zzz5080), Zero, bg) → new_mkVBalBranch3MkVBalBranch118(zzz498, zzz499, zzz500, zzz501, zzz502, zzz503, zzz504, zzz505, zzz506, zzz507, Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat2(Succ(new_primPlusNat3(new_primPlusNat1(zzz500), zzz500)), zzz500)), zzz500))), bg)
new_mkVBalBranch3MkVBalBranch223(zzz340, zzz341, Neg(Succ(Succ(Succ(zzz3420000)))), zzz343, zzz344, zzz510, zzz511, Succ(zzz512000), zzz513, zzz514, zzz31, Succ(Succ(zzz6700)), h) → new_mkVBalBranch3MkVBalBranch224(zzz340, zzz341, Succ(Succ(zzz3420000)), zzz343, zzz344, zzz510, zzz511, zzz512000, zzz513, zzz514, zzz31, Succ(zzz3420000), Succ(Succ(new_primPlusNat2(zzz6700, zzz512000))), h)
new_mkVBalBranch3MkVBalBranch223(zzz340, zzz341, Neg(Succ(Succ(Zero))), zzz343, zzz344, zzz510, zzz511, Zero, zzz513, zzz514, zzz31, Succ(Succ(zzz6700)), h) → new_mkVBalBranch3MkVBalBranch225(zzz340, zzz341, Succ(Zero), zzz343, zzz344, zzz510, zzz511, zzz513, zzz514, zzz31, Zero, Succ(zzz6700), h)
new_mkVBalBranch3MkVBalBranch115(zzz1986, zzz1987, zzz1988, zzz1989, zzz1990, zzz1991, zzz1992, zzz1993, zzz1994, zzz1995, zzz1996, Succ(zzz19970), Succ(zzz19980), bc) → new_mkVBalBranch3MkVBalBranch115(zzz1986, zzz1987, zzz1988, zzz1989, zzz1990, zzz1991, zzz1992, zzz1993, zzz1994, zzz1995, zzz1996, zzz19970, zzz19980, bc)
new_mkVBalBranch3MkVBalBranch215(zzz340, zzz341, Neg(Zero), zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, Succ(zzz660), h) → new_mkVBalBranch0(zzz31, zzz514, Branch(zzz340, zzz341, Neg(Zero), zzz343, zzz344), h)
new_mkVBalBranch3MkVBalBranch224(zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, zzz1125, zzz1126, zzz1127, zzz1128, zzz1129, Succ(zzz11300), Zero, bd) → new_mkVBalBranch3MkVBalBranch119(zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, zzz1125, zzz1126, zzz1127, zzz1128, zzz1129, Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat2(Succ(new_primPlusNat3(new_primPlusNat1(zzz1121), zzz1121)), zzz1121)), zzz1121))), bd)
new_mkVBalBranch3MkVBalBranch118(zzz498, zzz499, zzz500, zzz501, zzz502, zzz503, zzz504, zzz505, zzz506, zzz507, Succ(zzz8040), bg) → new_mkVBalBranch3MkVBalBranch120(zzz498, zzz499, zzz500, zzz501, zzz502, zzz503, zzz504, Zero, zzz505, zzz506, zzz507, Succ(Zero), Succ(zzz8040), bg)
new_mkVBalBranch3MkVBalBranch222(zzz461, zzz462, zzz463, zzz464, zzz465, zzz466, zzz467, zzz468, zzz469, zzz470, zzz471, bb) → new_mkVBalBranch3MkVBalBranch110(zzz461, zzz462, zzz463, zzz464, zzz465, zzz466, zzz467, zzz468, zzz469, zzz470, zzz471, Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat2(Succ(new_primPlusNat3(new_primPlusNat1(zzz463), zzz463)), zzz463)), zzz463))), bb)
new_mkVBalBranch3MkVBalBranch216(zzz1105, zzz1106, zzz1107, zzz1108, zzz1109, zzz1110, zzz1111, zzz1112, zzz1113, zzz1114, zzz1115, Succ(zzz11160), Zero, ba) → new_mkVBalBranch3MkVBalBranch218(zzz1105, zzz1106, zzz1107, zzz1108, zzz1109, zzz1110, zzz1111, zzz1112, zzz1113, zzz1114, zzz1115, ba)
new_mkVBalBranch3MkVBalBranch216(zzz1105, zzz1106, zzz1107, zzz1108, zzz1109, zzz1110, zzz1111, zzz1112, zzz1113, zzz1114, zzz1115, Zero, Zero, ba) → new_mkVBalBranch3MkVBalBranch222(zzz1105, zzz1106, zzz1107, zzz1108, zzz1109, zzz1110, zzz1111, zzz1112, zzz1113, zzz1114, zzz1115, ba)
new_mkVBalBranch3MkVBalBranch119(zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, zzz1125, zzz1126, zzz1127, zzz1128, zzz1129, Succ(zzz12130), bd) → new_mkVBalBranch3MkVBalBranch120(zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, zzz1125, Succ(zzz1126), zzz1127, zzz1128, zzz1129, Succ(Succ(zzz1126)), Succ(zzz12130), bd)

The TRS R consists of the following rules:

new_primPlusNat1(Zero) → Zero
new_primPlusNat1(Succ(zzz62000)) → Succ(Succ(new_primPlusNat1(zzz62000)))
new_primPlusNat3(zzz90, Succ(zzz910)) → Succ(Succ(new_primPlusNat2(zzz90, zzz910)))
new_primPlusNat3(zzz90, Zero) → Succ(zzz90)
new_primPlusNat2(Succ(zzz900), Succ(zzz9100)) → Succ(Succ(new_primPlusNat2(zzz900, zzz9100)))
new_primPlusNat2(Zero, Succ(zzz9100)) → Succ(zzz9100)
new_primPlusNat2(Zero, Zero) → Zero
new_primPlusNat2(Succ(zzz900), Zero) → Succ(zzz900)

The set Q consists of the following terms:

new_primPlusNat2(Zero, Succ(x0))
new_primPlusNat3(x0, Succ(x1))
new_primPlusNat2(Succ(x0), Succ(x1))
new_primPlusNat3(x0, Zero)
new_primPlusNat1(Zero)
new_primPlusNat2(Zero, Zero)
new_primPlusNat1(Succ(x0))
new_primPlusNat2(Succ(x0), Zero)

We have to consider all minimal (P,Q,R)-chains.
By instantiating [15] the rule new_mkVBalBranch3MkVBalBranch18(zzz340, zzz341, zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, Succ(zzz1480), h) → new_mkVBalBranch3MkVBalBranch115(zzz340, zzz341, Zero, zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, Succ(zzz1480), Succ(zzz51200), h) we obtained the following new rules:

new_mkVBalBranch3MkVBalBranch18(z0, z1, z2, z3, z4, z5, z6, z7, z8, z9, Succ(Succ(Succ(Succ(Succ(Zero))))), z11) → new_mkVBalBranch3MkVBalBranch115(z0, z1, Zero, z2, z3, z4, z5, z6, z7, z8, z9, Succ(Succ(Succ(Succ(Succ(Zero))))), Succ(z6), z11)



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

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

new_mkVBalBranch3MkVBalBranch225(zzz498, zzz499, zzz500, zzz501, zzz502, zzz503, zzz504, zzz505, zzz506, zzz507, Zero, Zero, bg) → new_mkVBalBranch3MkVBalBranch230(zzz498, zzz499, zzz500, zzz501, zzz502, zzz503, zzz504, zzz505, zzz506, zzz507, bg)
new_mkVBalBranch0(zzz31, Branch(zzz510, zzz511, Neg(Zero), zzz513, zzz514), Branch(zzz340, zzz341, Pos(Succ(zzz34200)), zzz343, zzz344), h) → new_mkVBalBranch0(zzz31, Branch(zzz510, zzz511, Neg(Zero), zzz513, zzz514), zzz343, h)
new_mkVBalBranch3MkVBalBranch215(zzz340, zzz341, Pos(Succ(Succ(zzz342000))), zzz343, zzz344, zzz510, zzz511, Succ(zzz512000), zzz513, zzz514, zzz31, Succ(Succ(zzz6600)), h) → new_mkVBalBranch3MkVBalBranch216(zzz340, zzz341, Succ(zzz342000), zzz343, zzz344, zzz510, zzz511, zzz512000, zzz513, zzz514, zzz31, Succ(Succ(new_primPlusNat2(zzz6600, zzz512000))), zzz342000, h)
new_mkVBalBranch3MkVBalBranch223(zzz340, zzz341, Neg(Succ(Succ(Succ(zzz3420000)))), zzz343, zzz344, zzz510, zzz511, Zero, zzz513, zzz514, zzz31, Succ(Succ(zzz6700)), h) → new_mkVBalBranch3MkVBalBranch225(zzz340, zzz341, Succ(Succ(zzz3420000)), zzz343, zzz344, zzz510, zzz511, zzz513, zzz514, zzz31, Succ(zzz3420000), Succ(zzz6700), h)
new_mkVBalBranch3MkVBalBranch120(zzz2050, zzz2051, zzz2052, zzz2053, zzz2054, zzz2055, zzz2056, zzz2057, zzz2058, zzz2059, zzz2060, Zero, Succ(zzz20620), be) → new_mkVBalBranch0(zzz2060, zzz2059, Branch(zzz2050, zzz2051, Neg(Succ(zzz2052)), zzz2053, zzz2054), be)
new_mkVBalBranch3MkVBalBranch121(zzz473, zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, zzz481, zzz482, Succ(zzz7390), bh) → new_mkVBalBranch3MkVBalBranch115(zzz473, zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, Zero, zzz480, zzz481, zzz482, Succ(zzz7390), Succ(Zero), bh)
new_mkVBalBranch0(zzz31, Branch(zzz510, zzz511, Pos(Zero), zzz513, zzz514), Branch(zzz340, zzz341, Pos(Succ(zzz34200)), zzz343, zzz344), h) → new_mkVBalBranch0(zzz31, Branch(zzz510, zzz511, Pos(Zero), zzz513, zzz514), zzz343, h)
new_mkVBalBranch0(zzz31, Branch(zzz510, zzz511, Pos(Succ(zzz51200)), zzz513, zzz514), Branch(zzz340, zzz341, zzz342, zzz343, zzz344), h) → new_mkVBalBranch3MkVBalBranch215(zzz340, zzz341, zzz342, zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat3(new_primPlusNat1(zzz51200), zzz51200)), zzz51200))), h)
new_mkVBalBranch3MkVBalBranch215(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, Succ(zzz660), h) → new_mkVBalBranch3MkVBalBranch19(zzz340, zzz341, zzz34200, zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat2(Succ(new_primPlusNat3(new_primPlusNat1(zzz34200), zzz34200)), zzz34200)), zzz34200))), h)
new_mkVBalBranch3MkVBalBranch230(zzz498, zzz499, zzz500, zzz501, zzz502, zzz503, zzz504, zzz505, zzz506, zzz507, bg) → new_mkVBalBranch3MkVBalBranch118(zzz498, zzz499, zzz500, zzz501, zzz502, zzz503, zzz504, zzz505, zzz506, zzz507, Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat2(Succ(new_primPlusNat3(new_primPlusNat1(zzz500), zzz500)), zzz500)), zzz500))), bg)
new_mkVBalBranch3MkVBalBranch223(zzz340, zzz341, Neg(Succ(Succ(Zero))), zzz343, zzz344, zzz510, zzz511, Succ(zzz512000), zzz513, zzz514, zzz31, Succ(Succ(zzz6700)), h) → new_mkVBalBranch3MkVBalBranch224(zzz340, zzz341, Succ(Zero), zzz343, zzz344, zzz510, zzz511, zzz512000, zzz513, zzz514, zzz31, Zero, Succ(Succ(new_primPlusNat2(zzz6700, zzz512000))), h)
new_mkVBalBranch0(zzz31, Branch(zzz510, zzz511, Pos(Zero), zzz513, zzz514), Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), h) → new_mkVBalBranch3MkVBalBranch116(zzz340, zzz341, zzz34200, zzz343, zzz344, zzz510, zzz511, zzz513, zzz514, zzz31, Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat2(Succ(new_primPlusNat3(new_primPlusNat1(zzz34200), zzz34200)), zzz34200)), zzz34200))), h)
new_mkVBalBranch0(zzz31, Branch(zzz510, zzz511, Neg(Zero), zzz513, zzz514), Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), h) → new_mkVBalBranch3MkVBalBranch117(zzz340, zzz341, zzz34200, zzz343, zzz344, zzz510, zzz511, zzz513, zzz514, zzz31, Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat2(Succ(new_primPlusNat3(new_primPlusNat1(zzz34200), zzz34200)), zzz34200)), zzz34200))), h)
new_mkVBalBranch3MkVBalBranch224(zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, zzz1125, zzz1126, zzz1127, zzz1128, zzz1129, Succ(zzz11300), Succ(zzz11310), bd) → new_mkVBalBranch3MkVBalBranch224(zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, zzz1125, zzz1126, zzz1127, zzz1128, zzz1129, zzz11300, zzz11310, bd)
new_mkVBalBranch3MkVBalBranch217(zzz473, zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, zzz481, zzz482, Succ(zzz4830), Zero, bh) → new_mkVBalBranch3MkVBalBranch121(zzz473, zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, zzz481, zzz482, Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat2(Succ(new_primPlusNat3(new_primPlusNat1(zzz475), zzz475)), zzz475)), zzz475))), bh)
new_mkVBalBranch3MkVBalBranch229(zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, zzz1125, zzz1126, zzz1127, zzz1128, zzz1129, bd) → new_mkVBalBranch3MkVBalBranch119(zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, zzz1125, zzz1126, zzz1127, zzz1128, zzz1129, Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat2(Succ(new_primPlusNat3(new_primPlusNat1(zzz1121), zzz1121)), zzz1121)), zzz1121))), bd)
new_mkVBalBranch3MkVBalBranch217(zzz473, zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, zzz481, zzz482, Zero, Succ(zzz4840), bh) → new_mkVBalBranch0(zzz482, Branch(zzz478, zzz479, Pos(Succ(Zero)), zzz480, zzz481), zzz476, bh)
new_mkVBalBranch3MkVBalBranch218(zzz461, zzz462, zzz463, zzz464, zzz465, zzz466, zzz467, zzz468, zzz469, zzz470, zzz471, bb) → new_mkVBalBranch3MkVBalBranch110(zzz461, zzz462, zzz463, zzz464, zzz465, zzz466, zzz467, zzz468, zzz469, zzz470, zzz471, Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat2(Succ(new_primPlusNat3(new_primPlusNat1(zzz463), zzz463)), zzz463)), zzz463))), bb)
new_mkVBalBranch3MkVBalBranch215(zzz340, zzz341, Pos(Succ(Zero)), zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, Succ(zzz660), h) → new_mkVBalBranch3MkVBalBranch18(zzz340, zzz341, zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, Succ(Succ(Succ(Succ(Succ(Zero))))), h)
new_mkVBalBranch3MkVBalBranch110(zzz461, zzz462, zzz463, zzz464, zzz465, zzz466, zzz467, zzz468, zzz469, zzz470, zzz471, Succ(zzz5800), bb) → new_mkVBalBranch3MkVBalBranch115(zzz461, zzz462, zzz463, zzz464, zzz465, zzz466, zzz467, Succ(zzz468), zzz469, zzz470, zzz471, Succ(zzz5800), Succ(Succ(zzz468)), bb)
new_mkVBalBranch3MkVBalBranch227(zzz486, zzz487, zzz488, zzz489, zzz490, zzz491, zzz492, zzz493, zzz494, zzz495, zzz496, bf) → new_mkVBalBranch0(zzz496, Branch(zzz491, zzz492, Neg(Succ(Succ(zzz493))), zzz494, zzz495), zzz489, bf)
new_mkVBalBranch3MkVBalBranch215(zzz340, zzz341, Pos(Zero), zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, Succ(zzz660), h) → new_mkVBalBranch0(zzz31, zzz514, Branch(zzz340, zzz341, Pos(Zero), zzz343, zzz344), h)
new_mkVBalBranch3MkVBalBranch223(zzz340, zzz341, Neg(Zero), zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, Succ(zzz670), h) → new_mkVBalBranch0(zzz31, Branch(zzz510, zzz511, Neg(Succ(zzz51200)), zzz513, zzz514), zzz343, h)
new_mkVBalBranch3MkVBalBranch216(zzz1105, zzz1106, zzz1107, zzz1108, zzz1109, zzz1110, zzz1111, zzz1112, zzz1113, zzz1114, zzz1115, Zero, Succ(zzz11170), ba) → new_mkVBalBranch0(zzz1115, Branch(zzz1110, zzz1111, Pos(Succ(Succ(zzz1112))), zzz1113, zzz1114), zzz1108, ba)
new_mkVBalBranch3MkVBalBranch115(zzz1986, zzz1987, zzz1988, zzz1989, zzz1990, zzz1991, zzz1992, zzz1993, zzz1994, zzz1995, zzz1996, Zero, Succ(zzz19980), bc) → new_mkVBalBranch0(zzz1996, zzz1995, Branch(zzz1986, zzz1987, Pos(Succ(zzz1988)), zzz1989, zzz1990), bc)
new_mkVBalBranch3MkVBalBranch233(zzz473, zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, zzz481, zzz482, bh) → new_mkVBalBranch3MkVBalBranch121(zzz473, zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, zzz481, zzz482, Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat2(Succ(new_primPlusNat3(new_primPlusNat1(zzz475), zzz475)), zzz475)), zzz475))), bh)
new_mkVBalBranch3MkVBalBranch217(zzz473, zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, zzz481, zzz482, Succ(zzz4830), Succ(zzz4840), bh) → new_mkVBalBranch3MkVBalBranch217(zzz473, zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, zzz481, zzz482, zzz4830, zzz4840, bh)
new_mkVBalBranch3MkVBalBranch116(zzz340, zzz341, zzz34200, zzz343, zzz344, zzz510, zzz511, zzz513, zzz514, zzz31, Succ(zzz1200), h) → new_mkVBalBranch0(zzz31, zzz514, Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), h)
new_mkVBalBranch3MkVBalBranch225(zzz498, zzz499, zzz500, zzz501, zzz502, zzz503, zzz504, zzz505, zzz506, zzz507, Zero, Succ(zzz5090), bg) → new_mkVBalBranch0(zzz507, Branch(zzz503, zzz504, Neg(Succ(Zero)), zzz505, zzz506), zzz501, bg)
new_mkVBalBranch0(zzz31, Branch(zzz510, zzz511, Neg(Succ(zzz51200)), zzz513, zzz514), Branch(zzz340, zzz341, zzz342, zzz343, zzz344), h) → new_mkVBalBranch3MkVBalBranch223(zzz340, zzz341, zzz342, zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat3(new_primPlusNat1(zzz51200), zzz51200)), zzz51200))), h)
new_mkVBalBranch3MkVBalBranch223(zzz340, zzz341, Neg(Succ(Zero)), zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, Succ(zzz670), h) → new_mkVBalBranch0(zzz31, Branch(zzz510, zzz511, Neg(Succ(zzz51200)), zzz513, zzz514), zzz343, h)
new_mkVBalBranch3MkVBalBranch215(zzz340, zzz341, Pos(Succ(Succ(zzz342000))), zzz343, zzz344, zzz510, zzz511, Zero, zzz513, zzz514, zzz31, Succ(Succ(zzz6600)), h) → new_mkVBalBranch3MkVBalBranch217(zzz340, zzz341, Succ(zzz342000), zzz343, zzz344, zzz510, zzz511, zzz513, zzz514, zzz31, Succ(zzz6600), zzz342000, h)
new_mkVBalBranch3MkVBalBranch117(zzz340, zzz341, zzz34200, zzz343, zzz344, zzz510, zzz511, zzz513, zzz514, zzz31, Succ(zzz1240), h) → new_mkVBalBranch0(zzz31, zzz514, Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), h)
new_mkVBalBranch3MkVBalBranch217(zzz473, zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, zzz481, zzz482, Zero, Zero, bh) → new_mkVBalBranch3MkVBalBranch233(zzz473, zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, zzz481, zzz482, bh)
new_mkVBalBranch3MkVBalBranch120(zzz2050, zzz2051, zzz2052, zzz2053, zzz2054, zzz2055, zzz2056, zzz2057, zzz2058, zzz2059, zzz2060, Succ(zzz20610), Succ(zzz20620), be) → new_mkVBalBranch3MkVBalBranch120(zzz2050, zzz2051, zzz2052, zzz2053, zzz2054, zzz2055, zzz2056, zzz2057, zzz2058, zzz2059, zzz2060, zzz20610, zzz20620, be)
new_mkVBalBranch3MkVBalBranch223(zzz340, zzz341, Pos(zzz3420), zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, Succ(zzz670), h) → new_mkVBalBranch0(zzz31, Branch(zzz510, zzz511, Neg(Succ(zzz51200)), zzz513, zzz514), zzz343, h)
new_mkVBalBranch3MkVBalBranch216(zzz1105, zzz1106, zzz1107, zzz1108, zzz1109, zzz1110, zzz1111, zzz1112, zzz1113, zzz1114, zzz1115, Succ(zzz11160), Succ(zzz11170), ba) → new_mkVBalBranch3MkVBalBranch216(zzz1105, zzz1106, zzz1107, zzz1108, zzz1109, zzz1110, zzz1111, zzz1112, zzz1113, zzz1114, zzz1115, zzz11160, zzz11170, ba)
new_mkVBalBranch3MkVBalBranch225(zzz498, zzz499, zzz500, zzz501, zzz502, zzz503, zzz504, zzz505, zzz506, zzz507, Succ(zzz5080), Succ(zzz5090), bg) → new_mkVBalBranch3MkVBalBranch225(zzz498, zzz499, zzz500, zzz501, zzz502, zzz503, zzz504, zzz505, zzz506, zzz507, zzz5080, zzz5090, bg)
new_mkVBalBranch3MkVBalBranch19(zzz340, zzz341, zzz34200, zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, Succ(zzz1410), h) → new_mkVBalBranch0(zzz31, zzz514, Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), h)
new_mkVBalBranch3MkVBalBranch224(zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, zzz1125, zzz1126, zzz1127, zzz1128, zzz1129, Zero, Zero, bd) → new_mkVBalBranch3MkVBalBranch229(zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, zzz1125, zzz1126, zzz1127, zzz1128, zzz1129, bd)
new_mkVBalBranch3MkVBalBranch224(zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, zzz1125, zzz1126, zzz1127, zzz1128, zzz1129, Zero, Succ(zzz11310), bd) → new_mkVBalBranch3MkVBalBranch227(zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, zzz1125, zzz1126, zzz1127, zzz1128, zzz1129, bd)
new_mkVBalBranch3MkVBalBranch223(zzz340, zzz341, Neg(Succ(Succ(Zero))), zzz343, zzz344, zzz510, zzz511, Zero, zzz513, zzz514, zzz31, Succ(Succ(zzz6700)), h) → new_mkVBalBranch3MkVBalBranch225(zzz340, zzz341, Succ(Zero), zzz343, zzz344, zzz510, zzz511, zzz513, zzz514, zzz31, Zero, Succ(zzz6700), h)
new_mkVBalBranch3MkVBalBranch223(zzz340, zzz341, Neg(Succ(Succ(Succ(zzz3420000)))), zzz343, zzz344, zzz510, zzz511, Succ(zzz512000), zzz513, zzz514, zzz31, Succ(Succ(zzz6700)), h) → new_mkVBalBranch3MkVBalBranch224(zzz340, zzz341, Succ(Succ(zzz3420000)), zzz343, zzz344, zzz510, zzz511, zzz512000, zzz513, zzz514, zzz31, Succ(zzz3420000), Succ(Succ(new_primPlusNat2(zzz6700, zzz512000))), h)
new_mkVBalBranch3MkVBalBranch225(zzz498, zzz499, zzz500, zzz501, zzz502, zzz503, zzz504, zzz505, zzz506, zzz507, Succ(zzz5080), Zero, bg) → new_mkVBalBranch3MkVBalBranch118(zzz498, zzz499, zzz500, zzz501, zzz502, zzz503, zzz504, zzz505, zzz506, zzz507, Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat2(Succ(new_primPlusNat3(new_primPlusNat1(zzz500), zzz500)), zzz500)), zzz500))), bg)
new_mkVBalBranch3MkVBalBranch115(zzz1986, zzz1987, zzz1988, zzz1989, zzz1990, zzz1991, zzz1992, zzz1993, zzz1994, zzz1995, zzz1996, Succ(zzz19970), Succ(zzz19980), bc) → new_mkVBalBranch3MkVBalBranch115(zzz1986, zzz1987, zzz1988, zzz1989, zzz1990, zzz1991, zzz1992, zzz1993, zzz1994, zzz1995, zzz1996, zzz19970, zzz19980, bc)
new_mkVBalBranch3MkVBalBranch215(zzz340, zzz341, Neg(Zero), zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, Succ(zzz660), h) → new_mkVBalBranch0(zzz31, zzz514, Branch(zzz340, zzz341, Neg(Zero), zzz343, zzz344), h)
new_mkVBalBranch3MkVBalBranch224(zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, zzz1125, zzz1126, zzz1127, zzz1128, zzz1129, Succ(zzz11300), Zero, bd) → new_mkVBalBranch3MkVBalBranch119(zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, zzz1125, zzz1126, zzz1127, zzz1128, zzz1129, Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat2(Succ(new_primPlusNat3(new_primPlusNat1(zzz1121), zzz1121)), zzz1121)), zzz1121))), bd)
new_mkVBalBranch3MkVBalBranch222(zzz461, zzz462, zzz463, zzz464, zzz465, zzz466, zzz467, zzz468, zzz469, zzz470, zzz471, bb) → new_mkVBalBranch3MkVBalBranch110(zzz461, zzz462, zzz463, zzz464, zzz465, zzz466, zzz467, zzz468, zzz469, zzz470, zzz471, Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat2(Succ(new_primPlusNat3(new_primPlusNat1(zzz463), zzz463)), zzz463)), zzz463))), bb)
new_mkVBalBranch3MkVBalBranch118(zzz498, zzz499, zzz500, zzz501, zzz502, zzz503, zzz504, zzz505, zzz506, zzz507, Succ(zzz8040), bg) → new_mkVBalBranch3MkVBalBranch120(zzz498, zzz499, zzz500, zzz501, zzz502, zzz503, zzz504, Zero, zzz505, zzz506, zzz507, Succ(Zero), Succ(zzz8040), bg)
new_mkVBalBranch3MkVBalBranch216(zzz1105, zzz1106, zzz1107, zzz1108, zzz1109, zzz1110, zzz1111, zzz1112, zzz1113, zzz1114, zzz1115, Succ(zzz11160), Zero, ba) → new_mkVBalBranch3MkVBalBranch218(zzz1105, zzz1106, zzz1107, zzz1108, zzz1109, zzz1110, zzz1111, zzz1112, zzz1113, zzz1114, zzz1115, ba)
new_mkVBalBranch3MkVBalBranch216(zzz1105, zzz1106, zzz1107, zzz1108, zzz1109, zzz1110, zzz1111, zzz1112, zzz1113, zzz1114, zzz1115, Zero, Zero, ba) → new_mkVBalBranch3MkVBalBranch222(zzz1105, zzz1106, zzz1107, zzz1108, zzz1109, zzz1110, zzz1111, zzz1112, zzz1113, zzz1114, zzz1115, ba)
new_mkVBalBranch3MkVBalBranch119(zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, zzz1125, zzz1126, zzz1127, zzz1128, zzz1129, Succ(zzz12130), bd) → new_mkVBalBranch3MkVBalBranch120(zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, zzz1125, Succ(zzz1126), zzz1127, zzz1128, zzz1129, Succ(Succ(zzz1126)), Succ(zzz12130), bd)
new_mkVBalBranch3MkVBalBranch18(z0, z1, z2, z3, z4, z5, z6, z7, z8, z9, Succ(Succ(Succ(Succ(Succ(Zero))))), z11) → new_mkVBalBranch3MkVBalBranch115(z0, z1, Zero, z2, z3, z4, z5, z6, z7, z8, z9, Succ(Succ(Succ(Succ(Succ(Zero))))), Succ(z6), z11)

The TRS R consists of the following rules:

new_primPlusNat1(Zero) → Zero
new_primPlusNat1(Succ(zzz62000)) → Succ(Succ(new_primPlusNat1(zzz62000)))
new_primPlusNat3(zzz90, Succ(zzz910)) → Succ(Succ(new_primPlusNat2(zzz90, zzz910)))
new_primPlusNat3(zzz90, Zero) → Succ(zzz90)
new_primPlusNat2(Succ(zzz900), Succ(zzz9100)) → Succ(Succ(new_primPlusNat2(zzz900, zzz9100)))
new_primPlusNat2(Zero, Succ(zzz9100)) → Succ(zzz9100)
new_primPlusNat2(Zero, Zero) → Zero
new_primPlusNat2(Succ(zzz900), Zero) → Succ(zzz900)

The set Q consists of the following terms:

new_primPlusNat2(Zero, Succ(x0))
new_primPlusNat3(x0, Succ(x1))
new_primPlusNat2(Succ(x0), Succ(x1))
new_primPlusNat3(x0, Zero)
new_primPlusNat1(Zero)
new_primPlusNat2(Zero, Zero)
new_primPlusNat1(Succ(x0))
new_primPlusNat2(Succ(x0), Zero)

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


The following pairs can be oriented strictly and are deleted.


new_mkVBalBranch0(zzz31, Branch(zzz510, zzz511, Pos(Zero), zzz513, zzz514), Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), h) → new_mkVBalBranch3MkVBalBranch116(zzz340, zzz341, zzz34200, zzz343, zzz344, zzz510, zzz511, zzz513, zzz514, zzz31, Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat2(Succ(new_primPlusNat3(new_primPlusNat1(zzz34200), zzz34200)), zzz34200)), zzz34200))), h)
new_mkVBalBranch3MkVBalBranch217(zzz473, zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, zzz481, zzz482, Succ(zzz4830), Zero, bh) → new_mkVBalBranch3MkVBalBranch121(zzz473, zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, zzz481, zzz482, Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat2(Succ(new_primPlusNat3(new_primPlusNat1(zzz475), zzz475)), zzz475)), zzz475))), bh)
new_mkVBalBranch3MkVBalBranch215(zzz340, zzz341, Pos(Succ(Zero)), zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, Succ(zzz660), h) → new_mkVBalBranch3MkVBalBranch18(zzz340, zzz341, zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, Succ(Succ(Succ(Succ(Succ(Zero))))), h)
new_mkVBalBranch3MkVBalBranch215(zzz340, zzz341, Pos(Zero), zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, Succ(zzz660), h) → new_mkVBalBranch0(zzz31, zzz514, Branch(zzz340, zzz341, Pos(Zero), zzz343, zzz344), h)
new_mkVBalBranch3MkVBalBranch233(zzz473, zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, zzz481, zzz482, bh) → new_mkVBalBranch3MkVBalBranch121(zzz473, zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, zzz481, zzz482, Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat2(Succ(new_primPlusNat3(new_primPlusNat1(zzz475), zzz475)), zzz475)), zzz475))), bh)
new_mkVBalBranch3MkVBalBranch19(zzz340, zzz341, zzz34200, zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, Succ(zzz1410), h) → new_mkVBalBranch0(zzz31, zzz514, Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), h)
new_mkVBalBranch3MkVBalBranch215(zzz340, zzz341, Neg(Zero), zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, Succ(zzz660), h) → new_mkVBalBranch0(zzz31, zzz514, Branch(zzz340, zzz341, Neg(Zero), zzz343, zzz344), h)
new_mkVBalBranch3MkVBalBranch222(zzz461, zzz462, zzz463, zzz464, zzz465, zzz466, zzz467, zzz468, zzz469, zzz470, zzz471, bb) → new_mkVBalBranch3MkVBalBranch110(zzz461, zzz462, zzz463, zzz464, zzz465, zzz466, zzz467, zzz468, zzz469, zzz470, zzz471, Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat2(Succ(new_primPlusNat3(new_primPlusNat1(zzz463), zzz463)), zzz463)), zzz463))), bb)
new_mkVBalBranch3MkVBalBranch216(zzz1105, zzz1106, zzz1107, zzz1108, zzz1109, zzz1110, zzz1111, zzz1112, zzz1113, zzz1114, zzz1115, Succ(zzz11160), Zero, ba) → new_mkVBalBranch3MkVBalBranch218(zzz1105, zzz1106, zzz1107, zzz1108, zzz1109, zzz1110, zzz1111, zzz1112, zzz1113, zzz1114, zzz1115, ba)
The remaining pairs can at least be oriented weakly.

new_mkVBalBranch3MkVBalBranch225(zzz498, zzz499, zzz500, zzz501, zzz502, zzz503, zzz504, zzz505, zzz506, zzz507, Zero, Zero, bg) → new_mkVBalBranch3MkVBalBranch230(zzz498, zzz499, zzz500, zzz501, zzz502, zzz503, zzz504, zzz505, zzz506, zzz507, bg)
new_mkVBalBranch0(zzz31, Branch(zzz510, zzz511, Neg(Zero), zzz513, zzz514), Branch(zzz340, zzz341, Pos(Succ(zzz34200)), zzz343, zzz344), h) → new_mkVBalBranch0(zzz31, Branch(zzz510, zzz511, Neg(Zero), zzz513, zzz514), zzz343, h)
new_mkVBalBranch3MkVBalBranch215(zzz340, zzz341, Pos(Succ(Succ(zzz342000))), zzz343, zzz344, zzz510, zzz511, Succ(zzz512000), zzz513, zzz514, zzz31, Succ(Succ(zzz6600)), h) → new_mkVBalBranch3MkVBalBranch216(zzz340, zzz341, Succ(zzz342000), zzz343, zzz344, zzz510, zzz511, zzz512000, zzz513, zzz514, zzz31, Succ(Succ(new_primPlusNat2(zzz6600, zzz512000))), zzz342000, h)
new_mkVBalBranch3MkVBalBranch223(zzz340, zzz341, Neg(Succ(Succ(Succ(zzz3420000)))), zzz343, zzz344, zzz510, zzz511, Zero, zzz513, zzz514, zzz31, Succ(Succ(zzz6700)), h) → new_mkVBalBranch3MkVBalBranch225(zzz340, zzz341, Succ(Succ(zzz3420000)), zzz343, zzz344, zzz510, zzz511, zzz513, zzz514, zzz31, Succ(zzz3420000), Succ(zzz6700), h)
new_mkVBalBranch3MkVBalBranch120(zzz2050, zzz2051, zzz2052, zzz2053, zzz2054, zzz2055, zzz2056, zzz2057, zzz2058, zzz2059, zzz2060, Zero, Succ(zzz20620), be) → new_mkVBalBranch0(zzz2060, zzz2059, Branch(zzz2050, zzz2051, Neg(Succ(zzz2052)), zzz2053, zzz2054), be)
new_mkVBalBranch3MkVBalBranch121(zzz473, zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, zzz481, zzz482, Succ(zzz7390), bh) → new_mkVBalBranch3MkVBalBranch115(zzz473, zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, Zero, zzz480, zzz481, zzz482, Succ(zzz7390), Succ(Zero), bh)
new_mkVBalBranch0(zzz31, Branch(zzz510, zzz511, Pos(Zero), zzz513, zzz514), Branch(zzz340, zzz341, Pos(Succ(zzz34200)), zzz343, zzz344), h) → new_mkVBalBranch0(zzz31, Branch(zzz510, zzz511, Pos(Zero), zzz513, zzz514), zzz343, h)
new_mkVBalBranch0(zzz31, Branch(zzz510, zzz511, Pos(Succ(zzz51200)), zzz513, zzz514), Branch(zzz340, zzz341, zzz342, zzz343, zzz344), h) → new_mkVBalBranch3MkVBalBranch215(zzz340, zzz341, zzz342, zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat3(new_primPlusNat1(zzz51200), zzz51200)), zzz51200))), h)
new_mkVBalBranch3MkVBalBranch215(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, Succ(zzz660), h) → new_mkVBalBranch3MkVBalBranch19(zzz340, zzz341, zzz34200, zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat2(Succ(new_primPlusNat3(new_primPlusNat1(zzz34200), zzz34200)), zzz34200)), zzz34200))), h)
new_mkVBalBranch3MkVBalBranch230(zzz498, zzz499, zzz500, zzz501, zzz502, zzz503, zzz504, zzz505, zzz506, zzz507, bg) → new_mkVBalBranch3MkVBalBranch118(zzz498, zzz499, zzz500, zzz501, zzz502, zzz503, zzz504, zzz505, zzz506, zzz507, Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat2(Succ(new_primPlusNat3(new_primPlusNat1(zzz500), zzz500)), zzz500)), zzz500))), bg)
new_mkVBalBranch3MkVBalBranch223(zzz340, zzz341, Neg(Succ(Succ(Zero))), zzz343, zzz344, zzz510, zzz511, Succ(zzz512000), zzz513, zzz514, zzz31, Succ(Succ(zzz6700)), h) → new_mkVBalBranch3MkVBalBranch224(zzz340, zzz341, Succ(Zero), zzz343, zzz344, zzz510, zzz511, zzz512000, zzz513, zzz514, zzz31, Zero, Succ(Succ(new_primPlusNat2(zzz6700, zzz512000))), h)
new_mkVBalBranch0(zzz31, Branch(zzz510, zzz511, Neg(Zero), zzz513, zzz514), Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), h) → new_mkVBalBranch3MkVBalBranch117(zzz340, zzz341, zzz34200, zzz343, zzz344, zzz510, zzz511, zzz513, zzz514, zzz31, Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat2(Succ(new_primPlusNat3(new_primPlusNat1(zzz34200), zzz34200)), zzz34200)), zzz34200))), h)
new_mkVBalBranch3MkVBalBranch224(zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, zzz1125, zzz1126, zzz1127, zzz1128, zzz1129, Succ(zzz11300), Succ(zzz11310), bd) → new_mkVBalBranch3MkVBalBranch224(zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, zzz1125, zzz1126, zzz1127, zzz1128, zzz1129, zzz11300, zzz11310, bd)
new_mkVBalBranch3MkVBalBranch229(zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, zzz1125, zzz1126, zzz1127, zzz1128, zzz1129, bd) → new_mkVBalBranch3MkVBalBranch119(zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, zzz1125, zzz1126, zzz1127, zzz1128, zzz1129, Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat2(Succ(new_primPlusNat3(new_primPlusNat1(zzz1121), zzz1121)), zzz1121)), zzz1121))), bd)
new_mkVBalBranch3MkVBalBranch217(zzz473, zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, zzz481, zzz482, Zero, Succ(zzz4840), bh) → new_mkVBalBranch0(zzz482, Branch(zzz478, zzz479, Pos(Succ(Zero)), zzz480, zzz481), zzz476, bh)
new_mkVBalBranch3MkVBalBranch218(zzz461, zzz462, zzz463, zzz464, zzz465, zzz466, zzz467, zzz468, zzz469, zzz470, zzz471, bb) → new_mkVBalBranch3MkVBalBranch110(zzz461, zzz462, zzz463, zzz464, zzz465, zzz466, zzz467, zzz468, zzz469, zzz470, zzz471, Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat2(Succ(new_primPlusNat3(new_primPlusNat1(zzz463), zzz463)), zzz463)), zzz463))), bb)
new_mkVBalBranch3MkVBalBranch110(zzz461, zzz462, zzz463, zzz464, zzz465, zzz466, zzz467, zzz468, zzz469, zzz470, zzz471, Succ(zzz5800), bb) → new_mkVBalBranch3MkVBalBranch115(zzz461, zzz462, zzz463, zzz464, zzz465, zzz466, zzz467, Succ(zzz468), zzz469, zzz470, zzz471, Succ(zzz5800), Succ(Succ(zzz468)), bb)
new_mkVBalBranch3MkVBalBranch227(zzz486, zzz487, zzz488, zzz489, zzz490, zzz491, zzz492, zzz493, zzz494, zzz495, zzz496, bf) → new_mkVBalBranch0(zzz496, Branch(zzz491, zzz492, Neg(Succ(Succ(zzz493))), zzz494, zzz495), zzz489, bf)
new_mkVBalBranch3MkVBalBranch223(zzz340, zzz341, Neg(Zero), zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, Succ(zzz670), h) → new_mkVBalBranch0(zzz31, Branch(zzz510, zzz511, Neg(Succ(zzz51200)), zzz513, zzz514), zzz343, h)
new_mkVBalBranch3MkVBalBranch216(zzz1105, zzz1106, zzz1107, zzz1108, zzz1109, zzz1110, zzz1111, zzz1112, zzz1113, zzz1114, zzz1115, Zero, Succ(zzz11170), ba) → new_mkVBalBranch0(zzz1115, Branch(zzz1110, zzz1111, Pos(Succ(Succ(zzz1112))), zzz1113, zzz1114), zzz1108, ba)
new_mkVBalBranch3MkVBalBranch115(zzz1986, zzz1987, zzz1988, zzz1989, zzz1990, zzz1991, zzz1992, zzz1993, zzz1994, zzz1995, zzz1996, Zero, Succ(zzz19980), bc) → new_mkVBalBranch0(zzz1996, zzz1995, Branch(zzz1986, zzz1987, Pos(Succ(zzz1988)), zzz1989, zzz1990), bc)
new_mkVBalBranch3MkVBalBranch217(zzz473, zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, zzz481, zzz482, Succ(zzz4830), Succ(zzz4840), bh) → new_mkVBalBranch3MkVBalBranch217(zzz473, zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, zzz481, zzz482, zzz4830, zzz4840, bh)
new_mkVBalBranch3MkVBalBranch116(zzz340, zzz341, zzz34200, zzz343, zzz344, zzz510, zzz511, zzz513, zzz514, zzz31, Succ(zzz1200), h) → new_mkVBalBranch0(zzz31, zzz514, Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), h)
new_mkVBalBranch3MkVBalBranch225(zzz498, zzz499, zzz500, zzz501, zzz502, zzz503, zzz504, zzz505, zzz506, zzz507, Zero, Succ(zzz5090), bg) → new_mkVBalBranch0(zzz507, Branch(zzz503, zzz504, Neg(Succ(Zero)), zzz505, zzz506), zzz501, bg)
new_mkVBalBranch0(zzz31, Branch(zzz510, zzz511, Neg(Succ(zzz51200)), zzz513, zzz514), Branch(zzz340, zzz341, zzz342, zzz343, zzz344), h) → new_mkVBalBranch3MkVBalBranch223(zzz340, zzz341, zzz342, zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat3(new_primPlusNat1(zzz51200), zzz51200)), zzz51200))), h)
new_mkVBalBranch3MkVBalBranch223(zzz340, zzz341, Neg(Succ(Zero)), zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, Succ(zzz670), h) → new_mkVBalBranch0(zzz31, Branch(zzz510, zzz511, Neg(Succ(zzz51200)), zzz513, zzz514), zzz343, h)
new_mkVBalBranch3MkVBalBranch215(zzz340, zzz341, Pos(Succ(Succ(zzz342000))), zzz343, zzz344, zzz510, zzz511, Zero, zzz513, zzz514, zzz31, Succ(Succ(zzz6600)), h) → new_mkVBalBranch3MkVBalBranch217(zzz340, zzz341, Succ(zzz342000), zzz343, zzz344, zzz510, zzz511, zzz513, zzz514, zzz31, Succ(zzz6600), zzz342000, h)
new_mkVBalBranch3MkVBalBranch117(zzz340, zzz341, zzz34200, zzz343, zzz344, zzz510, zzz511, zzz513, zzz514, zzz31, Succ(zzz1240), h) → new_mkVBalBranch0(zzz31, zzz514, Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), h)
new_mkVBalBranch3MkVBalBranch217(zzz473, zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, zzz481, zzz482, Zero, Zero, bh) → new_mkVBalBranch3MkVBalBranch233(zzz473, zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, zzz481, zzz482, bh)
new_mkVBalBranch3MkVBalBranch120(zzz2050, zzz2051, zzz2052, zzz2053, zzz2054, zzz2055, zzz2056, zzz2057, zzz2058, zzz2059, zzz2060, Succ(zzz20610), Succ(zzz20620), be) → new_mkVBalBranch3MkVBalBranch120(zzz2050, zzz2051, zzz2052, zzz2053, zzz2054, zzz2055, zzz2056, zzz2057, zzz2058, zzz2059, zzz2060, zzz20610, zzz20620, be)
new_mkVBalBranch3MkVBalBranch223(zzz340, zzz341, Pos(zzz3420), zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, Succ(zzz670), h) → new_mkVBalBranch0(zzz31, Branch(zzz510, zzz511, Neg(Succ(zzz51200)), zzz513, zzz514), zzz343, h)
new_mkVBalBranch3MkVBalBranch216(zzz1105, zzz1106, zzz1107, zzz1108, zzz1109, zzz1110, zzz1111, zzz1112, zzz1113, zzz1114, zzz1115, Succ(zzz11160), Succ(zzz11170), ba) → new_mkVBalBranch3MkVBalBranch216(zzz1105, zzz1106, zzz1107, zzz1108, zzz1109, zzz1110, zzz1111, zzz1112, zzz1113, zzz1114, zzz1115, zzz11160, zzz11170, ba)
new_mkVBalBranch3MkVBalBranch225(zzz498, zzz499, zzz500, zzz501, zzz502, zzz503, zzz504, zzz505, zzz506, zzz507, Succ(zzz5080), Succ(zzz5090), bg) → new_mkVBalBranch3MkVBalBranch225(zzz498, zzz499, zzz500, zzz501, zzz502, zzz503, zzz504, zzz505, zzz506, zzz507, zzz5080, zzz5090, bg)
new_mkVBalBranch3MkVBalBranch224(zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, zzz1125, zzz1126, zzz1127, zzz1128, zzz1129, Zero, Zero, bd) → new_mkVBalBranch3MkVBalBranch229(zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, zzz1125, zzz1126, zzz1127, zzz1128, zzz1129, bd)
new_mkVBalBranch3MkVBalBranch224(zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, zzz1125, zzz1126, zzz1127, zzz1128, zzz1129, Zero, Succ(zzz11310), bd) → new_mkVBalBranch3MkVBalBranch227(zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, zzz1125, zzz1126, zzz1127, zzz1128, zzz1129, bd)
new_mkVBalBranch3MkVBalBranch223(zzz340, zzz341, Neg(Succ(Succ(Zero))), zzz343, zzz344, zzz510, zzz511, Zero, zzz513, zzz514, zzz31, Succ(Succ(zzz6700)), h) → new_mkVBalBranch3MkVBalBranch225(zzz340, zzz341, Succ(Zero), zzz343, zzz344, zzz510, zzz511, zzz513, zzz514, zzz31, Zero, Succ(zzz6700), h)
new_mkVBalBranch3MkVBalBranch223(zzz340, zzz341, Neg(Succ(Succ(Succ(zzz3420000)))), zzz343, zzz344, zzz510, zzz511, Succ(zzz512000), zzz513, zzz514, zzz31, Succ(Succ(zzz6700)), h) → new_mkVBalBranch3MkVBalBranch224(zzz340, zzz341, Succ(Succ(zzz3420000)), zzz343, zzz344, zzz510, zzz511, zzz512000, zzz513, zzz514, zzz31, Succ(zzz3420000), Succ(Succ(new_primPlusNat2(zzz6700, zzz512000))), h)
new_mkVBalBranch3MkVBalBranch225(zzz498, zzz499, zzz500, zzz501, zzz502, zzz503, zzz504, zzz505, zzz506, zzz507, Succ(zzz5080), Zero, bg) → new_mkVBalBranch3MkVBalBranch118(zzz498, zzz499, zzz500, zzz501, zzz502, zzz503, zzz504, zzz505, zzz506, zzz507, Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat2(Succ(new_primPlusNat3(new_primPlusNat1(zzz500), zzz500)), zzz500)), zzz500))), bg)
new_mkVBalBranch3MkVBalBranch115(zzz1986, zzz1987, zzz1988, zzz1989, zzz1990, zzz1991, zzz1992, zzz1993, zzz1994, zzz1995, zzz1996, Succ(zzz19970), Succ(zzz19980), bc) → new_mkVBalBranch3MkVBalBranch115(zzz1986, zzz1987, zzz1988, zzz1989, zzz1990, zzz1991, zzz1992, zzz1993, zzz1994, zzz1995, zzz1996, zzz19970, zzz19980, bc)
new_mkVBalBranch3MkVBalBranch224(zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, zzz1125, zzz1126, zzz1127, zzz1128, zzz1129, Succ(zzz11300), Zero, bd) → new_mkVBalBranch3MkVBalBranch119(zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, zzz1125, zzz1126, zzz1127, zzz1128, zzz1129, Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat2(Succ(new_primPlusNat3(new_primPlusNat1(zzz1121), zzz1121)), zzz1121)), zzz1121))), bd)
new_mkVBalBranch3MkVBalBranch118(zzz498, zzz499, zzz500, zzz501, zzz502, zzz503, zzz504, zzz505, zzz506, zzz507, Succ(zzz8040), bg) → new_mkVBalBranch3MkVBalBranch120(zzz498, zzz499, zzz500, zzz501, zzz502, zzz503, zzz504, Zero, zzz505, zzz506, zzz507, Succ(Zero), Succ(zzz8040), bg)
new_mkVBalBranch3MkVBalBranch216(zzz1105, zzz1106, zzz1107, zzz1108, zzz1109, zzz1110, zzz1111, zzz1112, zzz1113, zzz1114, zzz1115, Zero, Zero, ba) → new_mkVBalBranch3MkVBalBranch222(zzz1105, zzz1106, zzz1107, zzz1108, zzz1109, zzz1110, zzz1111, zzz1112, zzz1113, zzz1114, zzz1115, ba)
new_mkVBalBranch3MkVBalBranch119(zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, zzz1125, zzz1126, zzz1127, zzz1128, zzz1129, Succ(zzz12130), bd) → new_mkVBalBranch3MkVBalBranch120(zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, zzz1125, Succ(zzz1126), zzz1127, zzz1128, zzz1129, Succ(Succ(zzz1126)), Succ(zzz12130), bd)
new_mkVBalBranch3MkVBalBranch18(z0, z1, z2, z3, z4, z5, z6, z7, z8, z9, Succ(Succ(Succ(Succ(Succ(Zero))))), z11) → new_mkVBalBranch3MkVBalBranch115(z0, z1, Zero, z2, z3, z4, z5, z6, z7, z8, z9, Succ(Succ(Succ(Succ(Succ(Zero))))), Succ(z6), z11)
Used ordering: Polynomial interpretation [25]:

POL(Branch(x1, x2, x3, x4, x5)) = x1 + x2 + x3 + x4 + x5   
POL(Neg(x1)) = 0   
POL(Pos(x1)) = 1 + x1   
POL(Succ(x1)) = 0   
POL(Zero) = 1   
POL(new_mkVBalBranch0(x1, x2, x3, x4)) = x2   
POL(new_mkVBalBranch3MkVBalBranch110(x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12, x13)) = x10   
POL(new_mkVBalBranch3MkVBalBranch115(x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12, x13, x14)) = x10   
POL(new_mkVBalBranch3MkVBalBranch116(x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12)) = x7 + x9   
POL(new_mkVBalBranch3MkVBalBranch117(x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12)) = x9   
POL(new_mkVBalBranch3MkVBalBranch118(x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12)) = x6 + x9   
POL(new_mkVBalBranch3MkVBalBranch119(x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12, x13)) = x10 + x6   
POL(new_mkVBalBranch3MkVBalBranch120(x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12, x13, x14)) = x10   
POL(new_mkVBalBranch3MkVBalBranch121(x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12)) = x6 + x9   
POL(new_mkVBalBranch3MkVBalBranch18(x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12)) = x8 + x9   
POL(new_mkVBalBranch3MkVBalBranch19(x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12, x13)) = 1 + x10 + x7   
POL(new_mkVBalBranch3MkVBalBranch215(x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12, x13)) = 1 + x10 + x6 + x7 + x9   
POL(new_mkVBalBranch3MkVBalBranch216(x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12, x13, x14)) = 1 + x10 + x3 + x6 + x7 + x9   
POL(new_mkVBalBranch3MkVBalBranch217(x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12, x13)) = 1 + x3 + x6 + x7 + x8 + x9   
POL(new_mkVBalBranch3MkVBalBranch218(x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12)) = x10 + x3 + x7 + x9   
POL(new_mkVBalBranch3MkVBalBranch222(x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12)) = 1 + x10 + x3 + x7   
POL(new_mkVBalBranch3MkVBalBranch223(x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12, x13)) = x10 + x6 + x7 + x9   
POL(new_mkVBalBranch3MkVBalBranch224(x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12, x13, x14)) = x10 + x3 + x6 + x7 + x9   
POL(new_mkVBalBranch3MkVBalBranch225(x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12, x13)) = x3 + x6 + x7 + x8 + x9   
POL(new_mkVBalBranch3MkVBalBranch227(x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12)) = x10 + x6 + x7 + x9   
POL(new_mkVBalBranch3MkVBalBranch229(x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12)) = x10 + x3 + x6   
POL(new_mkVBalBranch3MkVBalBranch230(x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11)) = x3 + x6 + x7 + x8 + x9   
POL(new_mkVBalBranch3MkVBalBranch233(x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11)) = 1 + x6 + x7 + x9   
POL(new_primPlusNat1(x1)) = 1 + x1   
POL(new_primPlusNat2(x1, x2)) = x2   
POL(new_primPlusNat3(x1, x2)) = 1 + 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
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                    ↳ DependencyGraphProof
                                      ↳ QDP
                                        ↳ Rewriting
                                          ↳ QDP
                                            ↳ Rewriting
                                              ↳ QDP
                                                ↳ Rewriting
                                                  ↳ QDP
                                                    ↳ Rewriting
                                                      ↳ QDP
                                                        ↳ Rewriting
                                                          ↳ QDP
                                                            ↳ Rewriting
                                                              ↳ QDP
                                                                ↳ Rewriting
                                                                  ↳ QDP
                                                                    ↳ Rewriting
                                                                      ↳ QDP
                                                                        ↳ Rewriting
                                                                          ↳ QDP
                                                                            ↳ Rewriting
                                                                              ↳ QDP
                                                                                ↳ Rewriting
                                                                                  ↳ QDP
                                                                                    ↳ Rewriting
                                                                                      ↳ QDP
                                                                                        ↳ Rewriting
                                                                                          ↳ QDP
                                                                                            ↳ Rewriting
                                                                                              ↳ QDP
                                                                                                ↳ Rewriting
                                                                                                  ↳ QDP
                                                                                                    ↳ Rewriting
                                                                                                      ↳ QDP
                                                                                                        ↳ Rewriting
                                                                                                          ↳ QDP
                                                                                                            ↳ UsableRulesProof
                                                                                                              ↳ QDP
                                                                                                                ↳ QReductionProof
                                                                                                                  ↳ QDP
                                                                                                                    ↳ Rewriting
                                                                                                                      ↳ QDP
                                                                                                                        ↳ Rewriting
                                                                                                                          ↳ QDP
                                                                                                                            ↳ DependencyGraphProof
                                                                                                                              ↳ QDP
                                                                                                                                ↳ Rewriting
                                                                                                                                  ↳ QDP
                                                                                                                                    ↳ Rewriting
                                                                                                                                      ↳ QDP
                                                                                                                                        ↳ DependencyGraphProof
                                                                                                                                          ↳ QDP
                                                                                                                                            ↳ Rewriting
                                                                                                                                              ↳ QDP
                                                                                                                                                ↳ Rewriting
                                                                                                                                                  ↳ QDP
                                                                                                                                                    ↳ Rewriting
                                                                                                                                                      ↳ QDP
                                                                                                                                                        ↳ Rewriting
                                                                                                                                                          ↳ QDP
                                                                                                                                                            ↳ Rewriting
                                                                                                                                                              ↳ QDP
                                                                                                                                                                ↳ Rewriting
                                                                                                                                                                  ↳ QDP
                                                                                                                                                                    ↳ Rewriting
                                                                                                                                                                      ↳ QDP
                                                                                                                                                                        ↳ Rewriting
                                                                                                                                                                          ↳ QDP
                                                                                                                                                                            ↳ Rewriting
                                                                                                                                                                              ↳ QDP
                                                                                                                                                                                ↳ Rewriting
                                                                                                                                                                                  ↳ QDP
                                                                                                                                                                                    ↳ Rewriting
                                                                                                                                                                                      ↳ QDP
                                                                                                                                                                                        ↳ Rewriting
                                                                                                                                                                                          ↳ QDP
                                                                                                                                                                                            ↳ UsableRulesProof
                                                                                                                                                                                              ↳ QDP
                                                                                                                                                                                                ↳ QReductionProof
                                                                                                                                                                                                  ↳ QDP
                                                                                                                                                                                                    ↳ Rewriting
                                                                                                                                                                                                      ↳ QDP
                                                                                                                                                                                                        ↳ Rewriting
                                                                                                                                                                                                          ↳ QDP
                                                                                                                                                                                                            ↳ Rewriting
                                                                                                                                                                                                              ↳ QDP
                                                                                                                                                                                                                ↳ Rewriting
                                                                                                                                                                                                                  ↳ QDP
                                                                                                                                                                                                                    ↳ Rewriting
                                                                                                                                                                                                                      ↳ QDP
                                                                                                                                                                                                                        ↳ Rewriting
                                                                                                                                                                                                                          ↳ QDP
                                                                                                                                                                                                                            ↳ Rewriting
                                                                                                                                                                                                                              ↳ QDP
                                                                                                                                                                                                                                ↳ Rewriting
                                                                                                                                                                                                                                  ↳ QDP
                                                                                                                                                                                                                                    ↳ Rewriting
                                                                                                                                                                                                                                      ↳ QDP
                                                                                                                                                                                                                                        ↳ Rewriting
                                                                                                                                                                                                                                          ↳ QDP
                                                                                                                                                                                                                                            ↳ Rewriting
                                                                                                                                                                                                                                              ↳ QDP
                                                                                                                                                                                                                                                ↳ Rewriting
                                                                                                                                                                                                                                                  ↳ QDP
                                                                                                                                                                                                                                                    ↳ Rewriting
                                                                                                                                                                                                                                                      ↳ QDP
                                                                                                                                                                                                                                                        ↳ Rewriting
                                                                                                                                                                                                                                                          ↳ QDP
                                                                                                                                                                                                                                                            ↳ DependencyGraphProof
                                                                                                                                                                                                                                                              ↳ QDP
                                                                                                                                                                                                                                                                ↳ Rewriting
                                                                                                                                                                                                                                                                  ↳ QDP
                                                                                                                                                                                                                                                                    ↳ Rewriting
                                                                                                                                                                                                                                                                      ↳ QDP
                                                                                                                                                                                                                                                                        ↳ Rewriting
                                                                                                                                                                                                                                                                          ↳ QDP
                                                                                                                                                                                                                                                                            ↳ Rewriting
                                                                                                                                                                                                                                                                              ↳ QDP
                                                                                                                                                                                                                                                                                ↳ Rewriting
                                                                                                                                                                                                                                                                                  ↳ QDP
                                                                                                                                                                                                                                                                                    ↳ Rewriting
                                                                                                                                                                                                                                                                                      ↳ QDP
                                                                                                                                                                                                                                                                                        ↳ DependencyGraphProof
                                                                                                                                                                                                                                                                                          ↳ QDP
                                                                                                                                                                                                                                                                                            ↳ Rewriting
                                                                                                                                                                                                                                                                                              ↳ QDP
                                                                                                                                                                                                                                                                                                ↳ DependencyGraphProof
                                                                                                                                                                                                                                                                                                  ↳ QDP
                                                                                                                                                                                                                                                                                                    ↳ Rewriting
                                                                                                                                                                                                                                                                                                      ↳ QDP
                                                                                                                                                                                                                                                                                                        ↳ DependencyGraphProof
                                                                                                                                                                                                                                                                                                          ↳ QDP
                                                                                                                                                                                                                                                                                                            ↳ Rewriting
                                                                                                                                                                                                                                                                                                              ↳ QDP
                                                                                                                                                                                                                                                                                                                ↳ Rewriting
                                                                                                                                                                                                                                                                                                                  ↳ QDP
                                                                                                                                                                                                                                                                                                                    ↳ Rewriting
                                                                                                                                                                                                                                                                                                                      ↳ QDP
                                                                                                                                                                                                                                                                                                                        ↳ Rewriting
                                                                                                                                                                                                                                                                                                                          ↳ QDP
                                                                                                                                                                                                                                                                                                                            ↳ Instantiation
                                                                                                                                                                                                                                                                                                                              ↳ QDP
                                                                                                                                                                                                                                                                                                                                ↳ QDPOrderProof
                                                                                                                                                                                                                                                                                                                                  ↳ QDP
                                                                                                                                                                                                                                                                                                                                    ↳ DependencyGraphProof
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP

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

new_mkVBalBranch3MkVBalBranch225(zzz498, zzz499, zzz500, zzz501, zzz502, zzz503, zzz504, zzz505, zzz506, zzz507, Zero, Zero, bg) → new_mkVBalBranch3MkVBalBranch230(zzz498, zzz499, zzz500, zzz501, zzz502, zzz503, zzz504, zzz505, zzz506, zzz507, bg)
new_mkVBalBranch3MkVBalBranch215(zzz340, zzz341, Pos(Succ(Succ(zzz342000))), zzz343, zzz344, zzz510, zzz511, Succ(zzz512000), zzz513, zzz514, zzz31, Succ(Succ(zzz6600)), h) → new_mkVBalBranch3MkVBalBranch216(zzz340, zzz341, Succ(zzz342000), zzz343, zzz344, zzz510, zzz511, zzz512000, zzz513, zzz514, zzz31, Succ(Succ(new_primPlusNat2(zzz6600, zzz512000))), zzz342000, h)
new_mkVBalBranch0(zzz31, Branch(zzz510, zzz511, Neg(Zero), zzz513, zzz514), Branch(zzz340, zzz341, Pos(Succ(zzz34200)), zzz343, zzz344), h) → new_mkVBalBranch0(zzz31, Branch(zzz510, zzz511, Neg(Zero), zzz513, zzz514), zzz343, h)
new_mkVBalBranch3MkVBalBranch223(zzz340, zzz341, Neg(Succ(Succ(Succ(zzz3420000)))), zzz343, zzz344, zzz510, zzz511, Zero, zzz513, zzz514, zzz31, Succ(Succ(zzz6700)), h) → new_mkVBalBranch3MkVBalBranch225(zzz340, zzz341, Succ(Succ(zzz3420000)), zzz343, zzz344, zzz510, zzz511, zzz513, zzz514, zzz31, Succ(zzz3420000), Succ(zzz6700), h)
new_mkVBalBranch3MkVBalBranch120(zzz2050, zzz2051, zzz2052, zzz2053, zzz2054, zzz2055, zzz2056, zzz2057, zzz2058, zzz2059, zzz2060, Zero, Succ(zzz20620), be) → new_mkVBalBranch0(zzz2060, zzz2059, Branch(zzz2050, zzz2051, Neg(Succ(zzz2052)), zzz2053, zzz2054), be)
new_mkVBalBranch0(zzz31, Branch(zzz510, zzz511, Pos(Zero), zzz513, zzz514), Branch(zzz340, zzz341, Pos(Succ(zzz34200)), zzz343, zzz344), h) → new_mkVBalBranch0(zzz31, Branch(zzz510, zzz511, Pos(Zero), zzz513, zzz514), zzz343, h)
new_mkVBalBranch3MkVBalBranch121(zzz473, zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, zzz481, zzz482, Succ(zzz7390), bh) → new_mkVBalBranch3MkVBalBranch115(zzz473, zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, Zero, zzz480, zzz481, zzz482, Succ(zzz7390), Succ(Zero), bh)
new_mkVBalBranch0(zzz31, Branch(zzz510, zzz511, Pos(Succ(zzz51200)), zzz513, zzz514), Branch(zzz340, zzz341, zzz342, zzz343, zzz344), h) → new_mkVBalBranch3MkVBalBranch215(zzz340, zzz341, zzz342, zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat3(new_primPlusNat1(zzz51200), zzz51200)), zzz51200))), h)
new_mkVBalBranch3MkVBalBranch215(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, Succ(zzz660), h) → new_mkVBalBranch3MkVBalBranch19(zzz340, zzz341, zzz34200, zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat2(Succ(new_primPlusNat3(new_primPlusNat1(zzz34200), zzz34200)), zzz34200)), zzz34200))), h)
new_mkVBalBranch3MkVBalBranch223(zzz340, zzz341, Neg(Succ(Succ(Zero))), zzz343, zzz344, zzz510, zzz511, Succ(zzz512000), zzz513, zzz514, zzz31, Succ(Succ(zzz6700)), h) → new_mkVBalBranch3MkVBalBranch224(zzz340, zzz341, Succ(Zero), zzz343, zzz344, zzz510, zzz511, zzz512000, zzz513, zzz514, zzz31, Zero, Succ(Succ(new_primPlusNat2(zzz6700, zzz512000))), h)
new_mkVBalBranch3MkVBalBranch230(zzz498, zzz499, zzz500, zzz501, zzz502, zzz503, zzz504, zzz505, zzz506, zzz507, bg) → new_mkVBalBranch3MkVBalBranch118(zzz498, zzz499, zzz500, zzz501, zzz502, zzz503, zzz504, zzz505, zzz506, zzz507, Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat2(Succ(new_primPlusNat3(new_primPlusNat1(zzz500), zzz500)), zzz500)), zzz500))), bg)
new_mkVBalBranch3MkVBalBranch215(zzz340, zzz341, Pos(Succ(Succ(zzz342000))), zzz343, zzz344, zzz510, zzz511, Zero, zzz513, zzz514, zzz31, Succ(Succ(zzz6600)), h) → new_mkVBalBranch3MkVBalBranch217(zzz340, zzz341, Succ(zzz342000), zzz343, zzz344, zzz510, zzz511, zzz513, zzz514, zzz31, Succ(zzz6600), zzz342000, h)
new_mkVBalBranch0(zzz31, Branch(zzz510, zzz511, Neg(Zero), zzz513, zzz514), Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), h) → new_mkVBalBranch3MkVBalBranch117(zzz340, zzz341, zzz34200, zzz343, zzz344, zzz510, zzz511, zzz513, zzz514, zzz31, Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat2(Succ(new_primPlusNat3(new_primPlusNat1(zzz34200), zzz34200)), zzz34200)), zzz34200))), h)
new_mkVBalBranch3MkVBalBranch117(zzz340, zzz341, zzz34200, zzz343, zzz344, zzz510, zzz511, zzz513, zzz514, zzz31, Succ(zzz1240), h) → new_mkVBalBranch0(zzz31, zzz514, Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), h)
new_mkVBalBranch3MkVBalBranch120(zzz2050, zzz2051, zzz2052, zzz2053, zzz2054, zzz2055, zzz2056, zzz2057, zzz2058, zzz2059, zzz2060, Succ(zzz20610), Succ(zzz20620), be) → new_mkVBalBranch3MkVBalBranch120(zzz2050, zzz2051, zzz2052, zzz2053, zzz2054, zzz2055, zzz2056, zzz2057, zzz2058, zzz2059, zzz2060, zzz20610, zzz20620, be)
new_mkVBalBranch3MkVBalBranch217(zzz473, zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, zzz481, zzz482, Zero, Zero, bh) → new_mkVBalBranch3MkVBalBranch233(zzz473, zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, zzz481, zzz482, bh)
new_mkVBalBranch3MkVBalBranch224(zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, zzz1125, zzz1126, zzz1127, zzz1128, zzz1129, Succ(zzz11300), Succ(zzz11310), bd) → new_mkVBalBranch3MkVBalBranch224(zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, zzz1125, zzz1126, zzz1127, zzz1128, zzz1129, zzz11300, zzz11310, bd)
new_mkVBalBranch3MkVBalBranch229(zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, zzz1125, zzz1126, zzz1127, zzz1128, zzz1129, bd) → new_mkVBalBranch3MkVBalBranch119(zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, zzz1125, zzz1126, zzz1127, zzz1128, zzz1129, Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat2(Succ(new_primPlusNat3(new_primPlusNat1(zzz1121), zzz1121)), zzz1121)), zzz1121))), bd)
new_mkVBalBranch3MkVBalBranch216(zzz1105, zzz1106, zzz1107, zzz1108, zzz1109, zzz1110, zzz1111, zzz1112, zzz1113, zzz1114, zzz1115, Succ(zzz11160), Succ(zzz11170), ba) → new_mkVBalBranch3MkVBalBranch216(zzz1105, zzz1106, zzz1107, zzz1108, zzz1109, zzz1110, zzz1111, zzz1112, zzz1113, zzz1114, zzz1115, zzz11160, zzz11170, ba)
new_mkVBalBranch3MkVBalBranch223(zzz340, zzz341, Pos(zzz3420), zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, Succ(zzz670), h) → new_mkVBalBranch0(zzz31, Branch(zzz510, zzz511, Neg(Succ(zzz51200)), zzz513, zzz514), zzz343, h)
new_mkVBalBranch3MkVBalBranch217(zzz473, zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, zzz481, zzz482, Zero, Succ(zzz4840), bh) → new_mkVBalBranch0(zzz482, Branch(zzz478, zzz479, Pos(Succ(Zero)), zzz480, zzz481), zzz476, bh)
new_mkVBalBranch3MkVBalBranch218(zzz461, zzz462, zzz463, zzz464, zzz465, zzz466, zzz467, zzz468, zzz469, zzz470, zzz471, bb) → new_mkVBalBranch3MkVBalBranch110(zzz461, zzz462, zzz463, zzz464, zzz465, zzz466, zzz467, zzz468, zzz469, zzz470, zzz471, Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat2(Succ(new_primPlusNat3(new_primPlusNat1(zzz463), zzz463)), zzz463)), zzz463))), bb)
new_mkVBalBranch3MkVBalBranch225(zzz498, zzz499, zzz500, zzz501, zzz502, zzz503, zzz504, zzz505, zzz506, zzz507, Succ(zzz5080), Succ(zzz5090), bg) → new_mkVBalBranch3MkVBalBranch225(zzz498, zzz499, zzz500, zzz501, zzz502, zzz503, zzz504, zzz505, zzz506, zzz507, zzz5080, zzz5090, bg)
new_mkVBalBranch3MkVBalBranch110(zzz461, zzz462, zzz463, zzz464, zzz465, zzz466, zzz467, zzz468, zzz469, zzz470, zzz471, Succ(zzz5800), bb) → new_mkVBalBranch3MkVBalBranch115(zzz461, zzz462, zzz463, zzz464, zzz465, zzz466, zzz467, Succ(zzz468), zzz469, zzz470, zzz471, Succ(zzz5800), Succ(Succ(zzz468)), bb)
new_mkVBalBranch3MkVBalBranch227(zzz486, zzz487, zzz488, zzz489, zzz490, zzz491, zzz492, zzz493, zzz494, zzz495, zzz496, bf) → new_mkVBalBranch0(zzz496, Branch(zzz491, zzz492, Neg(Succ(Succ(zzz493))), zzz494, zzz495), zzz489, bf)
new_mkVBalBranch3MkVBalBranch224(zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, zzz1125, zzz1126, zzz1127, zzz1128, zzz1129, Zero, Succ(zzz11310), bd) → new_mkVBalBranch3MkVBalBranch227(zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, zzz1125, zzz1126, zzz1127, zzz1128, zzz1129, bd)
new_mkVBalBranch3MkVBalBranch224(zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, zzz1125, zzz1126, zzz1127, zzz1128, zzz1129, Zero, Zero, bd) → new_mkVBalBranch3MkVBalBranch229(zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, zzz1125, zzz1126, zzz1127, zzz1128, zzz1129, bd)
new_mkVBalBranch3MkVBalBranch223(zzz340, zzz341, Neg(Zero), zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, Succ(zzz670), h) → new_mkVBalBranch0(zzz31, Branch(zzz510, zzz511, Neg(Succ(zzz51200)), zzz513, zzz514), zzz343, h)
new_mkVBalBranch3MkVBalBranch216(zzz1105, zzz1106, zzz1107, zzz1108, zzz1109, zzz1110, zzz1111, zzz1112, zzz1113, zzz1114, zzz1115, Zero, Succ(zzz11170), ba) → new_mkVBalBranch0(zzz1115, Branch(zzz1110, zzz1111, Pos(Succ(Succ(zzz1112))), zzz1113, zzz1114), zzz1108, ba)
new_mkVBalBranch3MkVBalBranch115(zzz1986, zzz1987, zzz1988, zzz1989, zzz1990, zzz1991, zzz1992, zzz1993, zzz1994, zzz1995, zzz1996, Zero, Succ(zzz19980), bc) → new_mkVBalBranch0(zzz1996, zzz1995, Branch(zzz1986, zzz1987, Pos(Succ(zzz1988)), zzz1989, zzz1990), bc)
new_mkVBalBranch3MkVBalBranch225(zzz498, zzz499, zzz500, zzz501, zzz502, zzz503, zzz504, zzz505, zzz506, zzz507, Succ(zzz5080), Zero, bg) → new_mkVBalBranch3MkVBalBranch118(zzz498, zzz499, zzz500, zzz501, zzz502, zzz503, zzz504, zzz505, zzz506, zzz507, Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat2(Succ(new_primPlusNat3(new_primPlusNat1(zzz500), zzz500)), zzz500)), zzz500))), bg)
new_mkVBalBranch3MkVBalBranch223(zzz340, zzz341, Neg(Succ(Succ(Succ(zzz3420000)))), zzz343, zzz344, zzz510, zzz511, Succ(zzz512000), zzz513, zzz514, zzz31, Succ(Succ(zzz6700)), h) → new_mkVBalBranch3MkVBalBranch224(zzz340, zzz341, Succ(Succ(zzz3420000)), zzz343, zzz344, zzz510, zzz511, zzz512000, zzz513, zzz514, zzz31, Succ(zzz3420000), Succ(Succ(new_primPlusNat2(zzz6700, zzz512000))), h)
new_mkVBalBranch3MkVBalBranch223(zzz340, zzz341, Neg(Succ(Succ(Zero))), zzz343, zzz344, zzz510, zzz511, Zero, zzz513, zzz514, zzz31, Succ(Succ(zzz6700)), h) → new_mkVBalBranch3MkVBalBranch225(zzz340, zzz341, Succ(Zero), zzz343, zzz344, zzz510, zzz511, zzz513, zzz514, zzz31, Zero, Succ(zzz6700), h)
new_mkVBalBranch3MkVBalBranch115(zzz1986, zzz1987, zzz1988, zzz1989, zzz1990, zzz1991, zzz1992, zzz1993, zzz1994, zzz1995, zzz1996, Succ(zzz19970), Succ(zzz19980), bc) → new_mkVBalBranch3MkVBalBranch115(zzz1986, zzz1987, zzz1988, zzz1989, zzz1990, zzz1991, zzz1992, zzz1993, zzz1994, zzz1995, zzz1996, zzz19970, zzz19980, bc)
new_mkVBalBranch3MkVBalBranch224(zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, zzz1125, zzz1126, zzz1127, zzz1128, zzz1129, Succ(zzz11300), Zero, bd) → new_mkVBalBranch3MkVBalBranch119(zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, zzz1125, zzz1126, zzz1127, zzz1128, zzz1129, Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat2(Succ(new_primPlusNat3(new_primPlusNat1(zzz1121), zzz1121)), zzz1121)), zzz1121))), bd)
new_mkVBalBranch3MkVBalBranch118(zzz498, zzz499, zzz500, zzz501, zzz502, zzz503, zzz504, zzz505, zzz506, zzz507, Succ(zzz8040), bg) → new_mkVBalBranch3MkVBalBranch120(zzz498, zzz499, zzz500, zzz501, zzz502, zzz503, zzz504, Zero, zzz505, zzz506, zzz507, Succ(Zero), Succ(zzz8040), bg)
new_mkVBalBranch3MkVBalBranch217(zzz473, zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, zzz481, zzz482, Succ(zzz4830), Succ(zzz4840), bh) → new_mkVBalBranch3MkVBalBranch217(zzz473, zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, zzz481, zzz482, zzz4830, zzz4840, bh)
new_mkVBalBranch3MkVBalBranch116(zzz340, zzz341, zzz34200, zzz343, zzz344, zzz510, zzz511, zzz513, zzz514, zzz31, Succ(zzz1200), h) → new_mkVBalBranch0(zzz31, zzz514, Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), h)
new_mkVBalBranch3MkVBalBranch216(zzz1105, zzz1106, zzz1107, zzz1108, zzz1109, zzz1110, zzz1111, zzz1112, zzz1113, zzz1114, zzz1115, Zero, Zero, ba) → new_mkVBalBranch3MkVBalBranch222(zzz1105, zzz1106, zzz1107, zzz1108, zzz1109, zzz1110, zzz1111, zzz1112, zzz1113, zzz1114, zzz1115, ba)
new_mkVBalBranch3MkVBalBranch225(zzz498, zzz499, zzz500, zzz501, zzz502, zzz503, zzz504, zzz505, zzz506, zzz507, Zero, Succ(zzz5090), bg) → new_mkVBalBranch0(zzz507, Branch(zzz503, zzz504, Neg(Succ(Zero)), zzz505, zzz506), zzz501, bg)
new_mkVBalBranch0(zzz31, Branch(zzz510, zzz511, Neg(Succ(zzz51200)), zzz513, zzz514), Branch(zzz340, zzz341, zzz342, zzz343, zzz344), h) → new_mkVBalBranch3MkVBalBranch223(zzz340, zzz341, zzz342, zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat3(new_primPlusNat1(zzz51200), zzz51200)), zzz51200))), h)
new_mkVBalBranch3MkVBalBranch119(zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, zzz1125, zzz1126, zzz1127, zzz1128, zzz1129, Succ(zzz12130), bd) → new_mkVBalBranch3MkVBalBranch120(zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, zzz1125, Succ(zzz1126), zzz1127, zzz1128, zzz1129, Succ(Succ(zzz1126)), Succ(zzz12130), bd)
new_mkVBalBranch3MkVBalBranch223(zzz340, zzz341, Neg(Succ(Zero)), zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, Succ(zzz670), h) → new_mkVBalBranch0(zzz31, Branch(zzz510, zzz511, Neg(Succ(zzz51200)), zzz513, zzz514), zzz343, h)
new_mkVBalBranch3MkVBalBranch18(z0, z1, z2, z3, z4, z5, z6, z7, z8, z9, Succ(Succ(Succ(Succ(Succ(Zero))))), z11) → new_mkVBalBranch3MkVBalBranch115(z0, z1, Zero, z2, z3, z4, z5, z6, z7, z8, z9, Succ(Succ(Succ(Succ(Succ(Zero))))), Succ(z6), z11)

The TRS R consists of the following rules:

new_primPlusNat1(Zero) → Zero
new_primPlusNat1(Succ(zzz62000)) → Succ(Succ(new_primPlusNat1(zzz62000)))
new_primPlusNat3(zzz90, Succ(zzz910)) → Succ(Succ(new_primPlusNat2(zzz90, zzz910)))
new_primPlusNat3(zzz90, Zero) → Succ(zzz90)
new_primPlusNat2(Succ(zzz900), Succ(zzz9100)) → Succ(Succ(new_primPlusNat2(zzz900, zzz9100)))
new_primPlusNat2(Zero, Succ(zzz9100)) → Succ(zzz9100)
new_primPlusNat2(Zero, Zero) → Zero
new_primPlusNat2(Succ(zzz900), Zero) → Succ(zzz900)

The set Q consists of the following terms:

new_primPlusNat2(Zero, Succ(x0))
new_primPlusNat3(x0, Succ(x1))
new_primPlusNat2(Succ(x0), Succ(x1))
new_primPlusNat3(x0, Zero)
new_primPlusNat1(Zero)
new_primPlusNat2(Zero, Zero)
new_primPlusNat1(Succ(x0))
new_primPlusNat2(Succ(x0), Zero)

We have to consider all minimal (P,Q,R)-chains.
The approximation of the Dependency Graph [15,17,22] contains 5 SCCs 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
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                    ↳ DependencyGraphProof
                                      ↳ QDP
                                        ↳ Rewriting
                                          ↳ QDP
                                            ↳ Rewriting
                                              ↳ QDP
                                                ↳ Rewriting
                                                  ↳ QDP
                                                    ↳ Rewriting
                                                      ↳ QDP
                                                        ↳ Rewriting
                                                          ↳ QDP
                                                            ↳ Rewriting
                                                              ↳ QDP
                                                                ↳ Rewriting
                                                                  ↳ QDP
                                                                    ↳ Rewriting
                                                                      ↳ QDP
                                                                        ↳ Rewriting
                                                                          ↳ QDP
                                                                            ↳ Rewriting
                                                                              ↳ QDP
                                                                                ↳ Rewriting
                                                                                  ↳ QDP
                                                                                    ↳ Rewriting
                                                                                      ↳ QDP
                                                                                        ↳ Rewriting
                                                                                          ↳ QDP
                                                                                            ↳ Rewriting
                                                                                              ↳ QDP
                                                                                                ↳ Rewriting
                                                                                                  ↳ QDP
                                                                                                    ↳ Rewriting
                                                                                                      ↳ QDP
                                                                                                        ↳ Rewriting
                                                                                                          ↳ QDP
                                                                                                            ↳ UsableRulesProof
                                                                                                              ↳ QDP
                                                                                                                ↳ QReductionProof
                                                                                                                  ↳ QDP
                                                                                                                    ↳ Rewriting
                                                                                                                      ↳ QDP
                                                                                                                        ↳ Rewriting
                                                                                                                          ↳ QDP
                                                                                                                            ↳ DependencyGraphProof
                                                                                                                              ↳ QDP
                                                                                                                                ↳ Rewriting
                                                                                                                                  ↳ QDP
                                                                                                                                    ↳ Rewriting
                                                                                                                                      ↳ QDP
                                                                                                                                        ↳ DependencyGraphProof
                                                                                                                                          ↳ QDP
                                                                                                                                            ↳ Rewriting
                                                                                                                                              ↳ QDP
                                                                                                                                                ↳ Rewriting
                                                                                                                                                  ↳ QDP
                                                                                                                                                    ↳ Rewriting
                                                                                                                                                      ↳ QDP
                                                                                                                                                        ↳ Rewriting
                                                                                                                                                          ↳ QDP
                                                                                                                                                            ↳ Rewriting
                                                                                                                                                              ↳ QDP
                                                                                                                                                                ↳ Rewriting
                                                                                                                                                                  ↳ QDP
                                                                                                                                                                    ↳ Rewriting
                                                                                                                                                                      ↳ QDP
                                                                                                                                                                        ↳ Rewriting
                                                                                                                                                                          ↳ QDP
                                                                                                                                                                            ↳ Rewriting
                                                                                                                                                                              ↳ QDP
                                                                                                                                                                                ↳ Rewriting
                                                                                                                                                                                  ↳ QDP
                                                                                                                                                                                    ↳ Rewriting
                                                                                                                                                                                      ↳ QDP
                                                                                                                                                                                        ↳ Rewriting
                                                                                                                                                                                          ↳ QDP
                                                                                                                                                                                            ↳ UsableRulesProof
                                                                                                                                                                                              ↳ QDP
                                                                                                                                                                                                ↳ QReductionProof
                                                                                                                                                                                                  ↳ QDP
                                                                                                                                                                                                    ↳ Rewriting
                                                                                                                                                                                                      ↳ QDP
                                                                                                                                                                                                        ↳ Rewriting
                                                                                                                                                                                                          ↳ QDP
                                                                                                                                                                                                            ↳ Rewriting
                                                                                                                                                                                                              ↳ QDP
                                                                                                                                                                                                                ↳ Rewriting
                                                                                                                                                                                                                  ↳ QDP
                                                                                                                                                                                                                    ↳ Rewriting
                                                                                                                                                                                                                      ↳ QDP
                                                                                                                                                                                                                        ↳ Rewriting
                                                                                                                                                                                                                          ↳ QDP
                                                                                                                                                                                                                            ↳ Rewriting
                                                                                                                                                                                                                              ↳ QDP
                                                                                                                                                                                                                                ↳ Rewriting
                                                                                                                                                                                                                                  ↳ QDP
                                                                                                                                                                                                                                    ↳ Rewriting
                                                                                                                                                                                                                                      ↳ QDP
                                                                                                                                                                                                                                        ↳ Rewriting
                                                                                                                                                                                                                                          ↳ QDP
                                                                                                                                                                                                                                            ↳ Rewriting
                                                                                                                                                                                                                                              ↳ QDP
                                                                                                                                                                                                                                                ↳ Rewriting
                                                                                                                                                                                                                                                  ↳ QDP
                                                                                                                                                                                                                                                    ↳ Rewriting
                                                                                                                                                                                                                                                      ↳ QDP
                                                                                                                                                                                                                                                        ↳ Rewriting
                                                                                                                                                                                                                                                          ↳ QDP
                                                                                                                                                                                                                                                            ↳ DependencyGraphProof
                                                                                                                                                                                                                                                              ↳ QDP
                                                                                                                                                                                                                                                                ↳ Rewriting
                                                                                                                                                                                                                                                                  ↳ QDP
                                                                                                                                                                                                                                                                    ↳ Rewriting
                                                                                                                                                                                                                                                                      ↳ QDP
                                                                                                                                                                                                                                                                        ↳ Rewriting
                                                                                                                                                                                                                                                                          ↳ QDP
                                                                                                                                                                                                                                                                            ↳ Rewriting
                                                                                                                                                                                                                                                                              ↳ QDP
                                                                                                                                                                                                                                                                                ↳ Rewriting
                                                                                                                                                                                                                                                                                  ↳ QDP
                                                                                                                                                                                                                                                                                    ↳ Rewriting
                                                                                                                                                                                                                                                                                      ↳ QDP
                                                                                                                                                                                                                                                                                        ↳ DependencyGraphProof
                                                                                                                                                                                                                                                                                          ↳ QDP
                                                                                                                                                                                                                                                                                            ↳ Rewriting
                                                                                                                                                                                                                                                                                              ↳ QDP
                                                                                                                                                                                                                                                                                                ↳ DependencyGraphProof
                                                                                                                                                                                                                                                                                                  ↳ QDP
                                                                                                                                                                                                                                                                                                    ↳ Rewriting
                                                                                                                                                                                                                                                                                                      ↳ QDP
                                                                                                                                                                                                                                                                                                        ↳ DependencyGraphProof
                                                                                                                                                                                                                                                                                                          ↳ QDP
                                                                                                                                                                                                                                                                                                            ↳ Rewriting
                                                                                                                                                                                                                                                                                                              ↳ QDP
                                                                                                                                                                                                                                                                                                                ↳ Rewriting
                                                                                                                                                                                                                                                                                                                  ↳ QDP
                                                                                                                                                                                                                                                                                                                    ↳ Rewriting
                                                                                                                                                                                                                                                                                                                      ↳ QDP
                                                                                                                                                                                                                                                                                                                        ↳ Rewriting
                                                                                                                                                                                                                                                                                                                          ↳ QDP
                                                                                                                                                                                                                                                                                                                            ↳ Instantiation
                                                                                                                                                                                                                                                                                                                              ↳ QDP
                                                                                                                                                                                                                                                                                                                                ↳ QDPOrderProof
                                                                                                                                                                                                                                                                                                                                  ↳ QDP
                                                                                                                                                                                                                                                                                                                                    ↳ DependencyGraphProof
                                                                                                                                                                                                                                                                                                                                      ↳ AND
                                                                                                                                                                                                                                                                                                                                        ↳ QDP
                                                                                                                                                                                                                                                                                                                                          ↳ UsableRulesProof
                                                                                                                                                                                                                                                                                                                                        ↳ QDP
                                                                                                                                                                                                                                                                                                                                        ↳ QDP
                                                                                                                                                                                                                                                                                                                                        ↳ QDP
                                                                                                                                                                                                                                                                                                                                        ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP

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

new_mkVBalBranch0(zzz31, Branch(zzz510, zzz511, Pos(Zero), zzz513, zzz514), Branch(zzz340, zzz341, Pos(Succ(zzz34200)), zzz343, zzz344), h) → new_mkVBalBranch0(zzz31, Branch(zzz510, zzz511, Pos(Zero), zzz513, zzz514), zzz343, h)

The TRS R consists of the following rules:

new_primPlusNat1(Zero) → Zero
new_primPlusNat1(Succ(zzz62000)) → Succ(Succ(new_primPlusNat1(zzz62000)))
new_primPlusNat3(zzz90, Succ(zzz910)) → Succ(Succ(new_primPlusNat2(zzz90, zzz910)))
new_primPlusNat3(zzz90, Zero) → Succ(zzz90)
new_primPlusNat2(Succ(zzz900), Succ(zzz9100)) → Succ(Succ(new_primPlusNat2(zzz900, zzz9100)))
new_primPlusNat2(Zero, Succ(zzz9100)) → Succ(zzz9100)
new_primPlusNat2(Zero, Zero) → Zero
new_primPlusNat2(Succ(zzz900), Zero) → Succ(zzz900)

The set Q consists of the following terms:

new_primPlusNat2(Zero, Succ(x0))
new_primPlusNat3(x0, Succ(x1))
new_primPlusNat2(Succ(x0), Succ(x1))
new_primPlusNat3(x0, Zero)
new_primPlusNat1(Zero)
new_primPlusNat2(Zero, Zero)
new_primPlusNat1(Succ(x0))
new_primPlusNat2(Succ(x0), Zero)

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

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

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

new_mkVBalBranch0(zzz31, Branch(zzz510, zzz511, Pos(Zero), zzz513, zzz514), Branch(zzz340, zzz341, Pos(Succ(zzz34200)), zzz343, zzz344), h) → new_mkVBalBranch0(zzz31, Branch(zzz510, zzz511, Pos(Zero), zzz513, zzz514), zzz343, h)

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

new_primPlusNat2(Zero, Succ(x0))
new_primPlusNat3(x0, Succ(x1))
new_primPlusNat2(Succ(x0), Succ(x1))
new_primPlusNat3(x0, Zero)
new_primPlusNat1(Zero)
new_primPlusNat2(Zero, Zero)
new_primPlusNat1(Succ(x0))
new_primPlusNat2(Succ(x0), Zero)

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

new_primPlusNat2(Zero, Succ(x0))
new_primPlusNat3(x0, Succ(x1))
new_primPlusNat2(Succ(x0), Succ(x1))
new_primPlusNat3(x0, Zero)
new_primPlusNat1(Zero)
new_primPlusNat2(Zero, Zero)
new_primPlusNat1(Succ(x0))
new_primPlusNat2(Succ(x0), 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
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                    ↳ DependencyGraphProof
                                      ↳ QDP
                                        ↳ Rewriting
                                          ↳ QDP
                                            ↳ Rewriting
                                              ↳ QDP
                                                ↳ Rewriting
                                                  ↳ QDP
                                                    ↳ Rewriting
                                                      ↳ QDP
                                                        ↳ Rewriting
                                                          ↳ QDP
                                                            ↳ Rewriting
                                                              ↳ QDP
                                                                ↳ Rewriting
                                                                  ↳ QDP
                                                                    ↳ Rewriting
                                                                      ↳ QDP
                                                                        ↳ Rewriting
                                                                          ↳ QDP
                                                                            ↳ Rewriting
                                                                              ↳ QDP
                                                                                ↳ Rewriting
                                                                                  ↳ QDP
                                                                                    ↳ Rewriting
                                                                                      ↳ QDP
                                                                                        ↳ Rewriting
                                                                                          ↳ QDP
                                                                                            ↳ Rewriting
                                                                                              ↳ QDP
                                                                                                ↳ Rewriting
                                                                                                  ↳ QDP
                                                                                                    ↳ Rewriting
                                                                                                      ↳ QDP
                                                                                                        ↳ Rewriting
                                                                                                          ↳ QDP
                                                                                                            ↳ UsableRulesProof
                                                                                                              ↳ QDP
                                                                                                                ↳ QReductionProof
                                                                                                                  ↳ QDP
                                                                                                                    ↳ Rewriting
                                                                                                                      ↳ QDP
                                                                                                                        ↳ Rewriting
                                                                                                                          ↳ QDP
                                                                                                                            ↳ DependencyGraphProof
                                                                                                                              ↳ QDP
                                                                                                                                ↳ Rewriting
                                                                                                                                  ↳ QDP
                                                                                                                                    ↳ Rewriting
                                                                                                                                      ↳ QDP
                                                                                                                                        ↳ DependencyGraphProof
                                                                                                                                          ↳ QDP
                                                                                                                                            ↳ Rewriting
                                                                                                                                              ↳ QDP
                                                                                                                                                ↳ Rewriting
                                                                                                                                                  ↳ QDP
                                                                                                                                                    ↳ Rewriting
                                                                                                                                                      ↳ QDP
                                                                                                                                                        ↳ Rewriting
                                                                                                                                                          ↳ QDP
                                                                                                                                                            ↳ Rewriting
                                                                                                                                                              ↳ QDP
                                                                                                                                                                ↳ Rewriting
                                                                                                                                                                  ↳ QDP
                                                                                                                                                                    ↳ Rewriting
                                                                                                                                                                      ↳ QDP
                                                                                                                                                                        ↳ Rewriting
                                                                                                                                                                          ↳ QDP
                                                                                                                                                                            ↳ Rewriting
                                                                                                                                                                              ↳ QDP
                                                                                                                                                                                ↳ Rewriting
                                                                                                                                                                                  ↳ QDP
                                                                                                                                                                                    ↳ Rewriting
                                                                                                                                                                                      ↳ QDP
                                                                                                                                                                                        ↳ Rewriting
                                                                                                                                                                                          ↳ QDP
                                                                                                                                                                                            ↳ UsableRulesProof
                                                                                                                                                                                              ↳ QDP
                                                                                                                                                                                                ↳ QReductionProof
                                                                                                                                                                                                  ↳ QDP
                                                                                                                                                                                                    ↳ Rewriting
                                                                                                                                                                                                      ↳ QDP
                                                                                                                                                                                                        ↳ Rewriting
                                                                                                                                                                                                          ↳ QDP
                                                                                                                                                                                                            ↳ Rewriting
                                                                                                                                                                                                              ↳ QDP
                                                                                                                                                                                                                ↳ Rewriting
                                                                                                                                                                                                                  ↳ QDP
                                                                                                                                                                                                                    ↳ Rewriting
                                                                                                                                                                                                                      ↳ QDP
                                                                                                                                                                                                                        ↳ Rewriting
                                                                                                                                                                                                                          ↳ QDP
                                                                                                                                                                                                                            ↳ Rewriting
                                                                                                                                                                                                                              ↳ QDP
                                                                                                                                                                                                                                ↳ Rewriting
                                                                                                                                                                                                                                  ↳ QDP
                                                                                                                                                                                                                                    ↳ Rewriting
                                                                                                                                                                                                                                      ↳ QDP
                                                                                                                                                                                                                                        ↳ Rewriting
                                                                                                                                                                                                                                          ↳ QDP
                                                                                                                                                                                                                                            ↳ Rewriting
                                                                                                                                                                                                                                              ↳ QDP
                                                                                                                                                                                                                                                ↳ Rewriting
                                                                                                                                                                                                                                                  ↳ QDP
                                                                                                                                                                                                                                                    ↳ Rewriting
                                                                                                                                                                                                                                                      ↳ QDP
                                                                                                                                                                                                                                                        ↳ Rewriting
                                                                                                                                                                                                                                                          ↳ QDP
                                                                                                                                                                                                                                                            ↳ DependencyGraphProof
                                                                                                                                                                                                                                                              ↳ QDP
                                                                                                                                                                                                                                                                ↳ Rewriting
                                                                                                                                                                                                                                                                  ↳ QDP
                                                                                                                                                                                                                                                                    ↳ Rewriting
                                                                                                                                                                                                                                                                      ↳ QDP
                                                                                                                                                                                                                                                                        ↳ Rewriting
                                                                                                                                                                                                                                                                          ↳ QDP
                                                                                                                                                                                                                                                                            ↳ Rewriting
                                                                                                                                                                                                                                                                              ↳ QDP
                                                                                                                                                                                                                                                                                ↳ Rewriting
                                                                                                                                                                                                                                                                                  ↳ QDP
                                                                                                                                                                                                                                                                                    ↳ Rewriting
                                                                                                                                                                                                                                                                                      ↳ QDP
                                                                                                                                                                                                                                                                                        ↳ DependencyGraphProof
                                                                                                                                                                                                                                                                                          ↳ QDP
                                                                                                                                                                                                                                                                                            ↳ Rewriting
                                                                                                                                                                                                                                                                                              ↳ QDP
                                                                                                                                                                                                                                                                                                ↳ DependencyGraphProof
                                                                                                                                                                                                                                                                                                  ↳ QDP
                                                                                                                                                                                                                                                                                                    ↳ Rewriting
                                                                                                                                                                                                                                                                                                      ↳ QDP
                                                                                                                                                                                                                                                                                                        ↳ DependencyGraphProof
                                                                                                                                                                                                                                                                                                          ↳ QDP
                                                                                                                                                                                                                                                                                                            ↳ Rewriting
                                                                                                                                                                                                                                                                                                              ↳ QDP
                                                                                                                                                                                                                                                                                                                ↳ Rewriting
                                                                                                                                                                                                                                                                                                                  ↳ QDP
                                                                                                                                                                                                                                                                                                                    ↳ Rewriting
                                                                                                                                                                                                                                                                                                                      ↳ QDP
                                                                                                                                                                                                                                                                                                                        ↳ Rewriting
                                                                                                                                                                                                                                                                                                                          ↳ QDP
                                                                                                                                                                                                                                                                                                                            ↳ Instantiation
                                                                                                                                                                                                                                                                                                                              ↳ QDP
                                                                                                                                                                                                                                                                                                                                ↳ QDPOrderProof
                                                                                                                                                                                                                                                                                                                                  ↳ QDP
                                                                                                                                                                                                                                                                                                                                    ↳ DependencyGraphProof
                                                                                                                                                                                                                                                                                                                                      ↳ AND
                                                                                                                                                                                                                                                                                                                                        ↳ QDP
                                                                                                                                                                                                                                                                                                                                          ↳ UsableRulesProof
                                                                                                                                                                                                                                                                                                                                            ↳ QDP
                                                                                                                                                                                                                                                                                                                                              ↳ QReductionProof
                                                                                                                                                                                                                                                                                                                                                ↳ QDP
                                                                                                                                                                                                                                                                                                                                                  ↳ QDPSizeChangeProof
                                                                                                                                                                                                                                                                                                                                        ↳ QDP
                                                                                                                                                                                                                                                                                                                                        ↳ QDP
                                                                                                                                                                                                                                                                                                                                        ↳ QDP
                                                                                                                                                                                                                                                                                                                                        ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP

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

new_mkVBalBranch0(zzz31, Branch(zzz510, zzz511, Pos(Zero), zzz513, zzz514), Branch(zzz340, zzz341, Pos(Succ(zzz34200)), zzz343, zzz344), h) → new_mkVBalBranch0(zzz31, Branch(zzz510, zzz511, Pos(Zero), zzz513, zzz514), 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
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                    ↳ DependencyGraphProof
                                      ↳ QDP
                                        ↳ Rewriting
                                          ↳ QDP
                                            ↳ Rewriting
                                              ↳ QDP
                                                ↳ Rewriting
                                                  ↳ QDP
                                                    ↳ Rewriting
                                                      ↳ QDP
                                                        ↳ Rewriting
                                                          ↳ QDP
                                                            ↳ Rewriting
                                                              ↳ QDP
                                                                ↳ Rewriting
                                                                  ↳ QDP
                                                                    ↳ Rewriting
                                                                      ↳ QDP
                                                                        ↳ Rewriting
                                                                          ↳ QDP
                                                                            ↳ Rewriting
                                                                              ↳ QDP
                                                                                ↳ Rewriting
                                                                                  ↳ QDP
                                                                                    ↳ Rewriting
                                                                                      ↳ QDP
                                                                                        ↳ Rewriting
                                                                                          ↳ QDP
                                                                                            ↳ Rewriting
                                                                                              ↳ QDP
                                                                                                ↳ Rewriting
                                                                                                  ↳ QDP
                                                                                                    ↳ Rewriting
                                                                                                      ↳ QDP
                                                                                                        ↳ Rewriting
                                                                                                          ↳ QDP
                                                                                                            ↳ UsableRulesProof
                                                                                                              ↳ QDP
                                                                                                                ↳ QReductionProof
                                                                                                                  ↳ QDP
                                                                                                                    ↳ Rewriting
                                                                                                                      ↳ QDP
                                                                                                                        ↳ Rewriting
                                                                                                                          ↳ QDP
                                                                                                                            ↳ DependencyGraphProof
                                                                                                                              ↳ QDP
                                                                                                                                ↳ Rewriting
                                                                                                                                  ↳ QDP
                                                                                                                                    ↳ Rewriting
                                                                                                                                      ↳ QDP
                                                                                                                                        ↳ DependencyGraphProof
                                                                                                                                          ↳ QDP
                                                                                                                                            ↳ Rewriting
                                                                                                                                              ↳ QDP
                                                                                                                                                ↳ Rewriting
                                                                                                                                                  ↳ QDP
                                                                                                                                                    ↳ Rewriting
                                                                                                                                                      ↳ QDP
                                                                                                                                                        ↳ Rewriting
                                                                                                                                                          ↳ QDP
                                                                                                                                                            ↳ Rewriting
                                                                                                                                                              ↳ QDP
                                                                                                                                                                ↳ Rewriting
                                                                                                                                                                  ↳ QDP
                                                                                                                                                                    ↳ Rewriting
                                                                                                                                                                      ↳ QDP
                                                                                                                                                                        ↳ Rewriting
                                                                                                                                                                          ↳ QDP
                                                                                                                                                                            ↳ Rewriting
                                                                                                                                                                              ↳ QDP
                                                                                                                                                                                ↳ Rewriting
                                                                                                                                                                                  ↳ QDP
                                                                                                                                                                                    ↳ Rewriting
                                                                                                                                                                                      ↳ QDP
                                                                                                                                                                                        ↳ Rewriting
                                                                                                                                                                                          ↳ QDP
                                                                                                                                                                                            ↳ UsableRulesProof
                                                                                                                                                                                              ↳ QDP
                                                                                                                                                                                                ↳ QReductionProof
                                                                                                                                                                                                  ↳ QDP
                                                                                                                                                                                                    ↳ Rewriting
                                                                                                                                                                                                      ↳ QDP
                                                                                                                                                                                                        ↳ Rewriting
                                                                                                                                                                                                          ↳ QDP
                                                                                                                                                                                                            ↳ Rewriting
                                                                                                                                                                                                              ↳ QDP
                                                                                                                                                                                                                ↳ Rewriting
                                                                                                                                                                                                                  ↳ QDP
                                                                                                                                                                                                                    ↳ Rewriting
                                                                                                                                                                                                                      ↳ QDP
                                                                                                                                                                                                                        ↳ Rewriting
                                                                                                                                                                                                                          ↳ QDP
                                                                                                                                                                                                                            ↳ Rewriting
                                                                                                                                                                                                                              ↳ QDP
                                                                                                                                                                                                                                ↳ Rewriting
                                                                                                                                                                                                                                  ↳ QDP
                                                                                                                                                                                                                                    ↳ Rewriting
                                                                                                                                                                                                                                      ↳ QDP
                                                                                                                                                                                                                                        ↳ Rewriting
                                                                                                                                                                                                                                          ↳ QDP
                                                                                                                                                                                                                                            ↳ Rewriting
                                                                                                                                                                                                                                              ↳ QDP
                                                                                                                                                                                                                                                ↳ Rewriting
                                                                                                                                                                                                                                                  ↳ QDP
                                                                                                                                                                                                                                                    ↳ Rewriting
                                                                                                                                                                                                                                                      ↳ QDP
                                                                                                                                                                                                                                                        ↳ Rewriting
                                                                                                                                                                                                                                                          ↳ QDP
                                                                                                                                                                                                                                                            ↳ DependencyGraphProof
                                                                                                                                                                                                                                                              ↳ QDP
                                                                                                                                                                                                                                                                ↳ Rewriting
                                                                                                                                                                                                                                                                  ↳ QDP
                                                                                                                                                                                                                                                                    ↳ Rewriting
                                                                                                                                                                                                                                                                      ↳ QDP
                                                                                                                                                                                                                                                                        ↳ Rewriting
                                                                                                                                                                                                                                                                          ↳ QDP
                                                                                                                                                                                                                                                                            ↳ Rewriting
                                                                                                                                                                                                                                                                              ↳ QDP
                                                                                                                                                                                                                                                                                ↳ Rewriting
                                                                                                                                                                                                                                                                                  ↳ QDP
                                                                                                                                                                                                                                                                                    ↳ Rewriting
                                                                                                                                                                                                                                                                                      ↳ QDP
                                                                                                                                                                                                                                                                                        ↳ DependencyGraphProof
                                                                                                                                                                                                                                                                                          ↳ QDP
                                                                                                                                                                                                                                                                                            ↳ Rewriting
                                                                                                                                                                                                                                                                                              ↳ QDP
                                                                                                                                                                                                                                                                                                ↳ DependencyGraphProof
                                                                                                                                                                                                                                                                                                  ↳ QDP
                                                                                                                                                                                                                                                                                                    ↳ Rewriting
                                                                                                                                                                                                                                                                                                      ↳ QDP
                                                                                                                                                                                                                                                                                                        ↳ DependencyGraphProof
                                                                                                                                                                                                                                                                                                          ↳ QDP
                                                                                                                                                                                                                                                                                                            ↳ Rewriting
                                                                                                                                                                                                                                                                                                              ↳ QDP
                                                                                                                                                                                                                                                                                                                ↳ Rewriting
                                                                                                                                                                                                                                                                                                                  ↳ QDP
                                                                                                                                                                                                                                                                                                                    ↳ Rewriting
                                                                                                                                                                                                                                                                                                                      ↳ QDP
                                                                                                                                                                                                                                                                                                                        ↳ Rewriting
                                                                                                                                                                                                                                                                                                                          ↳ QDP
                                                                                                                                                                                                                                                                                                                            ↳ Instantiation
                                                                                                                                                                                                                                                                                                                              ↳ QDP
                                                                                                                                                                                                                                                                                                                                ↳ QDPOrderProof
                                                                                                                                                                                                                                                                                                                                  ↳ QDP
                                                                                                                                                                                                                                                                                                                                    ↳ DependencyGraphProof
                                                                                                                                                                                                                                                                                                                                      ↳ AND
                                                                                                                                                                                                                                                                                                                                        ↳ QDP
                                                                                                                                                                                                                                                                                                                                        ↳ QDP
                                                                                                                                                                                                                                                                                                                                          ↳ QDPSizeChangeProof
                                                                                                                                                                                                                                                                                                                                        ↳ QDP
                                                                                                                                                                                                                                                                                                                                        ↳ QDP
                                                                                                                                                                                                                                                                                                                                        ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP

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

new_mkVBalBranch3MkVBalBranch216(zzz1105, zzz1106, zzz1107, zzz1108, zzz1109, zzz1110, zzz1111, zzz1112, zzz1113, zzz1114, zzz1115, Zero, Succ(zzz11170), ba) → new_mkVBalBranch0(zzz1115, Branch(zzz1110, zzz1111, Pos(Succ(Succ(zzz1112))), zzz1113, zzz1114), zzz1108, ba)
new_mkVBalBranch3MkVBalBranch215(zzz340, zzz341, Pos(Succ(Succ(zzz342000))), zzz343, zzz344, zzz510, zzz511, Succ(zzz512000), zzz513, zzz514, zzz31, Succ(Succ(zzz6600)), h) → new_mkVBalBranch3MkVBalBranch216(zzz340, zzz341, Succ(zzz342000), zzz343, zzz344, zzz510, zzz511, zzz512000, zzz513, zzz514, zzz31, Succ(Succ(new_primPlusNat2(zzz6600, zzz512000))), zzz342000, h)
new_mkVBalBranch3MkVBalBranch216(zzz1105, zzz1106, zzz1107, zzz1108, zzz1109, zzz1110, zzz1111, zzz1112, zzz1113, zzz1114, zzz1115, Succ(zzz11160), Succ(zzz11170), ba) → new_mkVBalBranch3MkVBalBranch216(zzz1105, zzz1106, zzz1107, zzz1108, zzz1109, zzz1110, zzz1111, zzz1112, zzz1113, zzz1114, zzz1115, zzz11160, zzz11170, ba)
new_mkVBalBranch3MkVBalBranch217(zzz473, zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, zzz481, zzz482, Zero, Succ(zzz4840), bh) → new_mkVBalBranch0(zzz482, Branch(zzz478, zzz479, Pos(Succ(Zero)), zzz480, zzz481), zzz476, bh)
new_mkVBalBranch0(zzz31, Branch(zzz510, zzz511, Pos(Succ(zzz51200)), zzz513, zzz514), Branch(zzz340, zzz341, zzz342, zzz343, zzz344), h) → new_mkVBalBranch3MkVBalBranch215(zzz340, zzz341, zzz342, zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat3(new_primPlusNat1(zzz51200), zzz51200)), zzz51200))), h)
new_mkVBalBranch3MkVBalBranch215(zzz340, zzz341, Pos(Succ(Succ(zzz342000))), zzz343, zzz344, zzz510, zzz511, Zero, zzz513, zzz514, zzz31, Succ(Succ(zzz6600)), h) → new_mkVBalBranch3MkVBalBranch217(zzz340, zzz341, Succ(zzz342000), zzz343, zzz344, zzz510, zzz511, zzz513, zzz514, zzz31, Succ(zzz6600), zzz342000, h)
new_mkVBalBranch3MkVBalBranch217(zzz473, zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, zzz481, zzz482, Succ(zzz4830), Succ(zzz4840), bh) → new_mkVBalBranch3MkVBalBranch217(zzz473, zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, zzz481, zzz482, zzz4830, zzz4840, bh)

The TRS R consists of the following rules:

new_primPlusNat1(Zero) → Zero
new_primPlusNat1(Succ(zzz62000)) → Succ(Succ(new_primPlusNat1(zzz62000)))
new_primPlusNat3(zzz90, Succ(zzz910)) → Succ(Succ(new_primPlusNat2(zzz90, zzz910)))
new_primPlusNat3(zzz90, Zero) → Succ(zzz90)
new_primPlusNat2(Succ(zzz900), Succ(zzz9100)) → Succ(Succ(new_primPlusNat2(zzz900, zzz9100)))
new_primPlusNat2(Zero, Succ(zzz9100)) → Succ(zzz9100)
new_primPlusNat2(Zero, Zero) → Zero
new_primPlusNat2(Succ(zzz900), Zero) → Succ(zzz900)

The set Q consists of the following terms:

new_primPlusNat2(Zero, Succ(x0))
new_primPlusNat3(x0, Succ(x1))
new_primPlusNat2(Succ(x0), Succ(x1))
new_primPlusNat3(x0, Zero)
new_primPlusNat1(Zero)
new_primPlusNat2(Zero, Zero)
new_primPlusNat1(Succ(x0))
new_primPlusNat2(Succ(x0), Zero)

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

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



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

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

new_mkVBalBranch3MkVBalBranch225(zzz498, zzz499, zzz500, zzz501, zzz502, zzz503, zzz504, zzz505, zzz506, zzz507, Zero, Zero, bg) → new_mkVBalBranch3MkVBalBranch230(zzz498, zzz499, zzz500, zzz501, zzz502, zzz503, zzz504, zzz505, zzz506, zzz507, bg)
new_mkVBalBranch3MkVBalBranch223(zzz340, zzz341, Neg(Succ(Succ(Succ(zzz3420000)))), zzz343, zzz344, zzz510, zzz511, Zero, zzz513, zzz514, zzz31, Succ(Succ(zzz6700)), h) → new_mkVBalBranch3MkVBalBranch225(zzz340, zzz341, Succ(Succ(zzz3420000)), zzz343, zzz344, zzz510, zzz511, zzz513, zzz514, zzz31, Succ(zzz3420000), Succ(zzz6700), h)
new_mkVBalBranch3MkVBalBranch120(zzz2050, zzz2051, zzz2052, zzz2053, zzz2054, zzz2055, zzz2056, zzz2057, zzz2058, zzz2059, zzz2060, Zero, Succ(zzz20620), be) → new_mkVBalBranch0(zzz2060, zzz2059, Branch(zzz2050, zzz2051, Neg(Succ(zzz2052)), zzz2053, zzz2054), be)
new_mkVBalBranch3MkVBalBranch223(zzz340, zzz341, Neg(Succ(Succ(Zero))), zzz343, zzz344, zzz510, zzz511, Succ(zzz512000), zzz513, zzz514, zzz31, Succ(Succ(zzz6700)), h) → new_mkVBalBranch3MkVBalBranch224(zzz340, zzz341, Succ(Zero), zzz343, zzz344, zzz510, zzz511, zzz512000, zzz513, zzz514, zzz31, Zero, Succ(Succ(new_primPlusNat2(zzz6700, zzz512000))), h)
new_mkVBalBranch3MkVBalBranch230(zzz498, zzz499, zzz500, zzz501, zzz502, zzz503, zzz504, zzz505, zzz506, zzz507, bg) → new_mkVBalBranch3MkVBalBranch118(zzz498, zzz499, zzz500, zzz501, zzz502, zzz503, zzz504, zzz505, zzz506, zzz507, Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat2(Succ(new_primPlusNat3(new_primPlusNat1(zzz500), zzz500)), zzz500)), zzz500))), bg)
new_mkVBalBranch0(zzz31, Branch(zzz510, zzz511, Neg(Zero), zzz513, zzz514), Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), h) → new_mkVBalBranch3MkVBalBranch117(zzz340, zzz341, zzz34200, zzz343, zzz344, zzz510, zzz511, zzz513, zzz514, zzz31, Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat2(Succ(new_primPlusNat3(new_primPlusNat1(zzz34200), zzz34200)), zzz34200)), zzz34200))), h)
new_mkVBalBranch3MkVBalBranch117(zzz340, zzz341, zzz34200, zzz343, zzz344, zzz510, zzz511, zzz513, zzz514, zzz31, Succ(zzz1240), h) → new_mkVBalBranch0(zzz31, zzz514, Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), h)
new_mkVBalBranch3MkVBalBranch120(zzz2050, zzz2051, zzz2052, zzz2053, zzz2054, zzz2055, zzz2056, zzz2057, zzz2058, zzz2059, zzz2060, Succ(zzz20610), Succ(zzz20620), be) → new_mkVBalBranch3MkVBalBranch120(zzz2050, zzz2051, zzz2052, zzz2053, zzz2054, zzz2055, zzz2056, zzz2057, zzz2058, zzz2059, zzz2060, zzz20610, zzz20620, be)
new_mkVBalBranch3MkVBalBranch224(zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, zzz1125, zzz1126, zzz1127, zzz1128, zzz1129, Succ(zzz11300), Succ(zzz11310), bd) → new_mkVBalBranch3MkVBalBranch224(zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, zzz1125, zzz1126, zzz1127, zzz1128, zzz1129, zzz11300, zzz11310, bd)
new_mkVBalBranch3MkVBalBranch229(zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, zzz1125, zzz1126, zzz1127, zzz1128, zzz1129, bd) → new_mkVBalBranch3MkVBalBranch119(zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, zzz1125, zzz1126, zzz1127, zzz1128, zzz1129, Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat2(Succ(new_primPlusNat3(new_primPlusNat1(zzz1121), zzz1121)), zzz1121)), zzz1121))), bd)
new_mkVBalBranch3MkVBalBranch223(zzz340, zzz341, Pos(zzz3420), zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, Succ(zzz670), h) → new_mkVBalBranch0(zzz31, Branch(zzz510, zzz511, Neg(Succ(zzz51200)), zzz513, zzz514), zzz343, h)
new_mkVBalBranch3MkVBalBranch225(zzz498, zzz499, zzz500, zzz501, zzz502, zzz503, zzz504, zzz505, zzz506, zzz507, Succ(zzz5080), Succ(zzz5090), bg) → new_mkVBalBranch3MkVBalBranch225(zzz498, zzz499, zzz500, zzz501, zzz502, zzz503, zzz504, zzz505, zzz506, zzz507, zzz5080, zzz5090, bg)
new_mkVBalBranch3MkVBalBranch227(zzz486, zzz487, zzz488, zzz489, zzz490, zzz491, zzz492, zzz493, zzz494, zzz495, zzz496, bf) → new_mkVBalBranch0(zzz496, Branch(zzz491, zzz492, Neg(Succ(Succ(zzz493))), zzz494, zzz495), zzz489, bf)
new_mkVBalBranch3MkVBalBranch224(zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, zzz1125, zzz1126, zzz1127, zzz1128, zzz1129, Zero, Succ(zzz11310), bd) → new_mkVBalBranch3MkVBalBranch227(zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, zzz1125, zzz1126, zzz1127, zzz1128, zzz1129, bd)
new_mkVBalBranch3MkVBalBranch223(zzz340, zzz341, Neg(Zero), zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, Succ(zzz670), h) → new_mkVBalBranch0(zzz31, Branch(zzz510, zzz511, Neg(Succ(zzz51200)), zzz513, zzz514), zzz343, h)
new_mkVBalBranch3MkVBalBranch224(zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, zzz1125, zzz1126, zzz1127, zzz1128, zzz1129, Zero, Zero, bd) → new_mkVBalBranch3MkVBalBranch229(zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, zzz1125, zzz1126, zzz1127, zzz1128, zzz1129, bd)
new_mkVBalBranch3MkVBalBranch225(zzz498, zzz499, zzz500, zzz501, zzz502, zzz503, zzz504, zzz505, zzz506, zzz507, Succ(zzz5080), Zero, bg) → new_mkVBalBranch3MkVBalBranch118(zzz498, zzz499, zzz500, zzz501, zzz502, zzz503, zzz504, zzz505, zzz506, zzz507, Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat2(Succ(new_primPlusNat3(new_primPlusNat1(zzz500), zzz500)), zzz500)), zzz500))), bg)
new_mkVBalBranch3MkVBalBranch223(zzz340, zzz341, Neg(Succ(Succ(Succ(zzz3420000)))), zzz343, zzz344, zzz510, zzz511, Succ(zzz512000), zzz513, zzz514, zzz31, Succ(Succ(zzz6700)), h) → new_mkVBalBranch3MkVBalBranch224(zzz340, zzz341, Succ(Succ(zzz3420000)), zzz343, zzz344, zzz510, zzz511, zzz512000, zzz513, zzz514, zzz31, Succ(zzz3420000), Succ(Succ(new_primPlusNat2(zzz6700, zzz512000))), h)
new_mkVBalBranch3MkVBalBranch223(zzz340, zzz341, Neg(Succ(Succ(Zero))), zzz343, zzz344, zzz510, zzz511, Zero, zzz513, zzz514, zzz31, Succ(Succ(zzz6700)), h) → new_mkVBalBranch3MkVBalBranch225(zzz340, zzz341, Succ(Zero), zzz343, zzz344, zzz510, zzz511, zzz513, zzz514, zzz31, Zero, Succ(zzz6700), h)
new_mkVBalBranch3MkVBalBranch224(zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, zzz1125, zzz1126, zzz1127, zzz1128, zzz1129, Succ(zzz11300), Zero, bd) → new_mkVBalBranch3MkVBalBranch119(zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, zzz1125, zzz1126, zzz1127, zzz1128, zzz1129, Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat2(Succ(new_primPlusNat3(new_primPlusNat1(zzz1121), zzz1121)), zzz1121)), zzz1121))), bd)
new_mkVBalBranch3MkVBalBranch118(zzz498, zzz499, zzz500, zzz501, zzz502, zzz503, zzz504, zzz505, zzz506, zzz507, Succ(zzz8040), bg) → new_mkVBalBranch3MkVBalBranch120(zzz498, zzz499, zzz500, zzz501, zzz502, zzz503, zzz504, Zero, zzz505, zzz506, zzz507, Succ(Zero), Succ(zzz8040), bg)
new_mkVBalBranch3MkVBalBranch225(zzz498, zzz499, zzz500, zzz501, zzz502, zzz503, zzz504, zzz505, zzz506, zzz507, Zero, Succ(zzz5090), bg) → new_mkVBalBranch0(zzz507, Branch(zzz503, zzz504, Neg(Succ(Zero)), zzz505, zzz506), zzz501, bg)
new_mkVBalBranch0(zzz31, Branch(zzz510, zzz511, Neg(Succ(zzz51200)), zzz513, zzz514), Branch(zzz340, zzz341, zzz342, zzz343, zzz344), h) → new_mkVBalBranch3MkVBalBranch223(zzz340, zzz341, zzz342, zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat3(new_primPlusNat1(zzz51200), zzz51200)), zzz51200))), h)
new_mkVBalBranch3MkVBalBranch223(zzz340, zzz341, Neg(Succ(Zero)), zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, Succ(zzz670), h) → new_mkVBalBranch0(zzz31, Branch(zzz510, zzz511, Neg(Succ(zzz51200)), zzz513, zzz514), zzz343, h)
new_mkVBalBranch3MkVBalBranch119(zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, zzz1125, zzz1126, zzz1127, zzz1128, zzz1129, Succ(zzz12130), bd) → new_mkVBalBranch3MkVBalBranch120(zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, zzz1125, Succ(zzz1126), zzz1127, zzz1128, zzz1129, Succ(Succ(zzz1126)), Succ(zzz12130), bd)

The TRS R consists of the following rules:

new_primPlusNat1(Zero) → Zero
new_primPlusNat1(Succ(zzz62000)) → Succ(Succ(new_primPlusNat1(zzz62000)))
new_primPlusNat3(zzz90, Succ(zzz910)) → Succ(Succ(new_primPlusNat2(zzz90, zzz910)))
new_primPlusNat3(zzz90, Zero) → Succ(zzz90)
new_primPlusNat2(Succ(zzz900), Succ(zzz9100)) → Succ(Succ(new_primPlusNat2(zzz900, zzz9100)))
new_primPlusNat2(Zero, Succ(zzz9100)) → Succ(zzz9100)
new_primPlusNat2(Zero, Zero) → Zero
new_primPlusNat2(Succ(zzz900), Zero) → Succ(zzz900)

The set Q consists of the following terms:

new_primPlusNat2(Zero, Succ(x0))
new_primPlusNat3(x0, Succ(x1))
new_primPlusNat2(Succ(x0), Succ(x1))
new_primPlusNat3(x0, Zero)
new_primPlusNat1(Zero)
new_primPlusNat2(Zero, Zero)
new_primPlusNat1(Succ(x0))
new_primPlusNat2(Succ(x0), Zero)

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


The following pairs can be oriented strictly and are deleted.


new_mkVBalBranch3MkVBalBranch230(zzz498, zzz499, zzz500, zzz501, zzz502, zzz503, zzz504, zzz505, zzz506, zzz507, bg) → new_mkVBalBranch3MkVBalBranch118(zzz498, zzz499, zzz500, zzz501, zzz502, zzz503, zzz504, zzz505, zzz506, zzz507, Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat2(Succ(new_primPlusNat3(new_primPlusNat1(zzz500), zzz500)), zzz500)), zzz500))), bg)
new_mkVBalBranch3MkVBalBranch117(zzz340, zzz341, zzz34200, zzz343, zzz344, zzz510, zzz511, zzz513, zzz514, zzz31, Succ(zzz1240), h) → new_mkVBalBranch0(zzz31, zzz514, Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), h)
new_mkVBalBranch3MkVBalBranch229(zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, zzz1125, zzz1126, zzz1127, zzz1128, zzz1129, bd) → new_mkVBalBranch3MkVBalBranch119(zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, zzz1125, zzz1126, zzz1127, zzz1128, zzz1129, Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat2(Succ(new_primPlusNat3(new_primPlusNat1(zzz1121), zzz1121)), zzz1121)), zzz1121))), bd)
new_mkVBalBranch3MkVBalBranch225(zzz498, zzz499, zzz500, zzz501, zzz502, zzz503, zzz504, zzz505, zzz506, zzz507, Succ(zzz5080), Zero, bg) → new_mkVBalBranch3MkVBalBranch118(zzz498, zzz499, zzz500, zzz501, zzz502, zzz503, zzz504, zzz505, zzz506, zzz507, Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat2(Succ(new_primPlusNat3(new_primPlusNat1(zzz500), zzz500)), zzz500)), zzz500))), bg)
new_mkVBalBranch3MkVBalBranch224(zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, zzz1125, zzz1126, zzz1127, zzz1128, zzz1129, Succ(zzz11300), Zero, bd) → new_mkVBalBranch3MkVBalBranch119(zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, zzz1125, zzz1126, zzz1127, zzz1128, zzz1129, Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat2(Succ(new_primPlusNat3(new_primPlusNat1(zzz1121), zzz1121)), zzz1121)), zzz1121))), bd)
The remaining pairs can at least be oriented weakly.

new_mkVBalBranch3MkVBalBranch225(zzz498, zzz499, zzz500, zzz501, zzz502, zzz503, zzz504, zzz505, zzz506, zzz507, Zero, Zero, bg) → new_mkVBalBranch3MkVBalBranch230(zzz498, zzz499, zzz500, zzz501, zzz502, zzz503, zzz504, zzz505, zzz506, zzz507, bg)
new_mkVBalBranch3MkVBalBranch223(zzz340, zzz341, Neg(Succ(Succ(Succ(zzz3420000)))), zzz343, zzz344, zzz510, zzz511, Zero, zzz513, zzz514, zzz31, Succ(Succ(zzz6700)), h) → new_mkVBalBranch3MkVBalBranch225(zzz340, zzz341, Succ(Succ(zzz3420000)), zzz343, zzz344, zzz510, zzz511, zzz513, zzz514, zzz31, Succ(zzz3420000), Succ(zzz6700), h)
new_mkVBalBranch3MkVBalBranch120(zzz2050, zzz2051, zzz2052, zzz2053, zzz2054, zzz2055, zzz2056, zzz2057, zzz2058, zzz2059, zzz2060, Zero, Succ(zzz20620), be) → new_mkVBalBranch0(zzz2060, zzz2059, Branch(zzz2050, zzz2051, Neg(Succ(zzz2052)), zzz2053, zzz2054), be)
new_mkVBalBranch3MkVBalBranch223(zzz340, zzz341, Neg(Succ(Succ(Zero))), zzz343, zzz344, zzz510, zzz511, Succ(zzz512000), zzz513, zzz514, zzz31, Succ(Succ(zzz6700)), h) → new_mkVBalBranch3MkVBalBranch224(zzz340, zzz341, Succ(Zero), zzz343, zzz344, zzz510, zzz511, zzz512000, zzz513, zzz514, zzz31, Zero, Succ(Succ(new_primPlusNat2(zzz6700, zzz512000))), h)
new_mkVBalBranch0(zzz31, Branch(zzz510, zzz511, Neg(Zero), zzz513, zzz514), Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), h) → new_mkVBalBranch3MkVBalBranch117(zzz340, zzz341, zzz34200, zzz343, zzz344, zzz510, zzz511, zzz513, zzz514, zzz31, Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat2(Succ(new_primPlusNat3(new_primPlusNat1(zzz34200), zzz34200)), zzz34200)), zzz34200))), h)
new_mkVBalBranch3MkVBalBranch120(zzz2050, zzz2051, zzz2052, zzz2053, zzz2054, zzz2055, zzz2056, zzz2057, zzz2058, zzz2059, zzz2060, Succ(zzz20610), Succ(zzz20620), be) → new_mkVBalBranch3MkVBalBranch120(zzz2050, zzz2051, zzz2052, zzz2053, zzz2054, zzz2055, zzz2056, zzz2057, zzz2058, zzz2059, zzz2060, zzz20610, zzz20620, be)
new_mkVBalBranch3MkVBalBranch224(zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, zzz1125, zzz1126, zzz1127, zzz1128, zzz1129, Succ(zzz11300), Succ(zzz11310), bd) → new_mkVBalBranch3MkVBalBranch224(zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, zzz1125, zzz1126, zzz1127, zzz1128, zzz1129, zzz11300, zzz11310, bd)
new_mkVBalBranch3MkVBalBranch223(zzz340, zzz341, Pos(zzz3420), zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, Succ(zzz670), h) → new_mkVBalBranch0(zzz31, Branch(zzz510, zzz511, Neg(Succ(zzz51200)), zzz513, zzz514), zzz343, h)
new_mkVBalBranch3MkVBalBranch225(zzz498, zzz499, zzz500, zzz501, zzz502, zzz503, zzz504, zzz505, zzz506, zzz507, Succ(zzz5080), Succ(zzz5090), bg) → new_mkVBalBranch3MkVBalBranch225(zzz498, zzz499, zzz500, zzz501, zzz502, zzz503, zzz504, zzz505, zzz506, zzz507, zzz5080, zzz5090, bg)
new_mkVBalBranch3MkVBalBranch227(zzz486, zzz487, zzz488, zzz489, zzz490, zzz491, zzz492, zzz493, zzz494, zzz495, zzz496, bf) → new_mkVBalBranch0(zzz496, Branch(zzz491, zzz492, Neg(Succ(Succ(zzz493))), zzz494, zzz495), zzz489, bf)
new_mkVBalBranch3MkVBalBranch224(zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, zzz1125, zzz1126, zzz1127, zzz1128, zzz1129, Zero, Succ(zzz11310), bd) → new_mkVBalBranch3MkVBalBranch227(zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, zzz1125, zzz1126, zzz1127, zzz1128, zzz1129, bd)
new_mkVBalBranch3MkVBalBranch223(zzz340, zzz341, Neg(Zero), zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, Succ(zzz670), h) → new_mkVBalBranch0(zzz31, Branch(zzz510, zzz511, Neg(Succ(zzz51200)), zzz513, zzz514), zzz343, h)
new_mkVBalBranch3MkVBalBranch224(zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, zzz1125, zzz1126, zzz1127, zzz1128, zzz1129, Zero, Zero, bd) → new_mkVBalBranch3MkVBalBranch229(zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, zzz1125, zzz1126, zzz1127, zzz1128, zzz1129, bd)
new_mkVBalBranch3MkVBalBranch223(zzz340, zzz341, Neg(Succ(Succ(Succ(zzz3420000)))), zzz343, zzz344, zzz510, zzz511, Succ(zzz512000), zzz513, zzz514, zzz31, Succ(Succ(zzz6700)), h) → new_mkVBalBranch3MkVBalBranch224(zzz340, zzz341, Succ(Succ(zzz3420000)), zzz343, zzz344, zzz510, zzz511, zzz512000, zzz513, zzz514, zzz31, Succ(zzz3420000), Succ(Succ(new_primPlusNat2(zzz6700, zzz512000))), h)
new_mkVBalBranch3MkVBalBranch223(zzz340, zzz341, Neg(Succ(Succ(Zero))), zzz343, zzz344, zzz510, zzz511, Zero, zzz513, zzz514, zzz31, Succ(Succ(zzz6700)), h) → new_mkVBalBranch3MkVBalBranch225(zzz340, zzz341, Succ(Zero), zzz343, zzz344, zzz510, zzz511, zzz513, zzz514, zzz31, Zero, Succ(zzz6700), h)
new_mkVBalBranch3MkVBalBranch118(zzz498, zzz499, zzz500, zzz501, zzz502, zzz503, zzz504, zzz505, zzz506, zzz507, Succ(zzz8040), bg) → new_mkVBalBranch3MkVBalBranch120(zzz498, zzz499, zzz500, zzz501, zzz502, zzz503, zzz504, Zero, zzz505, zzz506, zzz507, Succ(Zero), Succ(zzz8040), bg)
new_mkVBalBranch3MkVBalBranch225(zzz498, zzz499, zzz500, zzz501, zzz502, zzz503, zzz504, zzz505, zzz506, zzz507, Zero, Succ(zzz5090), bg) → new_mkVBalBranch0(zzz507, Branch(zzz503, zzz504, Neg(Succ(Zero)), zzz505, zzz506), zzz501, bg)
new_mkVBalBranch0(zzz31, Branch(zzz510, zzz511, Neg(Succ(zzz51200)), zzz513, zzz514), Branch(zzz340, zzz341, zzz342, zzz343, zzz344), h) → new_mkVBalBranch3MkVBalBranch223(zzz340, zzz341, zzz342, zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat3(new_primPlusNat1(zzz51200), zzz51200)), zzz51200))), h)
new_mkVBalBranch3MkVBalBranch223(zzz340, zzz341, Neg(Succ(Zero)), zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, Succ(zzz670), h) → new_mkVBalBranch0(zzz31, Branch(zzz510, zzz511, Neg(Succ(zzz51200)), zzz513, zzz514), zzz343, h)
new_mkVBalBranch3MkVBalBranch119(zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, zzz1125, zzz1126, zzz1127, zzz1128, zzz1129, Succ(zzz12130), bd) → new_mkVBalBranch3MkVBalBranch120(zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, zzz1125, Succ(zzz1126), zzz1127, zzz1128, zzz1129, Succ(Succ(zzz1126)), Succ(zzz12130), bd)
Used ordering: Polynomial interpretation [25]:

POL(Branch(x1, x2, x3, x4, x5)) = 1 + x4 + x5   
POL(Neg(x1)) = 0   
POL(Pos(x1)) = 0   
POL(Succ(x1)) = 0   
POL(Zero) = 0   
POL(new_mkVBalBranch0(x1, x2, x3, x4)) = x2   
POL(new_mkVBalBranch3MkVBalBranch117(x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12)) = 1 + x9   
POL(new_mkVBalBranch3MkVBalBranch118(x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12)) = x3 + x8 + x9   
POL(new_mkVBalBranch3MkVBalBranch119(x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12, x13)) = x10 + x3   
POL(new_mkVBalBranch3MkVBalBranch120(x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12, x13, x14)) = x10   
POL(new_mkVBalBranch3MkVBalBranch223(x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12, x13)) = 1 + x10 + x9   
POL(new_mkVBalBranch3MkVBalBranch224(x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12, x13, x14)) = 1 + x10 + x3 + x9   
POL(new_mkVBalBranch3MkVBalBranch225(x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12, x13)) = 1 + x3 + x8 + x9   
POL(new_mkVBalBranch3MkVBalBranch227(x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12)) = 1 + x10 + x9   
POL(new_mkVBalBranch3MkVBalBranch229(x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12)) = 1 + x10 + x3 + x9   
POL(new_mkVBalBranch3MkVBalBranch230(x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11)) = 1 + x3 + x8 + x9   
POL(new_primPlusNat1(x1)) = 1   
POL(new_primPlusNat2(x1, x2)) = 0   
POL(new_primPlusNat3(x1, x2)) = 0   

The following usable rules [17] were oriented: none



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

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

new_mkVBalBranch3MkVBalBranch227(zzz486, zzz487, zzz488, zzz489, zzz490, zzz491, zzz492, zzz493, zzz494, zzz495, zzz496, bf) → new_mkVBalBranch0(zzz496, Branch(zzz491, zzz492, Neg(Succ(Succ(zzz493))), zzz494, zzz495), zzz489, bf)
new_mkVBalBranch3MkVBalBranch225(zzz498, zzz499, zzz500, zzz501, zzz502, zzz503, zzz504, zzz505, zzz506, zzz507, Zero, Zero, bg) → new_mkVBalBranch3MkVBalBranch230(zzz498, zzz499, zzz500, zzz501, zzz502, zzz503, zzz504, zzz505, zzz506, zzz507, bg)
new_mkVBalBranch3MkVBalBranch224(zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, zzz1125, zzz1126, zzz1127, zzz1128, zzz1129, Zero, Succ(zzz11310), bd) → new_mkVBalBranch3MkVBalBranch227(zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, zzz1125, zzz1126, zzz1127, zzz1128, zzz1129, bd)
new_mkVBalBranch3MkVBalBranch223(zzz340, zzz341, Neg(Zero), zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, Succ(zzz670), h) → new_mkVBalBranch0(zzz31, Branch(zzz510, zzz511, Neg(Succ(zzz51200)), zzz513, zzz514), zzz343, h)
new_mkVBalBranch3MkVBalBranch224(zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, zzz1125, zzz1126, zzz1127, zzz1128, zzz1129, Zero, Zero, bd) → new_mkVBalBranch3MkVBalBranch229(zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, zzz1125, zzz1126, zzz1127, zzz1128, zzz1129, bd)
new_mkVBalBranch3MkVBalBranch223(zzz340, zzz341, Neg(Succ(Succ(Succ(zzz3420000)))), zzz343, zzz344, zzz510, zzz511, Zero, zzz513, zzz514, zzz31, Succ(Succ(zzz6700)), h) → new_mkVBalBranch3MkVBalBranch225(zzz340, zzz341, Succ(Succ(zzz3420000)), zzz343, zzz344, zzz510, zzz511, zzz513, zzz514, zzz31, Succ(zzz3420000), Succ(zzz6700), h)
new_mkVBalBranch3MkVBalBranch223(zzz340, zzz341, Neg(Succ(Succ(Zero))), zzz343, zzz344, zzz510, zzz511, Zero, zzz513, zzz514, zzz31, Succ(Succ(zzz6700)), h) → new_mkVBalBranch3MkVBalBranch225(zzz340, zzz341, Succ(Zero), zzz343, zzz344, zzz510, zzz511, zzz513, zzz514, zzz31, Zero, Succ(zzz6700), h)
new_mkVBalBranch3MkVBalBranch223(zzz340, zzz341, Neg(Succ(Succ(Succ(zzz3420000)))), zzz343, zzz344, zzz510, zzz511, Succ(zzz512000), zzz513, zzz514, zzz31, Succ(Succ(zzz6700)), h) → new_mkVBalBranch3MkVBalBranch224(zzz340, zzz341, Succ(Succ(zzz3420000)), zzz343, zzz344, zzz510, zzz511, zzz512000, zzz513, zzz514, zzz31, Succ(zzz3420000), Succ(Succ(new_primPlusNat2(zzz6700, zzz512000))), h)
new_mkVBalBranch3MkVBalBranch120(zzz2050, zzz2051, zzz2052, zzz2053, zzz2054, zzz2055, zzz2056, zzz2057, zzz2058, zzz2059, zzz2060, Zero, Succ(zzz20620), be) → new_mkVBalBranch0(zzz2060, zzz2059, Branch(zzz2050, zzz2051, Neg(Succ(zzz2052)), zzz2053, zzz2054), be)
new_mkVBalBranch3MkVBalBranch223(zzz340, zzz341, Neg(Succ(Succ(Zero))), zzz343, zzz344, zzz510, zzz511, Succ(zzz512000), zzz513, zzz514, zzz31, Succ(Succ(zzz6700)), h) → new_mkVBalBranch3MkVBalBranch224(zzz340, zzz341, Succ(Zero), zzz343, zzz344, zzz510, zzz511, zzz512000, zzz513, zzz514, zzz31, Zero, Succ(Succ(new_primPlusNat2(zzz6700, zzz512000))), h)
new_mkVBalBranch3MkVBalBranch118(zzz498, zzz499, zzz500, zzz501, zzz502, zzz503, zzz504, zzz505, zzz506, zzz507, Succ(zzz8040), bg) → new_mkVBalBranch3MkVBalBranch120(zzz498, zzz499, zzz500, zzz501, zzz502, zzz503, zzz504, Zero, zzz505, zzz506, zzz507, Succ(Zero), Succ(zzz8040), bg)
new_mkVBalBranch0(zzz31, Branch(zzz510, zzz511, Neg(Zero), zzz513, zzz514), Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), h) → new_mkVBalBranch3MkVBalBranch117(zzz340, zzz341, zzz34200, zzz343, zzz344, zzz510, zzz511, zzz513, zzz514, zzz31, Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat2(Succ(new_primPlusNat3(new_primPlusNat1(zzz34200), zzz34200)), zzz34200)), zzz34200))), h)
new_mkVBalBranch3MkVBalBranch225(zzz498, zzz499, zzz500, zzz501, zzz502, zzz503, zzz504, zzz505, zzz506, zzz507, Zero, Succ(zzz5090), bg) → new_mkVBalBranch0(zzz507, Branch(zzz503, zzz504, Neg(Succ(Zero)), zzz505, zzz506), zzz501, bg)
new_mkVBalBranch3MkVBalBranch120(zzz2050, zzz2051, zzz2052, zzz2053, zzz2054, zzz2055, zzz2056, zzz2057, zzz2058, zzz2059, zzz2060, Succ(zzz20610), Succ(zzz20620), be) → new_mkVBalBranch3MkVBalBranch120(zzz2050, zzz2051, zzz2052, zzz2053, zzz2054, zzz2055, zzz2056, zzz2057, zzz2058, zzz2059, zzz2060, zzz20610, zzz20620, be)
new_mkVBalBranch3MkVBalBranch224(zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, zzz1125, zzz1126, zzz1127, zzz1128, zzz1129, Succ(zzz11300), Succ(zzz11310), bd) → new_mkVBalBranch3MkVBalBranch224(zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, zzz1125, zzz1126, zzz1127, zzz1128, zzz1129, zzz11300, zzz11310, bd)
new_mkVBalBranch0(zzz31, Branch(zzz510, zzz511, Neg(Succ(zzz51200)), zzz513, zzz514), Branch(zzz340, zzz341, zzz342, zzz343, zzz344), h) → new_mkVBalBranch3MkVBalBranch223(zzz340, zzz341, zzz342, zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat3(new_primPlusNat1(zzz51200), zzz51200)), zzz51200))), h)
new_mkVBalBranch3MkVBalBranch223(zzz340, zzz341, Pos(zzz3420), zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, Succ(zzz670), h) → new_mkVBalBranch0(zzz31, Branch(zzz510, zzz511, Neg(Succ(zzz51200)), zzz513, zzz514), zzz343, h)
new_mkVBalBranch3MkVBalBranch119(zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, zzz1125, zzz1126, zzz1127, zzz1128, zzz1129, Succ(zzz12130), bd) → new_mkVBalBranch3MkVBalBranch120(zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, zzz1125, Succ(zzz1126), zzz1127, zzz1128, zzz1129, Succ(Succ(zzz1126)), Succ(zzz12130), bd)
new_mkVBalBranch3MkVBalBranch223(zzz340, zzz341, Neg(Succ(Zero)), zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, Succ(zzz670), h) → new_mkVBalBranch0(zzz31, Branch(zzz510, zzz511, Neg(Succ(zzz51200)), zzz513, zzz514), zzz343, h)
new_mkVBalBranch3MkVBalBranch225(zzz498, zzz499, zzz500, zzz501, zzz502, zzz503, zzz504, zzz505, zzz506, zzz507, Succ(zzz5080), Succ(zzz5090), bg) → new_mkVBalBranch3MkVBalBranch225(zzz498, zzz499, zzz500, zzz501, zzz502, zzz503, zzz504, zzz505, zzz506, zzz507, zzz5080, zzz5090, bg)

The TRS R consists of the following rules:

new_primPlusNat1(Zero) → Zero
new_primPlusNat1(Succ(zzz62000)) → Succ(Succ(new_primPlusNat1(zzz62000)))
new_primPlusNat3(zzz90, Succ(zzz910)) → Succ(Succ(new_primPlusNat2(zzz90, zzz910)))
new_primPlusNat3(zzz90, Zero) → Succ(zzz90)
new_primPlusNat2(Succ(zzz900), Succ(zzz9100)) → Succ(Succ(new_primPlusNat2(zzz900, zzz9100)))
new_primPlusNat2(Zero, Succ(zzz9100)) → Succ(zzz9100)
new_primPlusNat2(Zero, Zero) → Zero
new_primPlusNat2(Succ(zzz900), Zero) → Succ(zzz900)

The set Q consists of the following terms:

new_primPlusNat2(Zero, Succ(x0))
new_primPlusNat3(x0, Succ(x1))
new_primPlusNat2(Succ(x0), Succ(x1))
new_primPlusNat3(x0, Zero)
new_primPlusNat1(Zero)
new_primPlusNat2(Zero, Zero)
new_primPlusNat1(Succ(x0))
new_primPlusNat2(Succ(x0), Zero)

We have to consider all minimal (P,Q,R)-chains.
The approximation of the Dependency Graph [15,17,22] contains 2 SCCs 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
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                    ↳ DependencyGraphProof
                                      ↳ QDP
                                        ↳ Rewriting
                                          ↳ QDP
                                            ↳ Rewriting
                                              ↳ QDP
                                                ↳ Rewriting
                                                  ↳ QDP
                                                    ↳ Rewriting
                                                      ↳ QDP
                                                        ↳ Rewriting
                                                          ↳ QDP
                                                            ↳ Rewriting
                                                              ↳ QDP
                                                                ↳ Rewriting
                                                                  ↳ QDP
                                                                    ↳ Rewriting
                                                                      ↳ QDP
                                                                        ↳ Rewriting
                                                                          ↳ QDP
                                                                            ↳ Rewriting
                                                                              ↳ QDP
                                                                                ↳ Rewriting
                                                                                  ↳ QDP
                                                                                    ↳ Rewriting
                                                                                      ↳ QDP
                                                                                        ↳ Rewriting
                                                                                          ↳ QDP
                                                                                            ↳ Rewriting
                                                                                              ↳ QDP
                                                                                                ↳ Rewriting
                                                                                                  ↳ QDP
                                                                                                    ↳ Rewriting
                                                                                                      ↳ QDP
                                                                                                        ↳ Rewriting
                                                                                                          ↳ QDP
                                                                                                            ↳ UsableRulesProof
                                                                                                              ↳ QDP
                                                                                                                ↳ QReductionProof
                                                                                                                  ↳ QDP
                                                                                                                    ↳ Rewriting
                                                                                                                      ↳ QDP
                                                                                                                        ↳ Rewriting
                                                                                                                          ↳ QDP
                                                                                                                            ↳ DependencyGraphProof
                                                                                                                              ↳ QDP
                                                                                                                                ↳ Rewriting
                                                                                                                                  ↳ QDP
                                                                                                                                    ↳ Rewriting
                                                                                                                                      ↳ QDP
                                                                                                                                        ↳ DependencyGraphProof
                                                                                                                                          ↳ QDP
                                                                                                                                            ↳ Rewriting
                                                                                                                                              ↳ QDP
                                                                                                                                                ↳ Rewriting
                                                                                                                                                  ↳ QDP
                                                                                                                                                    ↳ Rewriting
                                                                                                                                                      ↳ QDP
                                                                                                                                                        ↳ Rewriting
                                                                                                                                                          ↳ QDP
                                                                                                                                                            ↳ Rewriting
                                                                                                                                                              ↳ QDP
                                                                                                                                                                ↳ Rewriting
                                                                                                                                                                  ↳ QDP
                                                                                                                                                                    ↳ Rewriting
                                                                                                                                                                      ↳ QDP
                                                                                                                                                                        ↳ Rewriting
                                                                                                                                                                          ↳ QDP
                                                                                                                                                                            ↳ Rewriting
                                                                                                                                                                              ↳ QDP
                                                                                                                                                                                ↳ Rewriting
                                                                                                                                                                                  ↳ QDP
                                                                                                                                                                                    ↳ Rewriting
                                                                                                                                                                                      ↳ QDP
                                                                                                                                                                                        ↳ Rewriting
                                                                                                                                                                                          ↳ QDP
                                                                                                                                                                                            ↳ UsableRulesProof
                                                                                                                                                                                              ↳ QDP
                                                                                                                                                                                                ↳ QReductionProof
                                                                                                                                                                                                  ↳ QDP
                                                                                                                                                                                                    ↳ Rewriting
                                                                                                                                                                                                      ↳ QDP
                                                                                                                                                                                                        ↳ Rewriting
                                                                                                                                                                                                          ↳ QDP
                                                                                                                                                                                                            ↳ Rewriting
                                                                                                                                                                                                              ↳ QDP
                                                                                                                                                                                                                ↳ Rewriting
                                                                                                                                                                                                                  ↳ QDP
                                                                                                                                                                                                                    ↳ Rewriting
                                                                                                                                                                                                                      ↳ QDP
                                                                                                                                                                                                                        ↳ Rewriting
                                                                                                                                                                                                                          ↳ QDP
                                                                                                                                                                                                                            ↳ Rewriting
                                                                                                                                                                                                                              ↳ QDP
                                                                                                                                                                                                                                ↳ Rewriting
                                                                                                                                                                                                                                  ↳ QDP
                                                                                                                                                                                                                                    ↳ Rewriting
                                                                                                                                                                                                                                      ↳ QDP
                                                                                                                                                                                                                                        ↳ Rewriting
                                                                                                                                                                                                                                          ↳ QDP
                                                                                                                                                                                                                                            ↳ Rewriting
                                                                                                                                                                                                                                              ↳ QDP
                                                                                                                                                                                                                                                ↳ Rewriting
                                                                                                                                                                                                                                                  ↳ QDP
                                                                                                                                                                                                                                                    ↳ Rewriting
                                                                                                                                                                                                                                                      ↳ QDP
                                                                                                                                                                                                                                                        ↳ Rewriting
                                                                                                                                                                                                                                                          ↳ QDP
                                                                                                                                                                                                                                                            ↳ DependencyGraphProof
                                                                                                                                                                                                                                                              ↳ QDP
                                                                                                                                                                                                                                                                ↳ Rewriting
                                                                                                                                                                                                                                                                  ↳ QDP
                                                                                                                                                                                                                                                                    ↳ Rewriting
                                                                                                                                                                                                                                                                      ↳ QDP
                                                                                                                                                                                                                                                                        ↳ Rewriting
                                                                                                                                                                                                                                                                          ↳ QDP
                                                                                                                                                                                                                                                                            ↳ Rewriting
                                                                                                                                                                                                                                                                              ↳ QDP
                                                                                                                                                                                                                                                                                ↳ Rewriting
                                                                                                                                                                                                                                                                                  ↳ QDP
                                                                                                                                                                                                                                                                                    ↳ Rewriting
                                                                                                                                                                                                                                                                                      ↳ QDP
                                                                                                                                                                                                                                                                                        ↳ DependencyGraphProof
                                                                                                                                                                                                                                                                                          ↳ QDP
                                                                                                                                                                                                                                                                                            ↳ Rewriting
                                                                                                                                                                                                                                                                                              ↳ QDP
                                                                                                                                                                                                                                                                                                ↳ DependencyGraphProof
                                                                                                                                                                                                                                                                                                  ↳ QDP
                                                                                                                                                                                                                                                                                                    ↳ Rewriting
                                                                                                                                                                                                                                                                                                      ↳ QDP
                                                                                                                                                                                                                                                                                                        ↳ DependencyGraphProof
                                                                                                                                                                                                                                                                                                          ↳ QDP
                                                                                                                                                                                                                                                                                                            ↳ Rewriting
                                                                                                                                                                                                                                                                                                              ↳ QDP
                                                                                                                                                                                                                                                                                                                ↳ Rewriting
                                                                                                                                                                                                                                                                                                                  ↳ QDP
                                                                                                                                                                                                                                                                                                                    ↳ Rewriting
                                                                                                                                                                                                                                                                                                                      ↳ QDP
                                                                                                                                                                                                                                                                                                                        ↳ Rewriting
                                                                                                                                                                                                                                                                                                                          ↳ QDP
                                                                                                                                                                                                                                                                                                                            ↳ Instantiation
                                                                                                                                                                                                                                                                                                                              ↳ QDP
                                                                                                                                                                                                                                                                                                                                ↳ QDPOrderProof
                                                                                                                                                                                                                                                                                                                                  ↳ QDP
                                                                                                                                                                                                                                                                                                                                    ↳ DependencyGraphProof
                                                                                                                                                                                                                                                                                                                                      ↳ AND
                                                                                                                                                                                                                                                                                                                                        ↳ QDP
                                                                                                                                                                                                                                                                                                                                        ↳ QDP
                                                                                                                                                                                                                                                                                                                                        ↳ QDP
                                                                                                                                                                                                                                                                                                                                          ↳ QDPOrderProof
                                                                                                                                                                                                                                                                                                                                            ↳ QDP
                                                                                                                                                                                                                                                                                                                                              ↳ DependencyGraphProof
                                                                                                                                                                                                                                                                                                                                                ↳ AND
                                                                                                                                                                                                                                                                                                                                                  ↳ QDP
                                                                                                                                                                                                                                                                                                                                                    ↳ QDPSizeChangeProof
                                                                                                                                                                                                                                                                                                                                                  ↳ QDP
                                                                                                                                                                                                                                                                                                                                        ↳ QDP
                                                                                                                                                                                                                                                                                                                                        ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP

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

new_mkVBalBranch3MkVBalBranch227(zzz486, zzz487, zzz488, zzz489, zzz490, zzz491, zzz492, zzz493, zzz494, zzz495, zzz496, bf) → new_mkVBalBranch0(zzz496, Branch(zzz491, zzz492, Neg(Succ(Succ(zzz493))), zzz494, zzz495), zzz489, bf)
new_mkVBalBranch3MkVBalBranch224(zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, zzz1125, zzz1126, zzz1127, zzz1128, zzz1129, Zero, Succ(zzz11310), bd) → new_mkVBalBranch3MkVBalBranch227(zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, zzz1125, zzz1126, zzz1127, zzz1128, zzz1129, bd)
new_mkVBalBranch3MkVBalBranch223(zzz340, zzz341, Neg(Zero), zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, Succ(zzz670), h) → new_mkVBalBranch0(zzz31, Branch(zzz510, zzz511, Neg(Succ(zzz51200)), zzz513, zzz514), zzz343, h)
new_mkVBalBranch3MkVBalBranch223(zzz340, zzz341, Neg(Succ(Succ(Succ(zzz3420000)))), zzz343, zzz344, zzz510, zzz511, Zero, zzz513, zzz514, zzz31, Succ(Succ(zzz6700)), h) → new_mkVBalBranch3MkVBalBranch225(zzz340, zzz341, Succ(Succ(zzz3420000)), zzz343, zzz344, zzz510, zzz511, zzz513, zzz514, zzz31, Succ(zzz3420000), Succ(zzz6700), h)
new_mkVBalBranch3MkVBalBranch223(zzz340, zzz341, Neg(Succ(Succ(Succ(zzz3420000)))), zzz343, zzz344, zzz510, zzz511, Succ(zzz512000), zzz513, zzz514, zzz31, Succ(Succ(zzz6700)), h) → new_mkVBalBranch3MkVBalBranch224(zzz340, zzz341, Succ(Succ(zzz3420000)), zzz343, zzz344, zzz510, zzz511, zzz512000, zzz513, zzz514, zzz31, Succ(zzz3420000), Succ(Succ(new_primPlusNat2(zzz6700, zzz512000))), h)
new_mkVBalBranch3MkVBalBranch223(zzz340, zzz341, Neg(Succ(Succ(Zero))), zzz343, zzz344, zzz510, zzz511, Zero, zzz513, zzz514, zzz31, Succ(Succ(zzz6700)), h) → new_mkVBalBranch3MkVBalBranch225(zzz340, zzz341, Succ(Zero), zzz343, zzz344, zzz510, zzz511, zzz513, zzz514, zzz31, Zero, Succ(zzz6700), h)
new_mkVBalBranch3MkVBalBranch223(zzz340, zzz341, Neg(Succ(Succ(Zero))), zzz343, zzz344, zzz510, zzz511, Succ(zzz512000), zzz513, zzz514, zzz31, Succ(Succ(zzz6700)), h) → new_mkVBalBranch3MkVBalBranch224(zzz340, zzz341, Succ(Zero), zzz343, zzz344, zzz510, zzz511, zzz512000, zzz513, zzz514, zzz31, Zero, Succ(Succ(new_primPlusNat2(zzz6700, zzz512000))), h)
new_mkVBalBranch3MkVBalBranch225(zzz498, zzz499, zzz500, zzz501, zzz502, zzz503, zzz504, zzz505, zzz506, zzz507, Zero, Succ(zzz5090), bg) → new_mkVBalBranch0(zzz507, Branch(zzz503, zzz504, Neg(Succ(Zero)), zzz505, zzz506), zzz501, bg)
new_mkVBalBranch3MkVBalBranch224(zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, zzz1125, zzz1126, zzz1127, zzz1128, zzz1129, Succ(zzz11300), Succ(zzz11310), bd) → new_mkVBalBranch3MkVBalBranch224(zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, zzz1125, zzz1126, zzz1127, zzz1128, zzz1129, zzz11300, zzz11310, bd)
new_mkVBalBranch0(zzz31, Branch(zzz510, zzz511, Neg(Succ(zzz51200)), zzz513, zzz514), Branch(zzz340, zzz341, zzz342, zzz343, zzz344), h) → new_mkVBalBranch3MkVBalBranch223(zzz340, zzz341, zzz342, zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat3(new_primPlusNat1(zzz51200), zzz51200)), zzz51200))), h)
new_mkVBalBranch3MkVBalBranch223(zzz340, zzz341, Pos(zzz3420), zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, Succ(zzz670), h) → new_mkVBalBranch0(zzz31, Branch(zzz510, zzz511, Neg(Succ(zzz51200)), zzz513, zzz514), zzz343, h)
new_mkVBalBranch3MkVBalBranch223(zzz340, zzz341, Neg(Succ(Zero)), zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, Succ(zzz670), h) → new_mkVBalBranch0(zzz31, Branch(zzz510, zzz511, Neg(Succ(zzz51200)), zzz513, zzz514), zzz343, h)
new_mkVBalBranch3MkVBalBranch225(zzz498, zzz499, zzz500, zzz501, zzz502, zzz503, zzz504, zzz505, zzz506, zzz507, Succ(zzz5080), Succ(zzz5090), bg) → new_mkVBalBranch3MkVBalBranch225(zzz498, zzz499, zzz500, zzz501, zzz502, zzz503, zzz504, zzz505, zzz506, zzz507, zzz5080, zzz5090, bg)

The TRS R consists of the following rules:

new_primPlusNat1(Zero) → Zero
new_primPlusNat1(Succ(zzz62000)) → Succ(Succ(new_primPlusNat1(zzz62000)))
new_primPlusNat3(zzz90, Succ(zzz910)) → Succ(Succ(new_primPlusNat2(zzz90, zzz910)))
new_primPlusNat3(zzz90, Zero) → Succ(zzz90)
new_primPlusNat2(Succ(zzz900), Succ(zzz9100)) → Succ(Succ(new_primPlusNat2(zzz900, zzz9100)))
new_primPlusNat2(Zero, Succ(zzz9100)) → Succ(zzz9100)
new_primPlusNat2(Zero, Zero) → Zero
new_primPlusNat2(Succ(zzz900), Zero) → Succ(zzz900)

The set Q consists of the following terms:

new_primPlusNat2(Zero, Succ(x0))
new_primPlusNat3(x0, Succ(x1))
new_primPlusNat2(Succ(x0), Succ(x1))
new_primPlusNat3(x0, Zero)
new_primPlusNat1(Zero)
new_primPlusNat2(Zero, Zero)
new_primPlusNat1(Succ(x0))
new_primPlusNat2(Succ(x0), Zero)

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

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



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

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

new_mkVBalBranch3MkVBalBranch120(zzz2050, zzz2051, zzz2052, zzz2053, zzz2054, zzz2055, zzz2056, zzz2057, zzz2058, zzz2059, zzz2060, Succ(zzz20610), Succ(zzz20620), be) → new_mkVBalBranch3MkVBalBranch120(zzz2050, zzz2051, zzz2052, zzz2053, zzz2054, zzz2055, zzz2056, zzz2057, zzz2058, zzz2059, zzz2060, zzz20610, zzz20620, be)

The TRS R consists of the following rules:

new_primPlusNat1(Zero) → Zero
new_primPlusNat1(Succ(zzz62000)) → Succ(Succ(new_primPlusNat1(zzz62000)))
new_primPlusNat3(zzz90, Succ(zzz910)) → Succ(Succ(new_primPlusNat2(zzz90, zzz910)))
new_primPlusNat3(zzz90, Zero) → Succ(zzz90)
new_primPlusNat2(Succ(zzz900), Succ(zzz9100)) → Succ(Succ(new_primPlusNat2(zzz900, zzz9100)))
new_primPlusNat2(Zero, Succ(zzz9100)) → Succ(zzz9100)
new_primPlusNat2(Zero, Zero) → Zero
new_primPlusNat2(Succ(zzz900), Zero) → Succ(zzz900)

The set Q consists of the following terms:

new_primPlusNat2(Zero, Succ(x0))
new_primPlusNat3(x0, Succ(x1))
new_primPlusNat2(Succ(x0), Succ(x1))
new_primPlusNat3(x0, Zero)
new_primPlusNat1(Zero)
new_primPlusNat2(Zero, Zero)
new_primPlusNat1(Succ(x0))
new_primPlusNat2(Succ(x0), Zero)

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

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

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

new_mkVBalBranch3MkVBalBranch120(zzz2050, zzz2051, zzz2052, zzz2053, zzz2054, zzz2055, zzz2056, zzz2057, zzz2058, zzz2059, zzz2060, Succ(zzz20610), Succ(zzz20620), be) → new_mkVBalBranch3MkVBalBranch120(zzz2050, zzz2051, zzz2052, zzz2053, zzz2054, zzz2055, zzz2056, zzz2057, zzz2058, zzz2059, zzz2060, zzz20610, zzz20620, be)

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

new_primPlusNat2(Zero, Succ(x0))
new_primPlusNat3(x0, Succ(x1))
new_primPlusNat2(Succ(x0), Succ(x1))
new_primPlusNat3(x0, Zero)
new_primPlusNat1(Zero)
new_primPlusNat2(Zero, Zero)
new_primPlusNat1(Succ(x0))
new_primPlusNat2(Succ(x0), Zero)

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

new_primPlusNat2(Zero, Succ(x0))
new_primPlusNat3(x0, Succ(x1))
new_primPlusNat2(Succ(x0), Succ(x1))
new_primPlusNat3(x0, Zero)
new_primPlusNat1(Zero)
new_primPlusNat2(Zero, Zero)
new_primPlusNat1(Succ(x0))
new_primPlusNat2(Succ(x0), 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
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                    ↳ DependencyGraphProof
                                      ↳ QDP
                                        ↳ Rewriting
                                          ↳ QDP
                                            ↳ Rewriting
                                              ↳ QDP
                                                ↳ Rewriting
                                                  ↳ QDP
                                                    ↳ Rewriting
                                                      ↳ QDP
                                                        ↳ Rewriting
                                                          ↳ QDP
                                                            ↳ Rewriting
                                                              ↳ QDP
                                                                ↳ Rewriting
                                                                  ↳ QDP
                                                                    ↳ Rewriting
                                                                      ↳ QDP
                                                                        ↳ Rewriting
                                                                          ↳ QDP
                                                                            ↳ Rewriting
                                                                              ↳ QDP
                                                                                ↳ Rewriting
                                                                                  ↳ QDP
                                                                                    ↳ Rewriting
                                                                                      ↳ QDP
                                                                                        ↳ Rewriting
                                                                                          ↳ QDP
                                                                                            ↳ Rewriting
                                                                                              ↳ QDP
                                                                                                ↳ Rewriting
                                                                                                  ↳ QDP
                                                                                                    ↳ Rewriting
                                                                                                      ↳ QDP
                                                                                                        ↳ Rewriting
                                                                                                          ↳ QDP
                                                                                                            ↳ UsableRulesProof
                                                                                                              ↳ QDP
                                                                                                                ↳ QReductionProof
                                                                                                                  ↳ QDP
                                                                                                                    ↳ Rewriting
                                                                                                                      ↳ QDP
                                                                                                                        ↳ Rewriting
                                                                                                                          ↳ QDP
                                                                                                                            ↳ DependencyGraphProof
                                                                                                                              ↳ QDP
                                                                                                                                ↳ Rewriting
                                                                                                                                  ↳ QDP
                                                                                                                                    ↳ Rewriting
                                                                                                                                      ↳ QDP
                                                                                                                                        ↳ DependencyGraphProof
                                                                                                                                          ↳ QDP
                                                                                                                                            ↳ Rewriting
                                                                                                                                              ↳ QDP
                                                                                                                                                ↳ Rewriting
                                                                                                                                                  ↳ QDP
                                                                                                                                                    ↳ Rewriting
                                                                                                                                                      ↳ QDP
                                                                                                                                                        ↳ Rewriting
                                                                                                                                                          ↳ QDP
                                                                                                                                                            ↳ Rewriting
                                                                                                                                                              ↳ QDP
                                                                                                                                                                ↳ Rewriting
                                                                                                                                                                  ↳ QDP
                                                                                                                                                                    ↳ Rewriting
                                                                                                                                                                      ↳ QDP
                                                                                                                                                                        ↳ Rewriting
                                                                                                                                                                          ↳ QDP
                                                                                                                                                                            ↳ Rewriting
                                                                                                                                                                              ↳ QDP
                                                                                                                                                                                ↳ Rewriting
                                                                                                                                                                                  ↳ QDP
                                                                                                                                                                                    ↳ Rewriting
                                                                                                                                                                                      ↳ QDP
                                                                                                                                                                                        ↳ Rewriting
                                                                                                                                                                                          ↳ QDP
                                                                                                                                                                                            ↳ UsableRulesProof
                                                                                                                                                                                              ↳ QDP
                                                                                                                                                                                                ↳ QReductionProof
                                                                                                                                                                                                  ↳ QDP
                                                                                                                                                                                                    ↳ Rewriting
                                                                                                                                                                                                      ↳ QDP
                                                                                                                                                                                                        ↳ Rewriting
                                                                                                                                                                                                          ↳ QDP
                                                                                                                                                                                                            ↳ Rewriting
                                                                                                                                                                                                              ↳ QDP
                                                                                                                                                                                                                ↳ Rewriting
                                                                                                                                                                                                                  ↳ QDP
                                                                                                                                                                                                                    ↳ Rewriting
                                                                                                                                                                                                                      ↳ QDP
                                                                                                                                                                                                                        ↳ Rewriting
                                                                                                                                                                                                                          ↳ QDP
                                                                                                                                                                                                                            ↳ Rewriting
                                                                                                                                                                                                                              ↳ QDP
                                                                                                                                                                                                                                ↳ Rewriting
                                                                                                                                                                                                                                  ↳ QDP
                                                                                                                                                                                                                                    ↳ Rewriting
                                                                                                                                                                                                                                      ↳ QDP
                                                                                                                                                                                                                                        ↳ Rewriting
                                                                                                                                                                                                                                          ↳ QDP
                                                                                                                                                                                                                                            ↳ Rewriting
                                                                                                                                                                                                                                              ↳ QDP
                                                                                                                                                                                                                                                ↳ Rewriting
                                                                                                                                                                                                                                                  ↳ QDP
                                                                                                                                                                                                                                                    ↳ Rewriting
                                                                                                                                                                                                                                                      ↳ QDP
                                                                                                                                                                                                                                                        ↳ Rewriting
                                                                                                                                                                                                                                                          ↳ QDP
                                                                                                                                                                                                                                                            ↳ DependencyGraphProof
                                                                                                                                                                                                                                                              ↳ QDP
                                                                                                                                                                                                                                                                ↳ Rewriting
                                                                                                                                                                                                                                                                  ↳ QDP
                                                                                                                                                                                                                                                                    ↳ Rewriting
                                                                                                                                                                                                                                                                      ↳ QDP
                                                                                                                                                                                                                                                                        ↳ Rewriting
                                                                                                                                                                                                                                                                          ↳ QDP
                                                                                                                                                                                                                                                                            ↳ Rewriting
                                                                                                                                                                                                                                                                              ↳ QDP
                                                                                                                                                                                                                                                                                ↳ Rewriting
                                                                                                                                                                                                                                                                                  ↳ QDP
                                                                                                                                                                                                                                                                                    ↳ Rewriting
                                                                                                                                                                                                                                                                                      ↳ QDP
                                                                                                                                                                                                                                                                                        ↳ DependencyGraphProof
                                                                                                                                                                                                                                                                                          ↳ QDP
                                                                                                                                                                                                                                                                                            ↳ Rewriting
                                                                                                                                                                                                                                                                                              ↳ QDP
                                                                                                                                                                                                                                                                                                ↳ DependencyGraphProof
                                                                                                                                                                                                                                                                                                  ↳ QDP
                                                                                                                                                                                                                                                                                                    ↳ Rewriting
                                                                                                                                                                                                                                                                                                      ↳ QDP
                                                                                                                                                                                                                                                                                                        ↳ DependencyGraphProof
                                                                                                                                                                                                                                                                                                          ↳ QDP
                                                                                                                                                                                                                                                                                                            ↳ Rewriting
                                                                                                                                                                                                                                                                                                              ↳ QDP
                                                                                                                                                                                                                                                                                                                ↳ Rewriting
                                                                                                                                                                                                                                                                                                                  ↳ QDP
                                                                                                                                                                                                                                                                                                                    ↳ Rewriting
                                                                                                                                                                                                                                                                                                                      ↳ QDP
                                                                                                                                                                                                                                                                                                                        ↳ Rewriting
                                                                                                                                                                                                                                                                                                                          ↳ QDP
                                                                                                                                                                                                                                                                                                                            ↳ Instantiation
                                                                                                                                                                                                                                                                                                                              ↳ QDP
                                                                                                                                                                                                                                                                                                                                ↳ QDPOrderProof
                                                                                                                                                                                                                                                                                                                                  ↳ QDP
                                                                                                                                                                                                                                                                                                                                    ↳ DependencyGraphProof
                                                                                                                                                                                                                                                                                                                                      ↳ AND
                                                                                                                                                                                                                                                                                                                                        ↳ QDP
                                                                                                                                                                                                                                                                                                                                        ↳ QDP
                                                                                                                                                                                                                                                                                                                                        ↳ QDP
                                                                                                                                                                                                                                                                                                                                          ↳ QDPOrderProof
                                                                                                                                                                                                                                                                                                                                            ↳ QDP
                                                                                                                                                                                                                                                                                                                                              ↳ DependencyGraphProof
                                                                                                                                                                                                                                                                                                                                                ↳ AND
                                                                                                                                                                                                                                                                                                                                                  ↳ QDP
                                                                                                                                                                                                                                                                                                                                                  ↳ QDP
                                                                                                                                                                                                                                                                                                                                                    ↳ UsableRulesProof
                                                                                                                                                                                                                                                                                                                                                      ↳ QDP
                                                                                                                                                                                                                                                                                                                                                        ↳ QReductionProof
                                                                                                                                                                                                                                                                                                                                                          ↳ QDP
                                                                                                                                                                                                                                                                                                                                                            ↳ QDPSizeChangeProof
                                                                                                                                                                                                                                                                                                                                        ↳ QDP
                                                                                                                                                                                                                                                                                                                                        ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP

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

new_mkVBalBranch3MkVBalBranch120(zzz2050, zzz2051, zzz2052, zzz2053, zzz2054, zzz2055, zzz2056, zzz2057, zzz2058, zzz2059, zzz2060, Succ(zzz20610), Succ(zzz20620), be) → new_mkVBalBranch3MkVBalBranch120(zzz2050, zzz2051, zzz2052, zzz2053, zzz2054, zzz2055, zzz2056, zzz2057, zzz2058, zzz2059, zzz2060, zzz20610, zzz20620, be)

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

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

new_mkVBalBranch0(zzz31, Branch(zzz510, zzz511, Neg(Zero), zzz513, zzz514), Branch(zzz340, zzz341, Pos(Succ(zzz34200)), zzz343, zzz344), h) → new_mkVBalBranch0(zzz31, Branch(zzz510, zzz511, Neg(Zero), zzz513, zzz514), zzz343, h)

The TRS R consists of the following rules:

new_primPlusNat1(Zero) → Zero
new_primPlusNat1(Succ(zzz62000)) → Succ(Succ(new_primPlusNat1(zzz62000)))
new_primPlusNat3(zzz90, Succ(zzz910)) → Succ(Succ(new_primPlusNat2(zzz90, zzz910)))
new_primPlusNat3(zzz90, Zero) → Succ(zzz90)
new_primPlusNat2(Succ(zzz900), Succ(zzz9100)) → Succ(Succ(new_primPlusNat2(zzz900, zzz9100)))
new_primPlusNat2(Zero, Succ(zzz9100)) → Succ(zzz9100)
new_primPlusNat2(Zero, Zero) → Zero
new_primPlusNat2(Succ(zzz900), Zero) → Succ(zzz900)

The set Q consists of the following terms:

new_primPlusNat2(Zero, Succ(x0))
new_primPlusNat3(x0, Succ(x1))
new_primPlusNat2(Succ(x0), Succ(x1))
new_primPlusNat3(x0, Zero)
new_primPlusNat1(Zero)
new_primPlusNat2(Zero, Zero)
new_primPlusNat1(Succ(x0))
new_primPlusNat2(Succ(x0), Zero)

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

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

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

new_mkVBalBranch0(zzz31, Branch(zzz510, zzz511, Neg(Zero), zzz513, zzz514), Branch(zzz340, zzz341, Pos(Succ(zzz34200)), zzz343, zzz344), h) → new_mkVBalBranch0(zzz31, Branch(zzz510, zzz511, Neg(Zero), zzz513, zzz514), zzz343, h)

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

new_primPlusNat2(Zero, Succ(x0))
new_primPlusNat3(x0, Succ(x1))
new_primPlusNat2(Succ(x0), Succ(x1))
new_primPlusNat3(x0, Zero)
new_primPlusNat1(Zero)
new_primPlusNat2(Zero, Zero)
new_primPlusNat1(Succ(x0))
new_primPlusNat2(Succ(x0), Zero)

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

new_primPlusNat2(Zero, Succ(x0))
new_primPlusNat3(x0, Succ(x1))
new_primPlusNat2(Succ(x0), Succ(x1))
new_primPlusNat3(x0, Zero)
new_primPlusNat1(Zero)
new_primPlusNat2(Zero, Zero)
new_primPlusNat1(Succ(x0))
new_primPlusNat2(Succ(x0), 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
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                    ↳ DependencyGraphProof
                                      ↳ QDP
                                        ↳ Rewriting
                                          ↳ QDP
                                            ↳ Rewriting
                                              ↳ QDP
                                                ↳ Rewriting
                                                  ↳ QDP
                                                    ↳ Rewriting
                                                      ↳ QDP
                                                        ↳ Rewriting
                                                          ↳ QDP
                                                            ↳ Rewriting
                                                              ↳ QDP
                                                                ↳ Rewriting
                                                                  ↳ QDP
                                                                    ↳ Rewriting
                                                                      ↳ QDP
                                                                        ↳ Rewriting
                                                                          ↳ QDP
                                                                            ↳ Rewriting
                                                                              ↳ QDP
                                                                                ↳ Rewriting
                                                                                  ↳ QDP
                                                                                    ↳ Rewriting
                                                                                      ↳ QDP
                                                                                        ↳ Rewriting
                                                                                          ↳ QDP
                                                                                            ↳ Rewriting
                                                                                              ↳ QDP
                                                                                                ↳ Rewriting
                                                                                                  ↳ QDP
                                                                                                    ↳ Rewriting
                                                                                                      ↳ QDP
                                                                                                        ↳ Rewriting
                                                                                                          ↳ QDP
                                                                                                            ↳ UsableRulesProof
                                                                                                              ↳ QDP
                                                                                                                ↳ QReductionProof
                                                                                                                  ↳ QDP
                                                                                                                    ↳ Rewriting
                                                                                                                      ↳ QDP
                                                                                                                        ↳ Rewriting
                                                                                                                          ↳ QDP
                                                                                                                            ↳ DependencyGraphProof
                                                                                                                              ↳ QDP
                                                                                                                                ↳ Rewriting
                                                                                                                                  ↳ QDP
                                                                                                                                    ↳ Rewriting
                                                                                                                                      ↳ QDP
                                                                                                                                        ↳ DependencyGraphProof
                                                                                                                                          ↳ QDP
                                                                                                                                            ↳ Rewriting
                                                                                                                                              ↳ QDP
                                                                                                                                                ↳ Rewriting
                                                                                                                                                  ↳ QDP
                                                                                                                                                    ↳ Rewriting
                                                                                                                                                      ↳ QDP
                                                                                                                                                        ↳ Rewriting
                                                                                                                                                          ↳ QDP
                                                                                                                                                            ↳ Rewriting
                                                                                                                                                              ↳ QDP
                                                                                                                                                                ↳ Rewriting
                                                                                                                                                                  ↳ QDP
                                                                                                                                                                    ↳ Rewriting
                                                                                                                                                                      ↳ QDP
                                                                                                                                                                        ↳ Rewriting
                                                                                                                                                                          ↳ QDP
                                                                                                                                                                            ↳ Rewriting
                                                                                                                                                                              ↳ QDP
                                                                                                                                                                                ↳ Rewriting
                                                                                                                                                                                  ↳ QDP
                                                                                                                                                                                    ↳ Rewriting
                                                                                                                                                                                      ↳ QDP
                                                                                                                                                                                        ↳ Rewriting
                                                                                                                                                                                          ↳ QDP
                                                                                                                                                                                            ↳ UsableRulesProof
                                                                                                                                                                                              ↳ QDP
                                                                                                                                                                                                ↳ QReductionProof
                                                                                                                                                                                                  ↳ QDP
                                                                                                                                                                                                    ↳ Rewriting
                                                                                                                                                                                                      ↳ QDP
                                                                                                                                                                                                        ↳ Rewriting
                                                                                                                                                                                                          ↳ QDP
                                                                                                                                                                                                            ↳ Rewriting
                                                                                                                                                                                                              ↳ QDP
                                                                                                                                                                                                                ↳ Rewriting
                                                                                                                                                                                                                  ↳ QDP
                                                                                                                                                                                                                    ↳ Rewriting
                                                                                                                                                                                                                      ↳ QDP
                                                                                                                                                                                                                        ↳ Rewriting
                                                                                                                                                                                                                          ↳ QDP
                                                                                                                                                                                                                            ↳ Rewriting
                                                                                                                                                                                                                              ↳ QDP
                                                                                                                                                                                                                                ↳ Rewriting
                                                                                                                                                                                                                                  ↳ QDP
                                                                                                                                                                                                                                    ↳ Rewriting
                                                                                                                                                                                                                                      ↳ QDP
                                                                                                                                                                                                                                        ↳ Rewriting
                                                                                                                                                                                                                                          ↳ QDP
                                                                                                                                                                                                                                            ↳ Rewriting
                                                                                                                                                                                                                                              ↳ QDP
                                                                                                                                                                                                                                                ↳ Rewriting
                                                                                                                                                                                                                                                  ↳ QDP
                                                                                                                                                                                                                                                    ↳ Rewriting
                                                                                                                                                                                                                                                      ↳ QDP
                                                                                                                                                                                                                                                        ↳ Rewriting
                                                                                                                                                                                                                                                          ↳ QDP
                                                                                                                                                                                                                                                            ↳ DependencyGraphProof
                                                                                                                                                                                                                                                              ↳ QDP
                                                                                                                                                                                                                                                                ↳ Rewriting
                                                                                                                                                                                                                                                                  ↳ QDP
                                                                                                                                                                                                                                                                    ↳ Rewriting
                                                                                                                                                                                                                                                                      ↳ QDP
                                                                                                                                                                                                                                                                        ↳ Rewriting
                                                                                                                                                                                                                                                                          ↳ QDP
                                                                                                                                                                                                                                                                            ↳ Rewriting
                                                                                                                                                                                                                                                                              ↳ QDP
                                                                                                                                                                                                                                                                                ↳ Rewriting
                                                                                                                                                                                                                                                                                  ↳ QDP
                                                                                                                                                                                                                                                                                    ↳ Rewriting
                                                                                                                                                                                                                                                                                      ↳ QDP
                                                                                                                                                                                                                                                                                        ↳ DependencyGraphProof
                                                                                                                                                                                                                                                                                          ↳ QDP
                                                                                                                                                                                                                                                                                            ↳ Rewriting
                                                                                                                                                                                                                                                                                              ↳ QDP
                                                                                                                                                                                                                                                                                                ↳ DependencyGraphProof
                                                                                                                                                                                                                                                                                                  ↳ QDP
                                                                                                                                                                                                                                                                                                    ↳ Rewriting
                                                                                                                                                                                                                                                                                                      ↳ QDP
                                                                                                                                                                                                                                                                                                        ↳ DependencyGraphProof
                                                                                                                                                                                                                                                                                                          ↳ QDP
                                                                                                                                                                                                                                                                                                            ↳ Rewriting
                                                                                                                                                                                                                                                                                                              ↳ QDP
                                                                                                                                                                                                                                                                                                                ↳ Rewriting
                                                                                                                                                                                                                                                                                                                  ↳ QDP
                                                                                                                                                                                                                                                                                                                    ↳ Rewriting
                                                                                                                                                                                                                                                                                                                      ↳ QDP
                                                                                                                                                                                                                                                                                                                        ↳ Rewriting
                                                                                                                                                                                                                                                                                                                          ↳ QDP
                                                                                                                                                                                                                                                                                                                            ↳ Instantiation
                                                                                                                                                                                                                                                                                                                              ↳ QDP
                                                                                                                                                                                                                                                                                                                                ↳ QDPOrderProof
                                                                                                                                                                                                                                                                                                                                  ↳ QDP
                                                                                                                                                                                                                                                                                                                                    ↳ DependencyGraphProof
                                                                                                                                                                                                                                                                                                                                      ↳ AND
                                                                                                                                                                                                                                                                                                                                        ↳ QDP
                                                                                                                                                                                                                                                                                                                                        ↳ QDP
                                                                                                                                                                                                                                                                                                                                        ↳ QDP
                                                                                                                                                                                                                                                                                                                                        ↳ QDP
                                                                                                                                                                                                                                                                                                                                          ↳ UsableRulesProof
                                                                                                                                                                                                                                                                                                                                            ↳ QDP
                                                                                                                                                                                                                                                                                                                                              ↳ QReductionProof
                                                                                                                                                                                                                                                                                                                                                ↳ QDP
                                                                                                                                                                                                                                                                                                                                                  ↳ QDPSizeChangeProof
                                                                                                                                                                                                                                                                                                                                        ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP

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

new_mkVBalBranch0(zzz31, Branch(zzz510, zzz511, Neg(Zero), zzz513, zzz514), Branch(zzz340, zzz341, Pos(Succ(zzz34200)), zzz343, zzz344), h) → new_mkVBalBranch0(zzz31, Branch(zzz510, zzz511, Neg(Zero), zzz513, zzz514), 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
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                    ↳ DependencyGraphProof
                                      ↳ QDP
                                        ↳ Rewriting
                                          ↳ QDP
                                            ↳ Rewriting
                                              ↳ QDP
                                                ↳ Rewriting
                                                  ↳ QDP
                                                    ↳ Rewriting
                                                      ↳ QDP
                                                        ↳ Rewriting
                                                          ↳ QDP
                                                            ↳ Rewriting
                                                              ↳ QDP
                                                                ↳ Rewriting
                                                                  ↳ QDP
                                                                    ↳ Rewriting
                                                                      ↳ QDP
                                                                        ↳ Rewriting
                                                                          ↳ QDP
                                                                            ↳ Rewriting
                                                                              ↳ QDP
                                                                                ↳ Rewriting
                                                                                  ↳ QDP
                                                                                    ↳ Rewriting
                                                                                      ↳ QDP
                                                                                        ↳ Rewriting
                                                                                          ↳ QDP
                                                                                            ↳ Rewriting
                                                                                              ↳ QDP
                                                                                                ↳ Rewriting
                                                                                                  ↳ QDP
                                                                                                    ↳ Rewriting
                                                                                                      ↳ QDP
                                                                                                        ↳ Rewriting
                                                                                                          ↳ QDP
                                                                                                            ↳ UsableRulesProof
                                                                                                              ↳ QDP
                                                                                                                ↳ QReductionProof
                                                                                                                  ↳ QDP
                                                                                                                    ↳ Rewriting
                                                                                                                      ↳ QDP
                                                                                                                        ↳ Rewriting
                                                                                                                          ↳ QDP
                                                                                                                            ↳ DependencyGraphProof
                                                                                                                              ↳ QDP
                                                                                                                                ↳ Rewriting
                                                                                                                                  ↳ QDP
                                                                                                                                    ↳ Rewriting
                                                                                                                                      ↳ QDP
                                                                                                                                        ↳ DependencyGraphProof
                                                                                                                                          ↳ QDP
                                                                                                                                            ↳ Rewriting
                                                                                                                                              ↳ QDP
                                                                                                                                                ↳ Rewriting
                                                                                                                                                  ↳ QDP
                                                                                                                                                    ↳ Rewriting
                                                                                                                                                      ↳ QDP
                                                                                                                                                        ↳ Rewriting
                                                                                                                                                          ↳ QDP
                                                                                                                                                            ↳ Rewriting
                                                                                                                                                              ↳ QDP
                                                                                                                                                                ↳ Rewriting
                                                                                                                                                                  ↳ QDP
                                                                                                                                                                    ↳ Rewriting
                                                                                                                                                                      ↳ QDP
                                                                                                                                                                        ↳ Rewriting
                                                                                                                                                                          ↳ QDP
                                                                                                                                                                            ↳ Rewriting
                                                                                                                                                                              ↳ QDP
                                                                                                                                                                                ↳ Rewriting
                                                                                                                                                                                  ↳ QDP
                                                                                                                                                                                    ↳ Rewriting
                                                                                                                                                                                      ↳ QDP
                                                                                                                                                                                        ↳ Rewriting
                                                                                                                                                                                          ↳ QDP
                                                                                                                                                                                            ↳ UsableRulesProof
                                                                                                                                                                                              ↳ QDP
                                                                                                                                                                                                ↳ QReductionProof
                                                                                                                                                                                                  ↳ QDP
                                                                                                                                                                                                    ↳ Rewriting
                                                                                                                                                                                                      ↳ QDP
                                                                                                                                                                                                        ↳ Rewriting
                                                                                                                                                                                                          ↳ QDP
                                                                                                                                                                                                            ↳ Rewriting
                                                                                                                                                                                                              ↳ QDP
                                                                                                                                                                                                                ↳ Rewriting
                                                                                                                                                                                                                  ↳ QDP
                                                                                                                                                                                                                    ↳ Rewriting
                                                                                                                                                                                                                      ↳ QDP
                                                                                                                                                                                                                        ↳ Rewriting
                                                                                                                                                                                                                          ↳ QDP
                                                                                                                                                                                                                            ↳ Rewriting
                                                                                                                                                                                                                              ↳ QDP
                                                                                                                                                                                                                                ↳ Rewriting
                                                                                                                                                                                                                                  ↳ QDP
                                                                                                                                                                                                                                    ↳ Rewriting
                                                                                                                                                                                                                                      ↳ QDP
                                                                                                                                                                                                                                        ↳ Rewriting
                                                                                                                                                                                                                                          ↳ QDP
                                                                                                                                                                                                                                            ↳ Rewriting
                                                                                                                                                                                                                                              ↳ QDP
                                                                                                                                                                                                                                                ↳ Rewriting
                                                                                                                                                                                                                                                  ↳ QDP
                                                                                                                                                                                                                                                    ↳ Rewriting
                                                                                                                                                                                                                                                      ↳ QDP
                                                                                                                                                                                                                                                        ↳ Rewriting
                                                                                                                                                                                                                                                          ↳ QDP
                                                                                                                                                                                                                                                            ↳ DependencyGraphProof
                                                                                                                                                                                                                                                              ↳ QDP
                                                                                                                                                                                                                                                                ↳ Rewriting
                                                                                                                                                                                                                                                                  ↳ QDP
                                                                                                                                                                                                                                                                    ↳ Rewriting
                                                                                                                                                                                                                                                                      ↳ QDP
                                                                                                                                                                                                                                                                        ↳ Rewriting
                                                                                                                                                                                                                                                                          ↳ QDP
                                                                                                                                                                                                                                                                            ↳ Rewriting
                                                                                                                                                                                                                                                                              ↳ QDP
                                                                                                                                                                                                                                                                                ↳ Rewriting
                                                                                                                                                                                                                                                                                  ↳ QDP
                                                                                                                                                                                                                                                                                    ↳ Rewriting
                                                                                                                                                                                                                                                                                      ↳ QDP
                                                                                                                                                                                                                                                                                        ↳ DependencyGraphProof
                                                                                                                                                                                                                                                                                          ↳ QDP
                                                                                                                                                                                                                                                                                            ↳ Rewriting
                                                                                                                                                                                                                                                                                              ↳ QDP
                                                                                                                                                                                                                                                                                                ↳ DependencyGraphProof
                                                                                                                                                                                                                                                                                                  ↳ QDP
                                                                                                                                                                                                                                                                                                    ↳ Rewriting
                                                                                                                                                                                                                                                                                                      ↳ QDP
                                                                                                                                                                                                                                                                                                        ↳ DependencyGraphProof
                                                                                                                                                                                                                                                                                                          ↳ QDP
                                                                                                                                                                                                                                                                                                            ↳ Rewriting
                                                                                                                                                                                                                                                                                                              ↳ QDP
                                                                                                                                                                                                                                                                                                                ↳ Rewriting
                                                                                                                                                                                                                                                                                                                  ↳ QDP
                                                                                                                                                                                                                                                                                                                    ↳ Rewriting
                                                                                                                                                                                                                                                                                                                      ↳ QDP
                                                                                                                                                                                                                                                                                                                        ↳ Rewriting
                                                                                                                                                                                                                                                                                                                          ↳ QDP
                                                                                                                                                                                                                                                                                                                            ↳ Instantiation
                                                                                                                                                                                                                                                                                                                              ↳ QDP
                                                                                                                                                                                                                                                                                                                                ↳ QDPOrderProof
                                                                                                                                                                                                                                                                                                                                  ↳ QDP
                                                                                                                                                                                                                                                                                                                                    ↳ DependencyGraphProof
                                                                                                                                                                                                                                                                                                                                      ↳ AND
                                                                                                                                                                                                                                                                                                                                        ↳ QDP
                                                                                                                                                                                                                                                                                                                                        ↳ QDP
                                                                                                                                                                                                                                                                                                                                        ↳ QDP
                                                                                                                                                                                                                                                                                                                                        ↳ QDP
                                                                                                                                                                                                                                                                                                                                        ↳ QDP
                                                                                                                                                                                                                                                                                                                                          ↳ UsableRulesProof
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP

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

new_mkVBalBranch3MkVBalBranch115(zzz1986, zzz1987, zzz1988, zzz1989, zzz1990, zzz1991, zzz1992, zzz1993, zzz1994, zzz1995, zzz1996, Succ(zzz19970), Succ(zzz19980), bc) → new_mkVBalBranch3MkVBalBranch115(zzz1986, zzz1987, zzz1988, zzz1989, zzz1990, zzz1991, zzz1992, zzz1993, zzz1994, zzz1995, zzz1996, zzz19970, zzz19980, bc)

The TRS R consists of the following rules:

new_primPlusNat1(Zero) → Zero
new_primPlusNat1(Succ(zzz62000)) → Succ(Succ(new_primPlusNat1(zzz62000)))
new_primPlusNat3(zzz90, Succ(zzz910)) → Succ(Succ(new_primPlusNat2(zzz90, zzz910)))
new_primPlusNat3(zzz90, Zero) → Succ(zzz90)
new_primPlusNat2(Succ(zzz900), Succ(zzz9100)) → Succ(Succ(new_primPlusNat2(zzz900, zzz9100)))
new_primPlusNat2(Zero, Succ(zzz9100)) → Succ(zzz9100)
new_primPlusNat2(Zero, Zero) → Zero
new_primPlusNat2(Succ(zzz900), Zero) → Succ(zzz900)

The set Q consists of the following terms:

new_primPlusNat2(Zero, Succ(x0))
new_primPlusNat3(x0, Succ(x1))
new_primPlusNat2(Succ(x0), Succ(x1))
new_primPlusNat3(x0, Zero)
new_primPlusNat1(Zero)
new_primPlusNat2(Zero, Zero)
new_primPlusNat1(Succ(x0))
new_primPlusNat2(Succ(x0), Zero)

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

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

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

new_mkVBalBranch3MkVBalBranch115(zzz1986, zzz1987, zzz1988, zzz1989, zzz1990, zzz1991, zzz1992, zzz1993, zzz1994, zzz1995, zzz1996, Succ(zzz19970), Succ(zzz19980), bc) → new_mkVBalBranch3MkVBalBranch115(zzz1986, zzz1987, zzz1988, zzz1989, zzz1990, zzz1991, zzz1992, zzz1993, zzz1994, zzz1995, zzz1996, zzz19970, zzz19980, bc)

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

new_primPlusNat2(Zero, Succ(x0))
new_primPlusNat3(x0, Succ(x1))
new_primPlusNat2(Succ(x0), Succ(x1))
new_primPlusNat3(x0, Zero)
new_primPlusNat1(Zero)
new_primPlusNat2(Zero, Zero)
new_primPlusNat1(Succ(x0))
new_primPlusNat2(Succ(x0), Zero)

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

new_primPlusNat2(Zero, Succ(x0))
new_primPlusNat3(x0, Succ(x1))
new_primPlusNat2(Succ(x0), Succ(x1))
new_primPlusNat3(x0, Zero)
new_primPlusNat1(Zero)
new_primPlusNat2(Zero, Zero)
new_primPlusNat1(Succ(x0))
new_primPlusNat2(Succ(x0), 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
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                    ↳ DependencyGraphProof
                                      ↳ QDP
                                        ↳ Rewriting
                                          ↳ QDP
                                            ↳ Rewriting
                                              ↳ QDP
                                                ↳ Rewriting
                                                  ↳ QDP
                                                    ↳ Rewriting
                                                      ↳ QDP
                                                        ↳ Rewriting
                                                          ↳ QDP
                                                            ↳ Rewriting
                                                              ↳ QDP
                                                                ↳ Rewriting
                                                                  ↳ QDP
                                                                    ↳ Rewriting
                                                                      ↳ QDP
                                                                        ↳ Rewriting
                                                                          ↳ QDP
                                                                            ↳ Rewriting
                                                                              ↳ QDP
                                                                                ↳ Rewriting
                                                                                  ↳ QDP
                                                                                    ↳ Rewriting
                                                                                      ↳ QDP
                                                                                        ↳ Rewriting
                                                                                          ↳ QDP
                                                                                            ↳ Rewriting
                                                                                              ↳ QDP
                                                                                                ↳ Rewriting
                                                                                                  ↳ QDP
                                                                                                    ↳ Rewriting
                                                                                                      ↳ QDP
                                                                                                        ↳ Rewriting
                                                                                                          ↳ QDP
                                                                                                            ↳ UsableRulesProof
                                                                                                              ↳ QDP
                                                                                                                ↳ QReductionProof
                                                                                                                  ↳ QDP
                                                                                                                    ↳ Rewriting
                                                                                                                      ↳ QDP
                                                                                                                        ↳ Rewriting
                                                                                                                          ↳ QDP
                                                                                                                            ↳ DependencyGraphProof
                                                                                                                              ↳ QDP
                                                                                                                                ↳ Rewriting
                                                                                                                                  ↳ QDP
                                                                                                                                    ↳ Rewriting
                                                                                                                                      ↳ QDP
                                                                                                                                        ↳ DependencyGraphProof
                                                                                                                                          ↳ QDP
                                                                                                                                            ↳ Rewriting
                                                                                                                                              ↳ QDP
                                                                                                                                                ↳ Rewriting
                                                                                                                                                  ↳ QDP
                                                                                                                                                    ↳ Rewriting
                                                                                                                                                      ↳ QDP
                                                                                                                                                        ↳ Rewriting
                                                                                                                                                          ↳ QDP
                                                                                                                                                            ↳ Rewriting
                                                                                                                                                              ↳ QDP
                                                                                                                                                                ↳ Rewriting
                                                                                                                                                                  ↳ QDP
                                                                                                                                                                    ↳ Rewriting
                                                                                                                                                                      ↳ QDP
                                                                                                                                                                        ↳ Rewriting
                                                                                                                                                                          ↳ QDP
                                                                                                                                                                            ↳ Rewriting
                                                                                                                                                                              ↳ QDP
                                                                                                                                                                                ↳ Rewriting
                                                                                                                                                                                  ↳ QDP
                                                                                                                                                                                    ↳ Rewriting
                                                                                                                                                                                      ↳ QDP
                                                                                                                                                                                        ↳ Rewriting
                                                                                                                                                                                          ↳ QDP
                                                                                                                                                                                            ↳ UsableRulesProof
                                                                                                                                                                                              ↳ QDP
                                                                                                                                                                                                ↳ QReductionProof
                                                                                                                                                                                                  ↳ QDP
                                                                                                                                                                                                    ↳ Rewriting
                                                                                                                                                                                                      ↳ QDP
                                                                                                                                                                                                        ↳ Rewriting
                                                                                                                                                                                                          ↳ QDP
                                                                                                                                                                                                            ↳ Rewriting
                                                                                                                                                                                                              ↳ QDP
                                                                                                                                                                                                                ↳ Rewriting
                                                                                                                                                                                                                  ↳ QDP
                                                                                                                                                                                                                    ↳ Rewriting
                                                                                                                                                                                                                      ↳ QDP
                                                                                                                                                                                                                        ↳ Rewriting
                                                                                                                                                                                                                          ↳ QDP
                                                                                                                                                                                                                            ↳ Rewriting
                                                                                                                                                                                                                              ↳ QDP
                                                                                                                                                                                                                                ↳ Rewriting
                                                                                                                                                                                                                                  ↳ QDP
                                                                                                                                                                                                                                    ↳ Rewriting
                                                                                                                                                                                                                                      ↳ QDP
                                                                                                                                                                                                                                        ↳ Rewriting
                                                                                                                                                                                                                                          ↳ QDP
                                                                                                                                                                                                                                            ↳ Rewriting
                                                                                                                                                                                                                                              ↳ QDP
                                                                                                                                                                                                                                                ↳ Rewriting
                                                                                                                                                                                                                                                  ↳ QDP
                                                                                                                                                                                                                                                    ↳ Rewriting
                                                                                                                                                                                                                                                      ↳ QDP
                                                                                                                                                                                                                                                        ↳ Rewriting
                                                                                                                                                                                                                                                          ↳ QDP
                                                                                                                                                                                                                                                            ↳ DependencyGraphProof
                                                                                                                                                                                                                                                              ↳ QDP
                                                                                                                                                                                                                                                                ↳ Rewriting
                                                                                                                                                                                                                                                                  ↳ QDP
                                                                                                                                                                                                                                                                    ↳ Rewriting
                                                                                                                                                                                                                                                                      ↳ QDP
                                                                                                                                                                                                                                                                        ↳ Rewriting
                                                                                                                                                                                                                                                                          ↳ QDP
                                                                                                                                                                                                                                                                            ↳ Rewriting
                                                                                                                                                                                                                                                                              ↳ QDP
                                                                                                                                                                                                                                                                                ↳ Rewriting
                                                                                                                                                                                                                                                                                  ↳ QDP
                                                                                                                                                                                                                                                                                    ↳ Rewriting
                                                                                                                                                                                                                                                                                      ↳ QDP
                                                                                                                                                                                                                                                                                        ↳ DependencyGraphProof
                                                                                                                                                                                                                                                                                          ↳ QDP
                                                                                                                                                                                                                                                                                            ↳ Rewriting
                                                                                                                                                                                                                                                                                              ↳ QDP
                                                                                                                                                                                                                                                                                                ↳ DependencyGraphProof
                                                                                                                                                                                                                                                                                                  ↳ QDP
                                                                                                                                                                                                                                                                                                    ↳ Rewriting
                                                                                                                                                                                                                                                                                                      ↳ QDP
                                                                                                                                                                                                                                                                                                        ↳ DependencyGraphProof
                                                                                                                                                                                                                                                                                                          ↳ QDP
                                                                                                                                                                                                                                                                                                            ↳ Rewriting
                                                                                                                                                                                                                                                                                                              ↳ QDP
                                                                                                                                                                                                                                                                                                                ↳ Rewriting
                                                                                                                                                                                                                                                                                                                  ↳ QDP
                                                                                                                                                                                                                                                                                                                    ↳ Rewriting
                                                                                                                                                                                                                                                                                                                      ↳ QDP
                                                                                                                                                                                                                                                                                                                        ↳ Rewriting
                                                                                                                                                                                                                                                                                                                          ↳ QDP
                                                                                                                                                                                                                                                                                                                            ↳ Instantiation
                                                                                                                                                                                                                                                                                                                              ↳ QDP
                                                                                                                                                                                                                                                                                                                                ↳ QDPOrderProof
                                                                                                                                                                                                                                                                                                                                  ↳ QDP
                                                                                                                                                                                                                                                                                                                                    ↳ DependencyGraphProof
                                                                                                                                                                                                                                                                                                                                      ↳ AND
                                                                                                                                                                                                                                                                                                                                        ↳ QDP
                                                                                                                                                                                                                                                                                                                                        ↳ QDP
                                                                                                                                                                                                                                                                                                                                        ↳ QDP
                                                                                                                                                                                                                                                                                                                                        ↳ QDP
                                                                                                                                                                                                                                                                                                                                        ↳ QDP
                                                                                                                                                                                                                                                                                                                                          ↳ UsableRulesProof
                                                                                                                                                                                                                                                                                                                                            ↳ QDP
                                                                                                                                                                                                                                                                                                                                              ↳ QReductionProof
                                                                                                                                                                                                                                                                                                                                                ↳ QDP
                                                                                                                                                                                                                                                                                                                                                  ↳ QDPSizeChangeProof
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP

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

new_mkVBalBranch3MkVBalBranch115(zzz1986, zzz1987, zzz1988, zzz1989, zzz1990, zzz1991, zzz1992, zzz1993, zzz1994, zzz1995, zzz1996, Succ(zzz19970), Succ(zzz19980), bc) → new_mkVBalBranch3MkVBalBranch115(zzz1986, zzz1987, zzz1988, zzz1989, zzz1990, zzz1991, zzz1992, zzz1993, zzz1994, zzz1995, zzz1996, zzz19970, zzz19980, bc)

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

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

new_splitGT1(Branch(GT, zzz8561, zzz8562, zzz8563, zzz8564), h) → new_splitGT23(zzz8561, zzz8562, zzz8563, zzz8564, h)
new_splitGT23(zzz869, zzz870, zzz871, zzz872, ba) → new_splitGT1(zzz871, ba)
new_splitGT1(Branch(EQ, zzz8561, zzz8562, zzz8563, zzz8564), h) → new_splitGT22(zzz8561, zzz8562, zzz8563, zzz8564, h)
new_splitGT22(zzz854, zzz855, Branch(EQ, zzz8561, zzz8562, zzz8563, zzz8564), zzz857, h) → new_splitGT22(zzz8561, zzz8562, zzz8563, zzz8564, h)
new_splitGT22(zzz854, zzz855, Branch(GT, zzz8561, zzz8562, zzz8563, zzz8564), zzz857, h) → new_splitGT23(zzz8561, zzz8562, zzz8563, zzz8564, 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
                                  ↳ QDP
                                    ↳ QDPSizeChangeProof
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP

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

new_addToFM_C1(Branch(EQ, zzz3171, zzz3172, zzz3173, zzz3174), zzz31, h) → new_addToFM_C1(zzz3173, zzz31, h)
new_addToFM_C1(Branch(GT, zzz3171, zzz3172, zzz3173, zzz3174), zzz31, h) → new_addToFM_C1(zzz3173, zzz31, 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
                                  ↳ QDP
                                  ↳ QDP
                                    ↳ DependencyGraphProof
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP

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

new_mkVBalBranch1(zzz31, Branch(zzz330, zzz331, Neg(Zero), zzz333, zzz334), Branch(zzz3170, zzz3171, Neg(Succ(zzz317200)), zzz3173, zzz3174), h) → new_mkVBalBranch3MkVBalBranch127(zzz3170, zzz3171, zzz317200, zzz3173, zzz3174, zzz330, zzz331, zzz333, zzz334, zzz31, new_primMulNat1(zzz317200), h)
new_mkVBalBranch3MkVBalBranch129(zzz1851, zzz1852, zzz1853, zzz1854, zzz1855, zzz1856, zzz1857, zzz1858, zzz1859, zzz1860, zzz1861, Zero, Succ(zzz18630), bd) → new_mkVBalBranch1(zzz1861, zzz1860, Branch(zzz1851, zzz1852, Neg(Succ(zzz1853)), zzz1854, zzz1855), bd)
new_mkVBalBranch3MkVBalBranch238(zzz3170, zzz3171, Succ(zzz317200), zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, h) → new_mkVBalBranch3MkVBalBranch123(zzz3170, zzz3171, zzz317200, zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, new_primPlusNat2(new_primMulNat0(zzz317200), Succ(zzz317200)), h)
new_mkVBalBranch1(zzz31, Branch(zzz330, zzz331, Neg(Succ(zzz33200)), zzz333, zzz334), Branch(zzz3170, zzz3171, zzz3172, zzz3173, zzz3174), h) → new_mkVBalBranch3MkVBalBranch241(zzz3170, zzz3171, zzz3172, zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, new_primPlusNat2(new_primMulNat0(zzz33200), Succ(zzz33200)), h)
new_mkVBalBranch3MkVBalBranch241(zzz3170, zzz3171, Pos(zzz31720), zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, Succ(zzz4190), h) → new_mkVBalBranch1(zzz31, Branch(zzz330, zzz331, Neg(Succ(zzz33200)), zzz333, zzz334), zzz3173, h)
new_mkVBalBranch3MkVBalBranch128(zzz972, zzz973, zzz974, zzz975, zzz976, zzz977, zzz978, zzz979, zzz980, zzz981, zzz982, Succ(zzz10190), bc) → new_mkVBalBranch3MkVBalBranch129(zzz972, zzz973, zzz974, zzz975, zzz976, zzz977, zzz978, zzz979, zzz980, zzz981, zzz982, Succ(zzz979), Succ(zzz10190), bc)
new_mkVBalBranch3MkVBalBranch127(zzz3170, zzz3171, zzz317200, zzz3173, zzz3174, zzz330, zzz331, zzz333, zzz334, zzz31, Succ(zzz5500), h) → new_mkVBalBranch1(zzz31, zzz334, Branch(zzz3170, zzz3171, Neg(Succ(zzz317200)), zzz3173, zzz3174), h)
new_mkVBalBranch3MkVBalBranch129(zzz1851, zzz1852, zzz1853, zzz1854, zzz1855, zzz1856, zzz1857, zzz1858, zzz1859, zzz1860, zzz1861, Succ(zzz18620), Succ(zzz18630), bd) → new_mkVBalBranch3MkVBalBranch129(zzz1851, zzz1852, zzz1853, zzz1854, zzz1855, zzz1856, zzz1857, zzz1858, zzz1859, zzz1860, zzz1861, zzz18620, zzz18630, bd)
new_mkVBalBranch3MkVBalBranch124(zzz958, zzz959, zzz960, zzz961, zzz962, zzz963, zzz964, zzz965, zzz966, zzz967, zzz968, Zero, ba) → new_mkVBalBranch3MkVBalBranch125(zzz958, zzz959, zzz960, zzz961, zzz962, zzz963, zzz964, zzz965, zzz966, zzz967, zzz968, Zero, Succ(zzz965), ba)
new_mkVBalBranch3MkVBalBranch235(zzz3170, zzz3171, Pos(Succ(zzz317200)), zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, Succ(zzz4170), h) → new_mkVBalBranch3MkVBalBranch236(zzz3170, zzz3171, zzz317200, zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, zzz4170, zzz317200, h)
new_mkVBalBranch3MkVBalBranch242(zzz972, zzz973, zzz974, zzz975, zzz976, zzz977, zzz978, zzz979, zzz980, zzz981, zzz982, Succ(zzz9830), Succ(zzz9840), bc) → new_mkVBalBranch3MkVBalBranch242(zzz972, zzz973, zzz974, zzz975, zzz976, zzz977, zzz978, zzz979, zzz980, zzz981, zzz982, zzz9830, zzz9840, bc)
new_mkVBalBranch3MkVBalBranch236(zzz958, zzz959, zzz960, zzz961, zzz962, zzz963, zzz964, zzz965, zzz966, zzz967, zzz968, Succ(zzz9690), Succ(zzz9700), ba) → new_mkVBalBranch3MkVBalBranch236(zzz958, zzz959, zzz960, zzz961, zzz962, zzz963, zzz964, zzz965, zzz966, zzz967, zzz968, zzz9690, zzz9700, ba)
new_mkVBalBranch3MkVBalBranch241(zzz3170, zzz3171, Neg(Succ(zzz317200)), zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, Succ(zzz4190), h) → new_mkVBalBranch3MkVBalBranch242(zzz3170, zzz3171, zzz317200, zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, zzz317200, zzz4190, h)
new_mkVBalBranch3MkVBalBranch241(zzz3170, zzz3171, Neg(Succ(zzz317200)), zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, Zero, h) → new_mkVBalBranch3MkVBalBranch242(zzz3170, zzz3171, zzz317200, zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, Succ(zzz317200), Zero, h)
new_mkVBalBranch1(zzz31, Branch(zzz330, zzz331, Pos(Zero), zzz333, zzz334), Branch(zzz3170, zzz3171, Pos(Succ(zzz317200)), zzz3173, zzz3174), h) → new_mkVBalBranch1(zzz31, Branch(zzz330, zzz331, Pos(Zero), zzz333, zzz334), zzz3173, h)
new_mkVBalBranch3MkVBalBranch237(zzz3170, zzz3171, zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, h) → new_mkVBalBranch1(zzz31, zzz334, Branch(zzz3170, zzz3171, Pos(Zero), zzz3173, zzz3174), h)
new_mkVBalBranch3MkVBalBranch243(zzz3170, zzz3171, zzz31720, zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, h) → new_mkVBalBranch1(zzz31, Branch(zzz330, zzz331, Neg(Succ(zzz33200)), zzz333, zzz334), zzz3173, h)
new_mkVBalBranch3MkVBalBranch235(zzz3170, zzz3171, Pos(Zero), zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, Succ(zzz4170), h) → new_mkVBalBranch3MkVBalBranch237(zzz3170, zzz3171, zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, h)
new_mkVBalBranch3MkVBalBranch235(zzz3170, zzz3171, Neg(Succ(zzz317200)), zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, Succ(zzz4170), h) → new_mkVBalBranch3MkVBalBranch123(zzz3170, zzz3171, zzz317200, zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, new_primPlusNat2(new_primMulNat0(zzz317200), Succ(zzz317200)), h)
new_mkVBalBranch3MkVBalBranch236(zzz958, zzz959, zzz960, zzz961, zzz962, zzz963, zzz964, zzz965, zzz966, zzz967, zzz968, Zero, Succ(zzz9700), ba) → new_mkVBalBranch1(zzz968, Branch(zzz963, zzz964, Pos(Succ(zzz965)), zzz966, zzz967), zzz961, ba)
new_mkVBalBranch3MkVBalBranch238(zzz3170, zzz3171, Zero, zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, h) → new_mkVBalBranch1(zzz31, zzz334, Branch(zzz3170, zzz3171, Neg(Zero), zzz3173, zzz3174), h)
new_mkVBalBranch3MkVBalBranch244(zzz972, zzz973, zzz974, zzz975, zzz976, zzz977, zzz978, zzz979, zzz980, zzz981, zzz982, bc) → new_mkVBalBranch3MkVBalBranch128(zzz972, zzz973, zzz974, zzz975, zzz976, zzz977, zzz978, zzz979, zzz980, zzz981, zzz982, new_primMulNat1(zzz974), bc)
new_mkVBalBranch3MkVBalBranch125(zzz1337, zzz1338, zzz1339, zzz1340, zzz1341, zzz1342, zzz1343, zzz1344, zzz1345, zzz1346, zzz1347, Succ(zzz13480), Succ(zzz13490), bb) → new_mkVBalBranch3MkVBalBranch125(zzz1337, zzz1338, zzz1339, zzz1340, zzz1341, zzz1342, zzz1343, zzz1344, zzz1345, zzz1346, zzz1347, zzz13480, zzz13490, bb)
new_mkVBalBranch3MkVBalBranch123(zzz3170, zzz3171, zzz317200, zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, Succ(zzz5620), h) → new_mkVBalBranch1(zzz31, zzz334, Branch(zzz3170, zzz3171, Neg(Succ(zzz317200)), zzz3173, zzz3174), h)
new_mkVBalBranch3MkVBalBranch125(zzz1337, zzz1338, zzz1339, zzz1340, zzz1341, zzz1342, zzz1343, zzz1344, zzz1345, zzz1346, zzz1347, Zero, Succ(zzz13490), bb) → new_mkVBalBranch1(zzz1347, zzz1346, Branch(zzz1337, zzz1338, Pos(Succ(zzz1339)), zzz1340, zzz1341), bb)
new_mkVBalBranch3MkVBalBranch242(zzz972, zzz973, zzz974, zzz975, zzz976, zzz977, zzz978, zzz979, zzz980, zzz981, zzz982, Zero, Succ(zzz9840), bc) → new_mkVBalBranch1(zzz982, Branch(zzz977, zzz978, Neg(Succ(zzz979)), zzz980, zzz981), zzz975, bc)
new_mkVBalBranch3MkVBalBranch128(zzz972, zzz973, zzz974, zzz975, zzz976, zzz977, zzz978, zzz979, zzz980, zzz981, zzz982, Zero, bc) → new_mkVBalBranch3MkVBalBranch129(zzz972, zzz973, zzz974, zzz975, zzz976, zzz977, zzz978, zzz979, zzz980, zzz981, zzz982, Succ(zzz979), Zero, bc)
new_mkVBalBranch3MkVBalBranch236(zzz958, zzz959, zzz960, zzz961, zzz962, zzz963, zzz964, zzz965, zzz966, zzz967, zzz968, Succ(zzz9690), Zero, ba) → new_mkVBalBranch3MkVBalBranch124(zzz958, zzz959, zzz960, zzz961, zzz962, zzz963, zzz964, zzz965, zzz966, zzz967, zzz968, new_primMulNat1(zzz960), ba)
new_mkVBalBranch3MkVBalBranch240(zzz958, zzz959, zzz960, zzz961, zzz962, zzz963, zzz964, zzz965, zzz966, zzz967, zzz968, ba) → new_mkVBalBranch3MkVBalBranch124(zzz958, zzz959, zzz960, zzz961, zzz962, zzz963, zzz964, zzz965, zzz966, zzz967, zzz968, new_primMulNat1(zzz960), ba)
new_mkVBalBranch3MkVBalBranch239(zzz3170, zzz3171, Succ(zzz317200), zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, h) → new_mkVBalBranch3MkVBalBranch123(zzz3170, zzz3171, zzz317200, zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, new_primPlusNat2(new_primMulNat0(zzz317200), Succ(zzz317200)), h)
new_mkVBalBranch3MkVBalBranch235(zzz3170, zzz3171, Neg(Succ(zzz317200)), zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, Zero, h) → new_mkVBalBranch3MkVBalBranch238(zzz3170, zzz3171, Succ(zzz317200), zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, h)
new_mkVBalBranch1(zzz31, Branch(zzz330, zzz331, Pos(Succ(zzz33200)), zzz333, zzz334), Branch(zzz3170, zzz3171, zzz3172, zzz3173, zzz3174), h) → new_mkVBalBranch3MkVBalBranch235(zzz3170, zzz3171, zzz3172, zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, new_primPlusNat2(new_primMulNat0(zzz33200), Succ(zzz33200)), h)
new_mkVBalBranch3MkVBalBranch241(zzz3170, zzz3171, Pos(Succ(zzz317200)), zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, Zero, h) → new_mkVBalBranch3MkVBalBranch243(zzz3170, zzz3171, Succ(zzz317200), zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, h)
new_mkVBalBranch3MkVBalBranch126(zzz3170, zzz3171, zzz317200, zzz3173, zzz3174, zzz330, zzz331, zzz333, zzz334, zzz31, Succ(zzz5350), h) → new_mkVBalBranch1(zzz31, zzz334, Branch(zzz3170, zzz3171, Neg(Succ(zzz317200)), zzz3173, zzz3174), h)
new_mkVBalBranch1(zzz31, Branch(zzz330, zzz331, Pos(Zero), zzz333, zzz334), Branch(zzz3170, zzz3171, Neg(Succ(zzz317200)), zzz3173, zzz3174), h) → new_mkVBalBranch3MkVBalBranch126(zzz3170, zzz3171, zzz317200, zzz3173, zzz3174, zzz330, zzz331, zzz333, zzz334, zzz31, new_primMulNat1(zzz317200), h)
new_mkVBalBranch3MkVBalBranch241(zzz3170, zzz3171, Neg(Zero), zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, Succ(zzz4190), h) → new_mkVBalBranch1(zzz31, Branch(zzz330, zzz331, Neg(Succ(zzz33200)), zzz333, zzz334), zzz3173, h)
new_mkVBalBranch3MkVBalBranch123(zzz3170, zzz3171, zzz317200, zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, Zero, h) → new_mkVBalBranch3MkVBalBranch130(zzz3170, zzz3171, zzz317200, zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, h)
new_mkVBalBranch3MkVBalBranch124(zzz958, zzz959, zzz960, zzz961, zzz962, zzz963, zzz964, zzz965, zzz966, zzz967, zzz968, Succ(zzz10180), ba) → new_mkVBalBranch3MkVBalBranch125(zzz958, zzz959, zzz960, zzz961, zzz962, zzz963, zzz964, zzz965, zzz966, zzz967, zzz968, Succ(zzz10180), Succ(zzz965), ba)
new_mkVBalBranch3MkVBalBranch235(zzz3170, zzz3171, Pos(Succ(zzz317200)), zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, Zero, h) → new_mkVBalBranch3MkVBalBranch236(zzz3170, zzz3171, zzz317200, zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, Zero, Succ(zzz317200), h)
new_mkVBalBranch3MkVBalBranch242(zzz972, zzz973, zzz974, zzz975, zzz976, zzz977, zzz978, zzz979, zzz980, zzz981, zzz982, Succ(zzz9830), Zero, bc) → new_mkVBalBranch3MkVBalBranch128(zzz972, zzz973, zzz974, zzz975, zzz976, zzz977, zzz978, zzz979, zzz980, zzz981, zzz982, new_primMulNat1(zzz974), bc)
new_mkVBalBranch3MkVBalBranch239(zzz3170, zzz3171, Zero, zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, h) → new_mkVBalBranch1(zzz31, zzz334, Branch(zzz3170, zzz3171, Neg(Zero), zzz3173, zzz3174), h)
new_mkVBalBranch3MkVBalBranch235(zzz3170, zzz3171, Pos(Zero), zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, Zero, h) → new_mkVBalBranch1(zzz31, zzz334, Branch(zzz3170, zzz3171, Pos(Zero), zzz3173, zzz3174), h)
new_mkVBalBranch3MkVBalBranch242(zzz972, zzz973, zzz974, zzz975, zzz976, zzz977, zzz978, zzz979, zzz980, zzz981, zzz982, Zero, Zero, bc) → new_mkVBalBranch3MkVBalBranch244(zzz972, zzz973, zzz974, zzz975, zzz976, zzz977, zzz978, zzz979, zzz980, zzz981, zzz982, bc)
new_mkVBalBranch3MkVBalBranch130(zzz3170, zzz3171, zzz317200, zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, h) → new_mkVBalBranch1(zzz31, zzz334, Branch(zzz3170, zzz3171, Neg(Succ(zzz317200)), zzz3173, zzz3174), h)
new_mkVBalBranch1(zzz31, Branch(zzz330, zzz331, Neg(Zero), zzz333, zzz334), Branch(zzz3170, zzz3171, Pos(Succ(zzz317200)), zzz3173, zzz3174), h) → new_mkVBalBranch1(zzz31, Branch(zzz330, zzz331, Neg(Zero), zzz333, zzz334), zzz3173, h)
new_mkVBalBranch3MkVBalBranch235(zzz3170, zzz3171, Neg(Zero), zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, Zero, h) → new_mkVBalBranch3MkVBalBranch239(zzz3170, zzz3171, Zero, zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, h)
new_mkVBalBranch3MkVBalBranch235(zzz3170, zzz3171, Neg(Zero), zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, Succ(zzz4170), h) → new_mkVBalBranch1(zzz31, zzz334, Branch(zzz3170, zzz3171, Neg(Zero), zzz3173, zzz3174), h)
new_mkVBalBranch3MkVBalBranch236(zzz958, zzz959, zzz960, zzz961, zzz962, zzz963, zzz964, zzz965, zzz966, zzz967, zzz968, Zero, Zero, ba) → new_mkVBalBranch3MkVBalBranch240(zzz958, zzz959, zzz960, zzz961, zzz962, zzz963, zzz964, zzz965, zzz966, zzz967, zzz968, ba)

The TRS R consists of the following rules:

new_primPlusNat1(Zero) → Zero
new_primMulNat0(zzz6200) → new_primPlusNat3(Succ(new_primPlusNat3(new_primPlusNat1(zzz6200), zzz6200)), Succ(zzz6200))
new_primPlusNat2(Succ(zzz900), Succ(zzz9100)) → Succ(Succ(new_primPlusNat2(zzz900, zzz9100)))
new_primPlusNat3(zzz90, Succ(zzz910)) → Succ(Succ(new_primPlusNat2(zzz90, zzz910)))
new_primPlusNat3(zzz90, Zero) → Succ(zzz90)
new_primMulNat1(zzz34200) → new_primPlusNat2(new_primMulNat0(zzz34200), Succ(zzz34200))
new_primPlusNat2(Zero, Zero) → Zero
new_primPlusNat1(Succ(zzz62000)) → Succ(Succ(new_primPlusNat1(zzz62000)))
new_primPlusNat2(Succ(zzz900), Zero) → Succ(zzz900)
new_primPlusNat2(Zero, Succ(zzz9100)) → Succ(zzz9100)

The set Q consists of the following terms:

new_primPlusNat2(Zero, Succ(x0))
new_primMulNat1(x0)
new_primMulNat0(x0)
new_primPlusNat3(x0, Succ(x1))
new_primPlusNat2(Succ(x0), Succ(x1))
new_primPlusNat3(x0, Zero)
new_primPlusNat1(Zero)
new_primPlusNat2(Zero, Zero)
new_primPlusNat1(Succ(x0))
new_primPlusNat2(Succ(x0), Zero)

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

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

new_mkVBalBranch3MkVBalBranch238(zzz3170, zzz3171, Succ(zzz317200), zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, h) → new_mkVBalBranch3MkVBalBranch123(zzz3170, zzz3171, zzz317200, zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, new_primPlusNat2(new_primMulNat0(zzz317200), Succ(zzz317200)), h)
new_mkVBalBranch3MkVBalBranch129(zzz1851, zzz1852, zzz1853, zzz1854, zzz1855, zzz1856, zzz1857, zzz1858, zzz1859, zzz1860, zzz1861, Zero, Succ(zzz18630), bd) → new_mkVBalBranch1(zzz1861, zzz1860, Branch(zzz1851, zzz1852, Neg(Succ(zzz1853)), zzz1854, zzz1855), bd)
new_mkVBalBranch1(zzz31, Branch(zzz330, zzz331, Neg(Zero), zzz333, zzz334), Branch(zzz3170, zzz3171, Neg(Succ(zzz317200)), zzz3173, zzz3174), h) → new_mkVBalBranch3MkVBalBranch127(zzz3170, zzz3171, zzz317200, zzz3173, zzz3174, zzz330, zzz331, zzz333, zzz334, zzz31, new_primMulNat1(zzz317200), h)
new_mkVBalBranch1(zzz31, Branch(zzz330, zzz331, Neg(Succ(zzz33200)), zzz333, zzz334), Branch(zzz3170, zzz3171, zzz3172, zzz3173, zzz3174), h) → new_mkVBalBranch3MkVBalBranch241(zzz3170, zzz3171, zzz3172, zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, new_primPlusNat2(new_primMulNat0(zzz33200), Succ(zzz33200)), h)
new_mkVBalBranch3MkVBalBranch128(zzz972, zzz973, zzz974, zzz975, zzz976, zzz977, zzz978, zzz979, zzz980, zzz981, zzz982, Succ(zzz10190), bc) → new_mkVBalBranch3MkVBalBranch129(zzz972, zzz973, zzz974, zzz975, zzz976, zzz977, zzz978, zzz979, zzz980, zzz981, zzz982, Succ(zzz979), Succ(zzz10190), bc)
new_mkVBalBranch3MkVBalBranch241(zzz3170, zzz3171, Pos(zzz31720), zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, Succ(zzz4190), h) → new_mkVBalBranch1(zzz31, Branch(zzz330, zzz331, Neg(Succ(zzz33200)), zzz333, zzz334), zzz3173, h)
new_mkVBalBranch3MkVBalBranch127(zzz3170, zzz3171, zzz317200, zzz3173, zzz3174, zzz330, zzz331, zzz333, zzz334, zzz31, Succ(zzz5500), h) → new_mkVBalBranch1(zzz31, zzz334, Branch(zzz3170, zzz3171, Neg(Succ(zzz317200)), zzz3173, zzz3174), h)
new_mkVBalBranch3MkVBalBranch129(zzz1851, zzz1852, zzz1853, zzz1854, zzz1855, zzz1856, zzz1857, zzz1858, zzz1859, zzz1860, zzz1861, Succ(zzz18620), Succ(zzz18630), bd) → new_mkVBalBranch3MkVBalBranch129(zzz1851, zzz1852, zzz1853, zzz1854, zzz1855, zzz1856, zzz1857, zzz1858, zzz1859, zzz1860, zzz1861, zzz18620, zzz18630, bd)
new_mkVBalBranch3MkVBalBranch124(zzz958, zzz959, zzz960, zzz961, zzz962, zzz963, zzz964, zzz965, zzz966, zzz967, zzz968, Zero, ba) → new_mkVBalBranch3MkVBalBranch125(zzz958, zzz959, zzz960, zzz961, zzz962, zzz963, zzz964, zzz965, zzz966, zzz967, zzz968, Zero, Succ(zzz965), ba)
new_mkVBalBranch3MkVBalBranch242(zzz972, zzz973, zzz974, zzz975, zzz976, zzz977, zzz978, zzz979, zzz980, zzz981, zzz982, Succ(zzz9830), Succ(zzz9840), bc) → new_mkVBalBranch3MkVBalBranch242(zzz972, zzz973, zzz974, zzz975, zzz976, zzz977, zzz978, zzz979, zzz980, zzz981, zzz982, zzz9830, zzz9840, bc)
new_mkVBalBranch3MkVBalBranch235(zzz3170, zzz3171, Pos(Succ(zzz317200)), zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, Succ(zzz4170), h) → new_mkVBalBranch3MkVBalBranch236(zzz3170, zzz3171, zzz317200, zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, zzz4170, zzz317200, h)
new_mkVBalBranch3MkVBalBranch236(zzz958, zzz959, zzz960, zzz961, zzz962, zzz963, zzz964, zzz965, zzz966, zzz967, zzz968, Succ(zzz9690), Succ(zzz9700), ba) → new_mkVBalBranch3MkVBalBranch236(zzz958, zzz959, zzz960, zzz961, zzz962, zzz963, zzz964, zzz965, zzz966, zzz967, zzz968, zzz9690, zzz9700, ba)
new_mkVBalBranch3MkVBalBranch241(zzz3170, zzz3171, Neg(Succ(zzz317200)), zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, Succ(zzz4190), h) → new_mkVBalBranch3MkVBalBranch242(zzz3170, zzz3171, zzz317200, zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, zzz317200, zzz4190, h)
new_mkVBalBranch3MkVBalBranch241(zzz3170, zzz3171, Neg(Succ(zzz317200)), zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, Zero, h) → new_mkVBalBranch3MkVBalBranch242(zzz3170, zzz3171, zzz317200, zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, Succ(zzz317200), Zero, h)
new_mkVBalBranch1(zzz31, Branch(zzz330, zzz331, Pos(Zero), zzz333, zzz334), Branch(zzz3170, zzz3171, Pos(Succ(zzz317200)), zzz3173, zzz3174), h) → new_mkVBalBranch1(zzz31, Branch(zzz330, zzz331, Pos(Zero), zzz333, zzz334), zzz3173, h)
new_mkVBalBranch3MkVBalBranch243(zzz3170, zzz3171, zzz31720, zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, h) → new_mkVBalBranch1(zzz31, Branch(zzz330, zzz331, Neg(Succ(zzz33200)), zzz333, zzz334), zzz3173, h)
new_mkVBalBranch3MkVBalBranch237(zzz3170, zzz3171, zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, h) → new_mkVBalBranch1(zzz31, zzz334, Branch(zzz3170, zzz3171, Pos(Zero), zzz3173, zzz3174), h)
new_mkVBalBranch3MkVBalBranch235(zzz3170, zzz3171, Pos(Zero), zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, Succ(zzz4170), h) → new_mkVBalBranch3MkVBalBranch237(zzz3170, zzz3171, zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, h)
new_mkVBalBranch3MkVBalBranch235(zzz3170, zzz3171, Neg(Succ(zzz317200)), zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, Succ(zzz4170), h) → new_mkVBalBranch3MkVBalBranch123(zzz3170, zzz3171, zzz317200, zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, new_primPlusNat2(new_primMulNat0(zzz317200), Succ(zzz317200)), h)
new_mkVBalBranch3MkVBalBranch236(zzz958, zzz959, zzz960, zzz961, zzz962, zzz963, zzz964, zzz965, zzz966, zzz967, zzz968, Zero, Succ(zzz9700), ba) → new_mkVBalBranch1(zzz968, Branch(zzz963, zzz964, Pos(Succ(zzz965)), zzz966, zzz967), zzz961, ba)
new_mkVBalBranch3MkVBalBranch244(zzz972, zzz973, zzz974, zzz975, zzz976, zzz977, zzz978, zzz979, zzz980, zzz981, zzz982, bc) → new_mkVBalBranch3MkVBalBranch128(zzz972, zzz973, zzz974, zzz975, zzz976, zzz977, zzz978, zzz979, zzz980, zzz981, zzz982, new_primMulNat1(zzz974), bc)
new_mkVBalBranch3MkVBalBranch125(zzz1337, zzz1338, zzz1339, zzz1340, zzz1341, zzz1342, zzz1343, zzz1344, zzz1345, zzz1346, zzz1347, Succ(zzz13480), Succ(zzz13490), bb) → new_mkVBalBranch3MkVBalBranch125(zzz1337, zzz1338, zzz1339, zzz1340, zzz1341, zzz1342, zzz1343, zzz1344, zzz1345, zzz1346, zzz1347, zzz13480, zzz13490, bb)
new_mkVBalBranch3MkVBalBranch123(zzz3170, zzz3171, zzz317200, zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, Succ(zzz5620), h) → new_mkVBalBranch1(zzz31, zzz334, Branch(zzz3170, zzz3171, Neg(Succ(zzz317200)), zzz3173, zzz3174), h)
new_mkVBalBranch3MkVBalBranch125(zzz1337, zzz1338, zzz1339, zzz1340, zzz1341, zzz1342, zzz1343, zzz1344, zzz1345, zzz1346, zzz1347, Zero, Succ(zzz13490), bb) → new_mkVBalBranch1(zzz1347, zzz1346, Branch(zzz1337, zzz1338, Pos(Succ(zzz1339)), zzz1340, zzz1341), bb)
new_mkVBalBranch3MkVBalBranch242(zzz972, zzz973, zzz974, zzz975, zzz976, zzz977, zzz978, zzz979, zzz980, zzz981, zzz982, Zero, Succ(zzz9840), bc) → new_mkVBalBranch1(zzz982, Branch(zzz977, zzz978, Neg(Succ(zzz979)), zzz980, zzz981), zzz975, bc)
new_mkVBalBranch3MkVBalBranch240(zzz958, zzz959, zzz960, zzz961, zzz962, zzz963, zzz964, zzz965, zzz966, zzz967, zzz968, ba) → new_mkVBalBranch3MkVBalBranch124(zzz958, zzz959, zzz960, zzz961, zzz962, zzz963, zzz964, zzz965, zzz966, zzz967, zzz968, new_primMulNat1(zzz960), ba)
new_mkVBalBranch3MkVBalBranch236(zzz958, zzz959, zzz960, zzz961, zzz962, zzz963, zzz964, zzz965, zzz966, zzz967, zzz968, Succ(zzz9690), Zero, ba) → new_mkVBalBranch3MkVBalBranch124(zzz958, zzz959, zzz960, zzz961, zzz962, zzz963, zzz964, zzz965, zzz966, zzz967, zzz968, new_primMulNat1(zzz960), ba)
new_mkVBalBranch3MkVBalBranch235(zzz3170, zzz3171, Neg(Succ(zzz317200)), zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, Zero, h) → new_mkVBalBranch3MkVBalBranch238(zzz3170, zzz3171, Succ(zzz317200), zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, h)
new_mkVBalBranch1(zzz31, Branch(zzz330, zzz331, Pos(Succ(zzz33200)), zzz333, zzz334), Branch(zzz3170, zzz3171, zzz3172, zzz3173, zzz3174), h) → new_mkVBalBranch3MkVBalBranch235(zzz3170, zzz3171, zzz3172, zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, new_primPlusNat2(new_primMulNat0(zzz33200), Succ(zzz33200)), h)
new_mkVBalBranch3MkVBalBranch241(zzz3170, zzz3171, Pos(Succ(zzz317200)), zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, Zero, h) → new_mkVBalBranch3MkVBalBranch243(zzz3170, zzz3171, Succ(zzz317200), zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, h)
new_mkVBalBranch3MkVBalBranch126(zzz3170, zzz3171, zzz317200, zzz3173, zzz3174, zzz330, zzz331, zzz333, zzz334, zzz31, Succ(zzz5350), h) → new_mkVBalBranch1(zzz31, zzz334, Branch(zzz3170, zzz3171, Neg(Succ(zzz317200)), zzz3173, zzz3174), h)
new_mkVBalBranch3MkVBalBranch241(zzz3170, zzz3171, Neg(Zero), zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, Succ(zzz4190), h) → new_mkVBalBranch1(zzz31, Branch(zzz330, zzz331, Neg(Succ(zzz33200)), zzz333, zzz334), zzz3173, h)
new_mkVBalBranch3MkVBalBranch123(zzz3170, zzz3171, zzz317200, zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, Zero, h) → new_mkVBalBranch3MkVBalBranch130(zzz3170, zzz3171, zzz317200, zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, h)
new_mkVBalBranch1(zzz31, Branch(zzz330, zzz331, Pos(Zero), zzz333, zzz334), Branch(zzz3170, zzz3171, Neg(Succ(zzz317200)), zzz3173, zzz3174), h) → new_mkVBalBranch3MkVBalBranch126(zzz3170, zzz3171, zzz317200, zzz3173, zzz3174, zzz330, zzz331, zzz333, zzz334, zzz31, new_primMulNat1(zzz317200), h)
new_mkVBalBranch3MkVBalBranch124(zzz958, zzz959, zzz960, zzz961, zzz962, zzz963, zzz964, zzz965, zzz966, zzz967, zzz968, Succ(zzz10180), ba) → new_mkVBalBranch3MkVBalBranch125(zzz958, zzz959, zzz960, zzz961, zzz962, zzz963, zzz964, zzz965, zzz966, zzz967, zzz968, Succ(zzz10180), Succ(zzz965), ba)
new_mkVBalBranch3MkVBalBranch235(zzz3170, zzz3171, Pos(Succ(zzz317200)), zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, Zero, h) → new_mkVBalBranch3MkVBalBranch236(zzz3170, zzz3171, zzz317200, zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, Zero, Succ(zzz317200), h)
new_mkVBalBranch3MkVBalBranch239(zzz3170, zzz3171, Zero, zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, h) → new_mkVBalBranch1(zzz31, zzz334, Branch(zzz3170, zzz3171, Neg(Zero), zzz3173, zzz3174), h)
new_mkVBalBranch3MkVBalBranch242(zzz972, zzz973, zzz974, zzz975, zzz976, zzz977, zzz978, zzz979, zzz980, zzz981, zzz982, Succ(zzz9830), Zero, bc) → new_mkVBalBranch3MkVBalBranch128(zzz972, zzz973, zzz974, zzz975, zzz976, zzz977, zzz978, zzz979, zzz980, zzz981, zzz982, new_primMulNat1(zzz974), bc)
new_mkVBalBranch3MkVBalBranch235(zzz3170, zzz3171, Pos(Zero), zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, Zero, h) → new_mkVBalBranch1(zzz31, zzz334, Branch(zzz3170, zzz3171, Pos(Zero), zzz3173, zzz3174), h)
new_mkVBalBranch3MkVBalBranch242(zzz972, zzz973, zzz974, zzz975, zzz976, zzz977, zzz978, zzz979, zzz980, zzz981, zzz982, Zero, Zero, bc) → new_mkVBalBranch3MkVBalBranch244(zzz972, zzz973, zzz974, zzz975, zzz976, zzz977, zzz978, zzz979, zzz980, zzz981, zzz982, bc)
new_mkVBalBranch3MkVBalBranch130(zzz3170, zzz3171, zzz317200, zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, h) → new_mkVBalBranch1(zzz31, zzz334, Branch(zzz3170, zzz3171, Neg(Succ(zzz317200)), zzz3173, zzz3174), h)
new_mkVBalBranch3MkVBalBranch235(zzz3170, zzz3171, Neg(Zero), zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, Zero, h) → new_mkVBalBranch3MkVBalBranch239(zzz3170, zzz3171, Zero, zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, h)
new_mkVBalBranch1(zzz31, Branch(zzz330, zzz331, Neg(Zero), zzz333, zzz334), Branch(zzz3170, zzz3171, Pos(Succ(zzz317200)), zzz3173, zzz3174), h) → new_mkVBalBranch1(zzz31, Branch(zzz330, zzz331, Neg(Zero), zzz333, zzz334), zzz3173, h)
new_mkVBalBranch3MkVBalBranch235(zzz3170, zzz3171, Neg(Zero), zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, Succ(zzz4170), h) → new_mkVBalBranch1(zzz31, zzz334, Branch(zzz3170, zzz3171, Neg(Zero), zzz3173, zzz3174), h)
new_mkVBalBranch3MkVBalBranch236(zzz958, zzz959, zzz960, zzz961, zzz962, zzz963, zzz964, zzz965, zzz966, zzz967, zzz968, Zero, Zero, ba) → new_mkVBalBranch3MkVBalBranch240(zzz958, zzz959, zzz960, zzz961, zzz962, zzz963, zzz964, zzz965, zzz966, zzz967, zzz968, ba)

The TRS R consists of the following rules:

new_primPlusNat1(Zero) → Zero
new_primMulNat0(zzz6200) → new_primPlusNat3(Succ(new_primPlusNat3(new_primPlusNat1(zzz6200), zzz6200)), Succ(zzz6200))
new_primPlusNat2(Succ(zzz900), Succ(zzz9100)) → Succ(Succ(new_primPlusNat2(zzz900, zzz9100)))
new_primPlusNat3(zzz90, Succ(zzz910)) → Succ(Succ(new_primPlusNat2(zzz90, zzz910)))
new_primPlusNat3(zzz90, Zero) → Succ(zzz90)
new_primMulNat1(zzz34200) → new_primPlusNat2(new_primMulNat0(zzz34200), Succ(zzz34200))
new_primPlusNat2(Zero, Zero) → Zero
new_primPlusNat1(Succ(zzz62000)) → Succ(Succ(new_primPlusNat1(zzz62000)))
new_primPlusNat2(Succ(zzz900), Zero) → Succ(zzz900)
new_primPlusNat2(Zero, Succ(zzz9100)) → Succ(zzz9100)

The set Q consists of the following terms:

new_primPlusNat2(Zero, Succ(x0))
new_primMulNat1(x0)
new_primMulNat0(x0)
new_primPlusNat3(x0, Succ(x1))
new_primPlusNat2(Succ(x0), Succ(x1))
new_primPlusNat3(x0, Zero)
new_primPlusNat1(Zero)
new_primPlusNat2(Zero, Zero)
new_primPlusNat1(Succ(x0))
new_primPlusNat2(Succ(x0), Zero)

We have to consider all minimal (P,Q,R)-chains.
By rewriting [15] the rule new_mkVBalBranch1(zzz31, Branch(zzz330, zzz331, Neg(Zero), zzz333, zzz334), Branch(zzz3170, zzz3171, Neg(Succ(zzz317200)), zzz3173, zzz3174), h) → new_mkVBalBranch3MkVBalBranch127(zzz3170, zzz3171, zzz317200, zzz3173, zzz3174, zzz330, zzz331, zzz333, zzz334, zzz31, new_primMulNat1(zzz317200), h) at position [10] we obtained the following new rules:

new_mkVBalBranch1(zzz31, Branch(zzz330, zzz331, Neg(Zero), zzz333, zzz334), Branch(zzz3170, zzz3171, Neg(Succ(zzz317200)), zzz3173, zzz3174), h) → new_mkVBalBranch3MkVBalBranch127(zzz3170, zzz3171, zzz317200, zzz3173, zzz3174, zzz330, zzz331, zzz333, zzz334, zzz31, new_primPlusNat2(new_primMulNat0(zzz317200), Succ(zzz317200)), 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
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                    ↳ DependencyGraphProof
                                      ↳ QDP
                                        ↳ Rewriting
                                          ↳ QDP
                                            ↳ Rewriting
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP

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

new_mkVBalBranch3MkVBalBranch129(zzz1851, zzz1852, zzz1853, zzz1854, zzz1855, zzz1856, zzz1857, zzz1858, zzz1859, zzz1860, zzz1861, Zero, Succ(zzz18630), bd) → new_mkVBalBranch1(zzz1861, zzz1860, Branch(zzz1851, zzz1852, Neg(Succ(zzz1853)), zzz1854, zzz1855), bd)
new_mkVBalBranch3MkVBalBranch238(zzz3170, zzz3171, Succ(zzz317200), zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, h) → new_mkVBalBranch3MkVBalBranch123(zzz3170, zzz3171, zzz317200, zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, new_primPlusNat2(new_primMulNat0(zzz317200), Succ(zzz317200)), h)
new_mkVBalBranch1(zzz31, Branch(zzz330, zzz331, Neg(Succ(zzz33200)), zzz333, zzz334), Branch(zzz3170, zzz3171, zzz3172, zzz3173, zzz3174), h) → new_mkVBalBranch3MkVBalBranch241(zzz3170, zzz3171, zzz3172, zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, new_primPlusNat2(new_primMulNat0(zzz33200), Succ(zzz33200)), h)
new_mkVBalBranch3MkVBalBranch127(zzz3170, zzz3171, zzz317200, zzz3173, zzz3174, zzz330, zzz331, zzz333, zzz334, zzz31, Succ(zzz5500), h) → new_mkVBalBranch1(zzz31, zzz334, Branch(zzz3170, zzz3171, Neg(Succ(zzz317200)), zzz3173, zzz3174), h)
new_mkVBalBranch3MkVBalBranch241(zzz3170, zzz3171, Pos(zzz31720), zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, Succ(zzz4190), h) → new_mkVBalBranch1(zzz31, Branch(zzz330, zzz331, Neg(Succ(zzz33200)), zzz333, zzz334), zzz3173, h)
new_mkVBalBranch3MkVBalBranch128(zzz972, zzz973, zzz974, zzz975, zzz976, zzz977, zzz978, zzz979, zzz980, zzz981, zzz982, Succ(zzz10190), bc) → new_mkVBalBranch3MkVBalBranch129(zzz972, zzz973, zzz974, zzz975, zzz976, zzz977, zzz978, zzz979, zzz980, zzz981, zzz982, Succ(zzz979), Succ(zzz10190), bc)
new_mkVBalBranch3MkVBalBranch129(zzz1851, zzz1852, zzz1853, zzz1854, zzz1855, zzz1856, zzz1857, zzz1858, zzz1859, zzz1860, zzz1861, Succ(zzz18620), Succ(zzz18630), bd) → new_mkVBalBranch3MkVBalBranch129(zzz1851, zzz1852, zzz1853, zzz1854, zzz1855, zzz1856, zzz1857, zzz1858, zzz1859, zzz1860, zzz1861, zzz18620, zzz18630, bd)
new_mkVBalBranch3MkVBalBranch124(zzz958, zzz959, zzz960, zzz961, zzz962, zzz963, zzz964, zzz965, zzz966, zzz967, zzz968, Zero, ba) → new_mkVBalBranch3MkVBalBranch125(zzz958, zzz959, zzz960, zzz961, zzz962, zzz963, zzz964, zzz965, zzz966, zzz967, zzz968, Zero, Succ(zzz965), ba)
new_mkVBalBranch3MkVBalBranch235(zzz3170, zzz3171, Pos(Succ(zzz317200)), zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, Succ(zzz4170), h) → new_mkVBalBranch3MkVBalBranch236(zzz3170, zzz3171, zzz317200, zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, zzz4170, zzz317200, h)
new_mkVBalBranch3MkVBalBranch242(zzz972, zzz973, zzz974, zzz975, zzz976, zzz977, zzz978, zzz979, zzz980, zzz981, zzz982, Succ(zzz9830), Succ(zzz9840), bc) → new_mkVBalBranch3MkVBalBranch242(zzz972, zzz973, zzz974, zzz975, zzz976, zzz977, zzz978, zzz979, zzz980, zzz981, zzz982, zzz9830, zzz9840, bc)
new_mkVBalBranch3MkVBalBranch236(zzz958, zzz959, zzz960, zzz961, zzz962, zzz963, zzz964, zzz965, zzz966, zzz967, zzz968, Succ(zzz9690), Succ(zzz9700), ba) → new_mkVBalBranch3MkVBalBranch236(zzz958, zzz959, zzz960, zzz961, zzz962, zzz963, zzz964, zzz965, zzz966, zzz967, zzz968, zzz9690, zzz9700, ba)
new_mkVBalBranch1(zzz31, Branch(zzz330, zzz331, Neg(Zero), zzz333, zzz334), Branch(zzz3170, zzz3171, Neg(Succ(zzz317200)), zzz3173, zzz3174), h) → new_mkVBalBranch3MkVBalBranch127(zzz3170, zzz3171, zzz317200, zzz3173, zzz3174, zzz330, zzz331, zzz333, zzz334, zzz31, new_primPlusNat2(new_primMulNat0(zzz317200), Succ(zzz317200)), h)
new_mkVBalBranch3MkVBalBranch241(zzz3170, zzz3171, Neg(Succ(zzz317200)), zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, Succ(zzz4190), h) → new_mkVBalBranch3MkVBalBranch242(zzz3170, zzz3171, zzz317200, zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, zzz317200, zzz4190, h)
new_mkVBalBranch3MkVBalBranch241(zzz3170, zzz3171, Neg(Succ(zzz317200)), zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, Zero, h) → new_mkVBalBranch3MkVBalBranch242(zzz3170, zzz3171, zzz317200, zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, Succ(zzz317200), Zero, h)
new_mkVBalBranch1(zzz31, Branch(zzz330, zzz331, Pos(Zero), zzz333, zzz334), Branch(zzz3170, zzz3171, Pos(Succ(zzz317200)), zzz3173, zzz3174), h) → new_mkVBalBranch1(zzz31, Branch(zzz330, zzz331, Pos(Zero), zzz333, zzz334), zzz3173, h)
new_mkVBalBranch3MkVBalBranch237(zzz3170, zzz3171, zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, h) → new_mkVBalBranch1(zzz31, zzz334, Branch(zzz3170, zzz3171, Pos(Zero), zzz3173, zzz3174), h)
new_mkVBalBranch3MkVBalBranch243(zzz3170, zzz3171, zzz31720, zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, h) → new_mkVBalBranch1(zzz31, Branch(zzz330, zzz331, Neg(Succ(zzz33200)), zzz333, zzz334), zzz3173, h)
new_mkVBalBranch3MkVBalBranch235(zzz3170, zzz3171, Pos(Zero), zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, Succ(zzz4170), h) → new_mkVBalBranch3MkVBalBranch237(zzz3170, zzz3171, zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, h)
new_mkVBalBranch3MkVBalBranch235(zzz3170, zzz3171, Neg(Succ(zzz317200)), zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, Succ(zzz4170), h) → new_mkVBalBranch3MkVBalBranch123(zzz3170, zzz3171, zzz317200, zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, new_primPlusNat2(new_primMulNat0(zzz317200), Succ(zzz317200)), h)
new_mkVBalBranch3MkVBalBranch236(zzz958, zzz959, zzz960, zzz961, zzz962, zzz963, zzz964, zzz965, zzz966, zzz967, zzz968, Zero, Succ(zzz9700), ba) → new_mkVBalBranch1(zzz968, Branch(zzz963, zzz964, Pos(Succ(zzz965)), zzz966, zzz967), zzz961, ba)
new_mkVBalBranch3MkVBalBranch125(zzz1337, zzz1338, zzz1339, zzz1340, zzz1341, zzz1342, zzz1343, zzz1344, zzz1345, zzz1346, zzz1347, Succ(zzz13480), Succ(zzz13490), bb) → new_mkVBalBranch3MkVBalBranch125(zzz1337, zzz1338, zzz1339, zzz1340, zzz1341, zzz1342, zzz1343, zzz1344, zzz1345, zzz1346, zzz1347, zzz13480, zzz13490, bb)
new_mkVBalBranch3MkVBalBranch244(zzz972, zzz973, zzz974, zzz975, zzz976, zzz977, zzz978, zzz979, zzz980, zzz981, zzz982, bc) → new_mkVBalBranch3MkVBalBranch128(zzz972, zzz973, zzz974, zzz975, zzz976, zzz977, zzz978, zzz979, zzz980, zzz981, zzz982, new_primMulNat1(zzz974), bc)
new_mkVBalBranch3MkVBalBranch123(zzz3170, zzz3171, zzz317200, zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, Succ(zzz5620), h) → new_mkVBalBranch1(zzz31, zzz334, Branch(zzz3170, zzz3171, Neg(Succ(zzz317200)), zzz3173, zzz3174), h)
new_mkVBalBranch3MkVBalBranch125(zzz1337, zzz1338, zzz1339, zzz1340, zzz1341, zzz1342, zzz1343, zzz1344, zzz1345, zzz1346, zzz1347, Zero, Succ(zzz13490), bb) → new_mkVBalBranch1(zzz1347, zzz1346, Branch(zzz1337, zzz1338, Pos(Succ(zzz1339)), zzz1340, zzz1341), bb)
new_mkVBalBranch3MkVBalBranch242(zzz972, zzz973, zzz974, zzz975, zzz976, zzz977, zzz978, zzz979, zzz980, zzz981, zzz982, Zero, Succ(zzz9840), bc) → new_mkVBalBranch1(zzz982, Branch(zzz977, zzz978, Neg(Succ(zzz979)), zzz980, zzz981), zzz975, bc)
new_mkVBalBranch3MkVBalBranch236(zzz958, zzz959, zzz960, zzz961, zzz962, zzz963, zzz964, zzz965, zzz966, zzz967, zzz968, Succ(zzz9690), Zero, ba) → new_mkVBalBranch3MkVBalBranch124(zzz958, zzz959, zzz960, zzz961, zzz962, zzz963, zzz964, zzz965, zzz966, zzz967, zzz968, new_primMulNat1(zzz960), ba)
new_mkVBalBranch3MkVBalBranch240(zzz958, zzz959, zzz960, zzz961, zzz962, zzz963, zzz964, zzz965, zzz966, zzz967, zzz968, ba) → new_mkVBalBranch3MkVBalBranch124(zzz958, zzz959, zzz960, zzz961, zzz962, zzz963, zzz964, zzz965, zzz966, zzz967, zzz968, new_primMulNat1(zzz960), ba)
new_mkVBalBranch3MkVBalBranch235(zzz3170, zzz3171, Neg(Succ(zzz317200)), zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, Zero, h) → new_mkVBalBranch3MkVBalBranch238(zzz3170, zzz3171, Succ(zzz317200), zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, h)
new_mkVBalBranch1(zzz31, Branch(zzz330, zzz331, Pos(Succ(zzz33200)), zzz333, zzz334), Branch(zzz3170, zzz3171, zzz3172, zzz3173, zzz3174), h) → new_mkVBalBranch3MkVBalBranch235(zzz3170, zzz3171, zzz3172, zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, new_primPlusNat2(new_primMulNat0(zzz33200), Succ(zzz33200)), h)
new_mkVBalBranch3MkVBalBranch241(zzz3170, zzz3171, Pos(Succ(zzz317200)), zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, Zero, h) → new_mkVBalBranch3MkVBalBranch243(zzz3170, zzz3171, Succ(zzz317200), zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, h)
new_mkVBalBranch3MkVBalBranch126(zzz3170, zzz3171, zzz317200, zzz3173, zzz3174, zzz330, zzz331, zzz333, zzz334, zzz31, Succ(zzz5350), h) → new_mkVBalBranch1(zzz31, zzz334, Branch(zzz3170, zzz3171, Neg(Succ(zzz317200)), zzz3173, zzz3174), h)
new_mkVBalBranch1(zzz31, Branch(zzz330, zzz331, Pos(Zero), zzz333, zzz334), Branch(zzz3170, zzz3171, Neg(Succ(zzz317200)), zzz3173, zzz3174), h) → new_mkVBalBranch3MkVBalBranch126(zzz3170, zzz3171, zzz317200, zzz3173, zzz3174, zzz330, zzz331, zzz333, zzz334, zzz31, new_primMulNat1(zzz317200), h)
new_mkVBalBranch3MkVBalBranch123(zzz3170, zzz3171, zzz317200, zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, Zero, h) → new_mkVBalBranch3MkVBalBranch130(zzz3170, zzz3171, zzz317200, zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, h)
new_mkVBalBranch3MkVBalBranch241(zzz3170, zzz3171, Neg(Zero), zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, Succ(zzz4190), h) → new_mkVBalBranch1(zzz31, Branch(zzz330, zzz331, Neg(Succ(zzz33200)), zzz333, zzz334), zzz3173, h)
new_mkVBalBranch3MkVBalBranch124(zzz958, zzz959, zzz960, zzz961, zzz962, zzz963, zzz964, zzz965, zzz966, zzz967, zzz968, Succ(zzz10180), ba) → new_mkVBalBranch3MkVBalBranch125(zzz958, zzz959, zzz960, zzz961, zzz962, zzz963, zzz964, zzz965, zzz966, zzz967, zzz968, Succ(zzz10180), Succ(zzz965), ba)
new_mkVBalBranch3MkVBalBranch235(zzz3170, zzz3171, Pos(Succ(zzz317200)), zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, Zero, h) → new_mkVBalBranch3MkVBalBranch236(zzz3170, zzz3171, zzz317200, zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, Zero, Succ(zzz317200), h)
new_mkVBalBranch3MkVBalBranch242(zzz972, zzz973, zzz974, zzz975, zzz976, zzz977, zzz978, zzz979, zzz980, zzz981, zzz982, Succ(zzz9830), Zero, bc) → new_mkVBalBranch3MkVBalBranch128(zzz972, zzz973, zzz974, zzz975, zzz976, zzz977, zzz978, zzz979, zzz980, zzz981, zzz982, new_primMulNat1(zzz974), bc)
new_mkVBalBranch3MkVBalBranch239(zzz3170, zzz3171, Zero, zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, h) → new_mkVBalBranch1(zzz31, zzz334, Branch(zzz3170, zzz3171, Neg(Zero), zzz3173, zzz3174), h)
new_mkVBalBranch3MkVBalBranch235(zzz3170, zzz3171, Pos(Zero), zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, Zero, h) → new_mkVBalBranch1(zzz31, zzz334, Branch(zzz3170, zzz3171, Pos(Zero), zzz3173, zzz3174), h)
new_mkVBalBranch3MkVBalBranch242(zzz972, zzz973, zzz974, zzz975, zzz976, zzz977, zzz978, zzz979, zzz980, zzz981, zzz982, Zero, Zero, bc) → new_mkVBalBranch3MkVBalBranch244(zzz972, zzz973, zzz974, zzz975, zzz976, zzz977, zzz978, zzz979, zzz980, zzz981, zzz982, bc)
new_mkVBalBranch3MkVBalBranch130(zzz3170, zzz3171, zzz317200, zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, h) → new_mkVBalBranch1(zzz31, zzz334, Branch(zzz3170, zzz3171, Neg(Succ(zzz317200)), zzz3173, zzz3174), h)
new_mkVBalBranch1(zzz31, Branch(zzz330, zzz331, Neg(Zero), zzz333, zzz334), Branch(zzz3170, zzz3171, Pos(Succ(zzz317200)), zzz3173, zzz3174), h) → new_mkVBalBranch1(zzz31, Branch(zzz330, zzz331, Neg(Zero), zzz333, zzz334), zzz3173, h)
new_mkVBalBranch3MkVBalBranch235(zzz3170, zzz3171, Neg(Zero), zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, Zero, h) → new_mkVBalBranch3MkVBalBranch239(zzz3170, zzz3171, Zero, zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, h)
new_mkVBalBranch3MkVBalBranch235(zzz3170, zzz3171, Neg(Zero), zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, Succ(zzz4170), h) → new_mkVBalBranch1(zzz31, zzz334, Branch(zzz3170, zzz3171, Neg(Zero), zzz3173, zzz3174), h)
new_mkVBalBranch3MkVBalBranch236(zzz958, zzz959, zzz960, zzz961, zzz962, zzz963, zzz964, zzz965, zzz966, zzz967, zzz968, Zero, Zero, ba) → new_mkVBalBranch3MkVBalBranch240(zzz958, zzz959, zzz960, zzz961, zzz962, zzz963, zzz964, zzz965, zzz966, zzz967, zzz968, ba)

The TRS R consists of the following rules:

new_primPlusNat1(Zero) → Zero
new_primMulNat0(zzz6200) → new_primPlusNat3(Succ(new_primPlusNat3(new_primPlusNat1(zzz6200), zzz6200)), Succ(zzz6200))
new_primPlusNat2(Succ(zzz900), Succ(zzz9100)) → Succ(Succ(new_primPlusNat2(zzz900, zzz9100)))
new_primPlusNat3(zzz90, Succ(zzz910)) → Succ(Succ(new_primPlusNat2(zzz90, zzz910)))
new_primPlusNat3(zzz90, Zero) → Succ(zzz90)
new_primMulNat1(zzz34200) → new_primPlusNat2(new_primMulNat0(zzz34200), Succ(zzz34200))
new_primPlusNat2(Zero, Zero) → Zero
new_primPlusNat1(Succ(zzz62000)) → Succ(Succ(new_primPlusNat1(zzz62000)))
new_primPlusNat2(Succ(zzz900), Zero) → Succ(zzz900)
new_primPlusNat2(Zero, Succ(zzz9100)) → Succ(zzz9100)

The set Q consists of the following terms:

new_primPlusNat2(Zero, Succ(x0))
new_primMulNat1(x0)
new_primMulNat0(x0)
new_primPlusNat3(x0, Succ(x1))
new_primPlusNat2(Succ(x0), Succ(x1))
new_primPlusNat3(x0, Zero)
new_primPlusNat1(Zero)
new_primPlusNat2(Zero, Zero)
new_primPlusNat1(Succ(x0))
new_primPlusNat2(Succ(x0), Zero)

We have to consider all minimal (P,Q,R)-chains.
By rewriting [15] the rule new_mkVBalBranch1(zzz31, Branch(zzz330, zzz331, Neg(Succ(zzz33200)), zzz333, zzz334), Branch(zzz3170, zzz3171, zzz3172, zzz3173, zzz3174), h) → new_mkVBalBranch3MkVBalBranch241(zzz3170, zzz3171, zzz3172, zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, new_primPlusNat2(new_primMulNat0(zzz33200), Succ(zzz33200)), h) at position [11,0] we obtained the following new rules:

new_mkVBalBranch1(zzz31, Branch(zzz330, zzz331, Neg(Succ(zzz33200)), zzz333, zzz334), Branch(zzz3170, zzz3171, zzz3172, zzz3173, zzz3174), h) → new_mkVBalBranch3MkVBalBranch241(zzz3170, zzz3171, zzz3172, zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, new_primPlusNat2(new_primPlusNat3(Succ(new_primPlusNat3(new_primPlusNat1(zzz33200), zzz33200)), Succ(zzz33200)), Succ(zzz33200)), 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
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                    ↳ DependencyGraphProof
                                      ↳ QDP
                                        ↳ Rewriting
                                          ↳ QDP
                                            ↳ Rewriting
                                              ↳ QDP
                                                ↳ Rewriting
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP

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

new_mkVBalBranch3MkVBalBranch238(zzz3170, zzz3171, Succ(zzz317200), zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, h) → new_mkVBalBranch3MkVBalBranch123(zzz3170, zzz3171, zzz317200, zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, new_primPlusNat2(new_primMulNat0(zzz317200), Succ(zzz317200)), h)
new_mkVBalBranch3MkVBalBranch129(zzz1851, zzz1852, zzz1853, zzz1854, zzz1855, zzz1856, zzz1857, zzz1858, zzz1859, zzz1860, zzz1861, Zero, Succ(zzz18630), bd) → new_mkVBalBranch1(zzz1861, zzz1860, Branch(zzz1851, zzz1852, Neg(Succ(zzz1853)), zzz1854, zzz1855), bd)
new_mkVBalBranch3MkVBalBranch128(zzz972, zzz973, zzz974, zzz975, zzz976, zzz977, zzz978, zzz979, zzz980, zzz981, zzz982, Succ(zzz10190), bc) → new_mkVBalBranch3MkVBalBranch129(zzz972, zzz973, zzz974, zzz975, zzz976, zzz977, zzz978, zzz979, zzz980, zzz981, zzz982, Succ(zzz979), Succ(zzz10190), bc)
new_mkVBalBranch3MkVBalBranch241(zzz3170, zzz3171, Pos(zzz31720), zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, Succ(zzz4190), h) → new_mkVBalBranch1(zzz31, Branch(zzz330, zzz331, Neg(Succ(zzz33200)), zzz333, zzz334), zzz3173, h)
new_mkVBalBranch3MkVBalBranch127(zzz3170, zzz3171, zzz317200, zzz3173, zzz3174, zzz330, zzz331, zzz333, zzz334, zzz31, Succ(zzz5500), h) → new_mkVBalBranch1(zzz31, zzz334, Branch(zzz3170, zzz3171, Neg(Succ(zzz317200)), zzz3173, zzz3174), h)
new_mkVBalBranch3MkVBalBranch129(zzz1851, zzz1852, zzz1853, zzz1854, zzz1855, zzz1856, zzz1857, zzz1858, zzz1859, zzz1860, zzz1861, Succ(zzz18620), Succ(zzz18630), bd) → new_mkVBalBranch3MkVBalBranch129(zzz1851, zzz1852, zzz1853, zzz1854, zzz1855, zzz1856, zzz1857, zzz1858, zzz1859, zzz1860, zzz1861, zzz18620, zzz18630, bd)
new_mkVBalBranch3MkVBalBranch124(zzz958, zzz959, zzz960, zzz961, zzz962, zzz963, zzz964, zzz965, zzz966, zzz967, zzz968, Zero, ba) → new_mkVBalBranch3MkVBalBranch125(zzz958, zzz959, zzz960, zzz961, zzz962, zzz963, zzz964, zzz965, zzz966, zzz967, zzz968, Zero, Succ(zzz965), ba)
new_mkVBalBranch3MkVBalBranch242(zzz972, zzz973, zzz974, zzz975, zzz976, zzz977, zzz978, zzz979, zzz980, zzz981, zzz982, Succ(zzz9830), Succ(zzz9840), bc) → new_mkVBalBranch3MkVBalBranch242(zzz972, zzz973, zzz974, zzz975, zzz976, zzz977, zzz978, zzz979, zzz980, zzz981, zzz982, zzz9830, zzz9840, bc)
new_mkVBalBranch3MkVBalBranch235(zzz3170, zzz3171, Pos(Succ(zzz317200)), zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, Succ(zzz4170), h) → new_mkVBalBranch3MkVBalBranch236(zzz3170, zzz3171, zzz317200, zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, zzz4170, zzz317200, h)
new_mkVBalBranch3MkVBalBranch236(zzz958, zzz959, zzz960, zzz961, zzz962, zzz963, zzz964, zzz965, zzz966, zzz967, zzz968, Succ(zzz9690), Succ(zzz9700), ba) → new_mkVBalBranch3MkVBalBranch236(zzz958, zzz959, zzz960, zzz961, zzz962, zzz963, zzz964, zzz965, zzz966, zzz967, zzz968, zzz9690, zzz9700, ba)
new_mkVBalBranch1(zzz31, Branch(zzz330, zzz331, Neg(Zero), zzz333, zzz334), Branch(zzz3170, zzz3171, Neg(Succ(zzz317200)), zzz3173, zzz3174), h) → new_mkVBalBranch3MkVBalBranch127(zzz3170, zzz3171, zzz317200, zzz3173, zzz3174, zzz330, zzz331, zzz333, zzz334, zzz31, new_primPlusNat2(new_primMulNat0(zzz317200), Succ(zzz317200)), h)
new_mkVBalBranch3MkVBalBranch241(zzz3170, zzz3171, Neg(Succ(zzz317200)), zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, Succ(zzz4190), h) → new_mkVBalBranch3MkVBalBranch242(zzz3170, zzz3171, zzz317200, zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, zzz317200, zzz4190, h)
new_mkVBalBranch3MkVBalBranch241(zzz3170, zzz3171, Neg(Succ(zzz317200)), zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, Zero, h) → new_mkVBalBranch3MkVBalBranch242(zzz3170, zzz3171, zzz317200, zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, Succ(zzz317200), Zero, h)
new_mkVBalBranch1(zzz31, Branch(zzz330, zzz331, Pos(Zero), zzz333, zzz334), Branch(zzz3170, zzz3171, Pos(Succ(zzz317200)), zzz3173, zzz3174), h) → new_mkVBalBranch1(zzz31, Branch(zzz330, zzz331, Pos(Zero), zzz333, zzz334), zzz3173, h)
new_mkVBalBranch3MkVBalBranch243(zzz3170, zzz3171, zzz31720, zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, h) → new_mkVBalBranch1(zzz31, Branch(zzz330, zzz331, Neg(Succ(zzz33200)), zzz333, zzz334), zzz3173, h)
new_mkVBalBranch3MkVBalBranch237(zzz3170, zzz3171, zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, h) → new_mkVBalBranch1(zzz31, zzz334, Branch(zzz3170, zzz3171, Pos(Zero), zzz3173, zzz3174), h)
new_mkVBalBranch1(zzz31, Branch(zzz330, zzz331, Neg(Succ(zzz33200)), zzz333, zzz334), Branch(zzz3170, zzz3171, zzz3172, zzz3173, zzz3174), h) → new_mkVBalBranch3MkVBalBranch241(zzz3170, zzz3171, zzz3172, zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, new_primPlusNat2(new_primPlusNat3(Succ(new_primPlusNat3(new_primPlusNat1(zzz33200), zzz33200)), Succ(zzz33200)), Succ(zzz33200)), h)
new_mkVBalBranch3MkVBalBranch235(zzz3170, zzz3171, Pos(Zero), zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, Succ(zzz4170), h) → new_mkVBalBranch3MkVBalBranch237(zzz3170, zzz3171, zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, h)
new_mkVBalBranch3MkVBalBranch235(zzz3170, zzz3171, Neg(Succ(zzz317200)), zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, Succ(zzz4170), h) → new_mkVBalBranch3MkVBalBranch123(zzz3170, zzz3171, zzz317200, zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, new_primPlusNat2(new_primMulNat0(zzz317200), Succ(zzz317200)), h)
new_mkVBalBranch3MkVBalBranch236(zzz958, zzz959, zzz960, zzz961, zzz962, zzz963, zzz964, zzz965, zzz966, zzz967, zzz968, Zero, Succ(zzz9700), ba) → new_mkVBalBranch1(zzz968, Branch(zzz963, zzz964, Pos(Succ(zzz965)), zzz966, zzz967), zzz961, ba)
new_mkVBalBranch3MkVBalBranch244(zzz972, zzz973, zzz974, zzz975, zzz976, zzz977, zzz978, zzz979, zzz980, zzz981, zzz982, bc) → new_mkVBalBranch3MkVBalBranch128(zzz972, zzz973, zzz974, zzz975, zzz976, zzz977, zzz978, zzz979, zzz980, zzz981, zzz982, new_primMulNat1(zzz974), bc)
new_mkVBalBranch3MkVBalBranch125(zzz1337, zzz1338, zzz1339, zzz1340, zzz1341, zzz1342, zzz1343, zzz1344, zzz1345, zzz1346, zzz1347, Succ(zzz13480), Succ(zzz13490), bb) → new_mkVBalBranch3MkVBalBranch125(zzz1337, zzz1338, zzz1339, zzz1340, zzz1341, zzz1342, zzz1343, zzz1344, zzz1345, zzz1346, zzz1347, zzz13480, zzz13490, bb)
new_mkVBalBranch3MkVBalBranch123(zzz3170, zzz3171, zzz317200, zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, Succ(zzz5620), h) → new_mkVBalBranch1(zzz31, zzz334, Branch(zzz3170, zzz3171, Neg(Succ(zzz317200)), zzz3173, zzz3174), h)
new_mkVBalBranch3MkVBalBranch125(zzz1337, zzz1338, zzz1339, zzz1340, zzz1341, zzz1342, zzz1343, zzz1344, zzz1345, zzz1346, zzz1347, Zero, Succ(zzz13490), bb) → new_mkVBalBranch1(zzz1347, zzz1346, Branch(zzz1337, zzz1338, Pos(Succ(zzz1339)), zzz1340, zzz1341), bb)
new_mkVBalBranch3MkVBalBranch242(zzz972, zzz973, zzz974, zzz975, zzz976, zzz977, zzz978, zzz979, zzz980, zzz981, zzz982, Zero, Succ(zzz9840), bc) → new_mkVBalBranch1(zzz982, Branch(zzz977, zzz978, Neg(Succ(zzz979)), zzz980, zzz981), zzz975, bc)
new_mkVBalBranch3MkVBalBranch240(zzz958, zzz959, zzz960, zzz961, zzz962, zzz963, zzz964, zzz965, zzz966, zzz967, zzz968, ba) → new_mkVBalBranch3MkVBalBranch124(zzz958, zzz959, zzz960, zzz961, zzz962, zzz963, zzz964, zzz965, zzz966, zzz967, zzz968, new_primMulNat1(zzz960), ba)
new_mkVBalBranch3MkVBalBranch236(zzz958, zzz959, zzz960, zzz961, zzz962, zzz963, zzz964, zzz965, zzz966, zzz967, zzz968, Succ(zzz9690), Zero, ba) → new_mkVBalBranch3MkVBalBranch124(zzz958, zzz959, zzz960, zzz961, zzz962, zzz963, zzz964, zzz965, zzz966, zzz967, zzz968, new_primMulNat1(zzz960), ba)
new_mkVBalBranch3MkVBalBranch235(zzz3170, zzz3171, Neg(Succ(zzz317200)), zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, Zero, h) → new_mkVBalBranch3MkVBalBranch238(zzz3170, zzz3171, Succ(zzz317200), zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, h)
new_mkVBalBranch1(zzz31, Branch(zzz330, zzz331, Pos(Succ(zzz33200)), zzz333, zzz334), Branch(zzz3170, zzz3171, zzz3172, zzz3173, zzz3174), h) → new_mkVBalBranch3MkVBalBranch235(zzz3170, zzz3171, zzz3172, zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, new_primPlusNat2(new_primMulNat0(zzz33200), Succ(zzz33200)), h)
new_mkVBalBranch3MkVBalBranch241(zzz3170, zzz3171, Pos(Succ(zzz317200)), zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, Zero, h) → new_mkVBalBranch3MkVBalBranch243(zzz3170, zzz3171, Succ(zzz317200), zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, h)
new_mkVBalBranch3MkVBalBranch126(zzz3170, zzz3171, zzz317200, zzz3173, zzz3174, zzz330, zzz331, zzz333, zzz334, zzz31, Succ(zzz5350), h) → new_mkVBalBranch1(zzz31, zzz334, Branch(zzz3170, zzz3171, Neg(Succ(zzz317200)), zzz3173, zzz3174), h)
new_mkVBalBranch3MkVBalBranch241(zzz3170, zzz3171, Neg(Zero), zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, Succ(zzz4190), h) → new_mkVBalBranch1(zzz31, Branch(zzz330, zzz331, Neg(Succ(zzz33200)), zzz333, zzz334), zzz3173, h)
new_mkVBalBranch3MkVBalBranch123(zzz3170, zzz3171, zzz317200, zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, Zero, h) → new_mkVBalBranch3MkVBalBranch130(zzz3170, zzz3171, zzz317200, zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, h)
new_mkVBalBranch1(zzz31, Branch(zzz330, zzz331, Pos(Zero), zzz333, zzz334), Branch(zzz3170, zzz3171, Neg(Succ(zzz317200)), zzz3173, zzz3174), h) → new_mkVBalBranch3MkVBalBranch126(zzz3170, zzz3171, zzz317200, zzz3173, zzz3174, zzz330, zzz331, zzz333, zzz334, zzz31, new_primMulNat1(zzz317200), h)
new_mkVBalBranch3MkVBalBranch124(zzz958, zzz959, zzz960, zzz961, zzz962, zzz963, zzz964, zzz965, zzz966, zzz967, zzz968, Succ(zzz10180), ba) → new_mkVBalBranch3MkVBalBranch125(zzz958, zzz959, zzz960, zzz961, zzz962, zzz963, zzz964, zzz965, zzz966, zzz967, zzz968, Succ(zzz10180), Succ(zzz965), ba)
new_mkVBalBranch3MkVBalBranch235(zzz3170, zzz3171, Pos(Succ(zzz317200)), zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, Zero, h) → new_mkVBalBranch3MkVBalBranch236(zzz3170, zzz3171, zzz317200, zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, Zero, Succ(zzz317200), h)
new_mkVBalBranch3MkVBalBranch239(zzz3170, zzz3171, Zero, zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, h) → new_mkVBalBranch1(zzz31, zzz334, Branch(zzz3170, zzz3171, Neg(Zero), zzz3173, zzz3174), h)
new_mkVBalBranch3MkVBalBranch242(zzz972, zzz973, zzz974, zzz975, zzz976, zzz977, zzz978, zzz979, zzz980, zzz981, zzz982, Succ(zzz9830), Zero, bc) → new_mkVBalBranch3MkVBalBranch128(zzz972, zzz973, zzz974, zzz975, zzz976, zzz977, zzz978, zzz979, zzz980, zzz981, zzz982, new_primMulNat1(zzz974), bc)
new_mkVBalBranch3MkVBalBranch235(zzz3170, zzz3171, Pos(Zero), zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, Zero, h) → new_mkVBalBranch1(zzz31, zzz334, Branch(zzz3170, zzz3171, Pos(Zero), zzz3173, zzz3174), h)
new_mkVBalBranch3MkVBalBranch242(zzz972, zzz973, zzz974, zzz975, zzz976, zzz977, zzz978, zzz979, zzz980, zzz981, zzz982, Zero, Zero, bc) → new_mkVBalBranch3MkVBalBranch244(zzz972, zzz973, zzz974, zzz975, zzz976, zzz977, zzz978, zzz979, zzz980, zzz981, zzz982, bc)
new_mkVBalBranch3MkVBalBranch130(zzz3170, zzz3171, zzz317200, zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, h) → new_mkVBalBranch1(zzz31, zzz334, Branch(zzz3170, zzz3171, Neg(Succ(zzz317200)), zzz3173, zzz3174), h)
new_mkVBalBranch3MkVBalBranch235(zzz3170, zzz3171, Neg(Zero), zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, Zero, h) → new_mkVBalBranch3MkVBalBranch239(zzz3170, zzz3171, Zero, zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, h)
new_mkVBalBranch1(zzz31, Branch(zzz330, zzz331, Neg(Zero), zzz333, zzz334), Branch(zzz3170, zzz3171, Pos(Succ(zzz317200)), zzz3173, zzz3174), h) → new_mkVBalBranch1(zzz31, Branch(zzz330, zzz331, Neg(Zero), zzz333, zzz334), zzz3173, h)
new_mkVBalBranch3MkVBalBranch235(zzz3170, zzz3171, Neg(Zero), zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, Succ(zzz4170), h) → new_mkVBalBranch1(zzz31, zzz334, Branch(zzz3170, zzz3171, Neg(Zero), zzz3173, zzz3174), h)
new_mkVBalBranch3MkVBalBranch236(zzz958, zzz959, zzz960, zzz961, zzz962, zzz963, zzz964, zzz965, zzz966, zzz967, zzz968, Zero, Zero, ba) → new_mkVBalBranch3MkVBalBranch240(zzz958, zzz959, zzz960, zzz961, zzz962, zzz963, zzz964, zzz965, zzz966, zzz967, zzz968, ba)

The TRS R consists of the following rules:

new_primPlusNat1(Zero) → Zero
new_primMulNat0(zzz6200) → new_primPlusNat3(Succ(new_primPlusNat3(new_primPlusNat1(zzz6200), zzz6200)), Succ(zzz6200))
new_primPlusNat2(Succ(zzz900), Succ(zzz9100)) → Succ(Succ(new_primPlusNat2(zzz900, zzz9100)))
new_primPlusNat3(zzz90, Succ(zzz910)) → Succ(Succ(new_primPlusNat2(zzz90, zzz910)))
new_primPlusNat3(zzz90, Zero) → Succ(zzz90)
new_primMulNat1(zzz34200) → new_primPlusNat2(new_primMulNat0(zzz34200), Succ(zzz34200))
new_primPlusNat2(Zero, Zero) → Zero
new_primPlusNat1(Succ(zzz62000)) → Succ(Succ(new_primPlusNat1(zzz62000)))
new_primPlusNat2(Succ(zzz900), Zero) → Succ(zzz900)
new_primPlusNat2(Zero, Succ(zzz9100)) → Succ(zzz9100)

The set Q consists of the following terms:

new_primPlusNat2(Zero, Succ(x0))
new_primMulNat1(x0)
new_primMulNat0(x0)
new_primPlusNat3(x0, Succ(x1))
new_primPlusNat2(Succ(x0), Succ(x1))
new_primPlusNat3(x0, Zero)
new_primPlusNat1(Zero)
new_primPlusNat2(Zero, Zero)
new_primPlusNat1(Succ(x0))
new_primPlusNat2(Succ(x0), Zero)

We have to consider all minimal (P,Q,R)-chains.
By rewriting [15] the rule new_mkVBalBranch3MkVBalBranch242(zzz972, zzz973, zzz974, zzz975, zzz976, zzz977, zzz978, zzz979, zzz980, zzz981, zzz982, Succ(zzz9830), Zero, bc) → new_mkVBalBranch3MkVBalBranch128(zzz972, zzz973, zzz974, zzz975, zzz976, zzz977, zzz978, zzz979, zzz980, zzz981, zzz982, new_primMulNat1(zzz974), bc) at position [11] we obtained the following new rules:

new_mkVBalBranch3MkVBalBranch242(zzz972, zzz973, zzz974, zzz975, zzz976, zzz977, zzz978, zzz979, zzz980, zzz981, zzz982, Succ(zzz9830), Zero, bc) → new_mkVBalBranch3MkVBalBranch128(zzz972, zzz973, zzz974, zzz975, zzz976, zzz977, zzz978, zzz979, zzz980, zzz981, zzz982, new_primPlusNat2(new_primMulNat0(zzz974), Succ(zzz974)), bc)



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

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

new_mkVBalBranch3MkVBalBranch242(zzz972, zzz973, zzz974, zzz975, zzz976, zzz977, zzz978, zzz979, zzz980, zzz981, zzz982, Succ(zzz9830), Zero, bc) → new_mkVBalBranch3MkVBalBranch128(zzz972, zzz973, zzz974, zzz975, zzz976, zzz977, zzz978, zzz979, zzz980, zzz981, zzz982, new_primPlusNat2(new_primMulNat0(zzz974), Succ(zzz974)), bc)
new_mkVBalBranch3MkVBalBranch129(zzz1851, zzz1852, zzz1853, zzz1854, zzz1855, zzz1856, zzz1857, zzz1858, zzz1859, zzz1860, zzz1861, Zero, Succ(zzz18630), bd) → new_mkVBalBranch1(zzz1861, zzz1860, Branch(zzz1851, zzz1852, Neg(Succ(zzz1853)), zzz1854, zzz1855), bd)
new_mkVBalBranch3MkVBalBranch238(zzz3170, zzz3171, Succ(zzz317200), zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, h) → new_mkVBalBranch3MkVBalBranch123(zzz3170, zzz3171, zzz317200, zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, new_primPlusNat2(new_primMulNat0(zzz317200), Succ(zzz317200)), h)
new_mkVBalBranch3MkVBalBranch127(zzz3170, zzz3171, zzz317200, zzz3173, zzz3174, zzz330, zzz331, zzz333, zzz334, zzz31, Succ(zzz5500), h) → new_mkVBalBranch1(zzz31, zzz334, Branch(zzz3170, zzz3171, Neg(Succ(zzz317200)), zzz3173, zzz3174), h)
new_mkVBalBranch3MkVBalBranch241(zzz3170, zzz3171, Pos(zzz31720), zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, Succ(zzz4190), h) → new_mkVBalBranch1(zzz31, Branch(zzz330, zzz331, Neg(Succ(zzz33200)), zzz333, zzz334), zzz3173, h)
new_mkVBalBranch3MkVBalBranch128(zzz972, zzz973, zzz974, zzz975, zzz976, zzz977, zzz978, zzz979, zzz980, zzz981, zzz982, Succ(zzz10190), bc) → new_mkVBalBranch3MkVBalBranch129(zzz972, zzz973, zzz974, zzz975, zzz976, zzz977, zzz978, zzz979, zzz980, zzz981, zzz982, Succ(zzz979), Succ(zzz10190), bc)
new_mkVBalBranch3MkVBalBranch129(zzz1851, zzz1852, zzz1853, zzz1854, zzz1855, zzz1856, zzz1857, zzz1858, zzz1859, zzz1860, zzz1861, Succ(zzz18620), Succ(zzz18630), bd) → new_mkVBalBranch3MkVBalBranch129(zzz1851, zzz1852, zzz1853, zzz1854, zzz1855, zzz1856, zzz1857, zzz1858, zzz1859, zzz1860, zzz1861, zzz18620, zzz18630, bd)
new_mkVBalBranch3MkVBalBranch124(zzz958, zzz959, zzz960, zzz961, zzz962, zzz963, zzz964, zzz965, zzz966, zzz967, zzz968, Zero, ba) → new_mkVBalBranch3MkVBalBranch125(zzz958, zzz959, zzz960, zzz961, zzz962, zzz963, zzz964, zzz965, zzz966, zzz967, zzz968, Zero, Succ(zzz965), ba)
new_mkVBalBranch3MkVBalBranch235(zzz3170, zzz3171, Pos(Succ(zzz317200)), zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, Succ(zzz4170), h) → new_mkVBalBranch3MkVBalBranch236(zzz3170, zzz3171, zzz317200, zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, zzz4170, zzz317200, h)
new_mkVBalBranch3MkVBalBranch242(zzz972, zzz973, zzz974, zzz975, zzz976, zzz977, zzz978, zzz979, zzz980, zzz981, zzz982, Succ(zzz9830), Succ(zzz9840), bc) → new_mkVBalBranch3MkVBalBranch242(zzz972, zzz973, zzz974, zzz975, zzz976, zzz977, zzz978, zzz979, zzz980, zzz981, zzz982, zzz9830, zzz9840, bc)
new_mkVBalBranch3MkVBalBranch236(zzz958, zzz959, zzz960, zzz961, zzz962, zzz963, zzz964, zzz965, zzz966, zzz967, zzz968, Succ(zzz9690), Succ(zzz9700), ba) → new_mkVBalBranch3MkVBalBranch236(zzz958, zzz959, zzz960, zzz961, zzz962, zzz963, zzz964, zzz965, zzz966, zzz967, zzz968, zzz9690, zzz9700, ba)
new_mkVBalBranch1(zzz31, Branch(zzz330, zzz331, Neg(Zero), zzz333, zzz334), Branch(zzz3170, zzz3171, Neg(Succ(zzz317200)), zzz3173, zzz3174), h) → new_mkVBalBranch3MkVBalBranch127(zzz3170, zzz3171, zzz317200, zzz3173, zzz3174, zzz330, zzz331, zzz333, zzz334, zzz31, new_primPlusNat2(new_primMulNat0(zzz317200), Succ(zzz317200)), h)
new_mkVBalBranch3MkVBalBranch241(zzz3170, zzz3171, Neg(Succ(zzz317200)), zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, Succ(zzz4190), h) → new_mkVBalBranch3MkVBalBranch242(zzz3170, zzz3171, zzz317200, zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, zzz317200, zzz4190, h)
new_mkVBalBranch3MkVBalBranch241(zzz3170, zzz3171, Neg(Succ(zzz317200)), zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, Zero, h) → new_mkVBalBranch3MkVBalBranch242(zzz3170, zzz3171, zzz317200, zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, Succ(zzz317200), Zero, h)
new_mkVBalBranch1(zzz31, Branch(zzz330, zzz331, Pos(Zero), zzz333, zzz334), Branch(zzz3170, zzz3171, Pos(Succ(zzz317200)), zzz3173, zzz3174), h) → new_mkVBalBranch1(zzz31, Branch(zzz330, zzz331, Pos(Zero), zzz333, zzz334), zzz3173, h)
new_mkVBalBranch3MkVBalBranch237(zzz3170, zzz3171, zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, h) → new_mkVBalBranch1(zzz31, zzz334, Branch(zzz3170, zzz3171, Pos(Zero), zzz3173, zzz3174), h)
new_mkVBalBranch3MkVBalBranch243(zzz3170, zzz3171, zzz31720, zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, h) → new_mkVBalBranch1(zzz31, Branch(zzz330, zzz331, Neg(Succ(zzz33200)), zzz333, zzz334), zzz3173, h)
new_mkVBalBranch1(zzz31, Branch(zzz330, zzz331, Neg(Succ(zzz33200)), zzz333, zzz334), Branch(zzz3170, zzz3171, zzz3172, zzz3173, zzz3174), h) → new_mkVBalBranch3MkVBalBranch241(zzz3170, zzz3171, zzz3172, zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, new_primPlusNat2(new_primPlusNat3(Succ(new_primPlusNat3(new_primPlusNat1(zzz33200), zzz33200)), Succ(zzz33200)), Succ(zzz33200)), h)
new_mkVBalBranch3MkVBalBranch235(zzz3170, zzz3171, Pos(Zero), zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, Succ(zzz4170), h) → new_mkVBalBranch3MkVBalBranch237(zzz3170, zzz3171, zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, h)
new_mkVBalBranch3MkVBalBranch235(zzz3170, zzz3171, Neg(Succ(zzz317200)), zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, Succ(zzz4170), h) → new_mkVBalBranch3MkVBalBranch123(zzz3170, zzz3171, zzz317200, zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, new_primPlusNat2(new_primMulNat0(zzz317200), Succ(zzz317200)), h)
new_mkVBalBranch3MkVBalBranch236(zzz958, zzz959, zzz960, zzz961, zzz962, zzz963, zzz964, zzz965, zzz966, zzz967, zzz968, Zero, Succ(zzz9700), ba) → new_mkVBalBranch1(zzz968, Branch(zzz963, zzz964, Pos(Succ(zzz965)), zzz966, zzz967), zzz961, ba)
new_mkVBalBranch3MkVBalBranch125(zzz1337, zzz1338, zzz1339, zzz1340, zzz1341, zzz1342, zzz1343, zzz1344, zzz1345, zzz1346, zzz1347, Succ(zzz13480), Succ(zzz13490), bb) → new_mkVBalBranch3MkVBalBranch125(zzz1337, zzz1338, zzz1339, zzz1340, zzz1341, zzz1342, zzz1343, zzz1344, zzz1345, zzz1346, zzz1347, zzz13480, zzz13490, bb)
new_mkVBalBranch3MkVBalBranch244(zzz972, zzz973, zzz974, zzz975, zzz976, zzz977, zzz978, zzz979, zzz980, zzz981, zzz982, bc) → new_mkVBalBranch3MkVBalBranch128(zzz972, zzz973, zzz974, zzz975, zzz976, zzz977, zzz978, zzz979, zzz980, zzz981, zzz982, new_primMulNat1(zzz974), bc)
new_mkVBalBranch3MkVBalBranch123(zzz3170, zzz3171, zzz317200, zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, Succ(zzz5620), h) → new_mkVBalBranch1(zzz31, zzz334, Branch(zzz3170, zzz3171, Neg(Succ(zzz317200)), zzz3173, zzz3174), h)
new_mkVBalBranch3MkVBalBranch125(zzz1337, zzz1338, zzz1339, zzz1340, zzz1341, zzz1342, zzz1343, zzz1344, zzz1345, zzz1346, zzz1347, Zero, Succ(zzz13490), bb) → new_mkVBalBranch1(zzz1347, zzz1346, Branch(zzz1337, zzz1338, Pos(Succ(zzz1339)), zzz1340, zzz1341), bb)
new_mkVBalBranch3MkVBalBranch242(zzz972, zzz973, zzz974, zzz975, zzz976, zzz977, zzz978, zzz979, zzz980, zzz981, zzz982, Zero, Succ(zzz9840), bc) → new_mkVBalBranch1(zzz982, Branch(zzz977, zzz978, Neg(Succ(zzz979)), zzz980, zzz981), zzz975, bc)
new_mkVBalBranch3MkVBalBranch236(zzz958, zzz959, zzz960, zzz961, zzz962, zzz963, zzz964, zzz965, zzz966, zzz967, zzz968, Succ(zzz9690), Zero, ba) → new_mkVBalBranch3MkVBalBranch124(zzz958, zzz959, zzz960, zzz961, zzz962, zzz963, zzz964, zzz965, zzz966, zzz967, zzz968, new_primMulNat1(zzz960), ba)
new_mkVBalBranch3MkVBalBranch240(zzz958, zzz959, zzz960, zzz961, zzz962, zzz963, zzz964, zzz965, zzz966, zzz967, zzz968, ba) → new_mkVBalBranch3MkVBalBranch124(zzz958, zzz959, zzz960, zzz961, zzz962, zzz963, zzz964, zzz965, zzz966, zzz967, zzz968, new_primMulNat1(zzz960), ba)
new_mkVBalBranch3MkVBalBranch235(zzz3170, zzz3171, Neg(Succ(zzz317200)), zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, Zero, h) → new_mkVBalBranch3MkVBalBranch238(zzz3170, zzz3171, Succ(zzz317200), zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, h)
new_mkVBalBranch1(zzz31, Branch(zzz330, zzz331, Pos(Succ(zzz33200)), zzz333, zzz334), Branch(zzz3170, zzz3171, zzz3172, zzz3173, zzz3174), h) → new_mkVBalBranch3MkVBalBranch235(zzz3170, zzz3171, zzz3172, zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, new_primPlusNat2(new_primMulNat0(zzz33200), Succ(zzz33200)), h)
new_mkVBalBranch3MkVBalBranch241(zzz3170, zzz3171, Pos(Succ(zzz317200)), zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, Zero, h) → new_mkVBalBranch3MkVBalBranch243(zzz3170, zzz3171, Succ(zzz317200), zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, h)
new_mkVBalBranch3MkVBalBranch126(zzz3170, zzz3171, zzz317200, zzz3173, zzz3174, zzz330, zzz331, zzz333, zzz334, zzz31, Succ(zzz5350), h) → new_mkVBalBranch1(zzz31, zzz334, Branch(zzz3170, zzz3171, Neg(Succ(zzz317200)), zzz3173, zzz3174), h)
new_mkVBalBranch1(zzz31, Branch(zzz330, zzz331, Pos(Zero), zzz333, zzz334), Branch(zzz3170, zzz3171, Neg(Succ(zzz317200)), zzz3173, zzz3174), h) → new_mkVBalBranch3MkVBalBranch126(zzz3170, zzz3171, zzz317200, zzz3173, zzz3174, zzz330, zzz331, zzz333, zzz334, zzz31, new_primMulNat1(zzz317200), h)
new_mkVBalBranch3MkVBalBranch123(zzz3170, zzz3171, zzz317200, zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, Zero, h) → new_mkVBalBranch3MkVBalBranch130(zzz3170, zzz3171, zzz317200, zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, h)
new_mkVBalBranch3MkVBalBranch241(zzz3170, zzz3171, Neg(Zero), zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, Succ(zzz4190), h) → new_mkVBalBranch1(zzz31, Branch(zzz330, zzz331, Neg(Succ(zzz33200)), zzz333, zzz334), zzz3173, h)
new_mkVBalBranch3MkVBalBranch124(zzz958, zzz959, zzz960, zzz961, zzz962, zzz963, zzz964, zzz965, zzz966, zzz967, zzz968, Succ(zzz10180), ba) → new_mkVBalBranch3MkVBalBranch125(zzz958, zzz959, zzz960, zzz961, zzz962, zzz963, zzz964, zzz965, zzz966, zzz967, zzz968, Succ(zzz10180), Succ(zzz965), ba)
new_mkVBalBranch3MkVBalBranch235(zzz3170, zzz3171, Pos(Succ(zzz317200)), zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, Zero, h) → new_mkVBalBranch3MkVBalBranch236(zzz3170, zzz3171, zzz317200, zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, Zero, Succ(zzz317200), h)
new_mkVBalBranch3MkVBalBranch239(zzz3170, zzz3171, Zero, zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, h) → new_mkVBalBranch1(zzz31, zzz334, Branch(zzz3170, zzz3171, Neg(Zero), zzz3173, zzz3174), h)
new_mkVBalBranch3MkVBalBranch235(zzz3170, zzz3171, Pos(Zero), zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, Zero, h) → new_mkVBalBranch1(zzz31, zzz334, Branch(zzz3170, zzz3171, Pos(Zero), zzz3173, zzz3174), h)
new_mkVBalBranch3MkVBalBranch242(zzz972, zzz973, zzz974, zzz975, zzz976, zzz977, zzz978, zzz979, zzz980, zzz981, zzz982, Zero, Zero, bc) → new_mkVBalBranch3MkVBalBranch244(zzz972, zzz973, zzz974, zzz975, zzz976, zzz977, zzz978, zzz979, zzz980, zzz981, zzz982, bc)
new_mkVBalBranch3MkVBalBranch130(zzz3170, zzz3171, zzz317200, zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, h) → new_mkVBalBranch1(zzz31, zzz334, Branch(zzz3170, zzz3171, Neg(Succ(zzz317200)), zzz3173, zzz3174), h)
new_mkVBalBranch1(zzz31, Branch(zzz330, zzz331, Neg(Zero), zzz333, zzz334), Branch(zzz3170, zzz3171, Pos(Succ(zzz317200)), zzz3173, zzz3174), h) → new_mkVBalBranch1(zzz31, Branch(zzz330, zzz331, Neg(Zero), zzz333, zzz334), zzz3173, h)
new_mkVBalBranch3MkVBalBranch235(zzz3170, zzz3171, Neg(Zero), zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, Zero, h) → new_mkVBalBranch3MkVBalBranch239(zzz3170, zzz3171, Zero, zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, h)
new_mkVBalBranch3MkVBalBranch235(zzz3170, zzz3171, Neg(Zero), zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, Succ(zzz4170), h) → new_mkVBalBranch1(zzz31, zzz334, Branch(zzz3170, zzz3171, Neg(Zero), zzz3173, zzz3174), h)
new_mkVBalBranch3MkVBalBranch236(zzz958, zzz959, zzz960, zzz961, zzz962, zzz963, zzz964, zzz965, zzz966, zzz967, zzz968, Zero, Zero, ba) → new_mkVBalBranch3MkVBalBranch240(zzz958, zzz959, zzz960, zzz961, zzz962, zzz963, zzz964, zzz965, zzz966, zzz967, zzz968, ba)

The TRS R consists of the following rules:

new_primPlusNat1(Zero) → Zero
new_primMulNat0(zzz6200) → new_primPlusNat3(Succ(new_primPlusNat3(new_primPlusNat1(zzz6200), zzz6200)), Succ(zzz6200))
new_primPlusNat2(Succ(zzz900), Succ(zzz9100)) → Succ(Succ(new_primPlusNat2(zzz900, zzz9100)))
new_primPlusNat3(zzz90, Succ(zzz910)) → Succ(Succ(new_primPlusNat2(zzz90, zzz910)))
new_primPlusNat3(zzz90, Zero) → Succ(zzz90)
new_primMulNat1(zzz34200) → new_primPlusNat2(new_primMulNat0(zzz34200), Succ(zzz34200))
new_primPlusNat2(Zero, Zero) → Zero
new_primPlusNat1(Succ(zzz62000)) → Succ(Succ(new_primPlusNat1(zzz62000)))
new_primPlusNat2(Succ(zzz900), Zero) → Succ(zzz900)
new_primPlusNat2(Zero, Succ(zzz9100)) → Succ(zzz9100)

The set Q consists of the following terms:

new_primPlusNat2(Zero, Succ(x0))
new_primMulNat1(x0)
new_primMulNat0(x0)
new_primPlusNat3(x0, Succ(x1))
new_primPlusNat2(Succ(x0), Succ(x1))
new_primPlusNat3(x0, Zero)
new_primPlusNat1(Zero)
new_primPlusNat2(Zero, Zero)
new_primPlusNat1(Succ(x0))
new_primPlusNat2(Succ(x0), Zero)

We have to consider all minimal (P,Q,R)-chains.
By rewriting [15] the rule new_mkVBalBranch1(zzz31, Branch(zzz330, zzz331, Pos(Succ(zzz33200)), zzz333, zzz334), Branch(zzz3170, zzz3171, zzz3172, zzz3173, zzz3174), h) → new_mkVBalBranch3MkVBalBranch235(zzz3170, zzz3171, zzz3172, zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, new_primPlusNat2(new_primMulNat0(zzz33200), Succ(zzz33200)), h) at position [11,0] we obtained the following new rules:

new_mkVBalBranch1(zzz31, Branch(zzz330, zzz331, Pos(Succ(zzz33200)), zzz333, zzz334), Branch(zzz3170, zzz3171, zzz3172, zzz3173, zzz3174), h) → new_mkVBalBranch3MkVBalBranch235(zzz3170, zzz3171, zzz3172, zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, new_primPlusNat2(new_primPlusNat3(Succ(new_primPlusNat3(new_primPlusNat1(zzz33200), zzz33200)), Succ(zzz33200)), Succ(zzz33200)), 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
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                    ↳ DependencyGraphProof
                                      ↳ QDP
                                        ↳ Rewriting
                                          ↳ QDP
                                            ↳ Rewriting
                                              ↳ QDP
                                                ↳ Rewriting
                                                  ↳ QDP
                                                    ↳ Rewriting
                                                      ↳ QDP
                                                        ↳ Rewriting
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP

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

new_mkVBalBranch3MkVBalBranch238(zzz3170, zzz3171, Succ(zzz317200), zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, h) → new_mkVBalBranch3MkVBalBranch123(zzz3170, zzz3171, zzz317200, zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, new_primPlusNat2(new_primMulNat0(zzz317200), Succ(zzz317200)), h)
new_mkVBalBranch3MkVBalBranch129(zzz1851, zzz1852, zzz1853, zzz1854, zzz1855, zzz1856, zzz1857, zzz1858, zzz1859, zzz1860, zzz1861, Zero, Succ(zzz18630), bd) → new_mkVBalBranch1(zzz1861, zzz1860, Branch(zzz1851, zzz1852, Neg(Succ(zzz1853)), zzz1854, zzz1855), bd)
new_mkVBalBranch3MkVBalBranch242(zzz972, zzz973, zzz974, zzz975, zzz976, zzz977, zzz978, zzz979, zzz980, zzz981, zzz982, Succ(zzz9830), Zero, bc) → new_mkVBalBranch3MkVBalBranch128(zzz972, zzz973, zzz974, zzz975, zzz976, zzz977, zzz978, zzz979, zzz980, zzz981, zzz982, new_primPlusNat2(new_primMulNat0(zzz974), Succ(zzz974)), bc)
new_mkVBalBranch3MkVBalBranch128(zzz972, zzz973, zzz974, zzz975, zzz976, zzz977, zzz978, zzz979, zzz980, zzz981, zzz982, Succ(zzz10190), bc) → new_mkVBalBranch3MkVBalBranch129(zzz972, zzz973, zzz974, zzz975, zzz976, zzz977, zzz978, zzz979, zzz980, zzz981, zzz982, Succ(zzz979), Succ(zzz10190), bc)
new_mkVBalBranch3MkVBalBranch241(zzz3170, zzz3171, Pos(zzz31720), zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, Succ(zzz4190), h) → new_mkVBalBranch1(zzz31, Branch(zzz330, zzz331, Neg(Succ(zzz33200)), zzz333, zzz334), zzz3173, h)
new_mkVBalBranch3MkVBalBranch127(zzz3170, zzz3171, zzz317200, zzz3173, zzz3174, zzz330, zzz331, zzz333, zzz334, zzz31, Succ(zzz5500), h) → new_mkVBalBranch1(zzz31, zzz334, Branch(zzz3170, zzz3171, Neg(Succ(zzz317200)), zzz3173, zzz3174), h)
new_mkVBalBranch1(zzz31, Branch(zzz330, zzz331, Pos(Succ(zzz33200)), zzz333, zzz334), Branch(zzz3170, zzz3171, zzz3172, zzz3173, zzz3174), h) → new_mkVBalBranch3MkVBalBranch235(zzz3170, zzz3171, zzz3172, zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, new_primPlusNat2(new_primPlusNat3(Succ(new_primPlusNat3(new_primPlusNat1(zzz33200), zzz33200)), Succ(zzz33200)), Succ(zzz33200)), h)
new_mkVBalBranch3MkVBalBranch129(zzz1851, zzz1852, zzz1853, zzz1854, zzz1855, zzz1856, zzz1857, zzz1858, zzz1859, zzz1860, zzz1861, Succ(zzz18620), Succ(zzz18630), bd) → new_mkVBalBranch3MkVBalBranch129(zzz1851, zzz1852, zzz1853, zzz1854, zzz1855, zzz1856, zzz1857, zzz1858, zzz1859, zzz1860, zzz1861, zzz18620, zzz18630, bd)
new_mkVBalBranch3MkVBalBranch124(zzz958, zzz959, zzz960, zzz961, zzz962, zzz963, zzz964, zzz965, zzz966, zzz967, zzz968, Zero, ba) → new_mkVBalBranch3MkVBalBranch125(zzz958, zzz959, zzz960, zzz961, zzz962, zzz963, zzz964, zzz965, zzz966, zzz967, zzz968, Zero, Succ(zzz965), ba)
new_mkVBalBranch3MkVBalBranch242(zzz972, zzz973, zzz974, zzz975, zzz976, zzz977, zzz978, zzz979, zzz980, zzz981, zzz982, Succ(zzz9830), Succ(zzz9840), bc) → new_mkVBalBranch3MkVBalBranch242(zzz972, zzz973, zzz974, zzz975, zzz976, zzz977, zzz978, zzz979, zzz980, zzz981, zzz982, zzz9830, zzz9840, bc)
new_mkVBalBranch3MkVBalBranch235(zzz3170, zzz3171, Pos(Succ(zzz317200)), zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, Succ(zzz4170), h) → new_mkVBalBranch3MkVBalBranch236(zzz3170, zzz3171, zzz317200, zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, zzz4170, zzz317200, h)
new_mkVBalBranch3MkVBalBranch236(zzz958, zzz959, zzz960, zzz961, zzz962, zzz963, zzz964, zzz965, zzz966, zzz967, zzz968, Succ(zzz9690), Succ(zzz9700), ba) → new_mkVBalBranch3MkVBalBranch236(zzz958, zzz959, zzz960, zzz961, zzz962, zzz963, zzz964, zzz965, zzz966, zzz967, zzz968, zzz9690, zzz9700, ba)
new_mkVBalBranch1(zzz31, Branch(zzz330, zzz331, Neg(Zero), zzz333, zzz334), Branch(zzz3170, zzz3171, Neg(Succ(zzz317200)), zzz3173, zzz3174), h) → new_mkVBalBranch3MkVBalBranch127(zzz3170, zzz3171, zzz317200, zzz3173, zzz3174, zzz330, zzz331, zzz333, zzz334, zzz31, new_primPlusNat2(new_primMulNat0(zzz317200), Succ(zzz317200)), h)
new_mkVBalBranch3MkVBalBranch241(zzz3170, zzz3171, Neg(Succ(zzz317200)), zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, Succ(zzz4190), h) → new_mkVBalBranch3MkVBalBranch242(zzz3170, zzz3171, zzz317200, zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, zzz317200, zzz4190, h)
new_mkVBalBranch3MkVBalBranch241(zzz3170, zzz3171, Neg(Succ(zzz317200)), zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, Zero, h) → new_mkVBalBranch3MkVBalBranch242(zzz3170, zzz3171, zzz317200, zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, Succ(zzz317200), Zero, h)
new_mkVBalBranch1(zzz31, Branch(zzz330, zzz331, Pos(Zero), zzz333, zzz334), Branch(zzz3170, zzz3171, Pos(Succ(zzz317200)), zzz3173, zzz3174), h) → new_mkVBalBranch1(zzz31, Branch(zzz330, zzz331, Pos(Zero), zzz333, zzz334), zzz3173, h)
new_mkVBalBranch3MkVBalBranch243(zzz3170, zzz3171, zzz31720, zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, h) → new_mkVBalBranch1(zzz31, Branch(zzz330, zzz331, Neg(Succ(zzz33200)), zzz333, zzz334), zzz3173, h)
new_mkVBalBranch3MkVBalBranch237(zzz3170, zzz3171, zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, h) → new_mkVBalBranch1(zzz31, zzz334, Branch(zzz3170, zzz3171, Pos(Zero), zzz3173, zzz3174), h)
new_mkVBalBranch1(zzz31, Branch(zzz330, zzz331, Neg(Succ(zzz33200)), zzz333, zzz334), Branch(zzz3170, zzz3171, zzz3172, zzz3173, zzz3174), h) → new_mkVBalBranch3MkVBalBranch241(zzz3170, zzz3171, zzz3172, zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, new_primPlusNat2(new_primPlusNat3(Succ(new_primPlusNat3(new_primPlusNat1(zzz33200), zzz33200)), Succ(zzz33200)), Succ(zzz33200)), h)
new_mkVBalBranch3MkVBalBranch235(zzz3170, zzz3171, Pos(Zero), zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, Succ(zzz4170), h) → new_mkVBalBranch3MkVBalBranch237(zzz3170, zzz3171, zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, h)
new_mkVBalBranch3MkVBalBranch235(zzz3170, zzz3171, Neg(Succ(zzz317200)), zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, Succ(zzz4170), h) → new_mkVBalBranch3MkVBalBranch123(zzz3170, zzz3171, zzz317200, zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, new_primPlusNat2(new_primMulNat0(zzz317200), Succ(zzz317200)), h)
new_mkVBalBranch3MkVBalBranch236(zzz958, zzz959, zzz960, zzz961, zzz962, zzz963, zzz964, zzz965, zzz966, zzz967, zzz968, Zero, Succ(zzz9700), ba) → new_mkVBalBranch1(zzz968, Branch(zzz963, zzz964, Pos(Succ(zzz965)), zzz966, zzz967), zzz961, ba)
new_mkVBalBranch3MkVBalBranch244(zzz972, zzz973, zzz974, zzz975, zzz976, zzz977, zzz978, zzz979, zzz980, zzz981, zzz982, bc) → new_mkVBalBranch3MkVBalBranch128(zzz972, zzz973, zzz974, zzz975, zzz976, zzz977, zzz978, zzz979, zzz980, zzz981, zzz982, new_primMulNat1(zzz974), bc)
new_mkVBalBranch3MkVBalBranch125(zzz1337, zzz1338, zzz1339, zzz1340, zzz1341, zzz1342, zzz1343, zzz1344, zzz1345, zzz1346, zzz1347, Succ(zzz13480), Succ(zzz13490), bb) → new_mkVBalBranch3MkVBalBranch125(zzz1337, zzz1338, zzz1339, zzz1340, zzz1341, zzz1342, zzz1343, zzz1344, zzz1345, zzz1346, zzz1347, zzz13480, zzz13490, bb)
new_mkVBalBranch3MkVBalBranch123(zzz3170, zzz3171, zzz317200, zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, Succ(zzz5620), h) → new_mkVBalBranch1(zzz31, zzz334, Branch(zzz3170, zzz3171, Neg(Succ(zzz317200)), zzz3173, zzz3174), h)
new_mkVBalBranch3MkVBalBranch125(zzz1337, zzz1338, zzz1339, zzz1340, zzz1341, zzz1342, zzz1343, zzz1344, zzz1345, zzz1346, zzz1347, Zero, Succ(zzz13490), bb) → new_mkVBalBranch1(zzz1347, zzz1346, Branch(zzz1337, zzz1338, Pos(Succ(zzz1339)), zzz1340, zzz1341), bb)
new_mkVBalBranch3MkVBalBranch242(zzz972, zzz973, zzz974, zzz975, zzz976, zzz977, zzz978, zzz979, zzz980, zzz981, zzz982, Zero, Succ(zzz9840), bc) → new_mkVBalBranch1(zzz982, Branch(zzz977, zzz978, Neg(Succ(zzz979)), zzz980, zzz981), zzz975, bc)
new_mkVBalBranch3MkVBalBranch240(zzz958, zzz959, zzz960, zzz961, zzz962, zzz963, zzz964, zzz965, zzz966, zzz967, zzz968, ba) → new_mkVBalBranch3MkVBalBranch124(zzz958, zzz959, zzz960, zzz961, zzz962, zzz963, zzz964, zzz965, zzz966, zzz967, zzz968, new_primMulNat1(zzz960), ba)
new_mkVBalBranch3MkVBalBranch236(zzz958, zzz959, zzz960, zzz961, zzz962, zzz963, zzz964, zzz965, zzz966, zzz967, zzz968, Succ(zzz9690), Zero, ba) → new_mkVBalBranch3MkVBalBranch124(zzz958, zzz959, zzz960, zzz961, zzz962, zzz963, zzz964, zzz965, zzz966, zzz967, zzz968, new_primMulNat1(zzz960), ba)
new_mkVBalBranch3MkVBalBranch235(zzz3170, zzz3171, Neg(Succ(zzz317200)), zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, Zero, h) → new_mkVBalBranch3MkVBalBranch238(zzz3170, zzz3171, Succ(zzz317200), zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, h)
new_mkVBalBranch3MkVBalBranch241(zzz3170, zzz3171, Pos(Succ(zzz317200)), zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, Zero, h) → new_mkVBalBranch3MkVBalBranch243(zzz3170, zzz3171, Succ(zzz317200), zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, h)
new_mkVBalBranch3MkVBalBranch126(zzz3170, zzz3171, zzz317200, zzz3173, zzz3174, zzz330, zzz331, zzz333, zzz334, zzz31, Succ(zzz5350), h) → new_mkVBalBranch1(zzz31, zzz334, Branch(zzz3170, zzz3171, Neg(Succ(zzz317200)), zzz3173, zzz3174), h)
new_mkVBalBranch3MkVBalBranch241(zzz3170, zzz3171, Neg(Zero), zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, Succ(zzz4190), h) → new_mkVBalBranch1(zzz31, Branch(zzz330, zzz331, Neg(Succ(zzz33200)), zzz333, zzz334), zzz3173, h)
new_mkVBalBranch3MkVBalBranch123(zzz3170, zzz3171, zzz317200, zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, Zero, h) → new_mkVBalBranch3MkVBalBranch130(zzz3170, zzz3171, zzz317200, zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, h)
new_mkVBalBranch1(zzz31, Branch(zzz330, zzz331, Pos(Zero), zzz333, zzz334), Branch(zzz3170, zzz3171, Neg(Succ(zzz317200)), zzz3173, zzz3174), h) → new_mkVBalBranch3MkVBalBranch126(zzz3170, zzz3171, zzz317200, zzz3173, zzz3174, zzz330, zzz331, zzz333, zzz334, zzz31, new_primMulNat1(zzz317200), h)
new_mkVBalBranch3MkVBalBranch124(zzz958, zzz959, zzz960, zzz961, zzz962, zzz963, zzz964, zzz965, zzz966, zzz967, zzz968, Succ(zzz10180), ba) → new_mkVBalBranch3MkVBalBranch125(zzz958, zzz959, zzz960, zzz961, zzz962, zzz963, zzz964, zzz965, zzz966, zzz967, zzz968, Succ(zzz10180), Succ(zzz965), ba)
new_mkVBalBranch3MkVBalBranch235(zzz3170, zzz3171, Pos(Succ(zzz317200)), zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, Zero, h) → new_mkVBalBranch3MkVBalBranch236(zzz3170, zzz3171, zzz317200, zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, Zero, Succ(zzz317200), h)
new_mkVBalBranch3MkVBalBranch239(zzz3170, zzz3171, Zero, zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, h) → new_mkVBalBranch1(zzz31, zzz334, Branch(zzz3170, zzz3171, Neg(Zero), zzz3173, zzz3174), h)
new_mkVBalBranch3MkVBalBranch235(zzz3170, zzz3171, Pos(Zero), zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, Zero, h) → new_mkVBalBranch1(zzz31, zzz334, Branch(zzz3170, zzz3171, Pos(Zero), zzz3173, zzz3174), h)
new_mkVBalBranch3MkVBalBranch242(zzz972, zzz973, zzz974, zzz975, zzz976, zzz977, zzz978, zzz979, zzz980, zzz981, zzz982, Zero, Zero, bc) → new_mkVBalBranch3MkVBalBranch244(zzz972, zzz973, zzz974, zzz975, zzz976, zzz977, zzz978, zzz979, zzz980, zzz981, zzz982, bc)
new_mkVBalBranch3MkVBalBranch130(zzz3170, zzz3171, zzz317200, zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, h) → new_mkVBalBranch1(zzz31, zzz334, Branch(zzz3170, zzz3171, Neg(Succ(zzz317200)), zzz3173, zzz3174), h)
new_mkVBalBranch3MkVBalBranch235(zzz3170, zzz3171, Neg(Zero), zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, Zero, h) → new_mkVBalBranch3MkVBalBranch239(zzz3170, zzz3171, Zero, zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, h)
new_mkVBalBranch1(zzz31, Branch(zzz330, zzz331, Neg(Zero), zzz333, zzz334), Branch(zzz3170, zzz3171, Pos(Succ(zzz317200)), zzz3173, zzz3174), h) → new_mkVBalBranch1(zzz31, Branch(zzz330, zzz331, Neg(Zero), zzz333, zzz334), zzz3173, h)
new_mkVBalBranch3MkVBalBranch235(zzz3170, zzz3171, Neg(Zero), zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, Succ(zzz4170), h) → new_mkVBalBranch1(zzz31, zzz334, Branch(zzz3170, zzz3171, Neg(Zero), zzz3173, zzz3174), h)
new_mkVBalBranch3MkVBalBranch236(zzz958, zzz959, zzz960, zzz961, zzz962, zzz963, zzz964, zzz965, zzz966, zzz967, zzz968, Zero, Zero, ba) → new_mkVBalBranch3MkVBalBranch240(zzz958, zzz959, zzz960, zzz961, zzz962, zzz963, zzz964, zzz965, zzz966, zzz967, zzz968, ba)

The TRS R consists of the following rules:

new_primPlusNat1(Zero) → Zero
new_primMulNat0(zzz6200) → new_primPlusNat3(Succ(new_primPlusNat3(new_primPlusNat1(zzz6200), zzz6200)), Succ(zzz6200))
new_primPlusNat2(Succ(zzz900), Succ(zzz9100)) → Succ(Succ(new_primPlusNat2(zzz900, zzz9100)))
new_primPlusNat3(zzz90, Succ(zzz910)) → Succ(Succ(new_primPlusNat2(zzz90, zzz910)))
new_primPlusNat3(zzz90, Zero) → Succ(zzz90)
new_primMulNat1(zzz34200) → new_primPlusNat2(new_primMulNat0(zzz34200), Succ(zzz34200))
new_primPlusNat2(Zero, Zero) → Zero
new_primPlusNat1(Succ(zzz62000)) → Succ(Succ(new_primPlusNat1(zzz62000)))
new_primPlusNat2(Succ(zzz900), Zero) → Succ(zzz900)
new_primPlusNat2(Zero, Succ(zzz9100)) → Succ(zzz9100)

The set Q consists of the following terms:

new_primPlusNat2(Zero, Succ(x0))
new_primMulNat1(x0)
new_primMulNat0(x0)
new_primPlusNat3(x0, Succ(x1))
new_primPlusNat2(Succ(x0), Succ(x1))
new_primPlusNat3(x0, Zero)
new_primPlusNat1(Zero)
new_primPlusNat2(Zero, Zero)
new_primPlusNat1(Succ(x0))
new_primPlusNat2(Succ(x0), Zero)

We have to consider all minimal (P,Q,R)-chains.
By rewriting [15] the rule new_mkVBalBranch3MkVBalBranch236(zzz958, zzz959, zzz960, zzz961, zzz962, zzz963, zzz964, zzz965, zzz966, zzz967, zzz968, Succ(zzz9690), Zero, ba) → new_mkVBalBranch3MkVBalBranch124(zzz958, zzz959, zzz960, zzz961, zzz962, zzz963, zzz964, zzz965, zzz966, zzz967, zzz968, new_primMulNat1(zzz960), ba) at position [11] we obtained the following new rules:

new_mkVBalBranch3MkVBalBranch236(zzz958, zzz959, zzz960, zzz961, zzz962, zzz963, zzz964, zzz965, zzz966, zzz967, zzz968, Succ(zzz9690), Zero, ba) → new_mkVBalBranch3MkVBalBranch124(zzz958, zzz959, zzz960, zzz961, zzz962, zzz963, zzz964, zzz965, zzz966, zzz967, zzz968, new_primPlusNat2(new_primMulNat0(zzz960), Succ(zzz960)), 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
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                    ↳ DependencyGraphProof
                                      ↳ QDP
                                        ↳ Rewriting
                                          ↳ QDP
                                            ↳ Rewriting
                                              ↳ QDP
                                                ↳ Rewriting
                                                  ↳ QDP
                                                    ↳ Rewriting
                                                      ↳ QDP
                                                        ↳ Rewriting
                                                          ↳ QDP
                                                            ↳ Rewriting
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP

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

new_mkVBalBranch3MkVBalBranch242(zzz972, zzz973, zzz974, zzz975, zzz976, zzz977, zzz978, zzz979, zzz980, zzz981, zzz982, Succ(zzz9830), Zero, bc) → new_mkVBalBranch3MkVBalBranch128(zzz972, zzz973, zzz974, zzz975, zzz976, zzz977, zzz978, zzz979, zzz980, zzz981, zzz982, new_primPlusNat2(new_primMulNat0(zzz974), Succ(zzz974)), bc)
new_mkVBalBranch3MkVBalBranch129(zzz1851, zzz1852, zzz1853, zzz1854, zzz1855, zzz1856, zzz1857, zzz1858, zzz1859, zzz1860, zzz1861, Zero, Succ(zzz18630), bd) → new_mkVBalBranch1(zzz1861, zzz1860, Branch(zzz1851, zzz1852, Neg(Succ(zzz1853)), zzz1854, zzz1855), bd)
new_mkVBalBranch3MkVBalBranch238(zzz3170, zzz3171, Succ(zzz317200), zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, h) → new_mkVBalBranch3MkVBalBranch123(zzz3170, zzz3171, zzz317200, zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, new_primPlusNat2(new_primMulNat0(zzz317200), Succ(zzz317200)), h)
new_mkVBalBranch3MkVBalBranch127(zzz3170, zzz3171, zzz317200, zzz3173, zzz3174, zzz330, zzz331, zzz333, zzz334, zzz31, Succ(zzz5500), h) → new_mkVBalBranch1(zzz31, zzz334, Branch(zzz3170, zzz3171, Neg(Succ(zzz317200)), zzz3173, zzz3174), h)
new_mkVBalBranch3MkVBalBranch241(zzz3170, zzz3171, Pos(zzz31720), zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, Succ(zzz4190), h) → new_mkVBalBranch1(zzz31, Branch(zzz330, zzz331, Neg(Succ(zzz33200)), zzz333, zzz334), zzz3173, h)
new_mkVBalBranch3MkVBalBranch128(zzz972, zzz973, zzz974, zzz975, zzz976, zzz977, zzz978, zzz979, zzz980, zzz981, zzz982, Succ(zzz10190), bc) → new_mkVBalBranch3MkVBalBranch129(zzz972, zzz973, zzz974, zzz975, zzz976, zzz977, zzz978, zzz979, zzz980, zzz981, zzz982, Succ(zzz979), Succ(zzz10190), bc)
new_mkVBalBranch1(zzz31, Branch(zzz330, zzz331, Pos(Succ(zzz33200)), zzz333, zzz334), Branch(zzz3170, zzz3171, zzz3172, zzz3173, zzz3174), h) → new_mkVBalBranch3MkVBalBranch235(zzz3170, zzz3171, zzz3172, zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, new_primPlusNat2(new_primPlusNat3(Succ(new_primPlusNat3(new_primPlusNat1(zzz33200), zzz33200)), Succ(zzz33200)), Succ(zzz33200)), h)
new_mkVBalBranch3MkVBalBranch129(zzz1851, zzz1852, zzz1853, zzz1854, zzz1855, zzz1856, zzz1857, zzz1858, zzz1859, zzz1860, zzz1861, Succ(zzz18620), Succ(zzz18630), bd) → new_mkVBalBranch3MkVBalBranch129(zzz1851, zzz1852, zzz1853, zzz1854, zzz1855, zzz1856, zzz1857, zzz1858, zzz1859, zzz1860, zzz1861, zzz18620, zzz18630, bd)
new_mkVBalBranch3MkVBalBranch124(zzz958, zzz959, zzz960, zzz961, zzz962, zzz963, zzz964, zzz965, zzz966, zzz967, zzz968, Zero, ba) → new_mkVBalBranch3MkVBalBranch125(zzz958, zzz959, zzz960, zzz961, zzz962, zzz963, zzz964, zzz965, zzz966, zzz967, zzz968, Zero, Succ(zzz965), ba)
new_mkVBalBranch3MkVBalBranch235(zzz3170, zzz3171, Pos(Succ(zzz317200)), zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, Succ(zzz4170), h) → new_mkVBalBranch3MkVBalBranch236(zzz3170, zzz3171, zzz317200, zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, zzz4170, zzz317200, h)
new_mkVBalBranch3MkVBalBranch242(zzz972, zzz973, zzz974, zzz975, zzz976, zzz977, zzz978, zzz979, zzz980, zzz981, zzz982, Succ(zzz9830), Succ(zzz9840), bc) → new_mkVBalBranch3MkVBalBranch242(zzz972, zzz973, zzz974, zzz975, zzz976, zzz977, zzz978, zzz979, zzz980, zzz981, zzz982, zzz9830, zzz9840, bc)
new_mkVBalBranch3MkVBalBranch236(zzz958, zzz959, zzz960, zzz961, zzz962, zzz963, zzz964, zzz965, zzz966, zzz967, zzz968, Succ(zzz9690), Succ(zzz9700), ba) → new_mkVBalBranch3MkVBalBranch236(zzz958, zzz959, zzz960, zzz961, zzz962, zzz963, zzz964, zzz965, zzz966, zzz967, zzz968, zzz9690, zzz9700, ba)
new_mkVBalBranch1(zzz31, Branch(zzz330, zzz331, Neg(Zero), zzz333, zzz334), Branch(zzz3170, zzz3171, Neg(Succ(zzz317200)), zzz3173, zzz3174), h) → new_mkVBalBranch3MkVBalBranch127(zzz3170, zzz3171, zzz317200, zzz3173, zzz3174, zzz330, zzz331, zzz333, zzz334, zzz31, new_primPlusNat2(new_primMulNat0(zzz317200), Succ(zzz317200)), h)
new_mkVBalBranch3MkVBalBranch241(zzz3170, zzz3171, Neg(Succ(zzz317200)), zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, Succ(zzz4190), h) → new_mkVBalBranch3MkVBalBranch242(zzz3170, zzz3171, zzz317200, zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, zzz317200, zzz4190, h)
new_mkVBalBranch3MkVBalBranch241(zzz3170, zzz3171, Neg(Succ(zzz317200)), zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, Zero, h) → new_mkVBalBranch3MkVBalBranch242(zzz3170, zzz3171, zzz317200, zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, Succ(zzz317200), Zero, h)
new_mkVBalBranch1(zzz31, Branch(zzz330, zzz331, Pos(Zero), zzz333, zzz334), Branch(zzz3170, zzz3171, Pos(Succ(zzz317200)), zzz3173, zzz3174), h) → new_mkVBalBranch1(zzz31, Branch(zzz330, zzz331, Pos(Zero), zzz333, zzz334), zzz3173, h)
new_mkVBalBranch3MkVBalBranch237(zzz3170, zzz3171, zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, h) → new_mkVBalBranch1(zzz31, zzz334, Branch(zzz3170, zzz3171, Pos(Zero), zzz3173, zzz3174), h)
new_mkVBalBranch3MkVBalBranch243(zzz3170, zzz3171, zzz31720, zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, h) → new_mkVBalBranch1(zzz31, Branch(zzz330, zzz331, Neg(Succ(zzz33200)), zzz333, zzz334), zzz3173, h)
new_mkVBalBranch1(zzz31, Branch(zzz330, zzz331, Neg(Succ(zzz33200)), zzz333, zzz334), Branch(zzz3170, zzz3171, zzz3172, zzz3173, zzz3174), h) → new_mkVBalBranch3MkVBalBranch241(zzz3170, zzz3171, zzz3172, zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, new_primPlusNat2(new_primPlusNat3(Succ(new_primPlusNat3(new_primPlusNat1(zzz33200), zzz33200)), Succ(zzz33200)), Succ(zzz33200)), h)
new_mkVBalBranch3MkVBalBranch235(zzz3170, zzz3171, Pos(Zero), zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, Succ(zzz4170), h) → new_mkVBalBranch3MkVBalBranch237(zzz3170, zzz3171, zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, h)
new_mkVBalBranch3MkVBalBranch235(zzz3170, zzz3171, Neg(Succ(zzz317200)), zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, Succ(zzz4170), h) → new_mkVBalBranch3MkVBalBranch123(zzz3170, zzz3171, zzz317200, zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, new_primPlusNat2(new_primMulNat0(zzz317200), Succ(zzz317200)), h)
new_mkVBalBranch3MkVBalBranch236(zzz958, zzz959, zzz960, zzz961, zzz962, zzz963, zzz964, zzz965, zzz966, zzz967, zzz968, Succ(zzz9690), Zero, ba) → new_mkVBalBranch3MkVBalBranch124(zzz958, zzz959, zzz960, zzz961, zzz962, zzz963, zzz964, zzz965, zzz966, zzz967, zzz968, new_primPlusNat2(new_primMulNat0(zzz960), Succ(zzz960)), ba)
new_mkVBalBranch3MkVBalBranch236(zzz958, zzz959, zzz960, zzz961, zzz962, zzz963, zzz964, zzz965, zzz966, zzz967, zzz968, Zero, Succ(zzz9700), ba) → new_mkVBalBranch1(zzz968, Branch(zzz963, zzz964, Pos(Succ(zzz965)), zzz966, zzz967), zzz961, ba)
new_mkVBalBranch3MkVBalBranch125(zzz1337, zzz1338, zzz1339, zzz1340, zzz1341, zzz1342, zzz1343, zzz1344, zzz1345, zzz1346, zzz1347, Succ(zzz13480), Succ(zzz13490), bb) → new_mkVBalBranch3MkVBalBranch125(zzz1337, zzz1338, zzz1339, zzz1340, zzz1341, zzz1342, zzz1343, zzz1344, zzz1345, zzz1346, zzz1347, zzz13480, zzz13490, bb)
new_mkVBalBranch3MkVBalBranch244(zzz972, zzz973, zzz974, zzz975, zzz976, zzz977, zzz978, zzz979, zzz980, zzz981, zzz982, bc) → new_mkVBalBranch3MkVBalBranch128(zzz972, zzz973, zzz974, zzz975, zzz976, zzz977, zzz978, zzz979, zzz980, zzz981, zzz982, new_primMulNat1(zzz974), bc)
new_mkVBalBranch3MkVBalBranch123(zzz3170, zzz3171, zzz317200, zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, Succ(zzz5620), h) → new_mkVBalBranch1(zzz31, zzz334, Branch(zzz3170, zzz3171, Neg(Succ(zzz317200)), zzz3173, zzz3174), h)
new_mkVBalBranch3MkVBalBranch125(zzz1337, zzz1338, zzz1339, zzz1340, zzz1341, zzz1342, zzz1343, zzz1344, zzz1345, zzz1346, zzz1347, Zero, Succ(zzz13490), bb) → new_mkVBalBranch1(zzz1347, zzz1346, Branch(zzz1337, zzz1338, Pos(Succ(zzz1339)), zzz1340, zzz1341), bb)
new_mkVBalBranch3MkVBalBranch242(zzz972, zzz973, zzz974, zzz975, zzz976, zzz977, zzz978, zzz979, zzz980, zzz981, zzz982, Zero, Succ(zzz9840), bc) → new_mkVBalBranch1(zzz982, Branch(zzz977, zzz978, Neg(Succ(zzz979)), zzz980, zzz981), zzz975, bc)
new_mkVBalBranch3MkVBalBranch240(zzz958, zzz959, zzz960, zzz961, zzz962, zzz963, zzz964, zzz965, zzz966, zzz967, zzz968, ba) → new_mkVBalBranch3MkVBalBranch124(zzz958, zzz959, zzz960, zzz961, zzz962, zzz963, zzz964, zzz965, zzz966, zzz967, zzz968, new_primMulNat1(zzz960), ba)
new_mkVBalBranch3MkVBalBranch235(zzz3170, zzz3171, Neg(Succ(zzz317200)), zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, Zero, h) → new_mkVBalBranch3MkVBalBranch238(zzz3170, zzz3171, Succ(zzz317200), zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, h)
new_mkVBalBranch3MkVBalBranch241(zzz3170, zzz3171, Pos(Succ(zzz317200)), zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, Zero, h) → new_mkVBalBranch3MkVBalBranch243(zzz3170, zzz3171, Succ(zzz317200), zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, h)
new_mkVBalBranch3MkVBalBranch126(zzz3170, zzz3171, zzz317200, zzz3173, zzz3174, zzz330, zzz331, zzz333, zzz334, zzz31, Succ(zzz5350), h) → new_mkVBalBranch1(zzz31, zzz334, Branch(zzz3170, zzz3171, Neg(Succ(zzz317200)), zzz3173, zzz3174), h)
new_mkVBalBranch1(zzz31, Branch(zzz330, zzz331, Pos(Zero), zzz333, zzz334), Branch(zzz3170, zzz3171, Neg(Succ(zzz317200)), zzz3173, zzz3174), h) → new_mkVBalBranch3MkVBalBranch126(zzz3170, zzz3171, zzz317200, zzz3173, zzz3174, zzz330, zzz331, zzz333, zzz334, zzz31, new_primMulNat1(zzz317200), h)
new_mkVBalBranch3MkVBalBranch123(zzz3170, zzz3171, zzz317200, zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, Zero, h) → new_mkVBalBranch3MkVBalBranch130(zzz3170, zzz3171, zzz317200, zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, h)
new_mkVBalBranch3MkVBalBranch241(zzz3170, zzz3171, Neg(Zero), zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, Succ(zzz4190), h) → new_mkVBalBranch1(zzz31, Branch(zzz330, zzz331, Neg(Succ(zzz33200)), zzz333, zzz334), zzz3173, h)
new_mkVBalBranch3MkVBalBranch124(zzz958, zzz959, zzz960, zzz961, zzz962, zzz963, zzz964, zzz965, zzz966, zzz967, zzz968, Succ(zzz10180), ba) → new_mkVBalBranch3MkVBalBranch125(zzz958, zzz959, zzz960, zzz961, zzz962, zzz963, zzz964, zzz965, zzz966, zzz967, zzz968, Succ(zzz10180), Succ(zzz965), ba)
new_mkVBalBranch3MkVBalBranch235(zzz3170, zzz3171, Pos(Succ(zzz317200)), zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, Zero, h) → new_mkVBalBranch3MkVBalBranch236(zzz3170, zzz3171, zzz317200, zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, Zero, Succ(zzz317200), h)
new_mkVBalBranch3MkVBalBranch239(zzz3170, zzz3171, Zero, zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, h) → new_mkVBalBranch1(zzz31, zzz334, Branch(zzz3170, zzz3171, Neg(Zero), zzz3173, zzz3174), h)
new_mkVBalBranch3MkVBalBranch235(zzz3170, zzz3171, Pos(Zero), zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, Zero, h) → new_mkVBalBranch1(zzz31, zzz334, Branch(zzz3170, zzz3171, Pos(Zero), zzz3173, zzz3174), h)
new_mkVBalBranch3MkVBalBranch242(zzz972, zzz973, zzz974, zzz975, zzz976, zzz977, zzz978, zzz979, zzz980, zzz981, zzz982, Zero, Zero, bc) → new_mkVBalBranch3MkVBalBranch244(zzz972, zzz973, zzz974, zzz975, zzz976, zzz977, zzz978, zzz979, zzz980, zzz981, zzz982, bc)
new_mkVBalBranch3MkVBalBranch130(zzz3170, zzz3171, zzz317200, zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, h) → new_mkVBalBranch1(zzz31, zzz334, Branch(zzz3170, zzz3171, Neg(Succ(zzz317200)), zzz3173, zzz3174), h)
new_mkVBalBranch1(zzz31, Branch(zzz330, zzz331, Neg(Zero), zzz333, zzz334), Branch(zzz3170, zzz3171, Pos(Succ(zzz317200)), zzz3173, zzz3174), h) → new_mkVBalBranch1(zzz31, Branch(zzz330, zzz331, Neg(Zero), zzz333, zzz334), zzz3173, h)
new_mkVBalBranch3MkVBalBranch235(zzz3170, zzz3171, Neg(Zero), zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, Zero, h) → new_mkVBalBranch3MkVBalBranch239(zzz3170, zzz3171, Zero, zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, h)
new_mkVBalBranch3MkVBalBranch235(zzz3170, zzz3171, Neg(Zero), zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, Succ(zzz4170), h) → new_mkVBalBranch1(zzz31, zzz334, Branch(zzz3170, zzz3171, Neg(Zero), zzz3173, zzz3174), h)
new_mkVBalBranch3MkVBalBranch236(zzz958, zzz959, zzz960, zzz961, zzz962, zzz963, zzz964, zzz965, zzz966, zzz967, zzz968, Zero, Zero, ba) → new_mkVBalBranch3MkVBalBranch240(zzz958, zzz959, zzz960, zzz961, zzz962, zzz963, zzz964, zzz965, zzz966, zzz967, zzz968, ba)

The TRS R consists of the following rules:

new_primPlusNat1(Zero) → Zero
new_primMulNat0(zzz6200) → new_primPlusNat3(Succ(new_primPlusNat3(new_primPlusNat1(zzz6200), zzz6200)), Succ(zzz6200))
new_primPlusNat2(Succ(zzz900), Succ(zzz9100)) → Succ(Succ(new_primPlusNat2(zzz900, zzz9100)))
new_primPlusNat3(zzz90, Succ(zzz910)) → Succ(Succ(new_primPlusNat2(zzz90, zzz910)))
new_primPlusNat3(zzz90, Zero) → Succ(zzz90)
new_primMulNat1(zzz34200) → new_primPlusNat2(new_primMulNat0(zzz34200), Succ(zzz34200))
new_primPlusNat2(Zero, Zero) → Zero
new_primPlusNat1(Succ(zzz62000)) → Succ(Succ(new_primPlusNat1(zzz62000)))
new_primPlusNat2(Succ(zzz900), Zero) → Succ(zzz900)
new_primPlusNat2(Zero, Succ(zzz9100)) → Succ(zzz9100)

The set Q consists of the following terms:

new_primPlusNat2(Zero, Succ(x0))
new_primMulNat1(x0)
new_primMulNat0(x0)
new_primPlusNat3(x0, Succ(x1))
new_primPlusNat2(Succ(x0), Succ(x1))
new_primPlusNat3(x0, Zero)
new_primPlusNat1(Zero)
new_primPlusNat2(Zero, Zero)
new_primPlusNat1(Succ(x0))
new_primPlusNat2(Succ(x0), Zero)

We have to consider all minimal (P,Q,R)-chains.
By rewriting [15] the rule new_mkVBalBranch1(zzz31, Branch(zzz330, zzz331, Pos(Zero), zzz333, zzz334), Branch(zzz3170, zzz3171, Neg(Succ(zzz317200)), zzz3173, zzz3174), h) → new_mkVBalBranch3MkVBalBranch126(zzz3170, zzz3171, zzz317200, zzz3173, zzz3174, zzz330, zzz331, zzz333, zzz334, zzz31, new_primMulNat1(zzz317200), h) at position [10] we obtained the following new rules:

new_mkVBalBranch1(zzz31, Branch(zzz330, zzz331, Pos(Zero), zzz333, zzz334), Branch(zzz3170, zzz3171, Neg(Succ(zzz317200)), zzz3173, zzz3174), h) → new_mkVBalBranch3MkVBalBranch126(zzz3170, zzz3171, zzz317200, zzz3173, zzz3174, zzz330, zzz331, zzz333, zzz334, zzz31, new_primPlusNat2(new_primMulNat0(zzz317200), Succ(zzz317200)), 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
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                    ↳ DependencyGraphProof
                                      ↳ QDP
                                        ↳ Rewriting
                                          ↳ QDP
                                            ↳ Rewriting
                                              ↳ QDP
                                                ↳ Rewriting
                                                  ↳ QDP
                                                    ↳ Rewriting
                                                      ↳ QDP
                                                        ↳ Rewriting
                                                          ↳ QDP
                                                            ↳ Rewriting
                                                              ↳ QDP
                                                                ↳ Rewriting
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP

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

new_mkVBalBranch3MkVBalBranch238(zzz3170, zzz3171, Succ(zzz317200), zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, h) → new_mkVBalBranch3MkVBalBranch123(zzz3170, zzz3171, zzz317200, zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, new_primPlusNat2(new_primMulNat0(zzz317200), Succ(zzz317200)), h)
new_mkVBalBranch3MkVBalBranch129(zzz1851, zzz1852, zzz1853, zzz1854, zzz1855, zzz1856, zzz1857, zzz1858, zzz1859, zzz1860, zzz1861, Zero, Succ(zzz18630), bd) → new_mkVBalBranch1(zzz1861, zzz1860, Branch(zzz1851, zzz1852, Neg(Succ(zzz1853)), zzz1854, zzz1855), bd)
new_mkVBalBranch3MkVBalBranch242(zzz972, zzz973, zzz974, zzz975, zzz976, zzz977, zzz978, zzz979, zzz980, zzz981, zzz982, Succ(zzz9830), Zero, bc) → new_mkVBalBranch3MkVBalBranch128(zzz972, zzz973, zzz974, zzz975, zzz976, zzz977, zzz978, zzz979, zzz980, zzz981, zzz982, new_primPlusNat2(new_primMulNat0(zzz974), Succ(zzz974)), bc)
new_mkVBalBranch3MkVBalBranch128(zzz972, zzz973, zzz974, zzz975, zzz976, zzz977, zzz978, zzz979, zzz980, zzz981, zzz982, Succ(zzz10190), bc) → new_mkVBalBranch3MkVBalBranch129(zzz972, zzz973, zzz974, zzz975, zzz976, zzz977, zzz978, zzz979, zzz980, zzz981, zzz982, Succ(zzz979), Succ(zzz10190), bc)
new_mkVBalBranch3MkVBalBranch241(zzz3170, zzz3171, Pos(zzz31720), zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, Succ(zzz4190), h) → new_mkVBalBranch1(zzz31, Branch(zzz330, zzz331, Neg(Succ(zzz33200)), zzz333, zzz334), zzz3173, h)
new_mkVBalBranch3MkVBalBranch127(zzz3170, zzz3171, zzz317200, zzz3173, zzz3174, zzz330, zzz331, zzz333, zzz334, zzz31, Succ(zzz5500), h) → new_mkVBalBranch1(zzz31, zzz334, Branch(zzz3170, zzz3171, Neg(Succ(zzz317200)), zzz3173, zzz3174), h)
new_mkVBalBranch1(zzz31, Branch(zzz330, zzz331, Pos(Succ(zzz33200)), zzz333, zzz334), Branch(zzz3170, zzz3171, zzz3172, zzz3173, zzz3174), h) → new_mkVBalBranch3MkVBalBranch235(zzz3170, zzz3171, zzz3172, zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, new_primPlusNat2(new_primPlusNat3(Succ(new_primPlusNat3(new_primPlusNat1(zzz33200), zzz33200)), Succ(zzz33200)), Succ(zzz33200)), h)
new_mkVBalBranch3MkVBalBranch129(zzz1851, zzz1852, zzz1853, zzz1854, zzz1855, zzz1856, zzz1857, zzz1858, zzz1859, zzz1860, zzz1861, Succ(zzz18620), Succ(zzz18630), bd) → new_mkVBalBranch3MkVBalBranch129(zzz1851, zzz1852, zzz1853, zzz1854, zzz1855, zzz1856, zzz1857, zzz1858, zzz1859, zzz1860, zzz1861, zzz18620, zzz18630, bd)
new_mkVBalBranch3MkVBalBranch124(zzz958, zzz959, zzz960, zzz961, zzz962, zzz963, zzz964, zzz965, zzz966, zzz967, zzz968, Zero, ba) → new_mkVBalBranch3MkVBalBranch125(zzz958, zzz959, zzz960, zzz961, zzz962, zzz963, zzz964, zzz965, zzz966, zzz967, zzz968, Zero, Succ(zzz965), ba)
new_mkVBalBranch3MkVBalBranch242(zzz972, zzz973, zzz974, zzz975, zzz976, zzz977, zzz978, zzz979, zzz980, zzz981, zzz982, Succ(zzz9830), Succ(zzz9840), bc) → new_mkVBalBranch3MkVBalBranch242(zzz972, zzz973, zzz974, zzz975, zzz976, zzz977, zzz978, zzz979, zzz980, zzz981, zzz982, zzz9830, zzz9840, bc)
new_mkVBalBranch3MkVBalBranch235(zzz3170, zzz3171, Pos(Succ(zzz317200)), zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, Succ(zzz4170), h) → new_mkVBalBranch3MkVBalBranch236(zzz3170, zzz3171, zzz317200, zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, zzz4170, zzz317200, h)
new_mkVBalBranch3MkVBalBranch236(zzz958, zzz959, zzz960, zzz961, zzz962, zzz963, zzz964, zzz965, zzz966, zzz967, zzz968, Succ(zzz9690), Succ(zzz9700), ba) → new_mkVBalBranch3MkVBalBranch236(zzz958, zzz959, zzz960, zzz961, zzz962, zzz963, zzz964, zzz965, zzz966, zzz967, zzz968, zzz9690, zzz9700, ba)
new_mkVBalBranch1(zzz31, Branch(zzz330, zzz331, Neg(Zero), zzz333, zzz334), Branch(zzz3170, zzz3171, Neg(Succ(zzz317200)), zzz3173, zzz3174), h) → new_mkVBalBranch3MkVBalBranch127(zzz3170, zzz3171, zzz317200, zzz3173, zzz3174, zzz330, zzz331, zzz333, zzz334, zzz31, new_primPlusNat2(new_primMulNat0(zzz317200), Succ(zzz317200)), h)
new_mkVBalBranch3MkVBalBranch241(zzz3170, zzz3171, Neg(Succ(zzz317200)), zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, Succ(zzz4190), h) → new_mkVBalBranch3MkVBalBranch242(zzz3170, zzz3171, zzz317200, zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, zzz317200, zzz4190, h)
new_mkVBalBranch3MkVBalBranch241(zzz3170, zzz3171, Neg(Succ(zzz317200)), zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, Zero, h) → new_mkVBalBranch3MkVBalBranch242(zzz3170, zzz3171, zzz317200, zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, Succ(zzz317200), Zero, h)
new_mkVBalBranch1(zzz31, Branch(zzz330, zzz331, Pos(Zero), zzz333, zzz334), Branch(zzz3170, zzz3171, Pos(Succ(zzz317200)), zzz3173, zzz3174), h) → new_mkVBalBranch1(zzz31, Branch(zzz330, zzz331, Pos(Zero), zzz333, zzz334), zzz3173, h)
new_mkVBalBranch3MkVBalBranch243(zzz3170, zzz3171, zzz31720, zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, h) → new_mkVBalBranch1(zzz31, Branch(zzz330, zzz331, Neg(Succ(zzz33200)), zzz333, zzz334), zzz3173, h)
new_mkVBalBranch3MkVBalBranch237(zzz3170, zzz3171, zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, h) → new_mkVBalBranch1(zzz31, zzz334, Branch(zzz3170, zzz3171, Pos(Zero), zzz3173, zzz3174), h)
new_mkVBalBranch1(zzz31, Branch(zzz330, zzz331, Neg(Succ(zzz33200)), zzz333, zzz334), Branch(zzz3170, zzz3171, zzz3172, zzz3173, zzz3174), h) → new_mkVBalBranch3MkVBalBranch241(zzz3170, zzz3171, zzz3172, zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, new_primPlusNat2(new_primPlusNat3(Succ(new_primPlusNat3(new_primPlusNat1(zzz33200), zzz33200)), Succ(zzz33200)), Succ(zzz33200)), h)
new_mkVBalBranch3MkVBalBranch235(zzz3170, zzz3171, Pos(Zero), zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, Succ(zzz4170), h) → new_mkVBalBranch3MkVBalBranch237(zzz3170, zzz3171, zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, h)
new_mkVBalBranch3MkVBalBranch235(zzz3170, zzz3171, Neg(Succ(zzz317200)), zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, Succ(zzz4170), h) → new_mkVBalBranch3MkVBalBranch123(zzz3170, zzz3171, zzz317200, zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, new_primPlusNat2(new_primMulNat0(zzz317200), Succ(zzz317200)), h)
new_mkVBalBranch3MkVBalBranch236(zzz958, zzz959, zzz960, zzz961, zzz962, zzz963, zzz964, zzz965, zzz966, zzz967, zzz968, Zero, Succ(zzz9700), ba) → new_mkVBalBranch1(zzz968, Branch(zzz963, zzz964, Pos(Succ(zzz965)), zzz966, zzz967), zzz961, ba)
new_mkVBalBranch3MkVBalBranch236(zzz958, zzz959, zzz960, zzz961, zzz962, zzz963, zzz964, zzz965, zzz966, zzz967, zzz968, Succ(zzz9690), Zero, ba) → new_mkVBalBranch3MkVBalBranch124(zzz958, zzz959, zzz960, zzz961, zzz962, zzz963, zzz964, zzz965, zzz966, zzz967, zzz968, new_primPlusNat2(new_primMulNat0(zzz960), Succ(zzz960)), ba)
new_mkVBalBranch3MkVBalBranch244(zzz972, zzz973, zzz974, zzz975, zzz976, zzz977, zzz978, zzz979, zzz980, zzz981, zzz982, bc) → new_mkVBalBranch3MkVBalBranch128(zzz972, zzz973, zzz974, zzz975, zzz976, zzz977, zzz978, zzz979, zzz980, zzz981, zzz982, new_primMulNat1(zzz974), bc)
new_mkVBalBranch3MkVBalBranch125(zzz1337, zzz1338, zzz1339, zzz1340, zzz1341, zzz1342, zzz1343, zzz1344, zzz1345, zzz1346, zzz1347, Succ(zzz13480), Succ(zzz13490), bb) → new_mkVBalBranch3MkVBalBranch125(zzz1337, zzz1338, zzz1339, zzz1340, zzz1341, zzz1342, zzz1343, zzz1344, zzz1345, zzz1346, zzz1347, zzz13480, zzz13490, bb)
new_mkVBalBranch3MkVBalBranch123(zzz3170, zzz3171, zzz317200, zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, Succ(zzz5620), h) → new_mkVBalBranch1(zzz31, zzz334, Branch(zzz3170, zzz3171, Neg(Succ(zzz317200)), zzz3173, zzz3174), h)
new_mkVBalBranch3MkVBalBranch125(zzz1337, zzz1338, zzz1339, zzz1340, zzz1341, zzz1342, zzz1343, zzz1344, zzz1345, zzz1346, zzz1347, Zero, Succ(zzz13490), bb) → new_mkVBalBranch1(zzz1347, zzz1346, Branch(zzz1337, zzz1338, Pos(Succ(zzz1339)), zzz1340, zzz1341), bb)
new_mkVBalBranch3MkVBalBranch242(zzz972, zzz973, zzz974, zzz975, zzz976, zzz977, zzz978, zzz979, zzz980, zzz981, zzz982, Zero, Succ(zzz9840), bc) → new_mkVBalBranch1(zzz982, Branch(zzz977, zzz978, Neg(Succ(zzz979)), zzz980, zzz981), zzz975, bc)
new_mkVBalBranch3MkVBalBranch240(zzz958, zzz959, zzz960, zzz961, zzz962, zzz963, zzz964, zzz965, zzz966, zzz967, zzz968, ba) → new_mkVBalBranch3MkVBalBranch124(zzz958, zzz959, zzz960, zzz961, zzz962, zzz963, zzz964, zzz965, zzz966, zzz967, zzz968, new_primMulNat1(zzz960), ba)
new_mkVBalBranch3MkVBalBranch235(zzz3170, zzz3171, Neg(Succ(zzz317200)), zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, Zero, h) → new_mkVBalBranch3MkVBalBranch238(zzz3170, zzz3171, Succ(zzz317200), zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, h)
new_mkVBalBranch3MkVBalBranch241(zzz3170, zzz3171, Pos(Succ(zzz317200)), zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, Zero, h) → new_mkVBalBranch3MkVBalBranch243(zzz3170, zzz3171, Succ(zzz317200), zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, h)
new_mkVBalBranch3MkVBalBranch126(zzz3170, zzz3171, zzz317200, zzz3173, zzz3174, zzz330, zzz331, zzz333, zzz334, zzz31, Succ(zzz5350), h) → new_mkVBalBranch1(zzz31, zzz334, Branch(zzz3170, zzz3171, Neg(Succ(zzz317200)), zzz3173, zzz3174), h)
new_mkVBalBranch3MkVBalBranch241(zzz3170, zzz3171, Neg(Zero), zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, Succ(zzz4190), h) → new_mkVBalBranch1(zzz31, Branch(zzz330, zzz331, Neg(Succ(zzz33200)), zzz333, zzz334), zzz3173, h)
new_mkVBalBranch3MkVBalBranch123(zzz3170, zzz3171, zzz317200, zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, Zero, h) → new_mkVBalBranch3MkVBalBranch130(zzz3170, zzz3171, zzz317200, zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, h)
new_mkVBalBranch3MkVBalBranch124(zzz958, zzz959, zzz960, zzz961, zzz962, zzz963, zzz964, zzz965, zzz966, zzz967, zzz968, Succ(zzz10180), ba) → new_mkVBalBranch3MkVBalBranch125(zzz958, zzz959, zzz960, zzz961, zzz962, zzz963, zzz964, zzz965, zzz966, zzz967, zzz968, Succ(zzz10180), Succ(zzz965), ba)
new_mkVBalBranch3MkVBalBranch235(zzz3170, zzz3171, Pos(Succ(zzz317200)), zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, Zero, h) → new_mkVBalBranch3MkVBalBranch236(zzz3170, zzz3171, zzz317200, zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, Zero, Succ(zzz317200), h)
new_mkVBalBranch3MkVBalBranch239(zzz3170, zzz3171, Zero, zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, h) → new_mkVBalBranch1(zzz31, zzz334, Branch(zzz3170, zzz3171, Neg(Zero), zzz3173, zzz3174), h)
new_mkVBalBranch3MkVBalBranch235(zzz3170, zzz3171, Pos(Zero), zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, Zero, h) → new_mkVBalBranch1(zzz31, zzz334, Branch(zzz3170, zzz3171, Pos(Zero), zzz3173, zzz3174), h)
new_mkVBalBranch3MkVBalBranch242(zzz972, zzz973, zzz974, zzz975, zzz976, zzz977, zzz978, zzz979, zzz980, zzz981, zzz982, Zero, Zero, bc) → new_mkVBalBranch3MkVBalBranch244(zzz972, zzz973, zzz974, zzz975, zzz976, zzz977, zzz978, zzz979, zzz980, zzz981, zzz982, bc)
new_mkVBalBranch1(zzz31, Branch(zzz330, zzz331, Pos(Zero), zzz333, zzz334), Branch(zzz3170, zzz3171, Neg(Succ(zzz317200)), zzz3173, zzz3174), h) → new_mkVBalBranch3MkVBalBranch126(zzz3170, zzz3171, zzz317200, zzz3173, zzz3174, zzz330, zzz331, zzz333, zzz334, zzz31, new_primPlusNat2(new_primMulNat0(zzz317200), Succ(zzz317200)), h)
new_mkVBalBranch3MkVBalBranch130(zzz3170, zzz3171, zzz317200, zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, h) → new_mkVBalBranch1(zzz31, zzz334, Branch(zzz3170, zzz3171, Neg(Succ(zzz317200)), zzz3173, zzz3174), h)
new_mkVBalBranch3MkVBalBranch235(zzz3170, zzz3171, Neg(Zero), zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, Zero, h) → new_mkVBalBranch3MkVBalBranch239(zzz3170, zzz3171, Zero, zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, h)
new_mkVBalBranch1(zzz31, Branch(zzz330, zzz331, Neg(Zero), zzz333, zzz334), Branch(zzz3170, zzz3171, Pos(Succ(zzz317200)), zzz3173, zzz3174), h) → new_mkVBalBranch1(zzz31, Branch(zzz330, zzz331, Neg(Zero), zzz333, zzz334), zzz3173, h)
new_mkVBalBranch3MkVBalBranch235(zzz3170, zzz3171, Neg(Zero), zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, Succ(zzz4170), h) → new_mkVBalBranch1(zzz31, zzz334, Branch(zzz3170, zzz3171, Neg(Zero), zzz3173, zzz3174), h)
new_mkVBalBranch3MkVBalBranch236(zzz958, zzz959, zzz960, zzz961, zzz962, zzz963, zzz964, zzz965, zzz966, zzz967, zzz968, Zero, Zero, ba) → new_mkVBalBranch3MkVBalBranch240(zzz958, zzz959, zzz960, zzz961, zzz962, zzz963, zzz964, zzz965, zzz966, zzz967, zzz968, ba)

The TRS R consists of the following rules:

new_primPlusNat1(Zero) → Zero
new_primMulNat0(zzz6200) → new_primPlusNat3(Succ(new_primPlusNat3(new_primPlusNat1(zzz6200), zzz6200)), Succ(zzz6200))
new_primPlusNat2(Succ(zzz900), Succ(zzz9100)) → Succ(Succ(new_primPlusNat2(zzz900, zzz9100)))
new_primPlusNat3(zzz90, Succ(zzz910)) → Succ(Succ(new_primPlusNat2(zzz90, zzz910)))
new_primPlusNat3(zzz90, Zero) → Succ(zzz90)
new_primMulNat1(zzz34200) → new_primPlusNat2(new_primMulNat0(zzz34200), Succ(zzz34200))
new_primPlusNat2(Zero, Zero) → Zero
new_primPlusNat1(Succ(zzz62000)) → Succ(Succ(new_primPlusNat1(zzz62000)))
new_primPlusNat2(Succ(zzz900), Zero) → Succ(zzz900)
new_primPlusNat2(Zero, Succ(zzz9100)) → Succ(zzz9100)

The set Q consists of the following terms:

new_primPlusNat2(Zero, Succ(x0))
new_primMulNat1(x0)
new_primMulNat0(x0)
new_primPlusNat3(x0, Succ(x1))
new_primPlusNat2(Succ(x0), Succ(x1))
new_primPlusNat3(x0, Zero)
new_primPlusNat1(Zero)
new_primPlusNat2(Zero, Zero)
new_primPlusNat1(Succ(x0))
new_primPlusNat2(Succ(x0), Zero)

We have to consider all minimal (P,Q,R)-chains.
By rewriting [15] the rule new_mkVBalBranch3MkVBalBranch240(zzz958, zzz959, zzz960, zzz961, zzz962, zzz963, zzz964, zzz965, zzz966, zzz967, zzz968, ba) → new_mkVBalBranch3MkVBalBranch124(zzz958, zzz959, zzz960, zzz961, zzz962, zzz963, zzz964, zzz965, zzz966, zzz967, zzz968, new_primMulNat1(zzz960), ba) at position [11] we obtained the following new rules:

new_mkVBalBranch3MkVBalBranch240(zzz958, zzz959, zzz960, zzz961, zzz962, zzz963, zzz964, zzz965, zzz966, zzz967, zzz968, ba) → new_mkVBalBranch3MkVBalBranch124(zzz958, zzz959, zzz960, zzz961, zzz962, zzz963, zzz964, zzz965, zzz966, zzz967, zzz968, new_primPlusNat2(new_primMulNat0(zzz960), Succ(zzz960)), 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
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                    ↳ DependencyGraphProof
                                      ↳ QDP
                                        ↳ Rewriting
                                          ↳ QDP
                                            ↳ Rewriting
                                              ↳ QDP
                                                ↳ Rewriting
                                                  ↳ QDP
                                                    ↳ Rewriting
                                                      ↳ QDP
                                                        ↳ Rewriting
                                                          ↳ QDP
                                                            ↳ Rewriting
                                                              ↳ QDP
                                                                ↳ Rewriting
                                                                  ↳ QDP
                                                                    ↳ Rewriting
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP

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

new_mkVBalBranch3MkVBalBranch242(zzz972, zzz973, zzz974, zzz975, zzz976, zzz977, zzz978, zzz979, zzz980, zzz981, zzz982, Succ(zzz9830), Zero, bc) → new_mkVBalBranch3MkVBalBranch128(zzz972, zzz973, zzz974, zzz975, zzz976, zzz977, zzz978, zzz979, zzz980, zzz981, zzz982, new_primPlusNat2(new_primMulNat0(zzz974), Succ(zzz974)), bc)
new_mkVBalBranch3MkVBalBranch129(zzz1851, zzz1852, zzz1853, zzz1854, zzz1855, zzz1856, zzz1857, zzz1858, zzz1859, zzz1860, zzz1861, Zero, Succ(zzz18630), bd) → new_mkVBalBranch1(zzz1861, zzz1860, Branch(zzz1851, zzz1852, Neg(Succ(zzz1853)), zzz1854, zzz1855), bd)
new_mkVBalBranch3MkVBalBranch238(zzz3170, zzz3171, Succ(zzz317200), zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, h) → new_mkVBalBranch3MkVBalBranch123(zzz3170, zzz3171, zzz317200, zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, new_primPlusNat2(new_primMulNat0(zzz317200), Succ(zzz317200)), h)
new_mkVBalBranch3MkVBalBranch127(zzz3170, zzz3171, zzz317200, zzz3173, zzz3174, zzz330, zzz331, zzz333, zzz334, zzz31, Succ(zzz5500), h) → new_mkVBalBranch1(zzz31, zzz334, Branch(zzz3170, zzz3171, Neg(Succ(zzz317200)), zzz3173, zzz3174), h)
new_mkVBalBranch3MkVBalBranch241(zzz3170, zzz3171, Pos(zzz31720), zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, Succ(zzz4190), h) → new_mkVBalBranch1(zzz31, Branch(zzz330, zzz331, Neg(Succ(zzz33200)), zzz333, zzz334), zzz3173, h)
new_mkVBalBranch3MkVBalBranch128(zzz972, zzz973, zzz974, zzz975, zzz976, zzz977, zzz978, zzz979, zzz980, zzz981, zzz982, Succ(zzz10190), bc) → new_mkVBalBranch3MkVBalBranch129(zzz972, zzz973, zzz974, zzz975, zzz976, zzz977, zzz978, zzz979, zzz980, zzz981, zzz982, Succ(zzz979), Succ(zzz10190), bc)
new_mkVBalBranch1(zzz31, Branch(zzz330, zzz331, Pos(Succ(zzz33200)), zzz333, zzz334), Branch(zzz3170, zzz3171, zzz3172, zzz3173, zzz3174), h) → new_mkVBalBranch3MkVBalBranch235(zzz3170, zzz3171, zzz3172, zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, new_primPlusNat2(new_primPlusNat3(Succ(new_primPlusNat3(new_primPlusNat1(zzz33200), zzz33200)), Succ(zzz33200)), Succ(zzz33200)), h)
new_mkVBalBranch3MkVBalBranch129(zzz1851, zzz1852, zzz1853, zzz1854, zzz1855, zzz1856, zzz1857, zzz1858, zzz1859, zzz1860, zzz1861, Succ(zzz18620), Succ(zzz18630), bd) → new_mkVBalBranch3MkVBalBranch129(zzz1851, zzz1852, zzz1853, zzz1854, zzz1855, zzz1856, zzz1857, zzz1858, zzz1859, zzz1860, zzz1861, zzz18620, zzz18630, bd)
new_mkVBalBranch3MkVBalBranch240(zzz958, zzz959, zzz960, zzz961, zzz962, zzz963, zzz964, zzz965, zzz966, zzz967, zzz968, ba) → new_mkVBalBranch3MkVBalBranch124(zzz958, zzz959, zzz960, zzz961, zzz962, zzz963, zzz964, zzz965, zzz966, zzz967, zzz968, new_primPlusNat2(new_primMulNat0(zzz960), Succ(zzz960)), ba)
new_mkVBalBranch3MkVBalBranch124(zzz958, zzz959, zzz960, zzz961, zzz962, zzz963, zzz964, zzz965, zzz966, zzz967, zzz968, Zero, ba) → new_mkVBalBranch3MkVBalBranch125(zzz958, zzz959, zzz960, zzz961, zzz962, zzz963, zzz964, zzz965, zzz966, zzz967, zzz968, Zero, Succ(zzz965), ba)
new_mkVBalBranch3MkVBalBranch235(zzz3170, zzz3171, Pos(Succ(zzz317200)), zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, Succ(zzz4170), h) → new_mkVBalBranch3MkVBalBranch236(zzz3170, zzz3171, zzz317200, zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, zzz4170, zzz317200, h)
new_mkVBalBranch3MkVBalBranch242(zzz972, zzz973, zzz974, zzz975, zzz976, zzz977, zzz978, zzz979, zzz980, zzz981, zzz982, Succ(zzz9830), Succ(zzz9840), bc) → new_mkVBalBranch3MkVBalBranch242(zzz972, zzz973, zzz974, zzz975, zzz976, zzz977, zzz978, zzz979, zzz980, zzz981, zzz982, zzz9830, zzz9840, bc)
new_mkVBalBranch3MkVBalBranch236(zzz958, zzz959, zzz960, zzz961, zzz962, zzz963, zzz964, zzz965, zzz966, zzz967, zzz968, Succ(zzz9690), Succ(zzz9700), ba) → new_mkVBalBranch3MkVBalBranch236(zzz958, zzz959, zzz960, zzz961, zzz962, zzz963, zzz964, zzz965, zzz966, zzz967, zzz968, zzz9690, zzz9700, ba)
new_mkVBalBranch1(zzz31, Branch(zzz330, zzz331, Neg(Zero), zzz333, zzz334), Branch(zzz3170, zzz3171, Neg(Succ(zzz317200)), zzz3173, zzz3174), h) → new_mkVBalBranch3MkVBalBranch127(zzz3170, zzz3171, zzz317200, zzz3173, zzz3174, zzz330, zzz331, zzz333, zzz334, zzz31, new_primPlusNat2(new_primMulNat0(zzz317200), Succ(zzz317200)), h)
new_mkVBalBranch3MkVBalBranch241(zzz3170, zzz3171, Neg(Succ(zzz317200)), zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, Succ(zzz4190), h) → new_mkVBalBranch3MkVBalBranch242(zzz3170, zzz3171, zzz317200, zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, zzz317200, zzz4190, h)
new_mkVBalBranch3MkVBalBranch241(zzz3170, zzz3171, Neg(Succ(zzz317200)), zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, Zero, h) → new_mkVBalBranch3MkVBalBranch242(zzz3170, zzz3171, zzz317200, zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, Succ(zzz317200), Zero, h)
new_mkVBalBranch1(zzz31, Branch(zzz330, zzz331, Pos(Zero), zzz333, zzz334), Branch(zzz3170, zzz3171, Pos(Succ(zzz317200)), zzz3173, zzz3174), h) → new_mkVBalBranch1(zzz31, Branch(zzz330, zzz331, Pos(Zero), zzz333, zzz334), zzz3173, h)
new_mkVBalBranch3MkVBalBranch237(zzz3170, zzz3171, zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, h) → new_mkVBalBranch1(zzz31, zzz334, Branch(zzz3170, zzz3171, Pos(Zero), zzz3173, zzz3174), h)
new_mkVBalBranch3MkVBalBranch243(zzz3170, zzz3171, zzz31720, zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, h) → new_mkVBalBranch1(zzz31, Branch(zzz330, zzz331, Neg(Succ(zzz33200)), zzz333, zzz334), zzz3173, h)
new_mkVBalBranch1(zzz31, Branch(zzz330, zzz331, Neg(Succ(zzz33200)), zzz333, zzz334), Branch(zzz3170, zzz3171, zzz3172, zzz3173, zzz3174), h) → new_mkVBalBranch3MkVBalBranch241(zzz3170, zzz3171, zzz3172, zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, new_primPlusNat2(new_primPlusNat3(Succ(new_primPlusNat3(new_primPlusNat1(zzz33200), zzz33200)), Succ(zzz33200)), Succ(zzz33200)), h)
new_mkVBalBranch3MkVBalBranch235(zzz3170, zzz3171, Pos(Zero), zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, Succ(zzz4170), h) → new_mkVBalBranch3MkVBalBranch237(zzz3170, zzz3171, zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, h)
new_mkVBalBranch3MkVBalBranch235(zzz3170, zzz3171, Neg(Succ(zzz317200)), zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, Succ(zzz4170), h) → new_mkVBalBranch3MkVBalBranch123(zzz3170, zzz3171, zzz317200, zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, new_primPlusNat2(new_primMulNat0(zzz317200), Succ(zzz317200)), h)
new_mkVBalBranch3MkVBalBranch236(zzz958, zzz959, zzz960, zzz961, zzz962, zzz963, zzz964, zzz965, zzz966, zzz967, zzz968, Succ(zzz9690), Zero, ba) → new_mkVBalBranch3MkVBalBranch124(zzz958, zzz959, zzz960, zzz961, zzz962, zzz963, zzz964, zzz965, zzz966, zzz967, zzz968, new_primPlusNat2(new_primMulNat0(zzz960), Succ(zzz960)), ba)
new_mkVBalBranch3MkVBalBranch236(zzz958, zzz959, zzz960, zzz961, zzz962, zzz963, zzz964, zzz965, zzz966, zzz967, zzz968, Zero, Succ(zzz9700), ba) → new_mkVBalBranch1(zzz968, Branch(zzz963, zzz964, Pos(Succ(zzz965)), zzz966, zzz967), zzz961, ba)
new_mkVBalBranch3MkVBalBranch125(zzz1337, zzz1338, zzz1339, zzz1340, zzz1341, zzz1342, zzz1343, zzz1344, zzz1345, zzz1346, zzz1347, Succ(zzz13480), Succ(zzz13490), bb) → new_mkVBalBranch3MkVBalBranch125(zzz1337, zzz1338, zzz1339, zzz1340, zzz1341, zzz1342, zzz1343, zzz1344, zzz1345, zzz1346, zzz1347, zzz13480, zzz13490, bb)
new_mkVBalBranch3MkVBalBranch244(zzz972, zzz973, zzz974, zzz975, zzz976, zzz977, zzz978, zzz979, zzz980, zzz981, zzz982, bc) → new_mkVBalBranch3MkVBalBranch128(zzz972, zzz973, zzz974, zzz975, zzz976, zzz977, zzz978, zzz979, zzz980, zzz981, zzz982, new_primMulNat1(zzz974), bc)
new_mkVBalBranch3MkVBalBranch123(zzz3170, zzz3171, zzz317200, zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, Succ(zzz5620), h) → new_mkVBalBranch1(zzz31, zzz334, Branch(zzz3170, zzz3171, Neg(Succ(zzz317200)), zzz3173, zzz3174), h)
new_mkVBalBranch3MkVBalBranch125(zzz1337, zzz1338, zzz1339, zzz1340, zzz1341, zzz1342, zzz1343, zzz1344, zzz1345, zzz1346, zzz1347, Zero, Succ(zzz13490), bb) → new_mkVBalBranch1(zzz1347, zzz1346, Branch(zzz1337, zzz1338, Pos(Succ(zzz1339)), zzz1340, zzz1341), bb)
new_mkVBalBranch3MkVBalBranch242(zzz972, zzz973, zzz974, zzz975, zzz976, zzz977, zzz978, zzz979, zzz980, zzz981, zzz982, Zero, Succ(zzz9840), bc) → new_mkVBalBranch1(zzz982, Branch(zzz977, zzz978, Neg(Succ(zzz979)), zzz980, zzz981), zzz975, bc)
new_mkVBalBranch3MkVBalBranch235(zzz3170, zzz3171, Neg(Succ(zzz317200)), zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, Zero, h) → new_mkVBalBranch3MkVBalBranch238(zzz3170, zzz3171, Succ(zzz317200), zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, h)
new_mkVBalBranch3MkVBalBranch241(zzz3170, zzz3171, Pos(Succ(zzz317200)), zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, Zero, h) → new_mkVBalBranch3MkVBalBranch243(zzz3170, zzz3171, Succ(zzz317200), zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, h)
new_mkVBalBranch3MkVBalBranch126(zzz3170, zzz3171, zzz317200, zzz3173, zzz3174, zzz330, zzz331, zzz333, zzz334, zzz31, Succ(zzz5350), h) → new_mkVBalBranch1(zzz31, zzz334, Branch(zzz3170, zzz3171, Neg(Succ(zzz317200)), zzz3173, zzz3174), h)
new_mkVBalBranch3MkVBalBranch123(zzz3170, zzz3171, zzz317200, zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, Zero, h) → new_mkVBalBranch3MkVBalBranch130(zzz3170, zzz3171, zzz317200, zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, h)
new_mkVBalBranch3MkVBalBranch241(zzz3170, zzz3171, Neg(Zero), zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, Succ(zzz4190), h) → new_mkVBalBranch1(zzz31, Branch(zzz330, zzz331, Neg(Succ(zzz33200)), zzz333, zzz334), zzz3173, h)
new_mkVBalBranch3MkVBalBranch124(zzz958, zzz959, zzz960, zzz961, zzz962, zzz963, zzz964, zzz965, zzz966, zzz967, zzz968, Succ(zzz10180), ba) → new_mkVBalBranch3MkVBalBranch125(zzz958, zzz959, zzz960, zzz961, zzz962, zzz963, zzz964, zzz965, zzz966, zzz967, zzz968, Succ(zzz10180), Succ(zzz965), ba)
new_mkVBalBranch3MkVBalBranch235(zzz3170, zzz3171, Pos(Succ(zzz317200)), zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, Zero, h) → new_mkVBalBranch3MkVBalBranch236(zzz3170, zzz3171, zzz317200, zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, Zero, Succ(zzz317200), h)
new_mkVBalBranch3MkVBalBranch239(zzz3170, zzz3171, Zero, zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, h) → new_mkVBalBranch1(zzz31, zzz334, Branch(zzz3170, zzz3171, Neg(Zero), zzz3173, zzz3174), h)
new_mkVBalBranch3MkVBalBranch235(zzz3170, zzz3171, Pos(Zero), zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, Zero, h) → new_mkVBalBranch1(zzz31, zzz334, Branch(zzz3170, zzz3171, Pos(Zero), zzz3173, zzz3174), h)
new_mkVBalBranch3MkVBalBranch242(zzz972, zzz973, zzz974, zzz975, zzz976, zzz977, zzz978, zzz979, zzz980, zzz981, zzz982, Zero, Zero, bc) → new_mkVBalBranch3MkVBalBranch244(zzz972, zzz973, zzz974, zzz975, zzz976, zzz977, zzz978, zzz979, zzz980, zzz981, zzz982, bc)
new_mkVBalBranch3MkVBalBranch130(zzz3170, zzz3171, zzz317200, zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, h) → new_mkVBalBranch1(zzz31, zzz334, Branch(zzz3170, zzz3171, Neg(Succ(zzz317200)), zzz3173, zzz3174), h)
new_mkVBalBranch1(zzz31, Branch(zzz330, zzz331, Pos(Zero), zzz333, zzz334), Branch(zzz3170, zzz3171, Neg(Succ(zzz317200)), zzz3173, zzz3174), h) → new_mkVBalBranch3MkVBalBranch126(zzz3170, zzz3171, zzz317200, zzz3173, zzz3174, zzz330, zzz331, zzz333, zzz334, zzz31, new_primPlusNat2(new_primMulNat0(zzz317200), Succ(zzz317200)), h)
new_mkVBalBranch1(zzz31, Branch(zzz330, zzz331, Neg(Zero), zzz333, zzz334), Branch(zzz3170, zzz3171, Pos(Succ(zzz317200)), zzz3173, zzz3174), h) → new_mkVBalBranch1(zzz31, Branch(zzz330, zzz331, Neg(Zero), zzz333, zzz334), zzz3173, h)
new_mkVBalBranch3MkVBalBranch235(zzz3170, zzz3171, Neg(Zero), zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, Zero, h) → new_mkVBalBranch3MkVBalBranch239(zzz3170, zzz3171, Zero, zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, h)
new_mkVBalBranch3MkVBalBranch235(zzz3170, zzz3171, Neg(Zero), zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, Succ(zzz4170), h) → new_mkVBalBranch1(zzz31, zzz334, Branch(zzz3170, zzz3171, Neg(Zero), zzz3173, zzz3174), h)
new_mkVBalBranch3MkVBalBranch236(zzz958, zzz959, zzz960, zzz961, zzz962, zzz963, zzz964, zzz965, zzz966, zzz967, zzz968, Zero, Zero, ba) → new_mkVBalBranch3MkVBalBranch240(zzz958, zzz959, zzz960, zzz961, zzz962, zzz963, zzz964, zzz965, zzz966, zzz967, zzz968, ba)

The TRS R consists of the following rules:

new_primPlusNat1(Zero) → Zero
new_primMulNat0(zzz6200) → new_primPlusNat3(Succ(new_primPlusNat3(new_primPlusNat1(zzz6200), zzz6200)), Succ(zzz6200))
new_primPlusNat2(Succ(zzz900), Succ(zzz9100)) → Succ(Succ(new_primPlusNat2(zzz900, zzz9100)))
new_primPlusNat3(zzz90, Succ(zzz910)) → Succ(Succ(new_primPlusNat2(zzz90, zzz910)))
new_primPlusNat3(zzz90, Zero) → Succ(zzz90)
new_primMulNat1(zzz34200) → new_primPlusNat2(new_primMulNat0(zzz34200), Succ(zzz34200))
new_primPlusNat2(Zero, Zero) → Zero
new_primPlusNat1(Succ(zzz62000)) → Succ(Succ(new_primPlusNat1(zzz62000)))
new_primPlusNat2(Succ(zzz900), Zero) → Succ(zzz900)
new_primPlusNat2(Zero, Succ(zzz9100)) → Succ(zzz9100)

The set Q consists of the following terms:

new_primPlusNat2(Zero, Succ(x0))
new_primMulNat1(x0)
new_primMulNat0(x0)
new_primPlusNat3(x0, Succ(x1))
new_primPlusNat2(Succ(x0), Succ(x1))
new_primPlusNat3(x0, Zero)
new_primPlusNat1(Zero)
new_primPlusNat2(Zero, Zero)
new_primPlusNat1(Succ(x0))
new_primPlusNat2(Succ(x0), Zero)

We have to consider all minimal (P,Q,R)-chains.
By rewriting [15] the rule new_mkVBalBranch3MkVBalBranch235(zzz3170, zzz3171, Neg(Succ(zzz317200)), zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, Succ(zzz4170), h) → new_mkVBalBranch3MkVBalBranch123(zzz3170, zzz3171, zzz317200, zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, new_primPlusNat2(new_primMulNat0(zzz317200), Succ(zzz317200)), h) at position [11,0] we obtained the following new rules:

new_mkVBalBranch3MkVBalBranch235(zzz3170, zzz3171, Neg(Succ(zzz317200)), zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, Succ(zzz4170), h) → new_mkVBalBranch3MkVBalBranch123(zzz3170, zzz3171, zzz317200, zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, new_primPlusNat2(new_primPlusNat3(Succ(new_primPlusNat3(new_primPlusNat1(zzz317200), zzz317200)), Succ(zzz317200)), Succ(zzz317200)), 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
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                    ↳ DependencyGraphProof
                                      ↳ QDP
                                        ↳ Rewriting
                                          ↳ QDP
                                            ↳ Rewriting
                                              ↳ QDP
                                                ↳ Rewriting
                                                  ↳ QDP
                                                    ↳ Rewriting
                                                      ↳ QDP
                                                        ↳ Rewriting
                                                          ↳ QDP
                                                            ↳ Rewriting
                                                              ↳ QDP
                                                                ↳ Rewriting
                                                                  ↳ QDP
                                                                    ↳ Rewriting
                                                                      ↳ QDP
                                                                        ↳ Rewriting
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP

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

new_mkVBalBranch3MkVBalBranch238(zzz3170, zzz3171, Succ(zzz317200), zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, h) → new_mkVBalBranch3MkVBalBranch123(zzz3170, zzz3171, zzz317200, zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, new_primPlusNat2(new_primMulNat0(zzz317200), Succ(zzz317200)), h)
new_mkVBalBranch3MkVBalBranch129(zzz1851, zzz1852, zzz1853, zzz1854, zzz1855, zzz1856, zzz1857, zzz1858, zzz1859, zzz1860, zzz1861, Zero, Succ(zzz18630), bd) → new_mkVBalBranch1(zzz1861, zzz1860, Branch(zzz1851, zzz1852, Neg(Succ(zzz1853)), zzz1854, zzz1855), bd)
new_mkVBalBranch3MkVBalBranch242(zzz972, zzz973, zzz974, zzz975, zzz976, zzz977, zzz978, zzz979, zzz980, zzz981, zzz982, Succ(zzz9830), Zero, bc) → new_mkVBalBranch3MkVBalBranch128(zzz972, zzz973, zzz974, zzz975, zzz976, zzz977, zzz978, zzz979, zzz980, zzz981, zzz982, new_primPlusNat2(new_primMulNat0(zzz974), Succ(zzz974)), bc)
new_mkVBalBranch3MkVBalBranch128(zzz972, zzz973, zzz974, zzz975, zzz976, zzz977, zzz978, zzz979, zzz980, zzz981, zzz982, Succ(zzz10190), bc) → new_mkVBalBranch3MkVBalBranch129(zzz972, zzz973, zzz974, zzz975, zzz976, zzz977, zzz978, zzz979, zzz980, zzz981, zzz982, Succ(zzz979), Succ(zzz10190), bc)
new_mkVBalBranch3MkVBalBranch241(zzz3170, zzz3171, Pos(zzz31720), zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, Succ(zzz4190), h) → new_mkVBalBranch1(zzz31, Branch(zzz330, zzz331, Neg(Succ(zzz33200)), zzz333, zzz334), zzz3173, h)
new_mkVBalBranch3MkVBalBranch127(zzz3170, zzz3171, zzz317200, zzz3173, zzz3174, zzz330, zzz331, zzz333, zzz334, zzz31, Succ(zzz5500), h) → new_mkVBalBranch1(zzz31, zzz334, Branch(zzz3170, zzz3171, Neg(Succ(zzz317200)), zzz3173, zzz3174), h)
new_mkVBalBranch1(zzz31, Branch(zzz330, zzz331, Pos(Succ(zzz33200)), zzz333, zzz334), Branch(zzz3170, zzz3171, zzz3172, zzz3173, zzz3174), h) → new_mkVBalBranch3MkVBalBranch235(zzz3170, zzz3171, zzz3172, zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, new_primPlusNat2(new_primPlusNat3(Succ(new_primPlusNat3(new_primPlusNat1(zzz33200), zzz33200)), Succ(zzz33200)), Succ(zzz33200)), h)
new_mkVBalBranch3MkVBalBranch129(zzz1851, zzz1852, zzz1853, zzz1854, zzz1855, zzz1856, zzz1857, zzz1858, zzz1859, zzz1860, zzz1861, Succ(zzz18620), Succ(zzz18630), bd) → new_mkVBalBranch3MkVBalBranch129(zzz1851, zzz1852, zzz1853, zzz1854, zzz1855, zzz1856, zzz1857, zzz1858, zzz1859, zzz1860, zzz1861, zzz18620, zzz18630, bd)
new_mkVBalBranch3MkVBalBranch240(zzz958, zzz959, zzz960, zzz961, zzz962, zzz963, zzz964, zzz965, zzz966, zzz967, zzz968, ba) → new_mkVBalBranch3MkVBalBranch124(zzz958, zzz959, zzz960, zzz961, zzz962, zzz963, zzz964, zzz965, zzz966, zzz967, zzz968, new_primPlusNat2(new_primMulNat0(zzz960), Succ(zzz960)), ba)
new_mkVBalBranch3MkVBalBranch124(zzz958, zzz959, zzz960, zzz961, zzz962, zzz963, zzz964, zzz965, zzz966, zzz967, zzz968, Zero, ba) → new_mkVBalBranch3MkVBalBranch125(zzz958, zzz959, zzz960, zzz961, zzz962, zzz963, zzz964, zzz965, zzz966, zzz967, zzz968, Zero, Succ(zzz965), ba)
new_mkVBalBranch3MkVBalBranch242(zzz972, zzz973, zzz974, zzz975, zzz976, zzz977, zzz978, zzz979, zzz980, zzz981, zzz982, Succ(zzz9830), Succ(zzz9840), bc) → new_mkVBalBranch3MkVBalBranch242(zzz972, zzz973, zzz974, zzz975, zzz976, zzz977, zzz978, zzz979, zzz980, zzz981, zzz982, zzz9830, zzz9840, bc)
new_mkVBalBranch3MkVBalBranch235(zzz3170, zzz3171, Pos(Succ(zzz317200)), zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, Succ(zzz4170), h) → new_mkVBalBranch3MkVBalBranch236(zzz3170, zzz3171, zzz317200, zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, zzz4170, zzz317200, h)
new_mkVBalBranch3MkVBalBranch236(zzz958, zzz959, zzz960, zzz961, zzz962, zzz963, zzz964, zzz965, zzz966, zzz967, zzz968, Succ(zzz9690), Succ(zzz9700), ba) → new_mkVBalBranch3MkVBalBranch236(zzz958, zzz959, zzz960, zzz961, zzz962, zzz963, zzz964, zzz965, zzz966, zzz967, zzz968, zzz9690, zzz9700, ba)
new_mkVBalBranch1(zzz31, Branch(zzz330, zzz331, Neg(Zero), zzz333, zzz334), Branch(zzz3170, zzz3171, Neg(Succ(zzz317200)), zzz3173, zzz3174), h) → new_mkVBalBranch3MkVBalBranch127(zzz3170, zzz3171, zzz317200, zzz3173, zzz3174, zzz330, zzz331, zzz333, zzz334, zzz31, new_primPlusNat2(new_primMulNat0(zzz317200), Succ(zzz317200)), h)
new_mkVBalBranch3MkVBalBranch241(zzz3170, zzz3171, Neg(Succ(zzz317200)), zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, Succ(zzz4190), h) → new_mkVBalBranch3MkVBalBranch242(zzz3170, zzz3171, zzz317200, zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, zzz317200, zzz4190, h)
new_mkVBalBranch3MkVBalBranch235(zzz3170, zzz3171, Neg(Succ(zzz317200)), zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, Succ(zzz4170), h) → new_mkVBalBranch3MkVBalBranch123(zzz3170, zzz3171, zzz317200, zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, new_primPlusNat2(new_primPlusNat3(Succ(new_primPlusNat3(new_primPlusNat1(zzz317200), zzz317200)), Succ(zzz317200)), Succ(zzz317200)), h)
new_mkVBalBranch3MkVBalBranch241(zzz3170, zzz3171, Neg(Succ(zzz317200)), zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, Zero, h) → new_mkVBalBranch3MkVBalBranch242(zzz3170, zzz3171, zzz317200, zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, Succ(zzz317200), Zero, h)
new_mkVBalBranch1(zzz31, Branch(zzz330, zzz331, Pos(Zero), zzz333, zzz334), Branch(zzz3170, zzz3171, Pos(Succ(zzz317200)), zzz3173, zzz3174), h) → new_mkVBalBranch1(zzz31, Branch(zzz330, zzz331, Pos(Zero), zzz333, zzz334), zzz3173, h)
new_mkVBalBranch3MkVBalBranch243(zzz3170, zzz3171, zzz31720, zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, h) → new_mkVBalBranch1(zzz31, Branch(zzz330, zzz331, Neg(Succ(zzz33200)), zzz333, zzz334), zzz3173, h)
new_mkVBalBranch3MkVBalBranch237(zzz3170, zzz3171, zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, h) → new_mkVBalBranch1(zzz31, zzz334, Branch(zzz3170, zzz3171, Pos(Zero), zzz3173, zzz3174), h)
new_mkVBalBranch1(zzz31, Branch(zzz330, zzz331, Neg(Succ(zzz33200)), zzz333, zzz334), Branch(zzz3170, zzz3171, zzz3172, zzz3173, zzz3174), h) → new_mkVBalBranch3MkVBalBranch241(zzz3170, zzz3171, zzz3172, zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, new_primPlusNat2(new_primPlusNat3(Succ(new_primPlusNat3(new_primPlusNat1(zzz33200), zzz33200)), Succ(zzz33200)), Succ(zzz33200)), h)
new_mkVBalBranch3MkVBalBranch235(zzz3170, zzz3171, Pos(Zero), zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, Succ(zzz4170), h) → new_mkVBalBranch3MkVBalBranch237(zzz3170, zzz3171, zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, h)
new_mkVBalBranch3MkVBalBranch236(zzz958, zzz959, zzz960, zzz961, zzz962, zzz963, zzz964, zzz965, zzz966, zzz967, zzz968, Zero, Succ(zzz9700), ba) → new_mkVBalBranch1(zzz968, Branch(zzz963, zzz964, Pos(Succ(zzz965)), zzz966, zzz967), zzz961, ba)
new_mkVBalBranch3MkVBalBranch236(zzz958, zzz959, zzz960, zzz961, zzz962, zzz963, zzz964, zzz965, zzz966, zzz967, zzz968, Succ(zzz9690), Zero, ba) → new_mkVBalBranch3MkVBalBranch124(zzz958, zzz959, zzz960, zzz961, zzz962, zzz963, zzz964, zzz965, zzz966, zzz967, zzz968, new_primPlusNat2(new_primMulNat0(zzz960), Succ(zzz960)), ba)
new_mkVBalBranch3MkVBalBranch244(zzz972, zzz973, zzz974, zzz975, zzz976, zzz977, zzz978, zzz979, zzz980, zzz981, zzz982, bc) → new_mkVBalBranch3MkVBalBranch128(zzz972, zzz973, zzz974, zzz975, zzz976, zzz977, zzz978, zzz979, zzz980, zzz981, zzz982, new_primMulNat1(zzz974), bc)
new_mkVBalBranch3MkVBalBranch125(zzz1337, zzz1338, zzz1339, zzz1340, zzz1341, zzz1342, zzz1343, zzz1344, zzz1345, zzz1346, zzz1347, Succ(zzz13480), Succ(zzz13490), bb) → new_mkVBalBranch3MkVBalBranch125(zzz1337, zzz1338, zzz1339, zzz1340, zzz1341, zzz1342, zzz1343, zzz1344, zzz1345, zzz1346, zzz1347, zzz13480, zzz13490, bb)
new_mkVBalBranch3MkVBalBranch123(zzz3170, zzz3171, zzz317200, zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, Succ(zzz5620), h) → new_mkVBalBranch1(zzz31, zzz334, Branch(zzz3170, zzz3171, Neg(Succ(zzz317200)), zzz3173, zzz3174), h)
new_mkVBalBranch3MkVBalBranch125(zzz1337, zzz1338, zzz1339, zzz1340, zzz1341, zzz1342, zzz1343, zzz1344, zzz1345, zzz1346, zzz1347, Zero, Succ(zzz13490), bb) → new_mkVBalBranch1(zzz1347, zzz1346, Branch(zzz1337, zzz1338, Pos(Succ(zzz1339)), zzz1340, zzz1341), bb)
new_mkVBalBranch3MkVBalBranch242(zzz972, zzz973, zzz974, zzz975, zzz976, zzz977, zzz978, zzz979, zzz980, zzz981, zzz982, Zero, Succ(zzz9840), bc) → new_mkVBalBranch1(zzz982, Branch(zzz977, zzz978, Neg(Succ(zzz979)), zzz980, zzz981), zzz975, bc)
new_mkVBalBranch3MkVBalBranch235(zzz3170, zzz3171, Neg(Succ(zzz317200)), zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, Zero, h) → new_mkVBalBranch3MkVBalBranch238(zzz3170, zzz3171, Succ(zzz317200), zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, h)
new_mkVBalBranch3MkVBalBranch241(zzz3170, zzz3171, Pos(Succ(zzz317200)), zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, Zero, h) → new_mkVBalBranch3MkVBalBranch243(zzz3170, zzz3171, Succ(zzz317200), zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, h)
new_mkVBalBranch3MkVBalBranch126(zzz3170, zzz3171, zzz317200, zzz3173, zzz3174, zzz330, zzz331, zzz333, zzz334, zzz31, Succ(zzz5350), h) → new_mkVBalBranch1(zzz31, zzz334, Branch(zzz3170, zzz3171, Neg(Succ(zzz317200)), zzz3173, zzz3174), h)
new_mkVBalBranch3MkVBalBranch241(zzz3170, zzz3171, Neg(Zero), zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, Succ(zzz4190), h) → new_mkVBalBranch1(zzz31, Branch(zzz330, zzz331, Neg(Succ(zzz33200)), zzz333, zzz334), zzz3173, h)
new_mkVBalBranch3MkVBalBranch123(zzz3170, zzz3171, zzz317200, zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, Zero, h) → new_mkVBalBranch3MkVBalBranch130(zzz3170, zzz3171, zzz317200, zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, h)
new_mkVBalBranch3MkVBalBranch124(zzz958, zzz959, zzz960, zzz961, zzz962, zzz963, zzz964, zzz965, zzz966, zzz967, zzz968, Succ(zzz10180), ba) → new_mkVBalBranch3MkVBalBranch125(zzz958, zzz959, zzz960, zzz961, zzz962, zzz963, zzz964, zzz965, zzz966, zzz967, zzz968, Succ(zzz10180), Succ(zzz965), ba)
new_mkVBalBranch3MkVBalBranch235(zzz3170, zzz3171, Pos(Succ(zzz317200)), zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, Zero, h) → new_mkVBalBranch3MkVBalBranch236(zzz3170, zzz3171, zzz317200, zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, Zero, Succ(zzz317200), h)
new_mkVBalBranch3MkVBalBranch239(zzz3170, zzz3171, Zero, zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, h) → new_mkVBalBranch1(zzz31, zzz334, Branch(zzz3170, zzz3171, Neg(Zero), zzz3173, zzz3174), h)
new_mkVBalBranch3MkVBalBranch235(zzz3170, zzz3171, Pos(Zero), zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, Zero, h) → new_mkVBalBranch1(zzz31, zzz334, Branch(zzz3170, zzz3171, Pos(Zero), zzz3173, zzz3174), h)
new_mkVBalBranch3MkVBalBranch242(zzz972, zzz973, zzz974, zzz975, zzz976, zzz977, zzz978, zzz979, zzz980, zzz981, zzz982, Zero, Zero, bc) → new_mkVBalBranch3MkVBalBranch244(zzz972, zzz973, zzz974, zzz975, zzz976, zzz977, zzz978, zzz979, zzz980, zzz981, zzz982, bc)
new_mkVBalBranch1(zzz31, Branch(zzz330, zzz331, Pos(Zero), zzz333, zzz334), Branch(zzz3170, zzz3171, Neg(Succ(zzz317200)), zzz3173, zzz3174), h) → new_mkVBalBranch3MkVBalBranch126(zzz3170, zzz3171, zzz317200, zzz3173, zzz3174, zzz330, zzz331, zzz333, zzz334, zzz31, new_primPlusNat2(new_primMulNat0(zzz317200), Succ(zzz317200)), h)
new_mkVBalBranch3MkVBalBranch130(zzz3170, zzz3171, zzz317200, zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, h) → new_mkVBalBranch1(zzz31, zzz334, Branch(zzz3170, zzz3171, Neg(Succ(zzz317200)), zzz3173, zzz3174), h)
new_mkVBalBranch3MkVBalBranch235(zzz3170, zzz3171, Neg(Zero), zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, Zero, h) → new_mkVBalBranch3MkVBalBranch239(zzz3170, zzz3171, Zero, zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, h)
new_mkVBalBranch1(zzz31, Branch(zzz330, zzz331, Neg(Zero), zzz333, zzz334), Branch(zzz3170, zzz3171, Pos(Succ(zzz317200)), zzz3173, zzz3174), h) → new_mkVBalBranch1(zzz31, Branch(zzz330, zzz331, Neg(Zero), zzz333, zzz334), zzz3173, h)
new_mkVBalBranch3MkVBalBranch235(zzz3170, zzz3171, Neg(Zero), zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, Succ(zzz4170), h) → new_mkVBalBranch1(zzz31, zzz334, Branch(zzz3170, zzz3171, Neg(Zero), zzz3173, zzz3174), h)
new_mkVBalBranch3MkVBalBranch236(zzz958, zzz959, zzz960, zzz961, zzz962, zzz963, zzz964, zzz965, zzz966, zzz967, zzz968, Zero, Zero, ba) → new_mkVBalBranch3MkVBalBranch240(zzz958, zzz959, zzz960, zzz961, zzz962, zzz963, zzz964, zzz965, zzz966, zzz967, zzz968, ba)

The TRS R consists of the following rules:

new_primPlusNat1(Zero) → Zero
new_primMulNat0(zzz6200) → new_primPlusNat3(Succ(new_primPlusNat3(new_primPlusNat1(zzz6200), zzz6200)), Succ(zzz6200))
new_primPlusNat2(Succ(zzz900), Succ(zzz9100)) → Succ(Succ(new_primPlusNat2(zzz900, zzz9100)))
new_primPlusNat3(zzz90, Succ(zzz910)) → Succ(Succ(new_primPlusNat2(zzz90, zzz910)))
new_primPlusNat3(zzz90, Zero) → Succ(zzz90)
new_primMulNat1(zzz34200) → new_primPlusNat2(new_primMulNat0(zzz34200), Succ(zzz34200))
new_primPlusNat2(Zero, Zero) → Zero
new_primPlusNat1(Succ(zzz62000)) → Succ(Succ(new_primPlusNat1(zzz62000)))
new_primPlusNat2(Succ(zzz900), Zero) → Succ(zzz900)
new_primPlusNat2(Zero, Succ(zzz9100)) → Succ(zzz9100)

The set Q consists of the following terms:

new_primPlusNat2(Zero, Succ(x0))
new_primMulNat1(x0)
new_primMulNat0(x0)
new_primPlusNat3(x0, Succ(x1))
new_primPlusNat2(Succ(x0), Succ(x1))
new_primPlusNat3(x0, Zero)
new_primPlusNat1(Zero)
new_primPlusNat2(Zero, Zero)
new_primPlusNat1(Succ(x0))
new_primPlusNat2(Succ(x0), Zero)

We have to consider all minimal (P,Q,R)-chains.
By rewriting [15] the rule new_mkVBalBranch3MkVBalBranch238(zzz3170, zzz3171, Succ(zzz317200), zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, h) → new_mkVBalBranch3MkVBalBranch123(zzz3170, zzz3171, zzz317200, zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, new_primPlusNat2(new_primMulNat0(zzz317200), Succ(zzz317200)), h) at position [11,0] we obtained the following new rules:

new_mkVBalBranch3MkVBalBranch238(zzz3170, zzz3171, Succ(zzz317200), zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, h) → new_mkVBalBranch3MkVBalBranch123(zzz3170, zzz3171, zzz317200, zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, new_primPlusNat2(new_primPlusNat3(Succ(new_primPlusNat3(new_primPlusNat1(zzz317200), zzz317200)), Succ(zzz317200)), Succ(zzz317200)), 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
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                    ↳ DependencyGraphProof
                                      ↳ QDP
                                        ↳ Rewriting
                                          ↳ QDP
                                            ↳ Rewriting
                                              ↳ QDP
                                                ↳ Rewriting
                                                  ↳ QDP
                                                    ↳ Rewriting
                                                      ↳ QDP
                                                        ↳ Rewriting
                                                          ↳ QDP
                                                            ↳ Rewriting
                                                              ↳ QDP
                                                                ↳ Rewriting
                                                                  ↳ QDP
                                                                    ↳ Rewriting
                                                                      ↳ QDP
                                                                        ↳ Rewriting
                                                                          ↳ QDP
                                                                            ↳ Rewriting
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP

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

new_mkVBalBranch3MkVBalBranch242(zzz972, zzz973, zzz974, zzz975, zzz976, zzz977, zzz978, zzz979, zzz980, zzz981, zzz982, Succ(zzz9830), Zero, bc) → new_mkVBalBranch3MkVBalBranch128(zzz972, zzz973, zzz974, zzz975, zzz976, zzz977, zzz978, zzz979, zzz980, zzz981, zzz982, new_primPlusNat2(new_primMulNat0(zzz974), Succ(zzz974)), bc)
new_mkVBalBranch3MkVBalBranch129(zzz1851, zzz1852, zzz1853, zzz1854, zzz1855, zzz1856, zzz1857, zzz1858, zzz1859, zzz1860, zzz1861, Zero, Succ(zzz18630), bd) → new_mkVBalBranch1(zzz1861, zzz1860, Branch(zzz1851, zzz1852, Neg(Succ(zzz1853)), zzz1854, zzz1855), bd)
new_mkVBalBranch3MkVBalBranch127(zzz3170, zzz3171, zzz317200, zzz3173, zzz3174, zzz330, zzz331, zzz333, zzz334, zzz31, Succ(zzz5500), h) → new_mkVBalBranch1(zzz31, zzz334, Branch(zzz3170, zzz3171, Neg(Succ(zzz317200)), zzz3173, zzz3174), h)
new_mkVBalBranch3MkVBalBranch241(zzz3170, zzz3171, Pos(zzz31720), zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, Succ(zzz4190), h) → new_mkVBalBranch1(zzz31, Branch(zzz330, zzz331, Neg(Succ(zzz33200)), zzz333, zzz334), zzz3173, h)
new_mkVBalBranch3MkVBalBranch128(zzz972, zzz973, zzz974, zzz975, zzz976, zzz977, zzz978, zzz979, zzz980, zzz981, zzz982, Succ(zzz10190), bc) → new_mkVBalBranch3MkVBalBranch129(zzz972, zzz973, zzz974, zzz975, zzz976, zzz977, zzz978, zzz979, zzz980, zzz981, zzz982, Succ(zzz979), Succ(zzz10190), bc)
new_mkVBalBranch1(zzz31, Branch(zzz330, zzz331, Pos(Succ(zzz33200)), zzz333, zzz334), Branch(zzz3170, zzz3171, zzz3172, zzz3173, zzz3174), h) → new_mkVBalBranch3MkVBalBranch235(zzz3170, zzz3171, zzz3172, zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, new_primPlusNat2(new_primPlusNat3(Succ(new_primPlusNat3(new_primPlusNat1(zzz33200), zzz33200)), Succ(zzz33200)), Succ(zzz33200)), h)
new_mkVBalBranch3MkVBalBranch129(zzz1851, zzz1852, zzz1853, zzz1854, zzz1855, zzz1856, zzz1857, zzz1858, zzz1859, zzz1860, zzz1861, Succ(zzz18620), Succ(zzz18630), bd) → new_mkVBalBranch3MkVBalBranch129(zzz1851, zzz1852, zzz1853, zzz1854, zzz1855, zzz1856, zzz1857, zzz1858, zzz1859, zzz1860, zzz1861, zzz18620, zzz18630, bd)
new_mkVBalBranch3MkVBalBranch240(zzz958, zzz959, zzz960, zzz961, zzz962, zzz963, zzz964, zzz965, zzz966, zzz967, zzz968, ba) → new_mkVBalBranch3MkVBalBranch124(zzz958, zzz959, zzz960, zzz961, zzz962, zzz963, zzz964, zzz965, zzz966, zzz967, zzz968, new_primPlusNat2(new_primMulNat0(zzz960), Succ(zzz960)), ba)
new_mkVBalBranch3MkVBalBranch124(zzz958, zzz959, zzz960, zzz961, zzz962, zzz963, zzz964, zzz965, zzz966, zzz967, zzz968, Zero, ba) → new_mkVBalBranch3MkVBalBranch125(zzz958, zzz959, zzz960, zzz961, zzz962, zzz963, zzz964, zzz965, zzz966, zzz967, zzz968, Zero, Succ(zzz965), ba)
new_mkVBalBranch3MkVBalBranch235(zzz3170, zzz3171, Pos(Succ(zzz317200)), zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, Succ(zzz4170), h) → new_mkVBalBranch3MkVBalBranch236(zzz3170, zzz3171, zzz317200, zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, zzz4170, zzz317200, h)
new_mkVBalBranch3MkVBalBranch242(zzz972, zzz973, zzz974, zzz975, zzz976, zzz977, zzz978, zzz979, zzz980, zzz981, zzz982, Succ(zzz9830), Succ(zzz9840), bc) → new_mkVBalBranch3MkVBalBranch242(zzz972, zzz973, zzz974, zzz975, zzz976, zzz977, zzz978, zzz979, zzz980, zzz981, zzz982, zzz9830, zzz9840, bc)
new_mkVBalBranch3MkVBalBranch236(zzz958, zzz959, zzz960, zzz961, zzz962, zzz963, zzz964, zzz965, zzz966, zzz967, zzz968, Succ(zzz9690), Succ(zzz9700), ba) → new_mkVBalBranch3MkVBalBranch236(zzz958, zzz959, zzz960, zzz961, zzz962, zzz963, zzz964, zzz965, zzz966, zzz967, zzz968, zzz9690, zzz9700, ba)
new_mkVBalBranch1(zzz31, Branch(zzz330, zzz331, Neg(Zero), zzz333, zzz334), Branch(zzz3170, zzz3171, Neg(Succ(zzz317200)), zzz3173, zzz3174), h) → new_mkVBalBranch3MkVBalBranch127(zzz3170, zzz3171, zzz317200, zzz3173, zzz3174, zzz330, zzz331, zzz333, zzz334, zzz31, new_primPlusNat2(new_primMulNat0(zzz317200), Succ(zzz317200)), h)
new_mkVBalBranch3MkVBalBranch241(zzz3170, zzz3171, Neg(Succ(zzz317200)), zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, Succ(zzz4190), h) → new_mkVBalBranch3MkVBalBranch242(zzz3170, zzz3171, zzz317200, zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, zzz317200, zzz4190, h)
new_mkVBalBranch3MkVBalBranch241(zzz3170, zzz3171, Neg(Succ(zzz317200)), zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, Zero, h) → new_mkVBalBranch3MkVBalBranch242(zzz3170, zzz3171, zzz317200, zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, Succ(zzz317200), Zero, h)
new_mkVBalBranch3MkVBalBranch235(zzz3170, zzz3171, Neg(Succ(zzz317200)), zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, Succ(zzz4170), h) → new_mkVBalBranch3MkVBalBranch123(zzz3170, zzz3171, zzz317200, zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, new_primPlusNat2(new_primPlusNat3(Succ(new_primPlusNat3(new_primPlusNat1(zzz317200), zzz317200)), Succ(zzz317200)), Succ(zzz317200)), h)
new_mkVBalBranch1(zzz31, Branch(zzz330, zzz331, Pos(Zero), zzz333, zzz334), Branch(zzz3170, zzz3171, Pos(Succ(zzz317200)), zzz3173, zzz3174), h) → new_mkVBalBranch1(zzz31, Branch(zzz330, zzz331, Pos(Zero), zzz333, zzz334), zzz3173, h)
new_mkVBalBranch3MkVBalBranch237(zzz3170, zzz3171, zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, h) → new_mkVBalBranch1(zzz31, zzz334, Branch(zzz3170, zzz3171, Pos(Zero), zzz3173, zzz3174), h)
new_mkVBalBranch3MkVBalBranch243(zzz3170, zzz3171, zzz31720, zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, h) → new_mkVBalBranch1(zzz31, Branch(zzz330, zzz331, Neg(Succ(zzz33200)), zzz333, zzz334), zzz3173, h)
new_mkVBalBranch1(zzz31, Branch(zzz330, zzz331, Neg(Succ(zzz33200)), zzz333, zzz334), Branch(zzz3170, zzz3171, zzz3172, zzz3173, zzz3174), h) → new_mkVBalBranch3MkVBalBranch241(zzz3170, zzz3171, zzz3172, zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, new_primPlusNat2(new_primPlusNat3(Succ(new_primPlusNat3(new_primPlusNat1(zzz33200), zzz33200)), Succ(zzz33200)), Succ(zzz33200)), h)
new_mkVBalBranch3MkVBalBranch235(zzz3170, zzz3171, Pos(Zero), zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, Succ(zzz4170), h) → new_mkVBalBranch3MkVBalBranch237(zzz3170, zzz3171, zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, h)
new_mkVBalBranch3MkVBalBranch236(zzz958, zzz959, zzz960, zzz961, zzz962, zzz963, zzz964, zzz965, zzz966, zzz967, zzz968, Succ(zzz9690), Zero, ba) → new_mkVBalBranch3MkVBalBranch124(zzz958, zzz959, zzz960, zzz961, zzz962, zzz963, zzz964, zzz965, zzz966, zzz967, zzz968, new_primPlusNat2(new_primMulNat0(zzz960), Succ(zzz960)), ba)
new_mkVBalBranch3MkVBalBranch236(zzz958, zzz959, zzz960, zzz961, zzz962, zzz963, zzz964, zzz965, zzz966, zzz967, zzz968, Zero, Succ(zzz9700), ba) → new_mkVBalBranch1(zzz968, Branch(zzz963, zzz964, Pos(Succ(zzz965)), zzz966, zzz967), zzz961, ba)
new_mkVBalBranch3MkVBalBranch125(zzz1337, zzz1338, zzz1339, zzz1340, zzz1341, zzz1342, zzz1343, zzz1344, zzz1345, zzz1346, zzz1347, Succ(zzz13480), Succ(zzz13490), bb) → new_mkVBalBranch3MkVBalBranch125(zzz1337, zzz1338, zzz1339, zzz1340, zzz1341, zzz1342, zzz1343, zzz1344, zzz1345, zzz1346, zzz1347, zzz13480, zzz13490, bb)
new_mkVBalBranch3MkVBalBranch244(zzz972, zzz973, zzz974, zzz975, zzz976, zzz977, zzz978, zzz979, zzz980, zzz981, zzz982, bc) → new_mkVBalBranch3MkVBalBranch128(zzz972, zzz973, zzz974, zzz975, zzz976, zzz977, zzz978, zzz979, zzz980, zzz981, zzz982, new_primMulNat1(zzz974), bc)
new_mkVBalBranch3MkVBalBranch123(zzz3170, zzz3171, zzz317200, zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, Succ(zzz5620), h) → new_mkVBalBranch1(zzz31, zzz334, Branch(zzz3170, zzz3171, Neg(Succ(zzz317200)), zzz3173, zzz3174), h)
new_mkVBalBranch3MkVBalBranch125(zzz1337, zzz1338, zzz1339, zzz1340, zzz1341, zzz1342, zzz1343, zzz1344, zzz1345, zzz1346, zzz1347, Zero, Succ(zzz13490), bb) → new_mkVBalBranch1(zzz1347, zzz1346, Branch(zzz1337, zzz1338, Pos(Succ(zzz1339)), zzz1340, zzz1341), bb)
new_mkVBalBranch3MkVBalBranch242(zzz972, zzz973, zzz974, zzz975, zzz976, zzz977, zzz978, zzz979, zzz980, zzz981, zzz982, Zero, Succ(zzz9840), bc) → new_mkVBalBranch1(zzz982, Branch(zzz977, zzz978, Neg(Succ(zzz979)), zzz980, zzz981), zzz975, bc)
new_mkVBalBranch3MkVBalBranch238(zzz3170, zzz3171, Succ(zzz317200), zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, h) → new_mkVBalBranch3MkVBalBranch123(zzz3170, zzz3171, zzz317200, zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, new_primPlusNat2(new_primPlusNat3(Succ(new_primPlusNat3(new_primPlusNat1(zzz317200), zzz317200)), Succ(zzz317200)), Succ(zzz317200)), h)
new_mkVBalBranch3MkVBalBranch235(zzz3170, zzz3171, Neg(Succ(zzz317200)), zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, Zero, h) → new_mkVBalBranch3MkVBalBranch238(zzz3170, zzz3171, Succ(zzz317200), zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, h)
new_mkVBalBranch3MkVBalBranch241(zzz3170, zzz3171, Pos(Succ(zzz317200)), zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, Zero, h) → new_mkVBalBranch3MkVBalBranch243(zzz3170, zzz3171, Succ(zzz317200), zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, h)
new_mkVBalBranch3MkVBalBranch126(zzz3170, zzz3171, zzz317200, zzz3173, zzz3174, zzz330, zzz331, zzz333, zzz334, zzz31, Succ(zzz5350), h) → new_mkVBalBranch1(zzz31, zzz334, Branch(zzz3170, zzz3171, Neg(Succ(zzz317200)), zzz3173, zzz3174), h)
new_mkVBalBranch3MkVBalBranch123(zzz3170, zzz3171, zzz317200, zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, Zero, h) → new_mkVBalBranch3MkVBalBranch130(zzz3170, zzz3171, zzz317200, zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, h)
new_mkVBalBranch3MkVBalBranch241(zzz3170, zzz3171, Neg(Zero), zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, Succ(zzz4190), h) → new_mkVBalBranch1(zzz31, Branch(zzz330, zzz331, Neg(Succ(zzz33200)), zzz333, zzz334), zzz3173, h)
new_mkVBalBranch3MkVBalBranch124(zzz958, zzz959, zzz960, zzz961, zzz962, zzz963, zzz964, zzz965, zzz966, zzz967, zzz968, Succ(zzz10180), ba) → new_mkVBalBranch3MkVBalBranch125(zzz958, zzz959, zzz960, zzz961, zzz962, zzz963, zzz964, zzz965, zzz966, zzz967, zzz968, Succ(zzz10180), Succ(zzz965), ba)
new_mkVBalBranch3MkVBalBranch235(zzz3170, zzz3171, Pos(Succ(zzz317200)), zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, Zero, h) → new_mkVBalBranch3MkVBalBranch236(zzz3170, zzz3171, zzz317200, zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, Zero, Succ(zzz317200), h)
new_mkVBalBranch3MkVBalBranch239(zzz3170, zzz3171, Zero, zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, h) → new_mkVBalBranch1(zzz31, zzz334, Branch(zzz3170, zzz3171, Neg(Zero), zzz3173, zzz3174), h)
new_mkVBalBranch3MkVBalBranch235(zzz3170, zzz3171, Pos(Zero), zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, Zero, h) → new_mkVBalBranch1(zzz31, zzz334, Branch(zzz3170, zzz3171, Pos(Zero), zzz3173, zzz3174), h)
new_mkVBalBranch3MkVBalBranch242(zzz972, zzz973, zzz974, zzz975, zzz976, zzz977, zzz978, zzz979, zzz980, zzz981, zzz982, Zero, Zero, bc) → new_mkVBalBranch3MkVBalBranch244(zzz972, zzz973, zzz974, zzz975, zzz976, zzz977, zzz978, zzz979, zzz980, zzz981, zzz982, bc)
new_mkVBalBranch3MkVBalBranch130(zzz3170, zzz3171, zzz317200, zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, h) → new_mkVBalBranch1(zzz31, zzz334, Branch(zzz3170, zzz3171, Neg(Succ(zzz317200)), zzz3173, zzz3174), h)
new_mkVBalBranch1(zzz31, Branch(zzz330, zzz331, Pos(Zero), zzz333, zzz334), Branch(zzz3170, zzz3171, Neg(Succ(zzz317200)), zzz3173, zzz3174), h) → new_mkVBalBranch3MkVBalBranch126(zzz3170, zzz3171, zzz317200, zzz3173, zzz3174, zzz330, zzz331, zzz333, zzz334, zzz31, new_primPlusNat2(new_primMulNat0(zzz317200), Succ(zzz317200)), h)
new_mkVBalBranch1(zzz31, Branch(zzz330, zzz331, Neg(Zero), zzz333, zzz334), Branch(zzz3170, zzz3171, Pos(Succ(zzz317200)), zzz3173, zzz3174), h) → new_mkVBalBranch1(zzz31, Branch(zzz330, zzz331, Neg(Zero), zzz333, zzz334), zzz3173, h)
new_mkVBalBranch3MkVBalBranch235(zzz3170, zzz3171, Neg(Zero), zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, Zero, h) → new_mkVBalBranch3MkVBalBranch239(zzz3170, zzz3171, Zero, zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, h)
new_mkVBalBranch3MkVBalBranch235(zzz3170, zzz3171, Neg(Zero), zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, Succ(zzz4170), h) → new_mkVBalBranch1(zzz31, zzz334, Branch(zzz3170, zzz3171, Neg(Zero), zzz3173, zzz3174), h)
new_mkVBalBranch3MkVBalBranch236(zzz958, zzz959, zzz960, zzz961, zzz962, zzz963, zzz964, zzz965, zzz966, zzz967, zzz968, Zero, Zero, ba) → new_mkVBalBranch3MkVBalBranch240(zzz958, zzz959, zzz960, zzz961, zzz962, zzz963, zzz964, zzz965, zzz966, zzz967, zzz968, ba)

The TRS R consists of the following rules:

new_primPlusNat1(Zero) → Zero
new_primMulNat0(zzz6200) → new_primPlusNat3(Succ(new_primPlusNat3(new_primPlusNat1(zzz6200), zzz6200)), Succ(zzz6200))
new_primPlusNat2(Succ(zzz900), Succ(zzz9100)) → Succ(Succ(new_primPlusNat2(zzz900, zzz9100)))
new_primPlusNat3(zzz90, Succ(zzz910)) → Succ(Succ(new_primPlusNat2(zzz90, zzz910)))
new_primPlusNat3(zzz90, Zero) → Succ(zzz90)
new_primMulNat1(zzz34200) → new_primPlusNat2(new_primMulNat0(zzz34200), Succ(zzz34200))
new_primPlusNat2(Zero, Zero) → Zero
new_primPlusNat1(Succ(zzz62000)) → Succ(Succ(new_primPlusNat1(zzz62000)))
new_primPlusNat2(Succ(zzz900), Zero) → Succ(zzz900)
new_primPlusNat2(Zero, Succ(zzz9100)) → Succ(zzz9100)

The set Q consists of the following terms:

new_primPlusNat2(Zero, Succ(x0))
new_primMulNat1(x0)
new_primMulNat0(x0)
new_primPlusNat3(x0, Succ(x1))
new_primPlusNat2(Succ(x0), Succ(x1))
new_primPlusNat3(x0, Zero)
new_primPlusNat1(Zero)
new_primPlusNat2(Zero, Zero)
new_primPlusNat1(Succ(x0))
new_primPlusNat2(Succ(x0), Zero)

We have to consider all minimal (P,Q,R)-chains.
By rewriting [15] the rule new_mkVBalBranch3MkVBalBranch244(zzz972, zzz973, zzz974, zzz975, zzz976, zzz977, zzz978, zzz979, zzz980, zzz981, zzz982, bc) → new_mkVBalBranch3MkVBalBranch128(zzz972, zzz973, zzz974, zzz975, zzz976, zzz977, zzz978, zzz979, zzz980, zzz981, zzz982, new_primMulNat1(zzz974), bc) at position [11] we obtained the following new rules:

new_mkVBalBranch3MkVBalBranch244(zzz972, zzz973, zzz974, zzz975, zzz976, zzz977, zzz978, zzz979, zzz980, zzz981, zzz982, bc) → new_mkVBalBranch3MkVBalBranch128(zzz972, zzz973, zzz974, zzz975, zzz976, zzz977, zzz978, zzz979, zzz980, zzz981, zzz982, new_primPlusNat2(new_primMulNat0(zzz974), Succ(zzz974)), bc)



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

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

new_mkVBalBranch3MkVBalBranch129(zzz1851, zzz1852, zzz1853, zzz1854, zzz1855, zzz1856, zzz1857, zzz1858, zzz1859, zzz1860, zzz1861, Zero, Succ(zzz18630), bd) → new_mkVBalBranch1(zzz1861, zzz1860, Branch(zzz1851, zzz1852, Neg(Succ(zzz1853)), zzz1854, zzz1855), bd)
new_mkVBalBranch3MkVBalBranch242(zzz972, zzz973, zzz974, zzz975, zzz976, zzz977, zzz978, zzz979, zzz980, zzz981, zzz982, Succ(zzz9830), Zero, bc) → new_mkVBalBranch3MkVBalBranch128(zzz972, zzz973, zzz974, zzz975, zzz976, zzz977, zzz978, zzz979, zzz980, zzz981, zzz982, new_primPlusNat2(new_primMulNat0(zzz974), Succ(zzz974)), bc)
new_mkVBalBranch3MkVBalBranch128(zzz972, zzz973, zzz974, zzz975, zzz976, zzz977, zzz978, zzz979, zzz980, zzz981, zzz982, Succ(zzz10190), bc) → new_mkVBalBranch3MkVBalBranch129(zzz972, zzz973, zzz974, zzz975, zzz976, zzz977, zzz978, zzz979, zzz980, zzz981, zzz982, Succ(zzz979), Succ(zzz10190), bc)
new_mkVBalBranch3MkVBalBranch241(zzz3170, zzz3171, Pos(zzz31720), zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, Succ(zzz4190), h) → new_mkVBalBranch1(zzz31, Branch(zzz330, zzz331, Neg(Succ(zzz33200)), zzz333, zzz334), zzz3173, h)
new_mkVBalBranch3MkVBalBranch127(zzz3170, zzz3171, zzz317200, zzz3173, zzz3174, zzz330, zzz331, zzz333, zzz334, zzz31, Succ(zzz5500), h) → new_mkVBalBranch1(zzz31, zzz334, Branch(zzz3170, zzz3171, Neg(Succ(zzz317200)), zzz3173, zzz3174), h)
new_mkVBalBranch1(zzz31, Branch(zzz330, zzz331, Pos(Succ(zzz33200)), zzz333, zzz334), Branch(zzz3170, zzz3171, zzz3172, zzz3173, zzz3174), h) → new_mkVBalBranch3MkVBalBranch235(zzz3170, zzz3171, zzz3172, zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, new_primPlusNat2(new_primPlusNat3(Succ(new_primPlusNat3(new_primPlusNat1(zzz33200), zzz33200)), Succ(zzz33200)), Succ(zzz33200)), h)
new_mkVBalBranch3MkVBalBranch129(zzz1851, zzz1852, zzz1853, zzz1854, zzz1855, zzz1856, zzz1857, zzz1858, zzz1859, zzz1860, zzz1861, Succ(zzz18620), Succ(zzz18630), bd) → new_mkVBalBranch3MkVBalBranch129(zzz1851, zzz1852, zzz1853, zzz1854, zzz1855, zzz1856, zzz1857, zzz1858, zzz1859, zzz1860, zzz1861, zzz18620, zzz18630, bd)
new_mkVBalBranch3MkVBalBranch240(zzz958, zzz959, zzz960, zzz961, zzz962, zzz963, zzz964, zzz965, zzz966, zzz967, zzz968, ba) → new_mkVBalBranch3MkVBalBranch124(zzz958, zzz959, zzz960, zzz961, zzz962, zzz963, zzz964, zzz965, zzz966, zzz967, zzz968, new_primPlusNat2(new_primMulNat0(zzz960), Succ(zzz960)), ba)
new_mkVBalBranch3MkVBalBranch124(zzz958, zzz959, zzz960, zzz961, zzz962, zzz963, zzz964, zzz965, zzz966, zzz967, zzz968, Zero, ba) → new_mkVBalBranch3MkVBalBranch125(zzz958, zzz959, zzz960, zzz961, zzz962, zzz963, zzz964, zzz965, zzz966, zzz967, zzz968, Zero, Succ(zzz965), ba)
new_mkVBalBranch3MkVBalBranch242(zzz972, zzz973, zzz974, zzz975, zzz976, zzz977, zzz978, zzz979, zzz980, zzz981, zzz982, Succ(zzz9830), Succ(zzz9840), bc) → new_mkVBalBranch3MkVBalBranch242(zzz972, zzz973, zzz974, zzz975, zzz976, zzz977, zzz978, zzz979, zzz980, zzz981, zzz982, zzz9830, zzz9840, bc)
new_mkVBalBranch3MkVBalBranch235(zzz3170, zzz3171, Pos(Succ(zzz317200)), zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, Succ(zzz4170), h) → new_mkVBalBranch3MkVBalBranch236(zzz3170, zzz3171, zzz317200, zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, zzz4170, zzz317200, h)
new_mkVBalBranch3MkVBalBranch236(zzz958, zzz959, zzz960, zzz961, zzz962, zzz963, zzz964, zzz965, zzz966, zzz967, zzz968, Succ(zzz9690), Succ(zzz9700), ba) → new_mkVBalBranch3MkVBalBranch236(zzz958, zzz959, zzz960, zzz961, zzz962, zzz963, zzz964, zzz965, zzz966, zzz967, zzz968, zzz9690, zzz9700, ba)
new_mkVBalBranch1(zzz31, Branch(zzz330, zzz331, Neg(Zero), zzz333, zzz334), Branch(zzz3170, zzz3171, Neg(Succ(zzz317200)), zzz3173, zzz3174), h) → new_mkVBalBranch3MkVBalBranch127(zzz3170, zzz3171, zzz317200, zzz3173, zzz3174, zzz330, zzz331, zzz333, zzz334, zzz31, new_primPlusNat2(new_primMulNat0(zzz317200), Succ(zzz317200)), h)
new_mkVBalBranch3MkVBalBranch241(zzz3170, zzz3171, Neg(Succ(zzz317200)), zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, Succ(zzz4190), h) → new_mkVBalBranch3MkVBalBranch242(zzz3170, zzz3171, zzz317200, zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, zzz317200, zzz4190, h)
new_mkVBalBranch3MkVBalBranch235(zzz3170, zzz3171, Neg(Succ(zzz317200)), zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, Succ(zzz4170), h) → new_mkVBalBranch3MkVBalBranch123(zzz3170, zzz3171, zzz317200, zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, new_primPlusNat2(new_primPlusNat3(Succ(new_primPlusNat3(new_primPlusNat1(zzz317200), zzz317200)), Succ(zzz317200)), Succ(zzz317200)), h)
new_mkVBalBranch3MkVBalBranch241(zzz3170, zzz3171, Neg(Succ(zzz317200)), zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, Zero, h) → new_mkVBalBranch3MkVBalBranch242(zzz3170, zzz3171, zzz317200, zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, Succ(zzz317200), Zero, h)
new_mkVBalBranch1(zzz31, Branch(zzz330, zzz331, Pos(Zero), zzz333, zzz334), Branch(zzz3170, zzz3171, Pos(Succ(zzz317200)), zzz3173, zzz3174), h) → new_mkVBalBranch1(zzz31, Branch(zzz330, zzz331, Pos(Zero), zzz333, zzz334), zzz3173, h)
new_mkVBalBranch3MkVBalBranch243(zzz3170, zzz3171, zzz31720, zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, h) → new_mkVBalBranch1(zzz31, Branch(zzz330, zzz331, Neg(Succ(zzz33200)), zzz333, zzz334), zzz3173, h)
new_mkVBalBranch3MkVBalBranch237(zzz3170, zzz3171, zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, h) → new_mkVBalBranch1(zzz31, zzz334, Branch(zzz3170, zzz3171, Pos(Zero), zzz3173, zzz3174), h)
new_mkVBalBranch1(zzz31, Branch(zzz330, zzz331, Neg(Succ(zzz33200)), zzz333, zzz334), Branch(zzz3170, zzz3171, zzz3172, zzz3173, zzz3174), h) → new_mkVBalBranch3MkVBalBranch241(zzz3170, zzz3171, zzz3172, zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, new_primPlusNat2(new_primPlusNat3(Succ(new_primPlusNat3(new_primPlusNat1(zzz33200), zzz33200)), Succ(zzz33200)), Succ(zzz33200)), h)
new_mkVBalBranch3MkVBalBranch235(zzz3170, zzz3171, Pos(Zero), zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, Succ(zzz4170), h) → new_mkVBalBranch3MkVBalBranch237(zzz3170, zzz3171, zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, h)
new_mkVBalBranch3MkVBalBranch236(zzz958, zzz959, zzz960, zzz961, zzz962, zzz963, zzz964, zzz965, zzz966, zzz967, zzz968, Zero, Succ(zzz9700), ba) → new_mkVBalBranch1(zzz968, Branch(zzz963, zzz964, Pos(Succ(zzz965)), zzz966, zzz967), zzz961, ba)
new_mkVBalBranch3MkVBalBranch236(zzz958, zzz959, zzz960, zzz961, zzz962, zzz963, zzz964, zzz965, zzz966, zzz967, zzz968, Succ(zzz9690), Zero, ba) → new_mkVBalBranch3MkVBalBranch124(zzz958, zzz959, zzz960, zzz961, zzz962, zzz963, zzz964, zzz965, zzz966, zzz967, zzz968, new_primPlusNat2(new_primMulNat0(zzz960), Succ(zzz960)), ba)
new_mkVBalBranch3MkVBalBranch125(zzz1337, zzz1338, zzz1339, zzz1340, zzz1341, zzz1342, zzz1343, zzz1344, zzz1345, zzz1346, zzz1347, Succ(zzz13480), Succ(zzz13490), bb) → new_mkVBalBranch3MkVBalBranch125(zzz1337, zzz1338, zzz1339, zzz1340, zzz1341, zzz1342, zzz1343, zzz1344, zzz1345, zzz1346, zzz1347, zzz13480, zzz13490, bb)
new_mkVBalBranch3MkVBalBranch123(zzz3170, zzz3171, zzz317200, zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, Succ(zzz5620), h) → new_mkVBalBranch1(zzz31, zzz334, Branch(zzz3170, zzz3171, Neg(Succ(zzz317200)), zzz3173, zzz3174), h)
new_mkVBalBranch3MkVBalBranch125(zzz1337, zzz1338, zzz1339, zzz1340, zzz1341, zzz1342, zzz1343, zzz1344, zzz1345, zzz1346, zzz1347, Zero, Succ(zzz13490), bb) → new_mkVBalBranch1(zzz1347, zzz1346, Branch(zzz1337, zzz1338, Pos(Succ(zzz1339)), zzz1340, zzz1341), bb)
new_mkVBalBranch3MkVBalBranch242(zzz972, zzz973, zzz974, zzz975, zzz976, zzz977, zzz978, zzz979, zzz980, zzz981, zzz982, Zero, Succ(zzz9840), bc) → new_mkVBalBranch1(zzz982, Branch(zzz977, zzz978, Neg(Succ(zzz979)), zzz980, zzz981), zzz975, bc)
new_mkVBalBranch3MkVBalBranch238(zzz3170, zzz3171, Succ(zzz317200), zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, h) → new_mkVBalBranch3MkVBalBranch123(zzz3170, zzz3171, zzz317200, zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, new_primPlusNat2(new_primPlusNat3(Succ(new_primPlusNat3(new_primPlusNat1(zzz317200), zzz317200)), Succ(zzz317200)), Succ(zzz317200)), h)
new_mkVBalBranch3MkVBalBranch244(zzz972, zzz973, zzz974, zzz975, zzz976, zzz977, zzz978, zzz979, zzz980, zzz981, zzz982, bc) → new_mkVBalBranch3MkVBalBranch128(zzz972, zzz973, zzz974, zzz975, zzz976, zzz977, zzz978, zzz979, zzz980, zzz981, zzz982, new_primPlusNat2(new_primMulNat0(zzz974), Succ(zzz974)), bc)
new_mkVBalBranch3MkVBalBranch235(zzz3170, zzz3171, Neg(Succ(zzz317200)), zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, Zero, h) → new_mkVBalBranch3MkVBalBranch238(zzz3170, zzz3171, Succ(zzz317200), zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, h)
new_mkVBalBranch3MkVBalBranch241(zzz3170, zzz3171, Pos(Succ(zzz317200)), zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, Zero, h) → new_mkVBalBranch3MkVBalBranch243(zzz3170, zzz3171, Succ(zzz317200), zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, h)
new_mkVBalBranch3MkVBalBranch126(zzz3170, zzz3171, zzz317200, zzz3173, zzz3174, zzz330, zzz331, zzz333, zzz334, zzz31, Succ(zzz5350), h) → new_mkVBalBranch1(zzz31, zzz334, Branch(zzz3170, zzz3171, Neg(Succ(zzz317200)), zzz3173, zzz3174), h)
new_mkVBalBranch3MkVBalBranch241(zzz3170, zzz3171, Neg(Zero), zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, Succ(zzz4190), h) → new_mkVBalBranch1(zzz31, Branch(zzz330, zzz331, Neg(Succ(zzz33200)), zzz333, zzz334), zzz3173, h)
new_mkVBalBranch3MkVBalBranch123(zzz3170, zzz3171, zzz317200, zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, Zero, h) → new_mkVBalBranch3MkVBalBranch130(zzz3170, zzz3171, zzz317200, zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, h)
new_mkVBalBranch3MkVBalBranch124(zzz958, zzz959, zzz960, zzz961, zzz962, zzz963, zzz964, zzz965, zzz966, zzz967, zzz968, Succ(zzz10180), ba) → new_mkVBalBranch3MkVBalBranch125(zzz958, zzz959, zzz960, zzz961, zzz962, zzz963, zzz964, zzz965, zzz966, zzz967, zzz968, Succ(zzz10180), Succ(zzz965), ba)
new_mkVBalBranch3MkVBalBranch235(zzz3170, zzz3171, Pos(Succ(zzz317200)), zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, Zero, h) → new_mkVBalBranch3MkVBalBranch236(zzz3170, zzz3171, zzz317200, zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, Zero, Succ(zzz317200), h)
new_mkVBalBranch3MkVBalBranch239(zzz3170, zzz3171, Zero, zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, h) → new_mkVBalBranch1(zzz31, zzz334, Branch(zzz3170, zzz3171, Neg(Zero), zzz3173, zzz3174), h)
new_mkVBalBranch3MkVBalBranch235(zzz3170, zzz3171, Pos(Zero), zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, Zero, h) → new_mkVBalBranch1(zzz31, zzz334, Branch(zzz3170, zzz3171, Pos(Zero), zzz3173, zzz3174), h)
new_mkVBalBranch3MkVBalBranch242(zzz972, zzz973, zzz974, zzz975, zzz976, zzz977, zzz978, zzz979, zzz980, zzz981, zzz982, Zero, Zero, bc) → new_mkVBalBranch3MkVBalBranch244(zzz972, zzz973, zzz974, zzz975, zzz976, zzz977, zzz978, zzz979, zzz980, zzz981, zzz982, bc)
new_mkVBalBranch1(zzz31, Branch(zzz330, zzz331, Pos(Zero), zzz333, zzz334), Branch(zzz3170, zzz3171, Neg(Succ(zzz317200)), zzz3173, zzz3174), h) → new_mkVBalBranch3MkVBalBranch126(zzz3170, zzz3171, zzz317200, zzz3173, zzz3174, zzz330, zzz331, zzz333, zzz334, zzz31, new_primPlusNat2(new_primMulNat0(zzz317200), Succ(zzz317200)), h)
new_mkVBalBranch3MkVBalBranch130(zzz3170, zzz3171, zzz317200, zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, h) → new_mkVBalBranch1(zzz31, zzz334, Branch(zzz3170, zzz3171, Neg(Succ(zzz317200)), zzz3173, zzz3174), h)
new_mkVBalBranch3MkVBalBranch235(zzz3170, zzz3171, Neg(Zero), zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, Zero, h) → new_mkVBalBranch3MkVBalBranch239(zzz3170, zzz3171, Zero, zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, h)
new_mkVBalBranch1(zzz31, Branch(zzz330, zzz331, Neg(Zero), zzz333, zzz334), Branch(zzz3170, zzz3171, Pos(Succ(zzz317200)), zzz3173, zzz3174), h) → new_mkVBalBranch1(zzz31, Branch(zzz330, zzz331, Neg(Zero), zzz333, zzz334), zzz3173, h)
new_mkVBalBranch3MkVBalBranch235(zzz3170, zzz3171, Neg(Zero), zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, Succ(zzz4170), h) → new_mkVBalBranch1(zzz31, zzz334, Branch(zzz3170, zzz3171, Neg(Zero), zzz3173, zzz3174), h)
new_mkVBalBranch3MkVBalBranch236(zzz958, zzz959, zzz960, zzz961, zzz962, zzz963, zzz964, zzz965, zzz966, zzz967, zzz968, Zero, Zero, ba) → new_mkVBalBranch3MkVBalBranch240(zzz958, zzz959, zzz960, zzz961, zzz962, zzz963, zzz964, zzz965, zzz966, zzz967, zzz968, ba)

The TRS R consists of the following rules:

new_primPlusNat1(Zero) → Zero
new_primMulNat0(zzz6200) → new_primPlusNat3(Succ(new_primPlusNat3(new_primPlusNat1(zzz6200), zzz6200)), Succ(zzz6200))
new_primPlusNat2(Succ(zzz900), Succ(zzz9100)) → Succ(Succ(new_primPlusNat2(zzz900, zzz9100)))
new_primPlusNat3(zzz90, Succ(zzz910)) → Succ(Succ(new_primPlusNat2(zzz90, zzz910)))
new_primPlusNat3(zzz90, Zero) → Succ(zzz90)
new_primMulNat1(zzz34200) → new_primPlusNat2(new_primMulNat0(zzz34200), Succ(zzz34200))
new_primPlusNat2(Zero, Zero) → Zero
new_primPlusNat1(Succ(zzz62000)) → Succ(Succ(new_primPlusNat1(zzz62000)))
new_primPlusNat2(Succ(zzz900), Zero) → Succ(zzz900)
new_primPlusNat2(Zero, Succ(zzz9100)) → Succ(zzz9100)

The set Q consists of the following terms:

new_primPlusNat2(Zero, Succ(x0))
new_primMulNat1(x0)
new_primMulNat0(x0)
new_primPlusNat3(x0, Succ(x1))
new_primPlusNat2(Succ(x0), Succ(x1))
new_primPlusNat3(x0, Zero)
new_primPlusNat1(Zero)
new_primPlusNat2(Zero, Zero)
new_primPlusNat1(Succ(x0))
new_primPlusNat2(Succ(x0), Zero)

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

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

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

new_mkVBalBranch3MkVBalBranch242(zzz972, zzz973, zzz974, zzz975, zzz976, zzz977, zzz978, zzz979, zzz980, zzz981, zzz982, Succ(zzz9830), Zero, bc) → new_mkVBalBranch3MkVBalBranch128(zzz972, zzz973, zzz974, zzz975, zzz976, zzz977, zzz978, zzz979, zzz980, zzz981, zzz982, new_primPlusNat2(new_primMulNat0(zzz974), Succ(zzz974)), bc)
new_mkVBalBranch3MkVBalBranch129(zzz1851, zzz1852, zzz1853, zzz1854, zzz1855, zzz1856, zzz1857, zzz1858, zzz1859, zzz1860, zzz1861, Zero, Succ(zzz18630), bd) → new_mkVBalBranch1(zzz1861, zzz1860, Branch(zzz1851, zzz1852, Neg(Succ(zzz1853)), zzz1854, zzz1855), bd)
new_mkVBalBranch3MkVBalBranch128(zzz972, zzz973, zzz974, zzz975, zzz976, zzz977, zzz978, zzz979, zzz980, zzz981, zzz982, Succ(zzz10190), bc) → new_mkVBalBranch3MkVBalBranch129(zzz972, zzz973, zzz974, zzz975, zzz976, zzz977, zzz978, zzz979, zzz980, zzz981, zzz982, Succ(zzz979), Succ(zzz10190), bc)
new_mkVBalBranch3MkVBalBranch241(zzz3170, zzz3171, Pos(zzz31720), zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, Succ(zzz4190), h) → new_mkVBalBranch1(zzz31, Branch(zzz330, zzz331, Neg(Succ(zzz33200)), zzz333, zzz334), zzz3173, h)
new_mkVBalBranch3MkVBalBranch127(zzz3170, zzz3171, zzz317200, zzz3173, zzz3174, zzz330, zzz331, zzz333, zzz334, zzz31, Succ(zzz5500), h) → new_mkVBalBranch1(zzz31, zzz334, Branch(zzz3170, zzz3171, Neg(Succ(zzz317200)), zzz3173, zzz3174), h)
new_mkVBalBranch1(zzz31, Branch(zzz330, zzz331, Pos(Succ(zzz33200)), zzz333, zzz334), Branch(zzz3170, zzz3171, zzz3172, zzz3173, zzz3174), h) → new_mkVBalBranch3MkVBalBranch235(zzz3170, zzz3171, zzz3172, zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, new_primPlusNat2(new_primPlusNat3(Succ(new_primPlusNat3(new_primPlusNat1(zzz33200), zzz33200)), Succ(zzz33200)), Succ(zzz33200)), h)
new_mkVBalBranch3MkVBalBranch129(zzz1851, zzz1852, zzz1853, zzz1854, zzz1855, zzz1856, zzz1857, zzz1858, zzz1859, zzz1860, zzz1861, Succ(zzz18620), Succ(zzz18630), bd) → new_mkVBalBranch3MkVBalBranch129(zzz1851, zzz1852, zzz1853, zzz1854, zzz1855, zzz1856, zzz1857, zzz1858, zzz1859, zzz1860, zzz1861, zzz18620, zzz18630, bd)
new_mkVBalBranch3MkVBalBranch240(zzz958, zzz959, zzz960, zzz961, zzz962, zzz963, zzz964, zzz965, zzz966, zzz967, zzz968, ba) → new_mkVBalBranch3MkVBalBranch124(zzz958, zzz959, zzz960, zzz961, zzz962, zzz963, zzz964, zzz965, zzz966, zzz967, zzz968, new_primPlusNat2(new_primMulNat0(zzz960), Succ(zzz960)), ba)
new_mkVBalBranch3MkVBalBranch124(zzz958, zzz959, zzz960, zzz961, zzz962, zzz963, zzz964, zzz965, zzz966, zzz967, zzz968, Zero, ba) → new_mkVBalBranch3MkVBalBranch125(zzz958, zzz959, zzz960, zzz961, zzz962, zzz963, zzz964, zzz965, zzz966, zzz967, zzz968, Zero, Succ(zzz965), ba)
new_mkVBalBranch3MkVBalBranch235(zzz3170, zzz3171, Pos(Succ(zzz317200)), zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, Succ(zzz4170), h) → new_mkVBalBranch3MkVBalBranch236(zzz3170, zzz3171, zzz317200, zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, zzz4170, zzz317200, h)
new_mkVBalBranch3MkVBalBranch242(zzz972, zzz973, zzz974, zzz975, zzz976, zzz977, zzz978, zzz979, zzz980, zzz981, zzz982, Succ(zzz9830), Succ(zzz9840), bc) → new_mkVBalBranch3MkVBalBranch242(zzz972, zzz973, zzz974, zzz975, zzz976, zzz977, zzz978, zzz979, zzz980, zzz981, zzz982, zzz9830, zzz9840, bc)
new_mkVBalBranch3MkVBalBranch236(zzz958, zzz959, zzz960, zzz961, zzz962, zzz963, zzz964, zzz965, zzz966, zzz967, zzz968, Succ(zzz9690), Succ(zzz9700), ba) → new_mkVBalBranch3MkVBalBranch236(zzz958, zzz959, zzz960, zzz961, zzz962, zzz963, zzz964, zzz965, zzz966, zzz967, zzz968, zzz9690, zzz9700, ba)
new_mkVBalBranch1(zzz31, Branch(zzz330, zzz331, Neg(Zero), zzz333, zzz334), Branch(zzz3170, zzz3171, Neg(Succ(zzz317200)), zzz3173, zzz3174), h) → new_mkVBalBranch3MkVBalBranch127(zzz3170, zzz3171, zzz317200, zzz3173, zzz3174, zzz330, zzz331, zzz333, zzz334, zzz31, new_primPlusNat2(new_primMulNat0(zzz317200), Succ(zzz317200)), h)
new_mkVBalBranch3MkVBalBranch241(zzz3170, zzz3171, Neg(Succ(zzz317200)), zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, Succ(zzz4190), h) → new_mkVBalBranch3MkVBalBranch242(zzz3170, zzz3171, zzz317200, zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, zzz317200, zzz4190, h)
new_mkVBalBranch3MkVBalBranch235(zzz3170, zzz3171, Neg(Succ(zzz317200)), zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, Succ(zzz4170), h) → new_mkVBalBranch3MkVBalBranch123(zzz3170, zzz3171, zzz317200, zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, new_primPlusNat2(new_primPlusNat3(Succ(new_primPlusNat3(new_primPlusNat1(zzz317200), zzz317200)), Succ(zzz317200)), Succ(zzz317200)), h)
new_mkVBalBranch3MkVBalBranch241(zzz3170, zzz3171, Neg(Succ(zzz317200)), zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, Zero, h) → new_mkVBalBranch3MkVBalBranch242(zzz3170, zzz3171, zzz317200, zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, Succ(zzz317200), Zero, h)
new_mkVBalBranch1(zzz31, Branch(zzz330, zzz331, Pos(Zero), zzz333, zzz334), Branch(zzz3170, zzz3171, Pos(Succ(zzz317200)), zzz3173, zzz3174), h) → new_mkVBalBranch1(zzz31, Branch(zzz330, zzz331, Pos(Zero), zzz333, zzz334), zzz3173, h)
new_mkVBalBranch3MkVBalBranch243(zzz3170, zzz3171, zzz31720, zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, h) → new_mkVBalBranch1(zzz31, Branch(zzz330, zzz331, Neg(Succ(zzz33200)), zzz333, zzz334), zzz3173, h)
new_mkVBalBranch3MkVBalBranch237(zzz3170, zzz3171, zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, h) → new_mkVBalBranch1(zzz31, zzz334, Branch(zzz3170, zzz3171, Pos(Zero), zzz3173, zzz3174), h)
new_mkVBalBranch1(zzz31, Branch(zzz330, zzz331, Neg(Succ(zzz33200)), zzz333, zzz334), Branch(zzz3170, zzz3171, zzz3172, zzz3173, zzz3174), h) → new_mkVBalBranch3MkVBalBranch241(zzz3170, zzz3171, zzz3172, zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, new_primPlusNat2(new_primPlusNat3(Succ(new_primPlusNat3(new_primPlusNat1(zzz33200), zzz33200)), Succ(zzz33200)), Succ(zzz33200)), h)
new_mkVBalBranch3MkVBalBranch235(zzz3170, zzz3171, Pos(Zero), zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, Succ(zzz4170), h) → new_mkVBalBranch3MkVBalBranch237(zzz3170, zzz3171, zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, h)
new_mkVBalBranch3MkVBalBranch236(zzz958, zzz959, zzz960, zzz961, zzz962, zzz963, zzz964, zzz965, zzz966, zzz967, zzz968, Succ(zzz9690), Zero, ba) → new_mkVBalBranch3MkVBalBranch124(zzz958, zzz959, zzz960, zzz961, zzz962, zzz963, zzz964, zzz965, zzz966, zzz967, zzz968, new_primPlusNat2(new_primMulNat0(zzz960), Succ(zzz960)), ba)
new_mkVBalBranch3MkVBalBranch236(zzz958, zzz959, zzz960, zzz961, zzz962, zzz963, zzz964, zzz965, zzz966, zzz967, zzz968, Zero, Succ(zzz9700), ba) → new_mkVBalBranch1(zzz968, Branch(zzz963, zzz964, Pos(Succ(zzz965)), zzz966, zzz967), zzz961, ba)
new_mkVBalBranch3MkVBalBranch125(zzz1337, zzz1338, zzz1339, zzz1340, zzz1341, zzz1342, zzz1343, zzz1344, zzz1345, zzz1346, zzz1347, Succ(zzz13480), Succ(zzz13490), bb) → new_mkVBalBranch3MkVBalBranch125(zzz1337, zzz1338, zzz1339, zzz1340, zzz1341, zzz1342, zzz1343, zzz1344, zzz1345, zzz1346, zzz1347, zzz13480, zzz13490, bb)
new_mkVBalBranch3MkVBalBranch123(zzz3170, zzz3171, zzz317200, zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, Succ(zzz5620), h) → new_mkVBalBranch1(zzz31, zzz334, Branch(zzz3170, zzz3171, Neg(Succ(zzz317200)), zzz3173, zzz3174), h)
new_mkVBalBranch3MkVBalBranch125(zzz1337, zzz1338, zzz1339, zzz1340, zzz1341, zzz1342, zzz1343, zzz1344, zzz1345, zzz1346, zzz1347, Zero, Succ(zzz13490), bb) → new_mkVBalBranch1(zzz1347, zzz1346, Branch(zzz1337, zzz1338, Pos(Succ(zzz1339)), zzz1340, zzz1341), bb)
new_mkVBalBranch3MkVBalBranch242(zzz972, zzz973, zzz974, zzz975, zzz976, zzz977, zzz978, zzz979, zzz980, zzz981, zzz982, Zero, Succ(zzz9840), bc) → new_mkVBalBranch1(zzz982, Branch(zzz977, zzz978, Neg(Succ(zzz979)), zzz980, zzz981), zzz975, bc)
new_mkVBalBranch3MkVBalBranch238(zzz3170, zzz3171, Succ(zzz317200), zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, h) → new_mkVBalBranch3MkVBalBranch123(zzz3170, zzz3171, zzz317200, zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, new_primPlusNat2(new_primPlusNat3(Succ(new_primPlusNat3(new_primPlusNat1(zzz317200), zzz317200)), Succ(zzz317200)), Succ(zzz317200)), h)
new_mkVBalBranch3MkVBalBranch244(zzz972, zzz973, zzz974, zzz975, zzz976, zzz977, zzz978, zzz979, zzz980, zzz981, zzz982, bc) → new_mkVBalBranch3MkVBalBranch128(zzz972, zzz973, zzz974, zzz975, zzz976, zzz977, zzz978, zzz979, zzz980, zzz981, zzz982, new_primPlusNat2(new_primMulNat0(zzz974), Succ(zzz974)), bc)
new_mkVBalBranch3MkVBalBranch235(zzz3170, zzz3171, Neg(Succ(zzz317200)), zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, Zero, h) → new_mkVBalBranch3MkVBalBranch238(zzz3170, zzz3171, Succ(zzz317200), zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, h)
new_mkVBalBranch3MkVBalBranch241(zzz3170, zzz3171, Pos(Succ(zzz317200)), zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, Zero, h) → new_mkVBalBranch3MkVBalBranch243(zzz3170, zzz3171, Succ(zzz317200), zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, h)
new_mkVBalBranch3MkVBalBranch126(zzz3170, zzz3171, zzz317200, zzz3173, zzz3174, zzz330, zzz331, zzz333, zzz334, zzz31, Succ(zzz5350), h) → new_mkVBalBranch1(zzz31, zzz334, Branch(zzz3170, zzz3171, Neg(Succ(zzz317200)), zzz3173, zzz3174), h)
new_mkVBalBranch3MkVBalBranch241(zzz3170, zzz3171, Neg(Zero), zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, Succ(zzz4190), h) → new_mkVBalBranch1(zzz31, Branch(zzz330, zzz331, Neg(Succ(zzz33200)), zzz333, zzz334), zzz3173, h)
new_mkVBalBranch3MkVBalBranch123(zzz3170, zzz3171, zzz317200, zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, Zero, h) → new_mkVBalBranch3MkVBalBranch130(zzz3170, zzz3171, zzz317200, zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, h)
new_mkVBalBranch3MkVBalBranch124(zzz958, zzz959, zzz960, zzz961, zzz962, zzz963, zzz964, zzz965, zzz966, zzz967, zzz968, Succ(zzz10180), ba) → new_mkVBalBranch3MkVBalBranch125(zzz958, zzz959, zzz960, zzz961, zzz962, zzz963, zzz964, zzz965, zzz966, zzz967, zzz968, Succ(zzz10180), Succ(zzz965), ba)
new_mkVBalBranch3MkVBalBranch235(zzz3170, zzz3171, Pos(Succ(zzz317200)), zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, Zero, h) → new_mkVBalBranch3MkVBalBranch236(zzz3170, zzz3171, zzz317200, zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, Zero, Succ(zzz317200), h)
new_mkVBalBranch3MkVBalBranch239(zzz3170, zzz3171, Zero, zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, h) → new_mkVBalBranch1(zzz31, zzz334, Branch(zzz3170, zzz3171, Neg(Zero), zzz3173, zzz3174), h)
new_mkVBalBranch3MkVBalBranch235(zzz3170, zzz3171, Pos(Zero), zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, Zero, h) → new_mkVBalBranch1(zzz31, zzz334, Branch(zzz3170, zzz3171, Pos(Zero), zzz3173, zzz3174), h)
new_mkVBalBranch3MkVBalBranch242(zzz972, zzz973, zzz974, zzz975, zzz976, zzz977, zzz978, zzz979, zzz980, zzz981, zzz982, Zero, Zero, bc) → new_mkVBalBranch3MkVBalBranch244(zzz972, zzz973, zzz974, zzz975, zzz976, zzz977, zzz978, zzz979, zzz980, zzz981, zzz982, bc)
new_mkVBalBranch1(zzz31, Branch(zzz330, zzz331, Pos(Zero), zzz333, zzz334), Branch(zzz3170, zzz3171, Neg(Succ(zzz317200)), zzz3173, zzz3174), h) → new_mkVBalBranch3MkVBalBranch126(zzz3170, zzz3171, zzz317200, zzz3173, zzz3174, zzz330, zzz331, zzz333, zzz334, zzz31, new_primPlusNat2(new_primMulNat0(zzz317200), Succ(zzz317200)), h)
new_mkVBalBranch3MkVBalBranch130(zzz3170, zzz3171, zzz317200, zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, h) → new_mkVBalBranch1(zzz31, zzz334, Branch(zzz3170, zzz3171, Neg(Succ(zzz317200)), zzz3173, zzz3174), h)
new_mkVBalBranch3MkVBalBranch235(zzz3170, zzz3171, Neg(Zero), zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, Zero, h) → new_mkVBalBranch3MkVBalBranch239(zzz3170, zzz3171, Zero, zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, h)
new_mkVBalBranch1(zzz31, Branch(zzz330, zzz331, Neg(Zero), zzz333, zzz334), Branch(zzz3170, zzz3171, Pos(Succ(zzz317200)), zzz3173, zzz3174), h) → new_mkVBalBranch1(zzz31, Branch(zzz330, zzz331, Neg(Zero), zzz333, zzz334), zzz3173, h)
new_mkVBalBranch3MkVBalBranch235(zzz3170, zzz3171, Neg(Zero), zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, Succ(zzz4170), h) → new_mkVBalBranch1(zzz31, zzz334, Branch(zzz3170, zzz3171, Neg(Zero), zzz3173, zzz3174), h)
new_mkVBalBranch3MkVBalBranch236(zzz958, zzz959, zzz960, zzz961, zzz962, zzz963, zzz964, zzz965, zzz966, zzz967, zzz968, Zero, Zero, ba) → new_mkVBalBranch3MkVBalBranch240(zzz958, zzz959, zzz960, zzz961, zzz962, zzz963, zzz964, zzz965, zzz966, zzz967, zzz968, ba)

The TRS R consists of the following rules:

new_primPlusNat1(Zero) → Zero
new_primPlusNat1(Succ(zzz62000)) → Succ(Succ(new_primPlusNat1(zzz62000)))
new_primPlusNat3(zzz90, Succ(zzz910)) → Succ(Succ(new_primPlusNat2(zzz90, zzz910)))
new_primPlusNat3(zzz90, Zero) → Succ(zzz90)
new_primPlusNat2(Succ(zzz900), Succ(zzz9100)) → Succ(Succ(new_primPlusNat2(zzz900, zzz9100)))
new_primPlusNat2(Zero, Succ(zzz9100)) → Succ(zzz9100)
new_primPlusNat2(Zero, Zero) → Zero
new_primPlusNat2(Succ(zzz900), Zero) → Succ(zzz900)
new_primMulNat0(zzz6200) → new_primPlusNat3(Succ(new_primPlusNat3(new_primPlusNat1(zzz6200), zzz6200)), Succ(zzz6200))

The set Q consists of the following terms:

new_primPlusNat2(Zero, Succ(x0))
new_primMulNat1(x0)
new_primMulNat0(x0)
new_primPlusNat3(x0, Succ(x1))
new_primPlusNat2(Succ(x0), Succ(x1))
new_primPlusNat3(x0, Zero)
new_primPlusNat1(Zero)
new_primPlusNat2(Zero, Zero)
new_primPlusNat1(Succ(x0))
new_primPlusNat2(Succ(x0), Zero)

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

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

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

new_mkVBalBranch3MkVBalBranch129(zzz1851, zzz1852, zzz1853, zzz1854, zzz1855, zzz1856, zzz1857, zzz1858, zzz1859, zzz1860, zzz1861, Zero, Succ(zzz18630), bd) → new_mkVBalBranch1(zzz1861, zzz1860, Branch(zzz1851, zzz1852, Neg(Succ(zzz1853)), zzz1854, zzz1855), bd)
new_mkVBalBranch3MkVBalBranch242(zzz972, zzz973, zzz974, zzz975, zzz976, zzz977, zzz978, zzz979, zzz980, zzz981, zzz982, Succ(zzz9830), Zero, bc) → new_mkVBalBranch3MkVBalBranch128(zzz972, zzz973, zzz974, zzz975, zzz976, zzz977, zzz978, zzz979, zzz980, zzz981, zzz982, new_primPlusNat2(new_primMulNat0(zzz974), Succ(zzz974)), bc)
new_mkVBalBranch3MkVBalBranch127(zzz3170, zzz3171, zzz317200, zzz3173, zzz3174, zzz330, zzz331, zzz333, zzz334, zzz31, Succ(zzz5500), h) → new_mkVBalBranch1(zzz31, zzz334, Branch(zzz3170, zzz3171, Neg(Succ(zzz317200)), zzz3173, zzz3174), h)
new_mkVBalBranch3MkVBalBranch241(zzz3170, zzz3171, Pos(zzz31720), zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, Succ(zzz4190), h) → new_mkVBalBranch1(zzz31, Branch(zzz330, zzz331, Neg(Succ(zzz33200)), zzz333, zzz334), zzz3173, h)
new_mkVBalBranch3MkVBalBranch128(zzz972, zzz973, zzz974, zzz975, zzz976, zzz977, zzz978, zzz979, zzz980, zzz981, zzz982, Succ(zzz10190), bc) → new_mkVBalBranch3MkVBalBranch129(zzz972, zzz973, zzz974, zzz975, zzz976, zzz977, zzz978, zzz979, zzz980, zzz981, zzz982, Succ(zzz979), Succ(zzz10190), bc)
new_mkVBalBranch1(zzz31, Branch(zzz330, zzz331, Pos(Succ(zzz33200)), zzz333, zzz334), Branch(zzz3170, zzz3171, zzz3172, zzz3173, zzz3174), h) → new_mkVBalBranch3MkVBalBranch235(zzz3170, zzz3171, zzz3172, zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, new_primPlusNat2(new_primPlusNat3(Succ(new_primPlusNat3(new_primPlusNat1(zzz33200), zzz33200)), Succ(zzz33200)), Succ(zzz33200)), h)
new_mkVBalBranch3MkVBalBranch129(zzz1851, zzz1852, zzz1853, zzz1854, zzz1855, zzz1856, zzz1857, zzz1858, zzz1859, zzz1860, zzz1861, Succ(zzz18620), Succ(zzz18630), bd) → new_mkVBalBranch3MkVBalBranch129(zzz1851, zzz1852, zzz1853, zzz1854, zzz1855, zzz1856, zzz1857, zzz1858, zzz1859, zzz1860, zzz1861, zzz18620, zzz18630, bd)
new_mkVBalBranch3MkVBalBranch240(zzz958, zzz959, zzz960, zzz961, zzz962, zzz963, zzz964, zzz965, zzz966, zzz967, zzz968, ba) → new_mkVBalBranch3MkVBalBranch124(zzz958, zzz959, zzz960, zzz961, zzz962, zzz963, zzz964, zzz965, zzz966, zzz967, zzz968, new_primPlusNat2(new_primMulNat0(zzz960), Succ(zzz960)), ba)
new_mkVBalBranch3MkVBalBranch124(zzz958, zzz959, zzz960, zzz961, zzz962, zzz963, zzz964, zzz965, zzz966, zzz967, zzz968, Zero, ba) → new_mkVBalBranch3MkVBalBranch125(zzz958, zzz959, zzz960, zzz961, zzz962, zzz963, zzz964, zzz965, zzz966, zzz967, zzz968, Zero, Succ(zzz965), ba)
new_mkVBalBranch3MkVBalBranch242(zzz972, zzz973, zzz974, zzz975, zzz976, zzz977, zzz978, zzz979, zzz980, zzz981, zzz982, Succ(zzz9830), Succ(zzz9840), bc) → new_mkVBalBranch3MkVBalBranch242(zzz972, zzz973, zzz974, zzz975, zzz976, zzz977, zzz978, zzz979, zzz980, zzz981, zzz982, zzz9830, zzz9840, bc)
new_mkVBalBranch3MkVBalBranch235(zzz3170, zzz3171, Pos(Succ(zzz317200)), zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, Succ(zzz4170), h) → new_mkVBalBranch3MkVBalBranch236(zzz3170, zzz3171, zzz317200, zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, zzz4170, zzz317200, h)
new_mkVBalBranch3MkVBalBranch236(zzz958, zzz959, zzz960, zzz961, zzz962, zzz963, zzz964, zzz965, zzz966, zzz967, zzz968, Succ(zzz9690), Succ(zzz9700), ba) → new_mkVBalBranch3MkVBalBranch236(zzz958, zzz959, zzz960, zzz961, zzz962, zzz963, zzz964, zzz965, zzz966, zzz967, zzz968, zzz9690, zzz9700, ba)
new_mkVBalBranch1(zzz31, Branch(zzz330, zzz331, Neg(Zero), zzz333, zzz334), Branch(zzz3170, zzz3171, Neg(Succ(zzz317200)), zzz3173, zzz3174), h) → new_mkVBalBranch3MkVBalBranch127(zzz3170, zzz3171, zzz317200, zzz3173, zzz3174, zzz330, zzz331, zzz333, zzz334, zzz31, new_primPlusNat2(new_primMulNat0(zzz317200), Succ(zzz317200)), h)
new_mkVBalBranch3MkVBalBranch241(zzz3170, zzz3171, Neg(Succ(zzz317200)), zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, Succ(zzz4190), h) → new_mkVBalBranch3MkVBalBranch242(zzz3170, zzz3171, zzz317200, zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, zzz317200, zzz4190, h)
new_mkVBalBranch3MkVBalBranch235(zzz3170, zzz3171, Neg(Succ(zzz317200)), zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, Succ(zzz4170), h) → new_mkVBalBranch3MkVBalBranch123(zzz3170, zzz3171, zzz317200, zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, new_primPlusNat2(new_primPlusNat3(Succ(new_primPlusNat3(new_primPlusNat1(zzz317200), zzz317200)), Succ(zzz317200)), Succ(zzz317200)), h)
new_mkVBalBranch3MkVBalBranch241(zzz3170, zzz3171, Neg(Succ(zzz317200)), zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, Zero, h) → new_mkVBalBranch3MkVBalBranch242(zzz3170, zzz3171, zzz317200, zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, Succ(zzz317200), Zero, h)
new_mkVBalBranch1(zzz31, Branch(zzz330, zzz331, Pos(Zero), zzz333, zzz334), Branch(zzz3170, zzz3171, Pos(Succ(zzz317200)), zzz3173, zzz3174), h) → new_mkVBalBranch1(zzz31, Branch(zzz330, zzz331, Pos(Zero), zzz333, zzz334), zzz3173, h)
new_mkVBalBranch3MkVBalBranch243(zzz3170, zzz3171, zzz31720, zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, h) → new_mkVBalBranch1(zzz31, Branch(zzz330, zzz331, Neg(Succ(zzz33200)), zzz333, zzz334), zzz3173, h)
new_mkVBalBranch3MkVBalBranch237(zzz3170, zzz3171, zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, h) → new_mkVBalBranch1(zzz31, zzz334, Branch(zzz3170, zzz3171, Pos(Zero), zzz3173, zzz3174), h)
new_mkVBalBranch1(zzz31, Branch(zzz330, zzz331, Neg(Succ(zzz33200)), zzz333, zzz334), Branch(zzz3170, zzz3171, zzz3172, zzz3173, zzz3174), h) → new_mkVBalBranch3MkVBalBranch241(zzz3170, zzz3171, zzz3172, zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, new_primPlusNat2(new_primPlusNat3(Succ(new_primPlusNat3(new_primPlusNat1(zzz33200), zzz33200)), Succ(zzz33200)), Succ(zzz33200)), h)
new_mkVBalBranch3MkVBalBranch235(zzz3170, zzz3171, Pos(Zero), zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, Succ(zzz4170), h) → new_mkVBalBranch3MkVBalBranch237(zzz3170, zzz3171, zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, h)
new_mkVBalBranch3MkVBalBranch236(zzz958, zzz959, zzz960, zzz961, zzz962, zzz963, zzz964, zzz965, zzz966, zzz967, zzz968, Succ(zzz9690), Zero, ba) → new_mkVBalBranch3MkVBalBranch124(zzz958, zzz959, zzz960, zzz961, zzz962, zzz963, zzz964, zzz965, zzz966, zzz967, zzz968, new_primPlusNat2(new_primMulNat0(zzz960), Succ(zzz960)), ba)
new_mkVBalBranch3MkVBalBranch236(zzz958, zzz959, zzz960, zzz961, zzz962, zzz963, zzz964, zzz965, zzz966, zzz967, zzz968, Zero, Succ(zzz9700), ba) → new_mkVBalBranch1(zzz968, Branch(zzz963, zzz964, Pos(Succ(zzz965)), zzz966, zzz967), zzz961, ba)
new_mkVBalBranch3MkVBalBranch125(zzz1337, zzz1338, zzz1339, zzz1340, zzz1341, zzz1342, zzz1343, zzz1344, zzz1345, zzz1346, zzz1347, Succ(zzz13480), Succ(zzz13490), bb) → new_mkVBalBranch3MkVBalBranch125(zzz1337, zzz1338, zzz1339, zzz1340, zzz1341, zzz1342, zzz1343, zzz1344, zzz1345, zzz1346, zzz1347, zzz13480, zzz13490, bb)
new_mkVBalBranch3MkVBalBranch123(zzz3170, zzz3171, zzz317200, zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, Succ(zzz5620), h) → new_mkVBalBranch1(zzz31, zzz334, Branch(zzz3170, zzz3171, Neg(Succ(zzz317200)), zzz3173, zzz3174), h)
new_mkVBalBranch3MkVBalBranch125(zzz1337, zzz1338, zzz1339, zzz1340, zzz1341, zzz1342, zzz1343, zzz1344, zzz1345, zzz1346, zzz1347, Zero, Succ(zzz13490), bb) → new_mkVBalBranch1(zzz1347, zzz1346, Branch(zzz1337, zzz1338, Pos(Succ(zzz1339)), zzz1340, zzz1341), bb)
new_mkVBalBranch3MkVBalBranch242(zzz972, zzz973, zzz974, zzz975, zzz976, zzz977, zzz978, zzz979, zzz980, zzz981, zzz982, Zero, Succ(zzz9840), bc) → new_mkVBalBranch1(zzz982, Branch(zzz977, zzz978, Neg(Succ(zzz979)), zzz980, zzz981), zzz975, bc)
new_mkVBalBranch3MkVBalBranch238(zzz3170, zzz3171, Succ(zzz317200), zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, h) → new_mkVBalBranch3MkVBalBranch123(zzz3170, zzz3171, zzz317200, zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, new_primPlusNat2(new_primPlusNat3(Succ(new_primPlusNat3(new_primPlusNat1(zzz317200), zzz317200)), Succ(zzz317200)), Succ(zzz317200)), h)
new_mkVBalBranch3MkVBalBranch244(zzz972, zzz973, zzz974, zzz975, zzz976, zzz977, zzz978, zzz979, zzz980, zzz981, zzz982, bc) → new_mkVBalBranch3MkVBalBranch128(zzz972, zzz973, zzz974, zzz975, zzz976, zzz977, zzz978, zzz979, zzz980, zzz981, zzz982, new_primPlusNat2(new_primMulNat0(zzz974), Succ(zzz974)), bc)
new_mkVBalBranch3MkVBalBranch235(zzz3170, zzz3171, Neg(Succ(zzz317200)), zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, Zero, h) → new_mkVBalBranch3MkVBalBranch238(zzz3170, zzz3171, Succ(zzz317200), zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, h)
new_mkVBalBranch3MkVBalBranch241(zzz3170, zzz3171, Pos(Succ(zzz317200)), zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, Zero, h) → new_mkVBalBranch3MkVBalBranch243(zzz3170, zzz3171, Succ(zzz317200), zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, h)
new_mkVBalBranch3MkVBalBranch126(zzz3170, zzz3171, zzz317200, zzz3173, zzz3174, zzz330, zzz331, zzz333, zzz334, zzz31, Succ(zzz5350), h) → new_mkVBalBranch1(zzz31, zzz334, Branch(zzz3170, zzz3171, Neg(Succ(zzz317200)), zzz3173, zzz3174), h)
new_mkVBalBranch3MkVBalBranch123(zzz3170, zzz3171, zzz317200, zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, Zero, h) → new_mkVBalBranch3MkVBalBranch130(zzz3170, zzz3171, zzz317200, zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, h)
new_mkVBalBranch3MkVBalBranch241(zzz3170, zzz3171, Neg(Zero), zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, Succ(zzz4190), h) → new_mkVBalBranch1(zzz31, Branch(zzz330, zzz331, Neg(Succ(zzz33200)), zzz333, zzz334), zzz3173, h)
new_mkVBalBranch3MkVBalBranch124(zzz958, zzz959, zzz960, zzz961, zzz962, zzz963, zzz964, zzz965, zzz966, zzz967, zzz968, Succ(zzz10180), ba) → new_mkVBalBranch3MkVBalBranch125(zzz958, zzz959, zzz960, zzz961, zzz962, zzz963, zzz964, zzz965, zzz966, zzz967, zzz968, Succ(zzz10180), Succ(zzz965), ba)
new_mkVBalBranch3MkVBalBranch235(zzz3170, zzz3171, Pos(Succ(zzz317200)), zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, Zero, h) → new_mkVBalBranch3MkVBalBranch236(zzz3170, zzz3171, zzz317200, zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, Zero, Succ(zzz317200), h)
new_mkVBalBranch3MkVBalBranch239(zzz3170, zzz3171, Zero, zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, h) → new_mkVBalBranch1(zzz31, zzz334, Branch(zzz3170, zzz3171, Neg(Zero), zzz3173, zzz3174), h)
new_mkVBalBranch3MkVBalBranch235(zzz3170, zzz3171, Pos(Zero), zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, Zero, h) → new_mkVBalBranch1(zzz31, zzz334, Branch(zzz3170, zzz3171, Pos(Zero), zzz3173, zzz3174), h)
new_mkVBalBranch3MkVBalBranch242(zzz972, zzz973, zzz974, zzz975, zzz976, zzz977, zzz978, zzz979, zzz980, zzz981, zzz982, Zero, Zero, bc) → new_mkVBalBranch3MkVBalBranch244(zzz972, zzz973, zzz974, zzz975, zzz976, zzz977, zzz978, zzz979, zzz980, zzz981, zzz982, bc)
new_mkVBalBranch3MkVBalBranch130(zzz3170, zzz3171, zzz317200, zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, h) → new_mkVBalBranch1(zzz31, zzz334, Branch(zzz3170, zzz3171, Neg(Succ(zzz317200)), zzz3173, zzz3174), h)
new_mkVBalBranch1(zzz31, Branch(zzz330, zzz331, Pos(Zero), zzz333, zzz334), Branch(zzz3170, zzz3171, Neg(Succ(zzz317200)), zzz3173, zzz3174), h) → new_mkVBalBranch3MkVBalBranch126(zzz3170, zzz3171, zzz317200, zzz3173, zzz3174, zzz330, zzz331, zzz333, zzz334, zzz31, new_primPlusNat2(new_primMulNat0(zzz317200), Succ(zzz317200)), h)
new_mkVBalBranch1(zzz31, Branch(zzz330, zzz331, Neg(Zero), zzz333, zzz334), Branch(zzz3170, zzz3171, Pos(Succ(zzz317200)), zzz3173, zzz3174), h) → new_mkVBalBranch1(zzz31, Branch(zzz330, zzz331, Neg(Zero), zzz333, zzz334), zzz3173, h)
new_mkVBalBranch3MkVBalBranch235(zzz3170, zzz3171, Neg(Zero), zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, Zero, h) → new_mkVBalBranch3MkVBalBranch239(zzz3170, zzz3171, Zero, zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, h)
new_mkVBalBranch3MkVBalBranch235(zzz3170, zzz3171, Neg(Zero), zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, Succ(zzz4170), h) → new_mkVBalBranch1(zzz31, zzz334, Branch(zzz3170, zzz3171, Neg(Zero), zzz3173, zzz3174), h)
new_mkVBalBranch3MkVBalBranch236(zzz958, zzz959, zzz960, zzz961, zzz962, zzz963, zzz964, zzz965, zzz966, zzz967, zzz968, Zero, Zero, ba) → new_mkVBalBranch3MkVBalBranch240(zzz958, zzz959, zzz960, zzz961, zzz962, zzz963, zzz964, zzz965, zzz966, zzz967, zzz968, ba)

The TRS R consists of the following rules:

new_primPlusNat1(Zero) → Zero
new_primPlusNat1(Succ(zzz62000)) → Succ(Succ(new_primPlusNat1(zzz62000)))
new_primPlusNat3(zzz90, Succ(zzz910)) → Succ(Succ(new_primPlusNat2(zzz90, zzz910)))
new_primPlusNat3(zzz90, Zero) → Succ(zzz90)
new_primPlusNat2(Succ(zzz900), Succ(zzz9100)) → Succ(Succ(new_primPlusNat2(zzz900, zzz9100)))
new_primPlusNat2(Zero, Succ(zzz9100)) → Succ(zzz9100)
new_primPlusNat2(Zero, Zero) → Zero
new_primPlusNat2(Succ(zzz900), Zero) → Succ(zzz900)
new_primMulNat0(zzz6200) → new_primPlusNat3(Succ(new_primPlusNat3(new_primPlusNat1(zzz6200), zzz6200)), Succ(zzz6200))

The set Q consists of the following terms:

new_primPlusNat2(Zero, Succ(x0))
new_primMulNat0(x0)
new_primPlusNat3(x0, Succ(x1))
new_primPlusNat2(Succ(x0), Succ(x1))
new_primPlusNat3(x0, Zero)
new_primPlusNat1(Zero)
new_primPlusNat2(Zero, Zero)
new_primPlusNat1(Succ(x0))
new_primPlusNat2(Succ(x0), Zero)

We have to consider all minimal (P,Q,R)-chains.
By rewriting [15] the rule new_mkVBalBranch3MkVBalBranch242(zzz972, zzz973, zzz974, zzz975, zzz976, zzz977, zzz978, zzz979, zzz980, zzz981, zzz982, Succ(zzz9830), Zero, bc) → new_mkVBalBranch3MkVBalBranch128(zzz972, zzz973, zzz974, zzz975, zzz976, zzz977, zzz978, zzz979, zzz980, zzz981, zzz982, new_primPlusNat2(new_primMulNat0(zzz974), Succ(zzz974)), bc) at position [11,0] we obtained the following new rules:

new_mkVBalBranch3MkVBalBranch242(zzz972, zzz973, zzz974, zzz975, zzz976, zzz977, zzz978, zzz979, zzz980, zzz981, zzz982, Succ(zzz9830), Zero, bc) → new_mkVBalBranch3MkVBalBranch128(zzz972, zzz973, zzz974, zzz975, zzz976, zzz977, zzz978, zzz979, zzz980, zzz981, zzz982, new_primPlusNat2(new_primPlusNat3(Succ(new_primPlusNat3(new_primPlusNat1(zzz974), zzz974)), Succ(zzz974)), Succ(zzz974)), bc)



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

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

new_mkVBalBranch3MkVBalBranch129(zzz1851, zzz1852, zzz1853, zzz1854, zzz1855, zzz1856, zzz1857, zzz1858, zzz1859, zzz1860, zzz1861, Zero, Succ(zzz18630), bd) → new_mkVBalBranch1(zzz1861, zzz1860, Branch(zzz1851, zzz1852, Neg(Succ(zzz1853)), zzz1854, zzz1855), bd)
new_mkVBalBranch3MkVBalBranch128(zzz972, zzz973, zzz974, zzz975, zzz976, zzz977, zzz978, zzz979, zzz980, zzz981, zzz982, Succ(zzz10190), bc) → new_mkVBalBranch3MkVBalBranch129(zzz972, zzz973, zzz974, zzz975, zzz976, zzz977, zzz978, zzz979, zzz980, zzz981, zzz982, Succ(zzz979), Succ(zzz10190), bc)
new_mkVBalBranch3MkVBalBranch241(zzz3170, zzz3171, Pos(zzz31720), zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, Succ(zzz4190), h) → new_mkVBalBranch1(zzz31, Branch(zzz330, zzz331, Neg(Succ(zzz33200)), zzz333, zzz334), zzz3173, h)
new_mkVBalBranch3MkVBalBranch127(zzz3170, zzz3171, zzz317200, zzz3173, zzz3174, zzz330, zzz331, zzz333, zzz334, zzz31, Succ(zzz5500), h) → new_mkVBalBranch1(zzz31, zzz334, Branch(zzz3170, zzz3171, Neg(Succ(zzz317200)), zzz3173, zzz3174), h)
new_mkVBalBranch1(zzz31, Branch(zzz330, zzz331, Pos(Succ(zzz33200)), zzz333, zzz334), Branch(zzz3170, zzz3171, zzz3172, zzz3173, zzz3174), h) → new_mkVBalBranch3MkVBalBranch235(zzz3170, zzz3171, zzz3172, zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, new_primPlusNat2(new_primPlusNat3(Succ(new_primPlusNat3(new_primPlusNat1(zzz33200), zzz33200)), Succ(zzz33200)), Succ(zzz33200)), h)
new_mkVBalBranch3MkVBalBranch242(zzz972, zzz973, zzz974, zzz975, zzz976, zzz977, zzz978, zzz979, zzz980, zzz981, zzz982, Succ(zzz9830), Zero, bc) → new_mkVBalBranch3MkVBalBranch128(zzz972, zzz973, zzz974, zzz975, zzz976, zzz977, zzz978, zzz979, zzz980, zzz981, zzz982, new_primPlusNat2(new_primPlusNat3(Succ(new_primPlusNat3(new_primPlusNat1(zzz974), zzz974)), Succ(zzz974)), Succ(zzz974)), bc)
new_mkVBalBranch3MkVBalBranch129(zzz1851, zzz1852, zzz1853, zzz1854, zzz1855, zzz1856, zzz1857, zzz1858, zzz1859, zzz1860, zzz1861, Succ(zzz18620), Succ(zzz18630), bd) → new_mkVBalBranch3MkVBalBranch129(zzz1851, zzz1852, zzz1853, zzz1854, zzz1855, zzz1856, zzz1857, zzz1858, zzz1859, zzz1860, zzz1861, zzz18620, zzz18630, bd)
new_mkVBalBranch3MkVBalBranch240(zzz958, zzz959, zzz960, zzz961, zzz962, zzz963, zzz964, zzz965, zzz966, zzz967, zzz968, ba) → new_mkVBalBranch3MkVBalBranch124(zzz958, zzz959, zzz960, zzz961, zzz962, zzz963, zzz964, zzz965, zzz966, zzz967, zzz968, new_primPlusNat2(new_primMulNat0(zzz960), Succ(zzz960)), ba)
new_mkVBalBranch3MkVBalBranch124(zzz958, zzz959, zzz960, zzz961, zzz962, zzz963, zzz964, zzz965, zzz966, zzz967, zzz968, Zero, ba) → new_mkVBalBranch3MkVBalBranch125(zzz958, zzz959, zzz960, zzz961, zzz962, zzz963, zzz964, zzz965, zzz966, zzz967, zzz968, Zero, Succ(zzz965), ba)
new_mkVBalBranch3MkVBalBranch235(zzz3170, zzz3171, Pos(Succ(zzz317200)), zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, Succ(zzz4170), h) → new_mkVBalBranch3MkVBalBranch236(zzz3170, zzz3171, zzz317200, zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, zzz4170, zzz317200, h)
new_mkVBalBranch3MkVBalBranch242(zzz972, zzz973, zzz974, zzz975, zzz976, zzz977, zzz978, zzz979, zzz980, zzz981, zzz982, Succ(zzz9830), Succ(zzz9840), bc) → new_mkVBalBranch3MkVBalBranch242(zzz972, zzz973, zzz974, zzz975, zzz976, zzz977, zzz978, zzz979, zzz980, zzz981, zzz982, zzz9830, zzz9840, bc)
new_mkVBalBranch3MkVBalBranch236(zzz958, zzz959, zzz960, zzz961, zzz962, zzz963, zzz964, zzz965, zzz966, zzz967, zzz968, Succ(zzz9690), Succ(zzz9700), ba) → new_mkVBalBranch3MkVBalBranch236(zzz958, zzz959, zzz960, zzz961, zzz962, zzz963, zzz964, zzz965, zzz966, zzz967, zzz968, zzz9690, zzz9700, ba)
new_mkVBalBranch1(zzz31, Branch(zzz330, zzz331, Neg(Zero), zzz333, zzz334), Branch(zzz3170, zzz3171, Neg(Succ(zzz317200)), zzz3173, zzz3174), h) → new_mkVBalBranch3MkVBalBranch127(zzz3170, zzz3171, zzz317200, zzz3173, zzz3174, zzz330, zzz331, zzz333, zzz334, zzz31, new_primPlusNat2(new_primMulNat0(zzz317200), Succ(zzz317200)), h)
new_mkVBalBranch3MkVBalBranch241(zzz3170, zzz3171, Neg(Succ(zzz317200)), zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, Succ(zzz4190), h) → new_mkVBalBranch3MkVBalBranch242(zzz3170, zzz3171, zzz317200, zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, zzz317200, zzz4190, h)
new_mkVBalBranch3MkVBalBranch241(zzz3170, zzz3171, Neg(Succ(zzz317200)), zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, Zero, h) → new_mkVBalBranch3MkVBalBranch242(zzz3170, zzz3171, zzz317200, zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, Succ(zzz317200), Zero, h)
new_mkVBalBranch3MkVBalBranch235(zzz3170, zzz3171, Neg(Succ(zzz317200)), zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, Succ(zzz4170), h) → new_mkVBalBranch3MkVBalBranch123(zzz3170, zzz3171, zzz317200, zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, new_primPlusNat2(new_primPlusNat3(Succ(new_primPlusNat3(new_primPlusNat1(zzz317200), zzz317200)), Succ(zzz317200)), Succ(zzz317200)), h)
new_mkVBalBranch1(zzz31, Branch(zzz330, zzz331, Pos(Zero), zzz333, zzz334), Branch(zzz3170, zzz3171, Pos(Succ(zzz317200)), zzz3173, zzz3174), h) → new_mkVBalBranch1(zzz31, Branch(zzz330, zzz331, Pos(Zero), zzz333, zzz334), zzz3173, h)
new_mkVBalBranch3MkVBalBranch237(zzz3170, zzz3171, zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, h) → new_mkVBalBranch1(zzz31, zzz334, Branch(zzz3170, zzz3171, Pos(Zero), zzz3173, zzz3174), h)
new_mkVBalBranch3MkVBalBranch243(zzz3170, zzz3171, zzz31720, zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, h) → new_mkVBalBranch1(zzz31, Branch(zzz330, zzz331, Neg(Succ(zzz33200)), zzz333, zzz334), zzz3173, h)
new_mkVBalBranch1(zzz31, Branch(zzz330, zzz331, Neg(Succ(zzz33200)), zzz333, zzz334), Branch(zzz3170, zzz3171, zzz3172, zzz3173, zzz3174), h) → new_mkVBalBranch3MkVBalBranch241(zzz3170, zzz3171, zzz3172, zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, new_primPlusNat2(new_primPlusNat3(Succ(new_primPlusNat3(new_primPlusNat1(zzz33200), zzz33200)), Succ(zzz33200)), Succ(zzz33200)), h)
new_mkVBalBranch3MkVBalBranch235(zzz3170, zzz3171, Pos(Zero), zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, Succ(zzz4170), h) → new_mkVBalBranch3MkVBalBranch237(zzz3170, zzz3171, zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, h)
new_mkVBalBranch3MkVBalBranch236(zzz958, zzz959, zzz960, zzz961, zzz962, zzz963, zzz964, zzz965, zzz966, zzz967, zzz968, Zero, Succ(zzz9700), ba) → new_mkVBalBranch1(zzz968, Branch(zzz963, zzz964, Pos(Succ(zzz965)), zzz966, zzz967), zzz961, ba)
new_mkVBalBranch3MkVBalBranch236(zzz958, zzz959, zzz960, zzz961, zzz962, zzz963, zzz964, zzz965, zzz966, zzz967, zzz968, Succ(zzz9690), Zero, ba) → new_mkVBalBranch3MkVBalBranch124(zzz958, zzz959, zzz960, zzz961, zzz962, zzz963, zzz964, zzz965, zzz966, zzz967, zzz968, new_primPlusNat2(new_primMulNat0(zzz960), Succ(zzz960)), ba)
new_mkVBalBranch3MkVBalBranch125(zzz1337, zzz1338, zzz1339, zzz1340, zzz1341, zzz1342, zzz1343, zzz1344, zzz1345, zzz1346, zzz1347, Succ(zzz13480), Succ(zzz13490), bb) → new_mkVBalBranch3MkVBalBranch125(zzz1337, zzz1338, zzz1339, zzz1340, zzz1341, zzz1342, zzz1343, zzz1344, zzz1345, zzz1346, zzz1347, zzz13480, zzz13490, bb)
new_mkVBalBranch3MkVBalBranch123(zzz3170, zzz3171, zzz317200, zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, Succ(zzz5620), h) → new_mkVBalBranch1(zzz31, zzz334, Branch(zzz3170, zzz3171, Neg(Succ(zzz317200)), zzz3173, zzz3174), h)
new_mkVBalBranch3MkVBalBranch125(zzz1337, zzz1338, zzz1339, zzz1340, zzz1341, zzz1342, zzz1343, zzz1344, zzz1345, zzz1346, zzz1347, Zero, Succ(zzz13490), bb) → new_mkVBalBranch1(zzz1347, zzz1346, Branch(zzz1337, zzz1338, Pos(Succ(zzz1339)), zzz1340, zzz1341), bb)
new_mkVBalBranch3MkVBalBranch242(zzz972, zzz973, zzz974, zzz975, zzz976, zzz977, zzz978, zzz979, zzz980, zzz981, zzz982, Zero, Succ(zzz9840), bc) → new_mkVBalBranch1(zzz982, Branch(zzz977, zzz978, Neg(Succ(zzz979)), zzz980, zzz981), zzz975, bc)
new_mkVBalBranch3MkVBalBranch238(zzz3170, zzz3171, Succ(zzz317200), zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, h) → new_mkVBalBranch3MkVBalBranch123(zzz3170, zzz3171, zzz317200, zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, new_primPlusNat2(new_primPlusNat3(Succ(new_primPlusNat3(new_primPlusNat1(zzz317200), zzz317200)), Succ(zzz317200)), Succ(zzz317200)), h)
new_mkVBalBranch3MkVBalBranch244(zzz972, zzz973, zzz974, zzz975, zzz976, zzz977, zzz978, zzz979, zzz980, zzz981, zzz982, bc) → new_mkVBalBranch3MkVBalBranch128(zzz972, zzz973, zzz974, zzz975, zzz976, zzz977, zzz978, zzz979, zzz980, zzz981, zzz982, new_primPlusNat2(new_primMulNat0(zzz974), Succ(zzz974)), bc)
new_mkVBalBranch3MkVBalBranch235(zzz3170, zzz3171, Neg(Succ(zzz317200)), zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, Zero, h) → new_mkVBalBranch3MkVBalBranch238(zzz3170, zzz3171, Succ(zzz317200), zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, h)
new_mkVBalBranch3MkVBalBranch241(zzz3170, zzz3171, Pos(Succ(zzz317200)), zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, Zero, h) → new_mkVBalBranch3MkVBalBranch243(zzz3170, zzz3171, Succ(zzz317200), zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, h)
new_mkVBalBranch3MkVBalBranch126(zzz3170, zzz3171, zzz317200, zzz3173, zzz3174, zzz330, zzz331, zzz333, zzz334, zzz31, Succ(zzz5350), h) → new_mkVBalBranch1(zzz31, zzz334, Branch(zzz3170, zzz3171, Neg(Succ(zzz317200)), zzz3173, zzz3174), h)
new_mkVBalBranch3MkVBalBranch241(zzz3170, zzz3171, Neg(Zero), zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, Succ(zzz4190), h) → new_mkVBalBranch1(zzz31, Branch(zzz330, zzz331, Neg(Succ(zzz33200)), zzz333, zzz334), zzz3173, h)
new_mkVBalBranch3MkVBalBranch123(zzz3170, zzz3171, zzz317200, zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, Zero, h) → new_mkVBalBranch3MkVBalBranch130(zzz3170, zzz3171, zzz317200, zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, h)
new_mkVBalBranch3MkVBalBranch124(zzz958, zzz959, zzz960, zzz961, zzz962, zzz963, zzz964, zzz965, zzz966, zzz967, zzz968, Succ(zzz10180), ba) → new_mkVBalBranch3MkVBalBranch125(zzz958, zzz959, zzz960, zzz961, zzz962, zzz963, zzz964, zzz965, zzz966, zzz967, zzz968, Succ(zzz10180), Succ(zzz965), ba)
new_mkVBalBranch3MkVBalBranch235(zzz3170, zzz3171, Pos(Succ(zzz317200)), zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, Zero, h) → new_mkVBalBranch3MkVBalBranch236(zzz3170, zzz3171, zzz317200, zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, Zero, Succ(zzz317200), h)
new_mkVBalBranch3MkVBalBranch239(zzz3170, zzz3171, Zero, zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, h) → new_mkVBalBranch1(zzz31, zzz334, Branch(zzz3170, zzz3171, Neg(Zero), zzz3173, zzz3174), h)
new_mkVBalBranch3MkVBalBranch235(zzz3170, zzz3171, Pos(Zero), zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, Zero, h) → new_mkVBalBranch1(zzz31, zzz334, Branch(zzz3170, zzz3171, Pos(Zero), zzz3173, zzz3174), h)
new_mkVBalBranch3MkVBalBranch242(zzz972, zzz973, zzz974, zzz975, zzz976, zzz977, zzz978, zzz979, zzz980, zzz981, zzz982, Zero, Zero, bc) → new_mkVBalBranch3MkVBalBranch244(zzz972, zzz973, zzz974, zzz975, zzz976, zzz977, zzz978, zzz979, zzz980, zzz981, zzz982, bc)
new_mkVBalBranch1(zzz31, Branch(zzz330, zzz331, Pos(Zero), zzz333, zzz334), Branch(zzz3170, zzz3171, Neg(Succ(zzz317200)), zzz3173, zzz3174), h) → new_mkVBalBranch3MkVBalBranch126(zzz3170, zzz3171, zzz317200, zzz3173, zzz3174, zzz330, zzz331, zzz333, zzz334, zzz31, new_primPlusNat2(new_primMulNat0(zzz317200), Succ(zzz317200)), h)
new_mkVBalBranch3MkVBalBranch130(zzz3170, zzz3171, zzz317200, zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, h) → new_mkVBalBranch1(zzz31, zzz334, Branch(zzz3170, zzz3171, Neg(Succ(zzz317200)), zzz3173, zzz3174), h)
new_mkVBalBranch3MkVBalBranch235(zzz3170, zzz3171, Neg(Zero), zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, Zero, h) → new_mkVBalBranch3MkVBalBranch239(zzz3170, zzz3171, Zero, zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, h)
new_mkVBalBranch1(zzz31, Branch(zzz330, zzz331, Neg(Zero), zzz333, zzz334), Branch(zzz3170, zzz3171, Pos(Succ(zzz317200)), zzz3173, zzz3174), h) → new_mkVBalBranch1(zzz31, Branch(zzz330, zzz331, Neg(Zero), zzz333, zzz334), zzz3173, h)
new_mkVBalBranch3MkVBalBranch235(zzz3170, zzz3171, Neg(Zero), zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, Succ(zzz4170), h) → new_mkVBalBranch1(zzz31, zzz334, Branch(zzz3170, zzz3171, Neg(Zero), zzz3173, zzz3174), h)
new_mkVBalBranch3MkVBalBranch236(zzz958, zzz959, zzz960, zzz961, zzz962, zzz963, zzz964, zzz965, zzz966, zzz967, zzz968, Zero, Zero, ba) → new_mkVBalBranch3MkVBalBranch240(zzz958, zzz959, zzz960, zzz961, zzz962, zzz963, zzz964, zzz965, zzz966, zzz967, zzz968, ba)

The TRS R consists of the following rules:

new_primPlusNat1(Zero) → Zero
new_primPlusNat1(Succ(zzz62000)) → Succ(Succ(new_primPlusNat1(zzz62000)))
new_primPlusNat3(zzz90, Succ(zzz910)) → Succ(Succ(new_primPlusNat2(zzz90, zzz910)))
new_primPlusNat3(zzz90, Zero) → Succ(zzz90)
new_primPlusNat2(Succ(zzz900), Succ(zzz9100)) → Succ(Succ(new_primPlusNat2(zzz900, zzz9100)))
new_primPlusNat2(Zero, Succ(zzz9100)) → Succ(zzz9100)
new_primPlusNat2(Zero, Zero) → Zero
new_primPlusNat2(Succ(zzz900), Zero) → Succ(zzz900)
new_primMulNat0(zzz6200) → new_primPlusNat3(Succ(new_primPlusNat3(new_primPlusNat1(zzz6200), zzz6200)), Succ(zzz6200))

The set Q consists of the following terms:

new_primPlusNat2(Zero, Succ(x0))
new_primMulNat0(x0)
new_primPlusNat3(x0, Succ(x1))
new_primPlusNat2(Succ(x0), Succ(x1))
new_primPlusNat3(x0, Zero)
new_primPlusNat1(Zero)
new_primPlusNat2(Zero, Zero)
new_primPlusNat1(Succ(x0))
new_primPlusNat2(Succ(x0), Zero)

We have to consider all minimal (P,Q,R)-chains.
By rewriting [15] the rule new_mkVBalBranch1(zzz31, Branch(zzz330, zzz331, Pos(Succ(zzz33200)), zzz333, zzz334), Branch(zzz3170, zzz3171, zzz3172, zzz3173, zzz3174), h) → new_mkVBalBranch3MkVBalBranch235(zzz3170, zzz3171, zzz3172, zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, new_primPlusNat2(new_primPlusNat3(Succ(new_primPlusNat3(new_primPlusNat1(zzz33200), zzz33200)), Succ(zzz33200)), Succ(zzz33200)), h) at position [11,0] we obtained the following new rules:

new_mkVBalBranch1(zzz31, Branch(zzz330, zzz331, Pos(Succ(zzz33200)), zzz333, zzz334), Branch(zzz3170, zzz3171, zzz3172, zzz3173, zzz3174), h) → new_mkVBalBranch3MkVBalBranch235(zzz3170, zzz3171, zzz3172, zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, new_primPlusNat2(Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat3(new_primPlusNat1(zzz33200), zzz33200)), zzz33200))), Succ(zzz33200)), 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
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                    ↳ DependencyGraphProof
                                      ↳ QDP
                                        ↳ Rewriting
                                          ↳ QDP
                                            ↳ Rewriting
                                              ↳ QDP
                                                ↳ Rewriting
                                                  ↳ QDP
                                                    ↳ Rewriting
                                                      ↳ QDP
                                                        ↳ Rewriting
                                                          ↳ QDP
                                                            ↳ Rewriting
                                                              ↳ QDP
                                                                ↳ Rewriting
                                                                  ↳ QDP
                                                                    ↳ Rewriting
                                                                      ↳ QDP
                                                                        ↳ Rewriting
                                                                          ↳ QDP
                                                                            ↳ Rewriting
                                                                              ↳ QDP
                                                                                ↳ UsableRulesProof
                                                                                  ↳ QDP
                                                                                    ↳ QReductionProof
                                                                                      ↳ QDP
                                                                                        ↳ Rewriting
                                                                                          ↳ QDP
                                                                                            ↳ Rewriting
                                                                                              ↳ QDP
                                                                                                ↳ Rewriting
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP

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

new_mkVBalBranch3MkVBalBranch129(zzz1851, zzz1852, zzz1853, zzz1854, zzz1855, zzz1856, zzz1857, zzz1858, zzz1859, zzz1860, zzz1861, Zero, Succ(zzz18630), bd) → new_mkVBalBranch1(zzz1861, zzz1860, Branch(zzz1851, zzz1852, Neg(Succ(zzz1853)), zzz1854, zzz1855), bd)
new_mkVBalBranch3MkVBalBranch127(zzz3170, zzz3171, zzz317200, zzz3173, zzz3174, zzz330, zzz331, zzz333, zzz334, zzz31, Succ(zzz5500), h) → new_mkVBalBranch1(zzz31, zzz334, Branch(zzz3170, zzz3171, Neg(Succ(zzz317200)), zzz3173, zzz3174), h)
new_mkVBalBranch3MkVBalBranch241(zzz3170, zzz3171, Pos(zzz31720), zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, Succ(zzz4190), h) → new_mkVBalBranch1(zzz31, Branch(zzz330, zzz331, Neg(Succ(zzz33200)), zzz333, zzz334), zzz3173, h)
new_mkVBalBranch3MkVBalBranch128(zzz972, zzz973, zzz974, zzz975, zzz976, zzz977, zzz978, zzz979, zzz980, zzz981, zzz982, Succ(zzz10190), bc) → new_mkVBalBranch3MkVBalBranch129(zzz972, zzz973, zzz974, zzz975, zzz976, zzz977, zzz978, zzz979, zzz980, zzz981, zzz982, Succ(zzz979), Succ(zzz10190), bc)
new_mkVBalBranch3MkVBalBranch242(zzz972, zzz973, zzz974, zzz975, zzz976, zzz977, zzz978, zzz979, zzz980, zzz981, zzz982, Succ(zzz9830), Zero, bc) → new_mkVBalBranch3MkVBalBranch128(zzz972, zzz973, zzz974, zzz975, zzz976, zzz977, zzz978, zzz979, zzz980, zzz981, zzz982, new_primPlusNat2(new_primPlusNat3(Succ(new_primPlusNat3(new_primPlusNat1(zzz974), zzz974)), Succ(zzz974)), Succ(zzz974)), bc)
new_mkVBalBranch3MkVBalBranch129(zzz1851, zzz1852, zzz1853, zzz1854, zzz1855, zzz1856, zzz1857, zzz1858, zzz1859, zzz1860, zzz1861, Succ(zzz18620), Succ(zzz18630), bd) → new_mkVBalBranch3MkVBalBranch129(zzz1851, zzz1852, zzz1853, zzz1854, zzz1855, zzz1856, zzz1857, zzz1858, zzz1859, zzz1860, zzz1861, zzz18620, zzz18630, bd)
new_mkVBalBranch3MkVBalBranch240(zzz958, zzz959, zzz960, zzz961, zzz962, zzz963, zzz964, zzz965, zzz966, zzz967, zzz968, ba) → new_mkVBalBranch3MkVBalBranch124(zzz958, zzz959, zzz960, zzz961, zzz962, zzz963, zzz964, zzz965, zzz966, zzz967, zzz968, new_primPlusNat2(new_primMulNat0(zzz960), Succ(zzz960)), ba)
new_mkVBalBranch3MkVBalBranch124(zzz958, zzz959, zzz960, zzz961, zzz962, zzz963, zzz964, zzz965, zzz966, zzz967, zzz968, Zero, ba) → new_mkVBalBranch3MkVBalBranch125(zzz958, zzz959, zzz960, zzz961, zzz962, zzz963, zzz964, zzz965, zzz966, zzz967, zzz968, Zero, Succ(zzz965), ba)
new_mkVBalBranch3MkVBalBranch242(zzz972, zzz973, zzz974, zzz975, zzz976, zzz977, zzz978, zzz979, zzz980, zzz981, zzz982, Succ(zzz9830), Succ(zzz9840), bc) → new_mkVBalBranch3MkVBalBranch242(zzz972, zzz973, zzz974, zzz975, zzz976, zzz977, zzz978, zzz979, zzz980, zzz981, zzz982, zzz9830, zzz9840, bc)
new_mkVBalBranch3MkVBalBranch235(zzz3170, zzz3171, Pos(Succ(zzz317200)), zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, Succ(zzz4170), h) → new_mkVBalBranch3MkVBalBranch236(zzz3170, zzz3171, zzz317200, zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, zzz4170, zzz317200, h)
new_mkVBalBranch1(zzz31, Branch(zzz330, zzz331, Pos(Succ(zzz33200)), zzz333, zzz334), Branch(zzz3170, zzz3171, zzz3172, zzz3173, zzz3174), h) → new_mkVBalBranch3MkVBalBranch235(zzz3170, zzz3171, zzz3172, zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, new_primPlusNat2(Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat3(new_primPlusNat1(zzz33200), zzz33200)), zzz33200))), Succ(zzz33200)), h)
new_mkVBalBranch3MkVBalBranch236(zzz958, zzz959, zzz960, zzz961, zzz962, zzz963, zzz964, zzz965, zzz966, zzz967, zzz968, Succ(zzz9690), Succ(zzz9700), ba) → new_mkVBalBranch3MkVBalBranch236(zzz958, zzz959, zzz960, zzz961, zzz962, zzz963, zzz964, zzz965, zzz966, zzz967, zzz968, zzz9690, zzz9700, ba)
new_mkVBalBranch1(zzz31, Branch(zzz330, zzz331, Neg(Zero), zzz333, zzz334), Branch(zzz3170, zzz3171, Neg(Succ(zzz317200)), zzz3173, zzz3174), h) → new_mkVBalBranch3MkVBalBranch127(zzz3170, zzz3171, zzz317200, zzz3173, zzz3174, zzz330, zzz331, zzz333, zzz334, zzz31, new_primPlusNat2(new_primMulNat0(zzz317200), Succ(zzz317200)), h)
new_mkVBalBranch3MkVBalBranch241(zzz3170, zzz3171, Neg(Succ(zzz317200)), zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, Succ(zzz4190), h) → new_mkVBalBranch3MkVBalBranch242(zzz3170, zzz3171, zzz317200, zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, zzz317200, zzz4190, h)
new_mkVBalBranch3MkVBalBranch235(zzz3170, zzz3171, Neg(Succ(zzz317200)), zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, Succ(zzz4170), h) → new_mkVBalBranch3MkVBalBranch123(zzz3170, zzz3171, zzz317200, zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, new_primPlusNat2(new_primPlusNat3(Succ(new_primPlusNat3(new_primPlusNat1(zzz317200), zzz317200)), Succ(zzz317200)), Succ(zzz317200)), h)
new_mkVBalBranch3MkVBalBranch241(zzz3170, zzz3171, Neg(Succ(zzz317200)), zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, Zero, h) → new_mkVBalBranch3MkVBalBranch242(zzz3170, zzz3171, zzz317200, zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, Succ(zzz317200), Zero, h)
new_mkVBalBranch1(zzz31, Branch(zzz330, zzz331, Pos(Zero), zzz333, zzz334), Branch(zzz3170, zzz3171, Pos(Succ(zzz317200)), zzz3173, zzz3174), h) → new_mkVBalBranch1(zzz31, Branch(zzz330, zzz331, Pos(Zero), zzz333, zzz334), zzz3173, h)
new_mkVBalBranch3MkVBalBranch243(zzz3170, zzz3171, zzz31720, zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, h) → new_mkVBalBranch1(zzz31, Branch(zzz330, zzz331, Neg(Succ(zzz33200)), zzz333, zzz334), zzz3173, h)
new_mkVBalBranch3MkVBalBranch237(zzz3170, zzz3171, zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, h) → new_mkVBalBranch1(zzz31, zzz334, Branch(zzz3170, zzz3171, Pos(Zero), zzz3173, zzz3174), h)
new_mkVBalBranch1(zzz31, Branch(zzz330, zzz331, Neg(Succ(zzz33200)), zzz333, zzz334), Branch(zzz3170, zzz3171, zzz3172, zzz3173, zzz3174), h) → new_mkVBalBranch3MkVBalBranch241(zzz3170, zzz3171, zzz3172, zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, new_primPlusNat2(new_primPlusNat3(Succ(new_primPlusNat3(new_primPlusNat1(zzz33200), zzz33200)), Succ(zzz33200)), Succ(zzz33200)), h)
new_mkVBalBranch3MkVBalBranch235(zzz3170, zzz3171, Pos(Zero), zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, Succ(zzz4170), h) → new_mkVBalBranch3MkVBalBranch237(zzz3170, zzz3171, zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, h)
new_mkVBalBranch3MkVBalBranch236(zzz958, zzz959, zzz960, zzz961, zzz962, zzz963, zzz964, zzz965, zzz966, zzz967, zzz968, Succ(zzz9690), Zero, ba) → new_mkVBalBranch3MkVBalBranch124(zzz958, zzz959, zzz960, zzz961, zzz962, zzz963, zzz964, zzz965, zzz966, zzz967, zzz968, new_primPlusNat2(new_primMulNat0(zzz960), Succ(zzz960)), ba)
new_mkVBalBranch3MkVBalBranch236(zzz958, zzz959, zzz960, zzz961, zzz962, zzz963, zzz964, zzz965, zzz966, zzz967, zzz968, Zero, Succ(zzz9700), ba) → new_mkVBalBranch1(zzz968, Branch(zzz963, zzz964, Pos(Succ(zzz965)), zzz966, zzz967), zzz961, ba)
new_mkVBalBranch3MkVBalBranch125(zzz1337, zzz1338, zzz1339, zzz1340, zzz1341, zzz1342, zzz1343, zzz1344, zzz1345, zzz1346, zzz1347, Succ(zzz13480), Succ(zzz13490), bb) → new_mkVBalBranch3MkVBalBranch125(zzz1337, zzz1338, zzz1339, zzz1340, zzz1341, zzz1342, zzz1343, zzz1344, zzz1345, zzz1346, zzz1347, zzz13480, zzz13490, bb)
new_mkVBalBranch3MkVBalBranch123(zzz3170, zzz3171, zzz317200, zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, Succ(zzz5620), h) → new_mkVBalBranch1(zzz31, zzz334, Branch(zzz3170, zzz3171, Neg(Succ(zzz317200)), zzz3173, zzz3174), h)
new_mkVBalBranch3MkVBalBranch125(zzz1337, zzz1338, zzz1339, zzz1340, zzz1341, zzz1342, zzz1343, zzz1344, zzz1345, zzz1346, zzz1347, Zero, Succ(zzz13490), bb) → new_mkVBalBranch1(zzz1347, zzz1346, Branch(zzz1337, zzz1338, Pos(Succ(zzz1339)), zzz1340, zzz1341), bb)
new_mkVBalBranch3MkVBalBranch242(zzz972, zzz973, zzz974, zzz975, zzz976, zzz977, zzz978, zzz979, zzz980, zzz981, zzz982, Zero, Succ(zzz9840), bc) → new_mkVBalBranch1(zzz982, Branch(zzz977, zzz978, Neg(Succ(zzz979)), zzz980, zzz981), zzz975, bc)
new_mkVBalBranch3MkVBalBranch238(zzz3170, zzz3171, Succ(zzz317200), zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, h) → new_mkVBalBranch3MkVBalBranch123(zzz3170, zzz3171, zzz317200, zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, new_primPlusNat2(new_primPlusNat3(Succ(new_primPlusNat3(new_primPlusNat1(zzz317200), zzz317200)), Succ(zzz317200)), Succ(zzz317200)), h)
new_mkVBalBranch3MkVBalBranch244(zzz972, zzz973, zzz974, zzz975, zzz976, zzz977, zzz978, zzz979, zzz980, zzz981, zzz982, bc) → new_mkVBalBranch3MkVBalBranch128(zzz972, zzz973, zzz974, zzz975, zzz976, zzz977, zzz978, zzz979, zzz980, zzz981, zzz982, new_primPlusNat2(new_primMulNat0(zzz974), Succ(zzz974)), bc)
new_mkVBalBranch3MkVBalBranch235(zzz3170, zzz3171, Neg(Succ(zzz317200)), zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, Zero, h) → new_mkVBalBranch3MkVBalBranch238(zzz3170, zzz3171, Succ(zzz317200), zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, h)
new_mkVBalBranch3MkVBalBranch241(zzz3170, zzz3171, Pos(Succ(zzz317200)), zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, Zero, h) → new_mkVBalBranch3MkVBalBranch243(zzz3170, zzz3171, Succ(zzz317200), zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, h)
new_mkVBalBranch3MkVBalBranch126(zzz3170, zzz3171, zzz317200, zzz3173, zzz3174, zzz330, zzz331, zzz333, zzz334, zzz31, Succ(zzz5350), h) → new_mkVBalBranch1(zzz31, zzz334, Branch(zzz3170, zzz3171, Neg(Succ(zzz317200)), zzz3173, zzz3174), h)
new_mkVBalBranch3MkVBalBranch123(zzz3170, zzz3171, zzz317200, zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, Zero, h) → new_mkVBalBranch3MkVBalBranch130(zzz3170, zzz3171, zzz317200, zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, h)
new_mkVBalBranch3MkVBalBranch241(zzz3170, zzz3171, Neg(Zero), zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, Succ(zzz4190), h) → new_mkVBalBranch1(zzz31, Branch(zzz330, zzz331, Neg(Succ(zzz33200)), zzz333, zzz334), zzz3173, h)
new_mkVBalBranch3MkVBalBranch124(zzz958, zzz959, zzz960, zzz961, zzz962, zzz963, zzz964, zzz965, zzz966, zzz967, zzz968, Succ(zzz10180), ba) → new_mkVBalBranch3MkVBalBranch125(zzz958, zzz959, zzz960, zzz961, zzz962, zzz963, zzz964, zzz965, zzz966, zzz967, zzz968, Succ(zzz10180), Succ(zzz965), ba)
new_mkVBalBranch3MkVBalBranch235(zzz3170, zzz3171, Pos(Succ(zzz317200)), zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, Zero, h) → new_mkVBalBranch3MkVBalBranch236(zzz3170, zzz3171, zzz317200, zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, Zero, Succ(zzz317200), h)
new_mkVBalBranch3MkVBalBranch239(zzz3170, zzz3171, Zero, zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, h) → new_mkVBalBranch1(zzz31, zzz334, Branch(zzz3170, zzz3171, Neg(Zero), zzz3173, zzz3174), h)
new_mkVBalBranch3MkVBalBranch235(zzz3170, zzz3171, Pos(Zero), zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, Zero, h) → new_mkVBalBranch1(zzz31, zzz334, Branch(zzz3170, zzz3171, Pos(Zero), zzz3173, zzz3174), h)
new_mkVBalBranch3MkVBalBranch242(zzz972, zzz973, zzz974, zzz975, zzz976, zzz977, zzz978, zzz979, zzz980, zzz981, zzz982, Zero, Zero, bc) → new_mkVBalBranch3MkVBalBranch244(zzz972, zzz973, zzz974, zzz975, zzz976, zzz977, zzz978, zzz979, zzz980, zzz981, zzz982, bc)
new_mkVBalBranch3MkVBalBranch130(zzz3170, zzz3171, zzz317200, zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, h) → new_mkVBalBranch1(zzz31, zzz334, Branch(zzz3170, zzz3171, Neg(Succ(zzz317200)), zzz3173, zzz3174), h)
new_mkVBalBranch1(zzz31, Branch(zzz330, zzz331, Pos(Zero), zzz333, zzz334), Branch(zzz3170, zzz3171, Neg(Succ(zzz317200)), zzz3173, zzz3174), h) → new_mkVBalBranch3MkVBalBranch126(zzz3170, zzz3171, zzz317200, zzz3173, zzz3174, zzz330, zzz331, zzz333, zzz334, zzz31, new_primPlusNat2(new_primMulNat0(zzz317200), Succ(zzz317200)), h)
new_mkVBalBranch1(zzz31, Branch(zzz330, zzz331, Neg(Zero), zzz333, zzz334), Branch(zzz3170, zzz3171, Pos(Succ(zzz317200)), zzz3173, zzz3174), h) → new_mkVBalBranch1(zzz31, Branch(zzz330, zzz331, Neg(Zero), zzz333, zzz334), zzz3173, h)
new_mkVBalBranch3MkVBalBranch235(zzz3170, zzz3171, Neg(Zero), zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, Zero, h) → new_mkVBalBranch3MkVBalBranch239(zzz3170, zzz3171, Zero, zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, h)
new_mkVBalBranch3MkVBalBranch235(zzz3170, zzz3171, Neg(Zero), zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, Succ(zzz4170), h) → new_mkVBalBranch1(zzz31, zzz334, Branch(zzz3170, zzz3171, Neg(Zero), zzz3173, zzz3174), h)
new_mkVBalBranch3MkVBalBranch236(zzz958, zzz959, zzz960, zzz961, zzz962, zzz963, zzz964, zzz965, zzz966, zzz967, zzz968, Zero, Zero, ba) → new_mkVBalBranch3MkVBalBranch240(zzz958, zzz959, zzz960, zzz961, zzz962, zzz963, zzz964, zzz965, zzz966, zzz967, zzz968, ba)

The TRS R consists of the following rules:

new_primPlusNat1(Zero) → Zero
new_primPlusNat1(Succ(zzz62000)) → Succ(Succ(new_primPlusNat1(zzz62000)))
new_primPlusNat3(zzz90, Succ(zzz910)) → Succ(Succ(new_primPlusNat2(zzz90, zzz910)))
new_primPlusNat3(zzz90, Zero) → Succ(zzz90)
new_primPlusNat2(Succ(zzz900), Succ(zzz9100)) → Succ(Succ(new_primPlusNat2(zzz900, zzz9100)))
new_primPlusNat2(Zero, Succ(zzz9100)) → Succ(zzz9100)
new_primPlusNat2(Zero, Zero) → Zero
new_primPlusNat2(Succ(zzz900), Zero) → Succ(zzz900)
new_primMulNat0(zzz6200) → new_primPlusNat3(Succ(new_primPlusNat3(new_primPlusNat1(zzz6200), zzz6200)), Succ(zzz6200))

The set Q consists of the following terms:

new_primPlusNat2(Zero, Succ(x0))
new_primMulNat0(x0)
new_primPlusNat3(x0, Succ(x1))
new_primPlusNat2(Succ(x0), Succ(x1))
new_primPlusNat3(x0, Zero)
new_primPlusNat1(Zero)
new_primPlusNat2(Zero, Zero)
new_primPlusNat1(Succ(x0))
new_primPlusNat2(Succ(x0), Zero)

We have to consider all minimal (P,Q,R)-chains.
By rewriting [15] the rule new_mkVBalBranch3MkVBalBranch240(zzz958, zzz959, zzz960, zzz961, zzz962, zzz963, zzz964, zzz965, zzz966, zzz967, zzz968, ba) → new_mkVBalBranch3MkVBalBranch124(zzz958, zzz959, zzz960, zzz961, zzz962, zzz963, zzz964, zzz965, zzz966, zzz967, zzz968, new_primPlusNat2(new_primMulNat0(zzz960), Succ(zzz960)), ba) at position [11,0] we obtained the following new rules:

new_mkVBalBranch3MkVBalBranch240(zzz958, zzz959, zzz960, zzz961, zzz962, zzz963, zzz964, zzz965, zzz966, zzz967, zzz968, ba) → new_mkVBalBranch3MkVBalBranch124(zzz958, zzz959, zzz960, zzz961, zzz962, zzz963, zzz964, zzz965, zzz966, zzz967, zzz968, new_primPlusNat2(new_primPlusNat3(Succ(new_primPlusNat3(new_primPlusNat1(zzz960), zzz960)), Succ(zzz960)), Succ(zzz960)), 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
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                    ↳ DependencyGraphProof
                                      ↳ QDP
                                        ↳ Rewriting
                                          ↳ QDP
                                            ↳ Rewriting
                                              ↳ QDP
                                                ↳ Rewriting
                                                  ↳ QDP
                                                    ↳ Rewriting
                                                      ↳ QDP
                                                        ↳ Rewriting
                                                          ↳ QDP
                                                            ↳ Rewriting
                                                              ↳ QDP
                                                                ↳ Rewriting
                                                                  ↳ QDP
                                                                    ↳ Rewriting
                                                                      ↳ QDP
                                                                        ↳ Rewriting
                                                                          ↳ QDP
                                                                            ↳ Rewriting
                                                                              ↳ QDP
                                                                                ↳ UsableRulesProof
                                                                                  ↳ QDP
                                                                                    ↳ QReductionProof
                                                                                      ↳ QDP
                                                                                        ↳ Rewriting
                                                                                          ↳ QDP
                                                                                            ↳ Rewriting
                                                                                              ↳ QDP
                                                                                                ↳ Rewriting
                                                                                                  ↳ QDP
                                                                                                    ↳ Rewriting
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP

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

new_mkVBalBranch3MkVBalBranch129(zzz1851, zzz1852, zzz1853, zzz1854, zzz1855, zzz1856, zzz1857, zzz1858, zzz1859, zzz1860, zzz1861, Zero, Succ(zzz18630), bd) → new_mkVBalBranch1(zzz1861, zzz1860, Branch(zzz1851, zzz1852, Neg(Succ(zzz1853)), zzz1854, zzz1855), bd)
new_mkVBalBranch3MkVBalBranch128(zzz972, zzz973, zzz974, zzz975, zzz976, zzz977, zzz978, zzz979, zzz980, zzz981, zzz982, Succ(zzz10190), bc) → new_mkVBalBranch3MkVBalBranch129(zzz972, zzz973, zzz974, zzz975, zzz976, zzz977, zzz978, zzz979, zzz980, zzz981, zzz982, Succ(zzz979), Succ(zzz10190), bc)
new_mkVBalBranch3MkVBalBranch241(zzz3170, zzz3171, Pos(zzz31720), zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, Succ(zzz4190), h) → new_mkVBalBranch1(zzz31, Branch(zzz330, zzz331, Neg(Succ(zzz33200)), zzz333, zzz334), zzz3173, h)
new_mkVBalBranch3MkVBalBranch127(zzz3170, zzz3171, zzz317200, zzz3173, zzz3174, zzz330, zzz331, zzz333, zzz334, zzz31, Succ(zzz5500), h) → new_mkVBalBranch1(zzz31, zzz334, Branch(zzz3170, zzz3171, Neg(Succ(zzz317200)), zzz3173, zzz3174), h)
new_mkVBalBranch3MkVBalBranch242(zzz972, zzz973, zzz974, zzz975, zzz976, zzz977, zzz978, zzz979, zzz980, zzz981, zzz982, Succ(zzz9830), Zero, bc) → new_mkVBalBranch3MkVBalBranch128(zzz972, zzz973, zzz974, zzz975, zzz976, zzz977, zzz978, zzz979, zzz980, zzz981, zzz982, new_primPlusNat2(new_primPlusNat3(Succ(new_primPlusNat3(new_primPlusNat1(zzz974), zzz974)), Succ(zzz974)), Succ(zzz974)), bc)
new_mkVBalBranch3MkVBalBranch129(zzz1851, zzz1852, zzz1853, zzz1854, zzz1855, zzz1856, zzz1857, zzz1858, zzz1859, zzz1860, zzz1861, Succ(zzz18620), Succ(zzz18630), bd) → new_mkVBalBranch3MkVBalBranch129(zzz1851, zzz1852, zzz1853, zzz1854, zzz1855, zzz1856, zzz1857, zzz1858, zzz1859, zzz1860, zzz1861, zzz18620, zzz18630, bd)
new_mkVBalBranch3MkVBalBranch124(zzz958, zzz959, zzz960, zzz961, zzz962, zzz963, zzz964, zzz965, zzz966, zzz967, zzz968, Zero, ba) → new_mkVBalBranch3MkVBalBranch125(zzz958, zzz959, zzz960, zzz961, zzz962, zzz963, zzz964, zzz965, zzz966, zzz967, zzz968, Zero, Succ(zzz965), ba)
new_mkVBalBranch3MkVBalBranch235(zzz3170, zzz3171, Pos(Succ(zzz317200)), zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, Succ(zzz4170), h) → new_mkVBalBranch3MkVBalBranch236(zzz3170, zzz3171, zzz317200, zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, zzz4170, zzz317200, h)
new_mkVBalBranch3MkVBalBranch242(zzz972, zzz973, zzz974, zzz975, zzz976, zzz977, zzz978, zzz979, zzz980, zzz981, zzz982, Succ(zzz9830), Succ(zzz9840), bc) → new_mkVBalBranch3MkVBalBranch242(zzz972, zzz973, zzz974, zzz975, zzz976, zzz977, zzz978, zzz979, zzz980, zzz981, zzz982, zzz9830, zzz9840, bc)
new_mkVBalBranch3MkVBalBranch236(zzz958, zzz959, zzz960, zzz961, zzz962, zzz963, zzz964, zzz965, zzz966, zzz967, zzz968, Succ(zzz9690), Succ(zzz9700), ba) → new_mkVBalBranch3MkVBalBranch236(zzz958, zzz959, zzz960, zzz961, zzz962, zzz963, zzz964, zzz965, zzz966, zzz967, zzz968, zzz9690, zzz9700, ba)
new_mkVBalBranch1(zzz31, Branch(zzz330, zzz331, Pos(Succ(zzz33200)), zzz333, zzz334), Branch(zzz3170, zzz3171, zzz3172, zzz3173, zzz3174), h) → new_mkVBalBranch3MkVBalBranch235(zzz3170, zzz3171, zzz3172, zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, new_primPlusNat2(Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat3(new_primPlusNat1(zzz33200), zzz33200)), zzz33200))), Succ(zzz33200)), h)
new_mkVBalBranch1(zzz31, Branch(zzz330, zzz331, Neg(Zero), zzz333, zzz334), Branch(zzz3170, zzz3171, Neg(Succ(zzz317200)), zzz3173, zzz3174), h) → new_mkVBalBranch3MkVBalBranch127(zzz3170, zzz3171, zzz317200, zzz3173, zzz3174, zzz330, zzz331, zzz333, zzz334, zzz31, new_primPlusNat2(new_primMulNat0(zzz317200), Succ(zzz317200)), h)
new_mkVBalBranch3MkVBalBranch241(zzz3170, zzz3171, Neg(Succ(zzz317200)), zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, Succ(zzz4190), h) → new_mkVBalBranch3MkVBalBranch242(zzz3170, zzz3171, zzz317200, zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, zzz317200, zzz4190, h)
new_mkVBalBranch3MkVBalBranch241(zzz3170, zzz3171, Neg(Succ(zzz317200)), zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, Zero, h) → new_mkVBalBranch3MkVBalBranch242(zzz3170, zzz3171, zzz317200, zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, Succ(zzz317200), Zero, h)
new_mkVBalBranch3MkVBalBranch235(zzz3170, zzz3171, Neg(Succ(zzz317200)), zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, Succ(zzz4170), h) → new_mkVBalBranch3MkVBalBranch123(zzz3170, zzz3171, zzz317200, zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, new_primPlusNat2(new_primPlusNat3(Succ(new_primPlusNat3(new_primPlusNat1(zzz317200), zzz317200)), Succ(zzz317200)), Succ(zzz317200)), h)
new_mkVBalBranch1(zzz31, Branch(zzz330, zzz331, Pos(Zero), zzz333, zzz334), Branch(zzz3170, zzz3171, Pos(Succ(zzz317200)), zzz3173, zzz3174), h) → new_mkVBalBranch1(zzz31, Branch(zzz330, zzz331, Pos(Zero), zzz333, zzz334), zzz3173, h)
new_mkVBalBranch3MkVBalBranch237(zzz3170, zzz3171, zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, h) → new_mkVBalBranch1(zzz31, zzz334, Branch(zzz3170, zzz3171, Pos(Zero), zzz3173, zzz3174), h)
new_mkVBalBranch3MkVBalBranch243(zzz3170, zzz3171, zzz31720, zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, h) → new_mkVBalBranch1(zzz31, Branch(zzz330, zzz331, Neg(Succ(zzz33200)), zzz333, zzz334), zzz3173, h)
new_mkVBalBranch1(zzz31, Branch(zzz330, zzz331, Neg(Succ(zzz33200)), zzz333, zzz334), Branch(zzz3170, zzz3171, zzz3172, zzz3173, zzz3174), h) → new_mkVBalBranch3MkVBalBranch241(zzz3170, zzz3171, zzz3172, zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, new_primPlusNat2(new_primPlusNat3(Succ(new_primPlusNat3(new_primPlusNat1(zzz33200), zzz33200)), Succ(zzz33200)), Succ(zzz33200)), h)
new_mkVBalBranch3MkVBalBranch235(zzz3170, zzz3171, Pos(Zero), zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, Succ(zzz4170), h) → new_mkVBalBranch3MkVBalBranch237(zzz3170, zzz3171, zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, h)
new_mkVBalBranch3MkVBalBranch236(zzz958, zzz959, zzz960, zzz961, zzz962, zzz963, zzz964, zzz965, zzz966, zzz967, zzz968, Zero, Succ(zzz9700), ba) → new_mkVBalBranch1(zzz968, Branch(zzz963, zzz964, Pos(Succ(zzz965)), zzz966, zzz967), zzz961, ba)
new_mkVBalBranch3MkVBalBranch236(zzz958, zzz959, zzz960, zzz961, zzz962, zzz963, zzz964, zzz965, zzz966, zzz967, zzz968, Succ(zzz9690), Zero, ba) → new_mkVBalBranch3MkVBalBranch124(zzz958, zzz959, zzz960, zzz961, zzz962, zzz963, zzz964, zzz965, zzz966, zzz967, zzz968, new_primPlusNat2(new_primMulNat0(zzz960), Succ(zzz960)), ba)
new_mkVBalBranch3MkVBalBranch125(zzz1337, zzz1338, zzz1339, zzz1340, zzz1341, zzz1342, zzz1343, zzz1344, zzz1345, zzz1346, zzz1347, Succ(zzz13480), Succ(zzz13490), bb) → new_mkVBalBranch3MkVBalBranch125(zzz1337, zzz1338, zzz1339, zzz1340, zzz1341, zzz1342, zzz1343, zzz1344, zzz1345, zzz1346, zzz1347, zzz13480, zzz13490, bb)
new_mkVBalBranch3MkVBalBranch123(zzz3170, zzz3171, zzz317200, zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, Succ(zzz5620), h) → new_mkVBalBranch1(zzz31, zzz334, Branch(zzz3170, zzz3171, Neg(Succ(zzz317200)), zzz3173, zzz3174), h)
new_mkVBalBranch3MkVBalBranch125(zzz1337, zzz1338, zzz1339, zzz1340, zzz1341, zzz1342, zzz1343, zzz1344, zzz1345, zzz1346, zzz1347, Zero, Succ(zzz13490), bb) → new_mkVBalBranch1(zzz1347, zzz1346, Branch(zzz1337, zzz1338, Pos(Succ(zzz1339)), zzz1340, zzz1341), bb)
new_mkVBalBranch3MkVBalBranch242(zzz972, zzz973, zzz974, zzz975, zzz976, zzz977, zzz978, zzz979, zzz980, zzz981, zzz982, Zero, Succ(zzz9840), bc) → new_mkVBalBranch1(zzz982, Branch(zzz977, zzz978, Neg(Succ(zzz979)), zzz980, zzz981), zzz975, bc)
new_mkVBalBranch3MkVBalBranch238(zzz3170, zzz3171, Succ(zzz317200), zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, h) → new_mkVBalBranch3MkVBalBranch123(zzz3170, zzz3171, zzz317200, zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, new_primPlusNat2(new_primPlusNat3(Succ(new_primPlusNat3(new_primPlusNat1(zzz317200), zzz317200)), Succ(zzz317200)), Succ(zzz317200)), h)
new_mkVBalBranch3MkVBalBranch244(zzz972, zzz973, zzz974, zzz975, zzz976, zzz977, zzz978, zzz979, zzz980, zzz981, zzz982, bc) → new_mkVBalBranch3MkVBalBranch128(zzz972, zzz973, zzz974, zzz975, zzz976, zzz977, zzz978, zzz979, zzz980, zzz981, zzz982, new_primPlusNat2(new_primMulNat0(zzz974), Succ(zzz974)), bc)
new_mkVBalBranch3MkVBalBranch235(zzz3170, zzz3171, Neg(Succ(zzz317200)), zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, Zero, h) → new_mkVBalBranch3MkVBalBranch238(zzz3170, zzz3171, Succ(zzz317200), zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, h)
new_mkVBalBranch3MkVBalBranch240(zzz958, zzz959, zzz960, zzz961, zzz962, zzz963, zzz964, zzz965, zzz966, zzz967, zzz968, ba) → new_mkVBalBranch3MkVBalBranch124(zzz958, zzz959, zzz960, zzz961, zzz962, zzz963, zzz964, zzz965, zzz966, zzz967, zzz968, new_primPlusNat2(new_primPlusNat3(Succ(new_primPlusNat3(new_primPlusNat1(zzz960), zzz960)), Succ(zzz960)), Succ(zzz960)), ba)
new_mkVBalBranch3MkVBalBranch241(zzz3170, zzz3171, Pos(Succ(zzz317200)), zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, Zero, h) → new_mkVBalBranch3MkVBalBranch243(zzz3170, zzz3171, Succ(zzz317200), zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, h)
new_mkVBalBranch3MkVBalBranch126(zzz3170, zzz3171, zzz317200, zzz3173, zzz3174, zzz330, zzz331, zzz333, zzz334, zzz31, Succ(zzz5350), h) → new_mkVBalBranch1(zzz31, zzz334, Branch(zzz3170, zzz3171, Neg(Succ(zzz317200)), zzz3173, zzz3174), h)
new_mkVBalBranch3MkVBalBranch241(zzz3170, zzz3171, Neg(Zero), zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, Succ(zzz4190), h) → new_mkVBalBranch1(zzz31, Branch(zzz330, zzz331, Neg(Succ(zzz33200)), zzz333, zzz334), zzz3173, h)
new_mkVBalBranch3MkVBalBranch123(zzz3170, zzz3171, zzz317200, zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, Zero, h) → new_mkVBalBranch3MkVBalBranch130(zzz3170, zzz3171, zzz317200, zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, h)
new_mkVBalBranch3MkVBalBranch124(zzz958, zzz959, zzz960, zzz961, zzz962, zzz963, zzz964, zzz965, zzz966, zzz967, zzz968, Succ(zzz10180), ba) → new_mkVBalBranch3MkVBalBranch125(zzz958, zzz959, zzz960, zzz961, zzz962, zzz963, zzz964, zzz965, zzz966, zzz967, zzz968, Succ(zzz10180), Succ(zzz965), ba)
new_mkVBalBranch3MkVBalBranch235(zzz3170, zzz3171, Pos(Succ(zzz317200)), zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, Zero, h) → new_mkVBalBranch3MkVBalBranch236(zzz3170, zzz3171, zzz317200, zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, Zero, Succ(zzz317200), h)
new_mkVBalBranch3MkVBalBranch239(zzz3170, zzz3171, Zero, zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, h) → new_mkVBalBranch1(zzz31, zzz334, Branch(zzz3170, zzz3171, Neg(Zero), zzz3173, zzz3174), h)
new_mkVBalBranch3MkVBalBranch235(zzz3170, zzz3171, Pos(Zero), zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, Zero, h) → new_mkVBalBranch1(zzz31, zzz334, Branch(zzz3170, zzz3171, Pos(Zero), zzz3173, zzz3174), h)
new_mkVBalBranch3MkVBalBranch242(zzz972, zzz973, zzz974, zzz975, zzz976, zzz977, zzz978, zzz979, zzz980, zzz981, zzz982, Zero, Zero, bc) → new_mkVBalBranch3MkVBalBranch244(zzz972, zzz973, zzz974, zzz975, zzz976, zzz977, zzz978, zzz979, zzz980, zzz981, zzz982, bc)
new_mkVBalBranch1(zzz31, Branch(zzz330, zzz331, Pos(Zero), zzz333, zzz334), Branch(zzz3170, zzz3171, Neg(Succ(zzz317200)), zzz3173, zzz3174), h) → new_mkVBalBranch3MkVBalBranch126(zzz3170, zzz3171, zzz317200, zzz3173, zzz3174, zzz330, zzz331, zzz333, zzz334, zzz31, new_primPlusNat2(new_primMulNat0(zzz317200), Succ(zzz317200)), h)
new_mkVBalBranch3MkVBalBranch130(zzz3170, zzz3171, zzz317200, zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, h) → new_mkVBalBranch1(zzz31, zzz334, Branch(zzz3170, zzz3171, Neg(Succ(zzz317200)), zzz3173, zzz3174), h)
new_mkVBalBranch3MkVBalBranch235(zzz3170, zzz3171, Neg(Zero), zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, Zero, h) → new_mkVBalBranch3MkVBalBranch239(zzz3170, zzz3171, Zero, zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, h)
new_mkVBalBranch1(zzz31, Branch(zzz330, zzz331, Neg(Zero), zzz333, zzz334), Branch(zzz3170, zzz3171, Pos(Succ(zzz317200)), zzz3173, zzz3174), h) → new_mkVBalBranch1(zzz31, Branch(zzz330, zzz331, Neg(Zero), zzz333, zzz334), zzz3173, h)
new_mkVBalBranch3MkVBalBranch235(zzz3170, zzz3171, Neg(Zero), zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, Succ(zzz4170), h) → new_mkVBalBranch1(zzz31, zzz334, Branch(zzz3170, zzz3171, Neg(Zero), zzz3173, zzz3174), h)
new_mkVBalBranch3MkVBalBranch236(zzz958, zzz959, zzz960, zzz961, zzz962, zzz963, zzz964, zzz965, zzz966, zzz967, zzz968, Zero, Zero, ba) → new_mkVBalBranch3MkVBalBranch240(zzz958, zzz959, zzz960, zzz961, zzz962, zzz963, zzz964, zzz965, zzz966, zzz967, zzz968, ba)

The TRS R consists of the following rules:

new_primPlusNat1(Zero) → Zero
new_primPlusNat1(Succ(zzz62000)) → Succ(Succ(new_primPlusNat1(zzz62000)))
new_primPlusNat3(zzz90, Succ(zzz910)) → Succ(Succ(new_primPlusNat2(zzz90, zzz910)))
new_primPlusNat3(zzz90, Zero) → Succ(zzz90)
new_primPlusNat2(Succ(zzz900), Succ(zzz9100)) → Succ(Succ(new_primPlusNat2(zzz900, zzz9100)))
new_primPlusNat2(Zero, Succ(zzz9100)) → Succ(zzz9100)
new_primPlusNat2(Zero, Zero) → Zero
new_primPlusNat2(Succ(zzz900), Zero) → Succ(zzz900)
new_primMulNat0(zzz6200) → new_primPlusNat3(Succ(new_primPlusNat3(new_primPlusNat1(zzz6200), zzz6200)), Succ(zzz6200))

The set Q consists of the following terms:

new_primPlusNat2(Zero, Succ(x0))
new_primMulNat0(x0)
new_primPlusNat3(x0, Succ(x1))
new_primPlusNat2(Succ(x0), Succ(x1))
new_primPlusNat3(x0, Zero)
new_primPlusNat1(Zero)
new_primPlusNat2(Zero, Zero)
new_primPlusNat1(Succ(x0))
new_primPlusNat2(Succ(x0), Zero)

We have to consider all minimal (P,Q,R)-chains.
By rewriting [15] the rule new_mkVBalBranch1(zzz31, Branch(zzz330, zzz331, Neg(Zero), zzz333, zzz334), Branch(zzz3170, zzz3171, Neg(Succ(zzz317200)), zzz3173, zzz3174), h) → new_mkVBalBranch3MkVBalBranch127(zzz3170, zzz3171, zzz317200, zzz3173, zzz3174, zzz330, zzz331, zzz333, zzz334, zzz31, new_primPlusNat2(new_primMulNat0(zzz317200), Succ(zzz317200)), h) at position [10,0] we obtained the following new rules:

new_mkVBalBranch1(zzz31, Branch(zzz330, zzz331, Neg(Zero), zzz333, zzz334), Branch(zzz3170, zzz3171, Neg(Succ(zzz317200)), zzz3173, zzz3174), h) → new_mkVBalBranch3MkVBalBranch127(zzz3170, zzz3171, zzz317200, zzz3173, zzz3174, zzz330, zzz331, zzz333, zzz334, zzz31, new_primPlusNat2(new_primPlusNat3(Succ(new_primPlusNat3(new_primPlusNat1(zzz317200), zzz317200)), Succ(zzz317200)), Succ(zzz317200)), 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
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                    ↳ DependencyGraphProof
                                      ↳ QDP
                                        ↳ Rewriting
                                          ↳ QDP
                                            ↳ Rewriting
                                              ↳ QDP
                                                ↳ Rewriting
                                                  ↳ QDP
                                                    ↳ Rewriting
                                                      ↳ QDP
                                                        ↳ Rewriting
                                                          ↳ QDP
                                                            ↳ Rewriting
                                                              ↳ QDP
                                                                ↳ Rewriting
                                                                  ↳ QDP
                                                                    ↳ Rewriting
                                                                      ↳ QDP
                                                                        ↳ Rewriting
                                                                          ↳ QDP
                                                                            ↳ Rewriting
                                                                              ↳ QDP
                                                                                ↳ UsableRulesProof
                                                                                  ↳ QDP
                                                                                    ↳ QReductionProof
                                                                                      ↳ QDP
                                                                                        ↳ Rewriting
                                                                                          ↳ QDP
                                                                                            ↳ Rewriting
                                                                                              ↳ QDP
                                                                                                ↳ Rewriting
                                                                                                  ↳ QDP
                                                                                                    ↳ Rewriting
                                                                                                      ↳ QDP
                                                                                                        ↳ Rewriting
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP

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

new_mkVBalBranch3MkVBalBranch129(zzz1851, zzz1852, zzz1853, zzz1854, zzz1855, zzz1856, zzz1857, zzz1858, zzz1859, zzz1860, zzz1861, Zero, Succ(zzz18630), bd) → new_mkVBalBranch1(zzz1861, zzz1860, Branch(zzz1851, zzz1852, Neg(Succ(zzz1853)), zzz1854, zzz1855), bd)
new_mkVBalBranch3MkVBalBranch127(zzz3170, zzz3171, zzz317200, zzz3173, zzz3174, zzz330, zzz331, zzz333, zzz334, zzz31, Succ(zzz5500), h) → new_mkVBalBranch1(zzz31, zzz334, Branch(zzz3170, zzz3171, Neg(Succ(zzz317200)), zzz3173, zzz3174), h)
new_mkVBalBranch3MkVBalBranch241(zzz3170, zzz3171, Pos(zzz31720), zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, Succ(zzz4190), h) → new_mkVBalBranch1(zzz31, Branch(zzz330, zzz331, Neg(Succ(zzz33200)), zzz333, zzz334), zzz3173, h)
new_mkVBalBranch3MkVBalBranch128(zzz972, zzz973, zzz974, zzz975, zzz976, zzz977, zzz978, zzz979, zzz980, zzz981, zzz982, Succ(zzz10190), bc) → new_mkVBalBranch3MkVBalBranch129(zzz972, zzz973, zzz974, zzz975, zzz976, zzz977, zzz978, zzz979, zzz980, zzz981, zzz982, Succ(zzz979), Succ(zzz10190), bc)
new_mkVBalBranch3MkVBalBranch242(zzz972, zzz973, zzz974, zzz975, zzz976, zzz977, zzz978, zzz979, zzz980, zzz981, zzz982, Succ(zzz9830), Zero, bc) → new_mkVBalBranch3MkVBalBranch128(zzz972, zzz973, zzz974, zzz975, zzz976, zzz977, zzz978, zzz979, zzz980, zzz981, zzz982, new_primPlusNat2(new_primPlusNat3(Succ(new_primPlusNat3(new_primPlusNat1(zzz974), zzz974)), Succ(zzz974)), Succ(zzz974)), bc)
new_mkVBalBranch3MkVBalBranch129(zzz1851, zzz1852, zzz1853, zzz1854, zzz1855, zzz1856, zzz1857, zzz1858, zzz1859, zzz1860, zzz1861, Succ(zzz18620), Succ(zzz18630), bd) → new_mkVBalBranch3MkVBalBranch129(zzz1851, zzz1852, zzz1853, zzz1854, zzz1855, zzz1856, zzz1857, zzz1858, zzz1859, zzz1860, zzz1861, zzz18620, zzz18630, bd)
new_mkVBalBranch3MkVBalBranch124(zzz958, zzz959, zzz960, zzz961, zzz962, zzz963, zzz964, zzz965, zzz966, zzz967, zzz968, Zero, ba) → new_mkVBalBranch3MkVBalBranch125(zzz958, zzz959, zzz960, zzz961, zzz962, zzz963, zzz964, zzz965, zzz966, zzz967, zzz968, Zero, Succ(zzz965), ba)
new_mkVBalBranch3MkVBalBranch242(zzz972, zzz973, zzz974, zzz975, zzz976, zzz977, zzz978, zzz979, zzz980, zzz981, zzz982, Succ(zzz9830), Succ(zzz9840), bc) → new_mkVBalBranch3MkVBalBranch242(zzz972, zzz973, zzz974, zzz975, zzz976, zzz977, zzz978, zzz979, zzz980, zzz981, zzz982, zzz9830, zzz9840, bc)
new_mkVBalBranch3MkVBalBranch235(zzz3170, zzz3171, Pos(Succ(zzz317200)), zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, Succ(zzz4170), h) → new_mkVBalBranch3MkVBalBranch236(zzz3170, zzz3171, zzz317200, zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, zzz4170, zzz317200, h)
new_mkVBalBranch1(zzz31, Branch(zzz330, zzz331, Pos(Succ(zzz33200)), zzz333, zzz334), Branch(zzz3170, zzz3171, zzz3172, zzz3173, zzz3174), h) → new_mkVBalBranch3MkVBalBranch235(zzz3170, zzz3171, zzz3172, zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, new_primPlusNat2(Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat3(new_primPlusNat1(zzz33200), zzz33200)), zzz33200))), Succ(zzz33200)), h)
new_mkVBalBranch3MkVBalBranch236(zzz958, zzz959, zzz960, zzz961, zzz962, zzz963, zzz964, zzz965, zzz966, zzz967, zzz968, Succ(zzz9690), Succ(zzz9700), ba) → new_mkVBalBranch3MkVBalBranch236(zzz958, zzz959, zzz960, zzz961, zzz962, zzz963, zzz964, zzz965, zzz966, zzz967, zzz968, zzz9690, zzz9700, ba)
new_mkVBalBranch3MkVBalBranch241(zzz3170, zzz3171, Neg(Succ(zzz317200)), zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, Succ(zzz4190), h) → new_mkVBalBranch3MkVBalBranch242(zzz3170, zzz3171, zzz317200, zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, zzz317200, zzz4190, h)
new_mkVBalBranch3MkVBalBranch235(zzz3170, zzz3171, Neg(Succ(zzz317200)), zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, Succ(zzz4170), h) → new_mkVBalBranch3MkVBalBranch123(zzz3170, zzz3171, zzz317200, zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, new_primPlusNat2(new_primPlusNat3(Succ(new_primPlusNat3(new_primPlusNat1(zzz317200), zzz317200)), Succ(zzz317200)), Succ(zzz317200)), h)
new_mkVBalBranch3MkVBalBranch241(zzz3170, zzz3171, Neg(Succ(zzz317200)), zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, Zero, h) → new_mkVBalBranch3MkVBalBranch242(zzz3170, zzz3171, zzz317200, zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, Succ(zzz317200), Zero, h)
new_mkVBalBranch1(zzz31, Branch(zzz330, zzz331, Pos(Zero), zzz333, zzz334), Branch(zzz3170, zzz3171, Pos(Succ(zzz317200)), zzz3173, zzz3174), h) → new_mkVBalBranch1(zzz31, Branch(zzz330, zzz331, Pos(Zero), zzz333, zzz334), zzz3173, h)
new_mkVBalBranch3MkVBalBranch243(zzz3170, zzz3171, zzz31720, zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, h) → new_mkVBalBranch1(zzz31, Branch(zzz330, zzz331, Neg(Succ(zzz33200)), zzz333, zzz334), zzz3173, h)
new_mkVBalBranch3MkVBalBranch237(zzz3170, zzz3171, zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, h) → new_mkVBalBranch1(zzz31, zzz334, Branch(zzz3170, zzz3171, Pos(Zero), zzz3173, zzz3174), h)
new_mkVBalBranch1(zzz31, Branch(zzz330, zzz331, Neg(Succ(zzz33200)), zzz333, zzz334), Branch(zzz3170, zzz3171, zzz3172, zzz3173, zzz3174), h) → new_mkVBalBranch3MkVBalBranch241(zzz3170, zzz3171, zzz3172, zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, new_primPlusNat2(new_primPlusNat3(Succ(new_primPlusNat3(new_primPlusNat1(zzz33200), zzz33200)), Succ(zzz33200)), Succ(zzz33200)), h)
new_mkVBalBranch3MkVBalBranch235(zzz3170, zzz3171, Pos(Zero), zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, Succ(zzz4170), h) → new_mkVBalBranch3MkVBalBranch237(zzz3170, zzz3171, zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, h)
new_mkVBalBranch3MkVBalBranch236(zzz958, zzz959, zzz960, zzz961, zzz962, zzz963, zzz964, zzz965, zzz966, zzz967, zzz968, Succ(zzz9690), Zero, ba) → new_mkVBalBranch3MkVBalBranch124(zzz958, zzz959, zzz960, zzz961, zzz962, zzz963, zzz964, zzz965, zzz966, zzz967, zzz968, new_primPlusNat2(new_primMulNat0(zzz960), Succ(zzz960)), ba)
new_mkVBalBranch3MkVBalBranch236(zzz958, zzz959, zzz960, zzz961, zzz962, zzz963, zzz964, zzz965, zzz966, zzz967, zzz968, Zero, Succ(zzz9700), ba) → new_mkVBalBranch1(zzz968, Branch(zzz963, zzz964, Pos(Succ(zzz965)), zzz966, zzz967), zzz961, ba)
new_mkVBalBranch3MkVBalBranch125(zzz1337, zzz1338, zzz1339, zzz1340, zzz1341, zzz1342, zzz1343, zzz1344, zzz1345, zzz1346, zzz1347, Succ(zzz13480), Succ(zzz13490), bb) → new_mkVBalBranch3MkVBalBranch125(zzz1337, zzz1338, zzz1339, zzz1340, zzz1341, zzz1342, zzz1343, zzz1344, zzz1345, zzz1346, zzz1347, zzz13480, zzz13490, bb)
new_mkVBalBranch3MkVBalBranch123(zzz3170, zzz3171, zzz317200, zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, Succ(zzz5620), h) → new_mkVBalBranch1(zzz31, zzz334, Branch(zzz3170, zzz3171, Neg(Succ(zzz317200)), zzz3173, zzz3174), h)
new_mkVBalBranch3MkVBalBranch125(zzz1337, zzz1338, zzz1339, zzz1340, zzz1341, zzz1342, zzz1343, zzz1344, zzz1345, zzz1346, zzz1347, Zero, Succ(zzz13490), bb) → new_mkVBalBranch1(zzz1347, zzz1346, Branch(zzz1337, zzz1338, Pos(Succ(zzz1339)), zzz1340, zzz1341), bb)
new_mkVBalBranch3MkVBalBranch242(zzz972, zzz973, zzz974, zzz975, zzz976, zzz977, zzz978, zzz979, zzz980, zzz981, zzz982, Zero, Succ(zzz9840), bc) → new_mkVBalBranch1(zzz982, Branch(zzz977, zzz978, Neg(Succ(zzz979)), zzz980, zzz981), zzz975, bc)
new_mkVBalBranch3MkVBalBranch238(zzz3170, zzz3171, Succ(zzz317200), zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, h) → new_mkVBalBranch3MkVBalBranch123(zzz3170, zzz3171, zzz317200, zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, new_primPlusNat2(new_primPlusNat3(Succ(new_primPlusNat3(new_primPlusNat1(zzz317200), zzz317200)), Succ(zzz317200)), Succ(zzz317200)), h)
new_mkVBalBranch3MkVBalBranch244(zzz972, zzz973, zzz974, zzz975, zzz976, zzz977, zzz978, zzz979, zzz980, zzz981, zzz982, bc) → new_mkVBalBranch3MkVBalBranch128(zzz972, zzz973, zzz974, zzz975, zzz976, zzz977, zzz978, zzz979, zzz980, zzz981, zzz982, new_primPlusNat2(new_primMulNat0(zzz974), Succ(zzz974)), bc)
new_mkVBalBranch1(zzz31, Branch(zzz330, zzz331, Neg(Zero), zzz333, zzz334), Branch(zzz3170, zzz3171, Neg(Succ(zzz317200)), zzz3173, zzz3174), h) → new_mkVBalBranch3MkVBalBranch127(zzz3170, zzz3171, zzz317200, zzz3173, zzz3174, zzz330, zzz331, zzz333, zzz334, zzz31, new_primPlusNat2(new_primPlusNat3(Succ(new_primPlusNat3(new_primPlusNat1(zzz317200), zzz317200)), Succ(zzz317200)), Succ(zzz317200)), h)
new_mkVBalBranch3MkVBalBranch235(zzz3170, zzz3171, Neg(Succ(zzz317200)), zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, Zero, h) → new_mkVBalBranch3MkVBalBranch238(zzz3170, zzz3171, Succ(zzz317200), zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, h)
new_mkVBalBranch3MkVBalBranch240(zzz958, zzz959, zzz960, zzz961, zzz962, zzz963, zzz964, zzz965, zzz966, zzz967, zzz968, ba) → new_mkVBalBranch3MkVBalBranch124(zzz958, zzz959, zzz960, zzz961, zzz962, zzz963, zzz964, zzz965, zzz966, zzz967, zzz968, new_primPlusNat2(new_primPlusNat3(Succ(new_primPlusNat3(new_primPlusNat1(zzz960), zzz960)), Succ(zzz960)), Succ(zzz960)), ba)
new_mkVBalBranch3MkVBalBranch241(zzz3170, zzz3171, Pos(Succ(zzz317200)), zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, Zero, h) → new_mkVBalBranch3MkVBalBranch243(zzz3170, zzz3171, Succ(zzz317200), zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, h)
new_mkVBalBranch3MkVBalBranch126(zzz3170, zzz3171, zzz317200, zzz3173, zzz3174, zzz330, zzz331, zzz333, zzz334, zzz31, Succ(zzz5350), h) → new_mkVBalBranch1(zzz31, zzz334, Branch(zzz3170, zzz3171, Neg(Succ(zzz317200)), zzz3173, zzz3174), h)
new_mkVBalBranch3MkVBalBranch123(zzz3170, zzz3171, zzz317200, zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, Zero, h) → new_mkVBalBranch3MkVBalBranch130(zzz3170, zzz3171, zzz317200, zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, h)
new_mkVBalBranch3MkVBalBranch241(zzz3170, zzz3171, Neg(Zero), zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, Succ(zzz4190), h) → new_mkVBalBranch1(zzz31, Branch(zzz330, zzz331, Neg(Succ(zzz33200)), zzz333, zzz334), zzz3173, h)
new_mkVBalBranch3MkVBalBranch124(zzz958, zzz959, zzz960, zzz961, zzz962, zzz963, zzz964, zzz965, zzz966, zzz967, zzz968, Succ(zzz10180), ba) → new_mkVBalBranch3MkVBalBranch125(zzz958, zzz959, zzz960, zzz961, zzz962, zzz963, zzz964, zzz965, zzz966, zzz967, zzz968, Succ(zzz10180), Succ(zzz965), ba)
new_mkVBalBranch3MkVBalBranch235(zzz3170, zzz3171, Pos(Succ(zzz317200)), zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, Zero, h) → new_mkVBalBranch3MkVBalBranch236(zzz3170, zzz3171, zzz317200, zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, Zero, Succ(zzz317200), h)
new_mkVBalBranch3MkVBalBranch239(zzz3170, zzz3171, Zero, zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, h) → new_mkVBalBranch1(zzz31, zzz334, Branch(zzz3170, zzz3171, Neg(Zero), zzz3173, zzz3174), h)
new_mkVBalBranch3MkVBalBranch235(zzz3170, zzz3171, Pos(Zero), zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, Zero, h) → new_mkVBalBranch1(zzz31, zzz334, Branch(zzz3170, zzz3171, Pos(Zero), zzz3173, zzz3174), h)
new_mkVBalBranch3MkVBalBranch242(zzz972, zzz973, zzz974, zzz975, zzz976, zzz977, zzz978, zzz979, zzz980, zzz981, zzz982, Zero, Zero, bc) → new_mkVBalBranch3MkVBalBranch244(zzz972, zzz973, zzz974, zzz975, zzz976, zzz977, zzz978, zzz979, zzz980, zzz981, zzz982, bc)
new_mkVBalBranch3MkVBalBranch130(zzz3170, zzz3171, zzz317200, zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, h) → new_mkVBalBranch1(zzz31, zzz334, Branch(zzz3170, zzz3171, Neg(Succ(zzz317200)), zzz3173, zzz3174), h)
new_mkVBalBranch1(zzz31, Branch(zzz330, zzz331, Pos(Zero), zzz333, zzz334), Branch(zzz3170, zzz3171, Neg(Succ(zzz317200)), zzz3173, zzz3174), h) → new_mkVBalBranch3MkVBalBranch126(zzz3170, zzz3171, zzz317200, zzz3173, zzz3174, zzz330, zzz331, zzz333, zzz334, zzz31, new_primPlusNat2(new_primMulNat0(zzz317200), Succ(zzz317200)), h)
new_mkVBalBranch1(zzz31, Branch(zzz330, zzz331, Neg(Zero), zzz333, zzz334), Branch(zzz3170, zzz3171, Pos(Succ(zzz317200)), zzz3173, zzz3174), h) → new_mkVBalBranch1(zzz31, Branch(zzz330, zzz331, Neg(Zero), zzz333, zzz334), zzz3173, h)
new_mkVBalBranch3MkVBalBranch235(zzz3170, zzz3171, Neg(Zero), zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, Zero, h) → new_mkVBalBranch3MkVBalBranch239(zzz3170, zzz3171, Zero, zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, h)
new_mkVBalBranch3MkVBalBranch235(zzz3170, zzz3171, Neg(Zero), zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, Succ(zzz4170), h) → new_mkVBalBranch1(zzz31, zzz334, Branch(zzz3170, zzz3171, Neg(Zero), zzz3173, zzz3174), h)
new_mkVBalBranch3MkVBalBranch236(zzz958, zzz959, zzz960, zzz961, zzz962, zzz963, zzz964, zzz965, zzz966, zzz967, zzz968, Zero, Zero, ba) → new_mkVBalBranch3MkVBalBranch240(zzz958, zzz959, zzz960, zzz961, zzz962, zzz963, zzz964, zzz965, zzz966, zzz967, zzz968, ba)

The TRS R consists of the following rules:

new_primPlusNat1(Zero) → Zero
new_primPlusNat1(Succ(zzz62000)) → Succ(Succ(new_primPlusNat1(zzz62000)))
new_primPlusNat3(zzz90, Succ(zzz910)) → Succ(Succ(new_primPlusNat2(zzz90, zzz910)))
new_primPlusNat3(zzz90, Zero) → Succ(zzz90)
new_primPlusNat2(Succ(zzz900), Succ(zzz9100)) → Succ(Succ(new_primPlusNat2(zzz900, zzz9100)))
new_primPlusNat2(Zero, Succ(zzz9100)) → Succ(zzz9100)
new_primPlusNat2(Zero, Zero) → Zero
new_primPlusNat2(Succ(zzz900), Zero) → Succ(zzz900)
new_primMulNat0(zzz6200) → new_primPlusNat3(Succ(new_primPlusNat3(new_primPlusNat1(zzz6200), zzz6200)), Succ(zzz6200))

The set Q consists of the following terms:

new_primPlusNat2(Zero, Succ(x0))
new_primMulNat0(x0)
new_primPlusNat3(x0, Succ(x1))
new_primPlusNat2(Succ(x0), Succ(x1))
new_primPlusNat3(x0, Zero)
new_primPlusNat1(Zero)
new_primPlusNat2(Zero, Zero)
new_primPlusNat1(Succ(x0))
new_primPlusNat2(Succ(x0), Zero)

We have to consider all minimal (P,Q,R)-chains.
By rewriting [15] the rule new_mkVBalBranch3MkVBalBranch235(zzz3170, zzz3171, Neg(Succ(zzz317200)), zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, Succ(zzz4170), h) → new_mkVBalBranch3MkVBalBranch123(zzz3170, zzz3171, zzz317200, zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, new_primPlusNat2(new_primPlusNat3(Succ(new_primPlusNat3(new_primPlusNat1(zzz317200), zzz317200)), Succ(zzz317200)), Succ(zzz317200)), h) at position [11,0] we obtained the following new rules:

new_mkVBalBranch3MkVBalBranch235(zzz3170, zzz3171, Neg(Succ(zzz317200)), zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, Succ(zzz4170), h) → new_mkVBalBranch3MkVBalBranch123(zzz3170, zzz3171, zzz317200, zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, new_primPlusNat2(Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat3(new_primPlusNat1(zzz317200), zzz317200)), zzz317200))), Succ(zzz317200)), 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
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                    ↳ DependencyGraphProof
                                      ↳ QDP
                                        ↳ Rewriting
                                          ↳ QDP
                                            ↳ Rewriting
                                              ↳ QDP
                                                ↳ Rewriting
                                                  ↳ QDP
                                                    ↳ Rewriting
                                                      ↳ QDP
                                                        ↳ Rewriting
                                                          ↳ QDP
                                                            ↳ Rewriting
                                                              ↳ QDP
                                                                ↳ Rewriting
                                                                  ↳ QDP
                                                                    ↳ Rewriting
                                                                      ↳ QDP
                                                                        ↳ Rewriting
                                                                          ↳ QDP
                                                                            ↳ Rewriting
                                                                              ↳ QDP
                                                                                ↳ UsableRulesProof
                                                                                  ↳ QDP
                                                                                    ↳ QReductionProof
                                                                                      ↳ QDP
                                                                                        ↳ Rewriting
                                                                                          ↳ QDP
                                                                                            ↳ Rewriting
                                                                                              ↳ QDP
                                                                                                ↳ Rewriting
                                                                                                  ↳ QDP
                                                                                                    ↳ Rewriting
                                                                                                      ↳ QDP
                                                                                                        ↳ Rewriting
                                                                                                          ↳ QDP
                                                                                                            ↳ Rewriting
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP

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

new_mkVBalBranch3MkVBalBranch129(zzz1851, zzz1852, zzz1853, zzz1854, zzz1855, zzz1856, zzz1857, zzz1858, zzz1859, zzz1860, zzz1861, Zero, Succ(zzz18630), bd) → new_mkVBalBranch1(zzz1861, zzz1860, Branch(zzz1851, zzz1852, Neg(Succ(zzz1853)), zzz1854, zzz1855), bd)
new_mkVBalBranch3MkVBalBranch128(zzz972, zzz973, zzz974, zzz975, zzz976, zzz977, zzz978, zzz979, zzz980, zzz981, zzz982, Succ(zzz10190), bc) → new_mkVBalBranch3MkVBalBranch129(zzz972, zzz973, zzz974, zzz975, zzz976, zzz977, zzz978, zzz979, zzz980, zzz981, zzz982, Succ(zzz979), Succ(zzz10190), bc)
new_mkVBalBranch3MkVBalBranch241(zzz3170, zzz3171, Pos(zzz31720), zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, Succ(zzz4190), h) → new_mkVBalBranch1(zzz31, Branch(zzz330, zzz331, Neg(Succ(zzz33200)), zzz333, zzz334), zzz3173, h)
new_mkVBalBranch3MkVBalBranch127(zzz3170, zzz3171, zzz317200, zzz3173, zzz3174, zzz330, zzz331, zzz333, zzz334, zzz31, Succ(zzz5500), h) → new_mkVBalBranch1(zzz31, zzz334, Branch(zzz3170, zzz3171, Neg(Succ(zzz317200)), zzz3173, zzz3174), h)
new_mkVBalBranch3MkVBalBranch242(zzz972, zzz973, zzz974, zzz975, zzz976, zzz977, zzz978, zzz979, zzz980, zzz981, zzz982, Succ(zzz9830), Zero, bc) → new_mkVBalBranch3MkVBalBranch128(zzz972, zzz973, zzz974, zzz975, zzz976, zzz977, zzz978, zzz979, zzz980, zzz981, zzz982, new_primPlusNat2(new_primPlusNat3(Succ(new_primPlusNat3(new_primPlusNat1(zzz974), zzz974)), Succ(zzz974)), Succ(zzz974)), bc)
new_mkVBalBranch3MkVBalBranch129(zzz1851, zzz1852, zzz1853, zzz1854, zzz1855, zzz1856, zzz1857, zzz1858, zzz1859, zzz1860, zzz1861, Succ(zzz18620), Succ(zzz18630), bd) → new_mkVBalBranch3MkVBalBranch129(zzz1851, zzz1852, zzz1853, zzz1854, zzz1855, zzz1856, zzz1857, zzz1858, zzz1859, zzz1860, zzz1861, zzz18620, zzz18630, bd)
new_mkVBalBranch3MkVBalBranch124(zzz958, zzz959, zzz960, zzz961, zzz962, zzz963, zzz964, zzz965, zzz966, zzz967, zzz968, Zero, ba) → new_mkVBalBranch3MkVBalBranch125(zzz958, zzz959, zzz960, zzz961, zzz962, zzz963, zzz964, zzz965, zzz966, zzz967, zzz968, Zero, Succ(zzz965), ba)
new_mkVBalBranch3MkVBalBranch235(zzz3170, zzz3171, Pos(Succ(zzz317200)), zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, Succ(zzz4170), h) → new_mkVBalBranch3MkVBalBranch236(zzz3170, zzz3171, zzz317200, zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, zzz4170, zzz317200, h)
new_mkVBalBranch3MkVBalBranch242(zzz972, zzz973, zzz974, zzz975, zzz976, zzz977, zzz978, zzz979, zzz980, zzz981, zzz982, Succ(zzz9830), Succ(zzz9840), bc) → new_mkVBalBranch3MkVBalBranch242(zzz972, zzz973, zzz974, zzz975, zzz976, zzz977, zzz978, zzz979, zzz980, zzz981, zzz982, zzz9830, zzz9840, bc)
new_mkVBalBranch3MkVBalBranch236(zzz958, zzz959, zzz960, zzz961, zzz962, zzz963, zzz964, zzz965, zzz966, zzz967, zzz968, Succ(zzz9690), Succ(zzz9700), ba) → new_mkVBalBranch3MkVBalBranch236(zzz958, zzz959, zzz960, zzz961, zzz962, zzz963, zzz964, zzz965, zzz966, zzz967, zzz968, zzz9690, zzz9700, ba)
new_mkVBalBranch1(zzz31, Branch(zzz330, zzz331, Pos(Succ(zzz33200)), zzz333, zzz334), Branch(zzz3170, zzz3171, zzz3172, zzz3173, zzz3174), h) → new_mkVBalBranch3MkVBalBranch235(zzz3170, zzz3171, zzz3172, zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, new_primPlusNat2(Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat3(new_primPlusNat1(zzz33200), zzz33200)), zzz33200))), Succ(zzz33200)), h)
new_mkVBalBranch3MkVBalBranch241(zzz3170, zzz3171, Neg(Succ(zzz317200)), zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, Succ(zzz4190), h) → new_mkVBalBranch3MkVBalBranch242(zzz3170, zzz3171, zzz317200, zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, zzz317200, zzz4190, h)
new_mkVBalBranch3MkVBalBranch241(zzz3170, zzz3171, Neg(Succ(zzz317200)), zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, Zero, h) → new_mkVBalBranch3MkVBalBranch242(zzz3170, zzz3171, zzz317200, zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, Succ(zzz317200), Zero, h)
new_mkVBalBranch1(zzz31, Branch(zzz330, zzz331, Pos(Zero), zzz333, zzz334), Branch(zzz3170, zzz3171, Pos(Succ(zzz317200)), zzz3173, zzz3174), h) → new_mkVBalBranch1(zzz31, Branch(zzz330, zzz331, Pos(Zero), zzz333, zzz334), zzz3173, h)
new_mkVBalBranch3MkVBalBranch235(zzz3170, zzz3171, Neg(Succ(zzz317200)), zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, Succ(zzz4170), h) → new_mkVBalBranch3MkVBalBranch123(zzz3170, zzz3171, zzz317200, zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, new_primPlusNat2(Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat3(new_primPlusNat1(zzz317200), zzz317200)), zzz317200))), Succ(zzz317200)), h)
new_mkVBalBranch3MkVBalBranch237(zzz3170, zzz3171, zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, h) → new_mkVBalBranch1(zzz31, zzz334, Branch(zzz3170, zzz3171, Pos(Zero), zzz3173, zzz3174), h)
new_mkVBalBranch3MkVBalBranch243(zzz3170, zzz3171, zzz31720, zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, h) → new_mkVBalBranch1(zzz31, Branch(zzz330, zzz331, Neg(Succ(zzz33200)), zzz333, zzz334), zzz3173, h)
new_mkVBalBranch1(zzz31, Branch(zzz330, zzz331, Neg(Succ(zzz33200)), zzz333, zzz334), Branch(zzz3170, zzz3171, zzz3172, zzz3173, zzz3174), h) → new_mkVBalBranch3MkVBalBranch241(zzz3170, zzz3171, zzz3172, zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, new_primPlusNat2(new_primPlusNat3(Succ(new_primPlusNat3(new_primPlusNat1(zzz33200), zzz33200)), Succ(zzz33200)), Succ(zzz33200)), h)
new_mkVBalBranch3MkVBalBranch235(zzz3170, zzz3171, Pos(Zero), zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, Succ(zzz4170), h) → new_mkVBalBranch3MkVBalBranch237(zzz3170, zzz3171, zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, h)
new_mkVBalBranch3MkVBalBranch236(zzz958, zzz959, zzz960, zzz961, zzz962, zzz963, zzz964, zzz965, zzz966, zzz967, zzz968, Zero, Succ(zzz9700), ba) → new_mkVBalBranch1(zzz968, Branch(zzz963, zzz964, Pos(Succ(zzz965)), zzz966, zzz967), zzz961, ba)
new_mkVBalBranch3MkVBalBranch236(zzz958, zzz959, zzz960, zzz961, zzz962, zzz963, zzz964, zzz965, zzz966, zzz967, zzz968, Succ(zzz9690), Zero, ba) → new_mkVBalBranch3MkVBalBranch124(zzz958, zzz959, zzz960, zzz961, zzz962, zzz963, zzz964, zzz965, zzz966, zzz967, zzz968, new_primPlusNat2(new_primMulNat0(zzz960), Succ(zzz960)), ba)
new_mkVBalBranch3MkVBalBranch125(zzz1337, zzz1338, zzz1339, zzz1340, zzz1341, zzz1342, zzz1343, zzz1344, zzz1345, zzz1346, zzz1347, Succ(zzz13480), Succ(zzz13490), bb) → new_mkVBalBranch3MkVBalBranch125(zzz1337, zzz1338, zzz1339, zzz1340, zzz1341, zzz1342, zzz1343, zzz1344, zzz1345, zzz1346, zzz1347, zzz13480, zzz13490, bb)
new_mkVBalBranch3MkVBalBranch123(zzz3170, zzz3171, zzz317200, zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, Succ(zzz5620), h) → new_mkVBalBranch1(zzz31, zzz334, Branch(zzz3170, zzz3171, Neg(Succ(zzz317200)), zzz3173, zzz3174), h)
new_mkVBalBranch3MkVBalBranch125(zzz1337, zzz1338, zzz1339, zzz1340, zzz1341, zzz1342, zzz1343, zzz1344, zzz1345, zzz1346, zzz1347, Zero, Succ(zzz13490), bb) → new_mkVBalBranch1(zzz1347, zzz1346, Branch(zzz1337, zzz1338, Pos(Succ(zzz1339)), zzz1340, zzz1341), bb)
new_mkVBalBranch3MkVBalBranch242(zzz972, zzz973, zzz974, zzz975, zzz976, zzz977, zzz978, zzz979, zzz980, zzz981, zzz982, Zero, Succ(zzz9840), bc) → new_mkVBalBranch1(zzz982, Branch(zzz977, zzz978, Neg(Succ(zzz979)), zzz980, zzz981), zzz975, bc)
new_mkVBalBranch3MkVBalBranch238(zzz3170, zzz3171, Succ(zzz317200), zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, h) → new_mkVBalBranch3MkVBalBranch123(zzz3170, zzz3171, zzz317200, zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, new_primPlusNat2(new_primPlusNat3(Succ(new_primPlusNat3(new_primPlusNat1(zzz317200), zzz317200)), Succ(zzz317200)), Succ(zzz317200)), h)
new_mkVBalBranch3MkVBalBranch244(zzz972, zzz973, zzz974, zzz975, zzz976, zzz977, zzz978, zzz979, zzz980, zzz981, zzz982, bc) → new_mkVBalBranch3MkVBalBranch128(zzz972, zzz973, zzz974, zzz975, zzz976, zzz977, zzz978, zzz979, zzz980, zzz981, zzz982, new_primPlusNat2(new_primMulNat0(zzz974), Succ(zzz974)), bc)
new_mkVBalBranch1(zzz31, Branch(zzz330, zzz331, Neg(Zero), zzz333, zzz334), Branch(zzz3170, zzz3171, Neg(Succ(zzz317200)), zzz3173, zzz3174), h) → new_mkVBalBranch3MkVBalBranch127(zzz3170, zzz3171, zzz317200, zzz3173, zzz3174, zzz330, zzz331, zzz333, zzz334, zzz31, new_primPlusNat2(new_primPlusNat3(Succ(new_primPlusNat3(new_primPlusNat1(zzz317200), zzz317200)), Succ(zzz317200)), Succ(zzz317200)), h)
new_mkVBalBranch3MkVBalBranch235(zzz3170, zzz3171, Neg(Succ(zzz317200)), zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, Zero, h) → new_mkVBalBranch3MkVBalBranch238(zzz3170, zzz3171, Succ(zzz317200), zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, h)
new_mkVBalBranch3MkVBalBranch240(zzz958, zzz959, zzz960, zzz961, zzz962, zzz963, zzz964, zzz965, zzz966, zzz967, zzz968, ba) → new_mkVBalBranch3MkVBalBranch124(zzz958, zzz959, zzz960, zzz961, zzz962, zzz963, zzz964, zzz965, zzz966, zzz967, zzz968, new_primPlusNat2(new_primPlusNat3(Succ(new_primPlusNat3(new_primPlusNat1(zzz960), zzz960)), Succ(zzz960)), Succ(zzz960)), ba)
new_mkVBalBranch3MkVBalBranch241(zzz3170, zzz3171, Pos(Succ(zzz317200)), zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, Zero, h) → new_mkVBalBranch3MkVBalBranch243(zzz3170, zzz3171, Succ(zzz317200), zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, h)
new_mkVBalBranch3MkVBalBranch126(zzz3170, zzz3171, zzz317200, zzz3173, zzz3174, zzz330, zzz331, zzz333, zzz334, zzz31, Succ(zzz5350), h) → new_mkVBalBranch1(zzz31, zzz334, Branch(zzz3170, zzz3171, Neg(Succ(zzz317200)), zzz3173, zzz3174), h)
new_mkVBalBranch3MkVBalBranch241(zzz3170, zzz3171, Neg(Zero), zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, Succ(zzz4190), h) → new_mkVBalBranch1(zzz31, Branch(zzz330, zzz331, Neg(Succ(zzz33200)), zzz333, zzz334), zzz3173, h)
new_mkVBalBranch3MkVBalBranch123(zzz3170, zzz3171, zzz317200, zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, Zero, h) → new_mkVBalBranch3MkVBalBranch130(zzz3170, zzz3171, zzz317200, zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, h)
new_mkVBalBranch3MkVBalBranch124(zzz958, zzz959, zzz960, zzz961, zzz962, zzz963, zzz964, zzz965, zzz966, zzz967, zzz968, Succ(zzz10180), ba) → new_mkVBalBranch3MkVBalBranch125(zzz958, zzz959, zzz960, zzz961, zzz962, zzz963, zzz964, zzz965, zzz966, zzz967, zzz968, Succ(zzz10180), Succ(zzz965), ba)
new_mkVBalBranch3MkVBalBranch235(zzz3170, zzz3171, Pos(Succ(zzz317200)), zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, Zero, h) → new_mkVBalBranch3MkVBalBranch236(zzz3170, zzz3171, zzz317200, zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, Zero, Succ(zzz317200), h)
new_mkVBalBranch3MkVBalBranch239(zzz3170, zzz3171, Zero, zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, h) → new_mkVBalBranch1(zzz31, zzz334, Branch(zzz3170, zzz3171, Neg(Zero), zzz3173, zzz3174), h)
new_mkVBalBranch3MkVBalBranch235(zzz3170, zzz3171, Pos(Zero), zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, Zero, h) → new_mkVBalBranch1(zzz31, zzz334, Branch(zzz3170, zzz3171, Pos(Zero), zzz3173, zzz3174), h)
new_mkVBalBranch3MkVBalBranch242(zzz972, zzz973, zzz974, zzz975, zzz976, zzz977, zzz978, zzz979, zzz980, zzz981, zzz982, Zero, Zero, bc) → new_mkVBalBranch3MkVBalBranch244(zzz972, zzz973, zzz974, zzz975, zzz976, zzz977, zzz978, zzz979, zzz980, zzz981, zzz982, bc)
new_mkVBalBranch1(zzz31, Branch(zzz330, zzz331, Pos(Zero), zzz333, zzz334), Branch(zzz3170, zzz3171, Neg(Succ(zzz317200)), zzz3173, zzz3174), h) → new_mkVBalBranch3MkVBalBranch126(zzz3170, zzz3171, zzz317200, zzz3173, zzz3174, zzz330, zzz331, zzz333, zzz334, zzz31, new_primPlusNat2(new_primMulNat0(zzz317200), Succ(zzz317200)), h)
new_mkVBalBranch3MkVBalBranch130(zzz3170, zzz3171, zzz317200, zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, h) → new_mkVBalBranch1(zzz31, zzz334, Branch(zzz3170, zzz3171, Neg(Succ(zzz317200)), zzz3173, zzz3174), h)
new_mkVBalBranch3MkVBalBranch235(zzz3170, zzz3171, Neg(Zero), zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, Zero, h) → new_mkVBalBranch3MkVBalBranch239(zzz3170, zzz3171, Zero, zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, h)
new_mkVBalBranch1(zzz31, Branch(zzz330, zzz331, Neg(Zero), zzz333, zzz334), Branch(zzz3170, zzz3171, Pos(Succ(zzz317200)), zzz3173, zzz3174), h) → new_mkVBalBranch1(zzz31, Branch(zzz330, zzz331, Neg(Zero), zzz333, zzz334), zzz3173, h)
new_mkVBalBranch3MkVBalBranch235(zzz3170, zzz3171, Neg(Zero), zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, Succ(zzz4170), h) → new_mkVBalBranch1(zzz31, zzz334, Branch(zzz3170, zzz3171, Neg(Zero), zzz3173, zzz3174), h)
new_mkVBalBranch3MkVBalBranch236(zzz958, zzz959, zzz960, zzz961, zzz962, zzz963, zzz964, zzz965, zzz966, zzz967, zzz968, Zero, Zero, ba) → new_mkVBalBranch3MkVBalBranch240(zzz958, zzz959, zzz960, zzz961, zzz962, zzz963, zzz964, zzz965, zzz966, zzz967, zzz968, ba)

The TRS R consists of the following rules:

new_primPlusNat1(Zero) → Zero
new_primPlusNat1(Succ(zzz62000)) → Succ(Succ(new_primPlusNat1(zzz62000)))
new_primPlusNat3(zzz90, Succ(zzz910)) → Succ(Succ(new_primPlusNat2(zzz90, zzz910)))
new_primPlusNat3(zzz90, Zero) → Succ(zzz90)
new_primPlusNat2(Succ(zzz900), Succ(zzz9100)) → Succ(Succ(new_primPlusNat2(zzz900, zzz9100)))
new_primPlusNat2(Zero, Succ(zzz9100)) → Succ(zzz9100)
new_primPlusNat2(Zero, Zero) → Zero
new_primPlusNat2(Succ(zzz900), Zero) → Succ(zzz900)
new_primMulNat0(zzz6200) → new_primPlusNat3(Succ(new_primPlusNat3(new_primPlusNat1(zzz6200), zzz6200)), Succ(zzz6200))

The set Q consists of the following terms:

new_primPlusNat2(Zero, Succ(x0))
new_primMulNat0(x0)
new_primPlusNat3(x0, Succ(x1))
new_primPlusNat2(Succ(x0), Succ(x1))
new_primPlusNat3(x0, Zero)
new_primPlusNat1(Zero)
new_primPlusNat2(Zero, Zero)
new_primPlusNat1(Succ(x0))
new_primPlusNat2(Succ(x0), Zero)

We have to consider all minimal (P,Q,R)-chains.
By rewriting [15] the rule new_mkVBalBranch1(zzz31, Branch(zzz330, zzz331, Neg(Succ(zzz33200)), zzz333, zzz334), Branch(zzz3170, zzz3171, zzz3172, zzz3173, zzz3174), h) → new_mkVBalBranch3MkVBalBranch241(zzz3170, zzz3171, zzz3172, zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, new_primPlusNat2(new_primPlusNat3(Succ(new_primPlusNat3(new_primPlusNat1(zzz33200), zzz33200)), Succ(zzz33200)), Succ(zzz33200)), h) at position [11,0] we obtained the following new rules:

new_mkVBalBranch1(zzz31, Branch(zzz330, zzz331, Neg(Succ(zzz33200)), zzz333, zzz334), Branch(zzz3170, zzz3171, zzz3172, zzz3173, zzz3174), h) → new_mkVBalBranch3MkVBalBranch241(zzz3170, zzz3171, zzz3172, zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, new_primPlusNat2(Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat3(new_primPlusNat1(zzz33200), zzz33200)), zzz33200))), Succ(zzz33200)), 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
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                    ↳ DependencyGraphProof
                                      ↳ QDP
                                        ↳ Rewriting
                                          ↳ QDP
                                            ↳ Rewriting
                                              ↳ QDP
                                                ↳ Rewriting
                                                  ↳ QDP
                                                    ↳ Rewriting
                                                      ↳ QDP
                                                        ↳ Rewriting
                                                          ↳ QDP
                                                            ↳ Rewriting
                                                              ↳ QDP
                                                                ↳ Rewriting
                                                                  ↳ QDP
                                                                    ↳ Rewriting
                                                                      ↳ QDP
                                                                        ↳ Rewriting
                                                                          ↳ QDP
                                                                            ↳ Rewriting
                                                                              ↳ QDP
                                                                                ↳ UsableRulesProof
                                                                                  ↳ QDP
                                                                                    ↳ QReductionProof
                                                                                      ↳ QDP
                                                                                        ↳ Rewriting
                                                                                          ↳ QDP
                                                                                            ↳ Rewriting
                                                                                              ↳ QDP
                                                                                                ↳ Rewriting
                                                                                                  ↳ QDP
                                                                                                    ↳ Rewriting
                                                                                                      ↳ QDP
                                                                                                        ↳ Rewriting
                                                                                                          ↳ QDP
                                                                                                            ↳ Rewriting
                                                                                                              ↳ QDP
                                                                                                                ↳ Rewriting
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP

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

new_mkVBalBranch3MkVBalBranch129(zzz1851, zzz1852, zzz1853, zzz1854, zzz1855, zzz1856, zzz1857, zzz1858, zzz1859, zzz1860, zzz1861, Zero, Succ(zzz18630), bd) → new_mkVBalBranch1(zzz1861, zzz1860, Branch(zzz1851, zzz1852, Neg(Succ(zzz1853)), zzz1854, zzz1855), bd)
new_mkVBalBranch3MkVBalBranch127(zzz3170, zzz3171, zzz317200, zzz3173, zzz3174, zzz330, zzz331, zzz333, zzz334, zzz31, Succ(zzz5500), h) → new_mkVBalBranch1(zzz31, zzz334, Branch(zzz3170, zzz3171, Neg(Succ(zzz317200)), zzz3173, zzz3174), h)
new_mkVBalBranch3MkVBalBranch241(zzz3170, zzz3171, Pos(zzz31720), zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, Succ(zzz4190), h) → new_mkVBalBranch1(zzz31, Branch(zzz330, zzz331, Neg(Succ(zzz33200)), zzz333, zzz334), zzz3173, h)
new_mkVBalBranch3MkVBalBranch128(zzz972, zzz973, zzz974, zzz975, zzz976, zzz977, zzz978, zzz979, zzz980, zzz981, zzz982, Succ(zzz10190), bc) → new_mkVBalBranch3MkVBalBranch129(zzz972, zzz973, zzz974, zzz975, zzz976, zzz977, zzz978, zzz979, zzz980, zzz981, zzz982, Succ(zzz979), Succ(zzz10190), bc)
new_mkVBalBranch3MkVBalBranch242(zzz972, zzz973, zzz974, zzz975, zzz976, zzz977, zzz978, zzz979, zzz980, zzz981, zzz982, Succ(zzz9830), Zero, bc) → new_mkVBalBranch3MkVBalBranch128(zzz972, zzz973, zzz974, zzz975, zzz976, zzz977, zzz978, zzz979, zzz980, zzz981, zzz982, new_primPlusNat2(new_primPlusNat3(Succ(new_primPlusNat3(new_primPlusNat1(zzz974), zzz974)), Succ(zzz974)), Succ(zzz974)), bc)
new_mkVBalBranch3MkVBalBranch129(zzz1851, zzz1852, zzz1853, zzz1854, zzz1855, zzz1856, zzz1857, zzz1858, zzz1859, zzz1860, zzz1861, Succ(zzz18620), Succ(zzz18630), bd) → new_mkVBalBranch3MkVBalBranch129(zzz1851, zzz1852, zzz1853, zzz1854, zzz1855, zzz1856, zzz1857, zzz1858, zzz1859, zzz1860, zzz1861, zzz18620, zzz18630, bd)
new_mkVBalBranch3MkVBalBranch124(zzz958, zzz959, zzz960, zzz961, zzz962, zzz963, zzz964, zzz965, zzz966, zzz967, zzz968, Zero, ba) → new_mkVBalBranch3MkVBalBranch125(zzz958, zzz959, zzz960, zzz961, zzz962, zzz963, zzz964, zzz965, zzz966, zzz967, zzz968, Zero, Succ(zzz965), ba)
new_mkVBalBranch3MkVBalBranch242(zzz972, zzz973, zzz974, zzz975, zzz976, zzz977, zzz978, zzz979, zzz980, zzz981, zzz982, Succ(zzz9830), Succ(zzz9840), bc) → new_mkVBalBranch3MkVBalBranch242(zzz972, zzz973, zzz974, zzz975, zzz976, zzz977, zzz978, zzz979, zzz980, zzz981, zzz982, zzz9830, zzz9840, bc)
new_mkVBalBranch3MkVBalBranch235(zzz3170, zzz3171, Pos(Succ(zzz317200)), zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, Succ(zzz4170), h) → new_mkVBalBranch3MkVBalBranch236(zzz3170, zzz3171, zzz317200, zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, zzz4170, zzz317200, h)
new_mkVBalBranch1(zzz31, Branch(zzz330, zzz331, Pos(Succ(zzz33200)), zzz333, zzz334), Branch(zzz3170, zzz3171, zzz3172, zzz3173, zzz3174), h) → new_mkVBalBranch3MkVBalBranch235(zzz3170, zzz3171, zzz3172, zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, new_primPlusNat2(Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat3(new_primPlusNat1(zzz33200), zzz33200)), zzz33200))), Succ(zzz33200)), h)
new_mkVBalBranch3MkVBalBranch236(zzz958, zzz959, zzz960, zzz961, zzz962, zzz963, zzz964, zzz965, zzz966, zzz967, zzz968, Succ(zzz9690), Succ(zzz9700), ba) → new_mkVBalBranch3MkVBalBranch236(zzz958, zzz959, zzz960, zzz961, zzz962, zzz963, zzz964, zzz965, zzz966, zzz967, zzz968, zzz9690, zzz9700, ba)
new_mkVBalBranch3MkVBalBranch241(zzz3170, zzz3171, Neg(Succ(zzz317200)), zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, Succ(zzz4190), h) → new_mkVBalBranch3MkVBalBranch242(zzz3170, zzz3171, zzz317200, zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, zzz317200, zzz4190, h)
new_mkVBalBranch3MkVBalBranch241(zzz3170, zzz3171, Neg(Succ(zzz317200)), zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, Zero, h) → new_mkVBalBranch3MkVBalBranch242(zzz3170, zzz3171, zzz317200, zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, Succ(zzz317200), Zero, h)
new_mkVBalBranch1(zzz31, Branch(zzz330, zzz331, Pos(Zero), zzz333, zzz334), Branch(zzz3170, zzz3171, Pos(Succ(zzz317200)), zzz3173, zzz3174), h) → new_mkVBalBranch1(zzz31, Branch(zzz330, zzz331, Pos(Zero), zzz333, zzz334), zzz3173, h)
new_mkVBalBranch3MkVBalBranch243(zzz3170, zzz3171, zzz31720, zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, h) → new_mkVBalBranch1(zzz31, Branch(zzz330, zzz331, Neg(Succ(zzz33200)), zzz333, zzz334), zzz3173, h)
new_mkVBalBranch3MkVBalBranch237(zzz3170, zzz3171, zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, h) → new_mkVBalBranch1(zzz31, zzz334, Branch(zzz3170, zzz3171, Pos(Zero), zzz3173, zzz3174), h)
new_mkVBalBranch3MkVBalBranch235(zzz3170, zzz3171, Neg(Succ(zzz317200)), zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, Succ(zzz4170), h) → new_mkVBalBranch3MkVBalBranch123(zzz3170, zzz3171, zzz317200, zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, new_primPlusNat2(Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat3(new_primPlusNat1(zzz317200), zzz317200)), zzz317200))), Succ(zzz317200)), h)
new_mkVBalBranch3MkVBalBranch235(zzz3170, zzz3171, Pos(Zero), zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, Succ(zzz4170), h) → new_mkVBalBranch3MkVBalBranch237(zzz3170, zzz3171, zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, h)
new_mkVBalBranch3MkVBalBranch236(zzz958, zzz959, zzz960, zzz961, zzz962, zzz963, zzz964, zzz965, zzz966, zzz967, zzz968, Succ(zzz9690), Zero, ba) → new_mkVBalBranch3MkVBalBranch124(zzz958, zzz959, zzz960, zzz961, zzz962, zzz963, zzz964, zzz965, zzz966, zzz967, zzz968, new_primPlusNat2(new_primMulNat0(zzz960), Succ(zzz960)), ba)
new_mkVBalBranch3MkVBalBranch236(zzz958, zzz959, zzz960, zzz961, zzz962, zzz963, zzz964, zzz965, zzz966, zzz967, zzz968, Zero, Succ(zzz9700), ba) → new_mkVBalBranch1(zzz968, Branch(zzz963, zzz964, Pos(Succ(zzz965)), zzz966, zzz967), zzz961, ba)
new_mkVBalBranch3MkVBalBranch125(zzz1337, zzz1338, zzz1339, zzz1340, zzz1341, zzz1342, zzz1343, zzz1344, zzz1345, zzz1346, zzz1347, Succ(zzz13480), Succ(zzz13490), bb) → new_mkVBalBranch3MkVBalBranch125(zzz1337, zzz1338, zzz1339, zzz1340, zzz1341, zzz1342, zzz1343, zzz1344, zzz1345, zzz1346, zzz1347, zzz13480, zzz13490, bb)
new_mkVBalBranch3MkVBalBranch123(zzz3170, zzz3171, zzz317200, zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, Succ(zzz5620), h) → new_mkVBalBranch1(zzz31, zzz334, Branch(zzz3170, zzz3171, Neg(Succ(zzz317200)), zzz3173, zzz3174), h)
new_mkVBalBranch3MkVBalBranch125(zzz1337, zzz1338, zzz1339, zzz1340, zzz1341, zzz1342, zzz1343, zzz1344, zzz1345, zzz1346, zzz1347, Zero, Succ(zzz13490), bb) → new_mkVBalBranch1(zzz1347, zzz1346, Branch(zzz1337, zzz1338, Pos(Succ(zzz1339)), zzz1340, zzz1341), bb)
new_mkVBalBranch3MkVBalBranch242(zzz972, zzz973, zzz974, zzz975, zzz976, zzz977, zzz978, zzz979, zzz980, zzz981, zzz982, Zero, Succ(zzz9840), bc) → new_mkVBalBranch1(zzz982, Branch(zzz977, zzz978, Neg(Succ(zzz979)), zzz980, zzz981), zzz975, bc)
new_mkVBalBranch3MkVBalBranch238(zzz3170, zzz3171, Succ(zzz317200), zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, h) → new_mkVBalBranch3MkVBalBranch123(zzz3170, zzz3171, zzz317200, zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, new_primPlusNat2(new_primPlusNat3(Succ(new_primPlusNat3(new_primPlusNat1(zzz317200), zzz317200)), Succ(zzz317200)), Succ(zzz317200)), h)
new_mkVBalBranch3MkVBalBranch244(zzz972, zzz973, zzz974, zzz975, zzz976, zzz977, zzz978, zzz979, zzz980, zzz981, zzz982, bc) → new_mkVBalBranch3MkVBalBranch128(zzz972, zzz973, zzz974, zzz975, zzz976, zzz977, zzz978, zzz979, zzz980, zzz981, zzz982, new_primPlusNat2(new_primMulNat0(zzz974), Succ(zzz974)), bc)
new_mkVBalBranch1(zzz31, Branch(zzz330, zzz331, Neg(Zero), zzz333, zzz334), Branch(zzz3170, zzz3171, Neg(Succ(zzz317200)), zzz3173, zzz3174), h) → new_mkVBalBranch3MkVBalBranch127(zzz3170, zzz3171, zzz317200, zzz3173, zzz3174, zzz330, zzz331, zzz333, zzz334, zzz31, new_primPlusNat2(new_primPlusNat3(Succ(new_primPlusNat3(new_primPlusNat1(zzz317200), zzz317200)), Succ(zzz317200)), Succ(zzz317200)), h)
new_mkVBalBranch3MkVBalBranch235(zzz3170, zzz3171, Neg(Succ(zzz317200)), zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, Zero, h) → new_mkVBalBranch3MkVBalBranch238(zzz3170, zzz3171, Succ(zzz317200), zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, h)
new_mkVBalBranch3MkVBalBranch240(zzz958, zzz959, zzz960, zzz961, zzz962, zzz963, zzz964, zzz965, zzz966, zzz967, zzz968, ba) → new_mkVBalBranch3MkVBalBranch124(zzz958, zzz959, zzz960, zzz961, zzz962, zzz963, zzz964, zzz965, zzz966, zzz967, zzz968, new_primPlusNat2(new_primPlusNat3(Succ(new_primPlusNat3(new_primPlusNat1(zzz960), zzz960)), Succ(zzz960)), Succ(zzz960)), ba)
new_mkVBalBranch3MkVBalBranch241(zzz3170, zzz3171, Pos(Succ(zzz317200)), zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, Zero, h) → new_mkVBalBranch3MkVBalBranch243(zzz3170, zzz3171, Succ(zzz317200), zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, h)
new_mkVBalBranch3MkVBalBranch126(zzz3170, zzz3171, zzz317200, zzz3173, zzz3174, zzz330, zzz331, zzz333, zzz334, zzz31, Succ(zzz5350), h) → new_mkVBalBranch1(zzz31, zzz334, Branch(zzz3170, zzz3171, Neg(Succ(zzz317200)), zzz3173, zzz3174), h)
new_mkVBalBranch3MkVBalBranch123(zzz3170, zzz3171, zzz317200, zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, Zero, h) → new_mkVBalBranch3MkVBalBranch130(zzz3170, zzz3171, zzz317200, zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, h)
new_mkVBalBranch3MkVBalBranch241(zzz3170, zzz3171, Neg(Zero), zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, Succ(zzz4190), h) → new_mkVBalBranch1(zzz31, Branch(zzz330, zzz331, Neg(Succ(zzz33200)), zzz333, zzz334), zzz3173, h)
new_mkVBalBranch3MkVBalBranch124(zzz958, zzz959, zzz960, zzz961, zzz962, zzz963, zzz964, zzz965, zzz966, zzz967, zzz968, Succ(zzz10180), ba) → new_mkVBalBranch3MkVBalBranch125(zzz958, zzz959, zzz960, zzz961, zzz962, zzz963, zzz964, zzz965, zzz966, zzz967, zzz968, Succ(zzz10180), Succ(zzz965), ba)
new_mkVBalBranch3MkVBalBranch235(zzz3170, zzz3171, Pos(Succ(zzz317200)), zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, Zero, h) → new_mkVBalBranch3MkVBalBranch236(zzz3170, zzz3171, zzz317200, zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, Zero, Succ(zzz317200), h)
new_mkVBalBranch3MkVBalBranch239(zzz3170, zzz3171, Zero, zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, h) → new_mkVBalBranch1(zzz31, zzz334, Branch(zzz3170, zzz3171, Neg(Zero), zzz3173, zzz3174), h)
new_mkVBalBranch3MkVBalBranch235(zzz3170, zzz3171, Pos(Zero), zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, Zero, h) → new_mkVBalBranch1(zzz31, zzz334, Branch(zzz3170, zzz3171, Pos(Zero), zzz3173, zzz3174), h)
new_mkVBalBranch3MkVBalBranch242(zzz972, zzz973, zzz974, zzz975, zzz976, zzz977, zzz978, zzz979, zzz980, zzz981, zzz982, Zero, Zero, bc) → new_mkVBalBranch3MkVBalBranch244(zzz972, zzz973, zzz974, zzz975, zzz976, zzz977, zzz978, zzz979, zzz980, zzz981, zzz982, bc)
new_mkVBalBranch3MkVBalBranch130(zzz3170, zzz3171, zzz317200, zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, h) → new_mkVBalBranch1(zzz31, zzz334, Branch(zzz3170, zzz3171, Neg(Succ(zzz317200)), zzz3173, zzz3174), h)
new_mkVBalBranch1(zzz31, Branch(zzz330, zzz331, Pos(Zero), zzz333, zzz334), Branch(zzz3170, zzz3171, Neg(Succ(zzz317200)), zzz3173, zzz3174), h) → new_mkVBalBranch3MkVBalBranch126(zzz3170, zzz3171, zzz317200, zzz3173, zzz3174, zzz330, zzz331, zzz333, zzz334, zzz31, new_primPlusNat2(new_primMulNat0(zzz317200), Succ(zzz317200)), h)
new_mkVBalBranch1(zzz31, Branch(zzz330, zzz331, Neg(Zero), zzz333, zzz334), Branch(zzz3170, zzz3171, Pos(Succ(zzz317200)), zzz3173, zzz3174), h) → new_mkVBalBranch1(zzz31, Branch(zzz330, zzz331, Neg(Zero), zzz333, zzz334), zzz3173, h)
new_mkVBalBranch3MkVBalBranch235(zzz3170, zzz3171, Neg(Zero), zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, Zero, h) → new_mkVBalBranch3MkVBalBranch239(zzz3170, zzz3171, Zero, zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, h)
new_mkVBalBranch1(zzz31, Branch(zzz330, zzz331, Neg(Succ(zzz33200)), zzz333, zzz334), Branch(zzz3170, zzz3171, zzz3172, zzz3173, zzz3174), h) → new_mkVBalBranch3MkVBalBranch241(zzz3170, zzz3171, zzz3172, zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, new_primPlusNat2(Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat3(new_primPlusNat1(zzz33200), zzz33200)), zzz33200))), Succ(zzz33200)), h)
new_mkVBalBranch3MkVBalBranch235(zzz3170, zzz3171, Neg(Zero), zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, Succ(zzz4170), h) → new_mkVBalBranch1(zzz31, zzz334, Branch(zzz3170, zzz3171, Neg(Zero), zzz3173, zzz3174), h)
new_mkVBalBranch3MkVBalBranch236(zzz958, zzz959, zzz960, zzz961, zzz962, zzz963, zzz964, zzz965, zzz966, zzz967, zzz968, Zero, Zero, ba) → new_mkVBalBranch3MkVBalBranch240(zzz958, zzz959, zzz960, zzz961, zzz962, zzz963, zzz964, zzz965, zzz966, zzz967, zzz968, ba)

The TRS R consists of the following rules:

new_primPlusNat1(Zero) → Zero
new_primPlusNat1(Succ(zzz62000)) → Succ(Succ(new_primPlusNat1(zzz62000)))
new_primPlusNat3(zzz90, Succ(zzz910)) → Succ(Succ(new_primPlusNat2(zzz90, zzz910)))
new_primPlusNat3(zzz90, Zero) → Succ(zzz90)
new_primPlusNat2(Succ(zzz900), Succ(zzz9100)) → Succ(Succ(new_primPlusNat2(zzz900, zzz9100)))
new_primPlusNat2(Zero, Succ(zzz9100)) → Succ(zzz9100)
new_primPlusNat2(Zero, Zero) → Zero
new_primPlusNat2(Succ(zzz900), Zero) → Succ(zzz900)
new_primMulNat0(zzz6200) → new_primPlusNat3(Succ(new_primPlusNat3(new_primPlusNat1(zzz6200), zzz6200)), Succ(zzz6200))

The set Q consists of the following terms:

new_primPlusNat2(Zero, Succ(x0))
new_primMulNat0(x0)
new_primPlusNat3(x0, Succ(x1))
new_primPlusNat2(Succ(x0), Succ(x1))
new_primPlusNat3(x0, Zero)
new_primPlusNat1(Zero)
new_primPlusNat2(Zero, Zero)
new_primPlusNat1(Succ(x0))
new_primPlusNat2(Succ(x0), Zero)

We have to consider all minimal (P,Q,R)-chains.
By rewriting [15] the rule new_mkVBalBranch3MkVBalBranch236(zzz958, zzz959, zzz960, zzz961, zzz962, zzz963, zzz964, zzz965, zzz966, zzz967, zzz968, Succ(zzz9690), Zero, ba) → new_mkVBalBranch3MkVBalBranch124(zzz958, zzz959, zzz960, zzz961, zzz962, zzz963, zzz964, zzz965, zzz966, zzz967, zzz968, new_primPlusNat2(new_primMulNat0(zzz960), Succ(zzz960)), ba) at position [11,0] we obtained the following new rules:

new_mkVBalBranch3MkVBalBranch236(zzz958, zzz959, zzz960, zzz961, zzz962, zzz963, zzz964, zzz965, zzz966, zzz967, zzz968, Succ(zzz9690), Zero, ba) → new_mkVBalBranch3MkVBalBranch124(zzz958, zzz959, zzz960, zzz961, zzz962, zzz963, zzz964, zzz965, zzz966, zzz967, zzz968, new_primPlusNat2(new_primPlusNat3(Succ(new_primPlusNat3(new_primPlusNat1(zzz960), zzz960)), Succ(zzz960)), Succ(zzz960)), 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
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                    ↳ DependencyGraphProof
                                      ↳ QDP
                                        ↳ Rewriting
                                          ↳ QDP
                                            ↳ Rewriting
                                              ↳ QDP
                                                ↳ Rewriting
                                                  ↳ QDP
                                                    ↳ Rewriting
                                                      ↳ QDP
                                                        ↳ Rewriting
                                                          ↳ QDP
                                                            ↳ Rewriting
                                                              ↳ QDP
                                                                ↳ Rewriting
                                                                  ↳ QDP
                                                                    ↳ Rewriting
                                                                      ↳ QDP
                                                                        ↳ Rewriting
                                                                          ↳ QDP
                                                                            ↳ Rewriting
                                                                              ↳ QDP
                                                                                ↳ UsableRulesProof
                                                                                  ↳ QDP
                                                                                    ↳ QReductionProof
                                                                                      ↳ QDP
                                                                                        ↳ Rewriting
                                                                                          ↳ QDP
                                                                                            ↳ Rewriting
                                                                                              ↳ QDP
                                                                                                ↳ Rewriting
                                                                                                  ↳ QDP
                                                                                                    ↳ Rewriting
                                                                                                      ↳ QDP
                                                                                                        ↳ Rewriting
                                                                                                          ↳ QDP
                                                                                                            ↳ Rewriting
                                                                                                              ↳ QDP
                                                                                                                ↳ Rewriting
                                                                                                                  ↳ QDP
                                                                                                                    ↳ Rewriting
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP

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

new_mkVBalBranch3MkVBalBranch129(zzz1851, zzz1852, zzz1853, zzz1854, zzz1855, zzz1856, zzz1857, zzz1858, zzz1859, zzz1860, zzz1861, Zero, Succ(zzz18630), bd) → new_mkVBalBranch1(zzz1861, zzz1860, Branch(zzz1851, zzz1852, Neg(Succ(zzz1853)), zzz1854, zzz1855), bd)
new_mkVBalBranch3MkVBalBranch128(zzz972, zzz973, zzz974, zzz975, zzz976, zzz977, zzz978, zzz979, zzz980, zzz981, zzz982, Succ(zzz10190), bc) → new_mkVBalBranch3MkVBalBranch129(zzz972, zzz973, zzz974, zzz975, zzz976, zzz977, zzz978, zzz979, zzz980, zzz981, zzz982, Succ(zzz979), Succ(zzz10190), bc)
new_mkVBalBranch3MkVBalBranch241(zzz3170, zzz3171, Pos(zzz31720), zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, Succ(zzz4190), h) → new_mkVBalBranch1(zzz31, Branch(zzz330, zzz331, Neg(Succ(zzz33200)), zzz333, zzz334), zzz3173, h)
new_mkVBalBranch3MkVBalBranch127(zzz3170, zzz3171, zzz317200, zzz3173, zzz3174, zzz330, zzz331, zzz333, zzz334, zzz31, Succ(zzz5500), h) → new_mkVBalBranch1(zzz31, zzz334, Branch(zzz3170, zzz3171, Neg(Succ(zzz317200)), zzz3173, zzz3174), h)
new_mkVBalBranch3MkVBalBranch236(zzz958, zzz959, zzz960, zzz961, zzz962, zzz963, zzz964, zzz965, zzz966, zzz967, zzz968, Succ(zzz9690), Zero, ba) → new_mkVBalBranch3MkVBalBranch124(zzz958, zzz959, zzz960, zzz961, zzz962, zzz963, zzz964, zzz965, zzz966, zzz967, zzz968, new_primPlusNat2(new_primPlusNat3(Succ(new_primPlusNat3(new_primPlusNat1(zzz960), zzz960)), Succ(zzz960)), Succ(zzz960)), ba)
new_mkVBalBranch3MkVBalBranch242(zzz972, zzz973, zzz974, zzz975, zzz976, zzz977, zzz978, zzz979, zzz980, zzz981, zzz982, Succ(zzz9830), Zero, bc) → new_mkVBalBranch3MkVBalBranch128(zzz972, zzz973, zzz974, zzz975, zzz976, zzz977, zzz978, zzz979, zzz980, zzz981, zzz982, new_primPlusNat2(new_primPlusNat3(Succ(new_primPlusNat3(new_primPlusNat1(zzz974), zzz974)), Succ(zzz974)), Succ(zzz974)), bc)
new_mkVBalBranch3MkVBalBranch129(zzz1851, zzz1852, zzz1853, zzz1854, zzz1855, zzz1856, zzz1857, zzz1858, zzz1859, zzz1860, zzz1861, Succ(zzz18620), Succ(zzz18630), bd) → new_mkVBalBranch3MkVBalBranch129(zzz1851, zzz1852, zzz1853, zzz1854, zzz1855, zzz1856, zzz1857, zzz1858, zzz1859, zzz1860, zzz1861, zzz18620, zzz18630, bd)
new_mkVBalBranch3MkVBalBranch124(zzz958, zzz959, zzz960, zzz961, zzz962, zzz963, zzz964, zzz965, zzz966, zzz967, zzz968, Zero, ba) → new_mkVBalBranch3MkVBalBranch125(zzz958, zzz959, zzz960, zzz961, zzz962, zzz963, zzz964, zzz965, zzz966, zzz967, zzz968, Zero, Succ(zzz965), ba)
new_mkVBalBranch3MkVBalBranch235(zzz3170, zzz3171, Pos(Succ(zzz317200)), zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, Succ(zzz4170), h) → new_mkVBalBranch3MkVBalBranch236(zzz3170, zzz3171, zzz317200, zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, zzz4170, zzz317200, h)
new_mkVBalBranch3MkVBalBranch242(zzz972, zzz973, zzz974, zzz975, zzz976, zzz977, zzz978, zzz979, zzz980, zzz981, zzz982, Succ(zzz9830), Succ(zzz9840), bc) → new_mkVBalBranch3MkVBalBranch242(zzz972, zzz973, zzz974, zzz975, zzz976, zzz977, zzz978, zzz979, zzz980, zzz981, zzz982, zzz9830, zzz9840, bc)
new_mkVBalBranch3MkVBalBranch236(zzz958, zzz959, zzz960, zzz961, zzz962, zzz963, zzz964, zzz965, zzz966, zzz967, zzz968, Succ(zzz9690), Succ(zzz9700), ba) → new_mkVBalBranch3MkVBalBranch236(zzz958, zzz959, zzz960, zzz961, zzz962, zzz963, zzz964, zzz965, zzz966, zzz967, zzz968, zzz9690, zzz9700, ba)
new_mkVBalBranch1(zzz31, Branch(zzz330, zzz331, Pos(Succ(zzz33200)), zzz333, zzz334), Branch(zzz3170, zzz3171, zzz3172, zzz3173, zzz3174), h) → new_mkVBalBranch3MkVBalBranch235(zzz3170, zzz3171, zzz3172, zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, new_primPlusNat2(Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat3(new_primPlusNat1(zzz33200), zzz33200)), zzz33200))), Succ(zzz33200)), h)
new_mkVBalBranch3MkVBalBranch241(zzz3170, zzz3171, Neg(Succ(zzz317200)), zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, Succ(zzz4190), h) → new_mkVBalBranch3MkVBalBranch242(zzz3170, zzz3171, zzz317200, zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, zzz317200, zzz4190, h)
new_mkVBalBranch3MkVBalBranch241(zzz3170, zzz3171, Neg(Succ(zzz317200)), zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, Zero, h) → new_mkVBalBranch3MkVBalBranch242(zzz3170, zzz3171, zzz317200, zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, Succ(zzz317200), Zero, h)
new_mkVBalBranch1(zzz31, Branch(zzz330, zzz331, Pos(Zero), zzz333, zzz334), Branch(zzz3170, zzz3171, Pos(Succ(zzz317200)), zzz3173, zzz3174), h) → new_mkVBalBranch1(zzz31, Branch(zzz330, zzz331, Pos(Zero), zzz333, zzz334), zzz3173, h)
new_mkVBalBranch3MkVBalBranch235(zzz3170, zzz3171, Neg(Succ(zzz317200)), zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, Succ(zzz4170), h) → new_mkVBalBranch3MkVBalBranch123(zzz3170, zzz3171, zzz317200, zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, new_primPlusNat2(Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat3(new_primPlusNat1(zzz317200), zzz317200)), zzz317200))), Succ(zzz317200)), h)
new_mkVBalBranch3MkVBalBranch237(zzz3170, zzz3171, zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, h) → new_mkVBalBranch1(zzz31, zzz334, Branch(zzz3170, zzz3171, Pos(Zero), zzz3173, zzz3174), h)
new_mkVBalBranch3MkVBalBranch243(zzz3170, zzz3171, zzz31720, zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, h) → new_mkVBalBranch1(zzz31, Branch(zzz330, zzz331, Neg(Succ(zzz33200)), zzz333, zzz334), zzz3173, h)
new_mkVBalBranch3MkVBalBranch235(zzz3170, zzz3171, Pos(Zero), zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, Succ(zzz4170), h) → new_mkVBalBranch3MkVBalBranch237(zzz3170, zzz3171, zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, h)
new_mkVBalBranch3MkVBalBranch236(zzz958, zzz959, zzz960, zzz961, zzz962, zzz963, zzz964, zzz965, zzz966, zzz967, zzz968, Zero, Succ(zzz9700), ba) → new_mkVBalBranch1(zzz968, Branch(zzz963, zzz964, Pos(Succ(zzz965)), zzz966, zzz967), zzz961, ba)
new_mkVBalBranch3MkVBalBranch125(zzz1337, zzz1338, zzz1339, zzz1340, zzz1341, zzz1342, zzz1343, zzz1344, zzz1345, zzz1346, zzz1347, Succ(zzz13480), Succ(zzz13490), bb) → new_mkVBalBranch3MkVBalBranch125(zzz1337, zzz1338, zzz1339, zzz1340, zzz1341, zzz1342, zzz1343, zzz1344, zzz1345, zzz1346, zzz1347, zzz13480, zzz13490, bb)
new_mkVBalBranch3MkVBalBranch123(zzz3170, zzz3171, zzz317200, zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, Succ(zzz5620), h) → new_mkVBalBranch1(zzz31, zzz334, Branch(zzz3170, zzz3171, Neg(Succ(zzz317200)), zzz3173, zzz3174), h)
new_mkVBalBranch3MkVBalBranch125(zzz1337, zzz1338, zzz1339, zzz1340, zzz1341, zzz1342, zzz1343, zzz1344, zzz1345, zzz1346, zzz1347, Zero, Succ(zzz13490), bb) → new_mkVBalBranch1(zzz1347, zzz1346, Branch(zzz1337, zzz1338, Pos(Succ(zzz1339)), zzz1340, zzz1341), bb)
new_mkVBalBranch3MkVBalBranch242(zzz972, zzz973, zzz974, zzz975, zzz976, zzz977, zzz978, zzz979, zzz980, zzz981, zzz982, Zero, Succ(zzz9840), bc) → new_mkVBalBranch1(zzz982, Branch(zzz977, zzz978, Neg(Succ(zzz979)), zzz980, zzz981), zzz975, bc)
new_mkVBalBranch3MkVBalBranch238(zzz3170, zzz3171, Succ(zzz317200), zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, h) → new_mkVBalBranch3MkVBalBranch123(zzz3170, zzz3171, zzz317200, zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, new_primPlusNat2(new_primPlusNat3(Succ(new_primPlusNat3(new_primPlusNat1(zzz317200), zzz317200)), Succ(zzz317200)), Succ(zzz317200)), h)
new_mkVBalBranch3MkVBalBranch244(zzz972, zzz973, zzz974, zzz975, zzz976, zzz977, zzz978, zzz979, zzz980, zzz981, zzz982, bc) → new_mkVBalBranch3MkVBalBranch128(zzz972, zzz973, zzz974, zzz975, zzz976, zzz977, zzz978, zzz979, zzz980, zzz981, zzz982, new_primPlusNat2(new_primMulNat0(zzz974), Succ(zzz974)), bc)
new_mkVBalBranch1(zzz31, Branch(zzz330, zzz331, Neg(Zero), zzz333, zzz334), Branch(zzz3170, zzz3171, Neg(Succ(zzz317200)), zzz3173, zzz3174), h) → new_mkVBalBranch3MkVBalBranch127(zzz3170, zzz3171, zzz317200, zzz3173, zzz3174, zzz330, zzz331, zzz333, zzz334, zzz31, new_primPlusNat2(new_primPlusNat3(Succ(new_primPlusNat3(new_primPlusNat1(zzz317200), zzz317200)), Succ(zzz317200)), Succ(zzz317200)), h)
new_mkVBalBranch3MkVBalBranch235(zzz3170, zzz3171, Neg(Succ(zzz317200)), zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, Zero, h) → new_mkVBalBranch3MkVBalBranch238(zzz3170, zzz3171, Succ(zzz317200), zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, h)
new_mkVBalBranch3MkVBalBranch240(zzz958, zzz959, zzz960, zzz961, zzz962, zzz963, zzz964, zzz965, zzz966, zzz967, zzz968, ba) → new_mkVBalBranch3MkVBalBranch124(zzz958, zzz959, zzz960, zzz961, zzz962, zzz963, zzz964, zzz965, zzz966, zzz967, zzz968, new_primPlusNat2(new_primPlusNat3(Succ(new_primPlusNat3(new_primPlusNat1(zzz960), zzz960)), Succ(zzz960)), Succ(zzz960)), ba)
new_mkVBalBranch3MkVBalBranch241(zzz3170, zzz3171, Pos(Succ(zzz317200)), zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, Zero, h) → new_mkVBalBranch3MkVBalBranch243(zzz3170, zzz3171, Succ(zzz317200), zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, h)
new_mkVBalBranch3MkVBalBranch126(zzz3170, zzz3171, zzz317200, zzz3173, zzz3174, zzz330, zzz331, zzz333, zzz334, zzz31, Succ(zzz5350), h) → new_mkVBalBranch1(zzz31, zzz334, Branch(zzz3170, zzz3171, Neg(Succ(zzz317200)), zzz3173, zzz3174), h)
new_mkVBalBranch3MkVBalBranch241(zzz3170, zzz3171, Neg(Zero), zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, Succ(zzz4190), h) → new_mkVBalBranch1(zzz31, Branch(zzz330, zzz331, Neg(Succ(zzz33200)), zzz333, zzz334), zzz3173, h)
new_mkVBalBranch3MkVBalBranch123(zzz3170, zzz3171, zzz317200, zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, Zero, h) → new_mkVBalBranch3MkVBalBranch130(zzz3170, zzz3171, zzz317200, zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, h)
new_mkVBalBranch3MkVBalBranch124(zzz958, zzz959, zzz960, zzz961, zzz962, zzz963, zzz964, zzz965, zzz966, zzz967, zzz968, Succ(zzz10180), ba) → new_mkVBalBranch3MkVBalBranch125(zzz958, zzz959, zzz960, zzz961, zzz962, zzz963, zzz964, zzz965, zzz966, zzz967, zzz968, Succ(zzz10180), Succ(zzz965), ba)
new_mkVBalBranch3MkVBalBranch235(zzz3170, zzz3171, Pos(Succ(zzz317200)), zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, Zero, h) → new_mkVBalBranch3MkVBalBranch236(zzz3170, zzz3171, zzz317200, zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, Zero, Succ(zzz317200), h)
new_mkVBalBranch3MkVBalBranch239(zzz3170, zzz3171, Zero, zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, h) → new_mkVBalBranch1(zzz31, zzz334, Branch(zzz3170, zzz3171, Neg(Zero), zzz3173, zzz3174), h)
new_mkVBalBranch3MkVBalBranch235(zzz3170, zzz3171, Pos(Zero), zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, Zero, h) → new_mkVBalBranch1(zzz31, zzz334, Branch(zzz3170, zzz3171, Pos(Zero), zzz3173, zzz3174), h)
new_mkVBalBranch3MkVBalBranch242(zzz972, zzz973, zzz974, zzz975, zzz976, zzz977, zzz978, zzz979, zzz980, zzz981, zzz982, Zero, Zero, bc) → new_mkVBalBranch3MkVBalBranch244(zzz972, zzz973, zzz974, zzz975, zzz976, zzz977, zzz978, zzz979, zzz980, zzz981, zzz982, bc)
new_mkVBalBranch1(zzz31, Branch(zzz330, zzz331, Pos(Zero), zzz333, zzz334), Branch(zzz3170, zzz3171, Neg(Succ(zzz317200)), zzz3173, zzz3174), h) → new_mkVBalBranch3MkVBalBranch126(zzz3170, zzz3171, zzz317200, zzz3173, zzz3174, zzz330, zzz331, zzz333, zzz334, zzz31, new_primPlusNat2(new_primMulNat0(zzz317200), Succ(zzz317200)), h)
new_mkVBalBranch3MkVBalBranch130(zzz3170, zzz3171, zzz317200, zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, h) → new_mkVBalBranch1(zzz31, zzz334, Branch(zzz3170, zzz3171, Neg(Succ(zzz317200)), zzz3173, zzz3174), h)
new_mkVBalBranch3MkVBalBranch235(zzz3170, zzz3171, Neg(Zero), zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, Zero, h) → new_mkVBalBranch3MkVBalBranch239(zzz3170, zzz3171, Zero, zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, h)
new_mkVBalBranch1(zzz31, Branch(zzz330, zzz331, Neg(Zero), zzz333, zzz334), Branch(zzz3170, zzz3171, Pos(Succ(zzz317200)), zzz3173, zzz3174), h) → new_mkVBalBranch1(zzz31, Branch(zzz330, zzz331, Neg(Zero), zzz333, zzz334), zzz3173, h)
new_mkVBalBranch3MkVBalBranch235(zzz3170, zzz3171, Neg(Zero), zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, Succ(zzz4170), h) → new_mkVBalBranch1(zzz31, zzz334, Branch(zzz3170, zzz3171, Neg(Zero), zzz3173, zzz3174), h)
new_mkVBalBranch1(zzz31, Branch(zzz330, zzz331, Neg(Succ(zzz33200)), zzz333, zzz334), Branch(zzz3170, zzz3171, zzz3172, zzz3173, zzz3174), h) → new_mkVBalBranch3MkVBalBranch241(zzz3170, zzz3171, zzz3172, zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, new_primPlusNat2(Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat3(new_primPlusNat1(zzz33200), zzz33200)), zzz33200))), Succ(zzz33200)), h)
new_mkVBalBranch3MkVBalBranch236(zzz958, zzz959, zzz960, zzz961, zzz962, zzz963, zzz964, zzz965, zzz966, zzz967, zzz968, Zero, Zero, ba) → new_mkVBalBranch3MkVBalBranch240(zzz958, zzz959, zzz960, zzz961, zzz962, zzz963, zzz964, zzz965, zzz966, zzz967, zzz968, ba)

The TRS R consists of the following rules:

new_primPlusNat1(Zero) → Zero
new_primPlusNat1(Succ(zzz62000)) → Succ(Succ(new_primPlusNat1(zzz62000)))
new_primPlusNat3(zzz90, Succ(zzz910)) → Succ(Succ(new_primPlusNat2(zzz90, zzz910)))
new_primPlusNat3(zzz90, Zero) → Succ(zzz90)
new_primPlusNat2(Succ(zzz900), Succ(zzz9100)) → Succ(Succ(new_primPlusNat2(zzz900, zzz9100)))
new_primPlusNat2(Zero, Succ(zzz9100)) → Succ(zzz9100)
new_primPlusNat2(Zero, Zero) → Zero
new_primPlusNat2(Succ(zzz900), Zero) → Succ(zzz900)
new_primMulNat0(zzz6200) → new_primPlusNat3(Succ(new_primPlusNat3(new_primPlusNat1(zzz6200), zzz6200)), Succ(zzz6200))

The set Q consists of the following terms:

new_primPlusNat2(Zero, Succ(x0))
new_primMulNat0(x0)
new_primPlusNat3(x0, Succ(x1))
new_primPlusNat2(Succ(x0), Succ(x1))
new_primPlusNat3(x0, Zero)
new_primPlusNat1(Zero)
new_primPlusNat2(Zero, Zero)
new_primPlusNat1(Succ(x0))
new_primPlusNat2(Succ(x0), Zero)

We have to consider all minimal (P,Q,R)-chains.
By rewriting [15] the rule new_mkVBalBranch3MkVBalBranch238(zzz3170, zzz3171, Succ(zzz317200), zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, h) → new_mkVBalBranch3MkVBalBranch123(zzz3170, zzz3171, zzz317200, zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, new_primPlusNat2(new_primPlusNat3(Succ(new_primPlusNat3(new_primPlusNat1(zzz317200), zzz317200)), Succ(zzz317200)), Succ(zzz317200)), h) at position [11,0] we obtained the following new rules:

new_mkVBalBranch3MkVBalBranch238(zzz3170, zzz3171, Succ(zzz317200), zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, h) → new_mkVBalBranch3MkVBalBranch123(zzz3170, zzz3171, zzz317200, zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, new_primPlusNat2(Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat3(new_primPlusNat1(zzz317200), zzz317200)), zzz317200))), Succ(zzz317200)), 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
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                    ↳ DependencyGraphProof
                                      ↳ QDP
                                        ↳ Rewriting
                                          ↳ QDP
                                            ↳ Rewriting
                                              ↳ QDP
                                                ↳ Rewriting
                                                  ↳ QDP
                                                    ↳ Rewriting
                                                      ↳ QDP
                                                        ↳ Rewriting
                                                          ↳ QDP
                                                            ↳ Rewriting
                                                              ↳ QDP
                                                                ↳ Rewriting
                                                                  ↳ QDP
                                                                    ↳ Rewriting
                                                                      ↳ QDP
                                                                        ↳ Rewriting
                                                                          ↳ QDP
                                                                            ↳ Rewriting
                                                                              ↳ QDP
                                                                                ↳ UsableRulesProof
                                                                                  ↳ QDP
                                                                                    ↳ QReductionProof
                                                                                      ↳ QDP
                                                                                        ↳ Rewriting
                                                                                          ↳ QDP
                                                                                            ↳ Rewriting
                                                                                              ↳ QDP
                                                                                                ↳ Rewriting
                                                                                                  ↳ QDP
                                                                                                    ↳ Rewriting
                                                                                                      ↳ QDP
                                                                                                        ↳ Rewriting
                                                                                                          ↳ QDP
                                                                                                            ↳ Rewriting
                                                                                                              ↳ QDP
                                                                                                                ↳ Rewriting
                                                                                                                  ↳ QDP
                                                                                                                    ↳ Rewriting
                                                                                                                      ↳ QDP
                                                                                                                        ↳ Rewriting
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP

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

new_mkVBalBranch3MkVBalBranch129(zzz1851, zzz1852, zzz1853, zzz1854, zzz1855, zzz1856, zzz1857, zzz1858, zzz1859, zzz1860, zzz1861, Zero, Succ(zzz18630), bd) → new_mkVBalBranch1(zzz1861, zzz1860, Branch(zzz1851, zzz1852, Neg(Succ(zzz1853)), zzz1854, zzz1855), bd)
new_mkVBalBranch3MkVBalBranch127(zzz3170, zzz3171, zzz317200, zzz3173, zzz3174, zzz330, zzz331, zzz333, zzz334, zzz31, Succ(zzz5500), h) → new_mkVBalBranch1(zzz31, zzz334, Branch(zzz3170, zzz3171, Neg(Succ(zzz317200)), zzz3173, zzz3174), h)
new_mkVBalBranch3MkVBalBranch241(zzz3170, zzz3171, Pos(zzz31720), zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, Succ(zzz4190), h) → new_mkVBalBranch1(zzz31, Branch(zzz330, zzz331, Neg(Succ(zzz33200)), zzz333, zzz334), zzz3173, h)
new_mkVBalBranch3MkVBalBranch128(zzz972, zzz973, zzz974, zzz975, zzz976, zzz977, zzz978, zzz979, zzz980, zzz981, zzz982, Succ(zzz10190), bc) → new_mkVBalBranch3MkVBalBranch129(zzz972, zzz973, zzz974, zzz975, zzz976, zzz977, zzz978, zzz979, zzz980, zzz981, zzz982, Succ(zzz979), Succ(zzz10190), bc)
new_mkVBalBranch3MkVBalBranch236(zzz958, zzz959, zzz960, zzz961, zzz962, zzz963, zzz964, zzz965, zzz966, zzz967, zzz968, Succ(zzz9690), Zero, ba) → new_mkVBalBranch3MkVBalBranch124(zzz958, zzz959, zzz960, zzz961, zzz962, zzz963, zzz964, zzz965, zzz966, zzz967, zzz968, new_primPlusNat2(new_primPlusNat3(Succ(new_primPlusNat3(new_primPlusNat1(zzz960), zzz960)), Succ(zzz960)), Succ(zzz960)), ba)
new_mkVBalBranch3MkVBalBranch242(zzz972, zzz973, zzz974, zzz975, zzz976, zzz977, zzz978, zzz979, zzz980, zzz981, zzz982, Succ(zzz9830), Zero, bc) → new_mkVBalBranch3MkVBalBranch128(zzz972, zzz973, zzz974, zzz975, zzz976, zzz977, zzz978, zzz979, zzz980, zzz981, zzz982, new_primPlusNat2(new_primPlusNat3(Succ(new_primPlusNat3(new_primPlusNat1(zzz974), zzz974)), Succ(zzz974)), Succ(zzz974)), bc)
new_mkVBalBranch3MkVBalBranch129(zzz1851, zzz1852, zzz1853, zzz1854, zzz1855, zzz1856, zzz1857, zzz1858, zzz1859, zzz1860, zzz1861, Succ(zzz18620), Succ(zzz18630), bd) → new_mkVBalBranch3MkVBalBranch129(zzz1851, zzz1852, zzz1853, zzz1854, zzz1855, zzz1856, zzz1857, zzz1858, zzz1859, zzz1860, zzz1861, zzz18620, zzz18630, bd)
new_mkVBalBranch3MkVBalBranch124(zzz958, zzz959, zzz960, zzz961, zzz962, zzz963, zzz964, zzz965, zzz966, zzz967, zzz968, Zero, ba) → new_mkVBalBranch3MkVBalBranch125(zzz958, zzz959, zzz960, zzz961, zzz962, zzz963, zzz964, zzz965, zzz966, zzz967, zzz968, Zero, Succ(zzz965), ba)
new_mkVBalBranch3MkVBalBranch242(zzz972, zzz973, zzz974, zzz975, zzz976, zzz977, zzz978, zzz979, zzz980, zzz981, zzz982, Succ(zzz9830), Succ(zzz9840), bc) → new_mkVBalBranch3MkVBalBranch242(zzz972, zzz973, zzz974, zzz975, zzz976, zzz977, zzz978, zzz979, zzz980, zzz981, zzz982, zzz9830, zzz9840, bc)
new_mkVBalBranch3MkVBalBranch235(zzz3170, zzz3171, Pos(Succ(zzz317200)), zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, Succ(zzz4170), h) → new_mkVBalBranch3MkVBalBranch236(zzz3170, zzz3171, zzz317200, zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, zzz4170, zzz317200, h)
new_mkVBalBranch1(zzz31, Branch(zzz330, zzz331, Pos(Succ(zzz33200)), zzz333, zzz334), Branch(zzz3170, zzz3171, zzz3172, zzz3173, zzz3174), h) → new_mkVBalBranch3MkVBalBranch235(zzz3170, zzz3171, zzz3172, zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, new_primPlusNat2(Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat3(new_primPlusNat1(zzz33200), zzz33200)), zzz33200))), Succ(zzz33200)), h)
new_mkVBalBranch3MkVBalBranch236(zzz958, zzz959, zzz960, zzz961, zzz962, zzz963, zzz964, zzz965, zzz966, zzz967, zzz968, Succ(zzz9690), Succ(zzz9700), ba) → new_mkVBalBranch3MkVBalBranch236(zzz958, zzz959, zzz960, zzz961, zzz962, zzz963, zzz964, zzz965, zzz966, zzz967, zzz968, zzz9690, zzz9700, ba)
new_mkVBalBranch3MkVBalBranch241(zzz3170, zzz3171, Neg(Succ(zzz317200)), zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, Succ(zzz4190), h) → new_mkVBalBranch3MkVBalBranch242(zzz3170, zzz3171, zzz317200, zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, zzz317200, zzz4190, h)
new_mkVBalBranch3MkVBalBranch241(zzz3170, zzz3171, Neg(Succ(zzz317200)), zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, Zero, h) → new_mkVBalBranch3MkVBalBranch242(zzz3170, zzz3171, zzz317200, zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, Succ(zzz317200), Zero, h)
new_mkVBalBranch1(zzz31, Branch(zzz330, zzz331, Pos(Zero), zzz333, zzz334), Branch(zzz3170, zzz3171, Pos(Succ(zzz317200)), zzz3173, zzz3174), h) → new_mkVBalBranch1(zzz31, Branch(zzz330, zzz331, Pos(Zero), zzz333, zzz334), zzz3173, h)
new_mkVBalBranch3MkVBalBranch243(zzz3170, zzz3171, zzz31720, zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, h) → new_mkVBalBranch1(zzz31, Branch(zzz330, zzz331, Neg(Succ(zzz33200)), zzz333, zzz334), zzz3173, h)
new_mkVBalBranch3MkVBalBranch237(zzz3170, zzz3171, zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, h) → new_mkVBalBranch1(zzz31, zzz334, Branch(zzz3170, zzz3171, Pos(Zero), zzz3173, zzz3174), h)
new_mkVBalBranch3MkVBalBranch235(zzz3170, zzz3171, Neg(Succ(zzz317200)), zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, Succ(zzz4170), h) → new_mkVBalBranch3MkVBalBranch123(zzz3170, zzz3171, zzz317200, zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, new_primPlusNat2(Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat3(new_primPlusNat1(zzz317200), zzz317200)), zzz317200))), Succ(zzz317200)), h)
new_mkVBalBranch3MkVBalBranch235(zzz3170, zzz3171, Pos(Zero), zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, Succ(zzz4170), h) → new_mkVBalBranch3MkVBalBranch237(zzz3170, zzz3171, zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, h)
new_mkVBalBranch3MkVBalBranch236(zzz958, zzz959, zzz960, zzz961, zzz962, zzz963, zzz964, zzz965, zzz966, zzz967, zzz968, Zero, Succ(zzz9700), ba) → new_mkVBalBranch1(zzz968, Branch(zzz963, zzz964, Pos(Succ(zzz965)), zzz966, zzz967), zzz961, ba)
new_mkVBalBranch3MkVBalBranch125(zzz1337, zzz1338, zzz1339, zzz1340, zzz1341, zzz1342, zzz1343, zzz1344, zzz1345, zzz1346, zzz1347, Succ(zzz13480), Succ(zzz13490), bb) → new_mkVBalBranch3MkVBalBranch125(zzz1337, zzz1338, zzz1339, zzz1340, zzz1341, zzz1342, zzz1343, zzz1344, zzz1345, zzz1346, zzz1347, zzz13480, zzz13490, bb)
new_mkVBalBranch3MkVBalBranch123(zzz3170, zzz3171, zzz317200, zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, Succ(zzz5620), h) → new_mkVBalBranch1(zzz31, zzz334, Branch(zzz3170, zzz3171, Neg(Succ(zzz317200)), zzz3173, zzz3174), h)
new_mkVBalBranch3MkVBalBranch125(zzz1337, zzz1338, zzz1339, zzz1340, zzz1341, zzz1342, zzz1343, zzz1344, zzz1345, zzz1346, zzz1347, Zero, Succ(zzz13490), bb) → new_mkVBalBranch1(zzz1347, zzz1346, Branch(zzz1337, zzz1338, Pos(Succ(zzz1339)), zzz1340, zzz1341), bb)
new_mkVBalBranch3MkVBalBranch242(zzz972, zzz973, zzz974, zzz975, zzz976, zzz977, zzz978, zzz979, zzz980, zzz981, zzz982, Zero, Succ(zzz9840), bc) → new_mkVBalBranch1(zzz982, Branch(zzz977, zzz978, Neg(Succ(zzz979)), zzz980, zzz981), zzz975, bc)
new_mkVBalBranch3MkVBalBranch244(zzz972, zzz973, zzz974, zzz975, zzz976, zzz977, zzz978, zzz979, zzz980, zzz981, zzz982, bc) → new_mkVBalBranch3MkVBalBranch128(zzz972, zzz973, zzz974, zzz975, zzz976, zzz977, zzz978, zzz979, zzz980, zzz981, zzz982, new_primPlusNat2(new_primMulNat0(zzz974), Succ(zzz974)), bc)
new_mkVBalBranch3MkVBalBranch238(zzz3170, zzz3171, Succ(zzz317200), zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, h) → new_mkVBalBranch3MkVBalBranch123(zzz3170, zzz3171, zzz317200, zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, new_primPlusNat2(Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat3(new_primPlusNat1(zzz317200), zzz317200)), zzz317200))), Succ(zzz317200)), h)
new_mkVBalBranch1(zzz31, Branch(zzz330, zzz331, Neg(Zero), zzz333, zzz334), Branch(zzz3170, zzz3171, Neg(Succ(zzz317200)), zzz3173, zzz3174), h) → new_mkVBalBranch3MkVBalBranch127(zzz3170, zzz3171, zzz317200, zzz3173, zzz3174, zzz330, zzz331, zzz333, zzz334, zzz31, new_primPlusNat2(new_primPlusNat3(Succ(new_primPlusNat3(new_primPlusNat1(zzz317200), zzz317200)), Succ(zzz317200)), Succ(zzz317200)), h)
new_mkVBalBranch3MkVBalBranch235(zzz3170, zzz3171, Neg(Succ(zzz317200)), zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, Zero, h) → new_mkVBalBranch3MkVBalBranch238(zzz3170, zzz3171, Succ(zzz317200), zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, h)
new_mkVBalBranch3MkVBalBranch240(zzz958, zzz959, zzz960, zzz961, zzz962, zzz963, zzz964, zzz965, zzz966, zzz967, zzz968, ba) → new_mkVBalBranch3MkVBalBranch124(zzz958, zzz959, zzz960, zzz961, zzz962, zzz963, zzz964, zzz965, zzz966, zzz967, zzz968, new_primPlusNat2(new_primPlusNat3(Succ(new_primPlusNat3(new_primPlusNat1(zzz960), zzz960)), Succ(zzz960)), Succ(zzz960)), ba)
new_mkVBalBranch3MkVBalBranch241(zzz3170, zzz3171, Pos(Succ(zzz317200)), zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, Zero, h) → new_mkVBalBranch3MkVBalBranch243(zzz3170, zzz3171, Succ(zzz317200), zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, h)
new_mkVBalBranch3MkVBalBranch126(zzz3170, zzz3171, zzz317200, zzz3173, zzz3174, zzz330, zzz331, zzz333, zzz334, zzz31, Succ(zzz5350), h) → new_mkVBalBranch1(zzz31, zzz334, Branch(zzz3170, zzz3171, Neg(Succ(zzz317200)), zzz3173, zzz3174), h)
new_mkVBalBranch3MkVBalBranch123(zzz3170, zzz3171, zzz317200, zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, Zero, h) → new_mkVBalBranch3MkVBalBranch130(zzz3170, zzz3171, zzz317200, zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, h)
new_mkVBalBranch3MkVBalBranch241(zzz3170, zzz3171, Neg(Zero), zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, Succ(zzz4190), h) → new_mkVBalBranch1(zzz31, Branch(zzz330, zzz331, Neg(Succ(zzz33200)), zzz333, zzz334), zzz3173, h)
new_mkVBalBranch3MkVBalBranch124(zzz958, zzz959, zzz960, zzz961, zzz962, zzz963, zzz964, zzz965, zzz966, zzz967, zzz968, Succ(zzz10180), ba) → new_mkVBalBranch3MkVBalBranch125(zzz958, zzz959, zzz960, zzz961, zzz962, zzz963, zzz964, zzz965, zzz966, zzz967, zzz968, Succ(zzz10180), Succ(zzz965), ba)
new_mkVBalBranch3MkVBalBranch235(zzz3170, zzz3171, Pos(Succ(zzz317200)), zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, Zero, h) → new_mkVBalBranch3MkVBalBranch236(zzz3170, zzz3171, zzz317200, zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, Zero, Succ(zzz317200), h)
new_mkVBalBranch3MkVBalBranch239(zzz3170, zzz3171, Zero, zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, h) → new_mkVBalBranch1(zzz31, zzz334, Branch(zzz3170, zzz3171, Neg(Zero), zzz3173, zzz3174), h)
new_mkVBalBranch3MkVBalBranch235(zzz3170, zzz3171, Pos(Zero), zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, Zero, h) → new_mkVBalBranch1(zzz31, zzz334, Branch(zzz3170, zzz3171, Pos(Zero), zzz3173, zzz3174), h)
new_mkVBalBranch3MkVBalBranch242(zzz972, zzz973, zzz974, zzz975, zzz976, zzz977, zzz978, zzz979, zzz980, zzz981, zzz982, Zero, Zero, bc) → new_mkVBalBranch3MkVBalBranch244(zzz972, zzz973, zzz974, zzz975, zzz976, zzz977, zzz978, zzz979, zzz980, zzz981, zzz982, bc)
new_mkVBalBranch3MkVBalBranch130(zzz3170, zzz3171, zzz317200, zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, h) → new_mkVBalBranch1(zzz31, zzz334, Branch(zzz3170, zzz3171, Neg(Succ(zzz317200)), zzz3173, zzz3174), h)
new_mkVBalBranch1(zzz31, Branch(zzz330, zzz331, Pos(Zero), zzz333, zzz334), Branch(zzz3170, zzz3171, Neg(Succ(zzz317200)), zzz3173, zzz3174), h) → new_mkVBalBranch3MkVBalBranch126(zzz3170, zzz3171, zzz317200, zzz3173, zzz3174, zzz330, zzz331, zzz333, zzz334, zzz31, new_primPlusNat2(new_primMulNat0(zzz317200), Succ(zzz317200)), h)
new_mkVBalBranch1(zzz31, Branch(zzz330, zzz331, Neg(Zero), zzz333, zzz334), Branch(zzz3170, zzz3171, Pos(Succ(zzz317200)), zzz3173, zzz3174), h) → new_mkVBalBranch1(zzz31, Branch(zzz330, zzz331, Neg(Zero), zzz333, zzz334), zzz3173, h)
new_mkVBalBranch3MkVBalBranch235(zzz3170, zzz3171, Neg(Zero), zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, Zero, h) → new_mkVBalBranch3MkVBalBranch239(zzz3170, zzz3171, Zero, zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, h)
new_mkVBalBranch1(zzz31, Branch(zzz330, zzz331, Neg(Succ(zzz33200)), zzz333, zzz334), Branch(zzz3170, zzz3171, zzz3172, zzz3173, zzz3174), h) → new_mkVBalBranch3MkVBalBranch241(zzz3170, zzz3171, zzz3172, zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, new_primPlusNat2(Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat3(new_primPlusNat1(zzz33200), zzz33200)), zzz33200))), Succ(zzz33200)), h)
new_mkVBalBranch3MkVBalBranch235(zzz3170, zzz3171, Neg(Zero), zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, Succ(zzz4170), h) → new_mkVBalBranch1(zzz31, zzz334, Branch(zzz3170, zzz3171, Neg(Zero), zzz3173, zzz3174), h)
new_mkVBalBranch3MkVBalBranch236(zzz958, zzz959, zzz960, zzz961, zzz962, zzz963, zzz964, zzz965, zzz966, zzz967, zzz968, Zero, Zero, ba) → new_mkVBalBranch3MkVBalBranch240(zzz958, zzz959, zzz960, zzz961, zzz962, zzz963, zzz964, zzz965, zzz966, zzz967, zzz968, ba)

The TRS R consists of the following rules:

new_primPlusNat1(Zero) → Zero
new_primPlusNat1(Succ(zzz62000)) → Succ(Succ(new_primPlusNat1(zzz62000)))
new_primPlusNat3(zzz90, Succ(zzz910)) → Succ(Succ(new_primPlusNat2(zzz90, zzz910)))
new_primPlusNat3(zzz90, Zero) → Succ(zzz90)
new_primPlusNat2(Succ(zzz900), Succ(zzz9100)) → Succ(Succ(new_primPlusNat2(zzz900, zzz9100)))
new_primPlusNat2(Zero, Succ(zzz9100)) → Succ(zzz9100)
new_primPlusNat2(Zero, Zero) → Zero
new_primPlusNat2(Succ(zzz900), Zero) → Succ(zzz900)
new_primMulNat0(zzz6200) → new_primPlusNat3(Succ(new_primPlusNat3(new_primPlusNat1(zzz6200), zzz6200)), Succ(zzz6200))

The set Q consists of the following terms:

new_primPlusNat2(Zero, Succ(x0))
new_primMulNat0(x0)
new_primPlusNat3(x0, Succ(x1))
new_primPlusNat2(Succ(x0), Succ(x1))
new_primPlusNat3(x0, Zero)
new_primPlusNat1(Zero)
new_primPlusNat2(Zero, Zero)
new_primPlusNat1(Succ(x0))
new_primPlusNat2(Succ(x0), Zero)

We have to consider all minimal (P,Q,R)-chains.
By rewriting [15] the rule new_mkVBalBranch3MkVBalBranch244(zzz972, zzz973, zzz974, zzz975, zzz976, zzz977, zzz978, zzz979, zzz980, zzz981, zzz982, bc) → new_mkVBalBranch3MkVBalBranch128(zzz972, zzz973, zzz974, zzz975, zzz976, zzz977, zzz978, zzz979, zzz980, zzz981, zzz982, new_primPlusNat2(new_primMulNat0(zzz974), Succ(zzz974)), bc) at position [11,0] we obtained the following new rules:

new_mkVBalBranch3MkVBalBranch244(zzz972, zzz973, zzz974, zzz975, zzz976, zzz977, zzz978, zzz979, zzz980, zzz981, zzz982, bc) → new_mkVBalBranch3MkVBalBranch128(zzz972, zzz973, zzz974, zzz975, zzz976, zzz977, zzz978, zzz979, zzz980, zzz981, zzz982, new_primPlusNat2(new_primPlusNat3(Succ(new_primPlusNat3(new_primPlusNat1(zzz974), zzz974)), Succ(zzz974)), Succ(zzz974)), bc)



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

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

new_mkVBalBranch3MkVBalBranch129(zzz1851, zzz1852, zzz1853, zzz1854, zzz1855, zzz1856, zzz1857, zzz1858, zzz1859, zzz1860, zzz1861, Zero, Succ(zzz18630), bd) → new_mkVBalBranch1(zzz1861, zzz1860, Branch(zzz1851, zzz1852, Neg(Succ(zzz1853)), zzz1854, zzz1855), bd)
new_mkVBalBranch3MkVBalBranch128(zzz972, zzz973, zzz974, zzz975, zzz976, zzz977, zzz978, zzz979, zzz980, zzz981, zzz982, Succ(zzz10190), bc) → new_mkVBalBranch3MkVBalBranch129(zzz972, zzz973, zzz974, zzz975, zzz976, zzz977, zzz978, zzz979, zzz980, zzz981, zzz982, Succ(zzz979), Succ(zzz10190), bc)
new_mkVBalBranch3MkVBalBranch241(zzz3170, zzz3171, Pos(zzz31720), zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, Succ(zzz4190), h) → new_mkVBalBranch1(zzz31, Branch(zzz330, zzz331, Neg(Succ(zzz33200)), zzz333, zzz334), zzz3173, h)
new_mkVBalBranch3MkVBalBranch127(zzz3170, zzz3171, zzz317200, zzz3173, zzz3174, zzz330, zzz331, zzz333, zzz334, zzz31, Succ(zzz5500), h) → new_mkVBalBranch1(zzz31, zzz334, Branch(zzz3170, zzz3171, Neg(Succ(zzz317200)), zzz3173, zzz3174), h)
new_mkVBalBranch3MkVBalBranch236(zzz958, zzz959, zzz960, zzz961, zzz962, zzz963, zzz964, zzz965, zzz966, zzz967, zzz968, Succ(zzz9690), Zero, ba) → new_mkVBalBranch3MkVBalBranch124(zzz958, zzz959, zzz960, zzz961, zzz962, zzz963, zzz964, zzz965, zzz966, zzz967, zzz968, new_primPlusNat2(new_primPlusNat3(Succ(new_primPlusNat3(new_primPlusNat1(zzz960), zzz960)), Succ(zzz960)), Succ(zzz960)), ba)
new_mkVBalBranch3MkVBalBranch242(zzz972, zzz973, zzz974, zzz975, zzz976, zzz977, zzz978, zzz979, zzz980, zzz981, zzz982, Succ(zzz9830), Zero, bc) → new_mkVBalBranch3MkVBalBranch128(zzz972, zzz973, zzz974, zzz975, zzz976, zzz977, zzz978, zzz979, zzz980, zzz981, zzz982, new_primPlusNat2(new_primPlusNat3(Succ(new_primPlusNat3(new_primPlusNat1(zzz974), zzz974)), Succ(zzz974)), Succ(zzz974)), bc)
new_mkVBalBranch3MkVBalBranch129(zzz1851, zzz1852, zzz1853, zzz1854, zzz1855, zzz1856, zzz1857, zzz1858, zzz1859, zzz1860, zzz1861, Succ(zzz18620), Succ(zzz18630), bd) → new_mkVBalBranch3MkVBalBranch129(zzz1851, zzz1852, zzz1853, zzz1854, zzz1855, zzz1856, zzz1857, zzz1858, zzz1859, zzz1860, zzz1861, zzz18620, zzz18630, bd)
new_mkVBalBranch3MkVBalBranch124(zzz958, zzz959, zzz960, zzz961, zzz962, zzz963, zzz964, zzz965, zzz966, zzz967, zzz968, Zero, ba) → new_mkVBalBranch3MkVBalBranch125(zzz958, zzz959, zzz960, zzz961, zzz962, zzz963, zzz964, zzz965, zzz966, zzz967, zzz968, Zero, Succ(zzz965), ba)
new_mkVBalBranch3MkVBalBranch235(zzz3170, zzz3171, Pos(Succ(zzz317200)), zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, Succ(zzz4170), h) → new_mkVBalBranch3MkVBalBranch236(zzz3170, zzz3171, zzz317200, zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, zzz4170, zzz317200, h)
new_mkVBalBranch3MkVBalBranch242(zzz972, zzz973, zzz974, zzz975, zzz976, zzz977, zzz978, zzz979, zzz980, zzz981, zzz982, Succ(zzz9830), Succ(zzz9840), bc) → new_mkVBalBranch3MkVBalBranch242(zzz972, zzz973, zzz974, zzz975, zzz976, zzz977, zzz978, zzz979, zzz980, zzz981, zzz982, zzz9830, zzz9840, bc)
new_mkVBalBranch3MkVBalBranch236(zzz958, zzz959, zzz960, zzz961, zzz962, zzz963, zzz964, zzz965, zzz966, zzz967, zzz968, Succ(zzz9690), Succ(zzz9700), ba) → new_mkVBalBranch3MkVBalBranch236(zzz958, zzz959, zzz960, zzz961, zzz962, zzz963, zzz964, zzz965, zzz966, zzz967, zzz968, zzz9690, zzz9700, ba)
new_mkVBalBranch1(zzz31, Branch(zzz330, zzz331, Pos(Succ(zzz33200)), zzz333, zzz334), Branch(zzz3170, zzz3171, zzz3172, zzz3173, zzz3174), h) → new_mkVBalBranch3MkVBalBranch235(zzz3170, zzz3171, zzz3172, zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, new_primPlusNat2(Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat3(new_primPlusNat1(zzz33200), zzz33200)), zzz33200))), Succ(zzz33200)), h)
new_mkVBalBranch3MkVBalBranch241(zzz3170, zzz3171, Neg(Succ(zzz317200)), zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, Succ(zzz4190), h) → new_mkVBalBranch3MkVBalBranch242(zzz3170, zzz3171, zzz317200, zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, zzz317200, zzz4190, h)
new_mkVBalBranch3MkVBalBranch241(zzz3170, zzz3171, Neg(Succ(zzz317200)), zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, Zero, h) → new_mkVBalBranch3MkVBalBranch242(zzz3170, zzz3171, zzz317200, zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, Succ(zzz317200), Zero, h)
new_mkVBalBranch1(zzz31, Branch(zzz330, zzz331, Pos(Zero), zzz333, zzz334), Branch(zzz3170, zzz3171, Pos(Succ(zzz317200)), zzz3173, zzz3174), h) → new_mkVBalBranch1(zzz31, Branch(zzz330, zzz331, Pos(Zero), zzz333, zzz334), zzz3173, h)
new_mkVBalBranch3MkVBalBranch235(zzz3170, zzz3171, Neg(Succ(zzz317200)), zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, Succ(zzz4170), h) → new_mkVBalBranch3MkVBalBranch123(zzz3170, zzz3171, zzz317200, zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, new_primPlusNat2(Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat3(new_primPlusNat1(zzz317200), zzz317200)), zzz317200))), Succ(zzz317200)), h)
new_mkVBalBranch3MkVBalBranch237(zzz3170, zzz3171, zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, h) → new_mkVBalBranch1(zzz31, zzz334, Branch(zzz3170, zzz3171, Pos(Zero), zzz3173, zzz3174), h)
new_mkVBalBranch3MkVBalBranch243(zzz3170, zzz3171, zzz31720, zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, h) → new_mkVBalBranch1(zzz31, Branch(zzz330, zzz331, Neg(Succ(zzz33200)), zzz333, zzz334), zzz3173, h)
new_mkVBalBranch3MkVBalBranch235(zzz3170, zzz3171, Pos(Zero), zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, Succ(zzz4170), h) → new_mkVBalBranch3MkVBalBranch237(zzz3170, zzz3171, zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, h)
new_mkVBalBranch3MkVBalBranch236(zzz958, zzz959, zzz960, zzz961, zzz962, zzz963, zzz964, zzz965, zzz966, zzz967, zzz968, Zero, Succ(zzz9700), ba) → new_mkVBalBranch1(zzz968, Branch(zzz963, zzz964, Pos(Succ(zzz965)), zzz966, zzz967), zzz961, ba)
new_mkVBalBranch3MkVBalBranch125(zzz1337, zzz1338, zzz1339, zzz1340, zzz1341, zzz1342, zzz1343, zzz1344, zzz1345, zzz1346, zzz1347, Succ(zzz13480), Succ(zzz13490), bb) → new_mkVBalBranch3MkVBalBranch125(zzz1337, zzz1338, zzz1339, zzz1340, zzz1341, zzz1342, zzz1343, zzz1344, zzz1345, zzz1346, zzz1347, zzz13480, zzz13490, bb)
new_mkVBalBranch3MkVBalBranch123(zzz3170, zzz3171, zzz317200, zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, Succ(zzz5620), h) → new_mkVBalBranch1(zzz31, zzz334, Branch(zzz3170, zzz3171, Neg(Succ(zzz317200)), zzz3173, zzz3174), h)
new_mkVBalBranch3MkVBalBranch125(zzz1337, zzz1338, zzz1339, zzz1340, zzz1341, zzz1342, zzz1343, zzz1344, zzz1345, zzz1346, zzz1347, Zero, Succ(zzz13490), bb) → new_mkVBalBranch1(zzz1347, zzz1346, Branch(zzz1337, zzz1338, Pos(Succ(zzz1339)), zzz1340, zzz1341), bb)
new_mkVBalBranch3MkVBalBranch242(zzz972, zzz973, zzz974, zzz975, zzz976, zzz977, zzz978, zzz979, zzz980, zzz981, zzz982, Zero, Succ(zzz9840), bc) → new_mkVBalBranch1(zzz982, Branch(zzz977, zzz978, Neg(Succ(zzz979)), zzz980, zzz981), zzz975, bc)
new_mkVBalBranch1(zzz31, Branch(zzz330, zzz331, Neg(Zero), zzz333, zzz334), Branch(zzz3170, zzz3171, Neg(Succ(zzz317200)), zzz3173, zzz3174), h) → new_mkVBalBranch3MkVBalBranch127(zzz3170, zzz3171, zzz317200, zzz3173, zzz3174, zzz330, zzz331, zzz333, zzz334, zzz31, new_primPlusNat2(new_primPlusNat3(Succ(new_primPlusNat3(new_primPlusNat1(zzz317200), zzz317200)), Succ(zzz317200)), Succ(zzz317200)), h)
new_mkVBalBranch3MkVBalBranch238(zzz3170, zzz3171, Succ(zzz317200), zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, h) → new_mkVBalBranch3MkVBalBranch123(zzz3170, zzz3171, zzz317200, zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, new_primPlusNat2(Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat3(new_primPlusNat1(zzz317200), zzz317200)), zzz317200))), Succ(zzz317200)), h)
new_mkVBalBranch3MkVBalBranch235(zzz3170, zzz3171, Neg(Succ(zzz317200)), zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, Zero, h) → new_mkVBalBranch3MkVBalBranch238(zzz3170, zzz3171, Succ(zzz317200), zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, h)
new_mkVBalBranch3MkVBalBranch240(zzz958, zzz959, zzz960, zzz961, zzz962, zzz963, zzz964, zzz965, zzz966, zzz967, zzz968, ba) → new_mkVBalBranch3MkVBalBranch124(zzz958, zzz959, zzz960, zzz961, zzz962, zzz963, zzz964, zzz965, zzz966, zzz967, zzz968, new_primPlusNat2(new_primPlusNat3(Succ(new_primPlusNat3(new_primPlusNat1(zzz960), zzz960)), Succ(zzz960)), Succ(zzz960)), ba)
new_mkVBalBranch3MkVBalBranch241(zzz3170, zzz3171, Pos(Succ(zzz317200)), zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, Zero, h) → new_mkVBalBranch3MkVBalBranch243(zzz3170, zzz3171, Succ(zzz317200), zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, h)
new_mkVBalBranch3MkVBalBranch126(zzz3170, zzz3171, zzz317200, zzz3173, zzz3174, zzz330, zzz331, zzz333, zzz334, zzz31, Succ(zzz5350), h) → new_mkVBalBranch1(zzz31, zzz334, Branch(zzz3170, zzz3171, Neg(Succ(zzz317200)), zzz3173, zzz3174), h)
new_mkVBalBranch3MkVBalBranch241(zzz3170, zzz3171, Neg(Zero), zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, Succ(zzz4190), h) → new_mkVBalBranch1(zzz31, Branch(zzz330, zzz331, Neg(Succ(zzz33200)), zzz333, zzz334), zzz3173, h)
new_mkVBalBranch3MkVBalBranch123(zzz3170, zzz3171, zzz317200, zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, Zero, h) → new_mkVBalBranch3MkVBalBranch130(zzz3170, zzz3171, zzz317200, zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, h)
new_mkVBalBranch3MkVBalBranch124(zzz958, zzz959, zzz960, zzz961, zzz962, zzz963, zzz964, zzz965, zzz966, zzz967, zzz968, Succ(zzz10180), ba) → new_mkVBalBranch3MkVBalBranch125(zzz958, zzz959, zzz960, zzz961, zzz962, zzz963, zzz964, zzz965, zzz966, zzz967, zzz968, Succ(zzz10180), Succ(zzz965), ba)
new_mkVBalBranch3MkVBalBranch235(zzz3170, zzz3171, Pos(Succ(zzz317200)), zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, Zero, h) → new_mkVBalBranch3MkVBalBranch236(zzz3170, zzz3171, zzz317200, zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, Zero, Succ(zzz317200), h)
new_mkVBalBranch3MkVBalBranch239(zzz3170, zzz3171, Zero, zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, h) → new_mkVBalBranch1(zzz31, zzz334, Branch(zzz3170, zzz3171, Neg(Zero), zzz3173, zzz3174), h)
new_mkVBalBranch3MkVBalBranch235(zzz3170, zzz3171, Pos(Zero), zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, Zero, h) → new_mkVBalBranch1(zzz31, zzz334, Branch(zzz3170, zzz3171, Pos(Zero), zzz3173, zzz3174), h)
new_mkVBalBranch3MkVBalBranch242(zzz972, zzz973, zzz974, zzz975, zzz976, zzz977, zzz978, zzz979, zzz980, zzz981, zzz982, Zero, Zero, bc) → new_mkVBalBranch3MkVBalBranch244(zzz972, zzz973, zzz974, zzz975, zzz976, zzz977, zzz978, zzz979, zzz980, zzz981, zzz982, bc)
new_mkVBalBranch1(zzz31, Branch(zzz330, zzz331, Pos(Zero), zzz333, zzz334), Branch(zzz3170, zzz3171, Neg(Succ(zzz317200)), zzz3173, zzz3174), h) → new_mkVBalBranch3MkVBalBranch126(zzz3170, zzz3171, zzz317200, zzz3173, zzz3174, zzz330, zzz331, zzz333, zzz334, zzz31, new_primPlusNat2(new_primMulNat0(zzz317200), Succ(zzz317200)), h)
new_mkVBalBranch3MkVBalBranch130(zzz3170, zzz3171, zzz317200, zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, h) → new_mkVBalBranch1(zzz31, zzz334, Branch(zzz3170, zzz3171, Neg(Succ(zzz317200)), zzz3173, zzz3174), h)
new_mkVBalBranch3MkVBalBranch235(zzz3170, zzz3171, Neg(Zero), zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, Zero, h) → new_mkVBalBranch3MkVBalBranch239(zzz3170, zzz3171, Zero, zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, h)
new_mkVBalBranch1(zzz31, Branch(zzz330, zzz331, Neg(Zero), zzz333, zzz334), Branch(zzz3170, zzz3171, Pos(Succ(zzz317200)), zzz3173, zzz3174), h) → new_mkVBalBranch1(zzz31, Branch(zzz330, zzz331, Neg(Zero), zzz333, zzz334), zzz3173, h)
new_mkVBalBranch3MkVBalBranch235(zzz3170, zzz3171, Neg(Zero), zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, Succ(zzz4170), h) → new_mkVBalBranch1(zzz31, zzz334, Branch(zzz3170, zzz3171, Neg(Zero), zzz3173, zzz3174), h)
new_mkVBalBranch1(zzz31, Branch(zzz330, zzz331, Neg(Succ(zzz33200)), zzz333, zzz334), Branch(zzz3170, zzz3171, zzz3172, zzz3173, zzz3174), h) → new_mkVBalBranch3MkVBalBranch241(zzz3170, zzz3171, zzz3172, zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, new_primPlusNat2(Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat3(new_primPlusNat1(zzz33200), zzz33200)), zzz33200))), Succ(zzz33200)), h)
new_mkVBalBranch3MkVBalBranch244(zzz972, zzz973, zzz974, zzz975, zzz976, zzz977, zzz978, zzz979, zzz980, zzz981, zzz982, bc) → new_mkVBalBranch3MkVBalBranch128(zzz972, zzz973, zzz974, zzz975, zzz976, zzz977, zzz978, zzz979, zzz980, zzz981, zzz982, new_primPlusNat2(new_primPlusNat3(Succ(new_primPlusNat3(new_primPlusNat1(zzz974), zzz974)), Succ(zzz974)), Succ(zzz974)), bc)
new_mkVBalBranch3MkVBalBranch236(zzz958, zzz959, zzz960, zzz961, zzz962, zzz963, zzz964, zzz965, zzz966, zzz967, zzz968, Zero, Zero, ba) → new_mkVBalBranch3MkVBalBranch240(zzz958, zzz959, zzz960, zzz961, zzz962, zzz963, zzz964, zzz965, zzz966, zzz967, zzz968, ba)

The TRS R consists of the following rules:

new_primPlusNat1(Zero) → Zero
new_primPlusNat1(Succ(zzz62000)) → Succ(Succ(new_primPlusNat1(zzz62000)))
new_primPlusNat3(zzz90, Succ(zzz910)) → Succ(Succ(new_primPlusNat2(zzz90, zzz910)))
new_primPlusNat3(zzz90, Zero) → Succ(zzz90)
new_primPlusNat2(Succ(zzz900), Succ(zzz9100)) → Succ(Succ(new_primPlusNat2(zzz900, zzz9100)))
new_primPlusNat2(Zero, Succ(zzz9100)) → Succ(zzz9100)
new_primPlusNat2(Zero, Zero) → Zero
new_primPlusNat2(Succ(zzz900), Zero) → Succ(zzz900)
new_primMulNat0(zzz6200) → new_primPlusNat3(Succ(new_primPlusNat3(new_primPlusNat1(zzz6200), zzz6200)), Succ(zzz6200))

The set Q consists of the following terms:

new_primPlusNat2(Zero, Succ(x0))
new_primMulNat0(x0)
new_primPlusNat3(x0, Succ(x1))
new_primPlusNat2(Succ(x0), Succ(x1))
new_primPlusNat3(x0, Zero)
new_primPlusNat1(Zero)
new_primPlusNat2(Zero, Zero)
new_primPlusNat1(Succ(x0))
new_primPlusNat2(Succ(x0), Zero)

We have to consider all minimal (P,Q,R)-chains.
By rewriting [15] the rule new_mkVBalBranch1(zzz31, Branch(zzz330, zzz331, Pos(Zero), zzz333, zzz334), Branch(zzz3170, zzz3171, Neg(Succ(zzz317200)), zzz3173, zzz3174), h) → new_mkVBalBranch3MkVBalBranch126(zzz3170, zzz3171, zzz317200, zzz3173, zzz3174, zzz330, zzz331, zzz333, zzz334, zzz31, new_primPlusNat2(new_primMulNat0(zzz317200), Succ(zzz317200)), h) at position [10,0] we obtained the following new rules:

new_mkVBalBranch1(zzz31, Branch(zzz330, zzz331, Pos(Zero), zzz333, zzz334), Branch(zzz3170, zzz3171, Neg(Succ(zzz317200)), zzz3173, zzz3174), h) → new_mkVBalBranch3MkVBalBranch126(zzz3170, zzz3171, zzz317200, zzz3173, zzz3174, zzz330, zzz331, zzz333, zzz334, zzz31, new_primPlusNat2(new_primPlusNat3(Succ(new_primPlusNat3(new_primPlusNat1(zzz317200), zzz317200)), Succ(zzz317200)), Succ(zzz317200)), 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
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                    ↳ DependencyGraphProof
                                      ↳ QDP
                                        ↳ Rewriting
                                          ↳ QDP
                                            ↳ Rewriting
                                              ↳ QDP
                                                ↳ Rewriting
                                                  ↳ QDP
                                                    ↳ Rewriting
                                                      ↳ QDP
                                                        ↳ Rewriting
                                                          ↳ QDP
                                                            ↳ Rewriting
                                                              ↳ QDP
                                                                ↳ Rewriting
                                                                  ↳ QDP
                                                                    ↳ Rewriting
                                                                      ↳ QDP
                                                                        ↳ Rewriting
                                                                          ↳ QDP
                                                                            ↳ Rewriting
                                                                              ↳ QDP
                                                                                ↳ UsableRulesProof
                                                                                  ↳ QDP
                                                                                    ↳ QReductionProof
                                                                                      ↳ QDP
                                                                                        ↳ Rewriting
                                                                                          ↳ QDP
                                                                                            ↳ Rewriting
                                                                                              ↳ QDP
                                                                                                ↳ Rewriting
                                                                                                  ↳ QDP
                                                                                                    ↳ Rewriting
                                                                                                      ↳ QDP
                                                                                                        ↳ Rewriting
                                                                                                          ↳ QDP
                                                                                                            ↳ Rewriting
                                                                                                              ↳ QDP
                                                                                                                ↳ Rewriting
                                                                                                                  ↳ QDP
                                                                                                                    ↳ Rewriting
                                                                                                                      ↳ QDP
                                                                                                                        ↳ Rewriting
                                                                                                                          ↳ QDP
                                                                                                                            ↳ Rewriting
                                                                                                                              ↳ QDP
                                                                                                                                ↳ UsableRulesProof
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP

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

new_mkVBalBranch3MkVBalBranch129(zzz1851, zzz1852, zzz1853, zzz1854, zzz1855, zzz1856, zzz1857, zzz1858, zzz1859, zzz1860, zzz1861, Zero, Succ(zzz18630), bd) → new_mkVBalBranch1(zzz1861, zzz1860, Branch(zzz1851, zzz1852, Neg(Succ(zzz1853)), zzz1854, zzz1855), bd)
new_mkVBalBranch3MkVBalBranch127(zzz3170, zzz3171, zzz317200, zzz3173, zzz3174, zzz330, zzz331, zzz333, zzz334, zzz31, Succ(zzz5500), h) → new_mkVBalBranch1(zzz31, zzz334, Branch(zzz3170, zzz3171, Neg(Succ(zzz317200)), zzz3173, zzz3174), h)
new_mkVBalBranch3MkVBalBranch241(zzz3170, zzz3171, Pos(zzz31720), zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, Succ(zzz4190), h) → new_mkVBalBranch1(zzz31, Branch(zzz330, zzz331, Neg(Succ(zzz33200)), zzz333, zzz334), zzz3173, h)
new_mkVBalBranch3MkVBalBranch128(zzz972, zzz973, zzz974, zzz975, zzz976, zzz977, zzz978, zzz979, zzz980, zzz981, zzz982, Succ(zzz10190), bc) → new_mkVBalBranch3MkVBalBranch129(zzz972, zzz973, zzz974, zzz975, zzz976, zzz977, zzz978, zzz979, zzz980, zzz981, zzz982, Succ(zzz979), Succ(zzz10190), bc)
new_mkVBalBranch3MkVBalBranch236(zzz958, zzz959, zzz960, zzz961, zzz962, zzz963, zzz964, zzz965, zzz966, zzz967, zzz968, Succ(zzz9690), Zero, ba) → new_mkVBalBranch3MkVBalBranch124(zzz958, zzz959, zzz960, zzz961, zzz962, zzz963, zzz964, zzz965, zzz966, zzz967, zzz968, new_primPlusNat2(new_primPlusNat3(Succ(new_primPlusNat3(new_primPlusNat1(zzz960), zzz960)), Succ(zzz960)), Succ(zzz960)), ba)
new_mkVBalBranch3MkVBalBranch242(zzz972, zzz973, zzz974, zzz975, zzz976, zzz977, zzz978, zzz979, zzz980, zzz981, zzz982, Succ(zzz9830), Zero, bc) → new_mkVBalBranch3MkVBalBranch128(zzz972, zzz973, zzz974, zzz975, zzz976, zzz977, zzz978, zzz979, zzz980, zzz981, zzz982, new_primPlusNat2(new_primPlusNat3(Succ(new_primPlusNat3(new_primPlusNat1(zzz974), zzz974)), Succ(zzz974)), Succ(zzz974)), bc)
new_mkVBalBranch3MkVBalBranch129(zzz1851, zzz1852, zzz1853, zzz1854, zzz1855, zzz1856, zzz1857, zzz1858, zzz1859, zzz1860, zzz1861, Succ(zzz18620), Succ(zzz18630), bd) → new_mkVBalBranch3MkVBalBranch129(zzz1851, zzz1852, zzz1853, zzz1854, zzz1855, zzz1856, zzz1857, zzz1858, zzz1859, zzz1860, zzz1861, zzz18620, zzz18630, bd)
new_mkVBalBranch3MkVBalBranch124(zzz958, zzz959, zzz960, zzz961, zzz962, zzz963, zzz964, zzz965, zzz966, zzz967, zzz968, Zero, ba) → new_mkVBalBranch3MkVBalBranch125(zzz958, zzz959, zzz960, zzz961, zzz962, zzz963, zzz964, zzz965, zzz966, zzz967, zzz968, Zero, Succ(zzz965), ba)
new_mkVBalBranch3MkVBalBranch242(zzz972, zzz973, zzz974, zzz975, zzz976, zzz977, zzz978, zzz979, zzz980, zzz981, zzz982, Succ(zzz9830), Succ(zzz9840), bc) → new_mkVBalBranch3MkVBalBranch242(zzz972, zzz973, zzz974, zzz975, zzz976, zzz977, zzz978, zzz979, zzz980, zzz981, zzz982, zzz9830, zzz9840, bc)
new_mkVBalBranch3MkVBalBranch235(zzz3170, zzz3171, Pos(Succ(zzz317200)), zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, Succ(zzz4170), h) → new_mkVBalBranch3MkVBalBranch236(zzz3170, zzz3171, zzz317200, zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, zzz4170, zzz317200, h)
new_mkVBalBranch1(zzz31, Branch(zzz330, zzz331, Pos(Succ(zzz33200)), zzz333, zzz334), Branch(zzz3170, zzz3171, zzz3172, zzz3173, zzz3174), h) → new_mkVBalBranch3MkVBalBranch235(zzz3170, zzz3171, zzz3172, zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, new_primPlusNat2(Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat3(new_primPlusNat1(zzz33200), zzz33200)), zzz33200))), Succ(zzz33200)), h)
new_mkVBalBranch3MkVBalBranch236(zzz958, zzz959, zzz960, zzz961, zzz962, zzz963, zzz964, zzz965, zzz966, zzz967, zzz968, Succ(zzz9690), Succ(zzz9700), ba) → new_mkVBalBranch3MkVBalBranch236(zzz958, zzz959, zzz960, zzz961, zzz962, zzz963, zzz964, zzz965, zzz966, zzz967, zzz968, zzz9690, zzz9700, ba)
new_mkVBalBranch3MkVBalBranch241(zzz3170, zzz3171, Neg(Succ(zzz317200)), zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, Succ(zzz4190), h) → new_mkVBalBranch3MkVBalBranch242(zzz3170, zzz3171, zzz317200, zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, zzz317200, zzz4190, h)
new_mkVBalBranch3MkVBalBranch241(zzz3170, zzz3171, Neg(Succ(zzz317200)), zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, Zero, h) → new_mkVBalBranch3MkVBalBranch242(zzz3170, zzz3171, zzz317200, zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, Succ(zzz317200), Zero, h)
new_mkVBalBranch1(zzz31, Branch(zzz330, zzz331, Pos(Zero), zzz333, zzz334), Branch(zzz3170, zzz3171, Pos(Succ(zzz317200)), zzz3173, zzz3174), h) → new_mkVBalBranch1(zzz31, Branch(zzz330, zzz331, Pos(Zero), zzz333, zzz334), zzz3173, h)
new_mkVBalBranch3MkVBalBranch243(zzz3170, zzz3171, zzz31720, zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, h) → new_mkVBalBranch1(zzz31, Branch(zzz330, zzz331, Neg(Succ(zzz33200)), zzz333, zzz334), zzz3173, h)
new_mkVBalBranch3MkVBalBranch237(zzz3170, zzz3171, zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, h) → new_mkVBalBranch1(zzz31, zzz334, Branch(zzz3170, zzz3171, Pos(Zero), zzz3173, zzz3174), h)
new_mkVBalBranch3MkVBalBranch235(zzz3170, zzz3171, Neg(Succ(zzz317200)), zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, Succ(zzz4170), h) → new_mkVBalBranch3MkVBalBranch123(zzz3170, zzz3171, zzz317200, zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, new_primPlusNat2(Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat3(new_primPlusNat1(zzz317200), zzz317200)), zzz317200))), Succ(zzz317200)), h)
new_mkVBalBranch3MkVBalBranch235(zzz3170, zzz3171, Pos(Zero), zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, Succ(zzz4170), h) → new_mkVBalBranch3MkVBalBranch237(zzz3170, zzz3171, zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, h)
new_mkVBalBranch3MkVBalBranch236(zzz958, zzz959, zzz960, zzz961, zzz962, zzz963, zzz964, zzz965, zzz966, zzz967, zzz968, Zero, Succ(zzz9700), ba) → new_mkVBalBranch1(zzz968, Branch(zzz963, zzz964, Pos(Succ(zzz965)), zzz966, zzz967), zzz961, ba)
new_mkVBalBranch3MkVBalBranch125(zzz1337, zzz1338, zzz1339, zzz1340, zzz1341, zzz1342, zzz1343, zzz1344, zzz1345, zzz1346, zzz1347, Succ(zzz13480), Succ(zzz13490), bb) → new_mkVBalBranch3MkVBalBranch125(zzz1337, zzz1338, zzz1339, zzz1340, zzz1341, zzz1342, zzz1343, zzz1344, zzz1345, zzz1346, zzz1347, zzz13480, zzz13490, bb)
new_mkVBalBranch3MkVBalBranch123(zzz3170, zzz3171, zzz317200, zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, Succ(zzz5620), h) → new_mkVBalBranch1(zzz31, zzz334, Branch(zzz3170, zzz3171, Neg(Succ(zzz317200)), zzz3173, zzz3174), h)
new_mkVBalBranch3MkVBalBranch125(zzz1337, zzz1338, zzz1339, zzz1340, zzz1341, zzz1342, zzz1343, zzz1344, zzz1345, zzz1346, zzz1347, Zero, Succ(zzz13490), bb) → new_mkVBalBranch1(zzz1347, zzz1346, Branch(zzz1337, zzz1338, Pos(Succ(zzz1339)), zzz1340, zzz1341), bb)
new_mkVBalBranch3MkVBalBranch242(zzz972, zzz973, zzz974, zzz975, zzz976, zzz977, zzz978, zzz979, zzz980, zzz981, zzz982, Zero, Succ(zzz9840), bc) → new_mkVBalBranch1(zzz982, Branch(zzz977, zzz978, Neg(Succ(zzz979)), zzz980, zzz981), zzz975, bc)
new_mkVBalBranch3MkVBalBranch238(zzz3170, zzz3171, Succ(zzz317200), zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, h) → new_mkVBalBranch3MkVBalBranch123(zzz3170, zzz3171, zzz317200, zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, new_primPlusNat2(Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat3(new_primPlusNat1(zzz317200), zzz317200)), zzz317200))), Succ(zzz317200)), h)
new_mkVBalBranch1(zzz31, Branch(zzz330, zzz331, Neg(Zero), zzz333, zzz334), Branch(zzz3170, zzz3171, Neg(Succ(zzz317200)), zzz3173, zzz3174), h) → new_mkVBalBranch3MkVBalBranch127(zzz3170, zzz3171, zzz317200, zzz3173, zzz3174, zzz330, zzz331, zzz333, zzz334, zzz31, new_primPlusNat2(new_primPlusNat3(Succ(new_primPlusNat3(new_primPlusNat1(zzz317200), zzz317200)), Succ(zzz317200)), Succ(zzz317200)), h)
new_mkVBalBranch3MkVBalBranch235(zzz3170, zzz3171, Neg(Succ(zzz317200)), zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, Zero, h) → new_mkVBalBranch3MkVBalBranch238(zzz3170, zzz3171, Succ(zzz317200), zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, h)
new_mkVBalBranch3MkVBalBranch240(zzz958, zzz959, zzz960, zzz961, zzz962, zzz963, zzz964, zzz965, zzz966, zzz967, zzz968, ba) → new_mkVBalBranch3MkVBalBranch124(zzz958, zzz959, zzz960, zzz961, zzz962, zzz963, zzz964, zzz965, zzz966, zzz967, zzz968, new_primPlusNat2(new_primPlusNat3(Succ(new_primPlusNat3(new_primPlusNat1(zzz960), zzz960)), Succ(zzz960)), Succ(zzz960)), ba)
new_mkVBalBranch3MkVBalBranch241(zzz3170, zzz3171, Pos(Succ(zzz317200)), zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, Zero, h) → new_mkVBalBranch3MkVBalBranch243(zzz3170, zzz3171, Succ(zzz317200), zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, h)
new_mkVBalBranch1(zzz31, Branch(zzz330, zzz331, Pos(Zero), zzz333, zzz334), Branch(zzz3170, zzz3171, Neg(Succ(zzz317200)), zzz3173, zzz3174), h) → new_mkVBalBranch3MkVBalBranch126(zzz3170, zzz3171, zzz317200, zzz3173, zzz3174, zzz330, zzz331, zzz333, zzz334, zzz31, new_primPlusNat2(new_primPlusNat3(Succ(new_primPlusNat3(new_primPlusNat1(zzz317200), zzz317200)), Succ(zzz317200)), Succ(zzz317200)), h)
new_mkVBalBranch3MkVBalBranch126(zzz3170, zzz3171, zzz317200, zzz3173, zzz3174, zzz330, zzz331, zzz333, zzz334, zzz31, Succ(zzz5350), h) → new_mkVBalBranch1(zzz31, zzz334, Branch(zzz3170, zzz3171, Neg(Succ(zzz317200)), zzz3173, zzz3174), h)
new_mkVBalBranch3MkVBalBranch123(zzz3170, zzz3171, zzz317200, zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, Zero, h) → new_mkVBalBranch3MkVBalBranch130(zzz3170, zzz3171, zzz317200, zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, h)
new_mkVBalBranch3MkVBalBranch241(zzz3170, zzz3171, Neg(Zero), zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, Succ(zzz4190), h) → new_mkVBalBranch1(zzz31, Branch(zzz330, zzz331, Neg(Succ(zzz33200)), zzz333, zzz334), zzz3173, h)
new_mkVBalBranch3MkVBalBranch124(zzz958, zzz959, zzz960, zzz961, zzz962, zzz963, zzz964, zzz965, zzz966, zzz967, zzz968, Succ(zzz10180), ba) → new_mkVBalBranch3MkVBalBranch125(zzz958, zzz959, zzz960, zzz961, zzz962, zzz963, zzz964, zzz965, zzz966, zzz967, zzz968, Succ(zzz10180), Succ(zzz965), ba)
new_mkVBalBranch3MkVBalBranch235(zzz3170, zzz3171, Pos(Succ(zzz317200)), zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, Zero, h) → new_mkVBalBranch3MkVBalBranch236(zzz3170, zzz3171, zzz317200, zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, Zero, Succ(zzz317200), h)
new_mkVBalBranch3MkVBalBranch239(zzz3170, zzz3171, Zero, zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, h) → new_mkVBalBranch1(zzz31, zzz334, Branch(zzz3170, zzz3171, Neg(Zero), zzz3173, zzz3174), h)
new_mkVBalBranch3MkVBalBranch235(zzz3170, zzz3171, Pos(Zero), zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, Zero, h) → new_mkVBalBranch1(zzz31, zzz334, Branch(zzz3170, zzz3171, Pos(Zero), zzz3173, zzz3174), h)
new_mkVBalBranch3MkVBalBranch242(zzz972, zzz973, zzz974, zzz975, zzz976, zzz977, zzz978, zzz979, zzz980, zzz981, zzz982, Zero, Zero, bc) → new_mkVBalBranch3MkVBalBranch244(zzz972, zzz973, zzz974, zzz975, zzz976, zzz977, zzz978, zzz979, zzz980, zzz981, zzz982, bc)
new_mkVBalBranch3MkVBalBranch130(zzz3170, zzz3171, zzz317200, zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, h) → new_mkVBalBranch1(zzz31, zzz334, Branch(zzz3170, zzz3171, Neg(Succ(zzz317200)), zzz3173, zzz3174), h)
new_mkVBalBranch1(zzz31, Branch(zzz330, zzz331, Neg(Zero), zzz333, zzz334), Branch(zzz3170, zzz3171, Pos(Succ(zzz317200)), zzz3173, zzz3174), h) → new_mkVBalBranch1(zzz31, Branch(zzz330, zzz331, Neg(Zero), zzz333, zzz334), zzz3173, h)
new_mkVBalBranch3MkVBalBranch235(zzz3170, zzz3171, Neg(Zero), zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, Zero, h) → new_mkVBalBranch3MkVBalBranch239(zzz3170, zzz3171, Zero, zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, h)
new_mkVBalBranch1(zzz31, Branch(zzz330, zzz331, Neg(Succ(zzz33200)), zzz333, zzz334), Branch(zzz3170, zzz3171, zzz3172, zzz3173, zzz3174), h) → new_mkVBalBranch3MkVBalBranch241(zzz3170, zzz3171, zzz3172, zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, new_primPlusNat2(Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat3(new_primPlusNat1(zzz33200), zzz33200)), zzz33200))), Succ(zzz33200)), h)
new_mkVBalBranch3MkVBalBranch235(zzz3170, zzz3171, Neg(Zero), zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, Succ(zzz4170), h) → new_mkVBalBranch1(zzz31, zzz334, Branch(zzz3170, zzz3171, Neg(Zero), zzz3173, zzz3174), h)
new_mkVBalBranch3MkVBalBranch236(zzz958, zzz959, zzz960, zzz961, zzz962, zzz963, zzz964, zzz965, zzz966, zzz967, zzz968, Zero, Zero, ba) → new_mkVBalBranch3MkVBalBranch240(zzz958, zzz959, zzz960, zzz961, zzz962, zzz963, zzz964, zzz965, zzz966, zzz967, zzz968, ba)
new_mkVBalBranch3MkVBalBranch244(zzz972, zzz973, zzz974, zzz975, zzz976, zzz977, zzz978, zzz979, zzz980, zzz981, zzz982, bc) → new_mkVBalBranch3MkVBalBranch128(zzz972, zzz973, zzz974, zzz975, zzz976, zzz977, zzz978, zzz979, zzz980, zzz981, zzz982, new_primPlusNat2(new_primPlusNat3(Succ(new_primPlusNat3(new_primPlusNat1(zzz974), zzz974)), Succ(zzz974)), Succ(zzz974)), bc)

The TRS R consists of the following rules:

new_primPlusNat1(Zero) → Zero
new_primPlusNat1(Succ(zzz62000)) → Succ(Succ(new_primPlusNat1(zzz62000)))
new_primPlusNat3(zzz90, Succ(zzz910)) → Succ(Succ(new_primPlusNat2(zzz90, zzz910)))
new_primPlusNat3(zzz90, Zero) → Succ(zzz90)
new_primPlusNat2(Succ(zzz900), Succ(zzz9100)) → Succ(Succ(new_primPlusNat2(zzz900, zzz9100)))
new_primPlusNat2(Zero, Succ(zzz9100)) → Succ(zzz9100)
new_primPlusNat2(Zero, Zero) → Zero
new_primPlusNat2(Succ(zzz900), Zero) → Succ(zzz900)
new_primMulNat0(zzz6200) → new_primPlusNat3(Succ(new_primPlusNat3(new_primPlusNat1(zzz6200), zzz6200)), Succ(zzz6200))

The set Q consists of the following terms:

new_primPlusNat2(Zero, Succ(x0))
new_primMulNat0(x0)
new_primPlusNat3(x0, Succ(x1))
new_primPlusNat2(Succ(x0), Succ(x1))
new_primPlusNat3(x0, Zero)
new_primPlusNat1(Zero)
new_primPlusNat2(Zero, Zero)
new_primPlusNat1(Succ(x0))
new_primPlusNat2(Succ(x0), Zero)

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

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

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

new_mkVBalBranch3MkVBalBranch129(zzz1851, zzz1852, zzz1853, zzz1854, zzz1855, zzz1856, zzz1857, zzz1858, zzz1859, zzz1860, zzz1861, Zero, Succ(zzz18630), bd) → new_mkVBalBranch1(zzz1861, zzz1860, Branch(zzz1851, zzz1852, Neg(Succ(zzz1853)), zzz1854, zzz1855), bd)
new_mkVBalBranch3MkVBalBranch127(zzz3170, zzz3171, zzz317200, zzz3173, zzz3174, zzz330, zzz331, zzz333, zzz334, zzz31, Succ(zzz5500), h) → new_mkVBalBranch1(zzz31, zzz334, Branch(zzz3170, zzz3171, Neg(Succ(zzz317200)), zzz3173, zzz3174), h)
new_mkVBalBranch3MkVBalBranch241(zzz3170, zzz3171, Pos(zzz31720), zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, Succ(zzz4190), h) → new_mkVBalBranch1(zzz31, Branch(zzz330, zzz331, Neg(Succ(zzz33200)), zzz333, zzz334), zzz3173, h)
new_mkVBalBranch3MkVBalBranch128(zzz972, zzz973, zzz974, zzz975, zzz976, zzz977, zzz978, zzz979, zzz980, zzz981, zzz982, Succ(zzz10190), bc) → new_mkVBalBranch3MkVBalBranch129(zzz972, zzz973, zzz974, zzz975, zzz976, zzz977, zzz978, zzz979, zzz980, zzz981, zzz982, Succ(zzz979), Succ(zzz10190), bc)
new_mkVBalBranch3MkVBalBranch236(zzz958, zzz959, zzz960, zzz961, zzz962, zzz963, zzz964, zzz965, zzz966, zzz967, zzz968, Succ(zzz9690), Zero, ba) → new_mkVBalBranch3MkVBalBranch124(zzz958, zzz959, zzz960, zzz961, zzz962, zzz963, zzz964, zzz965, zzz966, zzz967, zzz968, new_primPlusNat2(new_primPlusNat3(Succ(new_primPlusNat3(new_primPlusNat1(zzz960), zzz960)), Succ(zzz960)), Succ(zzz960)), ba)
new_mkVBalBranch3MkVBalBranch242(zzz972, zzz973, zzz974, zzz975, zzz976, zzz977, zzz978, zzz979, zzz980, zzz981, zzz982, Succ(zzz9830), Zero, bc) → new_mkVBalBranch3MkVBalBranch128(zzz972, zzz973, zzz974, zzz975, zzz976, zzz977, zzz978, zzz979, zzz980, zzz981, zzz982, new_primPlusNat2(new_primPlusNat3(Succ(new_primPlusNat3(new_primPlusNat1(zzz974), zzz974)), Succ(zzz974)), Succ(zzz974)), bc)
new_mkVBalBranch3MkVBalBranch129(zzz1851, zzz1852, zzz1853, zzz1854, zzz1855, zzz1856, zzz1857, zzz1858, zzz1859, zzz1860, zzz1861, Succ(zzz18620), Succ(zzz18630), bd) → new_mkVBalBranch3MkVBalBranch129(zzz1851, zzz1852, zzz1853, zzz1854, zzz1855, zzz1856, zzz1857, zzz1858, zzz1859, zzz1860, zzz1861, zzz18620, zzz18630, bd)
new_mkVBalBranch3MkVBalBranch124(zzz958, zzz959, zzz960, zzz961, zzz962, zzz963, zzz964, zzz965, zzz966, zzz967, zzz968, Zero, ba) → new_mkVBalBranch3MkVBalBranch125(zzz958, zzz959, zzz960, zzz961, zzz962, zzz963, zzz964, zzz965, zzz966, zzz967, zzz968, Zero, Succ(zzz965), ba)
new_mkVBalBranch3MkVBalBranch242(zzz972, zzz973, zzz974, zzz975, zzz976, zzz977, zzz978, zzz979, zzz980, zzz981, zzz982, Succ(zzz9830), Succ(zzz9840), bc) → new_mkVBalBranch3MkVBalBranch242(zzz972, zzz973, zzz974, zzz975, zzz976, zzz977, zzz978, zzz979, zzz980, zzz981, zzz982, zzz9830, zzz9840, bc)
new_mkVBalBranch3MkVBalBranch235(zzz3170, zzz3171, Pos(Succ(zzz317200)), zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, Succ(zzz4170), h) → new_mkVBalBranch3MkVBalBranch236(zzz3170, zzz3171, zzz317200, zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, zzz4170, zzz317200, h)
new_mkVBalBranch1(zzz31, Branch(zzz330, zzz331, Pos(Succ(zzz33200)), zzz333, zzz334), Branch(zzz3170, zzz3171, zzz3172, zzz3173, zzz3174), h) → new_mkVBalBranch3MkVBalBranch235(zzz3170, zzz3171, zzz3172, zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, new_primPlusNat2(Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat3(new_primPlusNat1(zzz33200), zzz33200)), zzz33200))), Succ(zzz33200)), h)
new_mkVBalBranch3MkVBalBranch236(zzz958, zzz959, zzz960, zzz961, zzz962, zzz963, zzz964, zzz965, zzz966, zzz967, zzz968, Succ(zzz9690), Succ(zzz9700), ba) → new_mkVBalBranch3MkVBalBranch236(zzz958, zzz959, zzz960, zzz961, zzz962, zzz963, zzz964, zzz965, zzz966, zzz967, zzz968, zzz9690, zzz9700, ba)
new_mkVBalBranch3MkVBalBranch241(zzz3170, zzz3171, Neg(Succ(zzz317200)), zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, Succ(zzz4190), h) → new_mkVBalBranch3MkVBalBranch242(zzz3170, zzz3171, zzz317200, zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, zzz317200, zzz4190, h)
new_mkVBalBranch3MkVBalBranch241(zzz3170, zzz3171, Neg(Succ(zzz317200)), zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, Zero, h) → new_mkVBalBranch3MkVBalBranch242(zzz3170, zzz3171, zzz317200, zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, Succ(zzz317200), Zero, h)
new_mkVBalBranch1(zzz31, Branch(zzz330, zzz331, Pos(Zero), zzz333, zzz334), Branch(zzz3170, zzz3171, Pos(Succ(zzz317200)), zzz3173, zzz3174), h) → new_mkVBalBranch1(zzz31, Branch(zzz330, zzz331, Pos(Zero), zzz333, zzz334), zzz3173, h)
new_mkVBalBranch3MkVBalBranch235(zzz3170, zzz3171, Neg(Succ(zzz317200)), zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, Succ(zzz4170), h) → new_mkVBalBranch3MkVBalBranch123(zzz3170, zzz3171, zzz317200, zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, new_primPlusNat2(Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat3(new_primPlusNat1(zzz317200), zzz317200)), zzz317200))), Succ(zzz317200)), h)
new_mkVBalBranch3MkVBalBranch243(zzz3170, zzz3171, zzz31720, zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, h) → new_mkVBalBranch1(zzz31, Branch(zzz330, zzz331, Neg(Succ(zzz33200)), zzz333, zzz334), zzz3173, h)
new_mkVBalBranch3MkVBalBranch237(zzz3170, zzz3171, zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, h) → new_mkVBalBranch1(zzz31, zzz334, Branch(zzz3170, zzz3171, Pos(Zero), zzz3173, zzz3174), h)
new_mkVBalBranch3MkVBalBranch235(zzz3170, zzz3171, Pos(Zero), zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, Succ(zzz4170), h) → new_mkVBalBranch3MkVBalBranch237(zzz3170, zzz3171, zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, h)
new_mkVBalBranch3MkVBalBranch236(zzz958, zzz959, zzz960, zzz961, zzz962, zzz963, zzz964, zzz965, zzz966, zzz967, zzz968, Zero, Succ(zzz9700), ba) → new_mkVBalBranch1(zzz968, Branch(zzz963, zzz964, Pos(Succ(zzz965)), zzz966, zzz967), zzz961, ba)
new_mkVBalBranch3MkVBalBranch125(zzz1337, zzz1338, zzz1339, zzz1340, zzz1341, zzz1342, zzz1343, zzz1344, zzz1345, zzz1346, zzz1347, Succ(zzz13480), Succ(zzz13490), bb) → new_mkVBalBranch3MkVBalBranch125(zzz1337, zzz1338, zzz1339, zzz1340, zzz1341, zzz1342, zzz1343, zzz1344, zzz1345, zzz1346, zzz1347, zzz13480, zzz13490, bb)
new_mkVBalBranch3MkVBalBranch123(zzz3170, zzz3171, zzz317200, zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, Succ(zzz5620), h) → new_mkVBalBranch1(zzz31, zzz334, Branch(zzz3170, zzz3171, Neg(Succ(zzz317200)), zzz3173, zzz3174), h)
new_mkVBalBranch3MkVBalBranch125(zzz1337, zzz1338, zzz1339, zzz1340, zzz1341, zzz1342, zzz1343, zzz1344, zzz1345, zzz1346, zzz1347, Zero, Succ(zzz13490), bb) → new_mkVBalBranch1(zzz1347, zzz1346, Branch(zzz1337, zzz1338, Pos(Succ(zzz1339)), zzz1340, zzz1341), bb)
new_mkVBalBranch3MkVBalBranch242(zzz972, zzz973, zzz974, zzz975, zzz976, zzz977, zzz978, zzz979, zzz980, zzz981, zzz982, Zero, Succ(zzz9840), bc) → new_mkVBalBranch1(zzz982, Branch(zzz977, zzz978, Neg(Succ(zzz979)), zzz980, zzz981), zzz975, bc)
new_mkVBalBranch3MkVBalBranch238(zzz3170, zzz3171, Succ(zzz317200), zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, h) → new_mkVBalBranch3MkVBalBranch123(zzz3170, zzz3171, zzz317200, zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, new_primPlusNat2(Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat3(new_primPlusNat1(zzz317200), zzz317200)), zzz317200))), Succ(zzz317200)), h)
new_mkVBalBranch1(zzz31, Branch(zzz330, zzz331, Neg(Zero), zzz333, zzz334), Branch(zzz3170, zzz3171, Neg(Succ(zzz317200)), zzz3173, zzz3174), h) → new_mkVBalBranch3MkVBalBranch127(zzz3170, zzz3171, zzz317200, zzz3173, zzz3174, zzz330, zzz331, zzz333, zzz334, zzz31, new_primPlusNat2(new_primPlusNat3(Succ(new_primPlusNat3(new_primPlusNat1(zzz317200), zzz317200)), Succ(zzz317200)), Succ(zzz317200)), h)
new_mkVBalBranch3MkVBalBranch235(zzz3170, zzz3171, Neg(Succ(zzz317200)), zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, Zero, h) → new_mkVBalBranch3MkVBalBranch238(zzz3170, zzz3171, Succ(zzz317200), zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, h)
new_mkVBalBranch3MkVBalBranch240(zzz958, zzz959, zzz960, zzz961, zzz962, zzz963, zzz964, zzz965, zzz966, zzz967, zzz968, ba) → new_mkVBalBranch3MkVBalBranch124(zzz958, zzz959, zzz960, zzz961, zzz962, zzz963, zzz964, zzz965, zzz966, zzz967, zzz968, new_primPlusNat2(new_primPlusNat3(Succ(new_primPlusNat3(new_primPlusNat1(zzz960), zzz960)), Succ(zzz960)), Succ(zzz960)), ba)
new_mkVBalBranch3MkVBalBranch241(zzz3170, zzz3171, Pos(Succ(zzz317200)), zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, Zero, h) → new_mkVBalBranch3MkVBalBranch243(zzz3170, zzz3171, Succ(zzz317200), zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, h)
new_mkVBalBranch1(zzz31, Branch(zzz330, zzz331, Pos(Zero), zzz333, zzz334), Branch(zzz3170, zzz3171, Neg(Succ(zzz317200)), zzz3173, zzz3174), h) → new_mkVBalBranch3MkVBalBranch126(zzz3170, zzz3171, zzz317200, zzz3173, zzz3174, zzz330, zzz331, zzz333, zzz334, zzz31, new_primPlusNat2(new_primPlusNat3(Succ(new_primPlusNat3(new_primPlusNat1(zzz317200), zzz317200)), Succ(zzz317200)), Succ(zzz317200)), h)
new_mkVBalBranch3MkVBalBranch126(zzz3170, zzz3171, zzz317200, zzz3173, zzz3174, zzz330, zzz331, zzz333, zzz334, zzz31, Succ(zzz5350), h) → new_mkVBalBranch1(zzz31, zzz334, Branch(zzz3170, zzz3171, Neg(Succ(zzz317200)), zzz3173, zzz3174), h)
new_mkVBalBranch3MkVBalBranch241(zzz3170, zzz3171, Neg(Zero), zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, Succ(zzz4190), h) → new_mkVBalBranch1(zzz31, Branch(zzz330, zzz331, Neg(Succ(zzz33200)), zzz333, zzz334), zzz3173, h)
new_mkVBalBranch3MkVBalBranch123(zzz3170, zzz3171, zzz317200, zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, Zero, h) → new_mkVBalBranch3MkVBalBranch130(zzz3170, zzz3171, zzz317200, zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, h)
new_mkVBalBranch3MkVBalBranch124(zzz958, zzz959, zzz960, zzz961, zzz962, zzz963, zzz964, zzz965, zzz966, zzz967, zzz968, Succ(zzz10180), ba) → new_mkVBalBranch3MkVBalBranch125(zzz958, zzz959, zzz960, zzz961, zzz962, zzz963, zzz964, zzz965, zzz966, zzz967, zzz968, Succ(zzz10180), Succ(zzz965), ba)
new_mkVBalBranch3MkVBalBranch235(zzz3170, zzz3171, Pos(Succ(zzz317200)), zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, Zero, h) → new_mkVBalBranch3MkVBalBranch236(zzz3170, zzz3171, zzz317200, zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, Zero, Succ(zzz317200), h)
new_mkVBalBranch3MkVBalBranch239(zzz3170, zzz3171, Zero, zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, h) → new_mkVBalBranch1(zzz31, zzz334, Branch(zzz3170, zzz3171, Neg(Zero), zzz3173, zzz3174), h)
new_mkVBalBranch3MkVBalBranch235(zzz3170, zzz3171, Pos(Zero), zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, Zero, h) → new_mkVBalBranch1(zzz31, zzz334, Branch(zzz3170, zzz3171, Pos(Zero), zzz3173, zzz3174), h)
new_mkVBalBranch3MkVBalBranch242(zzz972, zzz973, zzz974, zzz975, zzz976, zzz977, zzz978, zzz979, zzz980, zzz981, zzz982, Zero, Zero, bc) → new_mkVBalBranch3MkVBalBranch244(zzz972, zzz973, zzz974, zzz975, zzz976, zzz977, zzz978, zzz979, zzz980, zzz981, zzz982, bc)
new_mkVBalBranch3MkVBalBranch130(zzz3170, zzz3171, zzz317200, zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, h) → new_mkVBalBranch1(zzz31, zzz334, Branch(zzz3170, zzz3171, Neg(Succ(zzz317200)), zzz3173, zzz3174), h)
new_mkVBalBranch1(zzz31, Branch(zzz330, zzz331, Neg(Zero), zzz333, zzz334), Branch(zzz3170, zzz3171, Pos(Succ(zzz317200)), zzz3173, zzz3174), h) → new_mkVBalBranch1(zzz31, Branch(zzz330, zzz331, Neg(Zero), zzz333, zzz334), zzz3173, h)
new_mkVBalBranch3MkVBalBranch235(zzz3170, zzz3171, Neg(Zero), zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, Zero, h) → new_mkVBalBranch3MkVBalBranch239(zzz3170, zzz3171, Zero, zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, h)
new_mkVBalBranch1(zzz31, Branch(zzz330, zzz331, Neg(Succ(zzz33200)), zzz333, zzz334), Branch(zzz3170, zzz3171, zzz3172, zzz3173, zzz3174), h) → new_mkVBalBranch3MkVBalBranch241(zzz3170, zzz3171, zzz3172, zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, new_primPlusNat2(Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat3(new_primPlusNat1(zzz33200), zzz33200)), zzz33200))), Succ(zzz33200)), h)
new_mkVBalBranch3MkVBalBranch235(zzz3170, zzz3171, Neg(Zero), zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, Succ(zzz4170), h) → new_mkVBalBranch1(zzz31, zzz334, Branch(zzz3170, zzz3171, Neg(Zero), zzz3173, zzz3174), h)
new_mkVBalBranch3MkVBalBranch244(zzz972, zzz973, zzz974, zzz975, zzz976, zzz977, zzz978, zzz979, zzz980, zzz981, zzz982, bc) → new_mkVBalBranch3MkVBalBranch128(zzz972, zzz973, zzz974, zzz975, zzz976, zzz977, zzz978, zzz979, zzz980, zzz981, zzz982, new_primPlusNat2(new_primPlusNat3(Succ(new_primPlusNat3(new_primPlusNat1(zzz974), zzz974)), Succ(zzz974)), Succ(zzz974)), bc)
new_mkVBalBranch3MkVBalBranch236(zzz958, zzz959, zzz960, zzz961, zzz962, zzz963, zzz964, zzz965, zzz966, zzz967, zzz968, Zero, Zero, ba) → new_mkVBalBranch3MkVBalBranch240(zzz958, zzz959, zzz960, zzz961, zzz962, zzz963, zzz964, zzz965, zzz966, zzz967, zzz968, ba)

The TRS R consists of the following rules:

new_primPlusNat1(Zero) → Zero
new_primPlusNat1(Succ(zzz62000)) → Succ(Succ(new_primPlusNat1(zzz62000)))
new_primPlusNat3(zzz90, Succ(zzz910)) → Succ(Succ(new_primPlusNat2(zzz90, zzz910)))
new_primPlusNat3(zzz90, Zero) → Succ(zzz90)
new_primPlusNat2(Succ(zzz900), Succ(zzz9100)) → Succ(Succ(new_primPlusNat2(zzz900, zzz9100)))
new_primPlusNat2(Succ(zzz900), Zero) → Succ(zzz900)
new_primPlusNat2(Zero, Succ(zzz9100)) → Succ(zzz9100)
new_primPlusNat2(Zero, Zero) → Zero

The set Q consists of the following terms:

new_primPlusNat2(Zero, Succ(x0))
new_primMulNat0(x0)
new_primPlusNat3(x0, Succ(x1))
new_primPlusNat2(Succ(x0), Succ(x1))
new_primPlusNat3(x0, Zero)
new_primPlusNat1(Zero)
new_primPlusNat2(Zero, Zero)
new_primPlusNat1(Succ(x0))
new_primPlusNat2(Succ(x0), Zero)

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

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

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

new_mkVBalBranch3MkVBalBranch129(zzz1851, zzz1852, zzz1853, zzz1854, zzz1855, zzz1856, zzz1857, zzz1858, zzz1859, zzz1860, zzz1861, Zero, Succ(zzz18630), bd) → new_mkVBalBranch1(zzz1861, zzz1860, Branch(zzz1851, zzz1852, Neg(Succ(zzz1853)), zzz1854, zzz1855), bd)
new_mkVBalBranch3MkVBalBranch128(zzz972, zzz973, zzz974, zzz975, zzz976, zzz977, zzz978, zzz979, zzz980, zzz981, zzz982, Succ(zzz10190), bc) → new_mkVBalBranch3MkVBalBranch129(zzz972, zzz973, zzz974, zzz975, zzz976, zzz977, zzz978, zzz979, zzz980, zzz981, zzz982, Succ(zzz979), Succ(zzz10190), bc)
new_mkVBalBranch3MkVBalBranch241(zzz3170, zzz3171, Pos(zzz31720), zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, Succ(zzz4190), h) → new_mkVBalBranch1(zzz31, Branch(zzz330, zzz331, Neg(Succ(zzz33200)), zzz333, zzz334), zzz3173, h)
new_mkVBalBranch3MkVBalBranch127(zzz3170, zzz3171, zzz317200, zzz3173, zzz3174, zzz330, zzz331, zzz333, zzz334, zzz31, Succ(zzz5500), h) → new_mkVBalBranch1(zzz31, zzz334, Branch(zzz3170, zzz3171, Neg(Succ(zzz317200)), zzz3173, zzz3174), h)
new_mkVBalBranch3MkVBalBranch236(zzz958, zzz959, zzz960, zzz961, zzz962, zzz963, zzz964, zzz965, zzz966, zzz967, zzz968, Succ(zzz9690), Zero, ba) → new_mkVBalBranch3MkVBalBranch124(zzz958, zzz959, zzz960, zzz961, zzz962, zzz963, zzz964, zzz965, zzz966, zzz967, zzz968, new_primPlusNat2(new_primPlusNat3(Succ(new_primPlusNat3(new_primPlusNat1(zzz960), zzz960)), Succ(zzz960)), Succ(zzz960)), ba)
new_mkVBalBranch3MkVBalBranch242(zzz972, zzz973, zzz974, zzz975, zzz976, zzz977, zzz978, zzz979, zzz980, zzz981, zzz982, Succ(zzz9830), Zero, bc) → new_mkVBalBranch3MkVBalBranch128(zzz972, zzz973, zzz974, zzz975, zzz976, zzz977, zzz978, zzz979, zzz980, zzz981, zzz982, new_primPlusNat2(new_primPlusNat3(Succ(new_primPlusNat3(new_primPlusNat1(zzz974), zzz974)), Succ(zzz974)), Succ(zzz974)), bc)
new_mkVBalBranch3MkVBalBranch129(zzz1851, zzz1852, zzz1853, zzz1854, zzz1855, zzz1856, zzz1857, zzz1858, zzz1859, zzz1860, zzz1861, Succ(zzz18620), Succ(zzz18630), bd) → new_mkVBalBranch3MkVBalBranch129(zzz1851, zzz1852, zzz1853, zzz1854, zzz1855, zzz1856, zzz1857, zzz1858, zzz1859, zzz1860, zzz1861, zzz18620, zzz18630, bd)
new_mkVBalBranch3MkVBalBranch124(zzz958, zzz959, zzz960, zzz961, zzz962, zzz963, zzz964, zzz965, zzz966, zzz967, zzz968, Zero, ba) → new_mkVBalBranch3MkVBalBranch125(zzz958, zzz959, zzz960, zzz961, zzz962, zzz963, zzz964, zzz965, zzz966, zzz967, zzz968, Zero, Succ(zzz965), ba)
new_mkVBalBranch3MkVBalBranch235(zzz3170, zzz3171, Pos(Succ(zzz317200)), zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, Succ(zzz4170), h) → new_mkVBalBranch3MkVBalBranch236(zzz3170, zzz3171, zzz317200, zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, zzz4170, zzz317200, h)
new_mkVBalBranch3MkVBalBranch242(zzz972, zzz973, zzz974, zzz975, zzz976, zzz977, zzz978, zzz979, zzz980, zzz981, zzz982, Succ(zzz9830), Succ(zzz9840), bc) → new_mkVBalBranch3MkVBalBranch242(zzz972, zzz973, zzz974, zzz975, zzz976, zzz977, zzz978, zzz979, zzz980, zzz981, zzz982, zzz9830, zzz9840, bc)
new_mkVBalBranch3MkVBalBranch236(zzz958, zzz959, zzz960, zzz961, zzz962, zzz963, zzz964, zzz965, zzz966, zzz967, zzz968, Succ(zzz9690), Succ(zzz9700), ba) → new_mkVBalBranch3MkVBalBranch236(zzz958, zzz959, zzz960, zzz961, zzz962, zzz963, zzz964, zzz965, zzz966, zzz967, zzz968, zzz9690, zzz9700, ba)
new_mkVBalBranch1(zzz31, Branch(zzz330, zzz331, Pos(Succ(zzz33200)), zzz333, zzz334), Branch(zzz3170, zzz3171, zzz3172, zzz3173, zzz3174), h) → new_mkVBalBranch3MkVBalBranch235(zzz3170, zzz3171, zzz3172, zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, new_primPlusNat2(Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat3(new_primPlusNat1(zzz33200), zzz33200)), zzz33200))), Succ(zzz33200)), h)
new_mkVBalBranch3MkVBalBranch241(zzz3170, zzz3171, Neg(Succ(zzz317200)), zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, Succ(zzz4190), h) → new_mkVBalBranch3MkVBalBranch242(zzz3170, zzz3171, zzz317200, zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, zzz317200, zzz4190, h)
new_mkVBalBranch3MkVBalBranch241(zzz3170, zzz3171, Neg(Succ(zzz317200)), zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, Zero, h) → new_mkVBalBranch3MkVBalBranch242(zzz3170, zzz3171, zzz317200, zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, Succ(zzz317200), Zero, h)
new_mkVBalBranch1(zzz31, Branch(zzz330, zzz331, Pos(Zero), zzz333, zzz334), Branch(zzz3170, zzz3171, Pos(Succ(zzz317200)), zzz3173, zzz3174), h) → new_mkVBalBranch1(zzz31, Branch(zzz330, zzz331, Pos(Zero), zzz333, zzz334), zzz3173, h)
new_mkVBalBranch3MkVBalBranch235(zzz3170, zzz3171, Neg(Succ(zzz317200)), zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, Succ(zzz4170), h) → new_mkVBalBranch3MkVBalBranch123(zzz3170, zzz3171, zzz317200, zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, new_primPlusNat2(Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat3(new_primPlusNat1(zzz317200), zzz317200)), zzz317200))), Succ(zzz317200)), h)
new_mkVBalBranch3MkVBalBranch243(zzz3170, zzz3171, zzz31720, zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, h) → new_mkVBalBranch1(zzz31, Branch(zzz330, zzz331, Neg(Succ(zzz33200)), zzz333, zzz334), zzz3173, h)
new_mkVBalBranch3MkVBalBranch237(zzz3170, zzz3171, zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, h) → new_mkVBalBranch1(zzz31, zzz334, Branch(zzz3170, zzz3171, Pos(Zero), zzz3173, zzz3174), h)
new_mkVBalBranch3MkVBalBranch235(zzz3170, zzz3171, Pos(Zero), zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, Succ(zzz4170), h) → new_mkVBalBranch3MkVBalBranch237(zzz3170, zzz3171, zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, h)
new_mkVBalBranch3MkVBalBranch236(zzz958, zzz959, zzz960, zzz961, zzz962, zzz963, zzz964, zzz965, zzz966, zzz967, zzz968, Zero, Succ(zzz9700), ba) → new_mkVBalBranch1(zzz968, Branch(zzz963, zzz964, Pos(Succ(zzz965)), zzz966, zzz967), zzz961, ba)
new_mkVBalBranch3MkVBalBranch125(zzz1337, zzz1338, zzz1339, zzz1340, zzz1341, zzz1342, zzz1343, zzz1344, zzz1345, zzz1346, zzz1347, Succ(zzz13480), Succ(zzz13490), bb) → new_mkVBalBranch3MkVBalBranch125(zzz1337, zzz1338, zzz1339, zzz1340, zzz1341, zzz1342, zzz1343, zzz1344, zzz1345, zzz1346, zzz1347, zzz13480, zzz13490, bb)
new_mkVBalBranch3MkVBalBranch123(zzz3170, zzz3171, zzz317200, zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, Succ(zzz5620), h) → new_mkVBalBranch1(zzz31, zzz334, Branch(zzz3170, zzz3171, Neg(Succ(zzz317200)), zzz3173, zzz3174), h)
new_mkVBalBranch3MkVBalBranch125(zzz1337, zzz1338, zzz1339, zzz1340, zzz1341, zzz1342, zzz1343, zzz1344, zzz1345, zzz1346, zzz1347, Zero, Succ(zzz13490), bb) → new_mkVBalBranch1(zzz1347, zzz1346, Branch(zzz1337, zzz1338, Pos(Succ(zzz1339)), zzz1340, zzz1341), bb)
new_mkVBalBranch3MkVBalBranch242(zzz972, zzz973, zzz974, zzz975, zzz976, zzz977, zzz978, zzz979, zzz980, zzz981, zzz982, Zero, Succ(zzz9840), bc) → new_mkVBalBranch1(zzz982, Branch(zzz977, zzz978, Neg(Succ(zzz979)), zzz980, zzz981), zzz975, bc)
new_mkVBalBranch1(zzz31, Branch(zzz330, zzz331, Neg(Zero), zzz333, zzz334), Branch(zzz3170, zzz3171, Neg(Succ(zzz317200)), zzz3173, zzz3174), h) → new_mkVBalBranch3MkVBalBranch127(zzz3170, zzz3171, zzz317200, zzz3173, zzz3174, zzz330, zzz331, zzz333, zzz334, zzz31, new_primPlusNat2(new_primPlusNat3(Succ(new_primPlusNat3(new_primPlusNat1(zzz317200), zzz317200)), Succ(zzz317200)), Succ(zzz317200)), h)
new_mkVBalBranch3MkVBalBranch238(zzz3170, zzz3171, Succ(zzz317200), zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, h) → new_mkVBalBranch3MkVBalBranch123(zzz3170, zzz3171, zzz317200, zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, new_primPlusNat2(Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat3(new_primPlusNat1(zzz317200), zzz317200)), zzz317200))), Succ(zzz317200)), h)
new_mkVBalBranch3MkVBalBranch235(zzz3170, zzz3171, Neg(Succ(zzz317200)), zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, Zero, h) → new_mkVBalBranch3MkVBalBranch238(zzz3170, zzz3171, Succ(zzz317200), zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, h)
new_mkVBalBranch3MkVBalBranch240(zzz958, zzz959, zzz960, zzz961, zzz962, zzz963, zzz964, zzz965, zzz966, zzz967, zzz968, ba) → new_mkVBalBranch3MkVBalBranch124(zzz958, zzz959, zzz960, zzz961, zzz962, zzz963, zzz964, zzz965, zzz966, zzz967, zzz968, new_primPlusNat2(new_primPlusNat3(Succ(new_primPlusNat3(new_primPlusNat1(zzz960), zzz960)), Succ(zzz960)), Succ(zzz960)), ba)
new_mkVBalBranch3MkVBalBranch241(zzz3170, zzz3171, Pos(Succ(zzz317200)), zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, Zero, h) → new_mkVBalBranch3MkVBalBranch243(zzz3170, zzz3171, Succ(zzz317200), zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, h)
new_mkVBalBranch3MkVBalBranch126(zzz3170, zzz3171, zzz317200, zzz3173, zzz3174, zzz330, zzz331, zzz333, zzz334, zzz31, Succ(zzz5350), h) → new_mkVBalBranch1(zzz31, zzz334, Branch(zzz3170, zzz3171, Neg(Succ(zzz317200)), zzz3173, zzz3174), h)
new_mkVBalBranch1(zzz31, Branch(zzz330, zzz331, Pos(Zero), zzz333, zzz334), Branch(zzz3170, zzz3171, Neg(Succ(zzz317200)), zzz3173, zzz3174), h) → new_mkVBalBranch3MkVBalBranch126(zzz3170, zzz3171, zzz317200, zzz3173, zzz3174, zzz330, zzz331, zzz333, zzz334, zzz31, new_primPlusNat2(new_primPlusNat3(Succ(new_primPlusNat3(new_primPlusNat1(zzz317200), zzz317200)), Succ(zzz317200)), Succ(zzz317200)), h)
new_mkVBalBranch3MkVBalBranch123(zzz3170, zzz3171, zzz317200, zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, Zero, h) → new_mkVBalBranch3MkVBalBranch130(zzz3170, zzz3171, zzz317200, zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, h)
new_mkVBalBranch3MkVBalBranch241(zzz3170, zzz3171, Neg(Zero), zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, Succ(zzz4190), h) → new_mkVBalBranch1(zzz31, Branch(zzz330, zzz331, Neg(Succ(zzz33200)), zzz333, zzz334), zzz3173, h)
new_mkVBalBranch3MkVBalBranch124(zzz958, zzz959, zzz960, zzz961, zzz962, zzz963, zzz964, zzz965, zzz966, zzz967, zzz968, Succ(zzz10180), ba) → new_mkVBalBranch3MkVBalBranch125(zzz958, zzz959, zzz960, zzz961, zzz962, zzz963, zzz964, zzz965, zzz966, zzz967, zzz968, Succ(zzz10180), Succ(zzz965), ba)
new_mkVBalBranch3MkVBalBranch235(zzz3170, zzz3171, Pos(Succ(zzz317200)), zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, Zero, h) → new_mkVBalBranch3MkVBalBranch236(zzz3170, zzz3171, zzz317200, zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, Zero, Succ(zzz317200), h)
new_mkVBalBranch3MkVBalBranch239(zzz3170, zzz3171, Zero, zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, h) → new_mkVBalBranch1(zzz31, zzz334, Branch(zzz3170, zzz3171, Neg(Zero), zzz3173, zzz3174), h)
new_mkVBalBranch3MkVBalBranch235(zzz3170, zzz3171, Pos(Zero), zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, Zero, h) → new_mkVBalBranch1(zzz31, zzz334, Branch(zzz3170, zzz3171, Pos(Zero), zzz3173, zzz3174), h)
new_mkVBalBranch3MkVBalBranch242(zzz972, zzz973, zzz974, zzz975, zzz976, zzz977, zzz978, zzz979, zzz980, zzz981, zzz982, Zero, Zero, bc) → new_mkVBalBranch3MkVBalBranch244(zzz972, zzz973, zzz974, zzz975, zzz976, zzz977, zzz978, zzz979, zzz980, zzz981, zzz982, bc)
new_mkVBalBranch3MkVBalBranch130(zzz3170, zzz3171, zzz317200, zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, h) → new_mkVBalBranch1(zzz31, zzz334, Branch(zzz3170, zzz3171, Neg(Succ(zzz317200)), zzz3173, zzz3174), h)
new_mkVBalBranch3MkVBalBranch235(zzz3170, zzz3171, Neg(Zero), zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, Zero, h) → new_mkVBalBranch3MkVBalBranch239(zzz3170, zzz3171, Zero, zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, h)
new_mkVBalBranch1(zzz31, Branch(zzz330, zzz331, Neg(Zero), zzz333, zzz334), Branch(zzz3170, zzz3171, Pos(Succ(zzz317200)), zzz3173, zzz3174), h) → new_mkVBalBranch1(zzz31, Branch(zzz330, zzz331, Neg(Zero), zzz333, zzz334), zzz3173, h)
new_mkVBalBranch3MkVBalBranch235(zzz3170, zzz3171, Neg(Zero), zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, Succ(zzz4170), h) → new_mkVBalBranch1(zzz31, zzz334, Branch(zzz3170, zzz3171, Neg(Zero), zzz3173, zzz3174), h)
new_mkVBalBranch1(zzz31, Branch(zzz330, zzz331, Neg(Succ(zzz33200)), zzz333, zzz334), Branch(zzz3170, zzz3171, zzz3172, zzz3173, zzz3174), h) → new_mkVBalBranch3MkVBalBranch241(zzz3170, zzz3171, zzz3172, zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, new_primPlusNat2(Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat3(new_primPlusNat1(zzz33200), zzz33200)), zzz33200))), Succ(zzz33200)), h)
new_mkVBalBranch3MkVBalBranch236(zzz958, zzz959, zzz960, zzz961, zzz962, zzz963, zzz964, zzz965, zzz966, zzz967, zzz968, Zero, Zero, ba) → new_mkVBalBranch3MkVBalBranch240(zzz958, zzz959, zzz960, zzz961, zzz962, zzz963, zzz964, zzz965, zzz966, zzz967, zzz968, ba)
new_mkVBalBranch3MkVBalBranch244(zzz972, zzz973, zzz974, zzz975, zzz976, zzz977, zzz978, zzz979, zzz980, zzz981, zzz982, bc) → new_mkVBalBranch3MkVBalBranch128(zzz972, zzz973, zzz974, zzz975, zzz976, zzz977, zzz978, zzz979, zzz980, zzz981, zzz982, new_primPlusNat2(new_primPlusNat3(Succ(new_primPlusNat3(new_primPlusNat1(zzz974), zzz974)), Succ(zzz974)), Succ(zzz974)), bc)

The TRS R consists of the following rules:

new_primPlusNat1(Zero) → Zero
new_primPlusNat1(Succ(zzz62000)) → Succ(Succ(new_primPlusNat1(zzz62000)))
new_primPlusNat3(zzz90, Succ(zzz910)) → Succ(Succ(new_primPlusNat2(zzz90, zzz910)))
new_primPlusNat3(zzz90, Zero) → Succ(zzz90)
new_primPlusNat2(Succ(zzz900), Succ(zzz9100)) → Succ(Succ(new_primPlusNat2(zzz900, zzz9100)))
new_primPlusNat2(Succ(zzz900), Zero) → Succ(zzz900)
new_primPlusNat2(Zero, Succ(zzz9100)) → Succ(zzz9100)
new_primPlusNat2(Zero, Zero) → Zero

The set Q consists of the following terms:

new_primPlusNat2(Zero, Succ(x0))
new_primPlusNat3(x0, Succ(x1))
new_primPlusNat2(Succ(x0), Succ(x1))
new_primPlusNat3(x0, Zero)
new_primPlusNat1(Zero)
new_primPlusNat2(Zero, Zero)
new_primPlusNat1(Succ(x0))
new_primPlusNat2(Succ(x0), Zero)

We have to consider all minimal (P,Q,R)-chains.
By rewriting [15] the rule new_mkVBalBranch3MkVBalBranch236(zzz958, zzz959, zzz960, zzz961, zzz962, zzz963, zzz964, zzz965, zzz966, zzz967, zzz968, Succ(zzz9690), Zero, ba) → new_mkVBalBranch3MkVBalBranch124(zzz958, zzz959, zzz960, zzz961, zzz962, zzz963, zzz964, zzz965, zzz966, zzz967, zzz968, new_primPlusNat2(new_primPlusNat3(Succ(new_primPlusNat3(new_primPlusNat1(zzz960), zzz960)), Succ(zzz960)), Succ(zzz960)), ba) at position [11,0] we obtained the following new rules:

new_mkVBalBranch3MkVBalBranch236(zzz958, zzz959, zzz960, zzz961, zzz962, zzz963, zzz964, zzz965, zzz966, zzz967, zzz968, Succ(zzz9690), Zero, ba) → new_mkVBalBranch3MkVBalBranch124(zzz958, zzz959, zzz960, zzz961, zzz962, zzz963, zzz964, zzz965, zzz966, zzz967, zzz968, new_primPlusNat2(Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat3(new_primPlusNat1(zzz960), zzz960)), zzz960))), Succ(zzz960)), 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
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                    ↳ DependencyGraphProof
                                      ↳ QDP
                                        ↳ Rewriting
                                          ↳ QDP
                                            ↳ Rewriting
                                              ↳ QDP
                                                ↳ Rewriting
                                                  ↳ QDP
                                                    ↳ Rewriting
                                                      ↳ QDP
                                                        ↳ Rewriting
                                                          ↳ QDP
                                                            ↳ Rewriting
                                                              ↳ QDP
                                                                ↳ Rewriting
                                                                  ↳ QDP
                                                                    ↳ Rewriting
                                                                      ↳ QDP
                                                                        ↳ Rewriting
                                                                          ↳ QDP
                                                                            ↳ Rewriting
                                                                              ↳ QDP
                                                                                ↳ UsableRulesProof
                                                                                  ↳ QDP
                                                                                    ↳ QReductionProof
                                                                                      ↳ QDP
                                                                                        ↳ Rewriting
                                                                                          ↳ QDP
                                                                                            ↳ Rewriting
                                                                                              ↳ QDP
                                                                                                ↳ Rewriting
                                                                                                  ↳ QDP
                                                                                                    ↳ Rewriting
                                                                                                      ↳ QDP
                                                                                                        ↳ Rewriting
                                                                                                          ↳ QDP
                                                                                                            ↳ Rewriting
                                                                                                              ↳ QDP
                                                                                                                ↳ Rewriting
                                                                                                                  ↳ QDP
                                                                                                                    ↳ Rewriting
                                                                                                                      ↳ QDP
                                                                                                                        ↳ Rewriting
                                                                                                                          ↳ QDP
                                                                                                                            ↳ Rewriting
                                                                                                                              ↳ QDP
                                                                                                                                ↳ UsableRulesProof
                                                                                                                                  ↳ QDP
                                                                                                                                    ↳ QReductionProof
                                                                                                                                      ↳ QDP
                                                                                                                                        ↳ Rewriting
                                                                                                                                          ↳ QDP
                                                                                                                                            ↳ Rewriting
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP

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

new_mkVBalBranch3MkVBalBranch129(zzz1851, zzz1852, zzz1853, zzz1854, zzz1855, zzz1856, zzz1857, zzz1858, zzz1859, zzz1860, zzz1861, Zero, Succ(zzz18630), bd) → new_mkVBalBranch1(zzz1861, zzz1860, Branch(zzz1851, zzz1852, Neg(Succ(zzz1853)), zzz1854, zzz1855), bd)
new_mkVBalBranch3MkVBalBranch127(zzz3170, zzz3171, zzz317200, zzz3173, zzz3174, zzz330, zzz331, zzz333, zzz334, zzz31, Succ(zzz5500), h) → new_mkVBalBranch1(zzz31, zzz334, Branch(zzz3170, zzz3171, Neg(Succ(zzz317200)), zzz3173, zzz3174), h)
new_mkVBalBranch3MkVBalBranch241(zzz3170, zzz3171, Pos(zzz31720), zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, Succ(zzz4190), h) → new_mkVBalBranch1(zzz31, Branch(zzz330, zzz331, Neg(Succ(zzz33200)), zzz333, zzz334), zzz3173, h)
new_mkVBalBranch3MkVBalBranch128(zzz972, zzz973, zzz974, zzz975, zzz976, zzz977, zzz978, zzz979, zzz980, zzz981, zzz982, Succ(zzz10190), bc) → new_mkVBalBranch3MkVBalBranch129(zzz972, zzz973, zzz974, zzz975, zzz976, zzz977, zzz978, zzz979, zzz980, zzz981, zzz982, Succ(zzz979), Succ(zzz10190), bc)
new_mkVBalBranch3MkVBalBranch242(zzz972, zzz973, zzz974, zzz975, zzz976, zzz977, zzz978, zzz979, zzz980, zzz981, zzz982, Succ(zzz9830), Zero, bc) → new_mkVBalBranch3MkVBalBranch128(zzz972, zzz973, zzz974, zzz975, zzz976, zzz977, zzz978, zzz979, zzz980, zzz981, zzz982, new_primPlusNat2(new_primPlusNat3(Succ(new_primPlusNat3(new_primPlusNat1(zzz974), zzz974)), Succ(zzz974)), Succ(zzz974)), bc)
new_mkVBalBranch3MkVBalBranch129(zzz1851, zzz1852, zzz1853, zzz1854, zzz1855, zzz1856, zzz1857, zzz1858, zzz1859, zzz1860, zzz1861, Succ(zzz18620), Succ(zzz18630), bd) → new_mkVBalBranch3MkVBalBranch129(zzz1851, zzz1852, zzz1853, zzz1854, zzz1855, zzz1856, zzz1857, zzz1858, zzz1859, zzz1860, zzz1861, zzz18620, zzz18630, bd)
new_mkVBalBranch3MkVBalBranch124(zzz958, zzz959, zzz960, zzz961, zzz962, zzz963, zzz964, zzz965, zzz966, zzz967, zzz968, Zero, ba) → new_mkVBalBranch3MkVBalBranch125(zzz958, zzz959, zzz960, zzz961, zzz962, zzz963, zzz964, zzz965, zzz966, zzz967, zzz968, Zero, Succ(zzz965), ba)
new_mkVBalBranch3MkVBalBranch242(zzz972, zzz973, zzz974, zzz975, zzz976, zzz977, zzz978, zzz979, zzz980, zzz981, zzz982, Succ(zzz9830), Succ(zzz9840), bc) → new_mkVBalBranch3MkVBalBranch242(zzz972, zzz973, zzz974, zzz975, zzz976, zzz977, zzz978, zzz979, zzz980, zzz981, zzz982, zzz9830, zzz9840, bc)
new_mkVBalBranch3MkVBalBranch235(zzz3170, zzz3171, Pos(Succ(zzz317200)), zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, Succ(zzz4170), h) → new_mkVBalBranch3MkVBalBranch236(zzz3170, zzz3171, zzz317200, zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, zzz4170, zzz317200, h)
new_mkVBalBranch1(zzz31, Branch(zzz330, zzz331, Pos(Succ(zzz33200)), zzz333, zzz334), Branch(zzz3170, zzz3171, zzz3172, zzz3173, zzz3174), h) → new_mkVBalBranch3MkVBalBranch235(zzz3170, zzz3171, zzz3172, zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, new_primPlusNat2(Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat3(new_primPlusNat1(zzz33200), zzz33200)), zzz33200))), Succ(zzz33200)), h)
new_mkVBalBranch3MkVBalBranch236(zzz958, zzz959, zzz960, zzz961, zzz962, zzz963, zzz964, zzz965, zzz966, zzz967, zzz968, Succ(zzz9690), Succ(zzz9700), ba) → new_mkVBalBranch3MkVBalBranch236(zzz958, zzz959, zzz960, zzz961, zzz962, zzz963, zzz964, zzz965, zzz966, zzz967, zzz968, zzz9690, zzz9700, ba)
new_mkVBalBranch3MkVBalBranch241(zzz3170, zzz3171, Neg(Succ(zzz317200)), zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, Succ(zzz4190), h) → new_mkVBalBranch3MkVBalBranch242(zzz3170, zzz3171, zzz317200, zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, zzz317200, zzz4190, h)
new_mkVBalBranch3MkVBalBranch241(zzz3170, zzz3171, Neg(Succ(zzz317200)), zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, Zero, h) → new_mkVBalBranch3MkVBalBranch242(zzz3170, zzz3171, zzz317200, zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, Succ(zzz317200), Zero, h)
new_mkVBalBranch1(zzz31, Branch(zzz330, zzz331, Pos(Zero), zzz333, zzz334), Branch(zzz3170, zzz3171, Pos(Succ(zzz317200)), zzz3173, zzz3174), h) → new_mkVBalBranch1(zzz31, Branch(zzz330, zzz331, Pos(Zero), zzz333, zzz334), zzz3173, h)
new_mkVBalBranch3MkVBalBranch237(zzz3170, zzz3171, zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, h) → new_mkVBalBranch1(zzz31, zzz334, Branch(zzz3170, zzz3171, Pos(Zero), zzz3173, zzz3174), h)
new_mkVBalBranch3MkVBalBranch243(zzz3170, zzz3171, zzz31720, zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, h) → new_mkVBalBranch1(zzz31, Branch(zzz330, zzz331, Neg(Succ(zzz33200)), zzz333, zzz334), zzz3173, h)
new_mkVBalBranch3MkVBalBranch235(zzz3170, zzz3171, Neg(Succ(zzz317200)), zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, Succ(zzz4170), h) → new_mkVBalBranch3MkVBalBranch123(zzz3170, zzz3171, zzz317200, zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, new_primPlusNat2(Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat3(new_primPlusNat1(zzz317200), zzz317200)), zzz317200))), Succ(zzz317200)), h)
new_mkVBalBranch3MkVBalBranch235(zzz3170, zzz3171, Pos(Zero), zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, Succ(zzz4170), h) → new_mkVBalBranch3MkVBalBranch237(zzz3170, zzz3171, zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, h)
new_mkVBalBranch3MkVBalBranch236(zzz958, zzz959, zzz960, zzz961, zzz962, zzz963, zzz964, zzz965, zzz966, zzz967, zzz968, Succ(zzz9690), Zero, ba) → new_mkVBalBranch3MkVBalBranch124(zzz958, zzz959, zzz960, zzz961, zzz962, zzz963, zzz964, zzz965, zzz966, zzz967, zzz968, new_primPlusNat2(Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat3(new_primPlusNat1(zzz960), zzz960)), zzz960))), Succ(zzz960)), ba)
new_mkVBalBranch3MkVBalBranch236(zzz958, zzz959, zzz960, zzz961, zzz962, zzz963, zzz964, zzz965, zzz966, zzz967, zzz968, Zero, Succ(zzz9700), ba) → new_mkVBalBranch1(zzz968, Branch(zzz963, zzz964, Pos(Succ(zzz965)), zzz966, zzz967), zzz961, ba)
new_mkVBalBranch3MkVBalBranch125(zzz1337, zzz1338, zzz1339, zzz1340, zzz1341, zzz1342, zzz1343, zzz1344, zzz1345, zzz1346, zzz1347, Succ(zzz13480), Succ(zzz13490), bb) → new_mkVBalBranch3MkVBalBranch125(zzz1337, zzz1338, zzz1339, zzz1340, zzz1341, zzz1342, zzz1343, zzz1344, zzz1345, zzz1346, zzz1347, zzz13480, zzz13490, bb)
new_mkVBalBranch3MkVBalBranch123(zzz3170, zzz3171, zzz317200, zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, Succ(zzz5620), h) → new_mkVBalBranch1(zzz31, zzz334, Branch(zzz3170, zzz3171, Neg(Succ(zzz317200)), zzz3173, zzz3174), h)
new_mkVBalBranch3MkVBalBranch125(zzz1337, zzz1338, zzz1339, zzz1340, zzz1341, zzz1342, zzz1343, zzz1344, zzz1345, zzz1346, zzz1347, Zero, Succ(zzz13490), bb) → new_mkVBalBranch1(zzz1347, zzz1346, Branch(zzz1337, zzz1338, Pos(Succ(zzz1339)), zzz1340, zzz1341), bb)
new_mkVBalBranch3MkVBalBranch242(zzz972, zzz973, zzz974, zzz975, zzz976, zzz977, zzz978, zzz979, zzz980, zzz981, zzz982, Zero, Succ(zzz9840), bc) → new_mkVBalBranch1(zzz982, Branch(zzz977, zzz978, Neg(Succ(zzz979)), zzz980, zzz981), zzz975, bc)
new_mkVBalBranch3MkVBalBranch238(zzz3170, zzz3171, Succ(zzz317200), zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, h) → new_mkVBalBranch3MkVBalBranch123(zzz3170, zzz3171, zzz317200, zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, new_primPlusNat2(Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat3(new_primPlusNat1(zzz317200), zzz317200)), zzz317200))), Succ(zzz317200)), h)
new_mkVBalBranch1(zzz31, Branch(zzz330, zzz331, Neg(Zero), zzz333, zzz334), Branch(zzz3170, zzz3171, Neg(Succ(zzz317200)), zzz3173, zzz3174), h) → new_mkVBalBranch3MkVBalBranch127(zzz3170, zzz3171, zzz317200, zzz3173, zzz3174, zzz330, zzz331, zzz333, zzz334, zzz31, new_primPlusNat2(new_primPlusNat3(Succ(new_primPlusNat3(new_primPlusNat1(zzz317200), zzz317200)), Succ(zzz317200)), Succ(zzz317200)), h)
new_mkVBalBranch3MkVBalBranch235(zzz3170, zzz3171, Neg(Succ(zzz317200)), zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, Zero, h) → new_mkVBalBranch3MkVBalBranch238(zzz3170, zzz3171, Succ(zzz317200), zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, h)
new_mkVBalBranch3MkVBalBranch240(zzz958, zzz959, zzz960, zzz961, zzz962, zzz963, zzz964, zzz965, zzz966, zzz967, zzz968, ba) → new_mkVBalBranch3MkVBalBranch124(zzz958, zzz959, zzz960, zzz961, zzz962, zzz963, zzz964, zzz965, zzz966, zzz967, zzz968, new_primPlusNat2(new_primPlusNat3(Succ(new_primPlusNat3(new_primPlusNat1(zzz960), zzz960)), Succ(zzz960)), Succ(zzz960)), ba)
new_mkVBalBranch3MkVBalBranch241(zzz3170, zzz3171, Pos(Succ(zzz317200)), zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, Zero, h) → new_mkVBalBranch3MkVBalBranch243(zzz3170, zzz3171, Succ(zzz317200), zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, h)
new_mkVBalBranch1(zzz31, Branch(zzz330, zzz331, Pos(Zero), zzz333, zzz334), Branch(zzz3170, zzz3171, Neg(Succ(zzz317200)), zzz3173, zzz3174), h) → new_mkVBalBranch3MkVBalBranch126(zzz3170, zzz3171, zzz317200, zzz3173, zzz3174, zzz330, zzz331, zzz333, zzz334, zzz31, new_primPlusNat2(new_primPlusNat3(Succ(new_primPlusNat3(new_primPlusNat1(zzz317200), zzz317200)), Succ(zzz317200)), Succ(zzz317200)), h)
new_mkVBalBranch3MkVBalBranch126(zzz3170, zzz3171, zzz317200, zzz3173, zzz3174, zzz330, zzz331, zzz333, zzz334, zzz31, Succ(zzz5350), h) → new_mkVBalBranch1(zzz31, zzz334, Branch(zzz3170, zzz3171, Neg(Succ(zzz317200)), zzz3173, zzz3174), h)
new_mkVBalBranch3MkVBalBranch241(zzz3170, zzz3171, Neg(Zero), zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, Succ(zzz4190), h) → new_mkVBalBranch1(zzz31, Branch(zzz330, zzz331, Neg(Succ(zzz33200)), zzz333, zzz334), zzz3173, h)
new_mkVBalBranch3MkVBalBranch123(zzz3170, zzz3171, zzz317200, zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, Zero, h) → new_mkVBalBranch3MkVBalBranch130(zzz3170, zzz3171, zzz317200, zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, h)
new_mkVBalBranch3MkVBalBranch124(zzz958, zzz959, zzz960, zzz961, zzz962, zzz963, zzz964, zzz965, zzz966, zzz967, zzz968, Succ(zzz10180), ba) → new_mkVBalBranch3MkVBalBranch125(zzz958, zzz959, zzz960, zzz961, zzz962, zzz963, zzz964, zzz965, zzz966, zzz967, zzz968, Succ(zzz10180), Succ(zzz965), ba)
new_mkVBalBranch3MkVBalBranch235(zzz3170, zzz3171, Pos(Succ(zzz317200)), zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, Zero, h) → new_mkVBalBranch3MkVBalBranch236(zzz3170, zzz3171, zzz317200, zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, Zero, Succ(zzz317200), h)
new_mkVBalBranch3MkVBalBranch239(zzz3170, zzz3171, Zero, zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, h) → new_mkVBalBranch1(zzz31, zzz334, Branch(zzz3170, zzz3171, Neg(Zero), zzz3173, zzz3174), h)
new_mkVBalBranch3MkVBalBranch235(zzz3170, zzz3171, Pos(Zero), zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, Zero, h) → new_mkVBalBranch1(zzz31, zzz334, Branch(zzz3170, zzz3171, Pos(Zero), zzz3173, zzz3174), h)
new_mkVBalBranch3MkVBalBranch242(zzz972, zzz973, zzz974, zzz975, zzz976, zzz977, zzz978, zzz979, zzz980, zzz981, zzz982, Zero, Zero, bc) → new_mkVBalBranch3MkVBalBranch244(zzz972, zzz973, zzz974, zzz975, zzz976, zzz977, zzz978, zzz979, zzz980, zzz981, zzz982, bc)
new_mkVBalBranch3MkVBalBranch130(zzz3170, zzz3171, zzz317200, zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, h) → new_mkVBalBranch1(zzz31, zzz334, Branch(zzz3170, zzz3171, Neg(Succ(zzz317200)), zzz3173, zzz3174), h)
new_mkVBalBranch1(zzz31, Branch(zzz330, zzz331, Neg(Zero), zzz333, zzz334), Branch(zzz3170, zzz3171, Pos(Succ(zzz317200)), zzz3173, zzz3174), h) → new_mkVBalBranch1(zzz31, Branch(zzz330, zzz331, Neg(Zero), zzz333, zzz334), zzz3173, h)
new_mkVBalBranch3MkVBalBranch235(zzz3170, zzz3171, Neg(Zero), zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, Zero, h) → new_mkVBalBranch3MkVBalBranch239(zzz3170, zzz3171, Zero, zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, h)
new_mkVBalBranch1(zzz31, Branch(zzz330, zzz331, Neg(Succ(zzz33200)), zzz333, zzz334), Branch(zzz3170, zzz3171, zzz3172, zzz3173, zzz3174), h) → new_mkVBalBranch3MkVBalBranch241(zzz3170, zzz3171, zzz3172, zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, new_primPlusNat2(Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat3(new_primPlusNat1(zzz33200), zzz33200)), zzz33200))), Succ(zzz33200)), h)
new_mkVBalBranch3MkVBalBranch235(zzz3170, zzz3171, Neg(Zero), zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, Succ(zzz4170), h) → new_mkVBalBranch1(zzz31, zzz334, Branch(zzz3170, zzz3171, Neg(Zero), zzz3173, zzz3174), h)
new_mkVBalBranch3MkVBalBranch244(zzz972, zzz973, zzz974, zzz975, zzz976, zzz977, zzz978, zzz979, zzz980, zzz981, zzz982, bc) → new_mkVBalBranch3MkVBalBranch128(zzz972, zzz973, zzz974, zzz975, zzz976, zzz977, zzz978, zzz979, zzz980, zzz981, zzz982, new_primPlusNat2(new_primPlusNat3(Succ(new_primPlusNat3(new_primPlusNat1(zzz974), zzz974)), Succ(zzz974)), Succ(zzz974)), bc)
new_mkVBalBranch3MkVBalBranch236(zzz958, zzz959, zzz960, zzz961, zzz962, zzz963, zzz964, zzz965, zzz966, zzz967, zzz968, Zero, Zero, ba) → new_mkVBalBranch3MkVBalBranch240(zzz958, zzz959, zzz960, zzz961, zzz962, zzz963, zzz964, zzz965, zzz966, zzz967, zzz968, ba)

The TRS R consists of the following rules:

new_primPlusNat1(Zero) → Zero
new_primPlusNat1(Succ(zzz62000)) → Succ(Succ(new_primPlusNat1(zzz62000)))
new_primPlusNat3(zzz90, Succ(zzz910)) → Succ(Succ(new_primPlusNat2(zzz90, zzz910)))
new_primPlusNat3(zzz90, Zero) → Succ(zzz90)
new_primPlusNat2(Succ(zzz900), Succ(zzz9100)) → Succ(Succ(new_primPlusNat2(zzz900, zzz9100)))
new_primPlusNat2(Succ(zzz900), Zero) → Succ(zzz900)
new_primPlusNat2(Zero, Succ(zzz9100)) → Succ(zzz9100)
new_primPlusNat2(Zero, Zero) → Zero

The set Q consists of the following terms:

new_primPlusNat2(Zero, Succ(x0))
new_primPlusNat3(x0, Succ(x1))
new_primPlusNat2(Succ(x0), Succ(x1))
new_primPlusNat3(x0, Zero)
new_primPlusNat1(Zero)
new_primPlusNat2(Zero, Zero)
new_primPlusNat1(Succ(x0))
new_primPlusNat2(Succ(x0), Zero)

We have to consider all minimal (P,Q,R)-chains.
By rewriting [15] the rule new_mkVBalBranch3MkVBalBranch242(zzz972, zzz973, zzz974, zzz975, zzz976, zzz977, zzz978, zzz979, zzz980, zzz981, zzz982, Succ(zzz9830), Zero, bc) → new_mkVBalBranch3MkVBalBranch128(zzz972, zzz973, zzz974, zzz975, zzz976, zzz977, zzz978, zzz979, zzz980, zzz981, zzz982, new_primPlusNat2(new_primPlusNat3(Succ(new_primPlusNat3(new_primPlusNat1(zzz974), zzz974)), Succ(zzz974)), Succ(zzz974)), bc) at position [11,0] we obtained the following new rules:

new_mkVBalBranch3MkVBalBranch242(zzz972, zzz973, zzz974, zzz975, zzz976, zzz977, zzz978, zzz979, zzz980, zzz981, zzz982, Succ(zzz9830), Zero, bc) → new_mkVBalBranch3MkVBalBranch128(zzz972, zzz973, zzz974, zzz975, zzz976, zzz977, zzz978, zzz979, zzz980, zzz981, zzz982, new_primPlusNat2(Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat3(new_primPlusNat1(zzz974), zzz974)), zzz974))), Succ(zzz974)), bc)



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

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

new_mkVBalBranch3MkVBalBranch129(zzz1851, zzz1852, zzz1853, zzz1854, zzz1855, zzz1856, zzz1857, zzz1858, zzz1859, zzz1860, zzz1861, Zero, Succ(zzz18630), bd) → new_mkVBalBranch1(zzz1861, zzz1860, Branch(zzz1851, zzz1852, Neg(Succ(zzz1853)), zzz1854, zzz1855), bd)
new_mkVBalBranch3MkVBalBranch128(zzz972, zzz973, zzz974, zzz975, zzz976, zzz977, zzz978, zzz979, zzz980, zzz981, zzz982, Succ(zzz10190), bc) → new_mkVBalBranch3MkVBalBranch129(zzz972, zzz973, zzz974, zzz975, zzz976, zzz977, zzz978, zzz979, zzz980, zzz981, zzz982, Succ(zzz979), Succ(zzz10190), bc)
new_mkVBalBranch3MkVBalBranch241(zzz3170, zzz3171, Pos(zzz31720), zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, Succ(zzz4190), h) → new_mkVBalBranch1(zzz31, Branch(zzz330, zzz331, Neg(Succ(zzz33200)), zzz333, zzz334), zzz3173, h)
new_mkVBalBranch3MkVBalBranch127(zzz3170, zzz3171, zzz317200, zzz3173, zzz3174, zzz330, zzz331, zzz333, zzz334, zzz31, Succ(zzz5500), h) → new_mkVBalBranch1(zzz31, zzz334, Branch(zzz3170, zzz3171, Neg(Succ(zzz317200)), zzz3173, zzz3174), h)
new_mkVBalBranch3MkVBalBranch242(zzz972, zzz973, zzz974, zzz975, zzz976, zzz977, zzz978, zzz979, zzz980, zzz981, zzz982, Succ(zzz9830), Zero, bc) → new_mkVBalBranch3MkVBalBranch128(zzz972, zzz973, zzz974, zzz975, zzz976, zzz977, zzz978, zzz979, zzz980, zzz981, zzz982, new_primPlusNat2(Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat3(new_primPlusNat1(zzz974), zzz974)), zzz974))), Succ(zzz974)), bc)
new_mkVBalBranch3MkVBalBranch129(zzz1851, zzz1852, zzz1853, zzz1854, zzz1855, zzz1856, zzz1857, zzz1858, zzz1859, zzz1860, zzz1861, Succ(zzz18620), Succ(zzz18630), bd) → new_mkVBalBranch3MkVBalBranch129(zzz1851, zzz1852, zzz1853, zzz1854, zzz1855, zzz1856, zzz1857, zzz1858, zzz1859, zzz1860, zzz1861, zzz18620, zzz18630, bd)
new_mkVBalBranch3MkVBalBranch124(zzz958, zzz959, zzz960, zzz961, zzz962, zzz963, zzz964, zzz965, zzz966, zzz967, zzz968, Zero, ba) → new_mkVBalBranch3MkVBalBranch125(zzz958, zzz959, zzz960, zzz961, zzz962, zzz963, zzz964, zzz965, zzz966, zzz967, zzz968, Zero, Succ(zzz965), ba)
new_mkVBalBranch3MkVBalBranch235(zzz3170, zzz3171, Pos(Succ(zzz317200)), zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, Succ(zzz4170), h) → new_mkVBalBranch3MkVBalBranch236(zzz3170, zzz3171, zzz317200, zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, zzz4170, zzz317200, h)
new_mkVBalBranch3MkVBalBranch242(zzz972, zzz973, zzz974, zzz975, zzz976, zzz977, zzz978, zzz979, zzz980, zzz981, zzz982, Succ(zzz9830), Succ(zzz9840), bc) → new_mkVBalBranch3MkVBalBranch242(zzz972, zzz973, zzz974, zzz975, zzz976, zzz977, zzz978, zzz979, zzz980, zzz981, zzz982, zzz9830, zzz9840, bc)
new_mkVBalBranch3MkVBalBranch236(zzz958, zzz959, zzz960, zzz961, zzz962, zzz963, zzz964, zzz965, zzz966, zzz967, zzz968, Succ(zzz9690), Succ(zzz9700), ba) → new_mkVBalBranch3MkVBalBranch236(zzz958, zzz959, zzz960, zzz961, zzz962, zzz963, zzz964, zzz965, zzz966, zzz967, zzz968, zzz9690, zzz9700, ba)
new_mkVBalBranch1(zzz31, Branch(zzz330, zzz331, Pos(Succ(zzz33200)), zzz333, zzz334), Branch(zzz3170, zzz3171, zzz3172, zzz3173, zzz3174), h) → new_mkVBalBranch3MkVBalBranch235(zzz3170, zzz3171, zzz3172, zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, new_primPlusNat2(Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat3(new_primPlusNat1(zzz33200), zzz33200)), zzz33200))), Succ(zzz33200)), h)
new_mkVBalBranch3MkVBalBranch241(zzz3170, zzz3171, Neg(Succ(zzz317200)), zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, Succ(zzz4190), h) → new_mkVBalBranch3MkVBalBranch242(zzz3170, zzz3171, zzz317200, zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, zzz317200, zzz4190, h)
new_mkVBalBranch3MkVBalBranch241(zzz3170, zzz3171, Neg(Succ(zzz317200)), zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, Zero, h) → new_mkVBalBranch3MkVBalBranch242(zzz3170, zzz3171, zzz317200, zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, Succ(zzz317200), Zero, h)
new_mkVBalBranch1(zzz31, Branch(zzz330, zzz331, Pos(Zero), zzz333, zzz334), Branch(zzz3170, zzz3171, Pos(Succ(zzz317200)), zzz3173, zzz3174), h) → new_mkVBalBranch1(zzz31, Branch(zzz330, zzz331, Pos(Zero), zzz333, zzz334), zzz3173, h)
new_mkVBalBranch3MkVBalBranch235(zzz3170, zzz3171, Neg(Succ(zzz317200)), zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, Succ(zzz4170), h) → new_mkVBalBranch3MkVBalBranch123(zzz3170, zzz3171, zzz317200, zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, new_primPlusNat2(Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat3(new_primPlusNat1(zzz317200), zzz317200)), zzz317200))), Succ(zzz317200)), h)
new_mkVBalBranch3MkVBalBranch243(zzz3170, zzz3171, zzz31720, zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, h) → new_mkVBalBranch1(zzz31, Branch(zzz330, zzz331, Neg(Succ(zzz33200)), zzz333, zzz334), zzz3173, h)
new_mkVBalBranch3MkVBalBranch237(zzz3170, zzz3171, zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, h) → new_mkVBalBranch1(zzz31, zzz334, Branch(zzz3170, zzz3171, Pos(Zero), zzz3173, zzz3174), h)
new_mkVBalBranch3MkVBalBranch235(zzz3170, zzz3171, Pos(Zero), zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, Succ(zzz4170), h) → new_mkVBalBranch3MkVBalBranch237(zzz3170, zzz3171, zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, h)
new_mkVBalBranch3MkVBalBranch236(zzz958, zzz959, zzz960, zzz961, zzz962, zzz963, zzz964, zzz965, zzz966, zzz967, zzz968, Succ(zzz9690), Zero, ba) → new_mkVBalBranch3MkVBalBranch124(zzz958, zzz959, zzz960, zzz961, zzz962, zzz963, zzz964, zzz965, zzz966, zzz967, zzz968, new_primPlusNat2(Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat3(new_primPlusNat1(zzz960), zzz960)), zzz960))), Succ(zzz960)), ba)
new_mkVBalBranch3MkVBalBranch236(zzz958, zzz959, zzz960, zzz961, zzz962, zzz963, zzz964, zzz965, zzz966, zzz967, zzz968, Zero, Succ(zzz9700), ba) → new_mkVBalBranch1(zzz968, Branch(zzz963, zzz964, Pos(Succ(zzz965)), zzz966, zzz967), zzz961, ba)
new_mkVBalBranch3MkVBalBranch125(zzz1337, zzz1338, zzz1339, zzz1340, zzz1341, zzz1342, zzz1343, zzz1344, zzz1345, zzz1346, zzz1347, Succ(zzz13480), Succ(zzz13490), bb) → new_mkVBalBranch3MkVBalBranch125(zzz1337, zzz1338, zzz1339, zzz1340, zzz1341, zzz1342, zzz1343, zzz1344, zzz1345, zzz1346, zzz1347, zzz13480, zzz13490, bb)
new_mkVBalBranch3MkVBalBranch123(zzz3170, zzz3171, zzz317200, zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, Succ(zzz5620), h) → new_mkVBalBranch1(zzz31, zzz334, Branch(zzz3170, zzz3171, Neg(Succ(zzz317200)), zzz3173, zzz3174), h)
new_mkVBalBranch3MkVBalBranch125(zzz1337, zzz1338, zzz1339, zzz1340, zzz1341, zzz1342, zzz1343, zzz1344, zzz1345, zzz1346, zzz1347, Zero, Succ(zzz13490), bb) → new_mkVBalBranch1(zzz1347, zzz1346, Branch(zzz1337, zzz1338, Pos(Succ(zzz1339)), zzz1340, zzz1341), bb)
new_mkVBalBranch3MkVBalBranch242(zzz972, zzz973, zzz974, zzz975, zzz976, zzz977, zzz978, zzz979, zzz980, zzz981, zzz982, Zero, Succ(zzz9840), bc) → new_mkVBalBranch1(zzz982, Branch(zzz977, zzz978, Neg(Succ(zzz979)), zzz980, zzz981), zzz975, bc)
new_mkVBalBranch1(zzz31, Branch(zzz330, zzz331, Neg(Zero), zzz333, zzz334), Branch(zzz3170, zzz3171, Neg(Succ(zzz317200)), zzz3173, zzz3174), h) → new_mkVBalBranch3MkVBalBranch127(zzz3170, zzz3171, zzz317200, zzz3173, zzz3174, zzz330, zzz331, zzz333, zzz334, zzz31, new_primPlusNat2(new_primPlusNat3(Succ(new_primPlusNat3(new_primPlusNat1(zzz317200), zzz317200)), Succ(zzz317200)), Succ(zzz317200)), h)
new_mkVBalBranch3MkVBalBranch238(zzz3170, zzz3171, Succ(zzz317200), zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, h) → new_mkVBalBranch3MkVBalBranch123(zzz3170, zzz3171, zzz317200, zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, new_primPlusNat2(Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat3(new_primPlusNat1(zzz317200), zzz317200)), zzz317200))), Succ(zzz317200)), h)
new_mkVBalBranch3MkVBalBranch235(zzz3170, zzz3171, Neg(Succ(zzz317200)), zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, Zero, h) → new_mkVBalBranch3MkVBalBranch238(zzz3170, zzz3171, Succ(zzz317200), zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, h)
new_mkVBalBranch3MkVBalBranch240(zzz958, zzz959, zzz960, zzz961, zzz962, zzz963, zzz964, zzz965, zzz966, zzz967, zzz968, ba) → new_mkVBalBranch3MkVBalBranch124(zzz958, zzz959, zzz960, zzz961, zzz962, zzz963, zzz964, zzz965, zzz966, zzz967, zzz968, new_primPlusNat2(new_primPlusNat3(Succ(new_primPlusNat3(new_primPlusNat1(zzz960), zzz960)), Succ(zzz960)), Succ(zzz960)), ba)
new_mkVBalBranch3MkVBalBranch241(zzz3170, zzz3171, Pos(Succ(zzz317200)), zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, Zero, h) → new_mkVBalBranch3MkVBalBranch243(zzz3170, zzz3171, Succ(zzz317200), zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, h)
new_mkVBalBranch3MkVBalBranch126(zzz3170, zzz3171, zzz317200, zzz3173, zzz3174, zzz330, zzz331, zzz333, zzz334, zzz31, Succ(zzz5350), h) → new_mkVBalBranch1(zzz31, zzz334, Branch(zzz3170, zzz3171, Neg(Succ(zzz317200)), zzz3173, zzz3174), h)
new_mkVBalBranch1(zzz31, Branch(zzz330, zzz331, Pos(Zero), zzz333, zzz334), Branch(zzz3170, zzz3171, Neg(Succ(zzz317200)), zzz3173, zzz3174), h) → new_mkVBalBranch3MkVBalBranch126(zzz3170, zzz3171, zzz317200, zzz3173, zzz3174, zzz330, zzz331, zzz333, zzz334, zzz31, new_primPlusNat2(new_primPlusNat3(Succ(new_primPlusNat3(new_primPlusNat1(zzz317200), zzz317200)), Succ(zzz317200)), Succ(zzz317200)), h)
new_mkVBalBranch3MkVBalBranch123(zzz3170, zzz3171, zzz317200, zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, Zero, h) → new_mkVBalBranch3MkVBalBranch130(zzz3170, zzz3171, zzz317200, zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, h)
new_mkVBalBranch3MkVBalBranch241(zzz3170, zzz3171, Neg(Zero), zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, Succ(zzz4190), h) → new_mkVBalBranch1(zzz31, Branch(zzz330, zzz331, Neg(Succ(zzz33200)), zzz333, zzz334), zzz3173, h)
new_mkVBalBranch3MkVBalBranch124(zzz958, zzz959, zzz960, zzz961, zzz962, zzz963, zzz964, zzz965, zzz966, zzz967, zzz968, Succ(zzz10180), ba) → new_mkVBalBranch3MkVBalBranch125(zzz958, zzz959, zzz960, zzz961, zzz962, zzz963, zzz964, zzz965, zzz966, zzz967, zzz968, Succ(zzz10180), Succ(zzz965), ba)
new_mkVBalBranch3MkVBalBranch235(zzz3170, zzz3171, Pos(Succ(zzz317200)), zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, Zero, h) → new_mkVBalBranch3MkVBalBranch236(zzz3170, zzz3171, zzz317200, zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, Zero, Succ(zzz317200), h)
new_mkVBalBranch3MkVBalBranch239(zzz3170, zzz3171, Zero, zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, h) → new_mkVBalBranch1(zzz31, zzz334, Branch(zzz3170, zzz3171, Neg(Zero), zzz3173, zzz3174), h)
new_mkVBalBranch3MkVBalBranch235(zzz3170, zzz3171, Pos(Zero), zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, Zero, h) → new_mkVBalBranch1(zzz31, zzz334, Branch(zzz3170, zzz3171, Pos(Zero), zzz3173, zzz3174), h)
new_mkVBalBranch3MkVBalBranch242(zzz972, zzz973, zzz974, zzz975, zzz976, zzz977, zzz978, zzz979, zzz980, zzz981, zzz982, Zero, Zero, bc) → new_mkVBalBranch3MkVBalBranch244(zzz972, zzz973, zzz974, zzz975, zzz976, zzz977, zzz978, zzz979, zzz980, zzz981, zzz982, bc)
new_mkVBalBranch3MkVBalBranch130(zzz3170, zzz3171, zzz317200, zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, h) → new_mkVBalBranch1(zzz31, zzz334, Branch(zzz3170, zzz3171, Neg(Succ(zzz317200)), zzz3173, zzz3174), h)
new_mkVBalBranch3MkVBalBranch235(zzz3170, zzz3171, Neg(Zero), zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, Zero, h) → new_mkVBalBranch3MkVBalBranch239(zzz3170, zzz3171, Zero, zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, h)
new_mkVBalBranch1(zzz31, Branch(zzz330, zzz331, Neg(Zero), zzz333, zzz334), Branch(zzz3170, zzz3171, Pos(Succ(zzz317200)), zzz3173, zzz3174), h) → new_mkVBalBranch1(zzz31, Branch(zzz330, zzz331, Neg(Zero), zzz333, zzz334), zzz3173, h)
new_mkVBalBranch3MkVBalBranch235(zzz3170, zzz3171, Neg(Zero), zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, Succ(zzz4170), h) → new_mkVBalBranch1(zzz31, zzz334, Branch(zzz3170, zzz3171, Neg(Zero), zzz3173, zzz3174), h)
new_mkVBalBranch1(zzz31, Branch(zzz330, zzz331, Neg(Succ(zzz33200)), zzz333, zzz334), Branch(zzz3170, zzz3171, zzz3172, zzz3173, zzz3174), h) → new_mkVBalBranch3MkVBalBranch241(zzz3170, zzz3171, zzz3172, zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, new_primPlusNat2(Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat3(new_primPlusNat1(zzz33200), zzz33200)), zzz33200))), Succ(zzz33200)), h)
new_mkVBalBranch3MkVBalBranch236(zzz958, zzz959, zzz960, zzz961, zzz962, zzz963, zzz964, zzz965, zzz966, zzz967, zzz968, Zero, Zero, ba) → new_mkVBalBranch3MkVBalBranch240(zzz958, zzz959, zzz960, zzz961, zzz962, zzz963, zzz964, zzz965, zzz966, zzz967, zzz968, ba)
new_mkVBalBranch3MkVBalBranch244(zzz972, zzz973, zzz974, zzz975, zzz976, zzz977, zzz978, zzz979, zzz980, zzz981, zzz982, bc) → new_mkVBalBranch3MkVBalBranch128(zzz972, zzz973, zzz974, zzz975, zzz976, zzz977, zzz978, zzz979, zzz980, zzz981, zzz982, new_primPlusNat2(new_primPlusNat3(Succ(new_primPlusNat3(new_primPlusNat1(zzz974), zzz974)), Succ(zzz974)), Succ(zzz974)), bc)

The TRS R consists of the following rules:

new_primPlusNat1(Zero) → Zero
new_primPlusNat1(Succ(zzz62000)) → Succ(Succ(new_primPlusNat1(zzz62000)))
new_primPlusNat3(zzz90, Succ(zzz910)) → Succ(Succ(new_primPlusNat2(zzz90, zzz910)))
new_primPlusNat3(zzz90, Zero) → Succ(zzz90)
new_primPlusNat2(Succ(zzz900), Succ(zzz9100)) → Succ(Succ(new_primPlusNat2(zzz900, zzz9100)))
new_primPlusNat2(Succ(zzz900), Zero) → Succ(zzz900)
new_primPlusNat2(Zero, Succ(zzz9100)) → Succ(zzz9100)
new_primPlusNat2(Zero, Zero) → Zero

The set Q consists of the following terms:

new_primPlusNat2(Zero, Succ(x0))
new_primPlusNat3(x0, Succ(x1))
new_primPlusNat2(Succ(x0), Succ(x1))
new_primPlusNat3(x0, Zero)
new_primPlusNat1(Zero)
new_primPlusNat2(Zero, Zero)
new_primPlusNat1(Succ(x0))
new_primPlusNat2(Succ(x0), Zero)

We have to consider all minimal (P,Q,R)-chains.
By rewriting [15] the rule new_mkVBalBranch1(zzz31, Branch(zzz330, zzz331, Pos(Succ(zzz33200)), zzz333, zzz334), Branch(zzz3170, zzz3171, zzz3172, zzz3173, zzz3174), h) → new_mkVBalBranch3MkVBalBranch235(zzz3170, zzz3171, zzz3172, zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, new_primPlusNat2(Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat3(new_primPlusNat1(zzz33200), zzz33200)), zzz33200))), Succ(zzz33200)), h) at position [11] we obtained the following new rules:

new_mkVBalBranch1(zzz31, Branch(zzz330, zzz331, Pos(Succ(zzz33200)), zzz333, zzz334), Branch(zzz3170, zzz3171, zzz3172, zzz3173, zzz3174), h) → new_mkVBalBranch3MkVBalBranch235(zzz3170, zzz3171, zzz3172, zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat2(Succ(new_primPlusNat3(new_primPlusNat1(zzz33200), zzz33200)), zzz33200)), zzz33200))), 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
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                    ↳ DependencyGraphProof
                                      ↳ QDP
                                        ↳ Rewriting
                                          ↳ QDP
                                            ↳ Rewriting
                                              ↳ QDP
                                                ↳ Rewriting
                                                  ↳ QDP
                                                    ↳ Rewriting
                                                      ↳ QDP
                                                        ↳ Rewriting
                                                          ↳ QDP
                                                            ↳ Rewriting
                                                              ↳ QDP
                                                                ↳ Rewriting
                                                                  ↳ QDP
                                                                    ↳ Rewriting
                                                                      ↳ QDP
                                                                        ↳ Rewriting
                                                                          ↳ QDP
                                                                            ↳ Rewriting
                                                                              ↳ QDP
                                                                                ↳ UsableRulesProof
                                                                                  ↳ QDP
                                                                                    ↳ QReductionProof
                                                                                      ↳ QDP
                                                                                        ↳ Rewriting
                                                                                          ↳ QDP
                                                                                            ↳ Rewriting
                                                                                              ↳ QDP
                                                                                                ↳ Rewriting
                                                                                                  ↳ QDP
                                                                                                    ↳ Rewriting
                                                                                                      ↳ QDP
                                                                                                        ↳ Rewriting
                                                                                                          ↳ QDP
                                                                                                            ↳ Rewriting
                                                                                                              ↳ QDP
                                                                                                                ↳ Rewriting
                                                                                                                  ↳ QDP
                                                                                                                    ↳ Rewriting
                                                                                                                      ↳ QDP
                                                                                                                        ↳ Rewriting
                                                                                                                          ↳ QDP
                                                                                                                            ↳ Rewriting
                                                                                                                              ↳ QDP
                                                                                                                                ↳ UsableRulesProof
                                                                                                                                  ↳ QDP
                                                                                                                                    ↳ QReductionProof
                                                                                                                                      ↳ QDP
                                                                                                                                        ↳ Rewriting
                                                                                                                                          ↳ QDP
                                                                                                                                            ↳ Rewriting
                                                                                                                                              ↳ QDP
                                                                                                                                                ↳ Rewriting
                                                                                                                                                  ↳ QDP
                                                                                                                                                    ↳ DependencyGraphProof
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP

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

new_mkVBalBranch3MkVBalBranch129(zzz1851, zzz1852, zzz1853, zzz1854, zzz1855, zzz1856, zzz1857, zzz1858, zzz1859, zzz1860, zzz1861, Zero, Succ(zzz18630), bd) → new_mkVBalBranch1(zzz1861, zzz1860, Branch(zzz1851, zzz1852, Neg(Succ(zzz1853)), zzz1854, zzz1855), bd)
new_mkVBalBranch3MkVBalBranch127(zzz3170, zzz3171, zzz317200, zzz3173, zzz3174, zzz330, zzz331, zzz333, zzz334, zzz31, Succ(zzz5500), h) → new_mkVBalBranch1(zzz31, zzz334, Branch(zzz3170, zzz3171, Neg(Succ(zzz317200)), zzz3173, zzz3174), h)
new_mkVBalBranch3MkVBalBranch241(zzz3170, zzz3171, Pos(zzz31720), zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, Succ(zzz4190), h) → new_mkVBalBranch1(zzz31, Branch(zzz330, zzz331, Neg(Succ(zzz33200)), zzz333, zzz334), zzz3173, h)
new_mkVBalBranch3MkVBalBranch128(zzz972, zzz973, zzz974, zzz975, zzz976, zzz977, zzz978, zzz979, zzz980, zzz981, zzz982, Succ(zzz10190), bc) → new_mkVBalBranch3MkVBalBranch129(zzz972, zzz973, zzz974, zzz975, zzz976, zzz977, zzz978, zzz979, zzz980, zzz981, zzz982, Succ(zzz979), Succ(zzz10190), bc)
new_mkVBalBranch3MkVBalBranch242(zzz972, zzz973, zzz974, zzz975, zzz976, zzz977, zzz978, zzz979, zzz980, zzz981, zzz982, Succ(zzz9830), Zero, bc) → new_mkVBalBranch3MkVBalBranch128(zzz972, zzz973, zzz974, zzz975, zzz976, zzz977, zzz978, zzz979, zzz980, zzz981, zzz982, new_primPlusNat2(Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat3(new_primPlusNat1(zzz974), zzz974)), zzz974))), Succ(zzz974)), bc)
new_mkVBalBranch3MkVBalBranch129(zzz1851, zzz1852, zzz1853, zzz1854, zzz1855, zzz1856, zzz1857, zzz1858, zzz1859, zzz1860, zzz1861, Succ(zzz18620), Succ(zzz18630), bd) → new_mkVBalBranch3MkVBalBranch129(zzz1851, zzz1852, zzz1853, zzz1854, zzz1855, zzz1856, zzz1857, zzz1858, zzz1859, zzz1860, zzz1861, zzz18620, zzz18630, bd)
new_mkVBalBranch3MkVBalBranch124(zzz958, zzz959, zzz960, zzz961, zzz962, zzz963, zzz964, zzz965, zzz966, zzz967, zzz968, Zero, ba) → new_mkVBalBranch3MkVBalBranch125(zzz958, zzz959, zzz960, zzz961, zzz962, zzz963, zzz964, zzz965, zzz966, zzz967, zzz968, Zero, Succ(zzz965), ba)
new_mkVBalBranch3MkVBalBranch242(zzz972, zzz973, zzz974, zzz975, zzz976, zzz977, zzz978, zzz979, zzz980, zzz981, zzz982, Succ(zzz9830), Succ(zzz9840), bc) → new_mkVBalBranch3MkVBalBranch242(zzz972, zzz973, zzz974, zzz975, zzz976, zzz977, zzz978, zzz979, zzz980, zzz981, zzz982, zzz9830, zzz9840, bc)
new_mkVBalBranch3MkVBalBranch235(zzz3170, zzz3171, Pos(Succ(zzz317200)), zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, Succ(zzz4170), h) → new_mkVBalBranch3MkVBalBranch236(zzz3170, zzz3171, zzz317200, zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, zzz4170, zzz317200, h)
new_mkVBalBranch1(zzz31, Branch(zzz330, zzz331, Pos(Succ(zzz33200)), zzz333, zzz334), Branch(zzz3170, zzz3171, zzz3172, zzz3173, zzz3174), h) → new_mkVBalBranch3MkVBalBranch235(zzz3170, zzz3171, zzz3172, zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat2(Succ(new_primPlusNat3(new_primPlusNat1(zzz33200), zzz33200)), zzz33200)), zzz33200))), h)
new_mkVBalBranch3MkVBalBranch236(zzz958, zzz959, zzz960, zzz961, zzz962, zzz963, zzz964, zzz965, zzz966, zzz967, zzz968, Succ(zzz9690), Succ(zzz9700), ba) → new_mkVBalBranch3MkVBalBranch236(zzz958, zzz959, zzz960, zzz961, zzz962, zzz963, zzz964, zzz965, zzz966, zzz967, zzz968, zzz9690, zzz9700, ba)
new_mkVBalBranch3MkVBalBranch241(zzz3170, zzz3171, Neg(Succ(zzz317200)), zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, Succ(zzz4190), h) → new_mkVBalBranch3MkVBalBranch242(zzz3170, zzz3171, zzz317200, zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, zzz317200, zzz4190, h)
new_mkVBalBranch3MkVBalBranch241(zzz3170, zzz3171, Neg(Succ(zzz317200)), zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, Zero, h) → new_mkVBalBranch3MkVBalBranch242(zzz3170, zzz3171, zzz317200, zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, Succ(zzz317200), Zero, h)
new_mkVBalBranch1(zzz31, Branch(zzz330, zzz331, Pos(Zero), zzz333, zzz334), Branch(zzz3170, zzz3171, Pos(Succ(zzz317200)), zzz3173, zzz3174), h) → new_mkVBalBranch1(zzz31, Branch(zzz330, zzz331, Pos(Zero), zzz333, zzz334), zzz3173, h)
new_mkVBalBranch3MkVBalBranch237(zzz3170, zzz3171, zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, h) → new_mkVBalBranch1(zzz31, zzz334, Branch(zzz3170, zzz3171, Pos(Zero), zzz3173, zzz3174), h)
new_mkVBalBranch3MkVBalBranch243(zzz3170, zzz3171, zzz31720, zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, h) → new_mkVBalBranch1(zzz31, Branch(zzz330, zzz331, Neg(Succ(zzz33200)), zzz333, zzz334), zzz3173, h)
new_mkVBalBranch3MkVBalBranch235(zzz3170, zzz3171, Neg(Succ(zzz317200)), zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, Succ(zzz4170), h) → new_mkVBalBranch3MkVBalBranch123(zzz3170, zzz3171, zzz317200, zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, new_primPlusNat2(Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat3(new_primPlusNat1(zzz317200), zzz317200)), zzz317200))), Succ(zzz317200)), h)
new_mkVBalBranch3MkVBalBranch235(zzz3170, zzz3171, Pos(Zero), zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, Succ(zzz4170), h) → new_mkVBalBranch3MkVBalBranch237(zzz3170, zzz3171, zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, h)
new_mkVBalBranch3MkVBalBranch236(zzz958, zzz959, zzz960, zzz961, zzz962, zzz963, zzz964, zzz965, zzz966, zzz967, zzz968, Succ(zzz9690), Zero, ba) → new_mkVBalBranch3MkVBalBranch124(zzz958, zzz959, zzz960, zzz961, zzz962, zzz963, zzz964, zzz965, zzz966, zzz967, zzz968, new_primPlusNat2(Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat3(new_primPlusNat1(zzz960), zzz960)), zzz960))), Succ(zzz960)), ba)
new_mkVBalBranch3MkVBalBranch236(zzz958, zzz959, zzz960, zzz961, zzz962, zzz963, zzz964, zzz965, zzz966, zzz967, zzz968, Zero, Succ(zzz9700), ba) → new_mkVBalBranch1(zzz968, Branch(zzz963, zzz964, Pos(Succ(zzz965)), zzz966, zzz967), zzz961, ba)
new_mkVBalBranch3MkVBalBranch125(zzz1337, zzz1338, zzz1339, zzz1340, zzz1341, zzz1342, zzz1343, zzz1344, zzz1345, zzz1346, zzz1347, Succ(zzz13480), Succ(zzz13490), bb) → new_mkVBalBranch3MkVBalBranch125(zzz1337, zzz1338, zzz1339, zzz1340, zzz1341, zzz1342, zzz1343, zzz1344, zzz1345, zzz1346, zzz1347, zzz13480, zzz13490, bb)
new_mkVBalBranch3MkVBalBranch123(zzz3170, zzz3171, zzz317200, zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, Succ(zzz5620), h) → new_mkVBalBranch1(zzz31, zzz334, Branch(zzz3170, zzz3171, Neg(Succ(zzz317200)), zzz3173, zzz3174), h)
new_mkVBalBranch3MkVBalBranch125(zzz1337, zzz1338, zzz1339, zzz1340, zzz1341, zzz1342, zzz1343, zzz1344, zzz1345, zzz1346, zzz1347, Zero, Succ(zzz13490), bb) → new_mkVBalBranch1(zzz1347, zzz1346, Branch(zzz1337, zzz1338, Pos(Succ(zzz1339)), zzz1340, zzz1341), bb)
new_mkVBalBranch3MkVBalBranch242(zzz972, zzz973, zzz974, zzz975, zzz976, zzz977, zzz978, zzz979, zzz980, zzz981, zzz982, Zero, Succ(zzz9840), bc) → new_mkVBalBranch1(zzz982, Branch(zzz977, zzz978, Neg(Succ(zzz979)), zzz980, zzz981), zzz975, bc)
new_mkVBalBranch3MkVBalBranch238(zzz3170, zzz3171, Succ(zzz317200), zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, h) → new_mkVBalBranch3MkVBalBranch123(zzz3170, zzz3171, zzz317200, zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, new_primPlusNat2(Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat3(new_primPlusNat1(zzz317200), zzz317200)), zzz317200))), Succ(zzz317200)), h)
new_mkVBalBranch1(zzz31, Branch(zzz330, zzz331, Neg(Zero), zzz333, zzz334), Branch(zzz3170, zzz3171, Neg(Succ(zzz317200)), zzz3173, zzz3174), h) → new_mkVBalBranch3MkVBalBranch127(zzz3170, zzz3171, zzz317200, zzz3173, zzz3174, zzz330, zzz331, zzz333, zzz334, zzz31, new_primPlusNat2(new_primPlusNat3(Succ(new_primPlusNat3(new_primPlusNat1(zzz317200), zzz317200)), Succ(zzz317200)), Succ(zzz317200)), h)
new_mkVBalBranch3MkVBalBranch235(zzz3170, zzz3171, Neg(Succ(zzz317200)), zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, Zero, h) → new_mkVBalBranch3MkVBalBranch238(zzz3170, zzz3171, Succ(zzz317200), zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, h)
new_mkVBalBranch3MkVBalBranch240(zzz958, zzz959, zzz960, zzz961, zzz962, zzz963, zzz964, zzz965, zzz966, zzz967, zzz968, ba) → new_mkVBalBranch3MkVBalBranch124(zzz958, zzz959, zzz960, zzz961, zzz962, zzz963, zzz964, zzz965, zzz966, zzz967, zzz968, new_primPlusNat2(new_primPlusNat3(Succ(new_primPlusNat3(new_primPlusNat1(zzz960), zzz960)), Succ(zzz960)), Succ(zzz960)), ba)
new_mkVBalBranch3MkVBalBranch241(zzz3170, zzz3171, Pos(Succ(zzz317200)), zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, Zero, h) → new_mkVBalBranch3MkVBalBranch243(zzz3170, zzz3171, Succ(zzz317200), zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, h)
new_mkVBalBranch1(zzz31, Branch(zzz330, zzz331, Pos(Zero), zzz333, zzz334), Branch(zzz3170, zzz3171, Neg(Succ(zzz317200)), zzz3173, zzz3174), h) → new_mkVBalBranch3MkVBalBranch126(zzz3170, zzz3171, zzz317200, zzz3173, zzz3174, zzz330, zzz331, zzz333, zzz334, zzz31, new_primPlusNat2(new_primPlusNat3(Succ(new_primPlusNat3(new_primPlusNat1(zzz317200), zzz317200)), Succ(zzz317200)), Succ(zzz317200)), h)
new_mkVBalBranch3MkVBalBranch126(zzz3170, zzz3171, zzz317200, zzz3173, zzz3174, zzz330, zzz331, zzz333, zzz334, zzz31, Succ(zzz5350), h) → new_mkVBalBranch1(zzz31, zzz334, Branch(zzz3170, zzz3171, Neg(Succ(zzz317200)), zzz3173, zzz3174), h)
new_mkVBalBranch3MkVBalBranch241(zzz3170, zzz3171, Neg(Zero), zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, Succ(zzz4190), h) → new_mkVBalBranch1(zzz31, Branch(zzz330, zzz331, Neg(Succ(zzz33200)), zzz333, zzz334), zzz3173, h)
new_mkVBalBranch3MkVBalBranch123(zzz3170, zzz3171, zzz317200, zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, Zero, h) → new_mkVBalBranch3MkVBalBranch130(zzz3170, zzz3171, zzz317200, zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, h)
new_mkVBalBranch3MkVBalBranch124(zzz958, zzz959, zzz960, zzz961, zzz962, zzz963, zzz964, zzz965, zzz966, zzz967, zzz968, Succ(zzz10180), ba) → new_mkVBalBranch3MkVBalBranch125(zzz958, zzz959, zzz960, zzz961, zzz962, zzz963, zzz964, zzz965, zzz966, zzz967, zzz968, Succ(zzz10180), Succ(zzz965), ba)
new_mkVBalBranch3MkVBalBranch235(zzz3170, zzz3171, Pos(Succ(zzz317200)), zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, Zero, h) → new_mkVBalBranch3MkVBalBranch236(zzz3170, zzz3171, zzz317200, zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, Zero, Succ(zzz317200), h)
new_mkVBalBranch3MkVBalBranch239(zzz3170, zzz3171, Zero, zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, h) → new_mkVBalBranch1(zzz31, zzz334, Branch(zzz3170, zzz3171, Neg(Zero), zzz3173, zzz3174), h)
new_mkVBalBranch3MkVBalBranch235(zzz3170, zzz3171, Pos(Zero), zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, Zero, h) → new_mkVBalBranch1(zzz31, zzz334, Branch(zzz3170, zzz3171, Pos(Zero), zzz3173, zzz3174), h)
new_mkVBalBranch3MkVBalBranch242(zzz972, zzz973, zzz974, zzz975, zzz976, zzz977, zzz978, zzz979, zzz980, zzz981, zzz982, Zero, Zero, bc) → new_mkVBalBranch3MkVBalBranch244(zzz972, zzz973, zzz974, zzz975, zzz976, zzz977, zzz978, zzz979, zzz980, zzz981, zzz982, bc)
new_mkVBalBranch3MkVBalBranch130(zzz3170, zzz3171, zzz317200, zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, h) → new_mkVBalBranch1(zzz31, zzz334, Branch(zzz3170, zzz3171, Neg(Succ(zzz317200)), zzz3173, zzz3174), h)
new_mkVBalBranch1(zzz31, Branch(zzz330, zzz331, Neg(Zero), zzz333, zzz334), Branch(zzz3170, zzz3171, Pos(Succ(zzz317200)), zzz3173, zzz3174), h) → new_mkVBalBranch1(zzz31, Branch(zzz330, zzz331, Neg(Zero), zzz333, zzz334), zzz3173, h)
new_mkVBalBranch3MkVBalBranch235(zzz3170, zzz3171, Neg(Zero), zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, Zero, h) → new_mkVBalBranch3MkVBalBranch239(zzz3170, zzz3171, Zero, zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, h)
new_mkVBalBranch1(zzz31, Branch(zzz330, zzz331, Neg(Succ(zzz33200)), zzz333, zzz334), Branch(zzz3170, zzz3171, zzz3172, zzz3173, zzz3174), h) → new_mkVBalBranch3MkVBalBranch241(zzz3170, zzz3171, zzz3172, zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, new_primPlusNat2(Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat3(new_primPlusNat1(zzz33200), zzz33200)), zzz33200))), Succ(zzz33200)), h)
new_mkVBalBranch3MkVBalBranch235(zzz3170, zzz3171, Neg(Zero), zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, Succ(zzz4170), h) → new_mkVBalBranch1(zzz31, zzz334, Branch(zzz3170, zzz3171, Neg(Zero), zzz3173, zzz3174), h)
new_mkVBalBranch3MkVBalBranch244(zzz972, zzz973, zzz974, zzz975, zzz976, zzz977, zzz978, zzz979, zzz980, zzz981, zzz982, bc) → new_mkVBalBranch3MkVBalBranch128(zzz972, zzz973, zzz974, zzz975, zzz976, zzz977, zzz978, zzz979, zzz980, zzz981, zzz982, new_primPlusNat2(new_primPlusNat3(Succ(new_primPlusNat3(new_primPlusNat1(zzz974), zzz974)), Succ(zzz974)), Succ(zzz974)), bc)
new_mkVBalBranch3MkVBalBranch236(zzz958, zzz959, zzz960, zzz961, zzz962, zzz963, zzz964, zzz965, zzz966, zzz967, zzz968, Zero, Zero, ba) → new_mkVBalBranch3MkVBalBranch240(zzz958, zzz959, zzz960, zzz961, zzz962, zzz963, zzz964, zzz965, zzz966, zzz967, zzz968, ba)

The TRS R consists of the following rules:

new_primPlusNat1(Zero) → Zero
new_primPlusNat1(Succ(zzz62000)) → Succ(Succ(new_primPlusNat1(zzz62000)))
new_primPlusNat3(zzz90, Succ(zzz910)) → Succ(Succ(new_primPlusNat2(zzz90, zzz910)))
new_primPlusNat3(zzz90, Zero) → Succ(zzz90)
new_primPlusNat2(Succ(zzz900), Succ(zzz9100)) → Succ(Succ(new_primPlusNat2(zzz900, zzz9100)))
new_primPlusNat2(Succ(zzz900), Zero) → Succ(zzz900)
new_primPlusNat2(Zero, Succ(zzz9100)) → Succ(zzz9100)
new_primPlusNat2(Zero, Zero) → Zero

The set Q consists of the following terms:

new_primPlusNat2(Zero, Succ(x0))
new_primPlusNat3(x0, Succ(x1))
new_primPlusNat2(Succ(x0), Succ(x1))
new_primPlusNat3(x0, Zero)
new_primPlusNat1(Zero)
new_primPlusNat2(Zero, Zero)
new_primPlusNat1(Succ(x0))
new_primPlusNat2(Succ(x0), Zero)

We have to consider all minimal (P,Q,R)-chains.
The approximation of the Dependency Graph [15,17,22] contains 1 SCC with 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
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                    ↳ DependencyGraphProof
                                      ↳ QDP
                                        ↳ Rewriting
                                          ↳ QDP
                                            ↳ Rewriting
                                              ↳ QDP
                                                ↳ Rewriting
                                                  ↳ QDP
                                                    ↳ Rewriting
                                                      ↳ QDP
                                                        ↳ Rewriting
                                                          ↳ QDP
                                                            ↳ Rewriting
                                                              ↳ QDP
                                                                ↳ Rewriting
                                                                  ↳ QDP
                                                                    ↳ Rewriting
                                                                      ↳ QDP
                                                                        ↳ Rewriting
                                                                          ↳ QDP
                                                                            ↳ Rewriting
                                                                              ↳ QDP
                                                                                ↳ UsableRulesProof
                                                                                  ↳ QDP
                                                                                    ↳ QReductionProof
                                                                                      ↳ QDP
                                                                                        ↳ Rewriting
                                                                                          ↳ QDP
                                                                                            ↳ Rewriting
                                                                                              ↳ QDP
                                                                                                ↳ Rewriting
                                                                                                  ↳ QDP
                                                                                                    ↳ Rewriting
                                                                                                      ↳ QDP
                                                                                                        ↳ Rewriting
                                                                                                          ↳ QDP
                                                                                                            ↳ Rewriting
                                                                                                              ↳ QDP
                                                                                                                ↳ Rewriting
                                                                                                                  ↳ QDP
                                                                                                                    ↳ Rewriting
                                                                                                                      ↳ QDP
                                                                                                                        ↳ Rewriting
                                                                                                                          ↳ QDP
                                                                                                                            ↳ Rewriting
                                                                                                                              ↳ QDP
                                                                                                                                ↳ UsableRulesProof
                                                                                                                                  ↳ QDP
                                                                                                                                    ↳ QReductionProof
                                                                                                                                      ↳ QDP
                                                                                                                                        ↳ Rewriting
                                                                                                                                          ↳ QDP
                                                                                                                                            ↳ Rewriting
                                                                                                                                              ↳ QDP
                                                                                                                                                ↳ Rewriting
                                                                                                                                                  ↳ QDP
                                                                                                                                                    ↳ DependencyGraphProof
                                                                                                                                                      ↳ QDP
                                                                                                                                                        ↳ Rewriting
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP

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

new_mkVBalBranch3MkVBalBranch129(zzz1851, zzz1852, zzz1853, zzz1854, zzz1855, zzz1856, zzz1857, zzz1858, zzz1859, zzz1860, zzz1861, Zero, Succ(zzz18630), bd) → new_mkVBalBranch1(zzz1861, zzz1860, Branch(zzz1851, zzz1852, Neg(Succ(zzz1853)), zzz1854, zzz1855), bd)
new_mkVBalBranch3MkVBalBranch128(zzz972, zzz973, zzz974, zzz975, zzz976, zzz977, zzz978, zzz979, zzz980, zzz981, zzz982, Succ(zzz10190), bc) → new_mkVBalBranch3MkVBalBranch129(zzz972, zzz973, zzz974, zzz975, zzz976, zzz977, zzz978, zzz979, zzz980, zzz981, zzz982, Succ(zzz979), Succ(zzz10190), bc)
new_mkVBalBranch3MkVBalBranch241(zzz3170, zzz3171, Pos(zzz31720), zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, Succ(zzz4190), h) → new_mkVBalBranch1(zzz31, Branch(zzz330, zzz331, Neg(Succ(zzz33200)), zzz333, zzz334), zzz3173, h)
new_mkVBalBranch3MkVBalBranch127(zzz3170, zzz3171, zzz317200, zzz3173, zzz3174, zzz330, zzz331, zzz333, zzz334, zzz31, Succ(zzz5500), h) → new_mkVBalBranch1(zzz31, zzz334, Branch(zzz3170, zzz3171, Neg(Succ(zzz317200)), zzz3173, zzz3174), h)
new_mkVBalBranch3MkVBalBranch242(zzz972, zzz973, zzz974, zzz975, zzz976, zzz977, zzz978, zzz979, zzz980, zzz981, zzz982, Succ(zzz9830), Zero, bc) → new_mkVBalBranch3MkVBalBranch128(zzz972, zzz973, zzz974, zzz975, zzz976, zzz977, zzz978, zzz979, zzz980, zzz981, zzz982, new_primPlusNat2(Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat3(new_primPlusNat1(zzz974), zzz974)), zzz974))), Succ(zzz974)), bc)
new_mkVBalBranch3MkVBalBranch129(zzz1851, zzz1852, zzz1853, zzz1854, zzz1855, zzz1856, zzz1857, zzz1858, zzz1859, zzz1860, zzz1861, Succ(zzz18620), Succ(zzz18630), bd) → new_mkVBalBranch3MkVBalBranch129(zzz1851, zzz1852, zzz1853, zzz1854, zzz1855, zzz1856, zzz1857, zzz1858, zzz1859, zzz1860, zzz1861, zzz18620, zzz18630, bd)
new_mkVBalBranch3MkVBalBranch124(zzz958, zzz959, zzz960, zzz961, zzz962, zzz963, zzz964, zzz965, zzz966, zzz967, zzz968, Zero, ba) → new_mkVBalBranch3MkVBalBranch125(zzz958, zzz959, zzz960, zzz961, zzz962, zzz963, zzz964, zzz965, zzz966, zzz967, zzz968, Zero, Succ(zzz965), ba)
new_mkVBalBranch3MkVBalBranch242(zzz972, zzz973, zzz974, zzz975, zzz976, zzz977, zzz978, zzz979, zzz980, zzz981, zzz982, Succ(zzz9830), Succ(zzz9840), bc) → new_mkVBalBranch3MkVBalBranch242(zzz972, zzz973, zzz974, zzz975, zzz976, zzz977, zzz978, zzz979, zzz980, zzz981, zzz982, zzz9830, zzz9840, bc)
new_mkVBalBranch3MkVBalBranch235(zzz3170, zzz3171, Pos(Succ(zzz317200)), zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, Succ(zzz4170), h) → new_mkVBalBranch3MkVBalBranch236(zzz3170, zzz3171, zzz317200, zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, zzz4170, zzz317200, h)
new_mkVBalBranch1(zzz31, Branch(zzz330, zzz331, Pos(Succ(zzz33200)), zzz333, zzz334), Branch(zzz3170, zzz3171, zzz3172, zzz3173, zzz3174), h) → new_mkVBalBranch3MkVBalBranch235(zzz3170, zzz3171, zzz3172, zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat2(Succ(new_primPlusNat3(new_primPlusNat1(zzz33200), zzz33200)), zzz33200)), zzz33200))), h)
new_mkVBalBranch3MkVBalBranch236(zzz958, zzz959, zzz960, zzz961, zzz962, zzz963, zzz964, zzz965, zzz966, zzz967, zzz968, Succ(zzz9690), Succ(zzz9700), ba) → new_mkVBalBranch3MkVBalBranch236(zzz958, zzz959, zzz960, zzz961, zzz962, zzz963, zzz964, zzz965, zzz966, zzz967, zzz968, zzz9690, zzz9700, ba)
new_mkVBalBranch3MkVBalBranch241(zzz3170, zzz3171, Neg(Succ(zzz317200)), zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, Succ(zzz4190), h) → new_mkVBalBranch3MkVBalBranch242(zzz3170, zzz3171, zzz317200, zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, zzz317200, zzz4190, h)
new_mkVBalBranch3MkVBalBranch241(zzz3170, zzz3171, Neg(Succ(zzz317200)), zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, Zero, h) → new_mkVBalBranch3MkVBalBranch242(zzz3170, zzz3171, zzz317200, zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, Succ(zzz317200), Zero, h)
new_mkVBalBranch1(zzz31, Branch(zzz330, zzz331, Pos(Zero), zzz333, zzz334), Branch(zzz3170, zzz3171, Pos(Succ(zzz317200)), zzz3173, zzz3174), h) → new_mkVBalBranch1(zzz31, Branch(zzz330, zzz331, Pos(Zero), zzz333, zzz334), zzz3173, h)
new_mkVBalBranch3MkVBalBranch243(zzz3170, zzz3171, zzz31720, zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, h) → new_mkVBalBranch1(zzz31, Branch(zzz330, zzz331, Neg(Succ(zzz33200)), zzz333, zzz334), zzz3173, h)
new_mkVBalBranch3MkVBalBranch235(zzz3170, zzz3171, Neg(Succ(zzz317200)), zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, Succ(zzz4170), h) → new_mkVBalBranch3MkVBalBranch123(zzz3170, zzz3171, zzz317200, zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, new_primPlusNat2(Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat3(new_primPlusNat1(zzz317200), zzz317200)), zzz317200))), Succ(zzz317200)), h)
new_mkVBalBranch3MkVBalBranch237(zzz3170, zzz3171, zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, h) → new_mkVBalBranch1(zzz31, zzz334, Branch(zzz3170, zzz3171, Pos(Zero), zzz3173, zzz3174), h)
new_mkVBalBranch3MkVBalBranch235(zzz3170, zzz3171, Pos(Zero), zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, Succ(zzz4170), h) → new_mkVBalBranch3MkVBalBranch237(zzz3170, zzz3171, zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, h)
new_mkVBalBranch3MkVBalBranch236(zzz958, zzz959, zzz960, zzz961, zzz962, zzz963, zzz964, zzz965, zzz966, zzz967, zzz968, Succ(zzz9690), Zero, ba) → new_mkVBalBranch3MkVBalBranch124(zzz958, zzz959, zzz960, zzz961, zzz962, zzz963, zzz964, zzz965, zzz966, zzz967, zzz968, new_primPlusNat2(Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat3(new_primPlusNat1(zzz960), zzz960)), zzz960))), Succ(zzz960)), ba)
new_mkVBalBranch3MkVBalBranch236(zzz958, zzz959, zzz960, zzz961, zzz962, zzz963, zzz964, zzz965, zzz966, zzz967, zzz968, Zero, Succ(zzz9700), ba) → new_mkVBalBranch1(zzz968, Branch(zzz963, zzz964, Pos(Succ(zzz965)), zzz966, zzz967), zzz961, ba)
new_mkVBalBranch3MkVBalBranch125(zzz1337, zzz1338, zzz1339, zzz1340, zzz1341, zzz1342, zzz1343, zzz1344, zzz1345, zzz1346, zzz1347, Succ(zzz13480), Succ(zzz13490), bb) → new_mkVBalBranch3MkVBalBranch125(zzz1337, zzz1338, zzz1339, zzz1340, zzz1341, zzz1342, zzz1343, zzz1344, zzz1345, zzz1346, zzz1347, zzz13480, zzz13490, bb)
new_mkVBalBranch3MkVBalBranch123(zzz3170, zzz3171, zzz317200, zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, Succ(zzz5620), h) → new_mkVBalBranch1(zzz31, zzz334, Branch(zzz3170, zzz3171, Neg(Succ(zzz317200)), zzz3173, zzz3174), h)
new_mkVBalBranch3MkVBalBranch125(zzz1337, zzz1338, zzz1339, zzz1340, zzz1341, zzz1342, zzz1343, zzz1344, zzz1345, zzz1346, zzz1347, Zero, Succ(zzz13490), bb) → new_mkVBalBranch1(zzz1347, zzz1346, Branch(zzz1337, zzz1338, Pos(Succ(zzz1339)), zzz1340, zzz1341), bb)
new_mkVBalBranch3MkVBalBranch242(zzz972, zzz973, zzz974, zzz975, zzz976, zzz977, zzz978, zzz979, zzz980, zzz981, zzz982, Zero, Succ(zzz9840), bc) → new_mkVBalBranch1(zzz982, Branch(zzz977, zzz978, Neg(Succ(zzz979)), zzz980, zzz981), zzz975, bc)
new_mkVBalBranch1(zzz31, Branch(zzz330, zzz331, Neg(Zero), zzz333, zzz334), Branch(zzz3170, zzz3171, Neg(Succ(zzz317200)), zzz3173, zzz3174), h) → new_mkVBalBranch3MkVBalBranch127(zzz3170, zzz3171, zzz317200, zzz3173, zzz3174, zzz330, zzz331, zzz333, zzz334, zzz31, new_primPlusNat2(new_primPlusNat3(Succ(new_primPlusNat3(new_primPlusNat1(zzz317200), zzz317200)), Succ(zzz317200)), Succ(zzz317200)), h)
new_mkVBalBranch3MkVBalBranch240(zzz958, zzz959, zzz960, zzz961, zzz962, zzz963, zzz964, zzz965, zzz966, zzz967, zzz968, ba) → new_mkVBalBranch3MkVBalBranch124(zzz958, zzz959, zzz960, zzz961, zzz962, zzz963, zzz964, zzz965, zzz966, zzz967, zzz968, new_primPlusNat2(new_primPlusNat3(Succ(new_primPlusNat3(new_primPlusNat1(zzz960), zzz960)), Succ(zzz960)), Succ(zzz960)), ba)
new_mkVBalBranch3MkVBalBranch241(zzz3170, zzz3171, Pos(Succ(zzz317200)), zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, Zero, h) → new_mkVBalBranch3MkVBalBranch243(zzz3170, zzz3171, Succ(zzz317200), zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, h)
new_mkVBalBranch1(zzz31, Branch(zzz330, zzz331, Pos(Zero), zzz333, zzz334), Branch(zzz3170, zzz3171, Neg(Succ(zzz317200)), zzz3173, zzz3174), h) → new_mkVBalBranch3MkVBalBranch126(zzz3170, zzz3171, zzz317200, zzz3173, zzz3174, zzz330, zzz331, zzz333, zzz334, zzz31, new_primPlusNat2(new_primPlusNat3(Succ(new_primPlusNat3(new_primPlusNat1(zzz317200), zzz317200)), Succ(zzz317200)), Succ(zzz317200)), h)
new_mkVBalBranch3MkVBalBranch126(zzz3170, zzz3171, zzz317200, zzz3173, zzz3174, zzz330, zzz331, zzz333, zzz334, zzz31, Succ(zzz5350), h) → new_mkVBalBranch1(zzz31, zzz334, Branch(zzz3170, zzz3171, Neg(Succ(zzz317200)), zzz3173, zzz3174), h)
new_mkVBalBranch3MkVBalBranch241(zzz3170, zzz3171, Neg(Zero), zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, Succ(zzz4190), h) → new_mkVBalBranch1(zzz31, Branch(zzz330, zzz331, Neg(Succ(zzz33200)), zzz333, zzz334), zzz3173, h)
new_mkVBalBranch3MkVBalBranch123(zzz3170, zzz3171, zzz317200, zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, Zero, h) → new_mkVBalBranch3MkVBalBranch130(zzz3170, zzz3171, zzz317200, zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, h)
new_mkVBalBranch3MkVBalBranch124(zzz958, zzz959, zzz960, zzz961, zzz962, zzz963, zzz964, zzz965, zzz966, zzz967, zzz968, Succ(zzz10180), ba) → new_mkVBalBranch3MkVBalBranch125(zzz958, zzz959, zzz960, zzz961, zzz962, zzz963, zzz964, zzz965, zzz966, zzz967, zzz968, Succ(zzz10180), Succ(zzz965), ba)
new_mkVBalBranch3MkVBalBranch242(zzz972, zzz973, zzz974, zzz975, zzz976, zzz977, zzz978, zzz979, zzz980, zzz981, zzz982, Zero, Zero, bc) → new_mkVBalBranch3MkVBalBranch244(zzz972, zzz973, zzz974, zzz975, zzz976, zzz977, zzz978, zzz979, zzz980, zzz981, zzz982, bc)
new_mkVBalBranch3MkVBalBranch130(zzz3170, zzz3171, zzz317200, zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, h) → new_mkVBalBranch1(zzz31, zzz334, Branch(zzz3170, zzz3171, Neg(Succ(zzz317200)), zzz3173, zzz3174), h)
new_mkVBalBranch1(zzz31, Branch(zzz330, zzz331, Neg(Zero), zzz333, zzz334), Branch(zzz3170, zzz3171, Pos(Succ(zzz317200)), zzz3173, zzz3174), h) → new_mkVBalBranch1(zzz31, Branch(zzz330, zzz331, Neg(Zero), zzz333, zzz334), zzz3173, h)
new_mkVBalBranch3MkVBalBranch235(zzz3170, zzz3171, Neg(Zero), zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, Succ(zzz4170), h) → new_mkVBalBranch1(zzz31, zzz334, Branch(zzz3170, zzz3171, Neg(Zero), zzz3173, zzz3174), h)
new_mkVBalBranch1(zzz31, Branch(zzz330, zzz331, Neg(Succ(zzz33200)), zzz333, zzz334), Branch(zzz3170, zzz3171, zzz3172, zzz3173, zzz3174), h) → new_mkVBalBranch3MkVBalBranch241(zzz3170, zzz3171, zzz3172, zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, new_primPlusNat2(Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat3(new_primPlusNat1(zzz33200), zzz33200)), zzz33200))), Succ(zzz33200)), h)
new_mkVBalBranch3MkVBalBranch244(zzz972, zzz973, zzz974, zzz975, zzz976, zzz977, zzz978, zzz979, zzz980, zzz981, zzz982, bc) → new_mkVBalBranch3MkVBalBranch128(zzz972, zzz973, zzz974, zzz975, zzz976, zzz977, zzz978, zzz979, zzz980, zzz981, zzz982, new_primPlusNat2(new_primPlusNat3(Succ(new_primPlusNat3(new_primPlusNat1(zzz974), zzz974)), Succ(zzz974)), Succ(zzz974)), bc)
new_mkVBalBranch3MkVBalBranch236(zzz958, zzz959, zzz960, zzz961, zzz962, zzz963, zzz964, zzz965, zzz966, zzz967, zzz968, Zero, Zero, ba) → new_mkVBalBranch3MkVBalBranch240(zzz958, zzz959, zzz960, zzz961, zzz962, zzz963, zzz964, zzz965, zzz966, zzz967, zzz968, ba)

The TRS R consists of the following rules:

new_primPlusNat1(Zero) → Zero
new_primPlusNat1(Succ(zzz62000)) → Succ(Succ(new_primPlusNat1(zzz62000)))
new_primPlusNat3(zzz90, Succ(zzz910)) → Succ(Succ(new_primPlusNat2(zzz90, zzz910)))
new_primPlusNat3(zzz90, Zero) → Succ(zzz90)
new_primPlusNat2(Succ(zzz900), Succ(zzz9100)) → Succ(Succ(new_primPlusNat2(zzz900, zzz9100)))
new_primPlusNat2(Succ(zzz900), Zero) → Succ(zzz900)
new_primPlusNat2(Zero, Succ(zzz9100)) → Succ(zzz9100)
new_primPlusNat2(Zero, Zero) → Zero

The set Q consists of the following terms:

new_primPlusNat2(Zero, Succ(x0))
new_primPlusNat3(x0, Succ(x1))
new_primPlusNat2(Succ(x0), Succ(x1))
new_primPlusNat3(x0, Zero)
new_primPlusNat1(Zero)
new_primPlusNat2(Zero, Zero)
new_primPlusNat1(Succ(x0))
new_primPlusNat2(Succ(x0), Zero)

We have to consider all minimal (P,Q,R)-chains.
By rewriting [15] the rule new_mkVBalBranch1(zzz31, Branch(zzz330, zzz331, Neg(Zero), zzz333, zzz334), Branch(zzz3170, zzz3171, Neg(Succ(zzz317200)), zzz3173, zzz3174), h) → new_mkVBalBranch3MkVBalBranch127(zzz3170, zzz3171, zzz317200, zzz3173, zzz3174, zzz330, zzz331, zzz333, zzz334, zzz31, new_primPlusNat2(new_primPlusNat3(Succ(new_primPlusNat3(new_primPlusNat1(zzz317200), zzz317200)), Succ(zzz317200)), Succ(zzz317200)), h) at position [10,0] we obtained the following new rules:

new_mkVBalBranch1(zzz31, Branch(zzz330, zzz331, Neg(Zero), zzz333, zzz334), Branch(zzz3170, zzz3171, Neg(Succ(zzz317200)), zzz3173, zzz3174), h) → new_mkVBalBranch3MkVBalBranch127(zzz3170, zzz3171, zzz317200, zzz3173, zzz3174, zzz330, zzz331, zzz333, zzz334, zzz31, new_primPlusNat2(Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat3(new_primPlusNat1(zzz317200), zzz317200)), zzz317200))), Succ(zzz317200)), 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
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                    ↳ DependencyGraphProof
                                      ↳ QDP
                                        ↳ Rewriting
                                          ↳ QDP
                                            ↳ Rewriting
                                              ↳ QDP
                                                ↳ Rewriting
                                                  ↳ QDP
                                                    ↳ Rewriting
                                                      ↳ QDP
                                                        ↳ Rewriting
                                                          ↳ QDP
                                                            ↳ Rewriting
                                                              ↳ QDP
                                                                ↳ Rewriting
                                                                  ↳ QDP
                                                                    ↳ Rewriting
                                                                      ↳ QDP
                                                                        ↳ Rewriting
                                                                          ↳ QDP
                                                                            ↳ Rewriting
                                                                              ↳ QDP
                                                                                ↳ UsableRulesProof
                                                                                  ↳ QDP
                                                                                    ↳ QReductionProof
                                                                                      ↳ QDP
                                                                                        ↳ Rewriting
                                                                                          ↳ QDP
                                                                                            ↳ Rewriting
                                                                                              ↳ QDP
                                                                                                ↳ Rewriting
                                                                                                  ↳ QDP
                                                                                                    ↳ Rewriting
                                                                                                      ↳ QDP
                                                                                                        ↳ Rewriting
                                                                                                          ↳ QDP
                                                                                                            ↳ Rewriting
                                                                                                              ↳ QDP
                                                                                                                ↳ Rewriting
                                                                                                                  ↳ QDP
                                                                                                                    ↳ Rewriting
                                                                                                                      ↳ QDP
                                                                                                                        ↳ Rewriting
                                                                                                                          ↳ QDP
                                                                                                                            ↳ Rewriting
                                                                                                                              ↳ QDP
                                                                                                                                ↳ UsableRulesProof
                                                                                                                                  ↳ QDP
                                                                                                                                    ↳ QReductionProof
                                                                                                                                      ↳ QDP
                                                                                                                                        ↳ Rewriting
                                                                                                                                          ↳ QDP
                                                                                                                                            ↳ Rewriting
                                                                                                                                              ↳ QDP
                                                                                                                                                ↳ Rewriting
                                                                                                                                                  ↳ QDP
                                                                                                                                                    ↳ DependencyGraphProof
                                                                                                                                                      ↳ QDP
                                                                                                                                                        ↳ Rewriting
                                                                                                                                                          ↳ QDP
                                                                                                                                                            ↳ Rewriting
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP

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

new_mkVBalBranch3MkVBalBranch129(zzz1851, zzz1852, zzz1853, zzz1854, zzz1855, zzz1856, zzz1857, zzz1858, zzz1859, zzz1860, zzz1861, Zero, Succ(zzz18630), bd) → new_mkVBalBranch1(zzz1861, zzz1860, Branch(zzz1851, zzz1852, Neg(Succ(zzz1853)), zzz1854, zzz1855), bd)
new_mkVBalBranch3MkVBalBranch127(zzz3170, zzz3171, zzz317200, zzz3173, zzz3174, zzz330, zzz331, zzz333, zzz334, zzz31, Succ(zzz5500), h) → new_mkVBalBranch1(zzz31, zzz334, Branch(zzz3170, zzz3171, Neg(Succ(zzz317200)), zzz3173, zzz3174), h)
new_mkVBalBranch3MkVBalBranch241(zzz3170, zzz3171, Pos(zzz31720), zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, Succ(zzz4190), h) → new_mkVBalBranch1(zzz31, Branch(zzz330, zzz331, Neg(Succ(zzz33200)), zzz333, zzz334), zzz3173, h)
new_mkVBalBranch3MkVBalBranch128(zzz972, zzz973, zzz974, zzz975, zzz976, zzz977, zzz978, zzz979, zzz980, zzz981, zzz982, Succ(zzz10190), bc) → new_mkVBalBranch3MkVBalBranch129(zzz972, zzz973, zzz974, zzz975, zzz976, zzz977, zzz978, zzz979, zzz980, zzz981, zzz982, Succ(zzz979), Succ(zzz10190), bc)
new_mkVBalBranch3MkVBalBranch242(zzz972, zzz973, zzz974, zzz975, zzz976, zzz977, zzz978, zzz979, zzz980, zzz981, zzz982, Succ(zzz9830), Zero, bc) → new_mkVBalBranch3MkVBalBranch128(zzz972, zzz973, zzz974, zzz975, zzz976, zzz977, zzz978, zzz979, zzz980, zzz981, zzz982, new_primPlusNat2(Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat3(new_primPlusNat1(zzz974), zzz974)), zzz974))), Succ(zzz974)), bc)
new_mkVBalBranch3MkVBalBranch129(zzz1851, zzz1852, zzz1853, zzz1854, zzz1855, zzz1856, zzz1857, zzz1858, zzz1859, zzz1860, zzz1861, Succ(zzz18620), Succ(zzz18630), bd) → new_mkVBalBranch3MkVBalBranch129(zzz1851, zzz1852, zzz1853, zzz1854, zzz1855, zzz1856, zzz1857, zzz1858, zzz1859, zzz1860, zzz1861, zzz18620, zzz18630, bd)
new_mkVBalBranch3MkVBalBranch124(zzz958, zzz959, zzz960, zzz961, zzz962, zzz963, zzz964, zzz965, zzz966, zzz967, zzz968, Zero, ba) → new_mkVBalBranch3MkVBalBranch125(zzz958, zzz959, zzz960, zzz961, zzz962, zzz963, zzz964, zzz965, zzz966, zzz967, zzz968, Zero, Succ(zzz965), ba)
new_mkVBalBranch3MkVBalBranch235(zzz3170, zzz3171, Pos(Succ(zzz317200)), zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, Succ(zzz4170), h) → new_mkVBalBranch3MkVBalBranch236(zzz3170, zzz3171, zzz317200, zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, zzz4170, zzz317200, h)
new_mkVBalBranch3MkVBalBranch242(zzz972, zzz973, zzz974, zzz975, zzz976, zzz977, zzz978, zzz979, zzz980, zzz981, zzz982, Succ(zzz9830), Succ(zzz9840), bc) → new_mkVBalBranch3MkVBalBranch242(zzz972, zzz973, zzz974, zzz975, zzz976, zzz977, zzz978, zzz979, zzz980, zzz981, zzz982, zzz9830, zzz9840, bc)
new_mkVBalBranch1(zzz31, Branch(zzz330, zzz331, Pos(Succ(zzz33200)), zzz333, zzz334), Branch(zzz3170, zzz3171, zzz3172, zzz3173, zzz3174), h) → new_mkVBalBranch3MkVBalBranch235(zzz3170, zzz3171, zzz3172, zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat2(Succ(new_primPlusNat3(new_primPlusNat1(zzz33200), zzz33200)), zzz33200)), zzz33200))), h)
new_mkVBalBranch3MkVBalBranch236(zzz958, zzz959, zzz960, zzz961, zzz962, zzz963, zzz964, zzz965, zzz966, zzz967, zzz968, Succ(zzz9690), Succ(zzz9700), ba) → new_mkVBalBranch3MkVBalBranch236(zzz958, zzz959, zzz960, zzz961, zzz962, zzz963, zzz964, zzz965, zzz966, zzz967, zzz968, zzz9690, zzz9700, ba)
new_mkVBalBranch3MkVBalBranch241(zzz3170, zzz3171, Neg(Succ(zzz317200)), zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, Succ(zzz4190), h) → new_mkVBalBranch3MkVBalBranch242(zzz3170, zzz3171, zzz317200, zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, zzz317200, zzz4190, h)
new_mkVBalBranch3MkVBalBranch241(zzz3170, zzz3171, Neg(Succ(zzz317200)), zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, Zero, h) → new_mkVBalBranch3MkVBalBranch242(zzz3170, zzz3171, zzz317200, zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, Succ(zzz317200), Zero, h)
new_mkVBalBranch1(zzz31, Branch(zzz330, zzz331, Pos(Zero), zzz333, zzz334), Branch(zzz3170, zzz3171, Pos(Succ(zzz317200)), zzz3173, zzz3174), h) → new_mkVBalBranch1(zzz31, Branch(zzz330, zzz331, Pos(Zero), zzz333, zzz334), zzz3173, h)
new_mkVBalBranch3MkVBalBranch237(zzz3170, zzz3171, zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, h) → new_mkVBalBranch1(zzz31, zzz334, Branch(zzz3170, zzz3171, Pos(Zero), zzz3173, zzz3174), h)
new_mkVBalBranch3MkVBalBranch235(zzz3170, zzz3171, Neg(Succ(zzz317200)), zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, Succ(zzz4170), h) → new_mkVBalBranch3MkVBalBranch123(zzz3170, zzz3171, zzz317200, zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, new_primPlusNat2(Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat3(new_primPlusNat1(zzz317200), zzz317200)), zzz317200))), Succ(zzz317200)), h)
new_mkVBalBranch3MkVBalBranch243(zzz3170, zzz3171, zzz31720, zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, h) → new_mkVBalBranch1(zzz31, Branch(zzz330, zzz331, Neg(Succ(zzz33200)), zzz333, zzz334), zzz3173, h)
new_mkVBalBranch3MkVBalBranch235(zzz3170, zzz3171, Pos(Zero), zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, Succ(zzz4170), h) → new_mkVBalBranch3MkVBalBranch237(zzz3170, zzz3171, zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, h)
new_mkVBalBranch3MkVBalBranch236(zzz958, zzz959, zzz960, zzz961, zzz962, zzz963, zzz964, zzz965, zzz966, zzz967, zzz968, Succ(zzz9690), Zero, ba) → new_mkVBalBranch3MkVBalBranch124(zzz958, zzz959, zzz960, zzz961, zzz962, zzz963, zzz964, zzz965, zzz966, zzz967, zzz968, new_primPlusNat2(Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat3(new_primPlusNat1(zzz960), zzz960)), zzz960))), Succ(zzz960)), ba)
new_mkVBalBranch3MkVBalBranch236(zzz958, zzz959, zzz960, zzz961, zzz962, zzz963, zzz964, zzz965, zzz966, zzz967, zzz968, Zero, Succ(zzz9700), ba) → new_mkVBalBranch1(zzz968, Branch(zzz963, zzz964, Pos(Succ(zzz965)), zzz966, zzz967), zzz961, ba)
new_mkVBalBranch3MkVBalBranch125(zzz1337, zzz1338, zzz1339, zzz1340, zzz1341, zzz1342, zzz1343, zzz1344, zzz1345, zzz1346, zzz1347, Succ(zzz13480), Succ(zzz13490), bb) → new_mkVBalBranch3MkVBalBranch125(zzz1337, zzz1338, zzz1339, zzz1340, zzz1341, zzz1342, zzz1343, zzz1344, zzz1345, zzz1346, zzz1347, zzz13480, zzz13490, bb)
new_mkVBalBranch3MkVBalBranch123(zzz3170, zzz3171, zzz317200, zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, Succ(zzz5620), h) → new_mkVBalBranch1(zzz31, zzz334, Branch(zzz3170, zzz3171, Neg(Succ(zzz317200)), zzz3173, zzz3174), h)
new_mkVBalBranch3MkVBalBranch125(zzz1337, zzz1338, zzz1339, zzz1340, zzz1341, zzz1342, zzz1343, zzz1344, zzz1345, zzz1346, zzz1347, Zero, Succ(zzz13490), bb) → new_mkVBalBranch1(zzz1347, zzz1346, Branch(zzz1337, zzz1338, Pos(Succ(zzz1339)), zzz1340, zzz1341), bb)
new_mkVBalBranch3MkVBalBranch242(zzz972, zzz973, zzz974, zzz975, zzz976, zzz977, zzz978, zzz979, zzz980, zzz981, zzz982, Zero, Succ(zzz9840), bc) → new_mkVBalBranch1(zzz982, Branch(zzz977, zzz978, Neg(Succ(zzz979)), zzz980, zzz981), zzz975, bc)
new_mkVBalBranch3MkVBalBranch240(zzz958, zzz959, zzz960, zzz961, zzz962, zzz963, zzz964, zzz965, zzz966, zzz967, zzz968, ba) → new_mkVBalBranch3MkVBalBranch124(zzz958, zzz959, zzz960, zzz961, zzz962, zzz963, zzz964, zzz965, zzz966, zzz967, zzz968, new_primPlusNat2(new_primPlusNat3(Succ(new_primPlusNat3(new_primPlusNat1(zzz960), zzz960)), Succ(zzz960)), Succ(zzz960)), ba)
new_mkVBalBranch3MkVBalBranch241(zzz3170, zzz3171, Pos(Succ(zzz317200)), zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, Zero, h) → new_mkVBalBranch3MkVBalBranch243(zzz3170, zzz3171, Succ(zzz317200), zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, h)
new_mkVBalBranch3MkVBalBranch126(zzz3170, zzz3171, zzz317200, zzz3173, zzz3174, zzz330, zzz331, zzz333, zzz334, zzz31, Succ(zzz5350), h) → new_mkVBalBranch1(zzz31, zzz334, Branch(zzz3170, zzz3171, Neg(Succ(zzz317200)), zzz3173, zzz3174), h)
new_mkVBalBranch1(zzz31, Branch(zzz330, zzz331, Pos(Zero), zzz333, zzz334), Branch(zzz3170, zzz3171, Neg(Succ(zzz317200)), zzz3173, zzz3174), h) → new_mkVBalBranch3MkVBalBranch126(zzz3170, zzz3171, zzz317200, zzz3173, zzz3174, zzz330, zzz331, zzz333, zzz334, zzz31, new_primPlusNat2(new_primPlusNat3(Succ(new_primPlusNat3(new_primPlusNat1(zzz317200), zzz317200)), Succ(zzz317200)), Succ(zzz317200)), h)
new_mkVBalBranch3MkVBalBranch123(zzz3170, zzz3171, zzz317200, zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, Zero, h) → new_mkVBalBranch3MkVBalBranch130(zzz3170, zzz3171, zzz317200, zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, h)
new_mkVBalBranch3MkVBalBranch241(zzz3170, zzz3171, Neg(Zero), zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, Succ(zzz4190), h) → new_mkVBalBranch1(zzz31, Branch(zzz330, zzz331, Neg(Succ(zzz33200)), zzz333, zzz334), zzz3173, h)
new_mkVBalBranch3MkVBalBranch124(zzz958, zzz959, zzz960, zzz961, zzz962, zzz963, zzz964, zzz965, zzz966, zzz967, zzz968, Succ(zzz10180), ba) → new_mkVBalBranch3MkVBalBranch125(zzz958, zzz959, zzz960, zzz961, zzz962, zzz963, zzz964, zzz965, zzz966, zzz967, zzz968, Succ(zzz10180), Succ(zzz965), ba)
new_mkVBalBranch1(zzz31, Branch(zzz330, zzz331, Neg(Zero), zzz333, zzz334), Branch(zzz3170, zzz3171, Neg(Succ(zzz317200)), zzz3173, zzz3174), h) → new_mkVBalBranch3MkVBalBranch127(zzz3170, zzz3171, zzz317200, zzz3173, zzz3174, zzz330, zzz331, zzz333, zzz334, zzz31, new_primPlusNat2(Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat3(new_primPlusNat1(zzz317200), zzz317200)), zzz317200))), Succ(zzz317200)), h)
new_mkVBalBranch3MkVBalBranch242(zzz972, zzz973, zzz974, zzz975, zzz976, zzz977, zzz978, zzz979, zzz980, zzz981, zzz982, Zero, Zero, bc) → new_mkVBalBranch3MkVBalBranch244(zzz972, zzz973, zzz974, zzz975, zzz976, zzz977, zzz978, zzz979, zzz980, zzz981, zzz982, bc)
new_mkVBalBranch3MkVBalBranch130(zzz3170, zzz3171, zzz317200, zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, h) → new_mkVBalBranch1(zzz31, zzz334, Branch(zzz3170, zzz3171, Neg(Succ(zzz317200)), zzz3173, zzz3174), h)
new_mkVBalBranch1(zzz31, Branch(zzz330, zzz331, Neg(Zero), zzz333, zzz334), Branch(zzz3170, zzz3171, Pos(Succ(zzz317200)), zzz3173, zzz3174), h) → new_mkVBalBranch1(zzz31, Branch(zzz330, zzz331, Neg(Zero), zzz333, zzz334), zzz3173, h)
new_mkVBalBranch1(zzz31, Branch(zzz330, zzz331, Neg(Succ(zzz33200)), zzz333, zzz334), Branch(zzz3170, zzz3171, zzz3172, zzz3173, zzz3174), h) → new_mkVBalBranch3MkVBalBranch241(zzz3170, zzz3171, zzz3172, zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, new_primPlusNat2(Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat3(new_primPlusNat1(zzz33200), zzz33200)), zzz33200))), Succ(zzz33200)), h)
new_mkVBalBranch3MkVBalBranch235(zzz3170, zzz3171, Neg(Zero), zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, Succ(zzz4170), h) → new_mkVBalBranch1(zzz31, zzz334, Branch(zzz3170, zzz3171, Neg(Zero), zzz3173, zzz3174), h)
new_mkVBalBranch3MkVBalBranch236(zzz958, zzz959, zzz960, zzz961, zzz962, zzz963, zzz964, zzz965, zzz966, zzz967, zzz968, Zero, Zero, ba) → new_mkVBalBranch3MkVBalBranch240(zzz958, zzz959, zzz960, zzz961, zzz962, zzz963, zzz964, zzz965, zzz966, zzz967, zzz968, ba)
new_mkVBalBranch3MkVBalBranch244(zzz972, zzz973, zzz974, zzz975, zzz976, zzz977, zzz978, zzz979, zzz980, zzz981, zzz982, bc) → new_mkVBalBranch3MkVBalBranch128(zzz972, zzz973, zzz974, zzz975, zzz976, zzz977, zzz978, zzz979, zzz980, zzz981, zzz982, new_primPlusNat2(new_primPlusNat3(Succ(new_primPlusNat3(new_primPlusNat1(zzz974), zzz974)), Succ(zzz974)), Succ(zzz974)), bc)

The TRS R consists of the following rules:

new_primPlusNat1(Zero) → Zero
new_primPlusNat1(Succ(zzz62000)) → Succ(Succ(new_primPlusNat1(zzz62000)))
new_primPlusNat3(zzz90, Succ(zzz910)) → Succ(Succ(new_primPlusNat2(zzz90, zzz910)))
new_primPlusNat3(zzz90, Zero) → Succ(zzz90)
new_primPlusNat2(Succ(zzz900), Succ(zzz9100)) → Succ(Succ(new_primPlusNat2(zzz900, zzz9100)))
new_primPlusNat2(Succ(zzz900), Zero) → Succ(zzz900)
new_primPlusNat2(Zero, Succ(zzz9100)) → Succ(zzz9100)
new_primPlusNat2(Zero, Zero) → Zero

The set Q consists of the following terms:

new_primPlusNat2(Zero, Succ(x0))
new_primPlusNat3(x0, Succ(x1))
new_primPlusNat2(Succ(x0), Succ(x1))
new_primPlusNat3(x0, Zero)
new_primPlusNat1(Zero)
new_primPlusNat2(Zero, Zero)
new_primPlusNat1(Succ(x0))
new_primPlusNat2(Succ(x0), Zero)

We have to consider all minimal (P,Q,R)-chains.
By rewriting [15] the rule new_mkVBalBranch1(zzz31, Branch(zzz330, zzz331, Neg(Succ(zzz33200)), zzz333, zzz334), Branch(zzz3170, zzz3171, zzz3172, zzz3173, zzz3174), h) → new_mkVBalBranch3MkVBalBranch241(zzz3170, zzz3171, zzz3172, zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, new_primPlusNat2(Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat3(new_primPlusNat1(zzz33200), zzz33200)), zzz33200))), Succ(zzz33200)), h) at position [11] we obtained the following new rules:

new_mkVBalBranch1(zzz31, Branch(zzz330, zzz331, Neg(Succ(zzz33200)), zzz333, zzz334), Branch(zzz3170, zzz3171, zzz3172, zzz3173, zzz3174), h) → new_mkVBalBranch3MkVBalBranch241(zzz3170, zzz3171, zzz3172, zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat2(Succ(new_primPlusNat3(new_primPlusNat1(zzz33200), zzz33200)), zzz33200)), zzz33200))), 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
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                    ↳ DependencyGraphProof
                                      ↳ QDP
                                        ↳ Rewriting
                                          ↳ QDP
                                            ↳ Rewriting
                                              ↳ QDP
                                                ↳ Rewriting
                                                  ↳ QDP
                                                    ↳ Rewriting
                                                      ↳ QDP
                                                        ↳ Rewriting
                                                          ↳ QDP
                                                            ↳ Rewriting
                                                              ↳ QDP
                                                                ↳ Rewriting
                                                                  ↳ QDP
                                                                    ↳ Rewriting
                                                                      ↳ QDP
                                                                        ↳ Rewriting
                                                                          ↳ QDP
                                                                            ↳ Rewriting
                                                                              ↳ QDP
                                                                                ↳ UsableRulesProof
                                                                                  ↳ QDP
                                                                                    ↳ QReductionProof
                                                                                      ↳ QDP
                                                                                        ↳ Rewriting
                                                                                          ↳ QDP
                                                                                            ↳ Rewriting
                                                                                              ↳ QDP
                                                                                                ↳ Rewriting
                                                                                                  ↳ QDP
                                                                                                    ↳ Rewriting
                                                                                                      ↳ QDP
                                                                                                        ↳ Rewriting
                                                                                                          ↳ QDP
                                                                                                            ↳ Rewriting
                                                                                                              ↳ QDP
                                                                                                                ↳ Rewriting
                                                                                                                  ↳ QDP
                                                                                                                    ↳ Rewriting
                                                                                                                      ↳ QDP
                                                                                                                        ↳ Rewriting
                                                                                                                          ↳ QDP
                                                                                                                            ↳ Rewriting
                                                                                                                              ↳ QDP
                                                                                                                                ↳ UsableRulesProof
                                                                                                                                  ↳ QDP
                                                                                                                                    ↳ QReductionProof
                                                                                                                                      ↳ QDP
                                                                                                                                        ↳ Rewriting
                                                                                                                                          ↳ QDP
                                                                                                                                            ↳ Rewriting
                                                                                                                                              ↳ QDP
                                                                                                                                                ↳ Rewriting
                                                                                                                                                  ↳ QDP
                                                                                                                                                    ↳ DependencyGraphProof
                                                                                                                                                      ↳ QDP
                                                                                                                                                        ↳ Rewriting
                                                                                                                                                          ↳ QDP
                                                                                                                                                            ↳ Rewriting
                                                                                                                                                              ↳ QDP
                                                                                                                                                                ↳ DependencyGraphProof
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP

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

new_mkVBalBranch3MkVBalBranch129(zzz1851, zzz1852, zzz1853, zzz1854, zzz1855, zzz1856, zzz1857, zzz1858, zzz1859, zzz1860, zzz1861, Zero, Succ(zzz18630), bd) → new_mkVBalBranch1(zzz1861, zzz1860, Branch(zzz1851, zzz1852, Neg(Succ(zzz1853)), zzz1854, zzz1855), bd)
new_mkVBalBranch3MkVBalBranch128(zzz972, zzz973, zzz974, zzz975, zzz976, zzz977, zzz978, zzz979, zzz980, zzz981, zzz982, Succ(zzz10190), bc) → new_mkVBalBranch3MkVBalBranch129(zzz972, zzz973, zzz974, zzz975, zzz976, zzz977, zzz978, zzz979, zzz980, zzz981, zzz982, Succ(zzz979), Succ(zzz10190), bc)
new_mkVBalBranch3MkVBalBranch241(zzz3170, zzz3171, Pos(zzz31720), zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, Succ(zzz4190), h) → new_mkVBalBranch1(zzz31, Branch(zzz330, zzz331, Neg(Succ(zzz33200)), zzz333, zzz334), zzz3173, h)
new_mkVBalBranch3MkVBalBranch127(zzz3170, zzz3171, zzz317200, zzz3173, zzz3174, zzz330, zzz331, zzz333, zzz334, zzz31, Succ(zzz5500), h) → new_mkVBalBranch1(zzz31, zzz334, Branch(zzz3170, zzz3171, Neg(Succ(zzz317200)), zzz3173, zzz3174), h)
new_mkVBalBranch3MkVBalBranch242(zzz972, zzz973, zzz974, zzz975, zzz976, zzz977, zzz978, zzz979, zzz980, zzz981, zzz982, Succ(zzz9830), Zero, bc) → new_mkVBalBranch3MkVBalBranch128(zzz972, zzz973, zzz974, zzz975, zzz976, zzz977, zzz978, zzz979, zzz980, zzz981, zzz982, new_primPlusNat2(Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat3(new_primPlusNat1(zzz974), zzz974)), zzz974))), Succ(zzz974)), bc)
new_mkVBalBranch3MkVBalBranch129(zzz1851, zzz1852, zzz1853, zzz1854, zzz1855, zzz1856, zzz1857, zzz1858, zzz1859, zzz1860, zzz1861, Succ(zzz18620), Succ(zzz18630), bd) → new_mkVBalBranch3MkVBalBranch129(zzz1851, zzz1852, zzz1853, zzz1854, zzz1855, zzz1856, zzz1857, zzz1858, zzz1859, zzz1860, zzz1861, zzz18620, zzz18630, bd)
new_mkVBalBranch3MkVBalBranch124(zzz958, zzz959, zzz960, zzz961, zzz962, zzz963, zzz964, zzz965, zzz966, zzz967, zzz968, Zero, ba) → new_mkVBalBranch3MkVBalBranch125(zzz958, zzz959, zzz960, zzz961, zzz962, zzz963, zzz964, zzz965, zzz966, zzz967, zzz968, Zero, Succ(zzz965), ba)
new_mkVBalBranch3MkVBalBranch242(zzz972, zzz973, zzz974, zzz975, zzz976, zzz977, zzz978, zzz979, zzz980, zzz981, zzz982, Succ(zzz9830), Succ(zzz9840), bc) → new_mkVBalBranch3MkVBalBranch242(zzz972, zzz973, zzz974, zzz975, zzz976, zzz977, zzz978, zzz979, zzz980, zzz981, zzz982, zzz9830, zzz9840, bc)
new_mkVBalBranch3MkVBalBranch235(zzz3170, zzz3171, Pos(Succ(zzz317200)), zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, Succ(zzz4170), h) → new_mkVBalBranch3MkVBalBranch236(zzz3170, zzz3171, zzz317200, zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, zzz4170, zzz317200, h)
new_mkVBalBranch1(zzz31, Branch(zzz330, zzz331, Neg(Succ(zzz33200)), zzz333, zzz334), Branch(zzz3170, zzz3171, zzz3172, zzz3173, zzz3174), h) → new_mkVBalBranch3MkVBalBranch241(zzz3170, zzz3171, zzz3172, zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat2(Succ(new_primPlusNat3(new_primPlusNat1(zzz33200), zzz33200)), zzz33200)), zzz33200))), h)
new_mkVBalBranch1(zzz31, Branch(zzz330, zzz331, Pos(Succ(zzz33200)), zzz333, zzz334), Branch(zzz3170, zzz3171, zzz3172, zzz3173, zzz3174), h) → new_mkVBalBranch3MkVBalBranch235(zzz3170, zzz3171, zzz3172, zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat2(Succ(new_primPlusNat3(new_primPlusNat1(zzz33200), zzz33200)), zzz33200)), zzz33200))), h)
new_mkVBalBranch3MkVBalBranch236(zzz958, zzz959, zzz960, zzz961, zzz962, zzz963, zzz964, zzz965, zzz966, zzz967, zzz968, Succ(zzz9690), Succ(zzz9700), ba) → new_mkVBalBranch3MkVBalBranch236(zzz958, zzz959, zzz960, zzz961, zzz962, zzz963, zzz964, zzz965, zzz966, zzz967, zzz968, zzz9690, zzz9700, ba)
new_mkVBalBranch3MkVBalBranch241(zzz3170, zzz3171, Neg(Succ(zzz317200)), zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, Succ(zzz4190), h) → new_mkVBalBranch3MkVBalBranch242(zzz3170, zzz3171, zzz317200, zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, zzz317200, zzz4190, h)
new_mkVBalBranch3MkVBalBranch241(zzz3170, zzz3171, Neg(Succ(zzz317200)), zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, Zero, h) → new_mkVBalBranch3MkVBalBranch242(zzz3170, zzz3171, zzz317200, zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, Succ(zzz317200), Zero, h)
new_mkVBalBranch1(zzz31, Branch(zzz330, zzz331, Pos(Zero), zzz333, zzz334), Branch(zzz3170, zzz3171, Pos(Succ(zzz317200)), zzz3173, zzz3174), h) → new_mkVBalBranch1(zzz31, Branch(zzz330, zzz331, Pos(Zero), zzz333, zzz334), zzz3173, h)
new_mkVBalBranch3MkVBalBranch243(zzz3170, zzz3171, zzz31720, zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, h) → new_mkVBalBranch1(zzz31, Branch(zzz330, zzz331, Neg(Succ(zzz33200)), zzz333, zzz334), zzz3173, h)
new_mkVBalBranch3MkVBalBranch235(zzz3170, zzz3171, Neg(Succ(zzz317200)), zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, Succ(zzz4170), h) → new_mkVBalBranch3MkVBalBranch123(zzz3170, zzz3171, zzz317200, zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, new_primPlusNat2(Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat3(new_primPlusNat1(zzz317200), zzz317200)), zzz317200))), Succ(zzz317200)), h)
new_mkVBalBranch3MkVBalBranch237(zzz3170, zzz3171, zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, h) → new_mkVBalBranch1(zzz31, zzz334, Branch(zzz3170, zzz3171, Pos(Zero), zzz3173, zzz3174), h)
new_mkVBalBranch3MkVBalBranch235(zzz3170, zzz3171, Pos(Zero), zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, Succ(zzz4170), h) → new_mkVBalBranch3MkVBalBranch237(zzz3170, zzz3171, zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, h)
new_mkVBalBranch3MkVBalBranch236(zzz958, zzz959, zzz960, zzz961, zzz962, zzz963, zzz964, zzz965, zzz966, zzz967, zzz968, Succ(zzz9690), Zero, ba) → new_mkVBalBranch3MkVBalBranch124(zzz958, zzz959, zzz960, zzz961, zzz962, zzz963, zzz964, zzz965, zzz966, zzz967, zzz968, new_primPlusNat2(Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat3(new_primPlusNat1(zzz960), zzz960)), zzz960))), Succ(zzz960)), ba)
new_mkVBalBranch3MkVBalBranch236(zzz958, zzz959, zzz960, zzz961, zzz962, zzz963, zzz964, zzz965, zzz966, zzz967, zzz968, Zero, Succ(zzz9700), ba) → new_mkVBalBranch1(zzz968, Branch(zzz963, zzz964, Pos(Succ(zzz965)), zzz966, zzz967), zzz961, ba)
new_mkVBalBranch3MkVBalBranch125(zzz1337, zzz1338, zzz1339, zzz1340, zzz1341, zzz1342, zzz1343, zzz1344, zzz1345, zzz1346, zzz1347, Succ(zzz13480), Succ(zzz13490), bb) → new_mkVBalBranch3MkVBalBranch125(zzz1337, zzz1338, zzz1339, zzz1340, zzz1341, zzz1342, zzz1343, zzz1344, zzz1345, zzz1346, zzz1347, zzz13480, zzz13490, bb)
new_mkVBalBranch3MkVBalBranch123(zzz3170, zzz3171, zzz317200, zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, Succ(zzz5620), h) → new_mkVBalBranch1(zzz31, zzz334, Branch(zzz3170, zzz3171, Neg(Succ(zzz317200)), zzz3173, zzz3174), h)
new_mkVBalBranch3MkVBalBranch125(zzz1337, zzz1338, zzz1339, zzz1340, zzz1341, zzz1342, zzz1343, zzz1344, zzz1345, zzz1346, zzz1347, Zero, Succ(zzz13490), bb) → new_mkVBalBranch1(zzz1347, zzz1346, Branch(zzz1337, zzz1338, Pos(Succ(zzz1339)), zzz1340, zzz1341), bb)
new_mkVBalBranch3MkVBalBranch242(zzz972, zzz973, zzz974, zzz975, zzz976, zzz977, zzz978, zzz979, zzz980, zzz981, zzz982, Zero, Succ(zzz9840), bc) → new_mkVBalBranch1(zzz982, Branch(zzz977, zzz978, Neg(Succ(zzz979)), zzz980, zzz981), zzz975, bc)
new_mkVBalBranch3MkVBalBranch240(zzz958, zzz959, zzz960, zzz961, zzz962, zzz963, zzz964, zzz965, zzz966, zzz967, zzz968, ba) → new_mkVBalBranch3MkVBalBranch124(zzz958, zzz959, zzz960, zzz961, zzz962, zzz963, zzz964, zzz965, zzz966, zzz967, zzz968, new_primPlusNat2(new_primPlusNat3(Succ(new_primPlusNat3(new_primPlusNat1(zzz960), zzz960)), Succ(zzz960)), Succ(zzz960)), ba)
new_mkVBalBranch3MkVBalBranch241(zzz3170, zzz3171, Pos(Succ(zzz317200)), zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, Zero, h) → new_mkVBalBranch3MkVBalBranch243(zzz3170, zzz3171, Succ(zzz317200), zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, h)
new_mkVBalBranch1(zzz31, Branch(zzz330, zzz331, Pos(Zero), zzz333, zzz334), Branch(zzz3170, zzz3171, Neg(Succ(zzz317200)), zzz3173, zzz3174), h) → new_mkVBalBranch3MkVBalBranch126(zzz3170, zzz3171, zzz317200, zzz3173, zzz3174, zzz330, zzz331, zzz333, zzz334, zzz31, new_primPlusNat2(new_primPlusNat3(Succ(new_primPlusNat3(new_primPlusNat1(zzz317200), zzz317200)), Succ(zzz317200)), Succ(zzz317200)), h)
new_mkVBalBranch3MkVBalBranch126(zzz3170, zzz3171, zzz317200, zzz3173, zzz3174, zzz330, zzz331, zzz333, zzz334, zzz31, Succ(zzz5350), h) → new_mkVBalBranch1(zzz31, zzz334, Branch(zzz3170, zzz3171, Neg(Succ(zzz317200)), zzz3173, zzz3174), h)
new_mkVBalBranch3MkVBalBranch241(zzz3170, zzz3171, Neg(Zero), zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, Succ(zzz4190), h) → new_mkVBalBranch1(zzz31, Branch(zzz330, zzz331, Neg(Succ(zzz33200)), zzz333, zzz334), zzz3173, h)
new_mkVBalBranch3MkVBalBranch123(zzz3170, zzz3171, zzz317200, zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, Zero, h) → new_mkVBalBranch3MkVBalBranch130(zzz3170, zzz3171, zzz317200, zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, h)
new_mkVBalBranch3MkVBalBranch124(zzz958, zzz959, zzz960, zzz961, zzz962, zzz963, zzz964, zzz965, zzz966, zzz967, zzz968, Succ(zzz10180), ba) → new_mkVBalBranch3MkVBalBranch125(zzz958, zzz959, zzz960, zzz961, zzz962, zzz963, zzz964, zzz965, zzz966, zzz967, zzz968, Succ(zzz10180), Succ(zzz965), ba)
new_mkVBalBranch1(zzz31, Branch(zzz330, zzz331, Neg(Zero), zzz333, zzz334), Branch(zzz3170, zzz3171, Neg(Succ(zzz317200)), zzz3173, zzz3174), h) → new_mkVBalBranch3MkVBalBranch127(zzz3170, zzz3171, zzz317200, zzz3173, zzz3174, zzz330, zzz331, zzz333, zzz334, zzz31, new_primPlusNat2(Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat3(new_primPlusNat1(zzz317200), zzz317200)), zzz317200))), Succ(zzz317200)), h)
new_mkVBalBranch3MkVBalBranch242(zzz972, zzz973, zzz974, zzz975, zzz976, zzz977, zzz978, zzz979, zzz980, zzz981, zzz982, Zero, Zero, bc) → new_mkVBalBranch3MkVBalBranch244(zzz972, zzz973, zzz974, zzz975, zzz976, zzz977, zzz978, zzz979, zzz980, zzz981, zzz982, bc)
new_mkVBalBranch3MkVBalBranch130(zzz3170, zzz3171, zzz317200, zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, h) → new_mkVBalBranch1(zzz31, zzz334, Branch(zzz3170, zzz3171, Neg(Succ(zzz317200)), zzz3173, zzz3174), h)
new_mkVBalBranch1(zzz31, Branch(zzz330, zzz331, Neg(Zero), zzz333, zzz334), Branch(zzz3170, zzz3171, Pos(Succ(zzz317200)), zzz3173, zzz3174), h) → new_mkVBalBranch1(zzz31, Branch(zzz330, zzz331, Neg(Zero), zzz333, zzz334), zzz3173, h)
new_mkVBalBranch3MkVBalBranch235(zzz3170, zzz3171, Neg(Zero), zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, Succ(zzz4170), h) → new_mkVBalBranch1(zzz31, zzz334, Branch(zzz3170, zzz3171, Neg(Zero), zzz3173, zzz3174), h)
new_mkVBalBranch3MkVBalBranch244(zzz972, zzz973, zzz974, zzz975, zzz976, zzz977, zzz978, zzz979, zzz980, zzz981, zzz982, bc) → new_mkVBalBranch3MkVBalBranch128(zzz972, zzz973, zzz974, zzz975, zzz976, zzz977, zzz978, zzz979, zzz980, zzz981, zzz982, new_primPlusNat2(new_primPlusNat3(Succ(new_primPlusNat3(new_primPlusNat1(zzz974), zzz974)), Succ(zzz974)), Succ(zzz974)), bc)
new_mkVBalBranch3MkVBalBranch236(zzz958, zzz959, zzz960, zzz961, zzz962, zzz963, zzz964, zzz965, zzz966, zzz967, zzz968, Zero, Zero, ba) → new_mkVBalBranch3MkVBalBranch240(zzz958, zzz959, zzz960, zzz961, zzz962, zzz963, zzz964, zzz965, zzz966, zzz967, zzz968, ba)

The TRS R consists of the following rules:

new_primPlusNat1(Zero) → Zero
new_primPlusNat1(Succ(zzz62000)) → Succ(Succ(new_primPlusNat1(zzz62000)))
new_primPlusNat3(zzz90, Succ(zzz910)) → Succ(Succ(new_primPlusNat2(zzz90, zzz910)))
new_primPlusNat3(zzz90, Zero) → Succ(zzz90)
new_primPlusNat2(Succ(zzz900), Succ(zzz9100)) → Succ(Succ(new_primPlusNat2(zzz900, zzz9100)))
new_primPlusNat2(Succ(zzz900), Zero) → Succ(zzz900)
new_primPlusNat2(Zero, Succ(zzz9100)) → Succ(zzz9100)
new_primPlusNat2(Zero, Zero) → Zero

The set Q consists of the following terms:

new_primPlusNat2(Zero, Succ(x0))
new_primPlusNat3(x0, Succ(x1))
new_primPlusNat2(Succ(x0), Succ(x1))
new_primPlusNat3(x0, Zero)
new_primPlusNat1(Zero)
new_primPlusNat2(Zero, Zero)
new_primPlusNat1(Succ(x0))
new_primPlusNat2(Succ(x0), Zero)

We have to consider all minimal (P,Q,R)-chains.
The approximation of the Dependency Graph [15,17,22] contains 1 SCC with 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
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                    ↳ DependencyGraphProof
                                      ↳ QDP
                                        ↳ Rewriting
                                          ↳ QDP
                                            ↳ Rewriting
                                              ↳ QDP
                                                ↳ Rewriting
                                                  ↳ QDP
                                                    ↳ Rewriting
                                                      ↳ QDP
                                                        ↳ Rewriting
                                                          ↳ QDP
                                                            ↳ Rewriting
                                                              ↳ QDP
                                                                ↳ Rewriting
                                                                  ↳ QDP
                                                                    ↳ Rewriting
                                                                      ↳ QDP
                                                                        ↳ Rewriting
                                                                          ↳ QDP
                                                                            ↳ Rewriting
                                                                              ↳ QDP
                                                                                ↳ UsableRulesProof
                                                                                  ↳ QDP
                                                                                    ↳ QReductionProof
                                                                                      ↳ QDP
                                                                                        ↳ Rewriting
                                                                                          ↳ QDP
                                                                                            ↳ Rewriting
                                                                                              ↳ QDP
                                                                                                ↳ Rewriting
                                                                                                  ↳ QDP
                                                                                                    ↳ Rewriting
                                                                                                      ↳ QDP
                                                                                                        ↳ Rewriting
                                                                                                          ↳ QDP
                                                                                                            ↳ Rewriting
                                                                                                              ↳ QDP
                                                                                                                ↳ Rewriting
                                                                                                                  ↳ QDP
                                                                                                                    ↳ Rewriting
                                                                                                                      ↳ QDP
                                                                                                                        ↳ Rewriting
                                                                                                                          ↳ QDP
                                                                                                                            ↳ Rewriting
                                                                                                                              ↳ QDP
                                                                                                                                ↳ UsableRulesProof
                                                                                                                                  ↳ QDP
                                                                                                                                    ↳ QReductionProof
                                                                                                                                      ↳ QDP
                                                                                                                                        ↳ Rewriting
                                                                                                                                          ↳ QDP
                                                                                                                                            ↳ Rewriting
                                                                                                                                              ↳ QDP
                                                                                                                                                ↳ Rewriting
                                                                                                                                                  ↳ QDP
                                                                                                                                                    ↳ DependencyGraphProof
                                                                                                                                                      ↳ QDP
                                                                                                                                                        ↳ Rewriting
                                                                                                                                                          ↳ QDP
                                                                                                                                                            ↳ Rewriting
                                                                                                                                                              ↳ QDP
                                                                                                                                                                ↳ DependencyGraphProof
                                                                                                                                                                  ↳ QDP
                                                                                                                                                                    ↳ Rewriting
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP

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

new_mkVBalBranch3MkVBalBranch129(zzz1851, zzz1852, zzz1853, zzz1854, zzz1855, zzz1856, zzz1857, zzz1858, zzz1859, zzz1860, zzz1861, Zero, Succ(zzz18630), bd) → new_mkVBalBranch1(zzz1861, zzz1860, Branch(zzz1851, zzz1852, Neg(Succ(zzz1853)), zzz1854, zzz1855), bd)
new_mkVBalBranch3MkVBalBranch127(zzz3170, zzz3171, zzz317200, zzz3173, zzz3174, zzz330, zzz331, zzz333, zzz334, zzz31, Succ(zzz5500), h) → new_mkVBalBranch1(zzz31, zzz334, Branch(zzz3170, zzz3171, Neg(Succ(zzz317200)), zzz3173, zzz3174), h)
new_mkVBalBranch3MkVBalBranch241(zzz3170, zzz3171, Pos(zzz31720), zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, Succ(zzz4190), h) → new_mkVBalBranch1(zzz31, Branch(zzz330, zzz331, Neg(Succ(zzz33200)), zzz333, zzz334), zzz3173, h)
new_mkVBalBranch3MkVBalBranch128(zzz972, zzz973, zzz974, zzz975, zzz976, zzz977, zzz978, zzz979, zzz980, zzz981, zzz982, Succ(zzz10190), bc) → new_mkVBalBranch3MkVBalBranch129(zzz972, zzz973, zzz974, zzz975, zzz976, zzz977, zzz978, zzz979, zzz980, zzz981, zzz982, Succ(zzz979), Succ(zzz10190), bc)
new_mkVBalBranch3MkVBalBranch242(zzz972, zzz973, zzz974, zzz975, zzz976, zzz977, zzz978, zzz979, zzz980, zzz981, zzz982, Succ(zzz9830), Zero, bc) → new_mkVBalBranch3MkVBalBranch128(zzz972, zzz973, zzz974, zzz975, zzz976, zzz977, zzz978, zzz979, zzz980, zzz981, zzz982, new_primPlusNat2(Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat3(new_primPlusNat1(zzz974), zzz974)), zzz974))), Succ(zzz974)), bc)
new_mkVBalBranch3MkVBalBranch129(zzz1851, zzz1852, zzz1853, zzz1854, zzz1855, zzz1856, zzz1857, zzz1858, zzz1859, zzz1860, zzz1861, Succ(zzz18620), Succ(zzz18630), bd) → new_mkVBalBranch3MkVBalBranch129(zzz1851, zzz1852, zzz1853, zzz1854, zzz1855, zzz1856, zzz1857, zzz1858, zzz1859, zzz1860, zzz1861, zzz18620, zzz18630, bd)
new_mkVBalBranch3MkVBalBranch124(zzz958, zzz959, zzz960, zzz961, zzz962, zzz963, zzz964, zzz965, zzz966, zzz967, zzz968, Zero, ba) → new_mkVBalBranch3MkVBalBranch125(zzz958, zzz959, zzz960, zzz961, zzz962, zzz963, zzz964, zzz965, zzz966, zzz967, zzz968, Zero, Succ(zzz965), ba)
new_mkVBalBranch3MkVBalBranch235(zzz3170, zzz3171, Pos(Succ(zzz317200)), zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, Succ(zzz4170), h) → new_mkVBalBranch3MkVBalBranch236(zzz3170, zzz3171, zzz317200, zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, zzz4170, zzz317200, h)
new_mkVBalBranch3MkVBalBranch242(zzz972, zzz973, zzz974, zzz975, zzz976, zzz977, zzz978, zzz979, zzz980, zzz981, zzz982, Succ(zzz9830), Succ(zzz9840), bc) → new_mkVBalBranch3MkVBalBranch242(zzz972, zzz973, zzz974, zzz975, zzz976, zzz977, zzz978, zzz979, zzz980, zzz981, zzz982, zzz9830, zzz9840, bc)
new_mkVBalBranch1(zzz31, Branch(zzz330, zzz331, Pos(Succ(zzz33200)), zzz333, zzz334), Branch(zzz3170, zzz3171, zzz3172, zzz3173, zzz3174), h) → new_mkVBalBranch3MkVBalBranch235(zzz3170, zzz3171, zzz3172, zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat2(Succ(new_primPlusNat3(new_primPlusNat1(zzz33200), zzz33200)), zzz33200)), zzz33200))), h)
new_mkVBalBranch1(zzz31, Branch(zzz330, zzz331, Neg(Succ(zzz33200)), zzz333, zzz334), Branch(zzz3170, zzz3171, zzz3172, zzz3173, zzz3174), h) → new_mkVBalBranch3MkVBalBranch241(zzz3170, zzz3171, zzz3172, zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat2(Succ(new_primPlusNat3(new_primPlusNat1(zzz33200), zzz33200)), zzz33200)), zzz33200))), h)
new_mkVBalBranch3MkVBalBranch236(zzz958, zzz959, zzz960, zzz961, zzz962, zzz963, zzz964, zzz965, zzz966, zzz967, zzz968, Succ(zzz9690), Succ(zzz9700), ba) → new_mkVBalBranch3MkVBalBranch236(zzz958, zzz959, zzz960, zzz961, zzz962, zzz963, zzz964, zzz965, zzz966, zzz967, zzz968, zzz9690, zzz9700, ba)
new_mkVBalBranch3MkVBalBranch241(zzz3170, zzz3171, Neg(Succ(zzz317200)), zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, Succ(zzz4190), h) → new_mkVBalBranch3MkVBalBranch242(zzz3170, zzz3171, zzz317200, zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, zzz317200, zzz4190, h)
new_mkVBalBranch1(zzz31, Branch(zzz330, zzz331, Pos(Zero), zzz333, zzz334), Branch(zzz3170, zzz3171, Pos(Succ(zzz317200)), zzz3173, zzz3174), h) → new_mkVBalBranch1(zzz31, Branch(zzz330, zzz331, Pos(Zero), zzz333, zzz334), zzz3173, h)
new_mkVBalBranch3MkVBalBranch235(zzz3170, zzz3171, Neg(Succ(zzz317200)), zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, Succ(zzz4170), h) → new_mkVBalBranch3MkVBalBranch123(zzz3170, zzz3171, zzz317200, zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, new_primPlusNat2(Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat3(new_primPlusNat1(zzz317200), zzz317200)), zzz317200))), Succ(zzz317200)), h)
new_mkVBalBranch3MkVBalBranch237(zzz3170, zzz3171, zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, h) → new_mkVBalBranch1(zzz31, zzz334, Branch(zzz3170, zzz3171, Pos(Zero), zzz3173, zzz3174), h)
new_mkVBalBranch3MkVBalBranch235(zzz3170, zzz3171, Pos(Zero), zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, Succ(zzz4170), h) → new_mkVBalBranch3MkVBalBranch237(zzz3170, zzz3171, zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, h)
new_mkVBalBranch3MkVBalBranch236(zzz958, zzz959, zzz960, zzz961, zzz962, zzz963, zzz964, zzz965, zzz966, zzz967, zzz968, Succ(zzz9690), Zero, ba) → new_mkVBalBranch3MkVBalBranch124(zzz958, zzz959, zzz960, zzz961, zzz962, zzz963, zzz964, zzz965, zzz966, zzz967, zzz968, new_primPlusNat2(Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat3(new_primPlusNat1(zzz960), zzz960)), zzz960))), Succ(zzz960)), ba)
new_mkVBalBranch3MkVBalBranch236(zzz958, zzz959, zzz960, zzz961, zzz962, zzz963, zzz964, zzz965, zzz966, zzz967, zzz968, Zero, Succ(zzz9700), ba) → new_mkVBalBranch1(zzz968, Branch(zzz963, zzz964, Pos(Succ(zzz965)), zzz966, zzz967), zzz961, ba)
new_mkVBalBranch3MkVBalBranch125(zzz1337, zzz1338, zzz1339, zzz1340, zzz1341, zzz1342, zzz1343, zzz1344, zzz1345, zzz1346, zzz1347, Succ(zzz13480), Succ(zzz13490), bb) → new_mkVBalBranch3MkVBalBranch125(zzz1337, zzz1338, zzz1339, zzz1340, zzz1341, zzz1342, zzz1343, zzz1344, zzz1345, zzz1346, zzz1347, zzz13480, zzz13490, bb)
new_mkVBalBranch3MkVBalBranch123(zzz3170, zzz3171, zzz317200, zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, Succ(zzz5620), h) → new_mkVBalBranch1(zzz31, zzz334, Branch(zzz3170, zzz3171, Neg(Succ(zzz317200)), zzz3173, zzz3174), h)
new_mkVBalBranch3MkVBalBranch125(zzz1337, zzz1338, zzz1339, zzz1340, zzz1341, zzz1342, zzz1343, zzz1344, zzz1345, zzz1346, zzz1347, Zero, Succ(zzz13490), bb) → new_mkVBalBranch1(zzz1347, zzz1346, Branch(zzz1337, zzz1338, Pos(Succ(zzz1339)), zzz1340, zzz1341), bb)
new_mkVBalBranch3MkVBalBranch242(zzz972, zzz973, zzz974, zzz975, zzz976, zzz977, zzz978, zzz979, zzz980, zzz981, zzz982, Zero, Succ(zzz9840), bc) → new_mkVBalBranch1(zzz982, Branch(zzz977, zzz978, Neg(Succ(zzz979)), zzz980, zzz981), zzz975, bc)
new_mkVBalBranch3MkVBalBranch240(zzz958, zzz959, zzz960, zzz961, zzz962, zzz963, zzz964, zzz965, zzz966, zzz967, zzz968, ba) → new_mkVBalBranch3MkVBalBranch124(zzz958, zzz959, zzz960, zzz961, zzz962, zzz963, zzz964, zzz965, zzz966, zzz967, zzz968, new_primPlusNat2(new_primPlusNat3(Succ(new_primPlusNat3(new_primPlusNat1(zzz960), zzz960)), Succ(zzz960)), Succ(zzz960)), ba)
new_mkVBalBranch3MkVBalBranch126(zzz3170, zzz3171, zzz317200, zzz3173, zzz3174, zzz330, zzz331, zzz333, zzz334, zzz31, Succ(zzz5350), h) → new_mkVBalBranch1(zzz31, zzz334, Branch(zzz3170, zzz3171, Neg(Succ(zzz317200)), zzz3173, zzz3174), h)
new_mkVBalBranch1(zzz31, Branch(zzz330, zzz331, Pos(Zero), zzz333, zzz334), Branch(zzz3170, zzz3171, Neg(Succ(zzz317200)), zzz3173, zzz3174), h) → new_mkVBalBranch3MkVBalBranch126(zzz3170, zzz3171, zzz317200, zzz3173, zzz3174, zzz330, zzz331, zzz333, zzz334, zzz31, new_primPlusNat2(new_primPlusNat3(Succ(new_primPlusNat3(new_primPlusNat1(zzz317200), zzz317200)), Succ(zzz317200)), Succ(zzz317200)), h)
new_mkVBalBranch3MkVBalBranch123(zzz3170, zzz3171, zzz317200, zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, Zero, h) → new_mkVBalBranch3MkVBalBranch130(zzz3170, zzz3171, zzz317200, zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, h)
new_mkVBalBranch3MkVBalBranch241(zzz3170, zzz3171, Neg(Zero), zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, Succ(zzz4190), h) → new_mkVBalBranch1(zzz31, Branch(zzz330, zzz331, Neg(Succ(zzz33200)), zzz333, zzz334), zzz3173, h)
new_mkVBalBranch3MkVBalBranch124(zzz958, zzz959, zzz960, zzz961, zzz962, zzz963, zzz964, zzz965, zzz966, zzz967, zzz968, Succ(zzz10180), ba) → new_mkVBalBranch3MkVBalBranch125(zzz958, zzz959, zzz960, zzz961, zzz962, zzz963, zzz964, zzz965, zzz966, zzz967, zzz968, Succ(zzz10180), Succ(zzz965), ba)
new_mkVBalBranch1(zzz31, Branch(zzz330, zzz331, Neg(Zero), zzz333, zzz334), Branch(zzz3170, zzz3171, Neg(Succ(zzz317200)), zzz3173, zzz3174), h) → new_mkVBalBranch3MkVBalBranch127(zzz3170, zzz3171, zzz317200, zzz3173, zzz3174, zzz330, zzz331, zzz333, zzz334, zzz31, new_primPlusNat2(Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat3(new_primPlusNat1(zzz317200), zzz317200)), zzz317200))), Succ(zzz317200)), h)
new_mkVBalBranch3MkVBalBranch242(zzz972, zzz973, zzz974, zzz975, zzz976, zzz977, zzz978, zzz979, zzz980, zzz981, zzz982, Zero, Zero, bc) → new_mkVBalBranch3MkVBalBranch244(zzz972, zzz973, zzz974, zzz975, zzz976, zzz977, zzz978, zzz979, zzz980, zzz981, zzz982, bc)
new_mkVBalBranch3MkVBalBranch130(zzz3170, zzz3171, zzz317200, zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, h) → new_mkVBalBranch1(zzz31, zzz334, Branch(zzz3170, zzz3171, Neg(Succ(zzz317200)), zzz3173, zzz3174), h)
new_mkVBalBranch1(zzz31, Branch(zzz330, zzz331, Neg(Zero), zzz333, zzz334), Branch(zzz3170, zzz3171, Pos(Succ(zzz317200)), zzz3173, zzz3174), h) → new_mkVBalBranch1(zzz31, Branch(zzz330, zzz331, Neg(Zero), zzz333, zzz334), zzz3173, h)
new_mkVBalBranch3MkVBalBranch235(zzz3170, zzz3171, Neg(Zero), zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, Succ(zzz4170), h) → new_mkVBalBranch1(zzz31, zzz334, Branch(zzz3170, zzz3171, Neg(Zero), zzz3173, zzz3174), h)
new_mkVBalBranch3MkVBalBranch236(zzz958, zzz959, zzz960, zzz961, zzz962, zzz963, zzz964, zzz965, zzz966, zzz967, zzz968, Zero, Zero, ba) → new_mkVBalBranch3MkVBalBranch240(zzz958, zzz959, zzz960, zzz961, zzz962, zzz963, zzz964, zzz965, zzz966, zzz967, zzz968, ba)
new_mkVBalBranch3MkVBalBranch244(zzz972, zzz973, zzz974, zzz975, zzz976, zzz977, zzz978, zzz979, zzz980, zzz981, zzz982, bc) → new_mkVBalBranch3MkVBalBranch128(zzz972, zzz973, zzz974, zzz975, zzz976, zzz977, zzz978, zzz979, zzz980, zzz981, zzz982, new_primPlusNat2(new_primPlusNat3(Succ(new_primPlusNat3(new_primPlusNat1(zzz974), zzz974)), Succ(zzz974)), Succ(zzz974)), bc)

The TRS R consists of the following rules:

new_primPlusNat1(Zero) → Zero
new_primPlusNat1(Succ(zzz62000)) → Succ(Succ(new_primPlusNat1(zzz62000)))
new_primPlusNat3(zzz90, Succ(zzz910)) → Succ(Succ(new_primPlusNat2(zzz90, zzz910)))
new_primPlusNat3(zzz90, Zero) → Succ(zzz90)
new_primPlusNat2(Succ(zzz900), Succ(zzz9100)) → Succ(Succ(new_primPlusNat2(zzz900, zzz9100)))
new_primPlusNat2(Succ(zzz900), Zero) → Succ(zzz900)
new_primPlusNat2(Zero, Succ(zzz9100)) → Succ(zzz9100)
new_primPlusNat2(Zero, Zero) → Zero

The set Q consists of the following terms:

new_primPlusNat2(Zero, Succ(x0))
new_primPlusNat3(x0, Succ(x1))
new_primPlusNat2(Succ(x0), Succ(x1))
new_primPlusNat3(x0, Zero)
new_primPlusNat1(Zero)
new_primPlusNat2(Zero, Zero)
new_primPlusNat1(Succ(x0))
new_primPlusNat2(Succ(x0), Zero)

We have to consider all minimal (P,Q,R)-chains.
By rewriting [15] the rule new_mkVBalBranch1(zzz31, Branch(zzz330, zzz331, Pos(Zero), zzz333, zzz334), Branch(zzz3170, zzz3171, Neg(Succ(zzz317200)), zzz3173, zzz3174), h) → new_mkVBalBranch3MkVBalBranch126(zzz3170, zzz3171, zzz317200, zzz3173, zzz3174, zzz330, zzz331, zzz333, zzz334, zzz31, new_primPlusNat2(new_primPlusNat3(Succ(new_primPlusNat3(new_primPlusNat1(zzz317200), zzz317200)), Succ(zzz317200)), Succ(zzz317200)), h) at position [10,0] we obtained the following new rules:

new_mkVBalBranch1(zzz31, Branch(zzz330, zzz331, Pos(Zero), zzz333, zzz334), Branch(zzz3170, zzz3171, Neg(Succ(zzz317200)), zzz3173, zzz3174), h) → new_mkVBalBranch3MkVBalBranch126(zzz3170, zzz3171, zzz317200, zzz3173, zzz3174, zzz330, zzz331, zzz333, zzz334, zzz31, new_primPlusNat2(Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat3(new_primPlusNat1(zzz317200), zzz317200)), zzz317200))), Succ(zzz317200)), 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
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                    ↳ DependencyGraphProof
                                      ↳ QDP
                                        ↳ Rewriting
                                          ↳ QDP
                                            ↳ Rewriting
                                              ↳ QDP
                                                ↳ Rewriting
                                                  ↳ QDP
                                                    ↳ Rewriting
                                                      ↳ QDP
                                                        ↳ Rewriting
                                                          ↳ QDP
                                                            ↳ Rewriting
                                                              ↳ QDP
                                                                ↳ Rewriting
                                                                  ↳ QDP
                                                                    ↳ Rewriting
                                                                      ↳ QDP
                                                                        ↳ Rewriting
                                                                          ↳ QDP
                                                                            ↳ Rewriting
                                                                              ↳ QDP
                                                                                ↳ UsableRulesProof
                                                                                  ↳ QDP
                                                                                    ↳ QReductionProof
                                                                                      ↳ QDP
                                                                                        ↳ Rewriting
                                                                                          ↳ QDP
                                                                                            ↳ Rewriting
                                                                                              ↳ QDP
                                                                                                ↳ Rewriting
                                                                                                  ↳ QDP
                                                                                                    ↳ Rewriting
                                                                                                      ↳ QDP
                                                                                                        ↳ Rewriting
                                                                                                          ↳ QDP
                                                                                                            ↳ Rewriting
                                                                                                              ↳ QDP
                                                                                                                ↳ Rewriting
                                                                                                                  ↳ QDP
                                                                                                                    ↳ Rewriting
                                                                                                                      ↳ QDP
                                                                                                                        ↳ Rewriting
                                                                                                                          ↳ QDP
                                                                                                                            ↳ Rewriting
                                                                                                                              ↳ QDP
                                                                                                                                ↳ UsableRulesProof
                                                                                                                                  ↳ QDP
                                                                                                                                    ↳ QReductionProof
                                                                                                                                      ↳ QDP
                                                                                                                                        ↳ Rewriting
                                                                                                                                          ↳ QDP
                                                                                                                                            ↳ Rewriting
                                                                                                                                              ↳ QDP
                                                                                                                                                ↳ Rewriting
                                                                                                                                                  ↳ QDP
                                                                                                                                                    ↳ DependencyGraphProof
                                                                                                                                                      ↳ QDP
                                                                                                                                                        ↳ Rewriting
                                                                                                                                                          ↳ QDP
                                                                                                                                                            ↳ Rewriting
                                                                                                                                                              ↳ QDP
                                                                                                                                                                ↳ DependencyGraphProof
                                                                                                                                                                  ↳ QDP
                                                                                                                                                                    ↳ Rewriting
                                                                                                                                                                      ↳ QDP
                                                                                                                                                                        ↳ Rewriting
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP

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

new_mkVBalBranch3MkVBalBranch129(zzz1851, zzz1852, zzz1853, zzz1854, zzz1855, zzz1856, zzz1857, zzz1858, zzz1859, zzz1860, zzz1861, Zero, Succ(zzz18630), bd) → new_mkVBalBranch1(zzz1861, zzz1860, Branch(zzz1851, zzz1852, Neg(Succ(zzz1853)), zzz1854, zzz1855), bd)
new_mkVBalBranch3MkVBalBranch128(zzz972, zzz973, zzz974, zzz975, zzz976, zzz977, zzz978, zzz979, zzz980, zzz981, zzz982, Succ(zzz10190), bc) → new_mkVBalBranch3MkVBalBranch129(zzz972, zzz973, zzz974, zzz975, zzz976, zzz977, zzz978, zzz979, zzz980, zzz981, zzz982, Succ(zzz979), Succ(zzz10190), bc)
new_mkVBalBranch3MkVBalBranch241(zzz3170, zzz3171, Pos(zzz31720), zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, Succ(zzz4190), h) → new_mkVBalBranch1(zzz31, Branch(zzz330, zzz331, Neg(Succ(zzz33200)), zzz333, zzz334), zzz3173, h)
new_mkVBalBranch3MkVBalBranch127(zzz3170, zzz3171, zzz317200, zzz3173, zzz3174, zzz330, zzz331, zzz333, zzz334, zzz31, Succ(zzz5500), h) → new_mkVBalBranch1(zzz31, zzz334, Branch(zzz3170, zzz3171, Neg(Succ(zzz317200)), zzz3173, zzz3174), h)
new_mkVBalBranch3MkVBalBranch242(zzz972, zzz973, zzz974, zzz975, zzz976, zzz977, zzz978, zzz979, zzz980, zzz981, zzz982, Succ(zzz9830), Zero, bc) → new_mkVBalBranch3MkVBalBranch128(zzz972, zzz973, zzz974, zzz975, zzz976, zzz977, zzz978, zzz979, zzz980, zzz981, zzz982, new_primPlusNat2(Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat3(new_primPlusNat1(zzz974), zzz974)), zzz974))), Succ(zzz974)), bc)
new_mkVBalBranch3MkVBalBranch129(zzz1851, zzz1852, zzz1853, zzz1854, zzz1855, zzz1856, zzz1857, zzz1858, zzz1859, zzz1860, zzz1861, Succ(zzz18620), Succ(zzz18630), bd) → new_mkVBalBranch3MkVBalBranch129(zzz1851, zzz1852, zzz1853, zzz1854, zzz1855, zzz1856, zzz1857, zzz1858, zzz1859, zzz1860, zzz1861, zzz18620, zzz18630, bd)
new_mkVBalBranch3MkVBalBranch124(zzz958, zzz959, zzz960, zzz961, zzz962, zzz963, zzz964, zzz965, zzz966, zzz967, zzz968, Zero, ba) → new_mkVBalBranch3MkVBalBranch125(zzz958, zzz959, zzz960, zzz961, zzz962, zzz963, zzz964, zzz965, zzz966, zzz967, zzz968, Zero, Succ(zzz965), ba)
new_mkVBalBranch1(zzz31, Branch(zzz330, zzz331, Pos(Zero), zzz333, zzz334), Branch(zzz3170, zzz3171, Neg(Succ(zzz317200)), zzz3173, zzz3174), h) → new_mkVBalBranch3MkVBalBranch126(zzz3170, zzz3171, zzz317200, zzz3173, zzz3174, zzz330, zzz331, zzz333, zzz334, zzz31, new_primPlusNat2(Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat3(new_primPlusNat1(zzz317200), zzz317200)), zzz317200))), Succ(zzz317200)), h)
new_mkVBalBranch3MkVBalBranch242(zzz972, zzz973, zzz974, zzz975, zzz976, zzz977, zzz978, zzz979, zzz980, zzz981, zzz982, Succ(zzz9830), Succ(zzz9840), bc) → new_mkVBalBranch3MkVBalBranch242(zzz972, zzz973, zzz974, zzz975, zzz976, zzz977, zzz978, zzz979, zzz980, zzz981, zzz982, zzz9830, zzz9840, bc)
new_mkVBalBranch3MkVBalBranch235(zzz3170, zzz3171, Pos(Succ(zzz317200)), zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, Succ(zzz4170), h) → new_mkVBalBranch3MkVBalBranch236(zzz3170, zzz3171, zzz317200, zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, zzz4170, zzz317200, h)
new_mkVBalBranch1(zzz31, Branch(zzz330, zzz331, Neg(Succ(zzz33200)), zzz333, zzz334), Branch(zzz3170, zzz3171, zzz3172, zzz3173, zzz3174), h) → new_mkVBalBranch3MkVBalBranch241(zzz3170, zzz3171, zzz3172, zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat2(Succ(new_primPlusNat3(new_primPlusNat1(zzz33200), zzz33200)), zzz33200)), zzz33200))), h)
new_mkVBalBranch1(zzz31, Branch(zzz330, zzz331, Pos(Succ(zzz33200)), zzz333, zzz334), Branch(zzz3170, zzz3171, zzz3172, zzz3173, zzz3174), h) → new_mkVBalBranch3MkVBalBranch235(zzz3170, zzz3171, zzz3172, zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat2(Succ(new_primPlusNat3(new_primPlusNat1(zzz33200), zzz33200)), zzz33200)), zzz33200))), h)
new_mkVBalBranch3MkVBalBranch236(zzz958, zzz959, zzz960, zzz961, zzz962, zzz963, zzz964, zzz965, zzz966, zzz967, zzz968, Succ(zzz9690), Succ(zzz9700), ba) → new_mkVBalBranch3MkVBalBranch236(zzz958, zzz959, zzz960, zzz961, zzz962, zzz963, zzz964, zzz965, zzz966, zzz967, zzz968, zzz9690, zzz9700, ba)
new_mkVBalBranch3MkVBalBranch241(zzz3170, zzz3171, Neg(Succ(zzz317200)), zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, Succ(zzz4190), h) → new_mkVBalBranch3MkVBalBranch242(zzz3170, zzz3171, zzz317200, zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, zzz317200, zzz4190, h)
new_mkVBalBranch1(zzz31, Branch(zzz330, zzz331, Pos(Zero), zzz333, zzz334), Branch(zzz3170, zzz3171, Pos(Succ(zzz317200)), zzz3173, zzz3174), h) → new_mkVBalBranch1(zzz31, Branch(zzz330, zzz331, Pos(Zero), zzz333, zzz334), zzz3173, h)
new_mkVBalBranch3MkVBalBranch237(zzz3170, zzz3171, zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, h) → new_mkVBalBranch1(zzz31, zzz334, Branch(zzz3170, zzz3171, Pos(Zero), zzz3173, zzz3174), h)
new_mkVBalBranch3MkVBalBranch235(zzz3170, zzz3171, Neg(Succ(zzz317200)), zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, Succ(zzz4170), h) → new_mkVBalBranch3MkVBalBranch123(zzz3170, zzz3171, zzz317200, zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, new_primPlusNat2(Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat3(new_primPlusNat1(zzz317200), zzz317200)), zzz317200))), Succ(zzz317200)), h)
new_mkVBalBranch3MkVBalBranch235(zzz3170, zzz3171, Pos(Zero), zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, Succ(zzz4170), h) → new_mkVBalBranch3MkVBalBranch237(zzz3170, zzz3171, zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, h)
new_mkVBalBranch3MkVBalBranch236(zzz958, zzz959, zzz960, zzz961, zzz962, zzz963, zzz964, zzz965, zzz966, zzz967, zzz968, Succ(zzz9690), Zero, ba) → new_mkVBalBranch3MkVBalBranch124(zzz958, zzz959, zzz960, zzz961, zzz962, zzz963, zzz964, zzz965, zzz966, zzz967, zzz968, new_primPlusNat2(Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat3(new_primPlusNat1(zzz960), zzz960)), zzz960))), Succ(zzz960)), ba)
new_mkVBalBranch3MkVBalBranch236(zzz958, zzz959, zzz960, zzz961, zzz962, zzz963, zzz964, zzz965, zzz966, zzz967, zzz968, Zero, Succ(zzz9700), ba) → new_mkVBalBranch1(zzz968, Branch(zzz963, zzz964, Pos(Succ(zzz965)), zzz966, zzz967), zzz961, ba)
new_mkVBalBranch3MkVBalBranch125(zzz1337, zzz1338, zzz1339, zzz1340, zzz1341, zzz1342, zzz1343, zzz1344, zzz1345, zzz1346, zzz1347, Succ(zzz13480), Succ(zzz13490), bb) → new_mkVBalBranch3MkVBalBranch125(zzz1337, zzz1338, zzz1339, zzz1340, zzz1341, zzz1342, zzz1343, zzz1344, zzz1345, zzz1346, zzz1347, zzz13480, zzz13490, bb)
new_mkVBalBranch3MkVBalBranch123(zzz3170, zzz3171, zzz317200, zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, Succ(zzz5620), h) → new_mkVBalBranch1(zzz31, zzz334, Branch(zzz3170, zzz3171, Neg(Succ(zzz317200)), zzz3173, zzz3174), h)
new_mkVBalBranch3MkVBalBranch125(zzz1337, zzz1338, zzz1339, zzz1340, zzz1341, zzz1342, zzz1343, zzz1344, zzz1345, zzz1346, zzz1347, Zero, Succ(zzz13490), bb) → new_mkVBalBranch1(zzz1347, zzz1346, Branch(zzz1337, zzz1338, Pos(Succ(zzz1339)), zzz1340, zzz1341), bb)
new_mkVBalBranch3MkVBalBranch242(zzz972, zzz973, zzz974, zzz975, zzz976, zzz977, zzz978, zzz979, zzz980, zzz981, zzz982, Zero, Succ(zzz9840), bc) → new_mkVBalBranch1(zzz982, Branch(zzz977, zzz978, Neg(Succ(zzz979)), zzz980, zzz981), zzz975, bc)
new_mkVBalBranch3MkVBalBranch240(zzz958, zzz959, zzz960, zzz961, zzz962, zzz963, zzz964, zzz965, zzz966, zzz967, zzz968, ba) → new_mkVBalBranch3MkVBalBranch124(zzz958, zzz959, zzz960, zzz961, zzz962, zzz963, zzz964, zzz965, zzz966, zzz967, zzz968, new_primPlusNat2(new_primPlusNat3(Succ(new_primPlusNat3(new_primPlusNat1(zzz960), zzz960)), Succ(zzz960)), Succ(zzz960)), ba)
new_mkVBalBranch3MkVBalBranch126(zzz3170, zzz3171, zzz317200, zzz3173, zzz3174, zzz330, zzz331, zzz333, zzz334, zzz31, Succ(zzz5350), h) → new_mkVBalBranch1(zzz31, zzz334, Branch(zzz3170, zzz3171, Neg(Succ(zzz317200)), zzz3173, zzz3174), h)
new_mkVBalBranch3MkVBalBranch241(zzz3170, zzz3171, Neg(Zero), zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, Succ(zzz4190), h) → new_mkVBalBranch1(zzz31, Branch(zzz330, zzz331, Neg(Succ(zzz33200)), zzz333, zzz334), zzz3173, h)
new_mkVBalBranch3MkVBalBranch123(zzz3170, zzz3171, zzz317200, zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, Zero, h) → new_mkVBalBranch3MkVBalBranch130(zzz3170, zzz3171, zzz317200, zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, h)
new_mkVBalBranch3MkVBalBranch124(zzz958, zzz959, zzz960, zzz961, zzz962, zzz963, zzz964, zzz965, zzz966, zzz967, zzz968, Succ(zzz10180), ba) → new_mkVBalBranch3MkVBalBranch125(zzz958, zzz959, zzz960, zzz961, zzz962, zzz963, zzz964, zzz965, zzz966, zzz967, zzz968, Succ(zzz10180), Succ(zzz965), ba)
new_mkVBalBranch1(zzz31, Branch(zzz330, zzz331, Neg(Zero), zzz333, zzz334), Branch(zzz3170, zzz3171, Neg(Succ(zzz317200)), zzz3173, zzz3174), h) → new_mkVBalBranch3MkVBalBranch127(zzz3170, zzz3171, zzz317200, zzz3173, zzz3174, zzz330, zzz331, zzz333, zzz334, zzz31, new_primPlusNat2(Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat3(new_primPlusNat1(zzz317200), zzz317200)), zzz317200))), Succ(zzz317200)), h)
new_mkVBalBranch3MkVBalBranch242(zzz972, zzz973, zzz974, zzz975, zzz976, zzz977, zzz978, zzz979, zzz980, zzz981, zzz982, Zero, Zero, bc) → new_mkVBalBranch3MkVBalBranch244(zzz972, zzz973, zzz974, zzz975, zzz976, zzz977, zzz978, zzz979, zzz980, zzz981, zzz982, bc)
new_mkVBalBranch3MkVBalBranch130(zzz3170, zzz3171, zzz317200, zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, h) → new_mkVBalBranch1(zzz31, zzz334, Branch(zzz3170, zzz3171, Neg(Succ(zzz317200)), zzz3173, zzz3174), h)
new_mkVBalBranch1(zzz31, Branch(zzz330, zzz331, Neg(Zero), zzz333, zzz334), Branch(zzz3170, zzz3171, Pos(Succ(zzz317200)), zzz3173, zzz3174), h) → new_mkVBalBranch1(zzz31, Branch(zzz330, zzz331, Neg(Zero), zzz333, zzz334), zzz3173, h)
new_mkVBalBranch3MkVBalBranch235(zzz3170, zzz3171, Neg(Zero), zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, Succ(zzz4170), h) → new_mkVBalBranch1(zzz31, zzz334, Branch(zzz3170, zzz3171, Neg(Zero), zzz3173, zzz3174), h)
new_mkVBalBranch3MkVBalBranch244(zzz972, zzz973, zzz974, zzz975, zzz976, zzz977, zzz978, zzz979, zzz980, zzz981, zzz982, bc) → new_mkVBalBranch3MkVBalBranch128(zzz972, zzz973, zzz974, zzz975, zzz976, zzz977, zzz978, zzz979, zzz980, zzz981, zzz982, new_primPlusNat2(new_primPlusNat3(Succ(new_primPlusNat3(new_primPlusNat1(zzz974), zzz974)), Succ(zzz974)), Succ(zzz974)), bc)
new_mkVBalBranch3MkVBalBranch236(zzz958, zzz959, zzz960, zzz961, zzz962, zzz963, zzz964, zzz965, zzz966, zzz967, zzz968, Zero, Zero, ba) → new_mkVBalBranch3MkVBalBranch240(zzz958, zzz959, zzz960, zzz961, zzz962, zzz963, zzz964, zzz965, zzz966, zzz967, zzz968, ba)

The TRS R consists of the following rules:

new_primPlusNat1(Zero) → Zero
new_primPlusNat1(Succ(zzz62000)) → Succ(Succ(new_primPlusNat1(zzz62000)))
new_primPlusNat3(zzz90, Succ(zzz910)) → Succ(Succ(new_primPlusNat2(zzz90, zzz910)))
new_primPlusNat3(zzz90, Zero) → Succ(zzz90)
new_primPlusNat2(Succ(zzz900), Succ(zzz9100)) → Succ(Succ(new_primPlusNat2(zzz900, zzz9100)))
new_primPlusNat2(Succ(zzz900), Zero) → Succ(zzz900)
new_primPlusNat2(Zero, Succ(zzz9100)) → Succ(zzz9100)
new_primPlusNat2(Zero, Zero) → Zero

The set Q consists of the following terms:

new_primPlusNat2(Zero, Succ(x0))
new_primPlusNat3(x0, Succ(x1))
new_primPlusNat2(Succ(x0), Succ(x1))
new_primPlusNat3(x0, Zero)
new_primPlusNat1(Zero)
new_primPlusNat2(Zero, Zero)
new_primPlusNat1(Succ(x0))
new_primPlusNat2(Succ(x0), Zero)

We have to consider all minimal (P,Q,R)-chains.
By rewriting [15] the rule new_mkVBalBranch3MkVBalBranch240(zzz958, zzz959, zzz960, zzz961, zzz962, zzz963, zzz964, zzz965, zzz966, zzz967, zzz968, ba) → new_mkVBalBranch3MkVBalBranch124(zzz958, zzz959, zzz960, zzz961, zzz962, zzz963, zzz964, zzz965, zzz966, zzz967, zzz968, new_primPlusNat2(new_primPlusNat3(Succ(new_primPlusNat3(new_primPlusNat1(zzz960), zzz960)), Succ(zzz960)), Succ(zzz960)), ba) at position [11,0] we obtained the following new rules:

new_mkVBalBranch3MkVBalBranch240(zzz958, zzz959, zzz960, zzz961, zzz962, zzz963, zzz964, zzz965, zzz966, zzz967, zzz968, ba) → new_mkVBalBranch3MkVBalBranch124(zzz958, zzz959, zzz960, zzz961, zzz962, zzz963, zzz964, zzz965, zzz966, zzz967, zzz968, new_primPlusNat2(Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat3(new_primPlusNat1(zzz960), zzz960)), zzz960))), Succ(zzz960)), 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
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                    ↳ DependencyGraphProof
                                      ↳ QDP
                                        ↳ Rewriting
                                          ↳ QDP
                                            ↳ Rewriting
                                              ↳ QDP
                                                ↳ Rewriting
                                                  ↳ QDP
                                                    ↳ Rewriting
                                                      ↳ QDP
                                                        ↳ Rewriting
                                                          ↳ QDP
                                                            ↳ Rewriting
                                                              ↳ QDP
                                                                ↳ Rewriting
                                                                  ↳ QDP
                                                                    ↳ Rewriting
                                                                      ↳ QDP
                                                                        ↳ Rewriting
                                                                          ↳ QDP
                                                                            ↳ Rewriting
                                                                              ↳ QDP
                                                                                ↳ UsableRulesProof
                                                                                  ↳ QDP
                                                                                    ↳ QReductionProof
                                                                                      ↳ QDP
                                                                                        ↳ Rewriting
                                                                                          ↳ QDP
                                                                                            ↳ Rewriting
                                                                                              ↳ QDP
                                                                                                ↳ Rewriting
                                                                                                  ↳ QDP
                                                                                                    ↳ Rewriting
                                                                                                      ↳ QDP
                                                                                                        ↳ Rewriting
                                                                                                          ↳ QDP
                                                                                                            ↳ Rewriting
                                                                                                              ↳ QDP
                                                                                                                ↳ Rewriting
                                                                                                                  ↳ QDP
                                                                                                                    ↳ Rewriting
                                                                                                                      ↳ QDP
                                                                                                                        ↳ Rewriting
                                                                                                                          ↳ QDP
                                                                                                                            ↳ Rewriting
                                                                                                                              ↳ QDP
                                                                                                                                ↳ UsableRulesProof
                                                                                                                                  ↳ QDP
                                                                                                                                    ↳ QReductionProof
                                                                                                                                      ↳ QDP
                                                                                                                                        ↳ Rewriting
                                                                                                                                          ↳ QDP
                                                                                                                                            ↳ Rewriting
                                                                                                                                              ↳ QDP
                                                                                                                                                ↳ Rewriting
                                                                                                                                                  ↳ QDP
                                                                                                                                                    ↳ DependencyGraphProof
                                                                                                                                                      ↳ QDP
                                                                                                                                                        ↳ Rewriting
                                                                                                                                                          ↳ QDP
                                                                                                                                                            ↳ Rewriting
                                                                                                                                                              ↳ QDP
                                                                                                                                                                ↳ DependencyGraphProof
                                                                                                                                                                  ↳ QDP
                                                                                                                                                                    ↳ Rewriting
                                                                                                                                                                      ↳ QDP
                                                                                                                                                                        ↳ Rewriting
                                                                                                                                                                          ↳ QDP
                                                                                                                                                                            ↳ Rewriting
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP

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

new_mkVBalBranch3MkVBalBranch129(zzz1851, zzz1852, zzz1853, zzz1854, zzz1855, zzz1856, zzz1857, zzz1858, zzz1859, zzz1860, zzz1861, Zero, Succ(zzz18630), bd) → new_mkVBalBranch1(zzz1861, zzz1860, Branch(zzz1851, zzz1852, Neg(Succ(zzz1853)), zzz1854, zzz1855), bd)
new_mkVBalBranch3MkVBalBranch127(zzz3170, zzz3171, zzz317200, zzz3173, zzz3174, zzz330, zzz331, zzz333, zzz334, zzz31, Succ(zzz5500), h) → new_mkVBalBranch1(zzz31, zzz334, Branch(zzz3170, zzz3171, Neg(Succ(zzz317200)), zzz3173, zzz3174), h)
new_mkVBalBranch3MkVBalBranch241(zzz3170, zzz3171, Pos(zzz31720), zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, Succ(zzz4190), h) → new_mkVBalBranch1(zzz31, Branch(zzz330, zzz331, Neg(Succ(zzz33200)), zzz333, zzz334), zzz3173, h)
new_mkVBalBranch3MkVBalBranch128(zzz972, zzz973, zzz974, zzz975, zzz976, zzz977, zzz978, zzz979, zzz980, zzz981, zzz982, Succ(zzz10190), bc) → new_mkVBalBranch3MkVBalBranch129(zzz972, zzz973, zzz974, zzz975, zzz976, zzz977, zzz978, zzz979, zzz980, zzz981, zzz982, Succ(zzz979), Succ(zzz10190), bc)
new_mkVBalBranch3MkVBalBranch242(zzz972, zzz973, zzz974, zzz975, zzz976, zzz977, zzz978, zzz979, zzz980, zzz981, zzz982, Succ(zzz9830), Zero, bc) → new_mkVBalBranch3MkVBalBranch128(zzz972, zzz973, zzz974, zzz975, zzz976, zzz977, zzz978, zzz979, zzz980, zzz981, zzz982, new_primPlusNat2(Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat3(new_primPlusNat1(zzz974), zzz974)), zzz974))), Succ(zzz974)), bc)
new_mkVBalBranch3MkVBalBranch129(zzz1851, zzz1852, zzz1853, zzz1854, zzz1855, zzz1856, zzz1857, zzz1858, zzz1859, zzz1860, zzz1861, Succ(zzz18620), Succ(zzz18630), bd) → new_mkVBalBranch3MkVBalBranch129(zzz1851, zzz1852, zzz1853, zzz1854, zzz1855, zzz1856, zzz1857, zzz1858, zzz1859, zzz1860, zzz1861, zzz18620, zzz18630, bd)
new_mkVBalBranch3MkVBalBranch124(zzz958, zzz959, zzz960, zzz961, zzz962, zzz963, zzz964, zzz965, zzz966, zzz967, zzz968, Zero, ba) → new_mkVBalBranch3MkVBalBranch125(zzz958, zzz959, zzz960, zzz961, zzz962, zzz963, zzz964, zzz965, zzz966, zzz967, zzz968, Zero, Succ(zzz965), ba)
new_mkVBalBranch3MkVBalBranch235(zzz3170, zzz3171, Pos(Succ(zzz317200)), zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, Succ(zzz4170), h) → new_mkVBalBranch3MkVBalBranch236(zzz3170, zzz3171, zzz317200, zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, zzz4170, zzz317200, h)
new_mkVBalBranch3MkVBalBranch242(zzz972, zzz973, zzz974, zzz975, zzz976, zzz977, zzz978, zzz979, zzz980, zzz981, zzz982, Succ(zzz9830), Succ(zzz9840), bc) → new_mkVBalBranch3MkVBalBranch242(zzz972, zzz973, zzz974, zzz975, zzz976, zzz977, zzz978, zzz979, zzz980, zzz981, zzz982, zzz9830, zzz9840, bc)
new_mkVBalBranch1(zzz31, Branch(zzz330, zzz331, Pos(Zero), zzz333, zzz334), Branch(zzz3170, zzz3171, Neg(Succ(zzz317200)), zzz3173, zzz3174), h) → new_mkVBalBranch3MkVBalBranch126(zzz3170, zzz3171, zzz317200, zzz3173, zzz3174, zzz330, zzz331, zzz333, zzz334, zzz31, new_primPlusNat2(Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat3(new_primPlusNat1(zzz317200), zzz317200)), zzz317200))), Succ(zzz317200)), h)
new_mkVBalBranch1(zzz31, Branch(zzz330, zzz331, Pos(Succ(zzz33200)), zzz333, zzz334), Branch(zzz3170, zzz3171, zzz3172, zzz3173, zzz3174), h) → new_mkVBalBranch3MkVBalBranch235(zzz3170, zzz3171, zzz3172, zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat2(Succ(new_primPlusNat3(new_primPlusNat1(zzz33200), zzz33200)), zzz33200)), zzz33200))), h)
new_mkVBalBranch1(zzz31, Branch(zzz330, zzz331, Neg(Succ(zzz33200)), zzz333, zzz334), Branch(zzz3170, zzz3171, zzz3172, zzz3173, zzz3174), h) → new_mkVBalBranch3MkVBalBranch241(zzz3170, zzz3171, zzz3172, zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat2(Succ(new_primPlusNat3(new_primPlusNat1(zzz33200), zzz33200)), zzz33200)), zzz33200))), h)
new_mkVBalBranch3MkVBalBranch236(zzz958, zzz959, zzz960, zzz961, zzz962, zzz963, zzz964, zzz965, zzz966, zzz967, zzz968, Succ(zzz9690), Succ(zzz9700), ba) → new_mkVBalBranch3MkVBalBranch236(zzz958, zzz959, zzz960, zzz961, zzz962, zzz963, zzz964, zzz965, zzz966, zzz967, zzz968, zzz9690, zzz9700, ba)
new_mkVBalBranch3MkVBalBranch241(zzz3170, zzz3171, Neg(Succ(zzz317200)), zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, Succ(zzz4190), h) → new_mkVBalBranch3MkVBalBranch242(zzz3170, zzz3171, zzz317200, zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, zzz317200, zzz4190, h)
new_mkVBalBranch1(zzz31, Branch(zzz330, zzz331, Pos(Zero), zzz333, zzz334), Branch(zzz3170, zzz3171, Pos(Succ(zzz317200)), zzz3173, zzz3174), h) → new_mkVBalBranch1(zzz31, Branch(zzz330, zzz331, Pos(Zero), zzz333, zzz334), zzz3173, h)
new_mkVBalBranch3MkVBalBranch235(zzz3170, zzz3171, Neg(Succ(zzz317200)), zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, Succ(zzz4170), h) → new_mkVBalBranch3MkVBalBranch123(zzz3170, zzz3171, zzz317200, zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, new_primPlusNat2(Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat3(new_primPlusNat1(zzz317200), zzz317200)), zzz317200))), Succ(zzz317200)), h)
new_mkVBalBranch3MkVBalBranch237(zzz3170, zzz3171, zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, h) → new_mkVBalBranch1(zzz31, zzz334, Branch(zzz3170, zzz3171, Pos(Zero), zzz3173, zzz3174), h)
new_mkVBalBranch3MkVBalBranch235(zzz3170, zzz3171, Pos(Zero), zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, Succ(zzz4170), h) → new_mkVBalBranch3MkVBalBranch237(zzz3170, zzz3171, zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, h)
new_mkVBalBranch3MkVBalBranch236(zzz958, zzz959, zzz960, zzz961, zzz962, zzz963, zzz964, zzz965, zzz966, zzz967, zzz968, Succ(zzz9690), Zero, ba) → new_mkVBalBranch3MkVBalBranch124(zzz958, zzz959, zzz960, zzz961, zzz962, zzz963, zzz964, zzz965, zzz966, zzz967, zzz968, new_primPlusNat2(Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat3(new_primPlusNat1(zzz960), zzz960)), zzz960))), Succ(zzz960)), ba)
new_mkVBalBranch3MkVBalBranch236(zzz958, zzz959, zzz960, zzz961, zzz962, zzz963, zzz964, zzz965, zzz966, zzz967, zzz968, Zero, Succ(zzz9700), ba) → new_mkVBalBranch1(zzz968, Branch(zzz963, zzz964, Pos(Succ(zzz965)), zzz966, zzz967), zzz961, ba)
new_mkVBalBranch3MkVBalBranch125(zzz1337, zzz1338, zzz1339, zzz1340, zzz1341, zzz1342, zzz1343, zzz1344, zzz1345, zzz1346, zzz1347, Succ(zzz13480), Succ(zzz13490), bb) → new_mkVBalBranch3MkVBalBranch125(zzz1337, zzz1338, zzz1339, zzz1340, zzz1341, zzz1342, zzz1343, zzz1344, zzz1345, zzz1346, zzz1347, zzz13480, zzz13490, bb)
new_mkVBalBranch3MkVBalBranch123(zzz3170, zzz3171, zzz317200, zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, Succ(zzz5620), h) → new_mkVBalBranch1(zzz31, zzz334, Branch(zzz3170, zzz3171, Neg(Succ(zzz317200)), zzz3173, zzz3174), h)
new_mkVBalBranch3MkVBalBranch125(zzz1337, zzz1338, zzz1339, zzz1340, zzz1341, zzz1342, zzz1343, zzz1344, zzz1345, zzz1346, zzz1347, Zero, Succ(zzz13490), bb) → new_mkVBalBranch1(zzz1347, zzz1346, Branch(zzz1337, zzz1338, Pos(Succ(zzz1339)), zzz1340, zzz1341), bb)
new_mkVBalBranch3MkVBalBranch242(zzz972, zzz973, zzz974, zzz975, zzz976, zzz977, zzz978, zzz979, zzz980, zzz981, zzz982, Zero, Succ(zzz9840), bc) → new_mkVBalBranch1(zzz982, Branch(zzz977, zzz978, Neg(Succ(zzz979)), zzz980, zzz981), zzz975, bc)
new_mkVBalBranch3MkVBalBranch240(zzz958, zzz959, zzz960, zzz961, zzz962, zzz963, zzz964, zzz965, zzz966, zzz967, zzz968, ba) → new_mkVBalBranch3MkVBalBranch124(zzz958, zzz959, zzz960, zzz961, zzz962, zzz963, zzz964, zzz965, zzz966, zzz967, zzz968, new_primPlusNat2(Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat3(new_primPlusNat1(zzz960), zzz960)), zzz960))), Succ(zzz960)), ba)
new_mkVBalBranch3MkVBalBranch126(zzz3170, zzz3171, zzz317200, zzz3173, zzz3174, zzz330, zzz331, zzz333, zzz334, zzz31, Succ(zzz5350), h) → new_mkVBalBranch1(zzz31, zzz334, Branch(zzz3170, zzz3171, Neg(Succ(zzz317200)), zzz3173, zzz3174), h)
new_mkVBalBranch3MkVBalBranch123(zzz3170, zzz3171, zzz317200, zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, Zero, h) → new_mkVBalBranch3MkVBalBranch130(zzz3170, zzz3171, zzz317200, zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, h)
new_mkVBalBranch3MkVBalBranch241(zzz3170, zzz3171, Neg(Zero), zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, Succ(zzz4190), h) → new_mkVBalBranch1(zzz31, Branch(zzz330, zzz331, Neg(Succ(zzz33200)), zzz333, zzz334), zzz3173, h)
new_mkVBalBranch3MkVBalBranch124(zzz958, zzz959, zzz960, zzz961, zzz962, zzz963, zzz964, zzz965, zzz966, zzz967, zzz968, Succ(zzz10180), ba) → new_mkVBalBranch3MkVBalBranch125(zzz958, zzz959, zzz960, zzz961, zzz962, zzz963, zzz964, zzz965, zzz966, zzz967, zzz968, Succ(zzz10180), Succ(zzz965), ba)
new_mkVBalBranch1(zzz31, Branch(zzz330, zzz331, Neg(Zero), zzz333, zzz334), Branch(zzz3170, zzz3171, Neg(Succ(zzz317200)), zzz3173, zzz3174), h) → new_mkVBalBranch3MkVBalBranch127(zzz3170, zzz3171, zzz317200, zzz3173, zzz3174, zzz330, zzz331, zzz333, zzz334, zzz31, new_primPlusNat2(Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat3(new_primPlusNat1(zzz317200), zzz317200)), zzz317200))), Succ(zzz317200)), h)
new_mkVBalBranch3MkVBalBranch242(zzz972, zzz973, zzz974, zzz975, zzz976, zzz977, zzz978, zzz979, zzz980, zzz981, zzz982, Zero, Zero, bc) → new_mkVBalBranch3MkVBalBranch244(zzz972, zzz973, zzz974, zzz975, zzz976, zzz977, zzz978, zzz979, zzz980, zzz981, zzz982, bc)
new_mkVBalBranch3MkVBalBranch130(zzz3170, zzz3171, zzz317200, zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, h) → new_mkVBalBranch1(zzz31, zzz334, Branch(zzz3170, zzz3171, Neg(Succ(zzz317200)), zzz3173, zzz3174), h)
new_mkVBalBranch1(zzz31, Branch(zzz330, zzz331, Neg(Zero), zzz333, zzz334), Branch(zzz3170, zzz3171, Pos(Succ(zzz317200)), zzz3173, zzz3174), h) → new_mkVBalBranch1(zzz31, Branch(zzz330, zzz331, Neg(Zero), zzz333, zzz334), zzz3173, h)
new_mkVBalBranch3MkVBalBranch235(zzz3170, zzz3171, Neg(Zero), zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, Succ(zzz4170), h) → new_mkVBalBranch1(zzz31, zzz334, Branch(zzz3170, zzz3171, Neg(Zero), zzz3173, zzz3174), h)
new_mkVBalBranch3MkVBalBranch236(zzz958, zzz959, zzz960, zzz961, zzz962, zzz963, zzz964, zzz965, zzz966, zzz967, zzz968, Zero, Zero, ba) → new_mkVBalBranch3MkVBalBranch240(zzz958, zzz959, zzz960, zzz961, zzz962, zzz963, zzz964, zzz965, zzz966, zzz967, zzz968, ba)
new_mkVBalBranch3MkVBalBranch244(zzz972, zzz973, zzz974, zzz975, zzz976, zzz977, zzz978, zzz979, zzz980, zzz981, zzz982, bc) → new_mkVBalBranch3MkVBalBranch128(zzz972, zzz973, zzz974, zzz975, zzz976, zzz977, zzz978, zzz979, zzz980, zzz981, zzz982, new_primPlusNat2(new_primPlusNat3(Succ(new_primPlusNat3(new_primPlusNat1(zzz974), zzz974)), Succ(zzz974)), Succ(zzz974)), bc)

The TRS R consists of the following rules:

new_primPlusNat1(Zero) → Zero
new_primPlusNat1(Succ(zzz62000)) → Succ(Succ(new_primPlusNat1(zzz62000)))
new_primPlusNat3(zzz90, Succ(zzz910)) → Succ(Succ(new_primPlusNat2(zzz90, zzz910)))
new_primPlusNat3(zzz90, Zero) → Succ(zzz90)
new_primPlusNat2(Succ(zzz900), Succ(zzz9100)) → Succ(Succ(new_primPlusNat2(zzz900, zzz9100)))
new_primPlusNat2(Succ(zzz900), Zero) → Succ(zzz900)
new_primPlusNat2(Zero, Succ(zzz9100)) → Succ(zzz9100)
new_primPlusNat2(Zero, Zero) → Zero

The set Q consists of the following terms:

new_primPlusNat2(Zero, Succ(x0))
new_primPlusNat3(x0, Succ(x1))
new_primPlusNat2(Succ(x0), Succ(x1))
new_primPlusNat3(x0, Zero)
new_primPlusNat1(Zero)
new_primPlusNat2(Zero, Zero)
new_primPlusNat1(Succ(x0))
new_primPlusNat2(Succ(x0), Zero)

We have to consider all minimal (P,Q,R)-chains.
By rewriting [15] the rule new_mkVBalBranch1(zzz31, Branch(zzz330, zzz331, Neg(Zero), zzz333, zzz334), Branch(zzz3170, zzz3171, Neg(Succ(zzz317200)), zzz3173, zzz3174), h) → new_mkVBalBranch3MkVBalBranch127(zzz3170, zzz3171, zzz317200, zzz3173, zzz3174, zzz330, zzz331, zzz333, zzz334, zzz31, new_primPlusNat2(Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat3(new_primPlusNat1(zzz317200), zzz317200)), zzz317200))), Succ(zzz317200)), h) at position [10] we obtained the following new rules:

new_mkVBalBranch1(zzz31, Branch(zzz330, zzz331, Neg(Zero), zzz333, zzz334), Branch(zzz3170, zzz3171, Neg(Succ(zzz317200)), zzz3173, zzz3174), h) → new_mkVBalBranch3MkVBalBranch127(zzz3170, zzz3171, zzz317200, zzz3173, zzz3174, zzz330, zzz331, zzz333, zzz334, zzz31, Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat2(Succ(new_primPlusNat3(new_primPlusNat1(zzz317200), zzz317200)), zzz317200)), zzz317200))), 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
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                    ↳ DependencyGraphProof
                                      ↳ QDP
                                        ↳ Rewriting
                                          ↳ QDP
                                            ↳ Rewriting
                                              ↳ QDP
                                                ↳ Rewriting
                                                  ↳ QDP
                                                    ↳ Rewriting
                                                      ↳ QDP
                                                        ↳ Rewriting
                                                          ↳ QDP
                                                            ↳ Rewriting
                                                              ↳ QDP
                                                                ↳ Rewriting
                                                                  ↳ QDP
                                                                    ↳ Rewriting
                                                                      ↳ QDP
                                                                        ↳ Rewriting
                                                                          ↳ QDP
                                                                            ↳ Rewriting
                                                                              ↳ QDP
                                                                                ↳ UsableRulesProof
                                                                                  ↳ QDP
                                                                                    ↳ QReductionProof
                                                                                      ↳ QDP
                                                                                        ↳ Rewriting
                                                                                          ↳ QDP
                                                                                            ↳ Rewriting
                                                                                              ↳ QDP
                                                                                                ↳ Rewriting
                                                                                                  ↳ QDP
                                                                                                    ↳ Rewriting
                                                                                                      ↳ QDP
                                                                                                        ↳ Rewriting
                                                                                                          ↳ QDP
                                                                                                            ↳ Rewriting
                                                                                                              ↳ QDP
                                                                                                                ↳ Rewriting
                                                                                                                  ↳ QDP
                                                                                                                    ↳ Rewriting
                                                                                                                      ↳ QDP
                                                                                                                        ↳ Rewriting
                                                                                                                          ↳ QDP
                                                                                                                            ↳ Rewriting
                                                                                                                              ↳ QDP
                                                                                                                                ↳ UsableRulesProof
                                                                                                                                  ↳ QDP
                                                                                                                                    ↳ QReductionProof
                                                                                                                                      ↳ QDP
                                                                                                                                        ↳ Rewriting
                                                                                                                                          ↳ QDP
                                                                                                                                            ↳ Rewriting
                                                                                                                                              ↳ QDP
                                                                                                                                                ↳ Rewriting
                                                                                                                                                  ↳ QDP
                                                                                                                                                    ↳ DependencyGraphProof
                                                                                                                                                      ↳ QDP
                                                                                                                                                        ↳ Rewriting
                                                                                                                                                          ↳ QDP
                                                                                                                                                            ↳ Rewriting
                                                                                                                                                              ↳ QDP
                                                                                                                                                                ↳ DependencyGraphProof
                                                                                                                                                                  ↳ QDP
                                                                                                                                                                    ↳ Rewriting
                                                                                                                                                                      ↳ QDP
                                                                                                                                                                        ↳ Rewriting
                                                                                                                                                                          ↳ QDP
                                                                                                                                                                            ↳ Rewriting
                                                                                                                                                                              ↳ QDP
                                                                                                                                                                                ↳ Rewriting
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP

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

new_mkVBalBranch3MkVBalBranch129(zzz1851, zzz1852, zzz1853, zzz1854, zzz1855, zzz1856, zzz1857, zzz1858, zzz1859, zzz1860, zzz1861, Zero, Succ(zzz18630), bd) → new_mkVBalBranch1(zzz1861, zzz1860, Branch(zzz1851, zzz1852, Neg(Succ(zzz1853)), zzz1854, zzz1855), bd)
new_mkVBalBranch3MkVBalBranch128(zzz972, zzz973, zzz974, zzz975, zzz976, zzz977, zzz978, zzz979, zzz980, zzz981, zzz982, Succ(zzz10190), bc) → new_mkVBalBranch3MkVBalBranch129(zzz972, zzz973, zzz974, zzz975, zzz976, zzz977, zzz978, zzz979, zzz980, zzz981, zzz982, Succ(zzz979), Succ(zzz10190), bc)
new_mkVBalBranch3MkVBalBranch241(zzz3170, zzz3171, Pos(zzz31720), zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, Succ(zzz4190), h) → new_mkVBalBranch1(zzz31, Branch(zzz330, zzz331, Neg(Succ(zzz33200)), zzz333, zzz334), zzz3173, h)
new_mkVBalBranch3MkVBalBranch127(zzz3170, zzz3171, zzz317200, zzz3173, zzz3174, zzz330, zzz331, zzz333, zzz334, zzz31, Succ(zzz5500), h) → new_mkVBalBranch1(zzz31, zzz334, Branch(zzz3170, zzz3171, Neg(Succ(zzz317200)), zzz3173, zzz3174), h)
new_mkVBalBranch1(zzz31, Branch(zzz330, zzz331, Neg(Zero), zzz333, zzz334), Branch(zzz3170, zzz3171, Neg(Succ(zzz317200)), zzz3173, zzz3174), h) → new_mkVBalBranch3MkVBalBranch127(zzz3170, zzz3171, zzz317200, zzz3173, zzz3174, zzz330, zzz331, zzz333, zzz334, zzz31, Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat2(Succ(new_primPlusNat3(new_primPlusNat1(zzz317200), zzz317200)), zzz317200)), zzz317200))), h)
new_mkVBalBranch3MkVBalBranch242(zzz972, zzz973, zzz974, zzz975, zzz976, zzz977, zzz978, zzz979, zzz980, zzz981, zzz982, Succ(zzz9830), Zero, bc) → new_mkVBalBranch3MkVBalBranch128(zzz972, zzz973, zzz974, zzz975, zzz976, zzz977, zzz978, zzz979, zzz980, zzz981, zzz982, new_primPlusNat2(Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat3(new_primPlusNat1(zzz974), zzz974)), zzz974))), Succ(zzz974)), bc)
new_mkVBalBranch3MkVBalBranch129(zzz1851, zzz1852, zzz1853, zzz1854, zzz1855, zzz1856, zzz1857, zzz1858, zzz1859, zzz1860, zzz1861, Succ(zzz18620), Succ(zzz18630), bd) → new_mkVBalBranch3MkVBalBranch129(zzz1851, zzz1852, zzz1853, zzz1854, zzz1855, zzz1856, zzz1857, zzz1858, zzz1859, zzz1860, zzz1861, zzz18620, zzz18630, bd)
new_mkVBalBranch3MkVBalBranch124(zzz958, zzz959, zzz960, zzz961, zzz962, zzz963, zzz964, zzz965, zzz966, zzz967, zzz968, Zero, ba) → new_mkVBalBranch3MkVBalBranch125(zzz958, zzz959, zzz960, zzz961, zzz962, zzz963, zzz964, zzz965, zzz966, zzz967, zzz968, Zero, Succ(zzz965), ba)
new_mkVBalBranch1(zzz31, Branch(zzz330, zzz331, Pos(Zero), zzz333, zzz334), Branch(zzz3170, zzz3171, Neg(Succ(zzz317200)), zzz3173, zzz3174), h) → new_mkVBalBranch3MkVBalBranch126(zzz3170, zzz3171, zzz317200, zzz3173, zzz3174, zzz330, zzz331, zzz333, zzz334, zzz31, new_primPlusNat2(Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat3(new_primPlusNat1(zzz317200), zzz317200)), zzz317200))), Succ(zzz317200)), h)
new_mkVBalBranch3MkVBalBranch242(zzz972, zzz973, zzz974, zzz975, zzz976, zzz977, zzz978, zzz979, zzz980, zzz981, zzz982, Succ(zzz9830), Succ(zzz9840), bc) → new_mkVBalBranch3MkVBalBranch242(zzz972, zzz973, zzz974, zzz975, zzz976, zzz977, zzz978, zzz979, zzz980, zzz981, zzz982, zzz9830, zzz9840, bc)
new_mkVBalBranch3MkVBalBranch235(zzz3170, zzz3171, Pos(Succ(zzz317200)), zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, Succ(zzz4170), h) → new_mkVBalBranch3MkVBalBranch236(zzz3170, zzz3171, zzz317200, zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, zzz4170, zzz317200, h)
new_mkVBalBranch1(zzz31, Branch(zzz330, zzz331, Neg(Succ(zzz33200)), zzz333, zzz334), Branch(zzz3170, zzz3171, zzz3172, zzz3173, zzz3174), h) → new_mkVBalBranch3MkVBalBranch241(zzz3170, zzz3171, zzz3172, zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat2(Succ(new_primPlusNat3(new_primPlusNat1(zzz33200), zzz33200)), zzz33200)), zzz33200))), h)
new_mkVBalBranch1(zzz31, Branch(zzz330, zzz331, Pos(Succ(zzz33200)), zzz333, zzz334), Branch(zzz3170, zzz3171, zzz3172, zzz3173, zzz3174), h) → new_mkVBalBranch3MkVBalBranch235(zzz3170, zzz3171, zzz3172, zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat2(Succ(new_primPlusNat3(new_primPlusNat1(zzz33200), zzz33200)), zzz33200)), zzz33200))), h)
new_mkVBalBranch3MkVBalBranch236(zzz958, zzz959, zzz960, zzz961, zzz962, zzz963, zzz964, zzz965, zzz966, zzz967, zzz968, Succ(zzz9690), Succ(zzz9700), ba) → new_mkVBalBranch3MkVBalBranch236(zzz958, zzz959, zzz960, zzz961, zzz962, zzz963, zzz964, zzz965, zzz966, zzz967, zzz968, zzz9690, zzz9700, ba)
new_mkVBalBranch3MkVBalBranch241(zzz3170, zzz3171, Neg(Succ(zzz317200)), zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, Succ(zzz4190), h) → new_mkVBalBranch3MkVBalBranch242(zzz3170, zzz3171, zzz317200, zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, zzz317200, zzz4190, h)
new_mkVBalBranch1(zzz31, Branch(zzz330, zzz331, Pos(Zero), zzz333, zzz334), Branch(zzz3170, zzz3171, Pos(Succ(zzz317200)), zzz3173, zzz3174), h) → new_mkVBalBranch1(zzz31, Branch(zzz330, zzz331, Pos(Zero), zzz333, zzz334), zzz3173, h)
new_mkVBalBranch3MkVBalBranch237(zzz3170, zzz3171, zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, h) → new_mkVBalBranch1(zzz31, zzz334, Branch(zzz3170, zzz3171, Pos(Zero), zzz3173, zzz3174), h)
new_mkVBalBranch3MkVBalBranch235(zzz3170, zzz3171, Neg(Succ(zzz317200)), zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, Succ(zzz4170), h) → new_mkVBalBranch3MkVBalBranch123(zzz3170, zzz3171, zzz317200, zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, new_primPlusNat2(Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat3(new_primPlusNat1(zzz317200), zzz317200)), zzz317200))), Succ(zzz317200)), h)
new_mkVBalBranch3MkVBalBranch235(zzz3170, zzz3171, Pos(Zero), zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, Succ(zzz4170), h) → new_mkVBalBranch3MkVBalBranch237(zzz3170, zzz3171, zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, h)
new_mkVBalBranch3MkVBalBranch236(zzz958, zzz959, zzz960, zzz961, zzz962, zzz963, zzz964, zzz965, zzz966, zzz967, zzz968, Succ(zzz9690), Zero, ba) → new_mkVBalBranch3MkVBalBranch124(zzz958, zzz959, zzz960, zzz961, zzz962, zzz963, zzz964, zzz965, zzz966, zzz967, zzz968, new_primPlusNat2(Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat3(new_primPlusNat1(zzz960), zzz960)), zzz960))), Succ(zzz960)), ba)
new_mkVBalBranch3MkVBalBranch236(zzz958, zzz959, zzz960, zzz961, zzz962, zzz963, zzz964, zzz965, zzz966, zzz967, zzz968, Zero, Succ(zzz9700), ba) → new_mkVBalBranch1(zzz968, Branch(zzz963, zzz964, Pos(Succ(zzz965)), zzz966, zzz967), zzz961, ba)
new_mkVBalBranch3MkVBalBranch125(zzz1337, zzz1338, zzz1339, zzz1340, zzz1341, zzz1342, zzz1343, zzz1344, zzz1345, zzz1346, zzz1347, Succ(zzz13480), Succ(zzz13490), bb) → new_mkVBalBranch3MkVBalBranch125(zzz1337, zzz1338, zzz1339, zzz1340, zzz1341, zzz1342, zzz1343, zzz1344, zzz1345, zzz1346, zzz1347, zzz13480, zzz13490, bb)
new_mkVBalBranch3MkVBalBranch123(zzz3170, zzz3171, zzz317200, zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, Succ(zzz5620), h) → new_mkVBalBranch1(zzz31, zzz334, Branch(zzz3170, zzz3171, Neg(Succ(zzz317200)), zzz3173, zzz3174), h)
new_mkVBalBranch3MkVBalBranch125(zzz1337, zzz1338, zzz1339, zzz1340, zzz1341, zzz1342, zzz1343, zzz1344, zzz1345, zzz1346, zzz1347, Zero, Succ(zzz13490), bb) → new_mkVBalBranch1(zzz1347, zzz1346, Branch(zzz1337, zzz1338, Pos(Succ(zzz1339)), zzz1340, zzz1341), bb)
new_mkVBalBranch3MkVBalBranch242(zzz972, zzz973, zzz974, zzz975, zzz976, zzz977, zzz978, zzz979, zzz980, zzz981, zzz982, Zero, Succ(zzz9840), bc) → new_mkVBalBranch1(zzz982, Branch(zzz977, zzz978, Neg(Succ(zzz979)), zzz980, zzz981), zzz975, bc)
new_mkVBalBranch3MkVBalBranch240(zzz958, zzz959, zzz960, zzz961, zzz962, zzz963, zzz964, zzz965, zzz966, zzz967, zzz968, ba) → new_mkVBalBranch3MkVBalBranch124(zzz958, zzz959, zzz960, zzz961, zzz962, zzz963, zzz964, zzz965, zzz966, zzz967, zzz968, new_primPlusNat2(Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat3(new_primPlusNat1(zzz960), zzz960)), zzz960))), Succ(zzz960)), ba)
new_mkVBalBranch3MkVBalBranch126(zzz3170, zzz3171, zzz317200, zzz3173, zzz3174, zzz330, zzz331, zzz333, zzz334, zzz31, Succ(zzz5350), h) → new_mkVBalBranch1(zzz31, zzz334, Branch(zzz3170, zzz3171, Neg(Succ(zzz317200)), zzz3173, zzz3174), h)
new_mkVBalBranch3MkVBalBranch241(zzz3170, zzz3171, Neg(Zero), zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, Succ(zzz4190), h) → new_mkVBalBranch1(zzz31, Branch(zzz330, zzz331, Neg(Succ(zzz33200)), zzz333, zzz334), zzz3173, h)
new_mkVBalBranch3MkVBalBranch123(zzz3170, zzz3171, zzz317200, zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, Zero, h) → new_mkVBalBranch3MkVBalBranch130(zzz3170, zzz3171, zzz317200, zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, h)
new_mkVBalBranch3MkVBalBranch124(zzz958, zzz959, zzz960, zzz961, zzz962, zzz963, zzz964, zzz965, zzz966, zzz967, zzz968, Succ(zzz10180), ba) → new_mkVBalBranch3MkVBalBranch125(zzz958, zzz959, zzz960, zzz961, zzz962, zzz963, zzz964, zzz965, zzz966, zzz967, zzz968, Succ(zzz10180), Succ(zzz965), ba)
new_mkVBalBranch3MkVBalBranch242(zzz972, zzz973, zzz974, zzz975, zzz976, zzz977, zzz978, zzz979, zzz980, zzz981, zzz982, Zero, Zero, bc) → new_mkVBalBranch3MkVBalBranch244(zzz972, zzz973, zzz974, zzz975, zzz976, zzz977, zzz978, zzz979, zzz980, zzz981, zzz982, bc)
new_mkVBalBranch3MkVBalBranch130(zzz3170, zzz3171, zzz317200, zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, h) → new_mkVBalBranch1(zzz31, zzz334, Branch(zzz3170, zzz3171, Neg(Succ(zzz317200)), zzz3173, zzz3174), h)
new_mkVBalBranch1(zzz31, Branch(zzz330, zzz331, Neg(Zero), zzz333, zzz334), Branch(zzz3170, zzz3171, Pos(Succ(zzz317200)), zzz3173, zzz3174), h) → new_mkVBalBranch1(zzz31, Branch(zzz330, zzz331, Neg(Zero), zzz333, zzz334), zzz3173, h)
new_mkVBalBranch3MkVBalBranch235(zzz3170, zzz3171, Neg(Zero), zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, Succ(zzz4170), h) → new_mkVBalBranch1(zzz31, zzz334, Branch(zzz3170, zzz3171, Neg(Zero), zzz3173, zzz3174), h)
new_mkVBalBranch3MkVBalBranch244(zzz972, zzz973, zzz974, zzz975, zzz976, zzz977, zzz978, zzz979, zzz980, zzz981, zzz982, bc) → new_mkVBalBranch3MkVBalBranch128(zzz972, zzz973, zzz974, zzz975, zzz976, zzz977, zzz978, zzz979, zzz980, zzz981, zzz982, new_primPlusNat2(new_primPlusNat3(Succ(new_primPlusNat3(new_primPlusNat1(zzz974), zzz974)), Succ(zzz974)), Succ(zzz974)), bc)
new_mkVBalBranch3MkVBalBranch236(zzz958, zzz959, zzz960, zzz961, zzz962, zzz963, zzz964, zzz965, zzz966, zzz967, zzz968, Zero, Zero, ba) → new_mkVBalBranch3MkVBalBranch240(zzz958, zzz959, zzz960, zzz961, zzz962, zzz963, zzz964, zzz965, zzz966, zzz967, zzz968, ba)

The TRS R consists of the following rules:

new_primPlusNat1(Zero) → Zero
new_primPlusNat1(Succ(zzz62000)) → Succ(Succ(new_primPlusNat1(zzz62000)))
new_primPlusNat3(zzz90, Succ(zzz910)) → Succ(Succ(new_primPlusNat2(zzz90, zzz910)))
new_primPlusNat3(zzz90, Zero) → Succ(zzz90)
new_primPlusNat2(Succ(zzz900), Succ(zzz9100)) → Succ(Succ(new_primPlusNat2(zzz900, zzz9100)))
new_primPlusNat2(Succ(zzz900), Zero) → Succ(zzz900)
new_primPlusNat2(Zero, Succ(zzz9100)) → Succ(zzz9100)
new_primPlusNat2(Zero, Zero) → Zero

The set Q consists of the following terms:

new_primPlusNat2(Zero, Succ(x0))
new_primPlusNat3(x0, Succ(x1))
new_primPlusNat2(Succ(x0), Succ(x1))
new_primPlusNat3(x0, Zero)
new_primPlusNat1(Zero)
new_primPlusNat2(Zero, Zero)
new_primPlusNat1(Succ(x0))
new_primPlusNat2(Succ(x0), Zero)

We have to consider all minimal (P,Q,R)-chains.
By rewriting [15] the rule new_mkVBalBranch3MkVBalBranch244(zzz972, zzz973, zzz974, zzz975, zzz976, zzz977, zzz978, zzz979, zzz980, zzz981, zzz982, bc) → new_mkVBalBranch3MkVBalBranch128(zzz972, zzz973, zzz974, zzz975, zzz976, zzz977, zzz978, zzz979, zzz980, zzz981, zzz982, new_primPlusNat2(new_primPlusNat3(Succ(new_primPlusNat3(new_primPlusNat1(zzz974), zzz974)), Succ(zzz974)), Succ(zzz974)), bc) at position [11,0] we obtained the following new rules:

new_mkVBalBranch3MkVBalBranch244(zzz972, zzz973, zzz974, zzz975, zzz976, zzz977, zzz978, zzz979, zzz980, zzz981, zzz982, bc) → new_mkVBalBranch3MkVBalBranch128(zzz972, zzz973, zzz974, zzz975, zzz976, zzz977, zzz978, zzz979, zzz980, zzz981, zzz982, new_primPlusNat2(Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat3(new_primPlusNat1(zzz974), zzz974)), zzz974))), Succ(zzz974)), bc)



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

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

new_mkVBalBranch3MkVBalBranch129(zzz1851, zzz1852, zzz1853, zzz1854, zzz1855, zzz1856, zzz1857, zzz1858, zzz1859, zzz1860, zzz1861, Zero, Succ(zzz18630), bd) → new_mkVBalBranch1(zzz1861, zzz1860, Branch(zzz1851, zzz1852, Neg(Succ(zzz1853)), zzz1854, zzz1855), bd)
new_mkVBalBranch3MkVBalBranch127(zzz3170, zzz3171, zzz317200, zzz3173, zzz3174, zzz330, zzz331, zzz333, zzz334, zzz31, Succ(zzz5500), h) → new_mkVBalBranch1(zzz31, zzz334, Branch(zzz3170, zzz3171, Neg(Succ(zzz317200)), zzz3173, zzz3174), h)
new_mkVBalBranch3MkVBalBranch241(zzz3170, zzz3171, Pos(zzz31720), zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, Succ(zzz4190), h) → new_mkVBalBranch1(zzz31, Branch(zzz330, zzz331, Neg(Succ(zzz33200)), zzz333, zzz334), zzz3173, h)
new_mkVBalBranch3MkVBalBranch128(zzz972, zzz973, zzz974, zzz975, zzz976, zzz977, zzz978, zzz979, zzz980, zzz981, zzz982, Succ(zzz10190), bc) → new_mkVBalBranch3MkVBalBranch129(zzz972, zzz973, zzz974, zzz975, zzz976, zzz977, zzz978, zzz979, zzz980, zzz981, zzz982, Succ(zzz979), Succ(zzz10190), bc)
new_mkVBalBranch1(zzz31, Branch(zzz330, zzz331, Neg(Zero), zzz333, zzz334), Branch(zzz3170, zzz3171, Neg(Succ(zzz317200)), zzz3173, zzz3174), h) → new_mkVBalBranch3MkVBalBranch127(zzz3170, zzz3171, zzz317200, zzz3173, zzz3174, zzz330, zzz331, zzz333, zzz334, zzz31, Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat2(Succ(new_primPlusNat3(new_primPlusNat1(zzz317200), zzz317200)), zzz317200)), zzz317200))), h)
new_mkVBalBranch3MkVBalBranch242(zzz972, zzz973, zzz974, zzz975, zzz976, zzz977, zzz978, zzz979, zzz980, zzz981, zzz982, Succ(zzz9830), Zero, bc) → new_mkVBalBranch3MkVBalBranch128(zzz972, zzz973, zzz974, zzz975, zzz976, zzz977, zzz978, zzz979, zzz980, zzz981, zzz982, new_primPlusNat2(Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat3(new_primPlusNat1(zzz974), zzz974)), zzz974))), Succ(zzz974)), bc)
new_mkVBalBranch3MkVBalBranch129(zzz1851, zzz1852, zzz1853, zzz1854, zzz1855, zzz1856, zzz1857, zzz1858, zzz1859, zzz1860, zzz1861, Succ(zzz18620), Succ(zzz18630), bd) → new_mkVBalBranch3MkVBalBranch129(zzz1851, zzz1852, zzz1853, zzz1854, zzz1855, zzz1856, zzz1857, zzz1858, zzz1859, zzz1860, zzz1861, zzz18620, zzz18630, bd)
new_mkVBalBranch3MkVBalBranch124(zzz958, zzz959, zzz960, zzz961, zzz962, zzz963, zzz964, zzz965, zzz966, zzz967, zzz968, Zero, ba) → new_mkVBalBranch3MkVBalBranch125(zzz958, zzz959, zzz960, zzz961, zzz962, zzz963, zzz964, zzz965, zzz966, zzz967, zzz968, Zero, Succ(zzz965), ba)
new_mkVBalBranch3MkVBalBranch235(zzz3170, zzz3171, Pos(Succ(zzz317200)), zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, Succ(zzz4170), h) → new_mkVBalBranch3MkVBalBranch236(zzz3170, zzz3171, zzz317200, zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, zzz4170, zzz317200, h)
new_mkVBalBranch3MkVBalBranch242(zzz972, zzz973, zzz974, zzz975, zzz976, zzz977, zzz978, zzz979, zzz980, zzz981, zzz982, Succ(zzz9830), Succ(zzz9840), bc) → new_mkVBalBranch3MkVBalBranch242(zzz972, zzz973, zzz974, zzz975, zzz976, zzz977, zzz978, zzz979, zzz980, zzz981, zzz982, zzz9830, zzz9840, bc)
new_mkVBalBranch1(zzz31, Branch(zzz330, zzz331, Pos(Zero), zzz333, zzz334), Branch(zzz3170, zzz3171, Neg(Succ(zzz317200)), zzz3173, zzz3174), h) → new_mkVBalBranch3MkVBalBranch126(zzz3170, zzz3171, zzz317200, zzz3173, zzz3174, zzz330, zzz331, zzz333, zzz334, zzz31, new_primPlusNat2(Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat3(new_primPlusNat1(zzz317200), zzz317200)), zzz317200))), Succ(zzz317200)), h)
new_mkVBalBranch1(zzz31, Branch(zzz330, zzz331, Pos(Succ(zzz33200)), zzz333, zzz334), Branch(zzz3170, zzz3171, zzz3172, zzz3173, zzz3174), h) → new_mkVBalBranch3MkVBalBranch235(zzz3170, zzz3171, zzz3172, zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat2(Succ(new_primPlusNat3(new_primPlusNat1(zzz33200), zzz33200)), zzz33200)), zzz33200))), h)
new_mkVBalBranch1(zzz31, Branch(zzz330, zzz331, Neg(Succ(zzz33200)), zzz333, zzz334), Branch(zzz3170, zzz3171, zzz3172, zzz3173, zzz3174), h) → new_mkVBalBranch3MkVBalBranch241(zzz3170, zzz3171, zzz3172, zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat2(Succ(new_primPlusNat3(new_primPlusNat1(zzz33200), zzz33200)), zzz33200)), zzz33200))), h)
new_mkVBalBranch3MkVBalBranch236(zzz958, zzz959, zzz960, zzz961, zzz962, zzz963, zzz964, zzz965, zzz966, zzz967, zzz968, Succ(zzz9690), Succ(zzz9700), ba) → new_mkVBalBranch3MkVBalBranch236(zzz958, zzz959, zzz960, zzz961, zzz962, zzz963, zzz964, zzz965, zzz966, zzz967, zzz968, zzz9690, zzz9700, ba)
new_mkVBalBranch3MkVBalBranch241(zzz3170, zzz3171, Neg(Succ(zzz317200)), zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, Succ(zzz4190), h) → new_mkVBalBranch3MkVBalBranch242(zzz3170, zzz3171, zzz317200, zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, zzz317200, zzz4190, h)
new_mkVBalBranch1(zzz31, Branch(zzz330, zzz331, Pos(Zero), zzz333, zzz334), Branch(zzz3170, zzz3171, Pos(Succ(zzz317200)), zzz3173, zzz3174), h) → new_mkVBalBranch1(zzz31, Branch(zzz330, zzz331, Pos(Zero), zzz333, zzz334), zzz3173, h)
new_mkVBalBranch3MkVBalBranch235(zzz3170, zzz3171, Neg(Succ(zzz317200)), zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, Succ(zzz4170), h) → new_mkVBalBranch3MkVBalBranch123(zzz3170, zzz3171, zzz317200, zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, new_primPlusNat2(Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat3(new_primPlusNat1(zzz317200), zzz317200)), zzz317200))), Succ(zzz317200)), h)
new_mkVBalBranch3MkVBalBranch237(zzz3170, zzz3171, zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, h) → new_mkVBalBranch1(zzz31, zzz334, Branch(zzz3170, zzz3171, Pos(Zero), zzz3173, zzz3174), h)
new_mkVBalBranch3MkVBalBranch235(zzz3170, zzz3171, Pos(Zero), zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, Succ(zzz4170), h) → new_mkVBalBranch3MkVBalBranch237(zzz3170, zzz3171, zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, h)
new_mkVBalBranch3MkVBalBranch236(zzz958, zzz959, zzz960, zzz961, zzz962, zzz963, zzz964, zzz965, zzz966, zzz967, zzz968, Succ(zzz9690), Zero, ba) → new_mkVBalBranch3MkVBalBranch124(zzz958, zzz959, zzz960, zzz961, zzz962, zzz963, zzz964, zzz965, zzz966, zzz967, zzz968, new_primPlusNat2(Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat3(new_primPlusNat1(zzz960), zzz960)), zzz960))), Succ(zzz960)), ba)
new_mkVBalBranch3MkVBalBranch236(zzz958, zzz959, zzz960, zzz961, zzz962, zzz963, zzz964, zzz965, zzz966, zzz967, zzz968, Zero, Succ(zzz9700), ba) → new_mkVBalBranch1(zzz968, Branch(zzz963, zzz964, Pos(Succ(zzz965)), zzz966, zzz967), zzz961, ba)
new_mkVBalBranch3MkVBalBranch125(zzz1337, zzz1338, zzz1339, zzz1340, zzz1341, zzz1342, zzz1343, zzz1344, zzz1345, zzz1346, zzz1347, Succ(zzz13480), Succ(zzz13490), bb) → new_mkVBalBranch3MkVBalBranch125(zzz1337, zzz1338, zzz1339, zzz1340, zzz1341, zzz1342, zzz1343, zzz1344, zzz1345, zzz1346, zzz1347, zzz13480, zzz13490, bb)
new_mkVBalBranch3MkVBalBranch123(zzz3170, zzz3171, zzz317200, zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, Succ(zzz5620), h) → new_mkVBalBranch1(zzz31, zzz334, Branch(zzz3170, zzz3171, Neg(Succ(zzz317200)), zzz3173, zzz3174), h)
new_mkVBalBranch3MkVBalBranch125(zzz1337, zzz1338, zzz1339, zzz1340, zzz1341, zzz1342, zzz1343, zzz1344, zzz1345, zzz1346, zzz1347, Zero, Succ(zzz13490), bb) → new_mkVBalBranch1(zzz1347, zzz1346, Branch(zzz1337, zzz1338, Pos(Succ(zzz1339)), zzz1340, zzz1341), bb)
new_mkVBalBranch3MkVBalBranch242(zzz972, zzz973, zzz974, zzz975, zzz976, zzz977, zzz978, zzz979, zzz980, zzz981, zzz982, Zero, Succ(zzz9840), bc) → new_mkVBalBranch1(zzz982, Branch(zzz977, zzz978, Neg(Succ(zzz979)), zzz980, zzz981), zzz975, bc)
new_mkVBalBranch3MkVBalBranch240(zzz958, zzz959, zzz960, zzz961, zzz962, zzz963, zzz964, zzz965, zzz966, zzz967, zzz968, ba) → new_mkVBalBranch3MkVBalBranch124(zzz958, zzz959, zzz960, zzz961, zzz962, zzz963, zzz964, zzz965, zzz966, zzz967, zzz968, new_primPlusNat2(Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat3(new_primPlusNat1(zzz960), zzz960)), zzz960))), Succ(zzz960)), ba)
new_mkVBalBranch3MkVBalBranch126(zzz3170, zzz3171, zzz317200, zzz3173, zzz3174, zzz330, zzz331, zzz333, zzz334, zzz31, Succ(zzz5350), h) → new_mkVBalBranch1(zzz31, zzz334, Branch(zzz3170, zzz3171, Neg(Succ(zzz317200)), zzz3173, zzz3174), h)
new_mkVBalBranch3MkVBalBranch123(zzz3170, zzz3171, zzz317200, zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, Zero, h) → new_mkVBalBranch3MkVBalBranch130(zzz3170, zzz3171, zzz317200, zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, h)
new_mkVBalBranch3MkVBalBranch241(zzz3170, zzz3171, Neg(Zero), zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, Succ(zzz4190), h) → new_mkVBalBranch1(zzz31, Branch(zzz330, zzz331, Neg(Succ(zzz33200)), zzz333, zzz334), zzz3173, h)
new_mkVBalBranch3MkVBalBranch244(zzz972, zzz973, zzz974, zzz975, zzz976, zzz977, zzz978, zzz979, zzz980, zzz981, zzz982, bc) → new_mkVBalBranch3MkVBalBranch128(zzz972, zzz973, zzz974, zzz975, zzz976, zzz977, zzz978, zzz979, zzz980, zzz981, zzz982, new_primPlusNat2(Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat3(new_primPlusNat1(zzz974), zzz974)), zzz974))), Succ(zzz974)), bc)
new_mkVBalBranch3MkVBalBranch124(zzz958, zzz959, zzz960, zzz961, zzz962, zzz963, zzz964, zzz965, zzz966, zzz967, zzz968, Succ(zzz10180), ba) → new_mkVBalBranch3MkVBalBranch125(zzz958, zzz959, zzz960, zzz961, zzz962, zzz963, zzz964, zzz965, zzz966, zzz967, zzz968, Succ(zzz10180), Succ(zzz965), ba)
new_mkVBalBranch3MkVBalBranch242(zzz972, zzz973, zzz974, zzz975, zzz976, zzz977, zzz978, zzz979, zzz980, zzz981, zzz982, Zero, Zero, bc) → new_mkVBalBranch3MkVBalBranch244(zzz972, zzz973, zzz974, zzz975, zzz976, zzz977, zzz978, zzz979, zzz980, zzz981, zzz982, bc)
new_mkVBalBranch3MkVBalBranch130(zzz3170, zzz3171, zzz317200, zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, h) → new_mkVBalBranch1(zzz31, zzz334, Branch(zzz3170, zzz3171, Neg(Succ(zzz317200)), zzz3173, zzz3174), h)
new_mkVBalBranch1(zzz31, Branch(zzz330, zzz331, Neg(Zero), zzz333, zzz334), Branch(zzz3170, zzz3171, Pos(Succ(zzz317200)), zzz3173, zzz3174), h) → new_mkVBalBranch1(zzz31, Branch(zzz330, zzz331, Neg(Zero), zzz333, zzz334), zzz3173, h)
new_mkVBalBranch3MkVBalBranch235(zzz3170, zzz3171, Neg(Zero), zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, Succ(zzz4170), h) → new_mkVBalBranch1(zzz31, zzz334, Branch(zzz3170, zzz3171, Neg(Zero), zzz3173, zzz3174), h)
new_mkVBalBranch3MkVBalBranch236(zzz958, zzz959, zzz960, zzz961, zzz962, zzz963, zzz964, zzz965, zzz966, zzz967, zzz968, Zero, Zero, ba) → new_mkVBalBranch3MkVBalBranch240(zzz958, zzz959, zzz960, zzz961, zzz962, zzz963, zzz964, zzz965, zzz966, zzz967, zzz968, ba)

The TRS R consists of the following rules:

new_primPlusNat1(Zero) → Zero
new_primPlusNat1(Succ(zzz62000)) → Succ(Succ(new_primPlusNat1(zzz62000)))
new_primPlusNat3(zzz90, Succ(zzz910)) → Succ(Succ(new_primPlusNat2(zzz90, zzz910)))
new_primPlusNat3(zzz90, Zero) → Succ(zzz90)
new_primPlusNat2(Succ(zzz900), Succ(zzz9100)) → Succ(Succ(new_primPlusNat2(zzz900, zzz9100)))
new_primPlusNat2(Succ(zzz900), Zero) → Succ(zzz900)
new_primPlusNat2(Zero, Succ(zzz9100)) → Succ(zzz9100)
new_primPlusNat2(Zero, Zero) → Zero

The set Q consists of the following terms:

new_primPlusNat2(Zero, Succ(x0))
new_primPlusNat3(x0, Succ(x1))
new_primPlusNat2(Succ(x0), Succ(x1))
new_primPlusNat3(x0, Zero)
new_primPlusNat1(Zero)
new_primPlusNat2(Zero, Zero)
new_primPlusNat1(Succ(x0))
new_primPlusNat2(Succ(x0), Zero)

We have to consider all minimal (P,Q,R)-chains.
By rewriting [15] the rule new_mkVBalBranch3MkVBalBranch242(zzz972, zzz973, zzz974, zzz975, zzz976, zzz977, zzz978, zzz979, zzz980, zzz981, zzz982, Succ(zzz9830), Zero, bc) → new_mkVBalBranch3MkVBalBranch128(zzz972, zzz973, zzz974, zzz975, zzz976, zzz977, zzz978, zzz979, zzz980, zzz981, zzz982, new_primPlusNat2(Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat3(new_primPlusNat1(zzz974), zzz974)), zzz974))), Succ(zzz974)), bc) at position [11] we obtained the following new rules:

new_mkVBalBranch3MkVBalBranch242(zzz972, zzz973, zzz974, zzz975, zzz976, zzz977, zzz978, zzz979, zzz980, zzz981, zzz982, Succ(zzz9830), Zero, bc) → new_mkVBalBranch3MkVBalBranch128(zzz972, zzz973, zzz974, zzz975, zzz976, zzz977, zzz978, zzz979, zzz980, zzz981, zzz982, Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat2(Succ(new_primPlusNat3(new_primPlusNat1(zzz974), zzz974)), zzz974)), zzz974))), bc)



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

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

new_mkVBalBranch3MkVBalBranch129(zzz1851, zzz1852, zzz1853, zzz1854, zzz1855, zzz1856, zzz1857, zzz1858, zzz1859, zzz1860, zzz1861, Zero, Succ(zzz18630), bd) → new_mkVBalBranch1(zzz1861, zzz1860, Branch(zzz1851, zzz1852, Neg(Succ(zzz1853)), zzz1854, zzz1855), bd)
new_mkVBalBranch3MkVBalBranch128(zzz972, zzz973, zzz974, zzz975, zzz976, zzz977, zzz978, zzz979, zzz980, zzz981, zzz982, Succ(zzz10190), bc) → new_mkVBalBranch3MkVBalBranch129(zzz972, zzz973, zzz974, zzz975, zzz976, zzz977, zzz978, zzz979, zzz980, zzz981, zzz982, Succ(zzz979), Succ(zzz10190), bc)
new_mkVBalBranch3MkVBalBranch241(zzz3170, zzz3171, Pos(zzz31720), zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, Succ(zzz4190), h) → new_mkVBalBranch1(zzz31, Branch(zzz330, zzz331, Neg(Succ(zzz33200)), zzz333, zzz334), zzz3173, h)
new_mkVBalBranch3MkVBalBranch127(zzz3170, zzz3171, zzz317200, zzz3173, zzz3174, zzz330, zzz331, zzz333, zzz334, zzz31, Succ(zzz5500), h) → new_mkVBalBranch1(zzz31, zzz334, Branch(zzz3170, zzz3171, Neg(Succ(zzz317200)), zzz3173, zzz3174), h)
new_mkVBalBranch1(zzz31, Branch(zzz330, zzz331, Neg(Zero), zzz333, zzz334), Branch(zzz3170, zzz3171, Neg(Succ(zzz317200)), zzz3173, zzz3174), h) → new_mkVBalBranch3MkVBalBranch127(zzz3170, zzz3171, zzz317200, zzz3173, zzz3174, zzz330, zzz331, zzz333, zzz334, zzz31, Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat2(Succ(new_primPlusNat3(new_primPlusNat1(zzz317200), zzz317200)), zzz317200)), zzz317200))), h)
new_mkVBalBranch3MkVBalBranch129(zzz1851, zzz1852, zzz1853, zzz1854, zzz1855, zzz1856, zzz1857, zzz1858, zzz1859, zzz1860, zzz1861, Succ(zzz18620), Succ(zzz18630), bd) → new_mkVBalBranch3MkVBalBranch129(zzz1851, zzz1852, zzz1853, zzz1854, zzz1855, zzz1856, zzz1857, zzz1858, zzz1859, zzz1860, zzz1861, zzz18620, zzz18630, bd)
new_mkVBalBranch3MkVBalBranch124(zzz958, zzz959, zzz960, zzz961, zzz962, zzz963, zzz964, zzz965, zzz966, zzz967, zzz968, Zero, ba) → new_mkVBalBranch3MkVBalBranch125(zzz958, zzz959, zzz960, zzz961, zzz962, zzz963, zzz964, zzz965, zzz966, zzz967, zzz968, Zero, Succ(zzz965), ba)
new_mkVBalBranch1(zzz31, Branch(zzz330, zzz331, Pos(Zero), zzz333, zzz334), Branch(zzz3170, zzz3171, Neg(Succ(zzz317200)), zzz3173, zzz3174), h) → new_mkVBalBranch3MkVBalBranch126(zzz3170, zzz3171, zzz317200, zzz3173, zzz3174, zzz330, zzz331, zzz333, zzz334, zzz31, new_primPlusNat2(Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat3(new_primPlusNat1(zzz317200), zzz317200)), zzz317200))), Succ(zzz317200)), h)
new_mkVBalBranch3MkVBalBranch242(zzz972, zzz973, zzz974, zzz975, zzz976, zzz977, zzz978, zzz979, zzz980, zzz981, zzz982, Succ(zzz9830), Succ(zzz9840), bc) → new_mkVBalBranch3MkVBalBranch242(zzz972, zzz973, zzz974, zzz975, zzz976, zzz977, zzz978, zzz979, zzz980, zzz981, zzz982, zzz9830, zzz9840, bc)
new_mkVBalBranch3MkVBalBranch235(zzz3170, zzz3171, Pos(Succ(zzz317200)), zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, Succ(zzz4170), h) → new_mkVBalBranch3MkVBalBranch236(zzz3170, zzz3171, zzz317200, zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, zzz4170, zzz317200, h)
new_mkVBalBranch1(zzz31, Branch(zzz330, zzz331, Neg(Succ(zzz33200)), zzz333, zzz334), Branch(zzz3170, zzz3171, zzz3172, zzz3173, zzz3174), h) → new_mkVBalBranch3MkVBalBranch241(zzz3170, zzz3171, zzz3172, zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat2(Succ(new_primPlusNat3(new_primPlusNat1(zzz33200), zzz33200)), zzz33200)), zzz33200))), h)
new_mkVBalBranch1(zzz31, Branch(zzz330, zzz331, Pos(Succ(zzz33200)), zzz333, zzz334), Branch(zzz3170, zzz3171, zzz3172, zzz3173, zzz3174), h) → new_mkVBalBranch3MkVBalBranch235(zzz3170, zzz3171, zzz3172, zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat2(Succ(new_primPlusNat3(new_primPlusNat1(zzz33200), zzz33200)), zzz33200)), zzz33200))), h)
new_mkVBalBranch3MkVBalBranch236(zzz958, zzz959, zzz960, zzz961, zzz962, zzz963, zzz964, zzz965, zzz966, zzz967, zzz968, Succ(zzz9690), Succ(zzz9700), ba) → new_mkVBalBranch3MkVBalBranch236(zzz958, zzz959, zzz960, zzz961, zzz962, zzz963, zzz964, zzz965, zzz966, zzz967, zzz968, zzz9690, zzz9700, ba)
new_mkVBalBranch3MkVBalBranch241(zzz3170, zzz3171, Neg(Succ(zzz317200)), zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, Succ(zzz4190), h) → new_mkVBalBranch3MkVBalBranch242(zzz3170, zzz3171, zzz317200, zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, zzz317200, zzz4190, h)
new_mkVBalBranch1(zzz31, Branch(zzz330, zzz331, Pos(Zero), zzz333, zzz334), Branch(zzz3170, zzz3171, Pos(Succ(zzz317200)), zzz3173, zzz3174), h) → new_mkVBalBranch1(zzz31, Branch(zzz330, zzz331, Pos(Zero), zzz333, zzz334), zzz3173, h)
new_mkVBalBranch3MkVBalBranch237(zzz3170, zzz3171, zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, h) → new_mkVBalBranch1(zzz31, zzz334, Branch(zzz3170, zzz3171, Pos(Zero), zzz3173, zzz3174), h)
new_mkVBalBranch3MkVBalBranch235(zzz3170, zzz3171, Neg(Succ(zzz317200)), zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, Succ(zzz4170), h) → new_mkVBalBranch3MkVBalBranch123(zzz3170, zzz3171, zzz317200, zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, new_primPlusNat2(Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat3(new_primPlusNat1(zzz317200), zzz317200)), zzz317200))), Succ(zzz317200)), h)
new_mkVBalBranch3MkVBalBranch235(zzz3170, zzz3171, Pos(Zero), zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, Succ(zzz4170), h) → new_mkVBalBranch3MkVBalBranch237(zzz3170, zzz3171, zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, h)
new_mkVBalBranch3MkVBalBranch236(zzz958, zzz959, zzz960, zzz961, zzz962, zzz963, zzz964, zzz965, zzz966, zzz967, zzz968, Succ(zzz9690), Zero, ba) → new_mkVBalBranch3MkVBalBranch124(zzz958, zzz959, zzz960, zzz961, zzz962, zzz963, zzz964, zzz965, zzz966, zzz967, zzz968, new_primPlusNat2(Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat3(new_primPlusNat1(zzz960), zzz960)), zzz960))), Succ(zzz960)), ba)
new_mkVBalBranch3MkVBalBranch236(zzz958, zzz959, zzz960, zzz961, zzz962, zzz963, zzz964, zzz965, zzz966, zzz967, zzz968, Zero, Succ(zzz9700), ba) → new_mkVBalBranch1(zzz968, Branch(zzz963, zzz964, Pos(Succ(zzz965)), zzz966, zzz967), zzz961, ba)
new_mkVBalBranch3MkVBalBranch125(zzz1337, zzz1338, zzz1339, zzz1340, zzz1341, zzz1342, zzz1343, zzz1344, zzz1345, zzz1346, zzz1347, Succ(zzz13480), Succ(zzz13490), bb) → new_mkVBalBranch3MkVBalBranch125(zzz1337, zzz1338, zzz1339, zzz1340, zzz1341, zzz1342, zzz1343, zzz1344, zzz1345, zzz1346, zzz1347, zzz13480, zzz13490, bb)
new_mkVBalBranch3MkVBalBranch123(zzz3170, zzz3171, zzz317200, zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, Succ(zzz5620), h) → new_mkVBalBranch1(zzz31, zzz334, Branch(zzz3170, zzz3171, Neg(Succ(zzz317200)), zzz3173, zzz3174), h)
new_mkVBalBranch3MkVBalBranch125(zzz1337, zzz1338, zzz1339, zzz1340, zzz1341, zzz1342, zzz1343, zzz1344, zzz1345, zzz1346, zzz1347, Zero, Succ(zzz13490), bb) → new_mkVBalBranch1(zzz1347, zzz1346, Branch(zzz1337, zzz1338, Pos(Succ(zzz1339)), zzz1340, zzz1341), bb)
new_mkVBalBranch3MkVBalBranch242(zzz972, zzz973, zzz974, zzz975, zzz976, zzz977, zzz978, zzz979, zzz980, zzz981, zzz982, Zero, Succ(zzz9840), bc) → new_mkVBalBranch1(zzz982, Branch(zzz977, zzz978, Neg(Succ(zzz979)), zzz980, zzz981), zzz975, bc)
new_mkVBalBranch3MkVBalBranch240(zzz958, zzz959, zzz960, zzz961, zzz962, zzz963, zzz964, zzz965, zzz966, zzz967, zzz968, ba) → new_mkVBalBranch3MkVBalBranch124(zzz958, zzz959, zzz960, zzz961, zzz962, zzz963, zzz964, zzz965, zzz966, zzz967, zzz968, new_primPlusNat2(Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat3(new_primPlusNat1(zzz960), zzz960)), zzz960))), Succ(zzz960)), ba)
new_mkVBalBranch3MkVBalBranch242(zzz972, zzz973, zzz974, zzz975, zzz976, zzz977, zzz978, zzz979, zzz980, zzz981, zzz982, Succ(zzz9830), Zero, bc) → new_mkVBalBranch3MkVBalBranch128(zzz972, zzz973, zzz974, zzz975, zzz976, zzz977, zzz978, zzz979, zzz980, zzz981, zzz982, Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat2(Succ(new_primPlusNat3(new_primPlusNat1(zzz974), zzz974)), zzz974)), zzz974))), bc)
new_mkVBalBranch3MkVBalBranch126(zzz3170, zzz3171, zzz317200, zzz3173, zzz3174, zzz330, zzz331, zzz333, zzz334, zzz31, Succ(zzz5350), h) → new_mkVBalBranch1(zzz31, zzz334, Branch(zzz3170, zzz3171, Neg(Succ(zzz317200)), zzz3173, zzz3174), h)
new_mkVBalBranch3MkVBalBranch241(zzz3170, zzz3171, Neg(Zero), zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, Succ(zzz4190), h) → new_mkVBalBranch1(zzz31, Branch(zzz330, zzz331, Neg(Succ(zzz33200)), zzz333, zzz334), zzz3173, h)
new_mkVBalBranch3MkVBalBranch123(zzz3170, zzz3171, zzz317200, zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, Zero, h) → new_mkVBalBranch3MkVBalBranch130(zzz3170, zzz3171, zzz317200, zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, h)
new_mkVBalBranch3MkVBalBranch124(zzz958, zzz959, zzz960, zzz961, zzz962, zzz963, zzz964, zzz965, zzz966, zzz967, zzz968, Succ(zzz10180), ba) → new_mkVBalBranch3MkVBalBranch125(zzz958, zzz959, zzz960, zzz961, zzz962, zzz963, zzz964, zzz965, zzz966, zzz967, zzz968, Succ(zzz10180), Succ(zzz965), ba)
new_mkVBalBranch3MkVBalBranch244(zzz972, zzz973, zzz974, zzz975, zzz976, zzz977, zzz978, zzz979, zzz980, zzz981, zzz982, bc) → new_mkVBalBranch3MkVBalBranch128(zzz972, zzz973, zzz974, zzz975, zzz976, zzz977, zzz978, zzz979, zzz980, zzz981, zzz982, new_primPlusNat2(Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat3(new_primPlusNat1(zzz974), zzz974)), zzz974))), Succ(zzz974)), bc)
new_mkVBalBranch3MkVBalBranch242(zzz972, zzz973, zzz974, zzz975, zzz976, zzz977, zzz978, zzz979, zzz980, zzz981, zzz982, Zero, Zero, bc) → new_mkVBalBranch3MkVBalBranch244(zzz972, zzz973, zzz974, zzz975, zzz976, zzz977, zzz978, zzz979, zzz980, zzz981, zzz982, bc)
new_mkVBalBranch3MkVBalBranch130(zzz3170, zzz3171, zzz317200, zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, h) → new_mkVBalBranch1(zzz31, zzz334, Branch(zzz3170, zzz3171, Neg(Succ(zzz317200)), zzz3173, zzz3174), h)
new_mkVBalBranch1(zzz31, Branch(zzz330, zzz331, Neg(Zero), zzz333, zzz334), Branch(zzz3170, zzz3171, Pos(Succ(zzz317200)), zzz3173, zzz3174), h) → new_mkVBalBranch1(zzz31, Branch(zzz330, zzz331, Neg(Zero), zzz333, zzz334), zzz3173, h)
new_mkVBalBranch3MkVBalBranch235(zzz3170, zzz3171, Neg(Zero), zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, Succ(zzz4170), h) → new_mkVBalBranch1(zzz31, zzz334, Branch(zzz3170, zzz3171, Neg(Zero), zzz3173, zzz3174), h)
new_mkVBalBranch3MkVBalBranch236(zzz958, zzz959, zzz960, zzz961, zzz962, zzz963, zzz964, zzz965, zzz966, zzz967, zzz968, Zero, Zero, ba) → new_mkVBalBranch3MkVBalBranch240(zzz958, zzz959, zzz960, zzz961, zzz962, zzz963, zzz964, zzz965, zzz966, zzz967, zzz968, ba)

The TRS R consists of the following rules:

new_primPlusNat1(Zero) → Zero
new_primPlusNat1(Succ(zzz62000)) → Succ(Succ(new_primPlusNat1(zzz62000)))
new_primPlusNat3(zzz90, Succ(zzz910)) → Succ(Succ(new_primPlusNat2(zzz90, zzz910)))
new_primPlusNat3(zzz90, Zero) → Succ(zzz90)
new_primPlusNat2(Succ(zzz900), Succ(zzz9100)) → Succ(Succ(new_primPlusNat2(zzz900, zzz9100)))
new_primPlusNat2(Succ(zzz900), Zero) → Succ(zzz900)
new_primPlusNat2(Zero, Succ(zzz9100)) → Succ(zzz9100)
new_primPlusNat2(Zero, Zero) → Zero

The set Q consists of the following terms:

new_primPlusNat2(Zero, Succ(x0))
new_primPlusNat3(x0, Succ(x1))
new_primPlusNat2(Succ(x0), Succ(x1))
new_primPlusNat3(x0, Zero)
new_primPlusNat1(Zero)
new_primPlusNat2(Zero, Zero)
new_primPlusNat1(Succ(x0))
new_primPlusNat2(Succ(x0), Zero)

We have to consider all minimal (P,Q,R)-chains.
By rewriting [15] the rule new_mkVBalBranch3MkVBalBranch236(zzz958, zzz959, zzz960, zzz961, zzz962, zzz963, zzz964, zzz965, zzz966, zzz967, zzz968, Succ(zzz9690), Zero, ba) → new_mkVBalBranch3MkVBalBranch124(zzz958, zzz959, zzz960, zzz961, zzz962, zzz963, zzz964, zzz965, zzz966, zzz967, zzz968, new_primPlusNat2(Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat3(new_primPlusNat1(zzz960), zzz960)), zzz960))), Succ(zzz960)), ba) at position [11] we obtained the following new rules:

new_mkVBalBranch3MkVBalBranch236(zzz958, zzz959, zzz960, zzz961, zzz962, zzz963, zzz964, zzz965, zzz966, zzz967, zzz968, Succ(zzz9690), Zero, ba) → new_mkVBalBranch3MkVBalBranch124(zzz958, zzz959, zzz960, zzz961, zzz962, zzz963, zzz964, zzz965, zzz966, zzz967, zzz968, Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat2(Succ(new_primPlusNat3(new_primPlusNat1(zzz960), zzz960)), zzz960)), zzz960))), 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
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                    ↳ DependencyGraphProof
                                      ↳ QDP
                                        ↳ Rewriting
                                          ↳ QDP
                                            ↳ Rewriting
                                              ↳ QDP
                                                ↳ Rewriting
                                                  ↳ QDP
                                                    ↳ Rewriting
                                                      ↳ QDP
                                                        ↳ Rewriting
                                                          ↳ QDP
                                                            ↳ Rewriting
                                                              ↳ QDP
                                                                ↳ Rewriting
                                                                  ↳ QDP
                                                                    ↳ Rewriting
                                                                      ↳ QDP
                                                                        ↳ Rewriting
                                                                          ↳ QDP
                                                                            ↳ Rewriting
                                                                              ↳ QDP
                                                                                ↳ UsableRulesProof
                                                                                  ↳ QDP
                                                                                    ↳ QReductionProof
                                                                                      ↳ QDP
                                                                                        ↳ Rewriting
                                                                                          ↳ QDP
                                                                                            ↳ Rewriting
                                                                                              ↳ QDP
                                                                                                ↳ Rewriting
                                                                                                  ↳ QDP
                                                                                                    ↳ Rewriting
                                                                                                      ↳ QDP
                                                                                                        ↳ Rewriting
                                                                                                          ↳ QDP
                                                                                                            ↳ Rewriting
                                                                                                              ↳ QDP
                                                                                                                ↳ Rewriting
                                                                                                                  ↳ QDP
                                                                                                                    ↳ Rewriting
                                                                                                                      ↳ QDP
                                                                                                                        ↳ Rewriting
                                                                                                                          ↳ QDP
                                                                                                                            ↳ Rewriting
                                                                                                                              ↳ QDP
                                                                                                                                ↳ UsableRulesProof
                                                                                                                                  ↳ QDP
                                                                                                                                    ↳ QReductionProof
                                                                                                                                      ↳ QDP
                                                                                                                                        ↳ Rewriting
                                                                                                                                          ↳ QDP
                                                                                                                                            ↳ Rewriting
                                                                                                                                              ↳ QDP
                                                                                                                                                ↳ Rewriting
                                                                                                                                                  ↳ QDP
                                                                                                                                                    ↳ DependencyGraphProof
                                                                                                                                                      ↳ QDP
                                                                                                                                                        ↳ Rewriting
                                                                                                                                                          ↳ QDP
                                                                                                                                                            ↳ Rewriting
                                                                                                                                                              ↳ QDP
                                                                                                                                                                ↳ DependencyGraphProof
                                                                                                                                                                  ↳ QDP
                                                                                                                                                                    ↳ Rewriting
                                                                                                                                                                      ↳ QDP
                                                                                                                                                                        ↳ Rewriting
                                                                                                                                                                          ↳ QDP
                                                                                                                                                                            ↳ Rewriting
                                                                                                                                                                              ↳ QDP
                                                                                                                                                                                ↳ Rewriting
                                                                                                                                                                                  ↳ QDP
                                                                                                                                                                                    ↳ Rewriting
                                                                                                                                                                                      ↳ QDP
                                                                                                                                                                                        ↳ Rewriting
                                                                                                                                                                                          ↳ QDP
                                                                                                                                                                                            ↳ Rewriting
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP

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

new_mkVBalBranch3MkVBalBranch129(zzz1851, zzz1852, zzz1853, zzz1854, zzz1855, zzz1856, zzz1857, zzz1858, zzz1859, zzz1860, zzz1861, Zero, Succ(zzz18630), bd) → new_mkVBalBranch1(zzz1861, zzz1860, Branch(zzz1851, zzz1852, Neg(Succ(zzz1853)), zzz1854, zzz1855), bd)
new_mkVBalBranch3MkVBalBranch127(zzz3170, zzz3171, zzz317200, zzz3173, zzz3174, zzz330, zzz331, zzz333, zzz334, zzz31, Succ(zzz5500), h) → new_mkVBalBranch1(zzz31, zzz334, Branch(zzz3170, zzz3171, Neg(Succ(zzz317200)), zzz3173, zzz3174), h)
new_mkVBalBranch3MkVBalBranch241(zzz3170, zzz3171, Pos(zzz31720), zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, Succ(zzz4190), h) → new_mkVBalBranch1(zzz31, Branch(zzz330, zzz331, Neg(Succ(zzz33200)), zzz333, zzz334), zzz3173, h)
new_mkVBalBranch3MkVBalBranch128(zzz972, zzz973, zzz974, zzz975, zzz976, zzz977, zzz978, zzz979, zzz980, zzz981, zzz982, Succ(zzz10190), bc) → new_mkVBalBranch3MkVBalBranch129(zzz972, zzz973, zzz974, zzz975, zzz976, zzz977, zzz978, zzz979, zzz980, zzz981, zzz982, Succ(zzz979), Succ(zzz10190), bc)
new_mkVBalBranch1(zzz31, Branch(zzz330, zzz331, Neg(Zero), zzz333, zzz334), Branch(zzz3170, zzz3171, Neg(Succ(zzz317200)), zzz3173, zzz3174), h) → new_mkVBalBranch3MkVBalBranch127(zzz3170, zzz3171, zzz317200, zzz3173, zzz3174, zzz330, zzz331, zzz333, zzz334, zzz31, Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat2(Succ(new_primPlusNat3(new_primPlusNat1(zzz317200), zzz317200)), zzz317200)), zzz317200))), h)
new_mkVBalBranch3MkVBalBranch129(zzz1851, zzz1852, zzz1853, zzz1854, zzz1855, zzz1856, zzz1857, zzz1858, zzz1859, zzz1860, zzz1861, Succ(zzz18620), Succ(zzz18630), bd) → new_mkVBalBranch3MkVBalBranch129(zzz1851, zzz1852, zzz1853, zzz1854, zzz1855, zzz1856, zzz1857, zzz1858, zzz1859, zzz1860, zzz1861, zzz18620, zzz18630, bd)
new_mkVBalBranch3MkVBalBranch236(zzz958, zzz959, zzz960, zzz961, zzz962, zzz963, zzz964, zzz965, zzz966, zzz967, zzz968, Succ(zzz9690), Zero, ba) → new_mkVBalBranch3MkVBalBranch124(zzz958, zzz959, zzz960, zzz961, zzz962, zzz963, zzz964, zzz965, zzz966, zzz967, zzz968, Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat2(Succ(new_primPlusNat3(new_primPlusNat1(zzz960), zzz960)), zzz960)), zzz960))), ba)
new_mkVBalBranch3MkVBalBranch124(zzz958, zzz959, zzz960, zzz961, zzz962, zzz963, zzz964, zzz965, zzz966, zzz967, zzz968, Zero, ba) → new_mkVBalBranch3MkVBalBranch125(zzz958, zzz959, zzz960, zzz961, zzz962, zzz963, zzz964, zzz965, zzz966, zzz967, zzz968, Zero, Succ(zzz965), ba)
new_mkVBalBranch3MkVBalBranch235(zzz3170, zzz3171, Pos(Succ(zzz317200)), zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, Succ(zzz4170), h) → new_mkVBalBranch3MkVBalBranch236(zzz3170, zzz3171, zzz317200, zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, zzz4170, zzz317200, h)
new_mkVBalBranch3MkVBalBranch242(zzz972, zzz973, zzz974, zzz975, zzz976, zzz977, zzz978, zzz979, zzz980, zzz981, zzz982, Succ(zzz9830), Succ(zzz9840), bc) → new_mkVBalBranch3MkVBalBranch242(zzz972, zzz973, zzz974, zzz975, zzz976, zzz977, zzz978, zzz979, zzz980, zzz981, zzz982, zzz9830, zzz9840, bc)
new_mkVBalBranch1(zzz31, Branch(zzz330, zzz331, Pos(Zero), zzz333, zzz334), Branch(zzz3170, zzz3171, Neg(Succ(zzz317200)), zzz3173, zzz3174), h) → new_mkVBalBranch3MkVBalBranch126(zzz3170, zzz3171, zzz317200, zzz3173, zzz3174, zzz330, zzz331, zzz333, zzz334, zzz31, new_primPlusNat2(Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat3(new_primPlusNat1(zzz317200), zzz317200)), zzz317200))), Succ(zzz317200)), h)
new_mkVBalBranch1(zzz31, Branch(zzz330, zzz331, Pos(Succ(zzz33200)), zzz333, zzz334), Branch(zzz3170, zzz3171, zzz3172, zzz3173, zzz3174), h) → new_mkVBalBranch3MkVBalBranch235(zzz3170, zzz3171, zzz3172, zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat2(Succ(new_primPlusNat3(new_primPlusNat1(zzz33200), zzz33200)), zzz33200)), zzz33200))), h)
new_mkVBalBranch1(zzz31, Branch(zzz330, zzz331, Neg(Succ(zzz33200)), zzz333, zzz334), Branch(zzz3170, zzz3171, zzz3172, zzz3173, zzz3174), h) → new_mkVBalBranch3MkVBalBranch241(zzz3170, zzz3171, zzz3172, zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat2(Succ(new_primPlusNat3(new_primPlusNat1(zzz33200), zzz33200)), zzz33200)), zzz33200))), h)
new_mkVBalBranch3MkVBalBranch236(zzz958, zzz959, zzz960, zzz961, zzz962, zzz963, zzz964, zzz965, zzz966, zzz967, zzz968, Succ(zzz9690), Succ(zzz9700), ba) → new_mkVBalBranch3MkVBalBranch236(zzz958, zzz959, zzz960, zzz961, zzz962, zzz963, zzz964, zzz965, zzz966, zzz967, zzz968, zzz9690, zzz9700, ba)
new_mkVBalBranch3MkVBalBranch241(zzz3170, zzz3171, Neg(Succ(zzz317200)), zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, Succ(zzz4190), h) → new_mkVBalBranch3MkVBalBranch242(zzz3170, zzz3171, zzz317200, zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, zzz317200, zzz4190, h)
new_mkVBalBranch1(zzz31, Branch(zzz330, zzz331, Pos(Zero), zzz333, zzz334), Branch(zzz3170, zzz3171, Pos(Succ(zzz317200)), zzz3173, zzz3174), h) → new_mkVBalBranch1(zzz31, Branch(zzz330, zzz331, Pos(Zero), zzz333, zzz334), zzz3173, h)
new_mkVBalBranch3MkVBalBranch235(zzz3170, zzz3171, Neg(Succ(zzz317200)), zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, Succ(zzz4170), h) → new_mkVBalBranch3MkVBalBranch123(zzz3170, zzz3171, zzz317200, zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, new_primPlusNat2(Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat3(new_primPlusNat1(zzz317200), zzz317200)), zzz317200))), Succ(zzz317200)), h)
new_mkVBalBranch3MkVBalBranch237(zzz3170, zzz3171, zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, h) → new_mkVBalBranch1(zzz31, zzz334, Branch(zzz3170, zzz3171, Pos(Zero), zzz3173, zzz3174), h)
new_mkVBalBranch3MkVBalBranch235(zzz3170, zzz3171, Pos(Zero), zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, Succ(zzz4170), h) → new_mkVBalBranch3MkVBalBranch237(zzz3170, zzz3171, zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, h)
new_mkVBalBranch3MkVBalBranch236(zzz958, zzz959, zzz960, zzz961, zzz962, zzz963, zzz964, zzz965, zzz966, zzz967, zzz968, Zero, Succ(zzz9700), ba) → new_mkVBalBranch1(zzz968, Branch(zzz963, zzz964, Pos(Succ(zzz965)), zzz966, zzz967), zzz961, ba)
new_mkVBalBranch3MkVBalBranch125(zzz1337, zzz1338, zzz1339, zzz1340, zzz1341, zzz1342, zzz1343, zzz1344, zzz1345, zzz1346, zzz1347, Succ(zzz13480), Succ(zzz13490), bb) → new_mkVBalBranch3MkVBalBranch125(zzz1337, zzz1338, zzz1339, zzz1340, zzz1341, zzz1342, zzz1343, zzz1344, zzz1345, zzz1346, zzz1347, zzz13480, zzz13490, bb)
new_mkVBalBranch3MkVBalBranch123(zzz3170, zzz3171, zzz317200, zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, Succ(zzz5620), h) → new_mkVBalBranch1(zzz31, zzz334, Branch(zzz3170, zzz3171, Neg(Succ(zzz317200)), zzz3173, zzz3174), h)
new_mkVBalBranch3MkVBalBranch125(zzz1337, zzz1338, zzz1339, zzz1340, zzz1341, zzz1342, zzz1343, zzz1344, zzz1345, zzz1346, zzz1347, Zero, Succ(zzz13490), bb) → new_mkVBalBranch1(zzz1347, zzz1346, Branch(zzz1337, zzz1338, Pos(Succ(zzz1339)), zzz1340, zzz1341), bb)
new_mkVBalBranch3MkVBalBranch242(zzz972, zzz973, zzz974, zzz975, zzz976, zzz977, zzz978, zzz979, zzz980, zzz981, zzz982, Zero, Succ(zzz9840), bc) → new_mkVBalBranch1(zzz982, Branch(zzz977, zzz978, Neg(Succ(zzz979)), zzz980, zzz981), zzz975, bc)
new_mkVBalBranch3MkVBalBranch240(zzz958, zzz959, zzz960, zzz961, zzz962, zzz963, zzz964, zzz965, zzz966, zzz967, zzz968, ba) → new_mkVBalBranch3MkVBalBranch124(zzz958, zzz959, zzz960, zzz961, zzz962, zzz963, zzz964, zzz965, zzz966, zzz967, zzz968, new_primPlusNat2(Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat3(new_primPlusNat1(zzz960), zzz960)), zzz960))), Succ(zzz960)), ba)
new_mkVBalBranch3MkVBalBranch242(zzz972, zzz973, zzz974, zzz975, zzz976, zzz977, zzz978, zzz979, zzz980, zzz981, zzz982, Succ(zzz9830), Zero, bc) → new_mkVBalBranch3MkVBalBranch128(zzz972, zzz973, zzz974, zzz975, zzz976, zzz977, zzz978, zzz979, zzz980, zzz981, zzz982, Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat2(Succ(new_primPlusNat3(new_primPlusNat1(zzz974), zzz974)), zzz974)), zzz974))), bc)
new_mkVBalBranch3MkVBalBranch126(zzz3170, zzz3171, zzz317200, zzz3173, zzz3174, zzz330, zzz331, zzz333, zzz334, zzz31, Succ(zzz5350), h) → new_mkVBalBranch1(zzz31, zzz334, Branch(zzz3170, zzz3171, Neg(Succ(zzz317200)), zzz3173, zzz3174), h)
new_mkVBalBranch3MkVBalBranch123(zzz3170, zzz3171, zzz317200, zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, Zero, h) → new_mkVBalBranch3MkVBalBranch130(zzz3170, zzz3171, zzz317200, zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, h)
new_mkVBalBranch3MkVBalBranch241(zzz3170, zzz3171, Neg(Zero), zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, Succ(zzz4190), h) → new_mkVBalBranch1(zzz31, Branch(zzz330, zzz331, Neg(Succ(zzz33200)), zzz333, zzz334), zzz3173, h)
new_mkVBalBranch3MkVBalBranch244(zzz972, zzz973, zzz974, zzz975, zzz976, zzz977, zzz978, zzz979, zzz980, zzz981, zzz982, bc) → new_mkVBalBranch3MkVBalBranch128(zzz972, zzz973, zzz974, zzz975, zzz976, zzz977, zzz978, zzz979, zzz980, zzz981, zzz982, new_primPlusNat2(Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat3(new_primPlusNat1(zzz974), zzz974)), zzz974))), Succ(zzz974)), bc)
new_mkVBalBranch3MkVBalBranch124(zzz958, zzz959, zzz960, zzz961, zzz962, zzz963, zzz964, zzz965, zzz966, zzz967, zzz968, Succ(zzz10180), ba) → new_mkVBalBranch3MkVBalBranch125(zzz958, zzz959, zzz960, zzz961, zzz962, zzz963, zzz964, zzz965, zzz966, zzz967, zzz968, Succ(zzz10180), Succ(zzz965), ba)
new_mkVBalBranch3MkVBalBranch242(zzz972, zzz973, zzz974, zzz975, zzz976, zzz977, zzz978, zzz979, zzz980, zzz981, zzz982, Zero, Zero, bc) → new_mkVBalBranch3MkVBalBranch244(zzz972, zzz973, zzz974, zzz975, zzz976, zzz977, zzz978, zzz979, zzz980, zzz981, zzz982, bc)
new_mkVBalBranch3MkVBalBranch130(zzz3170, zzz3171, zzz317200, zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, h) → new_mkVBalBranch1(zzz31, zzz334, Branch(zzz3170, zzz3171, Neg(Succ(zzz317200)), zzz3173, zzz3174), h)
new_mkVBalBranch1(zzz31, Branch(zzz330, zzz331, Neg(Zero), zzz333, zzz334), Branch(zzz3170, zzz3171, Pos(Succ(zzz317200)), zzz3173, zzz3174), h) → new_mkVBalBranch1(zzz31, Branch(zzz330, zzz331, Neg(Zero), zzz333, zzz334), zzz3173, h)
new_mkVBalBranch3MkVBalBranch235(zzz3170, zzz3171, Neg(Zero), zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, Succ(zzz4170), h) → new_mkVBalBranch1(zzz31, zzz334, Branch(zzz3170, zzz3171, Neg(Zero), zzz3173, zzz3174), h)
new_mkVBalBranch3MkVBalBranch236(zzz958, zzz959, zzz960, zzz961, zzz962, zzz963, zzz964, zzz965, zzz966, zzz967, zzz968, Zero, Zero, ba) → new_mkVBalBranch3MkVBalBranch240(zzz958, zzz959, zzz960, zzz961, zzz962, zzz963, zzz964, zzz965, zzz966, zzz967, zzz968, ba)

The TRS R consists of the following rules:

new_primPlusNat1(Zero) → Zero
new_primPlusNat1(Succ(zzz62000)) → Succ(Succ(new_primPlusNat1(zzz62000)))
new_primPlusNat3(zzz90, Succ(zzz910)) → Succ(Succ(new_primPlusNat2(zzz90, zzz910)))
new_primPlusNat3(zzz90, Zero) → Succ(zzz90)
new_primPlusNat2(Succ(zzz900), Succ(zzz9100)) → Succ(Succ(new_primPlusNat2(zzz900, zzz9100)))
new_primPlusNat2(Succ(zzz900), Zero) → Succ(zzz900)
new_primPlusNat2(Zero, Succ(zzz9100)) → Succ(zzz9100)
new_primPlusNat2(Zero, Zero) → Zero

The set Q consists of the following terms:

new_primPlusNat2(Zero, Succ(x0))
new_primPlusNat3(x0, Succ(x1))
new_primPlusNat2(Succ(x0), Succ(x1))
new_primPlusNat3(x0, Zero)
new_primPlusNat1(Zero)
new_primPlusNat2(Zero, Zero)
new_primPlusNat1(Succ(x0))
new_primPlusNat2(Succ(x0), Zero)

We have to consider all minimal (P,Q,R)-chains.
By rewriting [15] the rule new_mkVBalBranch3MkVBalBranch235(zzz3170, zzz3171, Neg(Succ(zzz317200)), zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, Succ(zzz4170), h) → new_mkVBalBranch3MkVBalBranch123(zzz3170, zzz3171, zzz317200, zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, new_primPlusNat2(Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat3(new_primPlusNat1(zzz317200), zzz317200)), zzz317200))), Succ(zzz317200)), h) at position [11] we obtained the following new rules:

new_mkVBalBranch3MkVBalBranch235(zzz3170, zzz3171, Neg(Succ(zzz317200)), zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, Succ(zzz4170), h) → new_mkVBalBranch3MkVBalBranch123(zzz3170, zzz3171, zzz317200, zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat2(Succ(new_primPlusNat3(new_primPlusNat1(zzz317200), zzz317200)), zzz317200)), zzz317200))), 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
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                    ↳ DependencyGraphProof
                                      ↳ QDP
                                        ↳ Rewriting
                                          ↳ QDP
                                            ↳ Rewriting
                                              ↳ QDP
                                                ↳ Rewriting
                                                  ↳ QDP
                                                    ↳ Rewriting
                                                      ↳ QDP
                                                        ↳ Rewriting
                                                          ↳ QDP
                                                            ↳ Rewriting
                                                              ↳ QDP
                                                                ↳ Rewriting
                                                                  ↳ QDP
                                                                    ↳ Rewriting
                                                                      ↳ QDP
                                                                        ↳ Rewriting
                                                                          ↳ QDP
                                                                            ↳ Rewriting
                                                                              ↳ QDP
                                                                                ↳ UsableRulesProof
                                                                                  ↳ QDP
                                                                                    ↳ QReductionProof
                                                                                      ↳ QDP
                                                                                        ↳ Rewriting
                                                                                          ↳ QDP
                                                                                            ↳ Rewriting
                                                                                              ↳ QDP
                                                                                                ↳ Rewriting
                                                                                                  ↳ QDP
                                                                                                    ↳ Rewriting
                                                                                                      ↳ QDP
                                                                                                        ↳ Rewriting
                                                                                                          ↳ QDP
                                                                                                            ↳ Rewriting
                                                                                                              ↳ QDP
                                                                                                                ↳ Rewriting
                                                                                                                  ↳ QDP
                                                                                                                    ↳ Rewriting
                                                                                                                      ↳ QDP
                                                                                                                        ↳ Rewriting
                                                                                                                          ↳ QDP
                                                                                                                            ↳ Rewriting
                                                                                                                              ↳ QDP
                                                                                                                                ↳ UsableRulesProof
                                                                                                                                  ↳ QDP
                                                                                                                                    ↳ QReductionProof
                                                                                                                                      ↳ QDP
                                                                                                                                        ↳ Rewriting
                                                                                                                                          ↳ QDP
                                                                                                                                            ↳ Rewriting
                                                                                                                                              ↳ QDP
                                                                                                                                                ↳ Rewriting
                                                                                                                                                  ↳ QDP
                                                                                                                                                    ↳ DependencyGraphProof
                                                                                                                                                      ↳ QDP
                                                                                                                                                        ↳ Rewriting
                                                                                                                                                          ↳ QDP
                                                                                                                                                            ↳ Rewriting
                                                                                                                                                              ↳ QDP
                                                                                                                                                                ↳ DependencyGraphProof
                                                                                                                                                                  ↳ QDP
                                                                                                                                                                    ↳ Rewriting
                                                                                                                                                                      ↳ QDP
                                                                                                                                                                        ↳ Rewriting
                                                                                                                                                                          ↳ QDP
                                                                                                                                                                            ↳ Rewriting
                                                                                                                                                                              ↳ QDP
                                                                                                                                                                                ↳ Rewriting
                                                                                                                                                                                  ↳ QDP
                                                                                                                                                                                    ↳ Rewriting
                                                                                                                                                                                      ↳ QDP
                                                                                                                                                                                        ↳ Rewriting
                                                                                                                                                                                          ↳ QDP
                                                                                                                                                                                            ↳ Rewriting
                                                                                                                                                                                              ↳ QDP
                                                                                                                                                                                                ↳ DependencyGraphProof
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP

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

new_mkVBalBranch3MkVBalBranch129(zzz1851, zzz1852, zzz1853, zzz1854, zzz1855, zzz1856, zzz1857, zzz1858, zzz1859, zzz1860, zzz1861, Zero, Succ(zzz18630), bd) → new_mkVBalBranch1(zzz1861, zzz1860, Branch(zzz1851, zzz1852, Neg(Succ(zzz1853)), zzz1854, zzz1855), bd)
new_mkVBalBranch3MkVBalBranch128(zzz972, zzz973, zzz974, zzz975, zzz976, zzz977, zzz978, zzz979, zzz980, zzz981, zzz982, Succ(zzz10190), bc) → new_mkVBalBranch3MkVBalBranch129(zzz972, zzz973, zzz974, zzz975, zzz976, zzz977, zzz978, zzz979, zzz980, zzz981, zzz982, Succ(zzz979), Succ(zzz10190), bc)
new_mkVBalBranch3MkVBalBranch241(zzz3170, zzz3171, Pos(zzz31720), zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, Succ(zzz4190), h) → new_mkVBalBranch1(zzz31, Branch(zzz330, zzz331, Neg(Succ(zzz33200)), zzz333, zzz334), zzz3173, h)
new_mkVBalBranch3MkVBalBranch127(zzz3170, zzz3171, zzz317200, zzz3173, zzz3174, zzz330, zzz331, zzz333, zzz334, zzz31, Succ(zzz5500), h) → new_mkVBalBranch1(zzz31, zzz334, Branch(zzz3170, zzz3171, Neg(Succ(zzz317200)), zzz3173, zzz3174), h)
new_mkVBalBranch1(zzz31, Branch(zzz330, zzz331, Neg(Zero), zzz333, zzz334), Branch(zzz3170, zzz3171, Neg(Succ(zzz317200)), zzz3173, zzz3174), h) → new_mkVBalBranch3MkVBalBranch127(zzz3170, zzz3171, zzz317200, zzz3173, zzz3174, zzz330, zzz331, zzz333, zzz334, zzz31, Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat2(Succ(new_primPlusNat3(new_primPlusNat1(zzz317200), zzz317200)), zzz317200)), zzz317200))), h)
new_mkVBalBranch3MkVBalBranch129(zzz1851, zzz1852, zzz1853, zzz1854, zzz1855, zzz1856, zzz1857, zzz1858, zzz1859, zzz1860, zzz1861, Succ(zzz18620), Succ(zzz18630), bd) → new_mkVBalBranch3MkVBalBranch129(zzz1851, zzz1852, zzz1853, zzz1854, zzz1855, zzz1856, zzz1857, zzz1858, zzz1859, zzz1860, zzz1861, zzz18620, zzz18630, bd)
new_mkVBalBranch3MkVBalBranch236(zzz958, zzz959, zzz960, zzz961, zzz962, zzz963, zzz964, zzz965, zzz966, zzz967, zzz968, Succ(zzz9690), Zero, ba) → new_mkVBalBranch3MkVBalBranch124(zzz958, zzz959, zzz960, zzz961, zzz962, zzz963, zzz964, zzz965, zzz966, zzz967, zzz968, Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat2(Succ(new_primPlusNat3(new_primPlusNat1(zzz960), zzz960)), zzz960)), zzz960))), ba)
new_mkVBalBranch3MkVBalBranch124(zzz958, zzz959, zzz960, zzz961, zzz962, zzz963, zzz964, zzz965, zzz966, zzz967, zzz968, Zero, ba) → new_mkVBalBranch3MkVBalBranch125(zzz958, zzz959, zzz960, zzz961, zzz962, zzz963, zzz964, zzz965, zzz966, zzz967, zzz968, Zero, Succ(zzz965), ba)
new_mkVBalBranch1(zzz31, Branch(zzz330, zzz331, Pos(Zero), zzz333, zzz334), Branch(zzz3170, zzz3171, Neg(Succ(zzz317200)), zzz3173, zzz3174), h) → new_mkVBalBranch3MkVBalBranch126(zzz3170, zzz3171, zzz317200, zzz3173, zzz3174, zzz330, zzz331, zzz333, zzz334, zzz31, new_primPlusNat2(Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat3(new_primPlusNat1(zzz317200), zzz317200)), zzz317200))), Succ(zzz317200)), h)
new_mkVBalBranch3MkVBalBranch242(zzz972, zzz973, zzz974, zzz975, zzz976, zzz977, zzz978, zzz979, zzz980, zzz981, zzz982, Succ(zzz9830), Succ(zzz9840), bc) → new_mkVBalBranch3MkVBalBranch242(zzz972, zzz973, zzz974, zzz975, zzz976, zzz977, zzz978, zzz979, zzz980, zzz981, zzz982, zzz9830, zzz9840, bc)
new_mkVBalBranch3MkVBalBranch235(zzz3170, zzz3171, Pos(Succ(zzz317200)), zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, Succ(zzz4170), h) → new_mkVBalBranch3MkVBalBranch236(zzz3170, zzz3171, zzz317200, zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, zzz4170, zzz317200, h)
new_mkVBalBranch1(zzz31, Branch(zzz330, zzz331, Neg(Succ(zzz33200)), zzz333, zzz334), Branch(zzz3170, zzz3171, zzz3172, zzz3173, zzz3174), h) → new_mkVBalBranch3MkVBalBranch241(zzz3170, zzz3171, zzz3172, zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat2(Succ(new_primPlusNat3(new_primPlusNat1(zzz33200), zzz33200)), zzz33200)), zzz33200))), h)
new_mkVBalBranch1(zzz31, Branch(zzz330, zzz331, Pos(Succ(zzz33200)), zzz333, zzz334), Branch(zzz3170, zzz3171, zzz3172, zzz3173, zzz3174), h) → new_mkVBalBranch3MkVBalBranch235(zzz3170, zzz3171, zzz3172, zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat2(Succ(new_primPlusNat3(new_primPlusNat1(zzz33200), zzz33200)), zzz33200)), zzz33200))), h)
new_mkVBalBranch3MkVBalBranch236(zzz958, zzz959, zzz960, zzz961, zzz962, zzz963, zzz964, zzz965, zzz966, zzz967, zzz968, Succ(zzz9690), Succ(zzz9700), ba) → new_mkVBalBranch3MkVBalBranch236(zzz958, zzz959, zzz960, zzz961, zzz962, zzz963, zzz964, zzz965, zzz966, zzz967, zzz968, zzz9690, zzz9700, ba)
new_mkVBalBranch3MkVBalBranch241(zzz3170, zzz3171, Neg(Succ(zzz317200)), zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, Succ(zzz4190), h) → new_mkVBalBranch3MkVBalBranch242(zzz3170, zzz3171, zzz317200, zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, zzz317200, zzz4190, h)
new_mkVBalBranch1(zzz31, Branch(zzz330, zzz331, Pos(Zero), zzz333, zzz334), Branch(zzz3170, zzz3171, Pos(Succ(zzz317200)), zzz3173, zzz3174), h) → new_mkVBalBranch1(zzz31, Branch(zzz330, zzz331, Pos(Zero), zzz333, zzz334), zzz3173, h)
new_mkVBalBranch3MkVBalBranch237(zzz3170, zzz3171, zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, h) → new_mkVBalBranch1(zzz31, zzz334, Branch(zzz3170, zzz3171, Pos(Zero), zzz3173, zzz3174), h)
new_mkVBalBranch3MkVBalBranch235(zzz3170, zzz3171, Pos(Zero), zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, Succ(zzz4170), h) → new_mkVBalBranch3MkVBalBranch237(zzz3170, zzz3171, zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, h)
new_mkVBalBranch3MkVBalBranch236(zzz958, zzz959, zzz960, zzz961, zzz962, zzz963, zzz964, zzz965, zzz966, zzz967, zzz968, Zero, Succ(zzz9700), ba) → new_mkVBalBranch1(zzz968, Branch(zzz963, zzz964, Pos(Succ(zzz965)), zzz966, zzz967), zzz961, ba)
new_mkVBalBranch3MkVBalBranch125(zzz1337, zzz1338, zzz1339, zzz1340, zzz1341, zzz1342, zzz1343, zzz1344, zzz1345, zzz1346, zzz1347, Succ(zzz13480), Succ(zzz13490), bb) → new_mkVBalBranch3MkVBalBranch125(zzz1337, zzz1338, zzz1339, zzz1340, zzz1341, zzz1342, zzz1343, zzz1344, zzz1345, zzz1346, zzz1347, zzz13480, zzz13490, bb)
new_mkVBalBranch3MkVBalBranch123(zzz3170, zzz3171, zzz317200, zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, Succ(zzz5620), h) → new_mkVBalBranch1(zzz31, zzz334, Branch(zzz3170, zzz3171, Neg(Succ(zzz317200)), zzz3173, zzz3174), h)
new_mkVBalBranch3MkVBalBranch125(zzz1337, zzz1338, zzz1339, zzz1340, zzz1341, zzz1342, zzz1343, zzz1344, zzz1345, zzz1346, zzz1347, Zero, Succ(zzz13490), bb) → new_mkVBalBranch1(zzz1347, zzz1346, Branch(zzz1337, zzz1338, Pos(Succ(zzz1339)), zzz1340, zzz1341), bb)
new_mkVBalBranch3MkVBalBranch242(zzz972, zzz973, zzz974, zzz975, zzz976, zzz977, zzz978, zzz979, zzz980, zzz981, zzz982, Zero, Succ(zzz9840), bc) → new_mkVBalBranch1(zzz982, Branch(zzz977, zzz978, Neg(Succ(zzz979)), zzz980, zzz981), zzz975, bc)
new_mkVBalBranch3MkVBalBranch240(zzz958, zzz959, zzz960, zzz961, zzz962, zzz963, zzz964, zzz965, zzz966, zzz967, zzz968, ba) → new_mkVBalBranch3MkVBalBranch124(zzz958, zzz959, zzz960, zzz961, zzz962, zzz963, zzz964, zzz965, zzz966, zzz967, zzz968, new_primPlusNat2(Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat3(new_primPlusNat1(zzz960), zzz960)), zzz960))), Succ(zzz960)), ba)
new_mkVBalBranch3MkVBalBranch242(zzz972, zzz973, zzz974, zzz975, zzz976, zzz977, zzz978, zzz979, zzz980, zzz981, zzz982, Succ(zzz9830), Zero, bc) → new_mkVBalBranch3MkVBalBranch128(zzz972, zzz973, zzz974, zzz975, zzz976, zzz977, zzz978, zzz979, zzz980, zzz981, zzz982, Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat2(Succ(new_primPlusNat3(new_primPlusNat1(zzz974), zzz974)), zzz974)), zzz974))), bc)
new_mkVBalBranch3MkVBalBranch126(zzz3170, zzz3171, zzz317200, zzz3173, zzz3174, zzz330, zzz331, zzz333, zzz334, zzz31, Succ(zzz5350), h) → new_mkVBalBranch1(zzz31, zzz334, Branch(zzz3170, zzz3171, Neg(Succ(zzz317200)), zzz3173, zzz3174), h)
new_mkVBalBranch3MkVBalBranch241(zzz3170, zzz3171, Neg(Zero), zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, Succ(zzz4190), h) → new_mkVBalBranch1(zzz31, Branch(zzz330, zzz331, Neg(Succ(zzz33200)), zzz333, zzz334), zzz3173, h)
new_mkVBalBranch3MkVBalBranch123(zzz3170, zzz3171, zzz317200, zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, Zero, h) → new_mkVBalBranch3MkVBalBranch130(zzz3170, zzz3171, zzz317200, zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, h)
new_mkVBalBranch3MkVBalBranch124(zzz958, zzz959, zzz960, zzz961, zzz962, zzz963, zzz964, zzz965, zzz966, zzz967, zzz968, Succ(zzz10180), ba) → new_mkVBalBranch3MkVBalBranch125(zzz958, zzz959, zzz960, zzz961, zzz962, zzz963, zzz964, zzz965, zzz966, zzz967, zzz968, Succ(zzz10180), Succ(zzz965), ba)
new_mkVBalBranch3MkVBalBranch244(zzz972, zzz973, zzz974, zzz975, zzz976, zzz977, zzz978, zzz979, zzz980, zzz981, zzz982, bc) → new_mkVBalBranch3MkVBalBranch128(zzz972, zzz973, zzz974, zzz975, zzz976, zzz977, zzz978, zzz979, zzz980, zzz981, zzz982, new_primPlusNat2(Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat3(new_primPlusNat1(zzz974), zzz974)), zzz974))), Succ(zzz974)), bc)
new_mkVBalBranch3MkVBalBranch235(zzz3170, zzz3171, Neg(Succ(zzz317200)), zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, Succ(zzz4170), h) → new_mkVBalBranch3MkVBalBranch123(zzz3170, zzz3171, zzz317200, zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat2(Succ(new_primPlusNat3(new_primPlusNat1(zzz317200), zzz317200)), zzz317200)), zzz317200))), h)
new_mkVBalBranch3MkVBalBranch242(zzz972, zzz973, zzz974, zzz975, zzz976, zzz977, zzz978, zzz979, zzz980, zzz981, zzz982, Zero, Zero, bc) → new_mkVBalBranch3MkVBalBranch244(zzz972, zzz973, zzz974, zzz975, zzz976, zzz977, zzz978, zzz979, zzz980, zzz981, zzz982, bc)
new_mkVBalBranch3MkVBalBranch130(zzz3170, zzz3171, zzz317200, zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, h) → new_mkVBalBranch1(zzz31, zzz334, Branch(zzz3170, zzz3171, Neg(Succ(zzz317200)), zzz3173, zzz3174), h)
new_mkVBalBranch1(zzz31, Branch(zzz330, zzz331, Neg(Zero), zzz333, zzz334), Branch(zzz3170, zzz3171, Pos(Succ(zzz317200)), zzz3173, zzz3174), h) → new_mkVBalBranch1(zzz31, Branch(zzz330, zzz331, Neg(Zero), zzz333, zzz334), zzz3173, h)
new_mkVBalBranch3MkVBalBranch235(zzz3170, zzz3171, Neg(Zero), zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, Succ(zzz4170), h) → new_mkVBalBranch1(zzz31, zzz334, Branch(zzz3170, zzz3171, Neg(Zero), zzz3173, zzz3174), h)
new_mkVBalBranch3MkVBalBranch236(zzz958, zzz959, zzz960, zzz961, zzz962, zzz963, zzz964, zzz965, zzz966, zzz967, zzz968, Zero, Zero, ba) → new_mkVBalBranch3MkVBalBranch240(zzz958, zzz959, zzz960, zzz961, zzz962, zzz963, zzz964, zzz965, zzz966, zzz967, zzz968, ba)

The TRS R consists of the following rules:

new_primPlusNat1(Zero) → Zero
new_primPlusNat1(Succ(zzz62000)) → Succ(Succ(new_primPlusNat1(zzz62000)))
new_primPlusNat3(zzz90, Succ(zzz910)) → Succ(Succ(new_primPlusNat2(zzz90, zzz910)))
new_primPlusNat3(zzz90, Zero) → Succ(zzz90)
new_primPlusNat2(Succ(zzz900), Succ(zzz9100)) → Succ(Succ(new_primPlusNat2(zzz900, zzz9100)))
new_primPlusNat2(Succ(zzz900), Zero) → Succ(zzz900)
new_primPlusNat2(Zero, Succ(zzz9100)) → Succ(zzz9100)
new_primPlusNat2(Zero, Zero) → Zero

The set Q consists of the following terms:

new_primPlusNat2(Zero, Succ(x0))
new_primPlusNat3(x0, Succ(x1))
new_primPlusNat2(Succ(x0), Succ(x1))
new_primPlusNat3(x0, Zero)
new_primPlusNat1(Zero)
new_primPlusNat2(Zero, Zero)
new_primPlusNat1(Succ(x0))
new_primPlusNat2(Succ(x0), Zero)

We have to consider all minimal (P,Q,R)-chains.
The approximation of the Dependency Graph [15,17,22] contains 1 SCC with 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
                                  ↳ QDP
                                  ↳ QDP
                                    ↳ DependencyGraphProof
                                      ↳ QDP
                                        ↳ Rewriting
                                          ↳ QDP
                                            ↳ Rewriting
                                              ↳ QDP
                                                ↳ Rewriting
                                                  ↳ QDP
                                                    ↳ Rewriting
                                                      ↳ QDP
                                                        ↳ Rewriting
                                                          ↳ QDP
                                                            ↳ Rewriting
                                                              ↳ QDP
                                                                ↳ Rewriting
                                                                  ↳ QDP
                                                                    ↳ Rewriting
                                                                      ↳ QDP
                                                                        ↳ Rewriting
                                                                          ↳ QDP
                                                                            ↳ Rewriting
                                                                              ↳ QDP
                                                                                ↳ UsableRulesProof
                                                                                  ↳ QDP
                                                                                    ↳ QReductionProof
                                                                                      ↳ QDP
                                                                                        ↳ Rewriting
                                                                                          ↳ QDP
                                                                                            ↳ Rewriting
                                                                                              ↳ QDP
                                                                                                ↳ Rewriting
                                                                                                  ↳ QDP
                                                                                                    ↳ Rewriting
                                                                                                      ↳ QDP
                                                                                                        ↳ Rewriting
                                                                                                          ↳ QDP
                                                                                                            ↳ Rewriting
                                                                                                              ↳ QDP
                                                                                                                ↳ Rewriting
                                                                                                                  ↳ QDP
                                                                                                                    ↳ Rewriting
                                                                                                                      ↳ QDP
                                                                                                                        ↳ Rewriting
                                                                                                                          ↳ QDP
                                                                                                                            ↳ Rewriting
                                                                                                                              ↳ QDP
                                                                                                                                ↳ UsableRulesProof
                                                                                                                                  ↳ QDP
                                                                                                                                    ↳ QReductionProof
                                                                                                                                      ↳ QDP
                                                                                                                                        ↳ Rewriting
                                                                                                                                          ↳ QDP
                                                                                                                                            ↳ Rewriting
                                                                                                                                              ↳ QDP
                                                                                                                                                ↳ Rewriting
                                                                                                                                                  ↳ QDP
                                                                                                                                                    ↳ DependencyGraphProof
                                                                                                                                                      ↳ QDP
                                                                                                                                                        ↳ Rewriting
                                                                                                                                                          ↳ QDP
                                                                                                                                                            ↳ Rewriting
                                                                                                                                                              ↳ QDP
                                                                                                                                                                ↳ DependencyGraphProof
                                                                                                                                                                  ↳ QDP
                                                                                                                                                                    ↳ Rewriting
                                                                                                                                                                      ↳ QDP
                                                                                                                                                                        ↳ Rewriting
                                                                                                                                                                          ↳ QDP
                                                                                                                                                                            ↳ Rewriting
                                                                                                                                                                              ↳ QDP
                                                                                                                                                                                ↳ Rewriting
                                                                                                                                                                                  ↳ QDP
                                                                                                                                                                                    ↳ Rewriting
                                                                                                                                                                                      ↳ QDP
                                                                                                                                                                                        ↳ Rewriting
                                                                                                                                                                                          ↳ QDP
                                                                                                                                                                                            ↳ Rewriting
                                                                                                                                                                                              ↳ QDP
                                                                                                                                                                                                ↳ DependencyGraphProof
                                                                                                                                                                                                  ↳ QDP
                                                                                                                                                                                                    ↳ Rewriting
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP

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

new_mkVBalBranch3MkVBalBranch129(zzz1851, zzz1852, zzz1853, zzz1854, zzz1855, zzz1856, zzz1857, zzz1858, zzz1859, zzz1860, zzz1861, Zero, Succ(zzz18630), bd) → new_mkVBalBranch1(zzz1861, zzz1860, Branch(zzz1851, zzz1852, Neg(Succ(zzz1853)), zzz1854, zzz1855), bd)
new_mkVBalBranch3MkVBalBranch241(zzz3170, zzz3171, Pos(zzz31720), zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, Succ(zzz4190), h) → new_mkVBalBranch1(zzz31, Branch(zzz330, zzz331, Neg(Succ(zzz33200)), zzz333, zzz334), zzz3173, h)
new_mkVBalBranch3MkVBalBranch128(zzz972, zzz973, zzz974, zzz975, zzz976, zzz977, zzz978, zzz979, zzz980, zzz981, zzz982, Succ(zzz10190), bc) → new_mkVBalBranch3MkVBalBranch129(zzz972, zzz973, zzz974, zzz975, zzz976, zzz977, zzz978, zzz979, zzz980, zzz981, zzz982, Succ(zzz979), Succ(zzz10190), bc)
new_mkVBalBranch3MkVBalBranch127(zzz3170, zzz3171, zzz317200, zzz3173, zzz3174, zzz330, zzz331, zzz333, zzz334, zzz31, Succ(zzz5500), h) → new_mkVBalBranch1(zzz31, zzz334, Branch(zzz3170, zzz3171, Neg(Succ(zzz317200)), zzz3173, zzz3174), h)
new_mkVBalBranch1(zzz31, Branch(zzz330, zzz331, Neg(Zero), zzz333, zzz334), Branch(zzz3170, zzz3171, Neg(Succ(zzz317200)), zzz3173, zzz3174), h) → new_mkVBalBranch3MkVBalBranch127(zzz3170, zzz3171, zzz317200, zzz3173, zzz3174, zzz330, zzz331, zzz333, zzz334, zzz31, Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat2(Succ(new_primPlusNat3(new_primPlusNat1(zzz317200), zzz317200)), zzz317200)), zzz317200))), h)
new_mkVBalBranch3MkVBalBranch129(zzz1851, zzz1852, zzz1853, zzz1854, zzz1855, zzz1856, zzz1857, zzz1858, zzz1859, zzz1860, zzz1861, Succ(zzz18620), Succ(zzz18630), bd) → new_mkVBalBranch3MkVBalBranch129(zzz1851, zzz1852, zzz1853, zzz1854, zzz1855, zzz1856, zzz1857, zzz1858, zzz1859, zzz1860, zzz1861, zzz18620, zzz18630, bd)
new_mkVBalBranch3MkVBalBranch236(zzz958, zzz959, zzz960, zzz961, zzz962, zzz963, zzz964, zzz965, zzz966, zzz967, zzz968, Succ(zzz9690), Zero, ba) → new_mkVBalBranch3MkVBalBranch124(zzz958, zzz959, zzz960, zzz961, zzz962, zzz963, zzz964, zzz965, zzz966, zzz967, zzz968, Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat2(Succ(new_primPlusNat3(new_primPlusNat1(zzz960), zzz960)), zzz960)), zzz960))), ba)
new_mkVBalBranch3MkVBalBranch124(zzz958, zzz959, zzz960, zzz961, zzz962, zzz963, zzz964, zzz965, zzz966, zzz967, zzz968, Zero, ba) → new_mkVBalBranch3MkVBalBranch125(zzz958, zzz959, zzz960, zzz961, zzz962, zzz963, zzz964, zzz965, zzz966, zzz967, zzz968, Zero, Succ(zzz965), ba)
new_mkVBalBranch1(zzz31, Branch(zzz330, zzz331, Pos(Zero), zzz333, zzz334), Branch(zzz3170, zzz3171, Neg(Succ(zzz317200)), zzz3173, zzz3174), h) → new_mkVBalBranch3MkVBalBranch126(zzz3170, zzz3171, zzz317200, zzz3173, zzz3174, zzz330, zzz331, zzz333, zzz334, zzz31, new_primPlusNat2(Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat3(new_primPlusNat1(zzz317200), zzz317200)), zzz317200))), Succ(zzz317200)), h)
new_mkVBalBranch3MkVBalBranch235(zzz3170, zzz3171, Pos(Succ(zzz317200)), zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, Succ(zzz4170), h) → new_mkVBalBranch3MkVBalBranch236(zzz3170, zzz3171, zzz317200, zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, zzz4170, zzz317200, h)
new_mkVBalBranch3MkVBalBranch242(zzz972, zzz973, zzz974, zzz975, zzz976, zzz977, zzz978, zzz979, zzz980, zzz981, zzz982, Succ(zzz9830), Succ(zzz9840), bc) → new_mkVBalBranch3MkVBalBranch242(zzz972, zzz973, zzz974, zzz975, zzz976, zzz977, zzz978, zzz979, zzz980, zzz981, zzz982, zzz9830, zzz9840, bc)
new_mkVBalBranch1(zzz31, Branch(zzz330, zzz331, Neg(Succ(zzz33200)), zzz333, zzz334), Branch(zzz3170, zzz3171, zzz3172, zzz3173, zzz3174), h) → new_mkVBalBranch3MkVBalBranch241(zzz3170, zzz3171, zzz3172, zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat2(Succ(new_primPlusNat3(new_primPlusNat1(zzz33200), zzz33200)), zzz33200)), zzz33200))), h)
new_mkVBalBranch1(zzz31, Branch(zzz330, zzz331, Pos(Succ(zzz33200)), zzz333, zzz334), Branch(zzz3170, zzz3171, zzz3172, zzz3173, zzz3174), h) → new_mkVBalBranch3MkVBalBranch235(zzz3170, zzz3171, zzz3172, zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat2(Succ(new_primPlusNat3(new_primPlusNat1(zzz33200), zzz33200)), zzz33200)), zzz33200))), h)
new_mkVBalBranch3MkVBalBranch236(zzz958, zzz959, zzz960, zzz961, zzz962, zzz963, zzz964, zzz965, zzz966, zzz967, zzz968, Succ(zzz9690), Succ(zzz9700), ba) → new_mkVBalBranch3MkVBalBranch236(zzz958, zzz959, zzz960, zzz961, zzz962, zzz963, zzz964, zzz965, zzz966, zzz967, zzz968, zzz9690, zzz9700, ba)
new_mkVBalBranch3MkVBalBranch241(zzz3170, zzz3171, Neg(Succ(zzz317200)), zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, Succ(zzz4190), h) → new_mkVBalBranch3MkVBalBranch242(zzz3170, zzz3171, zzz317200, zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, zzz317200, zzz4190, h)
new_mkVBalBranch1(zzz31, Branch(zzz330, zzz331, Pos(Zero), zzz333, zzz334), Branch(zzz3170, zzz3171, Pos(Succ(zzz317200)), zzz3173, zzz3174), h) → new_mkVBalBranch1(zzz31, Branch(zzz330, zzz331, Pos(Zero), zzz333, zzz334), zzz3173, h)
new_mkVBalBranch3MkVBalBranch237(zzz3170, zzz3171, zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, h) → new_mkVBalBranch1(zzz31, zzz334, Branch(zzz3170, zzz3171, Pos(Zero), zzz3173, zzz3174), h)
new_mkVBalBranch3MkVBalBranch235(zzz3170, zzz3171, Pos(Zero), zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, Succ(zzz4170), h) → new_mkVBalBranch3MkVBalBranch237(zzz3170, zzz3171, zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, h)
new_mkVBalBranch3MkVBalBranch236(zzz958, zzz959, zzz960, zzz961, zzz962, zzz963, zzz964, zzz965, zzz966, zzz967, zzz968, Zero, Succ(zzz9700), ba) → new_mkVBalBranch1(zzz968, Branch(zzz963, zzz964, Pos(Succ(zzz965)), zzz966, zzz967), zzz961, ba)
new_mkVBalBranch3MkVBalBranch125(zzz1337, zzz1338, zzz1339, zzz1340, zzz1341, zzz1342, zzz1343, zzz1344, zzz1345, zzz1346, zzz1347, Succ(zzz13480), Succ(zzz13490), bb) → new_mkVBalBranch3MkVBalBranch125(zzz1337, zzz1338, zzz1339, zzz1340, zzz1341, zzz1342, zzz1343, zzz1344, zzz1345, zzz1346, zzz1347, zzz13480, zzz13490, bb)
new_mkVBalBranch3MkVBalBranch123(zzz3170, zzz3171, zzz317200, zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, Succ(zzz5620), h) → new_mkVBalBranch1(zzz31, zzz334, Branch(zzz3170, zzz3171, Neg(Succ(zzz317200)), zzz3173, zzz3174), h)
new_mkVBalBranch3MkVBalBranch125(zzz1337, zzz1338, zzz1339, zzz1340, zzz1341, zzz1342, zzz1343, zzz1344, zzz1345, zzz1346, zzz1347, Zero, Succ(zzz13490), bb) → new_mkVBalBranch1(zzz1347, zzz1346, Branch(zzz1337, zzz1338, Pos(Succ(zzz1339)), zzz1340, zzz1341), bb)
new_mkVBalBranch3MkVBalBranch242(zzz972, zzz973, zzz974, zzz975, zzz976, zzz977, zzz978, zzz979, zzz980, zzz981, zzz982, Zero, Succ(zzz9840), bc) → new_mkVBalBranch1(zzz982, Branch(zzz977, zzz978, Neg(Succ(zzz979)), zzz980, zzz981), zzz975, bc)
new_mkVBalBranch3MkVBalBranch240(zzz958, zzz959, zzz960, zzz961, zzz962, zzz963, zzz964, zzz965, zzz966, zzz967, zzz968, ba) → new_mkVBalBranch3MkVBalBranch124(zzz958, zzz959, zzz960, zzz961, zzz962, zzz963, zzz964, zzz965, zzz966, zzz967, zzz968, new_primPlusNat2(Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat3(new_primPlusNat1(zzz960), zzz960)), zzz960))), Succ(zzz960)), ba)
new_mkVBalBranch3MkVBalBranch242(zzz972, zzz973, zzz974, zzz975, zzz976, zzz977, zzz978, zzz979, zzz980, zzz981, zzz982, Succ(zzz9830), Zero, bc) → new_mkVBalBranch3MkVBalBranch128(zzz972, zzz973, zzz974, zzz975, zzz976, zzz977, zzz978, zzz979, zzz980, zzz981, zzz982, Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat2(Succ(new_primPlusNat3(new_primPlusNat1(zzz974), zzz974)), zzz974)), zzz974))), bc)
new_mkVBalBranch3MkVBalBranch126(zzz3170, zzz3171, zzz317200, zzz3173, zzz3174, zzz330, zzz331, zzz333, zzz334, zzz31, Succ(zzz5350), h) → new_mkVBalBranch1(zzz31, zzz334, Branch(zzz3170, zzz3171, Neg(Succ(zzz317200)), zzz3173, zzz3174), h)
new_mkVBalBranch3MkVBalBranch241(zzz3170, zzz3171, Neg(Zero), zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, Succ(zzz4190), h) → new_mkVBalBranch1(zzz31, Branch(zzz330, zzz331, Neg(Succ(zzz33200)), zzz333, zzz334), zzz3173, h)
new_mkVBalBranch3MkVBalBranch124(zzz958, zzz959, zzz960, zzz961, zzz962, zzz963, zzz964, zzz965, zzz966, zzz967, zzz968, Succ(zzz10180), ba) → new_mkVBalBranch3MkVBalBranch125(zzz958, zzz959, zzz960, zzz961, zzz962, zzz963, zzz964, zzz965, zzz966, zzz967, zzz968, Succ(zzz10180), Succ(zzz965), ba)
new_mkVBalBranch3MkVBalBranch244(zzz972, zzz973, zzz974, zzz975, zzz976, zzz977, zzz978, zzz979, zzz980, zzz981, zzz982, bc) → new_mkVBalBranch3MkVBalBranch128(zzz972, zzz973, zzz974, zzz975, zzz976, zzz977, zzz978, zzz979, zzz980, zzz981, zzz982, new_primPlusNat2(Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat3(new_primPlusNat1(zzz974), zzz974)), zzz974))), Succ(zzz974)), bc)
new_mkVBalBranch3MkVBalBranch235(zzz3170, zzz3171, Neg(Succ(zzz317200)), zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, Succ(zzz4170), h) → new_mkVBalBranch3MkVBalBranch123(zzz3170, zzz3171, zzz317200, zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat2(Succ(new_primPlusNat3(new_primPlusNat1(zzz317200), zzz317200)), zzz317200)), zzz317200))), h)
new_mkVBalBranch3MkVBalBranch242(zzz972, zzz973, zzz974, zzz975, zzz976, zzz977, zzz978, zzz979, zzz980, zzz981, zzz982, Zero, Zero, bc) → new_mkVBalBranch3MkVBalBranch244(zzz972, zzz973, zzz974, zzz975, zzz976, zzz977, zzz978, zzz979, zzz980, zzz981, zzz982, bc)
new_mkVBalBranch1(zzz31, Branch(zzz330, zzz331, Neg(Zero), zzz333, zzz334), Branch(zzz3170, zzz3171, Pos(Succ(zzz317200)), zzz3173, zzz3174), h) → new_mkVBalBranch1(zzz31, Branch(zzz330, zzz331, Neg(Zero), zzz333, zzz334), zzz3173, h)
new_mkVBalBranch3MkVBalBranch235(zzz3170, zzz3171, Neg(Zero), zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, Succ(zzz4170), h) → new_mkVBalBranch1(zzz31, zzz334, Branch(zzz3170, zzz3171, Neg(Zero), zzz3173, zzz3174), h)
new_mkVBalBranch3MkVBalBranch236(zzz958, zzz959, zzz960, zzz961, zzz962, zzz963, zzz964, zzz965, zzz966, zzz967, zzz968, Zero, Zero, ba) → new_mkVBalBranch3MkVBalBranch240(zzz958, zzz959, zzz960, zzz961, zzz962, zzz963, zzz964, zzz965, zzz966, zzz967, zzz968, ba)

The TRS R consists of the following rules:

new_primPlusNat1(Zero) → Zero
new_primPlusNat1(Succ(zzz62000)) → Succ(Succ(new_primPlusNat1(zzz62000)))
new_primPlusNat3(zzz90, Succ(zzz910)) → Succ(Succ(new_primPlusNat2(zzz90, zzz910)))
new_primPlusNat3(zzz90, Zero) → Succ(zzz90)
new_primPlusNat2(Succ(zzz900), Succ(zzz9100)) → Succ(Succ(new_primPlusNat2(zzz900, zzz9100)))
new_primPlusNat2(Succ(zzz900), Zero) → Succ(zzz900)
new_primPlusNat2(Zero, Succ(zzz9100)) → Succ(zzz9100)
new_primPlusNat2(Zero, Zero) → Zero

The set Q consists of the following terms:

new_primPlusNat2(Zero, Succ(x0))
new_primPlusNat3(x0, Succ(x1))
new_primPlusNat2(Succ(x0), Succ(x1))
new_primPlusNat3(x0, Zero)
new_primPlusNat1(Zero)
new_primPlusNat2(Zero, Zero)
new_primPlusNat1(Succ(x0))
new_primPlusNat2(Succ(x0), Zero)

We have to consider all minimal (P,Q,R)-chains.
By rewriting [15] the rule new_mkVBalBranch3MkVBalBranch240(zzz958, zzz959, zzz960, zzz961, zzz962, zzz963, zzz964, zzz965, zzz966, zzz967, zzz968, ba) → new_mkVBalBranch3MkVBalBranch124(zzz958, zzz959, zzz960, zzz961, zzz962, zzz963, zzz964, zzz965, zzz966, zzz967, zzz968, new_primPlusNat2(Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat3(new_primPlusNat1(zzz960), zzz960)), zzz960))), Succ(zzz960)), ba) at position [11] we obtained the following new rules:

new_mkVBalBranch3MkVBalBranch240(zzz958, zzz959, zzz960, zzz961, zzz962, zzz963, zzz964, zzz965, zzz966, zzz967, zzz968, ba) → new_mkVBalBranch3MkVBalBranch124(zzz958, zzz959, zzz960, zzz961, zzz962, zzz963, zzz964, zzz965, zzz966, zzz967, zzz968, Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat2(Succ(new_primPlusNat3(new_primPlusNat1(zzz960), zzz960)), zzz960)), zzz960))), 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
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                    ↳ DependencyGraphProof
                                      ↳ QDP
                                        ↳ Rewriting
                                          ↳ QDP
                                            ↳ Rewriting
                                              ↳ QDP
                                                ↳ Rewriting
                                                  ↳ QDP
                                                    ↳ Rewriting
                                                      ↳ QDP
                                                        ↳ Rewriting
                                                          ↳ QDP
                                                            ↳ Rewriting
                                                              ↳ QDP
                                                                ↳ Rewriting
                                                                  ↳ QDP
                                                                    ↳ Rewriting
                                                                      ↳ QDP
                                                                        ↳ Rewriting
                                                                          ↳ QDP
                                                                            ↳ Rewriting
                                                                              ↳ QDP
                                                                                ↳ UsableRulesProof
                                                                                  ↳ QDP
                                                                                    ↳ QReductionProof
                                                                                      ↳ QDP
                                                                                        ↳ Rewriting
                                                                                          ↳ QDP
                                                                                            ↳ Rewriting
                                                                                              ↳ QDP
                                                                                                ↳ Rewriting
                                                                                                  ↳ QDP
                                                                                                    ↳ Rewriting
                                                                                                      ↳ QDP
                                                                                                        ↳ Rewriting
                                                                                                          ↳ QDP
                                                                                                            ↳ Rewriting
                                                                                                              ↳ QDP
                                                                                                                ↳ Rewriting
                                                                                                                  ↳ QDP
                                                                                                                    ↳ Rewriting
                                                                                                                      ↳ QDP
                                                                                                                        ↳ Rewriting
                                                                                                                          ↳ QDP
                                                                                                                            ↳ Rewriting
                                                                                                                              ↳ QDP
                                                                                                                                ↳ UsableRulesProof
                                                                                                                                  ↳ QDP
                                                                                                                                    ↳ QReductionProof
                                                                                                                                      ↳ QDP
                                                                                                                                        ↳ Rewriting
                                                                                                                                          ↳ QDP
                                                                                                                                            ↳ Rewriting
                                                                                                                                              ↳ QDP
                                                                                                                                                ↳ Rewriting
                                                                                                                                                  ↳ QDP
                                                                                                                                                    ↳ DependencyGraphProof
                                                                                                                                                      ↳ QDP
                                                                                                                                                        ↳ Rewriting
                                                                                                                                                          ↳ QDP
                                                                                                                                                            ↳ Rewriting
                                                                                                                                                              ↳ QDP
                                                                                                                                                                ↳ DependencyGraphProof
                                                                                                                                                                  ↳ QDP
                                                                                                                                                                    ↳ Rewriting
                                                                                                                                                                      ↳ QDP
                                                                                                                                                                        ↳ Rewriting
                                                                                                                                                                          ↳ QDP
                                                                                                                                                                            ↳ Rewriting
                                                                                                                                                                              ↳ QDP
                                                                                                                                                                                ↳ Rewriting
                                                                                                                                                                                  ↳ QDP
                                                                                                                                                                                    ↳ Rewriting
                                                                                                                                                                                      ↳ QDP
                                                                                                                                                                                        ↳ Rewriting
                                                                                                                                                                                          ↳ QDP
                                                                                                                                                                                            ↳ Rewriting
                                                                                                                                                                                              ↳ QDP
                                                                                                                                                                                                ↳ DependencyGraphProof
                                                                                                                                                                                                  ↳ QDP
                                                                                                                                                                                                    ↳ Rewriting
                                                                                                                                                                                                      ↳ QDP
                                                                                                                                                                                                        ↳ DependencyGraphProof
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP

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

new_mkVBalBranch3MkVBalBranch129(zzz1851, zzz1852, zzz1853, zzz1854, zzz1855, zzz1856, zzz1857, zzz1858, zzz1859, zzz1860, zzz1861, Zero, Succ(zzz18630), bd) → new_mkVBalBranch1(zzz1861, zzz1860, Branch(zzz1851, zzz1852, Neg(Succ(zzz1853)), zzz1854, zzz1855), bd)
new_mkVBalBranch3MkVBalBranch127(zzz3170, zzz3171, zzz317200, zzz3173, zzz3174, zzz330, zzz331, zzz333, zzz334, zzz31, Succ(zzz5500), h) → new_mkVBalBranch1(zzz31, zzz334, Branch(zzz3170, zzz3171, Neg(Succ(zzz317200)), zzz3173, zzz3174), h)
new_mkVBalBranch3MkVBalBranch128(zzz972, zzz973, zzz974, zzz975, zzz976, zzz977, zzz978, zzz979, zzz980, zzz981, zzz982, Succ(zzz10190), bc) → new_mkVBalBranch3MkVBalBranch129(zzz972, zzz973, zzz974, zzz975, zzz976, zzz977, zzz978, zzz979, zzz980, zzz981, zzz982, Succ(zzz979), Succ(zzz10190), bc)
new_mkVBalBranch3MkVBalBranch241(zzz3170, zzz3171, Pos(zzz31720), zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, Succ(zzz4190), h) → new_mkVBalBranch1(zzz31, Branch(zzz330, zzz331, Neg(Succ(zzz33200)), zzz333, zzz334), zzz3173, h)
new_mkVBalBranch3MkVBalBranch240(zzz958, zzz959, zzz960, zzz961, zzz962, zzz963, zzz964, zzz965, zzz966, zzz967, zzz968, ba) → new_mkVBalBranch3MkVBalBranch124(zzz958, zzz959, zzz960, zzz961, zzz962, zzz963, zzz964, zzz965, zzz966, zzz967, zzz968, Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat2(Succ(new_primPlusNat3(new_primPlusNat1(zzz960), zzz960)), zzz960)), zzz960))), ba)
new_mkVBalBranch1(zzz31, Branch(zzz330, zzz331, Neg(Zero), zzz333, zzz334), Branch(zzz3170, zzz3171, Neg(Succ(zzz317200)), zzz3173, zzz3174), h) → new_mkVBalBranch3MkVBalBranch127(zzz3170, zzz3171, zzz317200, zzz3173, zzz3174, zzz330, zzz331, zzz333, zzz334, zzz31, Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat2(Succ(new_primPlusNat3(new_primPlusNat1(zzz317200), zzz317200)), zzz317200)), zzz317200))), h)
new_mkVBalBranch3MkVBalBranch129(zzz1851, zzz1852, zzz1853, zzz1854, zzz1855, zzz1856, zzz1857, zzz1858, zzz1859, zzz1860, zzz1861, Succ(zzz18620), Succ(zzz18630), bd) → new_mkVBalBranch3MkVBalBranch129(zzz1851, zzz1852, zzz1853, zzz1854, zzz1855, zzz1856, zzz1857, zzz1858, zzz1859, zzz1860, zzz1861, zzz18620, zzz18630, bd)
new_mkVBalBranch3MkVBalBranch236(zzz958, zzz959, zzz960, zzz961, zzz962, zzz963, zzz964, zzz965, zzz966, zzz967, zzz968, Succ(zzz9690), Zero, ba) → new_mkVBalBranch3MkVBalBranch124(zzz958, zzz959, zzz960, zzz961, zzz962, zzz963, zzz964, zzz965, zzz966, zzz967, zzz968, Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat2(Succ(new_primPlusNat3(new_primPlusNat1(zzz960), zzz960)), zzz960)), zzz960))), ba)
new_mkVBalBranch3MkVBalBranch124(zzz958, zzz959, zzz960, zzz961, zzz962, zzz963, zzz964, zzz965, zzz966, zzz967, zzz968, Zero, ba) → new_mkVBalBranch3MkVBalBranch125(zzz958, zzz959, zzz960, zzz961, zzz962, zzz963, zzz964, zzz965, zzz966, zzz967, zzz968, Zero, Succ(zzz965), ba)
new_mkVBalBranch3MkVBalBranch242(zzz972, zzz973, zzz974, zzz975, zzz976, zzz977, zzz978, zzz979, zzz980, zzz981, zzz982, Succ(zzz9830), Succ(zzz9840), bc) → new_mkVBalBranch3MkVBalBranch242(zzz972, zzz973, zzz974, zzz975, zzz976, zzz977, zzz978, zzz979, zzz980, zzz981, zzz982, zzz9830, zzz9840, bc)
new_mkVBalBranch3MkVBalBranch235(zzz3170, zzz3171, Pos(Succ(zzz317200)), zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, Succ(zzz4170), h) → new_mkVBalBranch3MkVBalBranch236(zzz3170, zzz3171, zzz317200, zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, zzz4170, zzz317200, h)
new_mkVBalBranch1(zzz31, Branch(zzz330, zzz331, Pos(Zero), zzz333, zzz334), Branch(zzz3170, zzz3171, Neg(Succ(zzz317200)), zzz3173, zzz3174), h) → new_mkVBalBranch3MkVBalBranch126(zzz3170, zzz3171, zzz317200, zzz3173, zzz3174, zzz330, zzz331, zzz333, zzz334, zzz31, new_primPlusNat2(Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat3(new_primPlusNat1(zzz317200), zzz317200)), zzz317200))), Succ(zzz317200)), h)
new_mkVBalBranch1(zzz31, Branch(zzz330, zzz331, Pos(Succ(zzz33200)), zzz333, zzz334), Branch(zzz3170, zzz3171, zzz3172, zzz3173, zzz3174), h) → new_mkVBalBranch3MkVBalBranch235(zzz3170, zzz3171, zzz3172, zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat2(Succ(new_primPlusNat3(new_primPlusNat1(zzz33200), zzz33200)), zzz33200)), zzz33200))), h)
new_mkVBalBranch1(zzz31, Branch(zzz330, zzz331, Neg(Succ(zzz33200)), zzz333, zzz334), Branch(zzz3170, zzz3171, zzz3172, zzz3173, zzz3174), h) → new_mkVBalBranch3MkVBalBranch241(zzz3170, zzz3171, zzz3172, zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat2(Succ(new_primPlusNat3(new_primPlusNat1(zzz33200), zzz33200)), zzz33200)), zzz33200))), h)
new_mkVBalBranch3MkVBalBranch236(zzz958, zzz959, zzz960, zzz961, zzz962, zzz963, zzz964, zzz965, zzz966, zzz967, zzz968, Succ(zzz9690), Succ(zzz9700), ba) → new_mkVBalBranch3MkVBalBranch236(zzz958, zzz959, zzz960, zzz961, zzz962, zzz963, zzz964, zzz965, zzz966, zzz967, zzz968, zzz9690, zzz9700, ba)
new_mkVBalBranch3MkVBalBranch241(zzz3170, zzz3171, Neg(Succ(zzz317200)), zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, Succ(zzz4190), h) → new_mkVBalBranch3MkVBalBranch242(zzz3170, zzz3171, zzz317200, zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, zzz317200, zzz4190, h)
new_mkVBalBranch1(zzz31, Branch(zzz330, zzz331, Pos(Zero), zzz333, zzz334), Branch(zzz3170, zzz3171, Pos(Succ(zzz317200)), zzz3173, zzz3174), h) → new_mkVBalBranch1(zzz31, Branch(zzz330, zzz331, Pos(Zero), zzz333, zzz334), zzz3173, h)
new_mkVBalBranch3MkVBalBranch237(zzz3170, zzz3171, zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, h) → new_mkVBalBranch1(zzz31, zzz334, Branch(zzz3170, zzz3171, Pos(Zero), zzz3173, zzz3174), h)
new_mkVBalBranch3MkVBalBranch235(zzz3170, zzz3171, Pos(Zero), zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, Succ(zzz4170), h) → new_mkVBalBranch3MkVBalBranch237(zzz3170, zzz3171, zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, h)
new_mkVBalBranch3MkVBalBranch236(zzz958, zzz959, zzz960, zzz961, zzz962, zzz963, zzz964, zzz965, zzz966, zzz967, zzz968, Zero, Succ(zzz9700), ba) → new_mkVBalBranch1(zzz968, Branch(zzz963, zzz964, Pos(Succ(zzz965)), zzz966, zzz967), zzz961, ba)
new_mkVBalBranch3MkVBalBranch125(zzz1337, zzz1338, zzz1339, zzz1340, zzz1341, zzz1342, zzz1343, zzz1344, zzz1345, zzz1346, zzz1347, Succ(zzz13480), Succ(zzz13490), bb) → new_mkVBalBranch3MkVBalBranch125(zzz1337, zzz1338, zzz1339, zzz1340, zzz1341, zzz1342, zzz1343, zzz1344, zzz1345, zzz1346, zzz1347, zzz13480, zzz13490, bb)
new_mkVBalBranch3MkVBalBranch123(zzz3170, zzz3171, zzz317200, zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, Succ(zzz5620), h) → new_mkVBalBranch1(zzz31, zzz334, Branch(zzz3170, zzz3171, Neg(Succ(zzz317200)), zzz3173, zzz3174), h)
new_mkVBalBranch3MkVBalBranch125(zzz1337, zzz1338, zzz1339, zzz1340, zzz1341, zzz1342, zzz1343, zzz1344, zzz1345, zzz1346, zzz1347, Zero, Succ(zzz13490), bb) → new_mkVBalBranch1(zzz1347, zzz1346, Branch(zzz1337, zzz1338, Pos(Succ(zzz1339)), zzz1340, zzz1341), bb)
new_mkVBalBranch3MkVBalBranch242(zzz972, zzz973, zzz974, zzz975, zzz976, zzz977, zzz978, zzz979, zzz980, zzz981, zzz982, Zero, Succ(zzz9840), bc) → new_mkVBalBranch1(zzz982, Branch(zzz977, zzz978, Neg(Succ(zzz979)), zzz980, zzz981), zzz975, bc)
new_mkVBalBranch3MkVBalBranch242(zzz972, zzz973, zzz974, zzz975, zzz976, zzz977, zzz978, zzz979, zzz980, zzz981, zzz982, Succ(zzz9830), Zero, bc) → new_mkVBalBranch3MkVBalBranch128(zzz972, zzz973, zzz974, zzz975, zzz976, zzz977, zzz978, zzz979, zzz980, zzz981, zzz982, Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat2(Succ(new_primPlusNat3(new_primPlusNat1(zzz974), zzz974)), zzz974)), zzz974))), bc)
new_mkVBalBranch3MkVBalBranch126(zzz3170, zzz3171, zzz317200, zzz3173, zzz3174, zzz330, zzz331, zzz333, zzz334, zzz31, Succ(zzz5350), h) → new_mkVBalBranch1(zzz31, zzz334, Branch(zzz3170, zzz3171, Neg(Succ(zzz317200)), zzz3173, zzz3174), h)
new_mkVBalBranch3MkVBalBranch241(zzz3170, zzz3171, Neg(Zero), zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, Succ(zzz4190), h) → new_mkVBalBranch1(zzz31, Branch(zzz330, zzz331, Neg(Succ(zzz33200)), zzz333, zzz334), zzz3173, h)
new_mkVBalBranch3MkVBalBranch244(zzz972, zzz973, zzz974, zzz975, zzz976, zzz977, zzz978, zzz979, zzz980, zzz981, zzz982, bc) → new_mkVBalBranch3MkVBalBranch128(zzz972, zzz973, zzz974, zzz975, zzz976, zzz977, zzz978, zzz979, zzz980, zzz981, zzz982, new_primPlusNat2(Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat3(new_primPlusNat1(zzz974), zzz974)), zzz974))), Succ(zzz974)), bc)
new_mkVBalBranch3MkVBalBranch124(zzz958, zzz959, zzz960, zzz961, zzz962, zzz963, zzz964, zzz965, zzz966, zzz967, zzz968, Succ(zzz10180), ba) → new_mkVBalBranch3MkVBalBranch125(zzz958, zzz959, zzz960, zzz961, zzz962, zzz963, zzz964, zzz965, zzz966, zzz967, zzz968, Succ(zzz10180), Succ(zzz965), ba)
new_mkVBalBranch3MkVBalBranch235(zzz3170, zzz3171, Neg(Succ(zzz317200)), zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, Succ(zzz4170), h) → new_mkVBalBranch3MkVBalBranch123(zzz3170, zzz3171, zzz317200, zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat2(Succ(new_primPlusNat3(new_primPlusNat1(zzz317200), zzz317200)), zzz317200)), zzz317200))), h)
new_mkVBalBranch3MkVBalBranch242(zzz972, zzz973, zzz974, zzz975, zzz976, zzz977, zzz978, zzz979, zzz980, zzz981, zzz982, Zero, Zero, bc) → new_mkVBalBranch3MkVBalBranch244(zzz972, zzz973, zzz974, zzz975, zzz976, zzz977, zzz978, zzz979, zzz980, zzz981, zzz982, bc)
new_mkVBalBranch1(zzz31, Branch(zzz330, zzz331, Neg(Zero), zzz333, zzz334), Branch(zzz3170, zzz3171, Pos(Succ(zzz317200)), zzz3173, zzz3174), h) → new_mkVBalBranch1(zzz31, Branch(zzz330, zzz331, Neg(Zero), zzz333, zzz334), zzz3173, h)
new_mkVBalBranch3MkVBalBranch235(zzz3170, zzz3171, Neg(Zero), zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, Succ(zzz4170), h) → new_mkVBalBranch1(zzz31, zzz334, Branch(zzz3170, zzz3171, Neg(Zero), zzz3173, zzz3174), h)
new_mkVBalBranch3MkVBalBranch236(zzz958, zzz959, zzz960, zzz961, zzz962, zzz963, zzz964, zzz965, zzz966, zzz967, zzz968, Zero, Zero, ba) → new_mkVBalBranch3MkVBalBranch240(zzz958, zzz959, zzz960, zzz961, zzz962, zzz963, zzz964, zzz965, zzz966, zzz967, zzz968, ba)

The TRS R consists of the following rules:

new_primPlusNat1(Zero) → Zero
new_primPlusNat1(Succ(zzz62000)) → Succ(Succ(new_primPlusNat1(zzz62000)))
new_primPlusNat3(zzz90, Succ(zzz910)) → Succ(Succ(new_primPlusNat2(zzz90, zzz910)))
new_primPlusNat3(zzz90, Zero) → Succ(zzz90)
new_primPlusNat2(Succ(zzz900), Succ(zzz9100)) → Succ(Succ(new_primPlusNat2(zzz900, zzz9100)))
new_primPlusNat2(Succ(zzz900), Zero) → Succ(zzz900)
new_primPlusNat2(Zero, Succ(zzz9100)) → Succ(zzz9100)
new_primPlusNat2(Zero, Zero) → Zero

The set Q consists of the following terms:

new_primPlusNat2(Zero, Succ(x0))
new_primPlusNat3(x0, Succ(x1))
new_primPlusNat2(Succ(x0), Succ(x1))
new_primPlusNat3(x0, Zero)
new_primPlusNat1(Zero)
new_primPlusNat2(Zero, Zero)
new_primPlusNat1(Succ(x0))
new_primPlusNat2(Succ(x0), Zero)

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

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

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

new_mkVBalBranch3MkVBalBranch129(zzz1851, zzz1852, zzz1853, zzz1854, zzz1855, zzz1856, zzz1857, zzz1858, zzz1859, zzz1860, zzz1861, Zero, Succ(zzz18630), bd) → new_mkVBalBranch1(zzz1861, zzz1860, Branch(zzz1851, zzz1852, Neg(Succ(zzz1853)), zzz1854, zzz1855), bd)
new_mkVBalBranch3MkVBalBranch241(zzz3170, zzz3171, Pos(zzz31720), zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, Succ(zzz4190), h) → new_mkVBalBranch1(zzz31, Branch(zzz330, zzz331, Neg(Succ(zzz33200)), zzz333, zzz334), zzz3173, h)
new_mkVBalBranch3MkVBalBranch128(zzz972, zzz973, zzz974, zzz975, zzz976, zzz977, zzz978, zzz979, zzz980, zzz981, zzz982, Succ(zzz10190), bc) → new_mkVBalBranch3MkVBalBranch129(zzz972, zzz973, zzz974, zzz975, zzz976, zzz977, zzz978, zzz979, zzz980, zzz981, zzz982, Succ(zzz979), Succ(zzz10190), bc)
new_mkVBalBranch3MkVBalBranch127(zzz3170, zzz3171, zzz317200, zzz3173, zzz3174, zzz330, zzz331, zzz333, zzz334, zzz31, Succ(zzz5500), h) → new_mkVBalBranch1(zzz31, zzz334, Branch(zzz3170, zzz3171, Neg(Succ(zzz317200)), zzz3173, zzz3174), h)
new_mkVBalBranch3MkVBalBranch240(zzz958, zzz959, zzz960, zzz961, zzz962, zzz963, zzz964, zzz965, zzz966, zzz967, zzz968, ba) → new_mkVBalBranch3MkVBalBranch124(zzz958, zzz959, zzz960, zzz961, zzz962, zzz963, zzz964, zzz965, zzz966, zzz967, zzz968, Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat2(Succ(new_primPlusNat3(new_primPlusNat1(zzz960), zzz960)), zzz960)), zzz960))), ba)
new_mkVBalBranch1(zzz31, Branch(zzz330, zzz331, Neg(Zero), zzz333, zzz334), Branch(zzz3170, zzz3171, Neg(Succ(zzz317200)), zzz3173, zzz3174), h) → new_mkVBalBranch3MkVBalBranch127(zzz3170, zzz3171, zzz317200, zzz3173, zzz3174, zzz330, zzz331, zzz333, zzz334, zzz31, Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat2(Succ(new_primPlusNat3(new_primPlusNat1(zzz317200), zzz317200)), zzz317200)), zzz317200))), h)
new_mkVBalBranch3MkVBalBranch129(zzz1851, zzz1852, zzz1853, zzz1854, zzz1855, zzz1856, zzz1857, zzz1858, zzz1859, zzz1860, zzz1861, Succ(zzz18620), Succ(zzz18630), bd) → new_mkVBalBranch3MkVBalBranch129(zzz1851, zzz1852, zzz1853, zzz1854, zzz1855, zzz1856, zzz1857, zzz1858, zzz1859, zzz1860, zzz1861, zzz18620, zzz18630, bd)
new_mkVBalBranch3MkVBalBranch236(zzz958, zzz959, zzz960, zzz961, zzz962, zzz963, zzz964, zzz965, zzz966, zzz967, zzz968, Succ(zzz9690), Zero, ba) → new_mkVBalBranch3MkVBalBranch124(zzz958, zzz959, zzz960, zzz961, zzz962, zzz963, zzz964, zzz965, zzz966, zzz967, zzz968, Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat2(Succ(new_primPlusNat3(new_primPlusNat1(zzz960), zzz960)), zzz960)), zzz960))), ba)
new_mkVBalBranch3MkVBalBranch242(zzz972, zzz973, zzz974, zzz975, zzz976, zzz977, zzz978, zzz979, zzz980, zzz981, zzz982, Succ(zzz9830), Succ(zzz9840), bc) → new_mkVBalBranch3MkVBalBranch242(zzz972, zzz973, zzz974, zzz975, zzz976, zzz977, zzz978, zzz979, zzz980, zzz981, zzz982, zzz9830, zzz9840, bc)
new_mkVBalBranch3MkVBalBranch235(zzz3170, zzz3171, Pos(Succ(zzz317200)), zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, Succ(zzz4170), h) → new_mkVBalBranch3MkVBalBranch236(zzz3170, zzz3171, zzz317200, zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, zzz4170, zzz317200, h)
new_mkVBalBranch1(zzz31, Branch(zzz330, zzz331, Pos(Zero), zzz333, zzz334), Branch(zzz3170, zzz3171, Neg(Succ(zzz317200)), zzz3173, zzz3174), h) → new_mkVBalBranch3MkVBalBranch126(zzz3170, zzz3171, zzz317200, zzz3173, zzz3174, zzz330, zzz331, zzz333, zzz334, zzz31, new_primPlusNat2(Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat3(new_primPlusNat1(zzz317200), zzz317200)), zzz317200))), Succ(zzz317200)), h)
new_mkVBalBranch1(zzz31, Branch(zzz330, zzz331, Neg(Succ(zzz33200)), zzz333, zzz334), Branch(zzz3170, zzz3171, zzz3172, zzz3173, zzz3174), h) → new_mkVBalBranch3MkVBalBranch241(zzz3170, zzz3171, zzz3172, zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat2(Succ(new_primPlusNat3(new_primPlusNat1(zzz33200), zzz33200)), zzz33200)), zzz33200))), h)
new_mkVBalBranch1(zzz31, Branch(zzz330, zzz331, Pos(Succ(zzz33200)), zzz333, zzz334), Branch(zzz3170, zzz3171, zzz3172, zzz3173, zzz3174), h) → new_mkVBalBranch3MkVBalBranch235(zzz3170, zzz3171, zzz3172, zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat2(Succ(new_primPlusNat3(new_primPlusNat1(zzz33200), zzz33200)), zzz33200)), zzz33200))), h)
new_mkVBalBranch3MkVBalBranch236(zzz958, zzz959, zzz960, zzz961, zzz962, zzz963, zzz964, zzz965, zzz966, zzz967, zzz968, Succ(zzz9690), Succ(zzz9700), ba) → new_mkVBalBranch3MkVBalBranch236(zzz958, zzz959, zzz960, zzz961, zzz962, zzz963, zzz964, zzz965, zzz966, zzz967, zzz968, zzz9690, zzz9700, ba)
new_mkVBalBranch3MkVBalBranch241(zzz3170, zzz3171, Neg(Succ(zzz317200)), zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, Succ(zzz4190), h) → new_mkVBalBranch3MkVBalBranch242(zzz3170, zzz3171, zzz317200, zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, zzz317200, zzz4190, h)
new_mkVBalBranch1(zzz31, Branch(zzz330, zzz331, Pos(Zero), zzz333, zzz334), Branch(zzz3170, zzz3171, Pos(Succ(zzz317200)), zzz3173, zzz3174), h) → new_mkVBalBranch1(zzz31, Branch(zzz330, zzz331, Pos(Zero), zzz333, zzz334), zzz3173, h)
new_mkVBalBranch3MkVBalBranch237(zzz3170, zzz3171, zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, h) → new_mkVBalBranch1(zzz31, zzz334, Branch(zzz3170, zzz3171, Pos(Zero), zzz3173, zzz3174), h)
new_mkVBalBranch3MkVBalBranch235(zzz3170, zzz3171, Pos(Zero), zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, Succ(zzz4170), h) → new_mkVBalBranch3MkVBalBranch237(zzz3170, zzz3171, zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, h)
new_mkVBalBranch3MkVBalBranch236(zzz958, zzz959, zzz960, zzz961, zzz962, zzz963, zzz964, zzz965, zzz966, zzz967, zzz968, Zero, Succ(zzz9700), ba) → new_mkVBalBranch1(zzz968, Branch(zzz963, zzz964, Pos(Succ(zzz965)), zzz966, zzz967), zzz961, ba)
new_mkVBalBranch3MkVBalBranch125(zzz1337, zzz1338, zzz1339, zzz1340, zzz1341, zzz1342, zzz1343, zzz1344, zzz1345, zzz1346, zzz1347, Succ(zzz13480), Succ(zzz13490), bb) → new_mkVBalBranch3MkVBalBranch125(zzz1337, zzz1338, zzz1339, zzz1340, zzz1341, zzz1342, zzz1343, zzz1344, zzz1345, zzz1346, zzz1347, zzz13480, zzz13490, bb)
new_mkVBalBranch3MkVBalBranch123(zzz3170, zzz3171, zzz317200, zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, Succ(zzz5620), h) → new_mkVBalBranch1(zzz31, zzz334, Branch(zzz3170, zzz3171, Neg(Succ(zzz317200)), zzz3173, zzz3174), h)
new_mkVBalBranch3MkVBalBranch125(zzz1337, zzz1338, zzz1339, zzz1340, zzz1341, zzz1342, zzz1343, zzz1344, zzz1345, zzz1346, zzz1347, Zero, Succ(zzz13490), bb) → new_mkVBalBranch1(zzz1347, zzz1346, Branch(zzz1337, zzz1338, Pos(Succ(zzz1339)), zzz1340, zzz1341), bb)
new_mkVBalBranch3MkVBalBranch242(zzz972, zzz973, zzz974, zzz975, zzz976, zzz977, zzz978, zzz979, zzz980, zzz981, zzz982, Zero, Succ(zzz9840), bc) → new_mkVBalBranch1(zzz982, Branch(zzz977, zzz978, Neg(Succ(zzz979)), zzz980, zzz981), zzz975, bc)
new_mkVBalBranch3MkVBalBranch242(zzz972, zzz973, zzz974, zzz975, zzz976, zzz977, zzz978, zzz979, zzz980, zzz981, zzz982, Succ(zzz9830), Zero, bc) → new_mkVBalBranch3MkVBalBranch128(zzz972, zzz973, zzz974, zzz975, zzz976, zzz977, zzz978, zzz979, zzz980, zzz981, zzz982, Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat2(Succ(new_primPlusNat3(new_primPlusNat1(zzz974), zzz974)), zzz974)), zzz974))), bc)
new_mkVBalBranch3MkVBalBranch126(zzz3170, zzz3171, zzz317200, zzz3173, zzz3174, zzz330, zzz331, zzz333, zzz334, zzz31, Succ(zzz5350), h) → new_mkVBalBranch1(zzz31, zzz334, Branch(zzz3170, zzz3171, Neg(Succ(zzz317200)), zzz3173, zzz3174), h)
new_mkVBalBranch3MkVBalBranch241(zzz3170, zzz3171, Neg(Zero), zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, Succ(zzz4190), h) → new_mkVBalBranch1(zzz31, Branch(zzz330, zzz331, Neg(Succ(zzz33200)), zzz333, zzz334), zzz3173, h)
new_mkVBalBranch3MkVBalBranch124(zzz958, zzz959, zzz960, zzz961, zzz962, zzz963, zzz964, zzz965, zzz966, zzz967, zzz968, Succ(zzz10180), ba) → new_mkVBalBranch3MkVBalBranch125(zzz958, zzz959, zzz960, zzz961, zzz962, zzz963, zzz964, zzz965, zzz966, zzz967, zzz968, Succ(zzz10180), Succ(zzz965), ba)
new_mkVBalBranch3MkVBalBranch244(zzz972, zzz973, zzz974, zzz975, zzz976, zzz977, zzz978, zzz979, zzz980, zzz981, zzz982, bc) → new_mkVBalBranch3MkVBalBranch128(zzz972, zzz973, zzz974, zzz975, zzz976, zzz977, zzz978, zzz979, zzz980, zzz981, zzz982, new_primPlusNat2(Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat3(new_primPlusNat1(zzz974), zzz974)), zzz974))), Succ(zzz974)), bc)
new_mkVBalBranch3MkVBalBranch235(zzz3170, zzz3171, Neg(Succ(zzz317200)), zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, Succ(zzz4170), h) → new_mkVBalBranch3MkVBalBranch123(zzz3170, zzz3171, zzz317200, zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat2(Succ(new_primPlusNat3(new_primPlusNat1(zzz317200), zzz317200)), zzz317200)), zzz317200))), h)
new_mkVBalBranch3MkVBalBranch242(zzz972, zzz973, zzz974, zzz975, zzz976, zzz977, zzz978, zzz979, zzz980, zzz981, zzz982, Zero, Zero, bc) → new_mkVBalBranch3MkVBalBranch244(zzz972, zzz973, zzz974, zzz975, zzz976, zzz977, zzz978, zzz979, zzz980, zzz981, zzz982, bc)
new_mkVBalBranch1(zzz31, Branch(zzz330, zzz331, Neg(Zero), zzz333, zzz334), Branch(zzz3170, zzz3171, Pos(Succ(zzz317200)), zzz3173, zzz3174), h) → new_mkVBalBranch1(zzz31, Branch(zzz330, zzz331, Neg(Zero), zzz333, zzz334), zzz3173, h)
new_mkVBalBranch3MkVBalBranch235(zzz3170, zzz3171, Neg(Zero), zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, Succ(zzz4170), h) → new_mkVBalBranch1(zzz31, zzz334, Branch(zzz3170, zzz3171, Neg(Zero), zzz3173, zzz3174), h)
new_mkVBalBranch3MkVBalBranch236(zzz958, zzz959, zzz960, zzz961, zzz962, zzz963, zzz964, zzz965, zzz966, zzz967, zzz968, Zero, Zero, ba) → new_mkVBalBranch3MkVBalBranch240(zzz958, zzz959, zzz960, zzz961, zzz962, zzz963, zzz964, zzz965, zzz966, zzz967, zzz968, ba)

The TRS R consists of the following rules:

new_primPlusNat1(Zero) → Zero
new_primPlusNat1(Succ(zzz62000)) → Succ(Succ(new_primPlusNat1(zzz62000)))
new_primPlusNat3(zzz90, Succ(zzz910)) → Succ(Succ(new_primPlusNat2(zzz90, zzz910)))
new_primPlusNat3(zzz90, Zero) → Succ(zzz90)
new_primPlusNat2(Succ(zzz900), Succ(zzz9100)) → Succ(Succ(new_primPlusNat2(zzz900, zzz9100)))
new_primPlusNat2(Succ(zzz900), Zero) → Succ(zzz900)
new_primPlusNat2(Zero, Succ(zzz9100)) → Succ(zzz9100)
new_primPlusNat2(Zero, Zero) → Zero

The set Q consists of the following terms:

new_primPlusNat2(Zero, Succ(x0))
new_primPlusNat3(x0, Succ(x1))
new_primPlusNat2(Succ(x0), Succ(x1))
new_primPlusNat3(x0, Zero)
new_primPlusNat1(Zero)
new_primPlusNat2(Zero, Zero)
new_primPlusNat1(Succ(x0))
new_primPlusNat2(Succ(x0), Zero)

We have to consider all minimal (P,Q,R)-chains.
By rewriting [15] the rule new_mkVBalBranch3MkVBalBranch244(zzz972, zzz973, zzz974, zzz975, zzz976, zzz977, zzz978, zzz979, zzz980, zzz981, zzz982, bc) → new_mkVBalBranch3MkVBalBranch128(zzz972, zzz973, zzz974, zzz975, zzz976, zzz977, zzz978, zzz979, zzz980, zzz981, zzz982, new_primPlusNat2(Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat3(new_primPlusNat1(zzz974), zzz974)), zzz974))), Succ(zzz974)), bc) at position [11] we obtained the following new rules:

new_mkVBalBranch3MkVBalBranch244(zzz972, zzz973, zzz974, zzz975, zzz976, zzz977, zzz978, zzz979, zzz980, zzz981, zzz982, bc) → new_mkVBalBranch3MkVBalBranch128(zzz972, zzz973, zzz974, zzz975, zzz976, zzz977, zzz978, zzz979, zzz980, zzz981, zzz982, Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat2(Succ(new_primPlusNat3(new_primPlusNat1(zzz974), zzz974)), zzz974)), zzz974))), bc)



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

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

new_mkVBalBranch3MkVBalBranch244(zzz972, zzz973, zzz974, zzz975, zzz976, zzz977, zzz978, zzz979, zzz980, zzz981, zzz982, bc) → new_mkVBalBranch3MkVBalBranch128(zzz972, zzz973, zzz974, zzz975, zzz976, zzz977, zzz978, zzz979, zzz980, zzz981, zzz982, Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat2(Succ(new_primPlusNat3(new_primPlusNat1(zzz974), zzz974)), zzz974)), zzz974))), bc)
new_mkVBalBranch3MkVBalBranch129(zzz1851, zzz1852, zzz1853, zzz1854, zzz1855, zzz1856, zzz1857, zzz1858, zzz1859, zzz1860, zzz1861, Zero, Succ(zzz18630), bd) → new_mkVBalBranch1(zzz1861, zzz1860, Branch(zzz1851, zzz1852, Neg(Succ(zzz1853)), zzz1854, zzz1855), bd)
new_mkVBalBranch3MkVBalBranch127(zzz3170, zzz3171, zzz317200, zzz3173, zzz3174, zzz330, zzz331, zzz333, zzz334, zzz31, Succ(zzz5500), h) → new_mkVBalBranch1(zzz31, zzz334, Branch(zzz3170, zzz3171, Neg(Succ(zzz317200)), zzz3173, zzz3174), h)
new_mkVBalBranch3MkVBalBranch128(zzz972, zzz973, zzz974, zzz975, zzz976, zzz977, zzz978, zzz979, zzz980, zzz981, zzz982, Succ(zzz10190), bc) → new_mkVBalBranch3MkVBalBranch129(zzz972, zzz973, zzz974, zzz975, zzz976, zzz977, zzz978, zzz979, zzz980, zzz981, zzz982, Succ(zzz979), Succ(zzz10190), bc)
new_mkVBalBranch3MkVBalBranch241(zzz3170, zzz3171, Pos(zzz31720), zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, Succ(zzz4190), h) → new_mkVBalBranch1(zzz31, Branch(zzz330, zzz331, Neg(Succ(zzz33200)), zzz333, zzz334), zzz3173, h)
new_mkVBalBranch1(zzz31, Branch(zzz330, zzz331, Neg(Zero), zzz333, zzz334), Branch(zzz3170, zzz3171, Neg(Succ(zzz317200)), zzz3173, zzz3174), h) → new_mkVBalBranch3MkVBalBranch127(zzz3170, zzz3171, zzz317200, zzz3173, zzz3174, zzz330, zzz331, zzz333, zzz334, zzz31, Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat2(Succ(new_primPlusNat3(new_primPlusNat1(zzz317200), zzz317200)), zzz317200)), zzz317200))), h)
new_mkVBalBranch3MkVBalBranch240(zzz958, zzz959, zzz960, zzz961, zzz962, zzz963, zzz964, zzz965, zzz966, zzz967, zzz968, ba) → new_mkVBalBranch3MkVBalBranch124(zzz958, zzz959, zzz960, zzz961, zzz962, zzz963, zzz964, zzz965, zzz966, zzz967, zzz968, Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat2(Succ(new_primPlusNat3(new_primPlusNat1(zzz960), zzz960)), zzz960)), zzz960))), ba)
new_mkVBalBranch3MkVBalBranch129(zzz1851, zzz1852, zzz1853, zzz1854, zzz1855, zzz1856, zzz1857, zzz1858, zzz1859, zzz1860, zzz1861, Succ(zzz18620), Succ(zzz18630), bd) → new_mkVBalBranch3MkVBalBranch129(zzz1851, zzz1852, zzz1853, zzz1854, zzz1855, zzz1856, zzz1857, zzz1858, zzz1859, zzz1860, zzz1861, zzz18620, zzz18630, bd)
new_mkVBalBranch3MkVBalBranch236(zzz958, zzz959, zzz960, zzz961, zzz962, zzz963, zzz964, zzz965, zzz966, zzz967, zzz968, Succ(zzz9690), Zero, ba) → new_mkVBalBranch3MkVBalBranch124(zzz958, zzz959, zzz960, zzz961, zzz962, zzz963, zzz964, zzz965, zzz966, zzz967, zzz968, Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat2(Succ(new_primPlusNat3(new_primPlusNat1(zzz960), zzz960)), zzz960)), zzz960))), ba)
new_mkVBalBranch1(zzz31, Branch(zzz330, zzz331, Pos(Zero), zzz333, zzz334), Branch(zzz3170, zzz3171, Neg(Succ(zzz317200)), zzz3173, zzz3174), h) → new_mkVBalBranch3MkVBalBranch126(zzz3170, zzz3171, zzz317200, zzz3173, zzz3174, zzz330, zzz331, zzz333, zzz334, zzz31, new_primPlusNat2(Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat3(new_primPlusNat1(zzz317200), zzz317200)), zzz317200))), Succ(zzz317200)), h)
new_mkVBalBranch3MkVBalBranch235(zzz3170, zzz3171, Pos(Succ(zzz317200)), zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, Succ(zzz4170), h) → new_mkVBalBranch3MkVBalBranch236(zzz3170, zzz3171, zzz317200, zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, zzz4170, zzz317200, h)
new_mkVBalBranch3MkVBalBranch242(zzz972, zzz973, zzz974, zzz975, zzz976, zzz977, zzz978, zzz979, zzz980, zzz981, zzz982, Succ(zzz9830), Succ(zzz9840), bc) → new_mkVBalBranch3MkVBalBranch242(zzz972, zzz973, zzz974, zzz975, zzz976, zzz977, zzz978, zzz979, zzz980, zzz981, zzz982, zzz9830, zzz9840, bc)
new_mkVBalBranch1(zzz31, Branch(zzz330, zzz331, Pos(Succ(zzz33200)), zzz333, zzz334), Branch(zzz3170, zzz3171, zzz3172, zzz3173, zzz3174), h) → new_mkVBalBranch3MkVBalBranch235(zzz3170, zzz3171, zzz3172, zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat2(Succ(new_primPlusNat3(new_primPlusNat1(zzz33200), zzz33200)), zzz33200)), zzz33200))), h)
new_mkVBalBranch1(zzz31, Branch(zzz330, zzz331, Neg(Succ(zzz33200)), zzz333, zzz334), Branch(zzz3170, zzz3171, zzz3172, zzz3173, zzz3174), h) → new_mkVBalBranch3MkVBalBranch241(zzz3170, zzz3171, zzz3172, zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat2(Succ(new_primPlusNat3(new_primPlusNat1(zzz33200), zzz33200)), zzz33200)), zzz33200))), h)
new_mkVBalBranch3MkVBalBranch236(zzz958, zzz959, zzz960, zzz961, zzz962, zzz963, zzz964, zzz965, zzz966, zzz967, zzz968, Succ(zzz9690), Succ(zzz9700), ba) → new_mkVBalBranch3MkVBalBranch236(zzz958, zzz959, zzz960, zzz961, zzz962, zzz963, zzz964, zzz965, zzz966, zzz967, zzz968, zzz9690, zzz9700, ba)
new_mkVBalBranch3MkVBalBranch241(zzz3170, zzz3171, Neg(Succ(zzz317200)), zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, Succ(zzz4190), h) → new_mkVBalBranch3MkVBalBranch242(zzz3170, zzz3171, zzz317200, zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, zzz317200, zzz4190, h)
new_mkVBalBranch1(zzz31, Branch(zzz330, zzz331, Pos(Zero), zzz333, zzz334), Branch(zzz3170, zzz3171, Pos(Succ(zzz317200)), zzz3173, zzz3174), h) → new_mkVBalBranch1(zzz31, Branch(zzz330, zzz331, Pos(Zero), zzz333, zzz334), zzz3173, h)
new_mkVBalBranch3MkVBalBranch237(zzz3170, zzz3171, zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, h) → new_mkVBalBranch1(zzz31, zzz334, Branch(zzz3170, zzz3171, Pos(Zero), zzz3173, zzz3174), h)
new_mkVBalBranch3MkVBalBranch235(zzz3170, zzz3171, Pos(Zero), zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, Succ(zzz4170), h) → new_mkVBalBranch3MkVBalBranch237(zzz3170, zzz3171, zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, h)
new_mkVBalBranch3MkVBalBranch236(zzz958, zzz959, zzz960, zzz961, zzz962, zzz963, zzz964, zzz965, zzz966, zzz967, zzz968, Zero, Succ(zzz9700), ba) → new_mkVBalBranch1(zzz968, Branch(zzz963, zzz964, Pos(Succ(zzz965)), zzz966, zzz967), zzz961, ba)
new_mkVBalBranch3MkVBalBranch125(zzz1337, zzz1338, zzz1339, zzz1340, zzz1341, zzz1342, zzz1343, zzz1344, zzz1345, zzz1346, zzz1347, Succ(zzz13480), Succ(zzz13490), bb) → new_mkVBalBranch3MkVBalBranch125(zzz1337, zzz1338, zzz1339, zzz1340, zzz1341, zzz1342, zzz1343, zzz1344, zzz1345, zzz1346, zzz1347, zzz13480, zzz13490, bb)
new_mkVBalBranch3MkVBalBranch123(zzz3170, zzz3171, zzz317200, zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, Succ(zzz5620), h) → new_mkVBalBranch1(zzz31, zzz334, Branch(zzz3170, zzz3171, Neg(Succ(zzz317200)), zzz3173, zzz3174), h)
new_mkVBalBranch3MkVBalBranch125(zzz1337, zzz1338, zzz1339, zzz1340, zzz1341, zzz1342, zzz1343, zzz1344, zzz1345, zzz1346, zzz1347, Zero, Succ(zzz13490), bb) → new_mkVBalBranch1(zzz1347, zzz1346, Branch(zzz1337, zzz1338, Pos(Succ(zzz1339)), zzz1340, zzz1341), bb)
new_mkVBalBranch3MkVBalBranch242(zzz972, zzz973, zzz974, zzz975, zzz976, zzz977, zzz978, zzz979, zzz980, zzz981, zzz982, Zero, Succ(zzz9840), bc) → new_mkVBalBranch1(zzz982, Branch(zzz977, zzz978, Neg(Succ(zzz979)), zzz980, zzz981), zzz975, bc)
new_mkVBalBranch3MkVBalBranch242(zzz972, zzz973, zzz974, zzz975, zzz976, zzz977, zzz978, zzz979, zzz980, zzz981, zzz982, Succ(zzz9830), Zero, bc) → new_mkVBalBranch3MkVBalBranch128(zzz972, zzz973, zzz974, zzz975, zzz976, zzz977, zzz978, zzz979, zzz980, zzz981, zzz982, Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat2(Succ(new_primPlusNat3(new_primPlusNat1(zzz974), zzz974)), zzz974)), zzz974))), bc)
new_mkVBalBranch3MkVBalBranch126(zzz3170, zzz3171, zzz317200, zzz3173, zzz3174, zzz330, zzz331, zzz333, zzz334, zzz31, Succ(zzz5350), h) → new_mkVBalBranch1(zzz31, zzz334, Branch(zzz3170, zzz3171, Neg(Succ(zzz317200)), zzz3173, zzz3174), h)
new_mkVBalBranch3MkVBalBranch241(zzz3170, zzz3171, Neg(Zero), zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, Succ(zzz4190), h) → new_mkVBalBranch1(zzz31, Branch(zzz330, zzz331, Neg(Succ(zzz33200)), zzz333, zzz334), zzz3173, h)
new_mkVBalBranch3MkVBalBranch124(zzz958, zzz959, zzz960, zzz961, zzz962, zzz963, zzz964, zzz965, zzz966, zzz967, zzz968, Succ(zzz10180), ba) → new_mkVBalBranch3MkVBalBranch125(zzz958, zzz959, zzz960, zzz961, zzz962, zzz963, zzz964, zzz965, zzz966, zzz967, zzz968, Succ(zzz10180), Succ(zzz965), ba)
new_mkVBalBranch3MkVBalBranch235(zzz3170, zzz3171, Neg(Succ(zzz317200)), zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, Succ(zzz4170), h) → new_mkVBalBranch3MkVBalBranch123(zzz3170, zzz3171, zzz317200, zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat2(Succ(new_primPlusNat3(new_primPlusNat1(zzz317200), zzz317200)), zzz317200)), zzz317200))), h)
new_mkVBalBranch3MkVBalBranch242(zzz972, zzz973, zzz974, zzz975, zzz976, zzz977, zzz978, zzz979, zzz980, zzz981, zzz982, Zero, Zero, bc) → new_mkVBalBranch3MkVBalBranch244(zzz972, zzz973, zzz974, zzz975, zzz976, zzz977, zzz978, zzz979, zzz980, zzz981, zzz982, bc)
new_mkVBalBranch1(zzz31, Branch(zzz330, zzz331, Neg(Zero), zzz333, zzz334), Branch(zzz3170, zzz3171, Pos(Succ(zzz317200)), zzz3173, zzz3174), h) → new_mkVBalBranch1(zzz31, Branch(zzz330, zzz331, Neg(Zero), zzz333, zzz334), zzz3173, h)
new_mkVBalBranch3MkVBalBranch235(zzz3170, zzz3171, Neg(Zero), zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, Succ(zzz4170), h) → new_mkVBalBranch1(zzz31, zzz334, Branch(zzz3170, zzz3171, Neg(Zero), zzz3173, zzz3174), h)
new_mkVBalBranch3MkVBalBranch236(zzz958, zzz959, zzz960, zzz961, zzz962, zzz963, zzz964, zzz965, zzz966, zzz967, zzz968, Zero, Zero, ba) → new_mkVBalBranch3MkVBalBranch240(zzz958, zzz959, zzz960, zzz961, zzz962, zzz963, zzz964, zzz965, zzz966, zzz967, zzz968, ba)

The TRS R consists of the following rules:

new_primPlusNat1(Zero) → Zero
new_primPlusNat1(Succ(zzz62000)) → Succ(Succ(new_primPlusNat1(zzz62000)))
new_primPlusNat3(zzz90, Succ(zzz910)) → Succ(Succ(new_primPlusNat2(zzz90, zzz910)))
new_primPlusNat3(zzz90, Zero) → Succ(zzz90)
new_primPlusNat2(Succ(zzz900), Succ(zzz9100)) → Succ(Succ(new_primPlusNat2(zzz900, zzz9100)))
new_primPlusNat2(Succ(zzz900), Zero) → Succ(zzz900)
new_primPlusNat2(Zero, Succ(zzz9100)) → Succ(zzz9100)
new_primPlusNat2(Zero, Zero) → Zero

The set Q consists of the following terms:

new_primPlusNat2(Zero, Succ(x0))
new_primPlusNat3(x0, Succ(x1))
new_primPlusNat2(Succ(x0), Succ(x1))
new_primPlusNat3(x0, Zero)
new_primPlusNat1(Zero)
new_primPlusNat2(Zero, Zero)
new_primPlusNat1(Succ(x0))
new_primPlusNat2(Succ(x0), Zero)

We have to consider all minimal (P,Q,R)-chains.
By rewriting [15] the rule new_mkVBalBranch1(zzz31, Branch(zzz330, zzz331, Pos(Zero), zzz333, zzz334), Branch(zzz3170, zzz3171, Neg(Succ(zzz317200)), zzz3173, zzz3174), h) → new_mkVBalBranch3MkVBalBranch126(zzz3170, zzz3171, zzz317200, zzz3173, zzz3174, zzz330, zzz331, zzz333, zzz334, zzz31, new_primPlusNat2(Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat3(new_primPlusNat1(zzz317200), zzz317200)), zzz317200))), Succ(zzz317200)), h) at position [10] we obtained the following new rules:

new_mkVBalBranch1(zzz31, Branch(zzz330, zzz331, Pos(Zero), zzz333, zzz334), Branch(zzz3170, zzz3171, Neg(Succ(zzz317200)), zzz3173, zzz3174), h) → new_mkVBalBranch3MkVBalBranch126(zzz3170, zzz3171, zzz317200, zzz3173, zzz3174, zzz330, zzz331, zzz333, zzz334, zzz31, Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat2(Succ(new_primPlusNat3(new_primPlusNat1(zzz317200), zzz317200)), zzz317200)), zzz317200))), 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
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                    ↳ DependencyGraphProof
                                      ↳ QDP
                                        ↳ Rewriting
                                          ↳ QDP
                                            ↳ Rewriting
                                              ↳ QDP
                                                ↳ Rewriting
                                                  ↳ QDP
                                                    ↳ Rewriting
                                                      ↳ QDP
                                                        ↳ Rewriting
                                                          ↳ QDP
                                                            ↳ Rewriting
                                                              ↳ QDP
                                                                ↳ Rewriting
                                                                  ↳ QDP
                                                                    ↳ Rewriting
                                                                      ↳ QDP
                                                                        ↳ Rewriting
                                                                          ↳ QDP
                                                                            ↳ Rewriting
                                                                              ↳ QDP
                                                                                ↳ UsableRulesProof
                                                                                  ↳ QDP
                                                                                    ↳ QReductionProof
                                                                                      ↳ QDP
                                                                                        ↳ Rewriting
                                                                                          ↳ QDP
                                                                                            ↳ Rewriting
                                                                                              ↳ QDP
                                                                                                ↳ Rewriting
                                                                                                  ↳ QDP
                                                                                                    ↳ Rewriting
                                                                                                      ↳ QDP
                                                                                                        ↳ Rewriting
                                                                                                          ↳ QDP
                                                                                                            ↳ Rewriting
                                                                                                              ↳ QDP
                                                                                                                ↳ Rewriting
                                                                                                                  ↳ QDP
                                                                                                                    ↳ Rewriting
                                                                                                                      ↳ QDP
                                                                                                                        ↳ Rewriting
                                                                                                                          ↳ QDP
                                                                                                                            ↳ Rewriting
                                                                                                                              ↳ QDP
                                                                                                                                ↳ UsableRulesProof
                                                                                                                                  ↳ QDP
                                                                                                                                    ↳ QReductionProof
                                                                                                                                      ↳ QDP
                                                                                                                                        ↳ Rewriting
                                                                                                                                          ↳ QDP
                                                                                                                                            ↳ Rewriting
                                                                                                                                              ↳ QDP
                                                                                                                                                ↳ Rewriting
                                                                                                                                                  ↳ QDP
                                                                                                                                                    ↳ DependencyGraphProof
                                                                                                                                                      ↳ QDP
                                                                                                                                                        ↳ Rewriting
                                                                                                                                                          ↳ QDP
                                                                                                                                                            ↳ Rewriting
                                                                                                                                                              ↳ QDP
                                                                                                                                                                ↳ DependencyGraphProof
                                                                                                                                                                  ↳ QDP
                                                                                                                                                                    ↳ Rewriting
                                                                                                                                                                      ↳ QDP
                                                                                                                                                                        ↳ Rewriting
                                                                                                                                                                          ↳ QDP
                                                                                                                                                                            ↳ Rewriting
                                                                                                                                                                              ↳ QDP
                                                                                                                                                                                ↳ Rewriting
                                                                                                                                                                                  ↳ QDP
                                                                                                                                                                                    ↳ Rewriting
                                                                                                                                                                                      ↳ QDP
                                                                                                                                                                                        ↳ Rewriting
                                                                                                                                                                                          ↳ QDP
                                                                                                                                                                                            ↳ Rewriting
                                                                                                                                                                                              ↳ QDP
                                                                                                                                                                                                ↳ DependencyGraphProof
                                                                                                                                                                                                  ↳ QDP
                                                                                                                                                                                                    ↳ Rewriting
                                                                                                                                                                                                      ↳ QDP
                                                                                                                                                                                                        ↳ DependencyGraphProof
                                                                                                                                                                                                          ↳ QDP
                                                                                                                                                                                                            ↳ Rewriting
                                                                                                                                                                                                              ↳ QDP
                                                                                                                                                                                                                ↳ Rewriting
                                                                                                                                                                                                                  ↳ QDP
                                                                                                                                                                                                                    ↳ QDPOrderProof
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP

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

new_mkVBalBranch3MkVBalBranch129(zzz1851, zzz1852, zzz1853, zzz1854, zzz1855, zzz1856, zzz1857, zzz1858, zzz1859, zzz1860, zzz1861, Zero, Succ(zzz18630), bd) → new_mkVBalBranch1(zzz1861, zzz1860, Branch(zzz1851, zzz1852, Neg(Succ(zzz1853)), zzz1854, zzz1855), bd)
new_mkVBalBranch3MkVBalBranch244(zzz972, zzz973, zzz974, zzz975, zzz976, zzz977, zzz978, zzz979, zzz980, zzz981, zzz982, bc) → new_mkVBalBranch3MkVBalBranch128(zzz972, zzz973, zzz974, zzz975, zzz976, zzz977, zzz978, zzz979, zzz980, zzz981, zzz982, Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat2(Succ(new_primPlusNat3(new_primPlusNat1(zzz974), zzz974)), zzz974)), zzz974))), bc)
new_mkVBalBranch3MkVBalBranch241(zzz3170, zzz3171, Pos(zzz31720), zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, Succ(zzz4190), h) → new_mkVBalBranch1(zzz31, Branch(zzz330, zzz331, Neg(Succ(zzz33200)), zzz333, zzz334), zzz3173, h)
new_mkVBalBranch3MkVBalBranch128(zzz972, zzz973, zzz974, zzz975, zzz976, zzz977, zzz978, zzz979, zzz980, zzz981, zzz982, Succ(zzz10190), bc) → new_mkVBalBranch3MkVBalBranch129(zzz972, zzz973, zzz974, zzz975, zzz976, zzz977, zzz978, zzz979, zzz980, zzz981, zzz982, Succ(zzz979), Succ(zzz10190), bc)
new_mkVBalBranch3MkVBalBranch127(zzz3170, zzz3171, zzz317200, zzz3173, zzz3174, zzz330, zzz331, zzz333, zzz334, zzz31, Succ(zzz5500), h) → new_mkVBalBranch1(zzz31, zzz334, Branch(zzz3170, zzz3171, Neg(Succ(zzz317200)), zzz3173, zzz3174), h)
new_mkVBalBranch3MkVBalBranch240(zzz958, zzz959, zzz960, zzz961, zzz962, zzz963, zzz964, zzz965, zzz966, zzz967, zzz968, ba) → new_mkVBalBranch3MkVBalBranch124(zzz958, zzz959, zzz960, zzz961, zzz962, zzz963, zzz964, zzz965, zzz966, zzz967, zzz968, Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat2(Succ(new_primPlusNat3(new_primPlusNat1(zzz960), zzz960)), zzz960)), zzz960))), ba)
new_mkVBalBranch1(zzz31, Branch(zzz330, zzz331, Neg(Zero), zzz333, zzz334), Branch(zzz3170, zzz3171, Neg(Succ(zzz317200)), zzz3173, zzz3174), h) → new_mkVBalBranch3MkVBalBranch127(zzz3170, zzz3171, zzz317200, zzz3173, zzz3174, zzz330, zzz331, zzz333, zzz334, zzz31, Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat2(Succ(new_primPlusNat3(new_primPlusNat1(zzz317200), zzz317200)), zzz317200)), zzz317200))), h)
new_mkVBalBranch3MkVBalBranch129(zzz1851, zzz1852, zzz1853, zzz1854, zzz1855, zzz1856, zzz1857, zzz1858, zzz1859, zzz1860, zzz1861, Succ(zzz18620), Succ(zzz18630), bd) → new_mkVBalBranch3MkVBalBranch129(zzz1851, zzz1852, zzz1853, zzz1854, zzz1855, zzz1856, zzz1857, zzz1858, zzz1859, zzz1860, zzz1861, zzz18620, zzz18630, bd)
new_mkVBalBranch3MkVBalBranch236(zzz958, zzz959, zzz960, zzz961, zzz962, zzz963, zzz964, zzz965, zzz966, zzz967, zzz968, Succ(zzz9690), Zero, ba) → new_mkVBalBranch3MkVBalBranch124(zzz958, zzz959, zzz960, zzz961, zzz962, zzz963, zzz964, zzz965, zzz966, zzz967, zzz968, Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat2(Succ(new_primPlusNat3(new_primPlusNat1(zzz960), zzz960)), zzz960)), zzz960))), ba)
new_mkVBalBranch3MkVBalBranch242(zzz972, zzz973, zzz974, zzz975, zzz976, zzz977, zzz978, zzz979, zzz980, zzz981, zzz982, Succ(zzz9830), Succ(zzz9840), bc) → new_mkVBalBranch3MkVBalBranch242(zzz972, zzz973, zzz974, zzz975, zzz976, zzz977, zzz978, zzz979, zzz980, zzz981, zzz982, zzz9830, zzz9840, bc)
new_mkVBalBranch3MkVBalBranch235(zzz3170, zzz3171, Pos(Succ(zzz317200)), zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, Succ(zzz4170), h) → new_mkVBalBranch3MkVBalBranch236(zzz3170, zzz3171, zzz317200, zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, zzz4170, zzz317200, h)
new_mkVBalBranch1(zzz31, Branch(zzz330, zzz331, Neg(Succ(zzz33200)), zzz333, zzz334), Branch(zzz3170, zzz3171, zzz3172, zzz3173, zzz3174), h) → new_mkVBalBranch3MkVBalBranch241(zzz3170, zzz3171, zzz3172, zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat2(Succ(new_primPlusNat3(new_primPlusNat1(zzz33200), zzz33200)), zzz33200)), zzz33200))), h)
new_mkVBalBranch1(zzz31, Branch(zzz330, zzz331, Pos(Succ(zzz33200)), zzz333, zzz334), Branch(zzz3170, zzz3171, zzz3172, zzz3173, zzz3174), h) → new_mkVBalBranch3MkVBalBranch235(zzz3170, zzz3171, zzz3172, zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat2(Succ(new_primPlusNat3(new_primPlusNat1(zzz33200), zzz33200)), zzz33200)), zzz33200))), h)
new_mkVBalBranch3MkVBalBranch236(zzz958, zzz959, zzz960, zzz961, zzz962, zzz963, zzz964, zzz965, zzz966, zzz967, zzz968, Succ(zzz9690), Succ(zzz9700), ba) → new_mkVBalBranch3MkVBalBranch236(zzz958, zzz959, zzz960, zzz961, zzz962, zzz963, zzz964, zzz965, zzz966, zzz967, zzz968, zzz9690, zzz9700, ba)
new_mkVBalBranch3MkVBalBranch241(zzz3170, zzz3171, Neg(Succ(zzz317200)), zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, Succ(zzz4190), h) → new_mkVBalBranch3MkVBalBranch242(zzz3170, zzz3171, zzz317200, zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, zzz317200, zzz4190, h)
new_mkVBalBranch1(zzz31, Branch(zzz330, zzz331, Pos(Zero), zzz333, zzz334), Branch(zzz3170, zzz3171, Pos(Succ(zzz317200)), zzz3173, zzz3174), h) → new_mkVBalBranch1(zzz31, Branch(zzz330, zzz331, Pos(Zero), zzz333, zzz334), zzz3173, h)
new_mkVBalBranch3MkVBalBranch237(zzz3170, zzz3171, zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, h) → new_mkVBalBranch1(zzz31, zzz334, Branch(zzz3170, zzz3171, Pos(Zero), zzz3173, zzz3174), h)
new_mkVBalBranch3MkVBalBranch235(zzz3170, zzz3171, Pos(Zero), zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, Succ(zzz4170), h) → new_mkVBalBranch3MkVBalBranch237(zzz3170, zzz3171, zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, h)
new_mkVBalBranch3MkVBalBranch236(zzz958, zzz959, zzz960, zzz961, zzz962, zzz963, zzz964, zzz965, zzz966, zzz967, zzz968, Zero, Succ(zzz9700), ba) → new_mkVBalBranch1(zzz968, Branch(zzz963, zzz964, Pos(Succ(zzz965)), zzz966, zzz967), zzz961, ba)
new_mkVBalBranch3MkVBalBranch125(zzz1337, zzz1338, zzz1339, zzz1340, zzz1341, zzz1342, zzz1343, zzz1344, zzz1345, zzz1346, zzz1347, Succ(zzz13480), Succ(zzz13490), bb) → new_mkVBalBranch3MkVBalBranch125(zzz1337, zzz1338, zzz1339, zzz1340, zzz1341, zzz1342, zzz1343, zzz1344, zzz1345, zzz1346, zzz1347, zzz13480, zzz13490, bb)
new_mkVBalBranch3MkVBalBranch123(zzz3170, zzz3171, zzz317200, zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, Succ(zzz5620), h) → new_mkVBalBranch1(zzz31, zzz334, Branch(zzz3170, zzz3171, Neg(Succ(zzz317200)), zzz3173, zzz3174), h)
new_mkVBalBranch3MkVBalBranch125(zzz1337, zzz1338, zzz1339, zzz1340, zzz1341, zzz1342, zzz1343, zzz1344, zzz1345, zzz1346, zzz1347, Zero, Succ(zzz13490), bb) → new_mkVBalBranch1(zzz1347, zzz1346, Branch(zzz1337, zzz1338, Pos(Succ(zzz1339)), zzz1340, zzz1341), bb)
new_mkVBalBranch3MkVBalBranch242(zzz972, zzz973, zzz974, zzz975, zzz976, zzz977, zzz978, zzz979, zzz980, zzz981, zzz982, Zero, Succ(zzz9840), bc) → new_mkVBalBranch1(zzz982, Branch(zzz977, zzz978, Neg(Succ(zzz979)), zzz980, zzz981), zzz975, bc)
new_mkVBalBranch3MkVBalBranch242(zzz972, zzz973, zzz974, zzz975, zzz976, zzz977, zzz978, zzz979, zzz980, zzz981, zzz982, Succ(zzz9830), Zero, bc) → new_mkVBalBranch3MkVBalBranch128(zzz972, zzz973, zzz974, zzz975, zzz976, zzz977, zzz978, zzz979, zzz980, zzz981, zzz982, Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat2(Succ(new_primPlusNat3(new_primPlusNat1(zzz974), zzz974)), zzz974)), zzz974))), bc)
new_mkVBalBranch3MkVBalBranch126(zzz3170, zzz3171, zzz317200, zzz3173, zzz3174, zzz330, zzz331, zzz333, zzz334, zzz31, Succ(zzz5350), h) → new_mkVBalBranch1(zzz31, zzz334, Branch(zzz3170, zzz3171, Neg(Succ(zzz317200)), zzz3173, zzz3174), h)
new_mkVBalBranch3MkVBalBranch241(zzz3170, zzz3171, Neg(Zero), zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, Succ(zzz4190), h) → new_mkVBalBranch1(zzz31, Branch(zzz330, zzz331, Neg(Succ(zzz33200)), zzz333, zzz334), zzz3173, h)
new_mkVBalBranch3MkVBalBranch124(zzz958, zzz959, zzz960, zzz961, zzz962, zzz963, zzz964, zzz965, zzz966, zzz967, zzz968, Succ(zzz10180), ba) → new_mkVBalBranch3MkVBalBranch125(zzz958, zzz959, zzz960, zzz961, zzz962, zzz963, zzz964, zzz965, zzz966, zzz967, zzz968, Succ(zzz10180), Succ(zzz965), ba)
new_mkVBalBranch1(zzz31, Branch(zzz330, zzz331, Pos(Zero), zzz333, zzz334), Branch(zzz3170, zzz3171, Neg(Succ(zzz317200)), zzz3173, zzz3174), h) → new_mkVBalBranch3MkVBalBranch126(zzz3170, zzz3171, zzz317200, zzz3173, zzz3174, zzz330, zzz331, zzz333, zzz334, zzz31, Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat2(Succ(new_primPlusNat3(new_primPlusNat1(zzz317200), zzz317200)), zzz317200)), zzz317200))), h)
new_mkVBalBranch3MkVBalBranch235(zzz3170, zzz3171, Neg(Succ(zzz317200)), zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, Succ(zzz4170), h) → new_mkVBalBranch3MkVBalBranch123(zzz3170, zzz3171, zzz317200, zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat2(Succ(new_primPlusNat3(new_primPlusNat1(zzz317200), zzz317200)), zzz317200)), zzz317200))), h)
new_mkVBalBranch3MkVBalBranch242(zzz972, zzz973, zzz974, zzz975, zzz976, zzz977, zzz978, zzz979, zzz980, zzz981, zzz982, Zero, Zero, bc) → new_mkVBalBranch3MkVBalBranch244(zzz972, zzz973, zzz974, zzz975, zzz976, zzz977, zzz978, zzz979, zzz980, zzz981, zzz982, bc)
new_mkVBalBranch1(zzz31, Branch(zzz330, zzz331, Neg(Zero), zzz333, zzz334), Branch(zzz3170, zzz3171, Pos(Succ(zzz317200)), zzz3173, zzz3174), h) → new_mkVBalBranch1(zzz31, Branch(zzz330, zzz331, Neg(Zero), zzz333, zzz334), zzz3173, h)
new_mkVBalBranch3MkVBalBranch235(zzz3170, zzz3171, Neg(Zero), zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, Succ(zzz4170), h) → new_mkVBalBranch1(zzz31, zzz334, Branch(zzz3170, zzz3171, Neg(Zero), zzz3173, zzz3174), h)
new_mkVBalBranch3MkVBalBranch236(zzz958, zzz959, zzz960, zzz961, zzz962, zzz963, zzz964, zzz965, zzz966, zzz967, zzz968, Zero, Zero, ba) → new_mkVBalBranch3MkVBalBranch240(zzz958, zzz959, zzz960, zzz961, zzz962, zzz963, zzz964, zzz965, zzz966, zzz967, zzz968, ba)

The TRS R consists of the following rules:

new_primPlusNat1(Zero) → Zero
new_primPlusNat1(Succ(zzz62000)) → Succ(Succ(new_primPlusNat1(zzz62000)))
new_primPlusNat3(zzz90, Succ(zzz910)) → Succ(Succ(new_primPlusNat2(zzz90, zzz910)))
new_primPlusNat3(zzz90, Zero) → Succ(zzz90)
new_primPlusNat2(Succ(zzz900), Succ(zzz9100)) → Succ(Succ(new_primPlusNat2(zzz900, zzz9100)))
new_primPlusNat2(Succ(zzz900), Zero) → Succ(zzz900)
new_primPlusNat2(Zero, Succ(zzz9100)) → Succ(zzz9100)
new_primPlusNat2(Zero, Zero) → Zero

The set Q consists of the following terms:

new_primPlusNat2(Zero, Succ(x0))
new_primPlusNat3(x0, Succ(x1))
new_primPlusNat2(Succ(x0), Succ(x1))
new_primPlusNat3(x0, Zero)
new_primPlusNat1(Zero)
new_primPlusNat2(Zero, Zero)
new_primPlusNat1(Succ(x0))
new_primPlusNat2(Succ(x0), Zero)

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


The following pairs can be oriented strictly and are deleted.


new_mkVBalBranch3MkVBalBranch244(zzz972, zzz973, zzz974, zzz975, zzz976, zzz977, zzz978, zzz979, zzz980, zzz981, zzz982, bc) → new_mkVBalBranch3MkVBalBranch128(zzz972, zzz973, zzz974, zzz975, zzz976, zzz977, zzz978, zzz979, zzz980, zzz981, zzz982, Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat2(Succ(new_primPlusNat3(new_primPlusNat1(zzz974), zzz974)), zzz974)), zzz974))), bc)
new_mkVBalBranch1(zzz31, Branch(zzz330, zzz331, Neg(Zero), zzz333, zzz334), Branch(zzz3170, zzz3171, Neg(Succ(zzz317200)), zzz3173, zzz3174), h) → new_mkVBalBranch3MkVBalBranch127(zzz3170, zzz3171, zzz317200, zzz3173, zzz3174, zzz330, zzz331, zzz333, zzz334, zzz31, Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat2(Succ(new_primPlusNat3(new_primPlusNat1(zzz317200), zzz317200)), zzz317200)), zzz317200))), h)
new_mkVBalBranch3MkVBalBranch242(zzz972, zzz973, zzz974, zzz975, zzz976, zzz977, zzz978, zzz979, zzz980, zzz981, zzz982, Succ(zzz9830), Zero, bc) → new_mkVBalBranch3MkVBalBranch128(zzz972, zzz973, zzz974, zzz975, zzz976, zzz977, zzz978, zzz979, zzz980, zzz981, zzz982, Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat2(Succ(new_primPlusNat3(new_primPlusNat1(zzz974), zzz974)), zzz974)), zzz974))), bc)
The remaining pairs can at least be oriented weakly.

new_mkVBalBranch3MkVBalBranch129(zzz1851, zzz1852, zzz1853, zzz1854, zzz1855, zzz1856, zzz1857, zzz1858, zzz1859, zzz1860, zzz1861, Zero, Succ(zzz18630), bd) → new_mkVBalBranch1(zzz1861, zzz1860, Branch(zzz1851, zzz1852, Neg(Succ(zzz1853)), zzz1854, zzz1855), bd)
new_mkVBalBranch3MkVBalBranch241(zzz3170, zzz3171, Pos(zzz31720), zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, Succ(zzz4190), h) → new_mkVBalBranch1(zzz31, Branch(zzz330, zzz331, Neg(Succ(zzz33200)), zzz333, zzz334), zzz3173, h)
new_mkVBalBranch3MkVBalBranch128(zzz972, zzz973, zzz974, zzz975, zzz976, zzz977, zzz978, zzz979, zzz980, zzz981, zzz982, Succ(zzz10190), bc) → new_mkVBalBranch3MkVBalBranch129(zzz972, zzz973, zzz974, zzz975, zzz976, zzz977, zzz978, zzz979, zzz980, zzz981, zzz982, Succ(zzz979), Succ(zzz10190), bc)
new_mkVBalBranch3MkVBalBranch127(zzz3170, zzz3171, zzz317200, zzz3173, zzz3174, zzz330, zzz331, zzz333, zzz334, zzz31, Succ(zzz5500), h) → new_mkVBalBranch1(zzz31, zzz334, Branch(zzz3170, zzz3171, Neg(Succ(zzz317200)), zzz3173, zzz3174), h)
new_mkVBalBranch3MkVBalBranch240(zzz958, zzz959, zzz960, zzz961, zzz962, zzz963, zzz964, zzz965, zzz966, zzz967, zzz968, ba) → new_mkVBalBranch3MkVBalBranch124(zzz958, zzz959, zzz960, zzz961, zzz962, zzz963, zzz964, zzz965, zzz966, zzz967, zzz968, Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat2(Succ(new_primPlusNat3(new_primPlusNat1(zzz960), zzz960)), zzz960)), zzz960))), ba)
new_mkVBalBranch3MkVBalBranch129(zzz1851, zzz1852, zzz1853, zzz1854, zzz1855, zzz1856, zzz1857, zzz1858, zzz1859, zzz1860, zzz1861, Succ(zzz18620), Succ(zzz18630), bd) → new_mkVBalBranch3MkVBalBranch129(zzz1851, zzz1852, zzz1853, zzz1854, zzz1855, zzz1856, zzz1857, zzz1858, zzz1859, zzz1860, zzz1861, zzz18620, zzz18630, bd)
new_mkVBalBranch3MkVBalBranch236(zzz958, zzz959, zzz960, zzz961, zzz962, zzz963, zzz964, zzz965, zzz966, zzz967, zzz968, Succ(zzz9690), Zero, ba) → new_mkVBalBranch3MkVBalBranch124(zzz958, zzz959, zzz960, zzz961, zzz962, zzz963, zzz964, zzz965, zzz966, zzz967, zzz968, Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat2(Succ(new_primPlusNat3(new_primPlusNat1(zzz960), zzz960)), zzz960)), zzz960))), ba)
new_mkVBalBranch3MkVBalBranch242(zzz972, zzz973, zzz974, zzz975, zzz976, zzz977, zzz978, zzz979, zzz980, zzz981, zzz982, Succ(zzz9830), Succ(zzz9840), bc) → new_mkVBalBranch3MkVBalBranch242(zzz972, zzz973, zzz974, zzz975, zzz976, zzz977, zzz978, zzz979, zzz980, zzz981, zzz982, zzz9830, zzz9840, bc)
new_mkVBalBranch3MkVBalBranch235(zzz3170, zzz3171, Pos(Succ(zzz317200)), zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, Succ(zzz4170), h) → new_mkVBalBranch3MkVBalBranch236(zzz3170, zzz3171, zzz317200, zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, zzz4170, zzz317200, h)
new_mkVBalBranch1(zzz31, Branch(zzz330, zzz331, Neg(Succ(zzz33200)), zzz333, zzz334), Branch(zzz3170, zzz3171, zzz3172, zzz3173, zzz3174), h) → new_mkVBalBranch3MkVBalBranch241(zzz3170, zzz3171, zzz3172, zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat2(Succ(new_primPlusNat3(new_primPlusNat1(zzz33200), zzz33200)), zzz33200)), zzz33200))), h)
new_mkVBalBranch1(zzz31, Branch(zzz330, zzz331, Pos(Succ(zzz33200)), zzz333, zzz334), Branch(zzz3170, zzz3171, zzz3172, zzz3173, zzz3174), h) → new_mkVBalBranch3MkVBalBranch235(zzz3170, zzz3171, zzz3172, zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat2(Succ(new_primPlusNat3(new_primPlusNat1(zzz33200), zzz33200)), zzz33200)), zzz33200))), h)
new_mkVBalBranch3MkVBalBranch236(zzz958, zzz959, zzz960, zzz961, zzz962, zzz963, zzz964, zzz965, zzz966, zzz967, zzz968, Succ(zzz9690), Succ(zzz9700), ba) → new_mkVBalBranch3MkVBalBranch236(zzz958, zzz959, zzz960, zzz961, zzz962, zzz963, zzz964, zzz965, zzz966, zzz967, zzz968, zzz9690, zzz9700, ba)
new_mkVBalBranch3MkVBalBranch241(zzz3170, zzz3171, Neg(Succ(zzz317200)), zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, Succ(zzz4190), h) → new_mkVBalBranch3MkVBalBranch242(zzz3170, zzz3171, zzz317200, zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, zzz317200, zzz4190, h)
new_mkVBalBranch1(zzz31, Branch(zzz330, zzz331, Pos(Zero), zzz333, zzz334), Branch(zzz3170, zzz3171, Pos(Succ(zzz317200)), zzz3173, zzz3174), h) → new_mkVBalBranch1(zzz31, Branch(zzz330, zzz331, Pos(Zero), zzz333, zzz334), zzz3173, h)
new_mkVBalBranch3MkVBalBranch237(zzz3170, zzz3171, zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, h) → new_mkVBalBranch1(zzz31, zzz334, Branch(zzz3170, zzz3171, Pos(Zero), zzz3173, zzz3174), h)
new_mkVBalBranch3MkVBalBranch235(zzz3170, zzz3171, Pos(Zero), zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, Succ(zzz4170), h) → new_mkVBalBranch3MkVBalBranch237(zzz3170, zzz3171, zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, h)
new_mkVBalBranch3MkVBalBranch236(zzz958, zzz959, zzz960, zzz961, zzz962, zzz963, zzz964, zzz965, zzz966, zzz967, zzz968, Zero, Succ(zzz9700), ba) → new_mkVBalBranch1(zzz968, Branch(zzz963, zzz964, Pos(Succ(zzz965)), zzz966, zzz967), zzz961, ba)
new_mkVBalBranch3MkVBalBranch125(zzz1337, zzz1338, zzz1339, zzz1340, zzz1341, zzz1342, zzz1343, zzz1344, zzz1345, zzz1346, zzz1347, Succ(zzz13480), Succ(zzz13490), bb) → new_mkVBalBranch3MkVBalBranch125(zzz1337, zzz1338, zzz1339, zzz1340, zzz1341, zzz1342, zzz1343, zzz1344, zzz1345, zzz1346, zzz1347, zzz13480, zzz13490, bb)
new_mkVBalBranch3MkVBalBranch123(zzz3170, zzz3171, zzz317200, zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, Succ(zzz5620), h) → new_mkVBalBranch1(zzz31, zzz334, Branch(zzz3170, zzz3171, Neg(Succ(zzz317200)), zzz3173, zzz3174), h)
new_mkVBalBranch3MkVBalBranch125(zzz1337, zzz1338, zzz1339, zzz1340, zzz1341, zzz1342, zzz1343, zzz1344, zzz1345, zzz1346, zzz1347, Zero, Succ(zzz13490), bb) → new_mkVBalBranch1(zzz1347, zzz1346, Branch(zzz1337, zzz1338, Pos(Succ(zzz1339)), zzz1340, zzz1341), bb)
new_mkVBalBranch3MkVBalBranch242(zzz972, zzz973, zzz974, zzz975, zzz976, zzz977, zzz978, zzz979, zzz980, zzz981, zzz982, Zero, Succ(zzz9840), bc) → new_mkVBalBranch1(zzz982, Branch(zzz977, zzz978, Neg(Succ(zzz979)), zzz980, zzz981), zzz975, bc)
new_mkVBalBranch3MkVBalBranch126(zzz3170, zzz3171, zzz317200, zzz3173, zzz3174, zzz330, zzz331, zzz333, zzz334, zzz31, Succ(zzz5350), h) → new_mkVBalBranch1(zzz31, zzz334, Branch(zzz3170, zzz3171, Neg(Succ(zzz317200)), zzz3173, zzz3174), h)
new_mkVBalBranch3MkVBalBranch241(zzz3170, zzz3171, Neg(Zero), zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, Succ(zzz4190), h) → new_mkVBalBranch1(zzz31, Branch(zzz330, zzz331, Neg(Succ(zzz33200)), zzz333, zzz334), zzz3173, h)
new_mkVBalBranch3MkVBalBranch124(zzz958, zzz959, zzz960, zzz961, zzz962, zzz963, zzz964, zzz965, zzz966, zzz967, zzz968, Succ(zzz10180), ba) → new_mkVBalBranch3MkVBalBranch125(zzz958, zzz959, zzz960, zzz961, zzz962, zzz963, zzz964, zzz965, zzz966, zzz967, zzz968, Succ(zzz10180), Succ(zzz965), ba)
new_mkVBalBranch1(zzz31, Branch(zzz330, zzz331, Pos(Zero), zzz333, zzz334), Branch(zzz3170, zzz3171, Neg(Succ(zzz317200)), zzz3173, zzz3174), h) → new_mkVBalBranch3MkVBalBranch126(zzz3170, zzz3171, zzz317200, zzz3173, zzz3174, zzz330, zzz331, zzz333, zzz334, zzz31, Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat2(Succ(new_primPlusNat3(new_primPlusNat1(zzz317200), zzz317200)), zzz317200)), zzz317200))), h)
new_mkVBalBranch3MkVBalBranch235(zzz3170, zzz3171, Neg(Succ(zzz317200)), zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, Succ(zzz4170), h) → new_mkVBalBranch3MkVBalBranch123(zzz3170, zzz3171, zzz317200, zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat2(Succ(new_primPlusNat3(new_primPlusNat1(zzz317200), zzz317200)), zzz317200)), zzz317200))), h)
new_mkVBalBranch3MkVBalBranch242(zzz972, zzz973, zzz974, zzz975, zzz976, zzz977, zzz978, zzz979, zzz980, zzz981, zzz982, Zero, Zero, bc) → new_mkVBalBranch3MkVBalBranch244(zzz972, zzz973, zzz974, zzz975, zzz976, zzz977, zzz978, zzz979, zzz980, zzz981, zzz982, bc)
new_mkVBalBranch1(zzz31, Branch(zzz330, zzz331, Neg(Zero), zzz333, zzz334), Branch(zzz3170, zzz3171, Pos(Succ(zzz317200)), zzz3173, zzz3174), h) → new_mkVBalBranch1(zzz31, Branch(zzz330, zzz331, Neg(Zero), zzz333, zzz334), zzz3173, h)
new_mkVBalBranch3MkVBalBranch235(zzz3170, zzz3171, Neg(Zero), zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, Succ(zzz4170), h) → new_mkVBalBranch1(zzz31, zzz334, Branch(zzz3170, zzz3171, Neg(Zero), zzz3173, zzz3174), h)
new_mkVBalBranch3MkVBalBranch236(zzz958, zzz959, zzz960, zzz961, zzz962, zzz963, zzz964, zzz965, zzz966, zzz967, zzz968, Zero, Zero, ba) → new_mkVBalBranch3MkVBalBranch240(zzz958, zzz959, zzz960, zzz961, zzz962, zzz963, zzz964, zzz965, zzz966, zzz967, zzz968, ba)
Used ordering: Polynomial interpretation [25]:

POL(Branch(x1, x2, x3, x4, x5)) = x1 + x2 + x3 + x4 + x5   
POL(Neg(x1)) = 1   
POL(Pos(x1)) = 0   
POL(Succ(x1)) = 0   
POL(Zero) = 0   
POL(new_mkVBalBranch1(x1, x2, x3, x4)) = x2   
POL(new_mkVBalBranch3MkVBalBranch123(x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12, x13)) = x10 + x6   
POL(new_mkVBalBranch3MkVBalBranch124(x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12, x13)) = x10 + x9   
POL(new_mkVBalBranch3MkVBalBranch125(x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12, x13, x14)) = x10   
POL(new_mkVBalBranch3MkVBalBranch126(x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12)) = x9   
POL(new_mkVBalBranch3MkVBalBranch127(x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12)) = x8 + x9   
POL(new_mkVBalBranch3MkVBalBranch128(x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12, x13)) = x10 + x7   
POL(new_mkVBalBranch3MkVBalBranch129(x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12, x13, x14)) = x10   
POL(new_mkVBalBranch3MkVBalBranch235(x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12, x13)) = x10 + x6 + x7 + x9   
POL(new_mkVBalBranch3MkVBalBranch236(x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12, x13, x14)) = x10 + x6 + x7 + x9   
POL(new_mkVBalBranch3MkVBalBranch237(x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11)) = x5 + x9   
POL(new_mkVBalBranch3MkVBalBranch240(x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12)) = x10 + x7 + x9   
POL(new_mkVBalBranch3MkVBalBranch241(x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12, x13)) = 1 + x10 + x6 + x7 + x9   
POL(new_mkVBalBranch3MkVBalBranch242(x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12, x13, x14)) = 1 + x10 + x6 + x7 + x9   
POL(new_mkVBalBranch3MkVBalBranch244(x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12)) = 1 + x10 + x6 + x7   
POL(new_primPlusNat1(x1)) = 0   
POL(new_primPlusNat2(x1, x2)) = 0   
POL(new_primPlusNat3(x1, x2)) = 1   

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

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

new_mkVBalBranch3MkVBalBranch129(zzz1851, zzz1852, zzz1853, zzz1854, zzz1855, zzz1856, zzz1857, zzz1858, zzz1859, zzz1860, zzz1861, Zero, Succ(zzz18630), bd) → new_mkVBalBranch1(zzz1861, zzz1860, Branch(zzz1851, zzz1852, Neg(Succ(zzz1853)), zzz1854, zzz1855), bd)
new_mkVBalBranch3MkVBalBranch127(zzz3170, zzz3171, zzz317200, zzz3173, zzz3174, zzz330, zzz331, zzz333, zzz334, zzz31, Succ(zzz5500), h) → new_mkVBalBranch1(zzz31, zzz334, Branch(zzz3170, zzz3171, Neg(Succ(zzz317200)), zzz3173, zzz3174), h)
new_mkVBalBranch3MkVBalBranch128(zzz972, zzz973, zzz974, zzz975, zzz976, zzz977, zzz978, zzz979, zzz980, zzz981, zzz982, Succ(zzz10190), bc) → new_mkVBalBranch3MkVBalBranch129(zzz972, zzz973, zzz974, zzz975, zzz976, zzz977, zzz978, zzz979, zzz980, zzz981, zzz982, Succ(zzz979), Succ(zzz10190), bc)
new_mkVBalBranch3MkVBalBranch241(zzz3170, zzz3171, Pos(zzz31720), zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, Succ(zzz4190), h) → new_mkVBalBranch1(zzz31, Branch(zzz330, zzz331, Neg(Succ(zzz33200)), zzz333, zzz334), zzz3173, h)
new_mkVBalBranch3MkVBalBranch240(zzz958, zzz959, zzz960, zzz961, zzz962, zzz963, zzz964, zzz965, zzz966, zzz967, zzz968, ba) → new_mkVBalBranch3MkVBalBranch124(zzz958, zzz959, zzz960, zzz961, zzz962, zzz963, zzz964, zzz965, zzz966, zzz967, zzz968, Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat2(Succ(new_primPlusNat3(new_primPlusNat1(zzz960), zzz960)), zzz960)), zzz960))), ba)
new_mkVBalBranch3MkVBalBranch129(zzz1851, zzz1852, zzz1853, zzz1854, zzz1855, zzz1856, zzz1857, zzz1858, zzz1859, zzz1860, zzz1861, Succ(zzz18620), Succ(zzz18630), bd) → new_mkVBalBranch3MkVBalBranch129(zzz1851, zzz1852, zzz1853, zzz1854, zzz1855, zzz1856, zzz1857, zzz1858, zzz1859, zzz1860, zzz1861, zzz18620, zzz18630, bd)
new_mkVBalBranch3MkVBalBranch236(zzz958, zzz959, zzz960, zzz961, zzz962, zzz963, zzz964, zzz965, zzz966, zzz967, zzz968, Succ(zzz9690), Zero, ba) → new_mkVBalBranch3MkVBalBranch124(zzz958, zzz959, zzz960, zzz961, zzz962, zzz963, zzz964, zzz965, zzz966, zzz967, zzz968, Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat2(Succ(new_primPlusNat3(new_primPlusNat1(zzz960), zzz960)), zzz960)), zzz960))), ba)
new_mkVBalBranch3MkVBalBranch235(zzz3170, zzz3171, Pos(Succ(zzz317200)), zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, Succ(zzz4170), h) → new_mkVBalBranch3MkVBalBranch236(zzz3170, zzz3171, zzz317200, zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, zzz4170, zzz317200, h)
new_mkVBalBranch3MkVBalBranch242(zzz972, zzz973, zzz974, zzz975, zzz976, zzz977, zzz978, zzz979, zzz980, zzz981, zzz982, Succ(zzz9830), Succ(zzz9840), bc) → new_mkVBalBranch3MkVBalBranch242(zzz972, zzz973, zzz974, zzz975, zzz976, zzz977, zzz978, zzz979, zzz980, zzz981, zzz982, zzz9830, zzz9840, bc)
new_mkVBalBranch1(zzz31, Branch(zzz330, zzz331, Pos(Succ(zzz33200)), zzz333, zzz334), Branch(zzz3170, zzz3171, zzz3172, zzz3173, zzz3174), h) → new_mkVBalBranch3MkVBalBranch235(zzz3170, zzz3171, zzz3172, zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat2(Succ(new_primPlusNat3(new_primPlusNat1(zzz33200), zzz33200)), zzz33200)), zzz33200))), h)
new_mkVBalBranch1(zzz31, Branch(zzz330, zzz331, Neg(Succ(zzz33200)), zzz333, zzz334), Branch(zzz3170, zzz3171, zzz3172, zzz3173, zzz3174), h) → new_mkVBalBranch3MkVBalBranch241(zzz3170, zzz3171, zzz3172, zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat2(Succ(new_primPlusNat3(new_primPlusNat1(zzz33200), zzz33200)), zzz33200)), zzz33200))), h)
new_mkVBalBranch3MkVBalBranch236(zzz958, zzz959, zzz960, zzz961, zzz962, zzz963, zzz964, zzz965, zzz966, zzz967, zzz968, Succ(zzz9690), Succ(zzz9700), ba) → new_mkVBalBranch3MkVBalBranch236(zzz958, zzz959, zzz960, zzz961, zzz962, zzz963, zzz964, zzz965, zzz966, zzz967, zzz968, zzz9690, zzz9700, ba)
new_mkVBalBranch3MkVBalBranch241(zzz3170, zzz3171, Neg(Succ(zzz317200)), zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, Succ(zzz4190), h) → new_mkVBalBranch3MkVBalBranch242(zzz3170, zzz3171, zzz317200, zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, zzz317200, zzz4190, h)
new_mkVBalBranch1(zzz31, Branch(zzz330, zzz331, Pos(Zero), zzz333, zzz334), Branch(zzz3170, zzz3171, Pos(Succ(zzz317200)), zzz3173, zzz3174), h) → new_mkVBalBranch1(zzz31, Branch(zzz330, zzz331, Pos(Zero), zzz333, zzz334), zzz3173, h)
new_mkVBalBranch3MkVBalBranch237(zzz3170, zzz3171, zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, h) → new_mkVBalBranch1(zzz31, zzz334, Branch(zzz3170, zzz3171, Pos(Zero), zzz3173, zzz3174), h)
new_mkVBalBranch3MkVBalBranch235(zzz3170, zzz3171, Pos(Zero), zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, Succ(zzz4170), h) → new_mkVBalBranch3MkVBalBranch237(zzz3170, zzz3171, zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, h)
new_mkVBalBranch3MkVBalBranch236(zzz958, zzz959, zzz960, zzz961, zzz962, zzz963, zzz964, zzz965, zzz966, zzz967, zzz968, Zero, Succ(zzz9700), ba) → new_mkVBalBranch1(zzz968, Branch(zzz963, zzz964, Pos(Succ(zzz965)), zzz966, zzz967), zzz961, ba)
new_mkVBalBranch3MkVBalBranch125(zzz1337, zzz1338, zzz1339, zzz1340, zzz1341, zzz1342, zzz1343, zzz1344, zzz1345, zzz1346, zzz1347, Succ(zzz13480), Succ(zzz13490), bb) → new_mkVBalBranch3MkVBalBranch125(zzz1337, zzz1338, zzz1339, zzz1340, zzz1341, zzz1342, zzz1343, zzz1344, zzz1345, zzz1346, zzz1347, zzz13480, zzz13490, bb)
new_mkVBalBranch3MkVBalBranch123(zzz3170, zzz3171, zzz317200, zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, Succ(zzz5620), h) → new_mkVBalBranch1(zzz31, zzz334, Branch(zzz3170, zzz3171, Neg(Succ(zzz317200)), zzz3173, zzz3174), h)
new_mkVBalBranch3MkVBalBranch125(zzz1337, zzz1338, zzz1339, zzz1340, zzz1341, zzz1342, zzz1343, zzz1344, zzz1345, zzz1346, zzz1347, Zero, Succ(zzz13490), bb) → new_mkVBalBranch1(zzz1347, zzz1346, Branch(zzz1337, zzz1338, Pos(Succ(zzz1339)), zzz1340, zzz1341), bb)
new_mkVBalBranch3MkVBalBranch242(zzz972, zzz973, zzz974, zzz975, zzz976, zzz977, zzz978, zzz979, zzz980, zzz981, zzz982, Zero, Succ(zzz9840), bc) → new_mkVBalBranch1(zzz982, Branch(zzz977, zzz978, Neg(Succ(zzz979)), zzz980, zzz981), zzz975, bc)
new_mkVBalBranch3MkVBalBranch126(zzz3170, zzz3171, zzz317200, zzz3173, zzz3174, zzz330, zzz331, zzz333, zzz334, zzz31, Succ(zzz5350), h) → new_mkVBalBranch1(zzz31, zzz334, Branch(zzz3170, zzz3171, Neg(Succ(zzz317200)), zzz3173, zzz3174), h)
new_mkVBalBranch3MkVBalBranch241(zzz3170, zzz3171, Neg(Zero), zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, Succ(zzz4190), h) → new_mkVBalBranch1(zzz31, Branch(zzz330, zzz331, Neg(Succ(zzz33200)), zzz333, zzz334), zzz3173, h)
new_mkVBalBranch3MkVBalBranch124(zzz958, zzz959, zzz960, zzz961, zzz962, zzz963, zzz964, zzz965, zzz966, zzz967, zzz968, Succ(zzz10180), ba) → new_mkVBalBranch3MkVBalBranch125(zzz958, zzz959, zzz960, zzz961, zzz962, zzz963, zzz964, zzz965, zzz966, zzz967, zzz968, Succ(zzz10180), Succ(zzz965), ba)
new_mkVBalBranch1(zzz31, Branch(zzz330, zzz331, Pos(Zero), zzz333, zzz334), Branch(zzz3170, zzz3171, Neg(Succ(zzz317200)), zzz3173, zzz3174), h) → new_mkVBalBranch3MkVBalBranch126(zzz3170, zzz3171, zzz317200, zzz3173, zzz3174, zzz330, zzz331, zzz333, zzz334, zzz31, Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat2(Succ(new_primPlusNat3(new_primPlusNat1(zzz317200), zzz317200)), zzz317200)), zzz317200))), h)
new_mkVBalBranch3MkVBalBranch235(zzz3170, zzz3171, Neg(Succ(zzz317200)), zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, Succ(zzz4170), h) → new_mkVBalBranch3MkVBalBranch123(zzz3170, zzz3171, zzz317200, zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat2(Succ(new_primPlusNat3(new_primPlusNat1(zzz317200), zzz317200)), zzz317200)), zzz317200))), h)
new_mkVBalBranch3MkVBalBranch242(zzz972, zzz973, zzz974, zzz975, zzz976, zzz977, zzz978, zzz979, zzz980, zzz981, zzz982, Zero, Zero, bc) → new_mkVBalBranch3MkVBalBranch244(zzz972, zzz973, zzz974, zzz975, zzz976, zzz977, zzz978, zzz979, zzz980, zzz981, zzz982, bc)
new_mkVBalBranch1(zzz31, Branch(zzz330, zzz331, Neg(Zero), zzz333, zzz334), Branch(zzz3170, zzz3171, Pos(Succ(zzz317200)), zzz3173, zzz3174), h) → new_mkVBalBranch1(zzz31, Branch(zzz330, zzz331, Neg(Zero), zzz333, zzz334), zzz3173, h)
new_mkVBalBranch3MkVBalBranch235(zzz3170, zzz3171, Neg(Zero), zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, Succ(zzz4170), h) → new_mkVBalBranch1(zzz31, zzz334, Branch(zzz3170, zzz3171, Neg(Zero), zzz3173, zzz3174), h)
new_mkVBalBranch3MkVBalBranch236(zzz958, zzz959, zzz960, zzz961, zzz962, zzz963, zzz964, zzz965, zzz966, zzz967, zzz968, Zero, Zero, ba) → new_mkVBalBranch3MkVBalBranch240(zzz958, zzz959, zzz960, zzz961, zzz962, zzz963, zzz964, zzz965, zzz966, zzz967, zzz968, ba)

The TRS R consists of the following rules:

new_primPlusNat1(Zero) → Zero
new_primPlusNat1(Succ(zzz62000)) → Succ(Succ(new_primPlusNat1(zzz62000)))
new_primPlusNat3(zzz90, Succ(zzz910)) → Succ(Succ(new_primPlusNat2(zzz90, zzz910)))
new_primPlusNat3(zzz90, Zero) → Succ(zzz90)
new_primPlusNat2(Succ(zzz900), Succ(zzz9100)) → Succ(Succ(new_primPlusNat2(zzz900, zzz9100)))
new_primPlusNat2(Succ(zzz900), Zero) → Succ(zzz900)
new_primPlusNat2(Zero, Succ(zzz9100)) → Succ(zzz9100)
new_primPlusNat2(Zero, Zero) → Zero

The set Q consists of the following terms:

new_primPlusNat2(Zero, Succ(x0))
new_primPlusNat3(x0, Succ(x1))
new_primPlusNat2(Succ(x0), Succ(x1))
new_primPlusNat3(x0, Zero)
new_primPlusNat1(Zero)
new_primPlusNat2(Zero, Zero)
new_primPlusNat1(Succ(x0))
new_primPlusNat2(Succ(x0), Zero)

We have to consider all minimal (P,Q,R)-chains.
The approximation of the Dependency Graph [15,17,22] contains 4 SCCs with 4 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
                                  ↳ QDP
                                  ↳ QDP
                                    ↳ DependencyGraphProof
                                      ↳ QDP
                                        ↳ Rewriting
                                          ↳ QDP
                                            ↳ Rewriting
                                              ↳ QDP
                                                ↳ Rewriting
                                                  ↳ QDP
                                                    ↳ Rewriting
                                                      ↳ QDP
                                                        ↳ Rewriting
                                                          ↳ QDP
                                                            ↳ Rewriting
                                                              ↳ QDP
                                                                ↳ Rewriting
                                                                  ↳ QDP
                                                                    ↳ Rewriting
                                                                      ↳ QDP
                                                                        ↳ Rewriting
                                                                          ↳ QDP
                                                                            ↳ Rewriting
                                                                              ↳ QDP
                                                                                ↳ UsableRulesProof
                                                                                  ↳ QDP
                                                                                    ↳ QReductionProof
                                                                                      ↳ QDP
                                                                                        ↳ Rewriting
                                                                                          ↳ QDP
                                                                                            ↳ Rewriting
                                                                                              ↳ QDP
                                                                                                ↳ Rewriting
                                                                                                  ↳ QDP
                                                                                                    ↳ Rewriting
                                                                                                      ↳ QDP
                                                                                                        ↳ Rewriting
                                                                                                          ↳ QDP
                                                                                                            ↳ Rewriting
                                                                                                              ↳ QDP
                                                                                                                ↳ Rewriting
                                                                                                                  ↳ QDP
                                                                                                                    ↳ Rewriting
                                                                                                                      ↳ QDP
                                                                                                                        ↳ Rewriting
                                                                                                                          ↳ QDP
                                                                                                                            ↳ Rewriting
                                                                                                                              ↳ QDP
                                                                                                                                ↳ UsableRulesProof
                                                                                                                                  ↳ QDP
                                                                                                                                    ↳ QReductionProof
                                                                                                                                      ↳ QDP
                                                                                                                                        ↳ Rewriting
                                                                                                                                          ↳ QDP
                                                                                                                                            ↳ Rewriting
                                                                                                                                              ↳ QDP
                                                                                                                                                ↳ Rewriting
                                                                                                                                                  ↳ QDP
                                                                                                                                                    ↳ DependencyGraphProof
                                                                                                                                                      ↳ QDP
                                                                                                                                                        ↳ Rewriting
                                                                                                                                                          ↳ QDP
                                                                                                                                                            ↳ Rewriting
                                                                                                                                                              ↳ QDP
                                                                                                                                                                ↳ DependencyGraphProof
                                                                                                                                                                  ↳ QDP
                                                                                                                                                                    ↳ Rewriting
                                                                                                                                                                      ↳ QDP
                                                                                                                                                                        ↳ Rewriting
                                                                                                                                                                          ↳ QDP
                                                                                                                                                                            ↳ Rewriting
                                                                                                                                                                              ↳ QDP
                                                                                                                                                                                ↳ Rewriting
                                                                                                                                                                                  ↳ QDP
                                                                                                                                                                                    ↳ Rewriting
                                                                                                                                                                                      ↳ QDP
                                                                                                                                                                                        ↳ Rewriting
                                                                                                                                                                                          ↳ QDP
                                                                                                                                                                                            ↳ Rewriting
                                                                                                                                                                                              ↳ QDP
                                                                                                                                                                                                ↳ DependencyGraphProof
                                                                                                                                                                                                  ↳ QDP
                                                                                                                                                                                                    ↳ Rewriting
                                                                                                                                                                                                      ↳ QDP
                                                                                                                                                                                                        ↳ DependencyGraphProof
                                                                                                                                                                                                          ↳ QDP
                                                                                                                                                                                                            ↳ Rewriting
                                                                                                                                                                                                              ↳ QDP
                                                                                                                                                                                                                ↳ Rewriting
                                                                                                                                                                                                                  ↳ 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(zzz31, Branch(zzz330, zzz331, Neg(Zero), zzz333, zzz334), Branch(zzz3170, zzz3171, Pos(Succ(zzz317200)), zzz3173, zzz3174), h) → new_mkVBalBranch1(zzz31, Branch(zzz330, zzz331, Neg(Zero), zzz333, zzz334), zzz3173, h)

The TRS R consists of the following rules:

new_primPlusNat1(Zero) → Zero
new_primPlusNat1(Succ(zzz62000)) → Succ(Succ(new_primPlusNat1(zzz62000)))
new_primPlusNat3(zzz90, Succ(zzz910)) → Succ(Succ(new_primPlusNat2(zzz90, zzz910)))
new_primPlusNat3(zzz90, Zero) → Succ(zzz90)
new_primPlusNat2(Succ(zzz900), Succ(zzz9100)) → Succ(Succ(new_primPlusNat2(zzz900, zzz9100)))
new_primPlusNat2(Succ(zzz900), Zero) → Succ(zzz900)
new_primPlusNat2(Zero, Succ(zzz9100)) → Succ(zzz9100)
new_primPlusNat2(Zero, Zero) → Zero

The set Q consists of the following terms:

new_primPlusNat2(Zero, Succ(x0))
new_primPlusNat3(x0, Succ(x1))
new_primPlusNat2(Succ(x0), Succ(x1))
new_primPlusNat3(x0, Zero)
new_primPlusNat1(Zero)
new_primPlusNat2(Zero, Zero)
new_primPlusNat1(Succ(x0))
new_primPlusNat2(Succ(x0), Zero)

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

↳ HASKELL
  ↳ LR
    ↳ HASKELL
      ↳ CR
        ↳ HASKELL
          ↳ IFR
            ↳ HASKELL
              ↳ BR
                ↳ HASKELL
                  ↳ COR
                    ↳ HASKELL
                      ↳ LetRed
                        ↳ HASKELL
                          ↳ NumRed
                            ↳ HASKELL
                              ↳ Narrow
                                ↳ AND
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                    ↳ DependencyGraphProof
                                      ↳ QDP
                                        ↳ Rewriting
                                          ↳ QDP
                                            ↳ Rewriting
                                              ↳ QDP
                                                ↳ Rewriting
                                                  ↳ QDP
                                                    ↳ Rewriting
                                                      ↳ QDP
                                                        ↳ Rewriting
                                                          ↳ QDP
                                                            ↳ Rewriting
                                                              ↳ QDP
                                                                ↳ Rewriting
                                                                  ↳ QDP
                                                                    ↳ Rewriting
                                                                      ↳ QDP
                                                                        ↳ Rewriting
                                                                          ↳ QDP
                                                                            ↳ Rewriting
                                                                              ↳ QDP
                                                                                ↳ UsableRulesProof
                                                                                  ↳ QDP
                                                                                    ↳ QReductionProof
                                                                                      ↳ QDP
                                                                                        ↳ Rewriting
                                                                                          ↳ QDP
                                                                                            ↳ Rewriting
                                                                                              ↳ QDP
                                                                                                ↳ Rewriting
                                                                                                  ↳ QDP
                                                                                                    ↳ Rewriting
                                                                                                      ↳ QDP
                                                                                                        ↳ Rewriting
                                                                                                          ↳ QDP
                                                                                                            ↳ Rewriting
                                                                                                              ↳ QDP
                                                                                                                ↳ Rewriting
                                                                                                                  ↳ QDP
                                                                                                                    ↳ Rewriting
                                                                                                                      ↳ QDP
                                                                                                                        ↳ Rewriting
                                                                                                                          ↳ QDP
                                                                                                                            ↳ Rewriting
                                                                                                                              ↳ QDP
                                                                                                                                ↳ UsableRulesProof
                                                                                                                                  ↳ QDP
                                                                                                                                    ↳ QReductionProof
                                                                                                                                      ↳ QDP
                                                                                                                                        ↳ Rewriting
                                                                                                                                          ↳ QDP
                                                                                                                                            ↳ Rewriting
                                                                                                                                              ↳ QDP
                                                                                                                                                ↳ Rewriting
                                                                                                                                                  ↳ QDP
                                                                                                                                                    ↳ DependencyGraphProof
                                                                                                                                                      ↳ QDP
                                                                                                                                                        ↳ Rewriting
                                                                                                                                                          ↳ QDP
                                                                                                                                                            ↳ Rewriting
                                                                                                                                                              ↳ QDP
                                                                                                                                                                ↳ DependencyGraphProof
                                                                                                                                                                  ↳ QDP
                                                                                                                                                                    ↳ Rewriting
                                                                                                                                                                      ↳ QDP
                                                                                                                                                                        ↳ Rewriting
                                                                                                                                                                          ↳ QDP
                                                                                                                                                                            ↳ Rewriting
                                                                                                                                                                              ↳ QDP
                                                                                                                                                                                ↳ Rewriting
                                                                                                                                                                                  ↳ QDP
                                                                                                                                                                                    ↳ Rewriting
                                                                                                                                                                                      ↳ QDP
                                                                                                                                                                                        ↳ Rewriting
                                                                                                                                                                                          ↳ QDP
                                                                                                                                                                                            ↳ Rewriting
                                                                                                                                                                                              ↳ QDP
                                                                                                                                                                                                ↳ DependencyGraphProof
                                                                                                                                                                                                  ↳ QDP
                                                                                                                                                                                                    ↳ Rewriting
                                                                                                                                                                                                      ↳ QDP
                                                                                                                                                                                                        ↳ DependencyGraphProof
                                                                                                                                                                                                          ↳ QDP
                                                                                                                                                                                                            ↳ Rewriting
                                                                                                                                                                                                              ↳ QDP
                                                                                                                                                                                                                ↳ Rewriting
                                                                                                                                                                                                                  ↳ 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(zzz31, Branch(zzz330, zzz331, Neg(Zero), zzz333, zzz334), Branch(zzz3170, zzz3171, Pos(Succ(zzz317200)), zzz3173, zzz3174), h) → new_mkVBalBranch1(zzz31, Branch(zzz330, zzz331, Neg(Zero), zzz333, zzz334), zzz3173, h)

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

new_primPlusNat2(Zero, Succ(x0))
new_primPlusNat3(x0, Succ(x1))
new_primPlusNat2(Succ(x0), Succ(x1))
new_primPlusNat3(x0, Zero)
new_primPlusNat1(Zero)
new_primPlusNat2(Zero, Zero)
new_primPlusNat1(Succ(x0))
new_primPlusNat2(Succ(x0), Zero)

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

new_primPlusNat2(Zero, Succ(x0))
new_primPlusNat3(x0, Succ(x1))
new_primPlusNat2(Succ(x0), Succ(x1))
new_primPlusNat3(x0, Zero)
new_primPlusNat1(Zero)
new_primPlusNat2(Zero, Zero)
new_primPlusNat1(Succ(x0))
new_primPlusNat2(Succ(x0), 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
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                    ↳ DependencyGraphProof
                                      ↳ QDP
                                        ↳ Rewriting
                                          ↳ QDP
                                            ↳ Rewriting
                                              ↳ QDP
                                                ↳ Rewriting
                                                  ↳ QDP
                                                    ↳ Rewriting
                                                      ↳ QDP
                                                        ↳ Rewriting
                                                          ↳ QDP
                                                            ↳ Rewriting
                                                              ↳ QDP
                                                                ↳ Rewriting
                                                                  ↳ QDP
                                                                    ↳ Rewriting
                                                                      ↳ QDP
                                                                        ↳ Rewriting
                                                                          ↳ QDP
                                                                            ↳ Rewriting
                                                                              ↳ QDP
                                                                                ↳ UsableRulesProof
                                                                                  ↳ QDP
                                                                                    ↳ QReductionProof
                                                                                      ↳ QDP
                                                                                        ↳ Rewriting
                                                                                          ↳ QDP
                                                                                            ↳ Rewriting
                                                                                              ↳ QDP
                                                                                                ↳ Rewriting
                                                                                                  ↳ QDP
                                                                                                    ↳ Rewriting
                                                                                                      ↳ QDP
                                                                                                        ↳ Rewriting
                                                                                                          ↳ QDP
                                                                                                            ↳ Rewriting
                                                                                                              ↳ QDP
                                                                                                                ↳ Rewriting
                                                                                                                  ↳ QDP
                                                                                                                    ↳ Rewriting
                                                                                                                      ↳ QDP
                                                                                                                        ↳ Rewriting
                                                                                                                          ↳ QDP
                                                                                                                            ↳ Rewriting
                                                                                                                              ↳ QDP
                                                                                                                                ↳ UsableRulesProof
                                                                                                                                  ↳ QDP
                                                                                                                                    ↳ QReductionProof
                                                                                                                                      ↳ QDP
                                                                                                                                        ↳ Rewriting
                                                                                                                                          ↳ QDP
                                                                                                                                            ↳ Rewriting
                                                                                                                                              ↳ QDP
                                                                                                                                                ↳ Rewriting
                                                                                                                                                  ↳ QDP
                                                                                                                                                    ↳ DependencyGraphProof
                                                                                                                                                      ↳ QDP
                                                                                                                                                        ↳ Rewriting
                                                                                                                                                          ↳ QDP
                                                                                                                                                            ↳ Rewriting
                                                                                                                                                              ↳ QDP
                                                                                                                                                                ↳ DependencyGraphProof
                                                                                                                                                                  ↳ QDP
                                                                                                                                                                    ↳ Rewriting
                                                                                                                                                                      ↳ QDP
                                                                                                                                                                        ↳ Rewriting
                                                                                                                                                                          ↳ QDP
                                                                                                                                                                            ↳ Rewriting
                                                                                                                                                                              ↳ QDP
                                                                                                                                                                                ↳ Rewriting
                                                                                                                                                                                  ↳ QDP
                                                                                                                                                                                    ↳ Rewriting
                                                                                                                                                                                      ↳ QDP
                                                                                                                                                                                        ↳ Rewriting
                                                                                                                                                                                          ↳ QDP
                                                                                                                                                                                            ↳ Rewriting
                                                                                                                                                                                              ↳ QDP
                                                                                                                                                                                                ↳ DependencyGraphProof
                                                                                                                                                                                                  ↳ QDP
                                                                                                                                                                                                    ↳ Rewriting
                                                                                                                                                                                                      ↳ QDP
                                                                                                                                                                                                        ↳ DependencyGraphProof
                                                                                                                                                                                                          ↳ QDP
                                                                                                                                                                                                            ↳ Rewriting
                                                                                                                                                                                                              ↳ QDP
                                                                                                                                                                                                                ↳ Rewriting
                                                                                                                                                                                                                  ↳ 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(zzz31, Branch(zzz330, zzz331, Neg(Zero), zzz333, zzz334), Branch(zzz3170, zzz3171, Pos(Succ(zzz317200)), zzz3173, zzz3174), h) → new_mkVBalBranch1(zzz31, Branch(zzz330, zzz331, Neg(Zero), zzz333, zzz334), zzz3173, 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
                                  ↳ QDP
                                  ↳ QDP
                                    ↳ DependencyGraphProof
                                      ↳ QDP
                                        ↳ Rewriting
                                          ↳ QDP
                                            ↳ Rewriting
                                              ↳ QDP
                                                ↳ Rewriting
                                                  ↳ QDP
                                                    ↳ Rewriting
                                                      ↳ QDP
                                                        ↳ Rewriting
                                                          ↳ QDP
                                                            ↳ Rewriting
                                                              ↳ QDP
                                                                ↳ Rewriting
                                                                  ↳ QDP
                                                                    ↳ Rewriting
                                                                      ↳ QDP
                                                                        ↳ Rewriting
                                                                          ↳ QDP
                                                                            ↳ Rewriting
                                                                              ↳ QDP
                                                                                ↳ UsableRulesProof
                                                                                  ↳ QDP
                                                                                    ↳ QReductionProof
                                                                                      ↳ QDP
                                                                                        ↳ Rewriting
                                                                                          ↳ QDP
                                                                                            ↳ Rewriting
                                                                                              ↳ QDP
                                                                                                ↳ Rewriting
                                                                                                  ↳ QDP
                                                                                                    ↳ Rewriting
                                                                                                      ↳ QDP
                                                                                                        ↳ Rewriting
                                                                                                          ↳ QDP
                                                                                                            ↳ Rewriting
                                                                                                              ↳ QDP
                                                                                                                ↳ Rewriting
                                                                                                                  ↳ QDP
                                                                                                                    ↳ Rewriting
                                                                                                                      ↳ QDP
                                                                                                                        ↳ Rewriting
                                                                                                                          ↳ QDP
                                                                                                                            ↳ Rewriting
                                                                                                                              ↳ QDP
                                                                                                                                ↳ UsableRulesProof
                                                                                                                                  ↳ QDP
                                                                                                                                    ↳ QReductionProof
                                                                                                                                      ↳ QDP
                                                                                                                                        ↳ Rewriting
                                                                                                                                          ↳ QDP
                                                                                                                                            ↳ Rewriting
                                                                                                                                              ↳ QDP
                                                                                                                                                ↳ Rewriting
                                                                                                                                                  ↳ QDP
                                                                                                                                                    ↳ DependencyGraphProof
                                                                                                                                                      ↳ QDP
                                                                                                                                                        ↳ Rewriting
                                                                                                                                                          ↳ QDP
                                                                                                                                                            ↳ Rewriting
                                                                                                                                                              ↳ QDP
                                                                                                                                                                ↳ DependencyGraphProof
                                                                                                                                                                  ↳ QDP
                                                                                                                                                                    ↳ Rewriting
                                                                                                                                                                      ↳ QDP
                                                                                                                                                                        ↳ Rewriting
                                                                                                                                                                          ↳ QDP
                                                                                                                                                                            ↳ Rewriting
                                                                                                                                                                              ↳ QDP
                                                                                                                                                                                ↳ Rewriting
                                                                                                                                                                                  ↳ QDP
                                                                                                                                                                                    ↳ Rewriting
                                                                                                                                                                                      ↳ QDP
                                                                                                                                                                                        ↳ Rewriting
                                                                                                                                                                                          ↳ QDP
                                                                                                                                                                                            ↳ Rewriting
                                                                                                                                                                                              ↳ QDP
                                                                                                                                                                                                ↳ DependencyGraphProof
                                                                                                                                                                                                  ↳ QDP
                                                                                                                                                                                                    ↳ Rewriting
                                                                                                                                                                                                      ↳ QDP
                                                                                                                                                                                                        ↳ DependencyGraphProof
                                                                                                                                                                                                          ↳ QDP
                                                                                                                                                                                                            ↳ Rewriting
                                                                                                                                                                                                              ↳ QDP
                                                                                                                                                                                                                ↳ Rewriting
                                                                                                                                                                                                                  ↳ QDP
                                                                                                                                                                                                                    ↳ QDPOrderProof
                                                                                                                                                                                                                      ↳ QDP
                                                                                                                                                                                                                        ↳ DependencyGraphProof
                                                                                                                                                                                                                          ↳ AND
                                                                                                                                                                                                                            ↳ QDP
                                                                                                                                                                                                                            ↳ QDP
                                                                                                                                                                                                                              ↳ QDPSizeChangeProof
                                                                                                                                                                                                                            ↳ QDP
                                                                                                                                                                                                                            ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP

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

new_mkVBalBranch3MkVBalBranch242(zzz972, zzz973, zzz974, zzz975, zzz976, zzz977, zzz978, zzz979, zzz980, zzz981, zzz982, Succ(zzz9830), Succ(zzz9840), bc) → new_mkVBalBranch3MkVBalBranch242(zzz972, zzz973, zzz974, zzz975, zzz976, zzz977, zzz978, zzz979, zzz980, zzz981, zzz982, zzz9830, zzz9840, bc)
new_mkVBalBranch3MkVBalBranch241(zzz3170, zzz3171, Neg(Zero), zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, Succ(zzz4190), h) → new_mkVBalBranch1(zzz31, Branch(zzz330, zzz331, Neg(Succ(zzz33200)), zzz333, zzz334), zzz3173, h)
new_mkVBalBranch3MkVBalBranch241(zzz3170, zzz3171, Pos(zzz31720), zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, Succ(zzz4190), h) → new_mkVBalBranch1(zzz31, Branch(zzz330, zzz331, Neg(Succ(zzz33200)), zzz333, zzz334), zzz3173, h)
new_mkVBalBranch1(zzz31, Branch(zzz330, zzz331, Neg(Succ(zzz33200)), zzz333, zzz334), Branch(zzz3170, zzz3171, zzz3172, zzz3173, zzz3174), h) → new_mkVBalBranch3MkVBalBranch241(zzz3170, zzz3171, zzz3172, zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat2(Succ(new_primPlusNat3(new_primPlusNat1(zzz33200), zzz33200)), zzz33200)), zzz33200))), h)
new_mkVBalBranch3MkVBalBranch242(zzz972, zzz973, zzz974, zzz975, zzz976, zzz977, zzz978, zzz979, zzz980, zzz981, zzz982, Zero, Succ(zzz9840), bc) → new_mkVBalBranch1(zzz982, Branch(zzz977, zzz978, Neg(Succ(zzz979)), zzz980, zzz981), zzz975, bc)
new_mkVBalBranch3MkVBalBranch241(zzz3170, zzz3171, Neg(Succ(zzz317200)), zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, Succ(zzz4190), h) → new_mkVBalBranch3MkVBalBranch242(zzz3170, zzz3171, zzz317200, zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, zzz317200, zzz4190, h)

The TRS R consists of the following rules:

new_primPlusNat1(Zero) → Zero
new_primPlusNat1(Succ(zzz62000)) → Succ(Succ(new_primPlusNat1(zzz62000)))
new_primPlusNat3(zzz90, Succ(zzz910)) → Succ(Succ(new_primPlusNat2(zzz90, zzz910)))
new_primPlusNat3(zzz90, Zero) → Succ(zzz90)
new_primPlusNat2(Succ(zzz900), Succ(zzz9100)) → Succ(Succ(new_primPlusNat2(zzz900, zzz9100)))
new_primPlusNat2(Succ(zzz900), Zero) → Succ(zzz900)
new_primPlusNat2(Zero, Succ(zzz9100)) → Succ(zzz9100)
new_primPlusNat2(Zero, Zero) → Zero

The set Q consists of the following terms:

new_primPlusNat2(Zero, Succ(x0))
new_primPlusNat3(x0, Succ(x1))
new_primPlusNat2(Succ(x0), Succ(x1))
new_primPlusNat3(x0, Zero)
new_primPlusNat1(Zero)
new_primPlusNat2(Zero, Zero)
new_primPlusNat1(Succ(x0))
new_primPlusNat2(Succ(x0), Zero)

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

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



↳ HASKELL
  ↳ LR
    ↳ HASKELL
      ↳ CR
        ↳ HASKELL
          ↳ IFR
            ↳ HASKELL
              ↳ BR
                ↳ HASKELL
                  ↳ COR
                    ↳ HASKELL
                      ↳ LetRed
                        ↳ HASKELL
                          ↳ NumRed
                            ↳ HASKELL
                              ↳ Narrow
                                ↳ AND
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                    ↳ DependencyGraphProof
                                      ↳ QDP
                                        ↳ Rewriting
                                          ↳ QDP
                                            ↳ Rewriting
                                              ↳ QDP
                                                ↳ Rewriting
                                                  ↳ QDP
                                                    ↳ Rewriting
                                                      ↳ QDP
                                                        ↳ Rewriting
                                                          ↳ QDP
                                                            ↳ Rewriting
                                                              ↳ QDP
                                                                ↳ Rewriting
                                                                  ↳ QDP
                                                                    ↳ Rewriting
                                                                      ↳ QDP
                                                                        ↳ Rewriting
                                                                          ↳ QDP
                                                                            ↳ Rewriting
                                                                              ↳ QDP
                                                                                ↳ UsableRulesProof
                                                                                  ↳ QDP
                                                                                    ↳ QReductionProof
                                                                                      ↳ QDP
                                                                                        ↳ Rewriting
                                                                                          ↳ QDP
                                                                                            ↳ Rewriting
                                                                                              ↳ QDP
                                                                                                ↳ Rewriting
                                                                                                  ↳ QDP
                                                                                                    ↳ Rewriting
                                                                                                      ↳ QDP
                                                                                                        ↳ Rewriting
                                                                                                          ↳ QDP
                                                                                                            ↳ Rewriting
                                                                                                              ↳ QDP
                                                                                                                ↳ Rewriting
                                                                                                                  ↳ QDP
                                                                                                                    ↳ Rewriting
                                                                                                                      ↳ QDP
                                                                                                                        ↳ Rewriting
                                                                                                                          ↳ QDP
                                                                                                                            ↳ Rewriting
                                                                                                                              ↳ QDP
                                                                                                                                ↳ UsableRulesProof
                                                                                                                                  ↳ QDP
                                                                                                                                    ↳ QReductionProof
                                                                                                                                      ↳ QDP
                                                                                                                                        ↳ Rewriting
                                                                                                                                          ↳ QDP
                                                                                                                                            ↳ Rewriting
                                                                                                                                              ↳ QDP
                                                                                                                                                ↳ Rewriting
                                                                                                                                                  ↳ QDP
                                                                                                                                                    ↳ DependencyGraphProof
                                                                                                                                                      ↳ QDP
                                                                                                                                                        ↳ Rewriting
                                                                                                                                                          ↳ QDP
                                                                                                                                                            ↳ Rewriting
                                                                                                                                                              ↳ QDP
                                                                                                                                                                ↳ DependencyGraphProof
                                                                                                                                                                  ↳ QDP
                                                                                                                                                                    ↳ Rewriting
                                                                                                                                                                      ↳ QDP
                                                                                                                                                                        ↳ Rewriting
                                                                                                                                                                          ↳ QDP
                                                                                                                                                                            ↳ Rewriting
                                                                                                                                                                              ↳ QDP
                                                                                                                                                                                ↳ Rewriting
                                                                                                                                                                                  ↳ QDP
                                                                                                                                                                                    ↳ Rewriting
                                                                                                                                                                                      ↳ QDP
                                                                                                                                                                                        ↳ Rewriting
                                                                                                                                                                                          ↳ QDP
                                                                                                                                                                                            ↳ Rewriting
                                                                                                                                                                                              ↳ QDP
                                                                                                                                                                                                ↳ DependencyGraphProof
                                                                                                                                                                                                  ↳ QDP
                                                                                                                                                                                                    ↳ Rewriting
                                                                                                                                                                                                      ↳ QDP
                                                                                                                                                                                                        ↳ DependencyGraphProof
                                                                                                                                                                                                          ↳ QDP
                                                                                                                                                                                                            ↳ Rewriting
                                                                                                                                                                                                              ↳ QDP
                                                                                                                                                                                                                ↳ Rewriting
                                                                                                                                                                                                                  ↳ 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_mkVBalBranch3MkVBalBranch236(zzz958, zzz959, zzz960, zzz961, zzz962, zzz963, zzz964, zzz965, zzz966, zzz967, zzz968, Zero, Succ(zzz9700), ba) → new_mkVBalBranch1(zzz968, Branch(zzz963, zzz964, Pos(Succ(zzz965)), zzz966, zzz967), zzz961, ba)
new_mkVBalBranch3MkVBalBranch125(zzz1337, zzz1338, zzz1339, zzz1340, zzz1341, zzz1342, zzz1343, zzz1344, zzz1345, zzz1346, zzz1347, Succ(zzz13480), Succ(zzz13490), bb) → new_mkVBalBranch3MkVBalBranch125(zzz1337, zzz1338, zzz1339, zzz1340, zzz1341, zzz1342, zzz1343, zzz1344, zzz1345, zzz1346, zzz1347, zzz13480, zzz13490, bb)
new_mkVBalBranch3MkVBalBranch123(zzz3170, zzz3171, zzz317200, zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, Succ(zzz5620), h) → new_mkVBalBranch1(zzz31, zzz334, Branch(zzz3170, zzz3171, Neg(Succ(zzz317200)), zzz3173, zzz3174), h)
new_mkVBalBranch3MkVBalBranch240(zzz958, zzz959, zzz960, zzz961, zzz962, zzz963, zzz964, zzz965, zzz966, zzz967, zzz968, ba) → new_mkVBalBranch3MkVBalBranch124(zzz958, zzz959, zzz960, zzz961, zzz962, zzz963, zzz964, zzz965, zzz966, zzz967, zzz968, Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat2(Succ(new_primPlusNat3(new_primPlusNat1(zzz960), zzz960)), zzz960)), zzz960))), ba)
new_mkVBalBranch3MkVBalBranch125(zzz1337, zzz1338, zzz1339, zzz1340, zzz1341, zzz1342, zzz1343, zzz1344, zzz1345, zzz1346, zzz1347, Zero, Succ(zzz13490), bb) → new_mkVBalBranch1(zzz1347, zzz1346, Branch(zzz1337, zzz1338, Pos(Succ(zzz1339)), zzz1340, zzz1341), bb)
new_mkVBalBranch3MkVBalBranch236(zzz958, zzz959, zzz960, zzz961, zzz962, zzz963, zzz964, zzz965, zzz966, zzz967, zzz968, Succ(zzz9690), Zero, ba) → new_mkVBalBranch3MkVBalBranch124(zzz958, zzz959, zzz960, zzz961, zzz962, zzz963, zzz964, zzz965, zzz966, zzz967, zzz968, Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat2(Succ(new_primPlusNat3(new_primPlusNat1(zzz960), zzz960)), zzz960)), zzz960))), ba)
new_mkVBalBranch3MkVBalBranch235(zzz3170, zzz3171, Pos(Succ(zzz317200)), zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, Succ(zzz4170), h) → new_mkVBalBranch3MkVBalBranch236(zzz3170, zzz3171, zzz317200, zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, zzz4170, zzz317200, h)
new_mkVBalBranch3MkVBalBranch126(zzz3170, zzz3171, zzz317200, zzz3173, zzz3174, zzz330, zzz331, zzz333, zzz334, zzz31, Succ(zzz5350), h) → new_mkVBalBranch1(zzz31, zzz334, Branch(zzz3170, zzz3171, Neg(Succ(zzz317200)), zzz3173, zzz3174), h)
new_mkVBalBranch1(zzz31, Branch(zzz330, zzz331, Pos(Succ(zzz33200)), zzz333, zzz334), Branch(zzz3170, zzz3171, zzz3172, zzz3173, zzz3174), h) → new_mkVBalBranch3MkVBalBranch235(zzz3170, zzz3171, zzz3172, zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat2(Succ(new_primPlusNat3(new_primPlusNat1(zzz33200), zzz33200)), zzz33200)), zzz33200))), h)
new_mkVBalBranch3MkVBalBranch124(zzz958, zzz959, zzz960, zzz961, zzz962, zzz963, zzz964, zzz965, zzz966, zzz967, zzz968, Succ(zzz10180), ba) → new_mkVBalBranch3MkVBalBranch125(zzz958, zzz959, zzz960, zzz961, zzz962, zzz963, zzz964, zzz965, zzz966, zzz967, zzz968, Succ(zzz10180), Succ(zzz965), ba)
new_mkVBalBranch3MkVBalBranch236(zzz958, zzz959, zzz960, zzz961, zzz962, zzz963, zzz964, zzz965, zzz966, zzz967, zzz968, Succ(zzz9690), Succ(zzz9700), ba) → new_mkVBalBranch3MkVBalBranch236(zzz958, zzz959, zzz960, zzz961, zzz962, zzz963, zzz964, zzz965, zzz966, zzz967, zzz968, zzz9690, zzz9700, ba)
new_mkVBalBranch1(zzz31, Branch(zzz330, zzz331, Pos(Zero), zzz333, zzz334), Branch(zzz3170, zzz3171, Neg(Succ(zzz317200)), zzz3173, zzz3174), h) → new_mkVBalBranch3MkVBalBranch126(zzz3170, zzz3171, zzz317200, zzz3173, zzz3174, zzz330, zzz331, zzz333, zzz334, zzz31, Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat2(Succ(new_primPlusNat3(new_primPlusNat1(zzz317200), zzz317200)), zzz317200)), zzz317200))), h)
new_mkVBalBranch3MkVBalBranch235(zzz3170, zzz3171, Neg(Succ(zzz317200)), zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, Succ(zzz4170), h) → new_mkVBalBranch3MkVBalBranch123(zzz3170, zzz3171, zzz317200, zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat2(Succ(new_primPlusNat3(new_primPlusNat1(zzz317200), zzz317200)), zzz317200)), zzz317200))), h)
new_mkVBalBranch1(zzz31, Branch(zzz330, zzz331, Pos(Zero), zzz333, zzz334), Branch(zzz3170, zzz3171, Pos(Succ(zzz317200)), zzz3173, zzz3174), h) → new_mkVBalBranch1(zzz31, Branch(zzz330, zzz331, Pos(Zero), zzz333, zzz334), zzz3173, h)
new_mkVBalBranch3MkVBalBranch237(zzz3170, zzz3171, zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, h) → new_mkVBalBranch1(zzz31, zzz334, Branch(zzz3170, zzz3171, Pos(Zero), zzz3173, zzz3174), h)
new_mkVBalBranch3MkVBalBranch235(zzz3170, zzz3171, Neg(Zero), zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, Succ(zzz4170), h) → new_mkVBalBranch1(zzz31, zzz334, Branch(zzz3170, zzz3171, Neg(Zero), zzz3173, zzz3174), h)
new_mkVBalBranch3MkVBalBranch235(zzz3170, zzz3171, Pos(Zero), zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, Succ(zzz4170), h) → new_mkVBalBranch3MkVBalBranch237(zzz3170, zzz3171, zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, h)
new_mkVBalBranch3MkVBalBranch236(zzz958, zzz959, zzz960, zzz961, zzz962, zzz963, zzz964, zzz965, zzz966, zzz967, zzz968, Zero, Zero, ba) → new_mkVBalBranch3MkVBalBranch240(zzz958, zzz959, zzz960, zzz961, zzz962, zzz963, zzz964, zzz965, zzz966, zzz967, zzz968, ba)

The TRS R consists of the following rules:

new_primPlusNat1(Zero) → Zero
new_primPlusNat1(Succ(zzz62000)) → Succ(Succ(new_primPlusNat1(zzz62000)))
new_primPlusNat3(zzz90, Succ(zzz910)) → Succ(Succ(new_primPlusNat2(zzz90, zzz910)))
new_primPlusNat3(zzz90, Zero) → Succ(zzz90)
new_primPlusNat2(Succ(zzz900), Succ(zzz9100)) → Succ(Succ(new_primPlusNat2(zzz900, zzz9100)))
new_primPlusNat2(Succ(zzz900), Zero) → Succ(zzz900)
new_primPlusNat2(Zero, Succ(zzz9100)) → Succ(zzz9100)
new_primPlusNat2(Zero, Zero) → Zero

The set Q consists of the following terms:

new_primPlusNat2(Zero, Succ(x0))
new_primPlusNat3(x0, Succ(x1))
new_primPlusNat2(Succ(x0), Succ(x1))
new_primPlusNat3(x0, Zero)
new_primPlusNat1(Zero)
new_primPlusNat2(Zero, Zero)
new_primPlusNat1(Succ(x0))
new_primPlusNat2(Succ(x0), Zero)

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


The following pairs can be oriented strictly and are deleted.


new_mkVBalBranch3MkVBalBranch126(zzz3170, zzz3171, zzz317200, zzz3173, zzz3174, zzz330, zzz331, zzz333, zzz334, zzz31, Succ(zzz5350), h) → new_mkVBalBranch1(zzz31, zzz334, Branch(zzz3170, zzz3171, Neg(Succ(zzz317200)), zzz3173, zzz3174), h)
The remaining pairs can at least be oriented weakly.

new_mkVBalBranch3MkVBalBranch236(zzz958, zzz959, zzz960, zzz961, zzz962, zzz963, zzz964, zzz965, zzz966, zzz967, zzz968, Zero, Succ(zzz9700), ba) → new_mkVBalBranch1(zzz968, Branch(zzz963, zzz964, Pos(Succ(zzz965)), zzz966, zzz967), zzz961, ba)
new_mkVBalBranch3MkVBalBranch125(zzz1337, zzz1338, zzz1339, zzz1340, zzz1341, zzz1342, zzz1343, zzz1344, zzz1345, zzz1346, zzz1347, Succ(zzz13480), Succ(zzz13490), bb) → new_mkVBalBranch3MkVBalBranch125(zzz1337, zzz1338, zzz1339, zzz1340, zzz1341, zzz1342, zzz1343, zzz1344, zzz1345, zzz1346, zzz1347, zzz13480, zzz13490, bb)
new_mkVBalBranch3MkVBalBranch123(zzz3170, zzz3171, zzz317200, zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, Succ(zzz5620), h) → new_mkVBalBranch1(zzz31, zzz334, Branch(zzz3170, zzz3171, Neg(Succ(zzz317200)), zzz3173, zzz3174), h)
new_mkVBalBranch3MkVBalBranch240(zzz958, zzz959, zzz960, zzz961, zzz962, zzz963, zzz964, zzz965, zzz966, zzz967, zzz968, ba) → new_mkVBalBranch3MkVBalBranch124(zzz958, zzz959, zzz960, zzz961, zzz962, zzz963, zzz964, zzz965, zzz966, zzz967, zzz968, Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat2(Succ(new_primPlusNat3(new_primPlusNat1(zzz960), zzz960)), zzz960)), zzz960))), ba)
new_mkVBalBranch3MkVBalBranch125(zzz1337, zzz1338, zzz1339, zzz1340, zzz1341, zzz1342, zzz1343, zzz1344, zzz1345, zzz1346, zzz1347, Zero, Succ(zzz13490), bb) → new_mkVBalBranch1(zzz1347, zzz1346, Branch(zzz1337, zzz1338, Pos(Succ(zzz1339)), zzz1340, zzz1341), bb)
new_mkVBalBranch3MkVBalBranch236(zzz958, zzz959, zzz960, zzz961, zzz962, zzz963, zzz964, zzz965, zzz966, zzz967, zzz968, Succ(zzz9690), Zero, ba) → new_mkVBalBranch3MkVBalBranch124(zzz958, zzz959, zzz960, zzz961, zzz962, zzz963, zzz964, zzz965, zzz966, zzz967, zzz968, Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat2(Succ(new_primPlusNat3(new_primPlusNat1(zzz960), zzz960)), zzz960)), zzz960))), ba)
new_mkVBalBranch3MkVBalBranch235(zzz3170, zzz3171, Pos(Succ(zzz317200)), zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, Succ(zzz4170), h) → new_mkVBalBranch3MkVBalBranch236(zzz3170, zzz3171, zzz317200, zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, zzz4170, zzz317200, h)
new_mkVBalBranch1(zzz31, Branch(zzz330, zzz331, Pos(Succ(zzz33200)), zzz333, zzz334), Branch(zzz3170, zzz3171, zzz3172, zzz3173, zzz3174), h) → new_mkVBalBranch3MkVBalBranch235(zzz3170, zzz3171, zzz3172, zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat2(Succ(new_primPlusNat3(new_primPlusNat1(zzz33200), zzz33200)), zzz33200)), zzz33200))), h)
new_mkVBalBranch3MkVBalBranch124(zzz958, zzz959, zzz960, zzz961, zzz962, zzz963, zzz964, zzz965, zzz966, zzz967, zzz968, Succ(zzz10180), ba) → new_mkVBalBranch3MkVBalBranch125(zzz958, zzz959, zzz960, zzz961, zzz962, zzz963, zzz964, zzz965, zzz966, zzz967, zzz968, Succ(zzz10180), Succ(zzz965), ba)
new_mkVBalBranch3MkVBalBranch236(zzz958, zzz959, zzz960, zzz961, zzz962, zzz963, zzz964, zzz965, zzz966, zzz967, zzz968, Succ(zzz9690), Succ(zzz9700), ba) → new_mkVBalBranch3MkVBalBranch236(zzz958, zzz959, zzz960, zzz961, zzz962, zzz963, zzz964, zzz965, zzz966, zzz967, zzz968, zzz9690, zzz9700, ba)
new_mkVBalBranch1(zzz31, Branch(zzz330, zzz331, Pos(Zero), zzz333, zzz334), Branch(zzz3170, zzz3171, Neg(Succ(zzz317200)), zzz3173, zzz3174), h) → new_mkVBalBranch3MkVBalBranch126(zzz3170, zzz3171, zzz317200, zzz3173, zzz3174, zzz330, zzz331, zzz333, zzz334, zzz31, Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat2(Succ(new_primPlusNat3(new_primPlusNat1(zzz317200), zzz317200)), zzz317200)), zzz317200))), h)
new_mkVBalBranch3MkVBalBranch235(zzz3170, zzz3171, Neg(Succ(zzz317200)), zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, Succ(zzz4170), h) → new_mkVBalBranch3MkVBalBranch123(zzz3170, zzz3171, zzz317200, zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat2(Succ(new_primPlusNat3(new_primPlusNat1(zzz317200), zzz317200)), zzz317200)), zzz317200))), h)
new_mkVBalBranch1(zzz31, Branch(zzz330, zzz331, Pos(Zero), zzz333, zzz334), Branch(zzz3170, zzz3171, Pos(Succ(zzz317200)), zzz3173, zzz3174), h) → new_mkVBalBranch1(zzz31, Branch(zzz330, zzz331, Pos(Zero), zzz333, zzz334), zzz3173, h)
new_mkVBalBranch3MkVBalBranch237(zzz3170, zzz3171, zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, h) → new_mkVBalBranch1(zzz31, zzz334, Branch(zzz3170, zzz3171, Pos(Zero), zzz3173, zzz3174), h)
new_mkVBalBranch3MkVBalBranch235(zzz3170, zzz3171, Neg(Zero), zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, Succ(zzz4170), h) → new_mkVBalBranch1(zzz31, zzz334, Branch(zzz3170, zzz3171, Neg(Zero), zzz3173, zzz3174), h)
new_mkVBalBranch3MkVBalBranch235(zzz3170, zzz3171, Pos(Zero), zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, Succ(zzz4170), h) → new_mkVBalBranch3MkVBalBranch237(zzz3170, zzz3171, zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, h)
new_mkVBalBranch3MkVBalBranch236(zzz958, zzz959, zzz960, zzz961, zzz962, zzz963, zzz964, zzz965, zzz966, zzz967, zzz968, Zero, Zero, ba) → new_mkVBalBranch3MkVBalBranch240(zzz958, zzz959, zzz960, zzz961, zzz962, zzz963, zzz964, zzz965, zzz966, zzz967, zzz968, ba)
Used ordering: Polynomial interpretation [25]:

POL(Branch(x1, x2, x3, x4, x5)) = x1 + x2 + x3 + x4 + x5   
POL(Neg(x1)) = 0   
POL(Pos(x1)) = x1   
POL(Succ(x1)) = 0   
POL(Zero) = 1   
POL(new_mkVBalBranch1(x1, x2, x3, x4)) = x2   
POL(new_mkVBalBranch3MkVBalBranch123(x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12, x13)) = x10 + x6 + x7 + x9   
POL(new_mkVBalBranch3MkVBalBranch124(x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12, x13)) = x10 + x6 + x7 + x9   
POL(new_mkVBalBranch3MkVBalBranch125(x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12, x13, x14)) = x10 + x7 + x9   
POL(new_mkVBalBranch3MkVBalBranch126(x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12)) = 1 + x6 + x9   
POL(new_mkVBalBranch3MkVBalBranch235(x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12, x13)) = x10 + x6 + x7 + x9   
POL(new_mkVBalBranch3MkVBalBranch236(x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12, x13, x14)) = x10 + x6 + x7 + x9   
POL(new_mkVBalBranch3MkVBalBranch237(x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11)) = x5 + x6 + x8 + x9   
POL(new_mkVBalBranch3MkVBalBranch240(x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12)) = x10 + x6 + x7 + x9   
POL(new_primPlusNat1(x1)) = 0   
POL(new_primPlusNat2(x1, x2)) = x2   
POL(new_primPlusNat3(x1, x2)) = x2   

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
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                    ↳ DependencyGraphProof
                                      ↳ QDP
                                        ↳ Rewriting
                                          ↳ QDP
                                            ↳ Rewriting
                                              ↳ QDP
                                                ↳ Rewriting
                                                  ↳ QDP
                                                    ↳ Rewriting
                                                      ↳ QDP
                                                        ↳ Rewriting
                                                          ↳ QDP
                                                            ↳ Rewriting
                                                              ↳ QDP
                                                                ↳ Rewriting
                                                                  ↳ QDP
                                                                    ↳ Rewriting
                                                                      ↳ QDP
                                                                        ↳ Rewriting
                                                                          ↳ QDP
                                                                            ↳ Rewriting
                                                                              ↳ QDP
                                                                                ↳ UsableRulesProof
                                                                                  ↳ QDP
                                                                                    ↳ QReductionProof
                                                                                      ↳ QDP
                                                                                        ↳ Rewriting
                                                                                          ↳ QDP
                                                                                            ↳ Rewriting
                                                                                              ↳ QDP
                                                                                                ↳ Rewriting
                                                                                                  ↳ QDP
                                                                                                    ↳ Rewriting
                                                                                                      ↳ QDP
                                                                                                        ↳ Rewriting
                                                                                                          ↳ QDP
                                                                                                            ↳ Rewriting
                                                                                                              ↳ QDP
                                                                                                                ↳ Rewriting
                                                                                                                  ↳ QDP
                                                                                                                    ↳ Rewriting
                                                                                                                      ↳ QDP
                                                                                                                        ↳ Rewriting
                                                                                                                          ↳ QDP
                                                                                                                            ↳ Rewriting
                                                                                                                              ↳ QDP
                                                                                                                                ↳ UsableRulesProof
                                                                                                                                  ↳ QDP
                                                                                                                                    ↳ QReductionProof
                                                                                                                                      ↳ QDP
                                                                                                                                        ↳ Rewriting
                                                                                                                                          ↳ QDP
                                                                                                                                            ↳ Rewriting
                                                                                                                                              ↳ QDP
                                                                                                                                                ↳ Rewriting
                                                                                                                                                  ↳ QDP
                                                                                                                                                    ↳ DependencyGraphProof
                                                                                                                                                      ↳ QDP
                                                                                                                                                        ↳ Rewriting
                                                                                                                                                          ↳ QDP
                                                                                                                                                            ↳ Rewriting
                                                                                                                                                              ↳ QDP
                                                                                                                                                                ↳ DependencyGraphProof
                                                                                                                                                                  ↳ QDP
                                                                                                                                                                    ↳ Rewriting
                                                                                                                                                                      ↳ QDP
                                                                                                                                                                        ↳ Rewriting
                                                                                                                                                                          ↳ QDP
                                                                                                                                                                            ↳ Rewriting
                                                                                                                                                                              ↳ QDP
                                                                                                                                                                                ↳ Rewriting
                                                                                                                                                                                  ↳ QDP
                                                                                                                                                                                    ↳ Rewriting
                                                                                                                                                                                      ↳ QDP
                                                                                                                                                                                        ↳ Rewriting
                                                                                                                                                                                          ↳ QDP
                                                                                                                                                                                            ↳ Rewriting
                                                                                                                                                                                              ↳ QDP
                                                                                                                                                                                                ↳ DependencyGraphProof
                                                                                                                                                                                                  ↳ QDP
                                                                                                                                                                                                    ↳ Rewriting
                                                                                                                                                                                                      ↳ QDP
                                                                                                                                                                                                        ↳ DependencyGraphProof
                                                                                                                                                                                                          ↳ QDP
                                                                                                                                                                                                            ↳ Rewriting
                                                                                                                                                                                                              ↳ QDP
                                                                                                                                                                                                                ↳ Rewriting
                                                                                                                                                                                                                  ↳ 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_mkVBalBranch3MkVBalBranch236(zzz958, zzz959, zzz960, zzz961, zzz962, zzz963, zzz964, zzz965, zzz966, zzz967, zzz968, Zero, Succ(zzz9700), ba) → new_mkVBalBranch1(zzz968, Branch(zzz963, zzz964, Pos(Succ(zzz965)), zzz966, zzz967), zzz961, ba)
new_mkVBalBranch3MkVBalBranch125(zzz1337, zzz1338, zzz1339, zzz1340, zzz1341, zzz1342, zzz1343, zzz1344, zzz1345, zzz1346, zzz1347, Succ(zzz13480), Succ(zzz13490), bb) → new_mkVBalBranch3MkVBalBranch125(zzz1337, zzz1338, zzz1339, zzz1340, zzz1341, zzz1342, zzz1343, zzz1344, zzz1345, zzz1346, zzz1347, zzz13480, zzz13490, bb)
new_mkVBalBranch3MkVBalBranch123(zzz3170, zzz3171, zzz317200, zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, Succ(zzz5620), h) → new_mkVBalBranch1(zzz31, zzz334, Branch(zzz3170, zzz3171, Neg(Succ(zzz317200)), zzz3173, zzz3174), h)
new_mkVBalBranch3MkVBalBranch240(zzz958, zzz959, zzz960, zzz961, zzz962, zzz963, zzz964, zzz965, zzz966, zzz967, zzz968, ba) → new_mkVBalBranch3MkVBalBranch124(zzz958, zzz959, zzz960, zzz961, zzz962, zzz963, zzz964, zzz965, zzz966, zzz967, zzz968, Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat2(Succ(new_primPlusNat3(new_primPlusNat1(zzz960), zzz960)), zzz960)), zzz960))), ba)
new_mkVBalBranch3MkVBalBranch125(zzz1337, zzz1338, zzz1339, zzz1340, zzz1341, zzz1342, zzz1343, zzz1344, zzz1345, zzz1346, zzz1347, Zero, Succ(zzz13490), bb) → new_mkVBalBranch1(zzz1347, zzz1346, Branch(zzz1337, zzz1338, Pos(Succ(zzz1339)), zzz1340, zzz1341), bb)
new_mkVBalBranch3MkVBalBranch236(zzz958, zzz959, zzz960, zzz961, zzz962, zzz963, zzz964, zzz965, zzz966, zzz967, zzz968, Succ(zzz9690), Zero, ba) → new_mkVBalBranch3MkVBalBranch124(zzz958, zzz959, zzz960, zzz961, zzz962, zzz963, zzz964, zzz965, zzz966, zzz967, zzz968, Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat2(Succ(new_primPlusNat3(new_primPlusNat1(zzz960), zzz960)), zzz960)), zzz960))), ba)
new_mkVBalBranch3MkVBalBranch235(zzz3170, zzz3171, Pos(Succ(zzz317200)), zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, Succ(zzz4170), h) → new_mkVBalBranch3MkVBalBranch236(zzz3170, zzz3171, zzz317200, zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, zzz4170, zzz317200, h)
new_mkVBalBranch1(zzz31, Branch(zzz330, zzz331, Pos(Succ(zzz33200)), zzz333, zzz334), Branch(zzz3170, zzz3171, zzz3172, zzz3173, zzz3174), h) → new_mkVBalBranch3MkVBalBranch235(zzz3170, zzz3171, zzz3172, zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat2(Succ(new_primPlusNat3(new_primPlusNat1(zzz33200), zzz33200)), zzz33200)), zzz33200))), h)
new_mkVBalBranch3MkVBalBranch124(zzz958, zzz959, zzz960, zzz961, zzz962, zzz963, zzz964, zzz965, zzz966, zzz967, zzz968, Succ(zzz10180), ba) → new_mkVBalBranch3MkVBalBranch125(zzz958, zzz959, zzz960, zzz961, zzz962, zzz963, zzz964, zzz965, zzz966, zzz967, zzz968, Succ(zzz10180), Succ(zzz965), ba)
new_mkVBalBranch3MkVBalBranch236(zzz958, zzz959, zzz960, zzz961, zzz962, zzz963, zzz964, zzz965, zzz966, zzz967, zzz968, Succ(zzz9690), Succ(zzz9700), ba) → new_mkVBalBranch3MkVBalBranch236(zzz958, zzz959, zzz960, zzz961, zzz962, zzz963, zzz964, zzz965, zzz966, zzz967, zzz968, zzz9690, zzz9700, ba)
new_mkVBalBranch1(zzz31, Branch(zzz330, zzz331, Pos(Zero), zzz333, zzz334), Branch(zzz3170, zzz3171, Neg(Succ(zzz317200)), zzz3173, zzz3174), h) → new_mkVBalBranch3MkVBalBranch126(zzz3170, zzz3171, zzz317200, zzz3173, zzz3174, zzz330, zzz331, zzz333, zzz334, zzz31, Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat2(Succ(new_primPlusNat3(new_primPlusNat1(zzz317200), zzz317200)), zzz317200)), zzz317200))), h)
new_mkVBalBranch3MkVBalBranch235(zzz3170, zzz3171, Neg(Succ(zzz317200)), zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, Succ(zzz4170), h) → new_mkVBalBranch3MkVBalBranch123(zzz3170, zzz3171, zzz317200, zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat2(Succ(new_primPlusNat3(new_primPlusNat1(zzz317200), zzz317200)), zzz317200)), zzz317200))), h)
new_mkVBalBranch1(zzz31, Branch(zzz330, zzz331, Pos(Zero), zzz333, zzz334), Branch(zzz3170, zzz3171, Pos(Succ(zzz317200)), zzz3173, zzz3174), h) → new_mkVBalBranch1(zzz31, Branch(zzz330, zzz331, Pos(Zero), zzz333, zzz334), zzz3173, h)
new_mkVBalBranch3MkVBalBranch237(zzz3170, zzz3171, zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, h) → new_mkVBalBranch1(zzz31, zzz334, Branch(zzz3170, zzz3171, Pos(Zero), zzz3173, zzz3174), h)
new_mkVBalBranch3MkVBalBranch235(zzz3170, zzz3171, Neg(Zero), zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, Succ(zzz4170), h) → new_mkVBalBranch1(zzz31, zzz334, Branch(zzz3170, zzz3171, Neg(Zero), zzz3173, zzz3174), h)
new_mkVBalBranch3MkVBalBranch236(zzz958, zzz959, zzz960, zzz961, zzz962, zzz963, zzz964, zzz965, zzz966, zzz967, zzz968, Zero, Zero, ba) → new_mkVBalBranch3MkVBalBranch240(zzz958, zzz959, zzz960, zzz961, zzz962, zzz963, zzz964, zzz965, zzz966, zzz967, zzz968, ba)
new_mkVBalBranch3MkVBalBranch235(zzz3170, zzz3171, Pos(Zero), zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, Succ(zzz4170), h) → new_mkVBalBranch3MkVBalBranch237(zzz3170, zzz3171, zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, h)

The TRS R consists of the following rules:

new_primPlusNat1(Zero) → Zero
new_primPlusNat1(Succ(zzz62000)) → Succ(Succ(new_primPlusNat1(zzz62000)))
new_primPlusNat3(zzz90, Succ(zzz910)) → Succ(Succ(new_primPlusNat2(zzz90, zzz910)))
new_primPlusNat3(zzz90, Zero) → Succ(zzz90)
new_primPlusNat2(Succ(zzz900), Succ(zzz9100)) → Succ(Succ(new_primPlusNat2(zzz900, zzz9100)))
new_primPlusNat2(Succ(zzz900), Zero) → Succ(zzz900)
new_primPlusNat2(Zero, Succ(zzz9100)) → Succ(zzz9100)
new_primPlusNat2(Zero, Zero) → Zero

The set Q consists of the following terms:

new_primPlusNat2(Zero, Succ(x0))
new_primPlusNat3(x0, Succ(x1))
new_primPlusNat2(Succ(x0), Succ(x1))
new_primPlusNat3(x0, Zero)
new_primPlusNat1(Zero)
new_primPlusNat2(Zero, Zero)
new_primPlusNat1(Succ(x0))
new_primPlusNat2(Succ(x0), Zero)

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

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

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

new_mkVBalBranch1(zzz31, Branch(zzz330, zzz331, Pos(Zero), zzz333, zzz334), Branch(zzz3170, zzz3171, Pos(Succ(zzz317200)), zzz3173, zzz3174), h) → new_mkVBalBranch1(zzz31, Branch(zzz330, zzz331, Pos(Zero), zzz333, zzz334), zzz3173, h)

The TRS R consists of the following rules:

new_primPlusNat1(Zero) → Zero
new_primPlusNat1(Succ(zzz62000)) → Succ(Succ(new_primPlusNat1(zzz62000)))
new_primPlusNat3(zzz90, Succ(zzz910)) → Succ(Succ(new_primPlusNat2(zzz90, zzz910)))
new_primPlusNat3(zzz90, Zero) → Succ(zzz90)
new_primPlusNat2(Succ(zzz900), Succ(zzz9100)) → Succ(Succ(new_primPlusNat2(zzz900, zzz9100)))
new_primPlusNat2(Succ(zzz900), Zero) → Succ(zzz900)
new_primPlusNat2(Zero, Succ(zzz9100)) → Succ(zzz9100)
new_primPlusNat2(Zero, Zero) → Zero

The set Q consists of the following terms:

new_primPlusNat2(Zero, Succ(x0))
new_primPlusNat3(x0, Succ(x1))
new_primPlusNat2(Succ(x0), Succ(x1))
new_primPlusNat3(x0, Zero)
new_primPlusNat1(Zero)
new_primPlusNat2(Zero, Zero)
new_primPlusNat1(Succ(x0))
new_primPlusNat2(Succ(x0), Zero)

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

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

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

new_mkVBalBranch1(zzz31, Branch(zzz330, zzz331, Pos(Zero), zzz333, zzz334), Branch(zzz3170, zzz3171, Pos(Succ(zzz317200)), zzz3173, zzz3174), h) → new_mkVBalBranch1(zzz31, Branch(zzz330, zzz331, Pos(Zero), zzz333, zzz334), zzz3173, h)

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

new_primPlusNat2(Zero, Succ(x0))
new_primPlusNat3(x0, Succ(x1))
new_primPlusNat2(Succ(x0), Succ(x1))
new_primPlusNat3(x0, Zero)
new_primPlusNat1(Zero)
new_primPlusNat2(Zero, Zero)
new_primPlusNat1(Succ(x0))
new_primPlusNat2(Succ(x0), Zero)

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

new_primPlusNat2(Zero, Succ(x0))
new_primPlusNat3(x0, Succ(x1))
new_primPlusNat2(Succ(x0), Succ(x1))
new_primPlusNat3(x0, Zero)
new_primPlusNat1(Zero)
new_primPlusNat2(Zero, Zero)
new_primPlusNat1(Succ(x0))
new_primPlusNat2(Succ(x0), 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
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                    ↳ DependencyGraphProof
                                      ↳ QDP
                                        ↳ Rewriting
                                          ↳ QDP
                                            ↳ Rewriting
                                              ↳ QDP
                                                ↳ Rewriting
                                                  ↳ QDP
                                                    ↳ Rewriting
                                                      ↳ QDP
                                                        ↳ Rewriting
                                                          ↳ QDP
                                                            ↳ Rewriting
                                                              ↳ QDP
                                                                ↳ Rewriting
                                                                  ↳ QDP
                                                                    ↳ Rewriting
                                                                      ↳ QDP
                                                                        ↳ Rewriting
                                                                          ↳ QDP
                                                                            ↳ Rewriting
                                                                              ↳ QDP
                                                                                ↳ UsableRulesProof
                                                                                  ↳ QDP
                                                                                    ↳ QReductionProof
                                                                                      ↳ QDP
                                                                                        ↳ Rewriting
                                                                                          ↳ QDP
                                                                                            ↳ Rewriting
                                                                                              ↳ QDP
                                                                                                ↳ Rewriting
                                                                                                  ↳ QDP
                                                                                                    ↳ Rewriting
                                                                                                      ↳ QDP
                                                                                                        ↳ Rewriting
                                                                                                          ↳ QDP
                                                                                                            ↳ Rewriting
                                                                                                              ↳ QDP
                                                                                                                ↳ Rewriting
                                                                                                                  ↳ QDP
                                                                                                                    ↳ Rewriting
                                                                                                                      ↳ QDP
                                                                                                                        ↳ Rewriting
                                                                                                                          ↳ QDP
                                                                                                                            ↳ Rewriting
                                                                                                                              ↳ QDP
                                                                                                                                ↳ UsableRulesProof
                                                                                                                                  ↳ QDP
                                                                                                                                    ↳ QReductionProof
                                                                                                                                      ↳ QDP
                                                                                                                                        ↳ Rewriting
                                                                                                                                          ↳ QDP
                                                                                                                                            ↳ Rewriting
                                                                                                                                              ↳ QDP
                                                                                                                                                ↳ Rewriting
                                                                                                                                                  ↳ QDP
                                                                                                                                                    ↳ DependencyGraphProof
                                                                                                                                                      ↳ QDP
                                                                                                                                                        ↳ Rewriting
                                                                                                                                                          ↳ QDP
                                                                                                                                                            ↳ Rewriting
                                                                                                                                                              ↳ QDP
                                                                                                                                                                ↳ DependencyGraphProof
                                                                                                                                                                  ↳ QDP
                                                                                                                                                                    ↳ Rewriting
                                                                                                                                                                      ↳ QDP
                                                                                                                                                                        ↳ Rewriting
                                                                                                                                                                          ↳ QDP
                                                                                                                                                                            ↳ Rewriting
                                                                                                                                                                              ↳ QDP
                                                                                                                                                                                ↳ Rewriting
                                                                                                                                                                                  ↳ QDP
                                                                                                                                                                                    ↳ Rewriting
                                                                                                                                                                                      ↳ QDP
                                                                                                                                                                                        ↳ Rewriting
                                                                                                                                                                                          ↳ QDP
                                                                                                                                                                                            ↳ Rewriting
                                                                                                                                                                                              ↳ QDP
                                                                                                                                                                                                ↳ DependencyGraphProof
                                                                                                                                                                                                  ↳ QDP
                                                                                                                                                                                                    ↳ Rewriting
                                                                                                                                                                                                      ↳ QDP
                                                                                                                                                                                                        ↳ DependencyGraphProof
                                                                                                                                                                                                          ↳ QDP
                                                                                                                                                                                                            ↳ Rewriting
                                                                                                                                                                                                              ↳ QDP
                                                                                                                                                                                                                ↳ Rewriting
                                                                                                                                                                                                                  ↳ QDP
                                                                                                                                                                                                                    ↳ QDPOrderProof
                                                                                                                                                                                                                      ↳ QDP
                                                                                                                                                                                                                        ↳ DependencyGraphProof
                                                                                                                                                                                                                          ↳ AND
                                                                                                                                                                                                                            ↳ QDP
                                                                                                                                                                                                                            ↳ QDP
                                                                                                                                                                                                                            ↳ QDP
                                                                                                                                                                                                                              ↳ QDPOrderProof
                                                                                                                                                                                                                                ↳ QDP
                                                                                                                                                                                                                                  ↳ DependencyGraphProof
                                                                                                                                                                                                                                    ↳ AND
                                                                                                                                                                                                                                      ↳ QDP
                                                                                                                                                                                                                                        ↳ UsableRulesProof
                                                                                                                                                                                                                                          ↳ QDP
                                                                                                                                                                                                                                            ↳ QReductionProof
                                                                                                                                                                                                                                              ↳ QDP
                                                                                                                                                                                                                                                ↳ QDPSizeChangeProof
                                                                                                                                                                                                                                      ↳ QDP
                                                                                                                                                                                                                            ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP

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

new_mkVBalBranch1(zzz31, Branch(zzz330, zzz331, Pos(Zero), zzz333, zzz334), Branch(zzz3170, zzz3171, Pos(Succ(zzz317200)), zzz3173, zzz3174), h) → new_mkVBalBranch1(zzz31, Branch(zzz330, zzz331, Pos(Zero), zzz333, zzz334), zzz3173, 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
                                  ↳ QDP
                                  ↳ QDP
                                    ↳ DependencyGraphProof
                                      ↳ QDP
                                        ↳ Rewriting
                                          ↳ QDP
                                            ↳ Rewriting
                                              ↳ QDP
                                                ↳ Rewriting
                                                  ↳ QDP
                                                    ↳ Rewriting
                                                      ↳ QDP
                                                        ↳ Rewriting
                                                          ↳ QDP
                                                            ↳ Rewriting
                                                              ↳ QDP
                                                                ↳ Rewriting
                                                                  ↳ QDP
                                                                    ↳ Rewriting
                                                                      ↳ QDP
                                                                        ↳ Rewriting
                                                                          ↳ QDP
                                                                            ↳ Rewriting
                                                                              ↳ QDP
                                                                                ↳ UsableRulesProof
                                                                                  ↳ QDP
                                                                                    ↳ QReductionProof
                                                                                      ↳ QDP
                                                                                        ↳ Rewriting
                                                                                          ↳ QDP
                                                                                            ↳ Rewriting
                                                                                              ↳ QDP
                                                                                                ↳ Rewriting
                                                                                                  ↳ QDP
                                                                                                    ↳ Rewriting
                                                                                                      ↳ QDP
                                                                                                        ↳ Rewriting
                                                                                                          ↳ QDP
                                                                                                            ↳ Rewriting
                                                                                                              ↳ QDP
                                                                                                                ↳ Rewriting
                                                                                                                  ↳ QDP
                                                                                                                    ↳ Rewriting
                                                                                                                      ↳ QDP
                                                                                                                        ↳ Rewriting
                                                                                                                          ↳ QDP
                                                                                                                            ↳ Rewriting
                                                                                                                              ↳ QDP
                                                                                                                                ↳ UsableRulesProof
                                                                                                                                  ↳ QDP
                                                                                                                                    ↳ QReductionProof
                                                                                                                                      ↳ QDP
                                                                                                                                        ↳ Rewriting
                                                                                                                                          ↳ QDP
                                                                                                                                            ↳ Rewriting
                                                                                                                                              ↳ QDP
                                                                                                                                                ↳ Rewriting
                                                                                                                                                  ↳ QDP
                                                                                                                                                    ↳ DependencyGraphProof
                                                                                                                                                      ↳ QDP
                                                                                                                                                        ↳ Rewriting
                                                                                                                                                          ↳ QDP
                                                                                                                                                            ↳ Rewriting
                                                                                                                                                              ↳ QDP
                                                                                                                                                                ↳ DependencyGraphProof
                                                                                                                                                                  ↳ QDP
                                                                                                                                                                    ↳ Rewriting
                                                                                                                                                                      ↳ QDP
                                                                                                                                                                        ↳ Rewriting
                                                                                                                                                                          ↳ QDP
                                                                                                                                                                            ↳ Rewriting
                                                                                                                                                                              ↳ QDP
                                                                                                                                                                                ↳ Rewriting
                                                                                                                                                                                  ↳ QDP
                                                                                                                                                                                    ↳ Rewriting
                                                                                                                                                                                      ↳ QDP
                                                                                                                                                                                        ↳ Rewriting
                                                                                                                                                                                          ↳ QDP
                                                                                                                                                                                            ↳ Rewriting
                                                                                                                                                                                              ↳ QDP
                                                                                                                                                                                                ↳ DependencyGraphProof
                                                                                                                                                                                                  ↳ QDP
                                                                                                                                                                                                    ↳ Rewriting
                                                                                                                                                                                                      ↳ QDP
                                                                                                                                                                                                        ↳ DependencyGraphProof
                                                                                                                                                                                                          ↳ QDP
                                                                                                                                                                                                            ↳ Rewriting
                                                                                                                                                                                                              ↳ QDP
                                                                                                                                                                                                                ↳ Rewriting
                                                                                                                                                                                                                  ↳ QDP
                                                                                                                                                                                                                    ↳ QDPOrderProof
                                                                                                                                                                                                                      ↳ QDP
                                                                                                                                                                                                                        ↳ DependencyGraphProof
                                                                                                                                                                                                                          ↳ AND
                                                                                                                                                                                                                            ↳ QDP
                                                                                                                                                                                                                            ↳ QDP
                                                                                                                                                                                                                            ↳ QDP
                                                                                                                                                                                                                              ↳ QDPOrderProof
                                                                                                                                                                                                                                ↳ QDP
                                                                                                                                                                                                                                  ↳ DependencyGraphProof
                                                                                                                                                                                                                                    ↳ AND
                                                                                                                                                                                                                                      ↳ QDP
                                                                                                                                                                                                                                      ↳ QDP
                                                                                                                                                                                                                                        ↳ QDPOrderProof
                                                                                                                                                                                                                            ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP

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

new_mkVBalBranch3MkVBalBranch236(zzz958, zzz959, zzz960, zzz961, zzz962, zzz963, zzz964, zzz965, zzz966, zzz967, zzz968, Zero, Succ(zzz9700), ba) → new_mkVBalBranch1(zzz968, Branch(zzz963, zzz964, Pos(Succ(zzz965)), zzz966, zzz967), zzz961, ba)
new_mkVBalBranch3MkVBalBranch125(zzz1337, zzz1338, zzz1339, zzz1340, zzz1341, zzz1342, zzz1343, zzz1344, zzz1345, zzz1346, zzz1347, Succ(zzz13480), Succ(zzz13490), bb) → new_mkVBalBranch3MkVBalBranch125(zzz1337, zzz1338, zzz1339, zzz1340, zzz1341, zzz1342, zzz1343, zzz1344, zzz1345, zzz1346, zzz1347, zzz13480, zzz13490, bb)
new_mkVBalBranch3MkVBalBranch123(zzz3170, zzz3171, zzz317200, zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, Succ(zzz5620), h) → new_mkVBalBranch1(zzz31, zzz334, Branch(zzz3170, zzz3171, Neg(Succ(zzz317200)), zzz3173, zzz3174), h)
new_mkVBalBranch3MkVBalBranch240(zzz958, zzz959, zzz960, zzz961, zzz962, zzz963, zzz964, zzz965, zzz966, zzz967, zzz968, ba) → new_mkVBalBranch3MkVBalBranch124(zzz958, zzz959, zzz960, zzz961, zzz962, zzz963, zzz964, zzz965, zzz966, zzz967, zzz968, Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat2(Succ(new_primPlusNat3(new_primPlusNat1(zzz960), zzz960)), zzz960)), zzz960))), ba)
new_mkVBalBranch3MkVBalBranch125(zzz1337, zzz1338, zzz1339, zzz1340, zzz1341, zzz1342, zzz1343, zzz1344, zzz1345, zzz1346, zzz1347, Zero, Succ(zzz13490), bb) → new_mkVBalBranch1(zzz1347, zzz1346, Branch(zzz1337, zzz1338, Pos(Succ(zzz1339)), zzz1340, zzz1341), bb)
new_mkVBalBranch3MkVBalBranch236(zzz958, zzz959, zzz960, zzz961, zzz962, zzz963, zzz964, zzz965, zzz966, zzz967, zzz968, Succ(zzz9690), Zero, ba) → new_mkVBalBranch3MkVBalBranch124(zzz958, zzz959, zzz960, zzz961, zzz962, zzz963, zzz964, zzz965, zzz966, zzz967, zzz968, Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat2(Succ(new_primPlusNat3(new_primPlusNat1(zzz960), zzz960)), zzz960)), zzz960))), ba)
new_mkVBalBranch3MkVBalBranch235(zzz3170, zzz3171, Pos(Succ(zzz317200)), zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, Succ(zzz4170), h) → new_mkVBalBranch3MkVBalBranch236(zzz3170, zzz3171, zzz317200, zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, zzz4170, zzz317200, h)
new_mkVBalBranch1(zzz31, Branch(zzz330, zzz331, Pos(Succ(zzz33200)), zzz333, zzz334), Branch(zzz3170, zzz3171, zzz3172, zzz3173, zzz3174), h) → new_mkVBalBranch3MkVBalBranch235(zzz3170, zzz3171, zzz3172, zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat2(Succ(new_primPlusNat3(new_primPlusNat1(zzz33200), zzz33200)), zzz33200)), zzz33200))), h)
new_mkVBalBranch3MkVBalBranch124(zzz958, zzz959, zzz960, zzz961, zzz962, zzz963, zzz964, zzz965, zzz966, zzz967, zzz968, Succ(zzz10180), ba) → new_mkVBalBranch3MkVBalBranch125(zzz958, zzz959, zzz960, zzz961, zzz962, zzz963, zzz964, zzz965, zzz966, zzz967, zzz968, Succ(zzz10180), Succ(zzz965), ba)
new_mkVBalBranch3MkVBalBranch236(zzz958, zzz959, zzz960, zzz961, zzz962, zzz963, zzz964, zzz965, zzz966, zzz967, zzz968, Succ(zzz9690), Succ(zzz9700), ba) → new_mkVBalBranch3MkVBalBranch236(zzz958, zzz959, zzz960, zzz961, zzz962, zzz963, zzz964, zzz965, zzz966, zzz967, zzz968, zzz9690, zzz9700, ba)
new_mkVBalBranch3MkVBalBranch235(zzz3170, zzz3171, Neg(Succ(zzz317200)), zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, Succ(zzz4170), h) → new_mkVBalBranch3MkVBalBranch123(zzz3170, zzz3171, zzz317200, zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat2(Succ(new_primPlusNat3(new_primPlusNat1(zzz317200), zzz317200)), zzz317200)), zzz317200))), h)
new_mkVBalBranch3MkVBalBranch237(zzz3170, zzz3171, zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, h) → new_mkVBalBranch1(zzz31, zzz334, Branch(zzz3170, zzz3171, Pos(Zero), zzz3173, zzz3174), h)
new_mkVBalBranch3MkVBalBranch235(zzz3170, zzz3171, Neg(Zero), zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, Succ(zzz4170), h) → new_mkVBalBranch1(zzz31, zzz334, Branch(zzz3170, zzz3171, Neg(Zero), zzz3173, zzz3174), h)
new_mkVBalBranch3MkVBalBranch236(zzz958, zzz959, zzz960, zzz961, zzz962, zzz963, zzz964, zzz965, zzz966, zzz967, zzz968, Zero, Zero, ba) → new_mkVBalBranch3MkVBalBranch240(zzz958, zzz959, zzz960, zzz961, zzz962, zzz963, zzz964, zzz965, zzz966, zzz967, zzz968, ba)
new_mkVBalBranch3MkVBalBranch235(zzz3170, zzz3171, Pos(Zero), zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, Succ(zzz4170), h) → new_mkVBalBranch3MkVBalBranch237(zzz3170, zzz3171, zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, h)

The TRS R consists of the following rules:

new_primPlusNat1(Zero) → Zero
new_primPlusNat1(Succ(zzz62000)) → Succ(Succ(new_primPlusNat1(zzz62000)))
new_primPlusNat3(zzz90, Succ(zzz910)) → Succ(Succ(new_primPlusNat2(zzz90, zzz910)))
new_primPlusNat3(zzz90, Zero) → Succ(zzz90)
new_primPlusNat2(Succ(zzz900), Succ(zzz9100)) → Succ(Succ(new_primPlusNat2(zzz900, zzz9100)))
new_primPlusNat2(Succ(zzz900), Zero) → Succ(zzz900)
new_primPlusNat2(Zero, Succ(zzz9100)) → Succ(zzz9100)
new_primPlusNat2(Zero, Zero) → Zero

The set Q consists of the following terms:

new_primPlusNat2(Zero, Succ(x0))
new_primPlusNat3(x0, Succ(x1))
new_primPlusNat2(Succ(x0), Succ(x1))
new_primPlusNat3(x0, Zero)
new_primPlusNat1(Zero)
new_primPlusNat2(Zero, Zero)
new_primPlusNat1(Succ(x0))
new_primPlusNat2(Succ(x0), Zero)

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


The following pairs can be oriented strictly and are deleted.


new_mkVBalBranch3MkVBalBranch236(zzz958, zzz959, zzz960, zzz961, zzz962, zzz963, zzz964, zzz965, zzz966, zzz967, zzz968, Succ(zzz9690), Zero, ba) → new_mkVBalBranch3MkVBalBranch124(zzz958, zzz959, zzz960, zzz961, zzz962, zzz963, zzz964, zzz965, zzz966, zzz967, zzz968, Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat2(Succ(new_primPlusNat3(new_primPlusNat1(zzz960), zzz960)), zzz960)), zzz960))), ba)
new_mkVBalBranch3MkVBalBranch235(zzz3170, zzz3171, Neg(Succ(zzz317200)), zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, Succ(zzz4170), h) → new_mkVBalBranch3MkVBalBranch123(zzz3170, zzz3171, zzz317200, zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat2(Succ(new_primPlusNat3(new_primPlusNat1(zzz317200), zzz317200)), zzz317200)), zzz317200))), h)
new_mkVBalBranch3MkVBalBranch235(zzz3170, zzz3171, Neg(Zero), zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, Succ(zzz4170), h) → new_mkVBalBranch1(zzz31, zzz334, Branch(zzz3170, zzz3171, Neg(Zero), zzz3173, zzz3174), h)
new_mkVBalBranch3MkVBalBranch236(zzz958, zzz959, zzz960, zzz961, zzz962, zzz963, zzz964, zzz965, zzz966, zzz967, zzz968, Zero, Zero, ba) → new_mkVBalBranch3MkVBalBranch240(zzz958, zzz959, zzz960, zzz961, zzz962, zzz963, zzz964, zzz965, zzz966, zzz967, zzz968, ba)
new_mkVBalBranch3MkVBalBranch235(zzz3170, zzz3171, Pos(Zero), zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, Succ(zzz4170), h) → new_mkVBalBranch3MkVBalBranch237(zzz3170, zzz3171, zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, h)
The remaining pairs can at least be oriented weakly.

new_mkVBalBranch3MkVBalBranch236(zzz958, zzz959, zzz960, zzz961, zzz962, zzz963, zzz964, zzz965, zzz966, zzz967, zzz968, Zero, Succ(zzz9700), ba) → new_mkVBalBranch1(zzz968, Branch(zzz963, zzz964, Pos(Succ(zzz965)), zzz966, zzz967), zzz961, ba)
new_mkVBalBranch3MkVBalBranch125(zzz1337, zzz1338, zzz1339, zzz1340, zzz1341, zzz1342, zzz1343, zzz1344, zzz1345, zzz1346, zzz1347, Succ(zzz13480), Succ(zzz13490), bb) → new_mkVBalBranch3MkVBalBranch125(zzz1337, zzz1338, zzz1339, zzz1340, zzz1341, zzz1342, zzz1343, zzz1344, zzz1345, zzz1346, zzz1347, zzz13480, zzz13490, bb)
new_mkVBalBranch3MkVBalBranch123(zzz3170, zzz3171, zzz317200, zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, Succ(zzz5620), h) → new_mkVBalBranch1(zzz31, zzz334, Branch(zzz3170, zzz3171, Neg(Succ(zzz317200)), zzz3173, zzz3174), h)
new_mkVBalBranch3MkVBalBranch240(zzz958, zzz959, zzz960, zzz961, zzz962, zzz963, zzz964, zzz965, zzz966, zzz967, zzz968, ba) → new_mkVBalBranch3MkVBalBranch124(zzz958, zzz959, zzz960, zzz961, zzz962, zzz963, zzz964, zzz965, zzz966, zzz967, zzz968, Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat2(Succ(new_primPlusNat3(new_primPlusNat1(zzz960), zzz960)), zzz960)), zzz960))), ba)
new_mkVBalBranch3MkVBalBranch125(zzz1337, zzz1338, zzz1339, zzz1340, zzz1341, zzz1342, zzz1343, zzz1344, zzz1345, zzz1346, zzz1347, Zero, Succ(zzz13490), bb) → new_mkVBalBranch1(zzz1347, zzz1346, Branch(zzz1337, zzz1338, Pos(Succ(zzz1339)), zzz1340, zzz1341), bb)
new_mkVBalBranch3MkVBalBranch235(zzz3170, zzz3171, Pos(Succ(zzz317200)), zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, Succ(zzz4170), h) → new_mkVBalBranch3MkVBalBranch236(zzz3170, zzz3171, zzz317200, zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, zzz4170, zzz317200, h)
new_mkVBalBranch1(zzz31, Branch(zzz330, zzz331, Pos(Succ(zzz33200)), zzz333, zzz334), Branch(zzz3170, zzz3171, zzz3172, zzz3173, zzz3174), h) → new_mkVBalBranch3MkVBalBranch235(zzz3170, zzz3171, zzz3172, zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat2(Succ(new_primPlusNat3(new_primPlusNat1(zzz33200), zzz33200)), zzz33200)), zzz33200))), h)
new_mkVBalBranch3MkVBalBranch124(zzz958, zzz959, zzz960, zzz961, zzz962, zzz963, zzz964, zzz965, zzz966, zzz967, zzz968, Succ(zzz10180), ba) → new_mkVBalBranch3MkVBalBranch125(zzz958, zzz959, zzz960, zzz961, zzz962, zzz963, zzz964, zzz965, zzz966, zzz967, zzz968, Succ(zzz10180), Succ(zzz965), ba)
new_mkVBalBranch3MkVBalBranch236(zzz958, zzz959, zzz960, zzz961, zzz962, zzz963, zzz964, zzz965, zzz966, zzz967, zzz968, Succ(zzz9690), Succ(zzz9700), ba) → new_mkVBalBranch3MkVBalBranch236(zzz958, zzz959, zzz960, zzz961, zzz962, zzz963, zzz964, zzz965, zzz966, zzz967, zzz968, zzz9690, zzz9700, ba)
new_mkVBalBranch3MkVBalBranch237(zzz3170, zzz3171, zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, h) → new_mkVBalBranch1(zzz31, zzz334, Branch(zzz3170, zzz3171, Pos(Zero), zzz3173, zzz3174), h)
Used ordering: Polynomial interpretation [25]:

POL(Branch(x1, x2, x3, x4, x5)) = x1 + x3 + x4 + x5   
POL(Neg(x1)) = 0   
POL(Pos(x1)) = 1   
POL(Succ(x1)) = 0   
POL(Zero) = 0   
POL(new_mkVBalBranch1(x1, x2, x3, x4)) = x2   
POL(new_mkVBalBranch3MkVBalBranch123(x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12, x13)) = x10 + x9   
POL(new_mkVBalBranch3MkVBalBranch124(x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12, x13)) = x10 + x6 + x9   
POL(new_mkVBalBranch3MkVBalBranch125(x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12, x13, x14)) = x10 + x9   
POL(new_mkVBalBranch3MkVBalBranch235(x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12, x13)) = 1 + x10 + x6 + x9   
POL(new_mkVBalBranch3MkVBalBranch236(x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12, x13, x14)) = 1 + x10 + x6 + x9   
POL(new_mkVBalBranch3MkVBalBranch237(x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11)) = x5 + x9   
POL(new_mkVBalBranch3MkVBalBranch240(x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12)) = x10 + x6 + x9   
POL(new_primPlusNat1(x1)) = 0   
POL(new_primPlusNat2(x1, x2)) = 0   
POL(new_primPlusNat3(x1, x2)) = 1 + 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
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                    ↳ DependencyGraphProof
                                      ↳ QDP
                                        ↳ Rewriting
                                          ↳ QDP
                                            ↳ Rewriting
                                              ↳ QDP
                                                ↳ Rewriting
                                                  ↳ QDP
                                                    ↳ Rewriting
                                                      ↳ QDP
                                                        ↳ Rewriting
                                                          ↳ QDP
                                                            ↳ Rewriting
                                                              ↳ QDP
                                                                ↳ Rewriting
                                                                  ↳ QDP
                                                                    ↳ Rewriting
                                                                      ↳ QDP
                                                                        ↳ Rewriting
                                                                          ↳ QDP
                                                                            ↳ Rewriting
                                                                              ↳ QDP
                                                                                ↳ UsableRulesProof
                                                                                  ↳ QDP
                                                                                    ↳ QReductionProof
                                                                                      ↳ QDP
                                                                                        ↳ Rewriting
                                                                                          ↳ QDP
                                                                                            ↳ Rewriting
                                                                                              ↳ QDP
                                                                                                ↳ Rewriting
                                                                                                  ↳ QDP
                                                                                                    ↳ Rewriting
                                                                                                      ↳ QDP
                                                                                                        ↳ Rewriting
                                                                                                          ↳ QDP
                                                                                                            ↳ Rewriting
                                                                                                              ↳ QDP
                                                                                                                ↳ Rewriting
                                                                                                                  ↳ QDP
                                                                                                                    ↳ Rewriting
                                                                                                                      ↳ QDP
                                                                                                                        ↳ Rewriting
                                                                                                                          ↳ QDP
                                                                                                                            ↳ Rewriting
                                                                                                                              ↳ QDP
                                                                                                                                ↳ UsableRulesProof
                                                                                                                                  ↳ QDP
                                                                                                                                    ↳ QReductionProof
                                                                                                                                      ↳ QDP
                                                                                                                                        ↳ Rewriting
                                                                                                                                          ↳ QDP
                                                                                                                                            ↳ Rewriting
                                                                                                                                              ↳ QDP
                                                                                                                                                ↳ Rewriting
                                                                                                                                                  ↳ QDP
                                                                                                                                                    ↳ DependencyGraphProof
                                                                                                                                                      ↳ QDP
                                                                                                                                                        ↳ Rewriting
                                                                                                                                                          ↳ QDP
                                                                                                                                                            ↳ Rewriting
                                                                                                                                                              ↳ QDP
                                                                                                                                                                ↳ DependencyGraphProof
                                                                                                                                                                  ↳ QDP
                                                                                                                                                                    ↳ Rewriting
                                                                                                                                                                      ↳ QDP
                                                                                                                                                                        ↳ Rewriting
                                                                                                                                                                          ↳ QDP
                                                                                                                                                                            ↳ Rewriting
                                                                                                                                                                              ↳ QDP
                                                                                                                                                                                ↳ Rewriting
                                                                                                                                                                                  ↳ QDP
                                                                                                                                                                                    ↳ Rewriting
                                                                                                                                                                                      ↳ QDP
                                                                                                                                                                                        ↳ Rewriting
                                                                                                                                                                                          ↳ QDP
                                                                                                                                                                                            ↳ Rewriting
                                                                                                                                                                                              ↳ QDP
                                                                                                                                                                                                ↳ DependencyGraphProof
                                                                                                                                                                                                  ↳ QDP
                                                                                                                                                                                                    ↳ Rewriting
                                                                                                                                                                                                      ↳ QDP
                                                                                                                                                                                                        ↳ DependencyGraphProof
                                                                                                                                                                                                          ↳ QDP
                                                                                                                                                                                                            ↳ Rewriting
                                                                                                                                                                                                              ↳ QDP
                                                                                                                                                                                                                ↳ Rewriting
                                                                                                                                                                                                                  ↳ QDP
                                                                                                                                                                                                                    ↳ QDPOrderProof
                                                                                                                                                                                                                      ↳ QDP
                                                                                                                                                                                                                        ↳ DependencyGraphProof
                                                                                                                                                                                                                          ↳ AND
                                                                                                                                                                                                                            ↳ QDP
                                                                                                                                                                                                                            ↳ QDP
                                                                                                                                                                                                                            ↳ QDP
                                                                                                                                                                                                                              ↳ QDPOrderProof
                                                                                                                                                                                                                                ↳ QDP
                                                                                                                                                                                                                                  ↳ DependencyGraphProof
                                                                                                                                                                                                                                    ↳ AND
                                                                                                                                                                                                                                      ↳ QDP
                                                                                                                                                                                                                                      ↳ QDP
                                                                                                                                                                                                                                        ↳ QDPOrderProof
                                                                                                                                                                                                                                          ↳ QDP
                                                                                                                                                                                                                                            ↳ DependencyGraphProof
                                                                                                                                                                                                                            ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP

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

new_mkVBalBranch3MkVBalBranch236(zzz958, zzz959, zzz960, zzz961, zzz962, zzz963, zzz964, zzz965, zzz966, zzz967, zzz968, Zero, Succ(zzz9700), ba) → new_mkVBalBranch1(zzz968, Branch(zzz963, zzz964, Pos(Succ(zzz965)), zzz966, zzz967), zzz961, ba)
new_mkVBalBranch3MkVBalBranch235(zzz3170, zzz3171, Pos(Succ(zzz317200)), zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, Succ(zzz4170), h) → new_mkVBalBranch3MkVBalBranch236(zzz3170, zzz3171, zzz317200, zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, zzz4170, zzz317200, h)
new_mkVBalBranch3MkVBalBranch125(zzz1337, zzz1338, zzz1339, zzz1340, zzz1341, zzz1342, zzz1343, zzz1344, zzz1345, zzz1346, zzz1347, Succ(zzz13480), Succ(zzz13490), bb) → new_mkVBalBranch3MkVBalBranch125(zzz1337, zzz1338, zzz1339, zzz1340, zzz1341, zzz1342, zzz1343, zzz1344, zzz1345, zzz1346, zzz1347, zzz13480, zzz13490, bb)
new_mkVBalBranch3MkVBalBranch123(zzz3170, zzz3171, zzz317200, zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, Succ(zzz5620), h) → new_mkVBalBranch1(zzz31, zzz334, Branch(zzz3170, zzz3171, Neg(Succ(zzz317200)), zzz3173, zzz3174), h)
new_mkVBalBranch3MkVBalBranch124(zzz958, zzz959, zzz960, zzz961, zzz962, zzz963, zzz964, zzz965, zzz966, zzz967, zzz968, Succ(zzz10180), ba) → new_mkVBalBranch3MkVBalBranch125(zzz958, zzz959, zzz960, zzz961, zzz962, zzz963, zzz964, zzz965, zzz966, zzz967, zzz968, Succ(zzz10180), Succ(zzz965), ba)
new_mkVBalBranch1(zzz31, Branch(zzz330, zzz331, Pos(Succ(zzz33200)), zzz333, zzz334), Branch(zzz3170, zzz3171, zzz3172, zzz3173, zzz3174), h) → new_mkVBalBranch3MkVBalBranch235(zzz3170, zzz3171, zzz3172, zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat2(Succ(new_primPlusNat3(new_primPlusNat1(zzz33200), zzz33200)), zzz33200)), zzz33200))), h)
new_mkVBalBranch3MkVBalBranch125(zzz1337, zzz1338, zzz1339, zzz1340, zzz1341, zzz1342, zzz1343, zzz1344, zzz1345, zzz1346, zzz1347, Zero, Succ(zzz13490), bb) → new_mkVBalBranch1(zzz1347, zzz1346, Branch(zzz1337, zzz1338, Pos(Succ(zzz1339)), zzz1340, zzz1341), bb)
new_mkVBalBranch3MkVBalBranch240(zzz958, zzz959, zzz960, zzz961, zzz962, zzz963, zzz964, zzz965, zzz966, zzz967, zzz968, ba) → new_mkVBalBranch3MkVBalBranch124(zzz958, zzz959, zzz960, zzz961, zzz962, zzz963, zzz964, zzz965, zzz966, zzz967, zzz968, Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat2(Succ(new_primPlusNat3(new_primPlusNat1(zzz960), zzz960)), zzz960)), zzz960))), ba)
new_mkVBalBranch3MkVBalBranch236(zzz958, zzz959, zzz960, zzz961, zzz962, zzz963, zzz964, zzz965, zzz966, zzz967, zzz968, Succ(zzz9690), Succ(zzz9700), ba) → new_mkVBalBranch3MkVBalBranch236(zzz958, zzz959, zzz960, zzz961, zzz962, zzz963, zzz964, zzz965, zzz966, zzz967, zzz968, zzz9690, zzz9700, ba)
new_mkVBalBranch3MkVBalBranch237(zzz3170, zzz3171, zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, h) → new_mkVBalBranch1(zzz31, zzz334, Branch(zzz3170, zzz3171, Pos(Zero), zzz3173, zzz3174), h)

The TRS R consists of the following rules:

new_primPlusNat1(Zero) → Zero
new_primPlusNat1(Succ(zzz62000)) → Succ(Succ(new_primPlusNat1(zzz62000)))
new_primPlusNat3(zzz90, Succ(zzz910)) → Succ(Succ(new_primPlusNat2(zzz90, zzz910)))
new_primPlusNat3(zzz90, Zero) → Succ(zzz90)
new_primPlusNat2(Succ(zzz900), Succ(zzz9100)) → Succ(Succ(new_primPlusNat2(zzz900, zzz9100)))
new_primPlusNat2(Succ(zzz900), Zero) → Succ(zzz900)
new_primPlusNat2(Zero, Succ(zzz9100)) → Succ(zzz9100)
new_primPlusNat2(Zero, Zero) → Zero

The set Q consists of the following terms:

new_primPlusNat2(Zero, Succ(x0))
new_primPlusNat3(x0, Succ(x1))
new_primPlusNat2(Succ(x0), Succ(x1))
new_primPlusNat3(x0, Zero)
new_primPlusNat1(Zero)
new_primPlusNat2(Zero, Zero)
new_primPlusNat1(Succ(x0))
new_primPlusNat2(Succ(x0), Zero)

We have to consider all minimal (P,Q,R)-chains.
The approximation of the Dependency Graph [15,17,22] contains 2 SCCs 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
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                    ↳ DependencyGraphProof
                                      ↳ QDP
                                        ↳ Rewriting
                                          ↳ QDP
                                            ↳ Rewriting
                                              ↳ QDP
                                                ↳ Rewriting
                                                  ↳ QDP
                                                    ↳ Rewriting
                                                      ↳ QDP
                                                        ↳ Rewriting
                                                          ↳ QDP
                                                            ↳ Rewriting
                                                              ↳ QDP
                                                                ↳ Rewriting
                                                                  ↳ QDP
                                                                    ↳ Rewriting
                                                                      ↳ QDP
                                                                        ↳ Rewriting
                                                                          ↳ QDP
                                                                            ↳ Rewriting
                                                                              ↳ QDP
                                                                                ↳ UsableRulesProof
                                                                                  ↳ QDP
                                                                                    ↳ QReductionProof
                                                                                      ↳ QDP
                                                                                        ↳ Rewriting
                                                                                          ↳ QDP
                                                                                            ↳ Rewriting
                                                                                              ↳ QDP
                                                                                                ↳ Rewriting
                                                                                                  ↳ QDP
                                                                                                    ↳ Rewriting
                                                                                                      ↳ QDP
                                                                                                        ↳ Rewriting
                                                                                                          ↳ QDP
                                                                                                            ↳ Rewriting
                                                                                                              ↳ QDP
                                                                                                                ↳ Rewriting
                                                                                                                  ↳ QDP
                                                                                                                    ↳ Rewriting
                                                                                                                      ↳ QDP
                                                                                                                        ↳ Rewriting
                                                                                                                          ↳ QDP
                                                                                                                            ↳ Rewriting
                                                                                                                              ↳ QDP
                                                                                                                                ↳ UsableRulesProof
                                                                                                                                  ↳ QDP
                                                                                                                                    ↳ QReductionProof
                                                                                                                                      ↳ QDP
                                                                                                                                        ↳ Rewriting
                                                                                                                                          ↳ QDP
                                                                                                                                            ↳ Rewriting
                                                                                                                                              ↳ QDP
                                                                                                                                                ↳ Rewriting
                                                                                                                                                  ↳ QDP
                                                                                                                                                    ↳ DependencyGraphProof
                                                                                                                                                      ↳ QDP
                                                                                                                                                        ↳ Rewriting
                                                                                                                                                          ↳ QDP
                                                                                                                                                            ↳ Rewriting
                                                                                                                                                              ↳ QDP
                                                                                                                                                                ↳ DependencyGraphProof
                                                                                                                                                                  ↳ QDP
                                                                                                                                                                    ↳ Rewriting
                                                                                                                                                                      ↳ QDP
                                                                                                                                                                        ↳ Rewriting
                                                                                                                                                                          ↳ QDP
                                                                                                                                                                            ↳ Rewriting
                                                                                                                                                                              ↳ QDP
                                                                                                                                                                                ↳ Rewriting
                                                                                                                                                                                  ↳ QDP
                                                                                                                                                                                    ↳ Rewriting
                                                                                                                                                                                      ↳ QDP
                                                                                                                                                                                        ↳ Rewriting
                                                                                                                                                                                          ↳ QDP
                                                                                                                                                                                            ↳ Rewriting
                                                                                                                                                                                              ↳ QDP
                                                                                                                                                                                                ↳ DependencyGraphProof
                                                                                                                                                                                                  ↳ QDP
                                                                                                                                                                                                    ↳ Rewriting
                                                                                                                                                                                                      ↳ QDP
                                                                                                                                                                                                        ↳ DependencyGraphProof
                                                                                                                                                                                                          ↳ QDP
                                                                                                                                                                                                            ↳ Rewriting
                                                                                                                                                                                                              ↳ QDP
                                                                                                                                                                                                                ↳ Rewriting
                                                                                                                                                                                                                  ↳ QDP
                                                                                                                                                                                                                    ↳ QDPOrderProof
                                                                                                                                                                                                                      ↳ QDP
                                                                                                                                                                                                                        ↳ DependencyGraphProof
                                                                                                                                                                                                                          ↳ AND
                                                                                                                                                                                                                            ↳ QDP
                                                                                                                                                                                                                            ↳ QDP
                                                                                                                                                                                                                            ↳ QDP
                                                                                                                                                                                                                              ↳ QDPOrderProof
                                                                                                                                                                                                                                ↳ QDP
                                                                                                                                                                                                                                  ↳ DependencyGraphProof
                                                                                                                                                                                                                                    ↳ AND
                                                                                                                                                                                                                                      ↳ QDP
                                                                                                                                                                                                                                      ↳ QDP
                                                                                                                                                                                                                                        ↳ QDPOrderProof
                                                                                                                                                                                                                                          ↳ QDP
                                                                                                                                                                                                                                            ↳ DependencyGraphProof
                                                                                                                                                                                                                                              ↳ AND
                                                                                                                                                                                                                                                ↳ QDP
                                                                                                                                                                                                                                                  ↳ QDPSizeChangeProof
                                                                                                                                                                                                                                                ↳ QDP
                                                                                                                                                                                                                            ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP

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

new_mkVBalBranch3MkVBalBranch236(zzz958, zzz959, zzz960, zzz961, zzz962, zzz963, zzz964, zzz965, zzz966, zzz967, zzz968, Zero, Succ(zzz9700), ba) → new_mkVBalBranch1(zzz968, Branch(zzz963, zzz964, Pos(Succ(zzz965)), zzz966, zzz967), zzz961, ba)
new_mkVBalBranch3MkVBalBranch235(zzz3170, zzz3171, Pos(Succ(zzz317200)), zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, Succ(zzz4170), h) → new_mkVBalBranch3MkVBalBranch236(zzz3170, zzz3171, zzz317200, zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, zzz4170, zzz317200, h)
new_mkVBalBranch1(zzz31, Branch(zzz330, zzz331, Pos(Succ(zzz33200)), zzz333, zzz334), Branch(zzz3170, zzz3171, zzz3172, zzz3173, zzz3174), h) → new_mkVBalBranch3MkVBalBranch235(zzz3170, zzz3171, zzz3172, zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat2(Succ(new_primPlusNat3(new_primPlusNat1(zzz33200), zzz33200)), zzz33200)), zzz33200))), h)
new_mkVBalBranch3MkVBalBranch236(zzz958, zzz959, zzz960, zzz961, zzz962, zzz963, zzz964, zzz965, zzz966, zzz967, zzz968, Succ(zzz9690), Succ(zzz9700), ba) → new_mkVBalBranch3MkVBalBranch236(zzz958, zzz959, zzz960, zzz961, zzz962, zzz963, zzz964, zzz965, zzz966, zzz967, zzz968, zzz9690, zzz9700, ba)

The TRS R consists of the following rules:

new_primPlusNat1(Zero) → Zero
new_primPlusNat1(Succ(zzz62000)) → Succ(Succ(new_primPlusNat1(zzz62000)))
new_primPlusNat3(zzz90, Succ(zzz910)) → Succ(Succ(new_primPlusNat2(zzz90, zzz910)))
new_primPlusNat3(zzz90, Zero) → Succ(zzz90)
new_primPlusNat2(Succ(zzz900), Succ(zzz9100)) → Succ(Succ(new_primPlusNat2(zzz900, zzz9100)))
new_primPlusNat2(Succ(zzz900), Zero) → Succ(zzz900)
new_primPlusNat2(Zero, Succ(zzz9100)) → Succ(zzz9100)
new_primPlusNat2(Zero, Zero) → Zero

The set Q consists of the following terms:

new_primPlusNat2(Zero, Succ(x0))
new_primPlusNat3(x0, Succ(x1))
new_primPlusNat2(Succ(x0), Succ(x1))
new_primPlusNat3(x0, Zero)
new_primPlusNat1(Zero)
new_primPlusNat2(Zero, Zero)
new_primPlusNat1(Succ(x0))
new_primPlusNat2(Succ(x0), Zero)

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

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



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

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

new_mkVBalBranch3MkVBalBranch125(zzz1337, zzz1338, zzz1339, zzz1340, zzz1341, zzz1342, zzz1343, zzz1344, zzz1345, zzz1346, zzz1347, Succ(zzz13480), Succ(zzz13490), bb) → new_mkVBalBranch3MkVBalBranch125(zzz1337, zzz1338, zzz1339, zzz1340, zzz1341, zzz1342, zzz1343, zzz1344, zzz1345, zzz1346, zzz1347, zzz13480, zzz13490, bb)

The TRS R consists of the following rules:

new_primPlusNat1(Zero) → Zero
new_primPlusNat1(Succ(zzz62000)) → Succ(Succ(new_primPlusNat1(zzz62000)))
new_primPlusNat3(zzz90, Succ(zzz910)) → Succ(Succ(new_primPlusNat2(zzz90, zzz910)))
new_primPlusNat3(zzz90, Zero) → Succ(zzz90)
new_primPlusNat2(Succ(zzz900), Succ(zzz9100)) → Succ(Succ(new_primPlusNat2(zzz900, zzz9100)))
new_primPlusNat2(Succ(zzz900), Zero) → Succ(zzz900)
new_primPlusNat2(Zero, Succ(zzz9100)) → Succ(zzz9100)
new_primPlusNat2(Zero, Zero) → Zero

The set Q consists of the following terms:

new_primPlusNat2(Zero, Succ(x0))
new_primPlusNat3(x0, Succ(x1))
new_primPlusNat2(Succ(x0), Succ(x1))
new_primPlusNat3(x0, Zero)
new_primPlusNat1(Zero)
new_primPlusNat2(Zero, Zero)
new_primPlusNat1(Succ(x0))
new_primPlusNat2(Succ(x0), Zero)

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

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

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

new_mkVBalBranch3MkVBalBranch125(zzz1337, zzz1338, zzz1339, zzz1340, zzz1341, zzz1342, zzz1343, zzz1344, zzz1345, zzz1346, zzz1347, Succ(zzz13480), Succ(zzz13490), bb) → new_mkVBalBranch3MkVBalBranch125(zzz1337, zzz1338, zzz1339, zzz1340, zzz1341, zzz1342, zzz1343, zzz1344, zzz1345, zzz1346, zzz1347, zzz13480, zzz13490, bb)

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

new_primPlusNat2(Zero, Succ(x0))
new_primPlusNat3(x0, Succ(x1))
new_primPlusNat2(Succ(x0), Succ(x1))
new_primPlusNat3(x0, Zero)
new_primPlusNat1(Zero)
new_primPlusNat2(Zero, Zero)
new_primPlusNat1(Succ(x0))
new_primPlusNat2(Succ(x0), Zero)

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

new_primPlusNat2(Zero, Succ(x0))
new_primPlusNat3(x0, Succ(x1))
new_primPlusNat2(Succ(x0), Succ(x1))
new_primPlusNat3(x0, Zero)
new_primPlusNat1(Zero)
new_primPlusNat2(Zero, Zero)
new_primPlusNat1(Succ(x0))
new_primPlusNat2(Succ(x0), 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
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                    ↳ DependencyGraphProof
                                      ↳ QDP
                                        ↳ Rewriting
                                          ↳ QDP
                                            ↳ Rewriting
                                              ↳ QDP
                                                ↳ Rewriting
                                                  ↳ QDP
                                                    ↳ Rewriting
                                                      ↳ QDP
                                                        ↳ Rewriting
                                                          ↳ QDP
                                                            ↳ Rewriting
                                                              ↳ QDP
                                                                ↳ Rewriting
                                                                  ↳ QDP
                                                                    ↳ Rewriting
                                                                      ↳ QDP
                                                                        ↳ Rewriting
                                                                          ↳ QDP
                                                                            ↳ Rewriting
                                                                              ↳ QDP
                                                                                ↳ UsableRulesProof
                                                                                  ↳ QDP
                                                                                    ↳ QReductionProof
                                                                                      ↳ QDP
                                                                                        ↳ Rewriting
                                                                                          ↳ QDP
                                                                                            ↳ Rewriting
                                                                                              ↳ QDP
                                                                                                ↳ Rewriting
                                                                                                  ↳ QDP
                                                                                                    ↳ Rewriting
                                                                                                      ↳ QDP
                                                                                                        ↳ Rewriting
                                                                                                          ↳ QDP
                                                                                                            ↳ Rewriting
                                                                                                              ↳ QDP
                                                                                                                ↳ Rewriting
                                                                                                                  ↳ QDP
                                                                                                                    ↳ Rewriting
                                                                                                                      ↳ QDP
                                                                                                                        ↳ Rewriting
                                                                                                                          ↳ QDP
                                                                                                                            ↳ Rewriting
                                                                                                                              ↳ QDP
                                                                                                                                ↳ UsableRulesProof
                                                                                                                                  ↳ QDP
                                                                                                                                    ↳ QReductionProof
                                                                                                                                      ↳ QDP
                                                                                                                                        ↳ Rewriting
                                                                                                                                          ↳ QDP
                                                                                                                                            ↳ Rewriting
                                                                                                                                              ↳ QDP
                                                                                                                                                ↳ Rewriting
                                                                                                                                                  ↳ QDP
                                                                                                                                                    ↳ DependencyGraphProof
                                                                                                                                                      ↳ QDP
                                                                                                                                                        ↳ Rewriting
                                                                                                                                                          ↳ QDP
                                                                                                                                                            ↳ Rewriting
                                                                                                                                                              ↳ QDP
                                                                                                                                                                ↳ DependencyGraphProof
                                                                                                                                                                  ↳ QDP
                                                                                                                                                                    ↳ Rewriting
                                                                                                                                                                      ↳ QDP
                                                                                                                                                                        ↳ Rewriting
                                                                                                                                                                          ↳ QDP
                                                                                                                                                                            ↳ Rewriting
                                                                                                                                                                              ↳ QDP
                                                                                                                                                                                ↳ Rewriting
                                                                                                                                                                                  ↳ QDP
                                                                                                                                                                                    ↳ Rewriting
                                                                                                                                                                                      ↳ QDP
                                                                                                                                                                                        ↳ Rewriting
                                                                                                                                                                                          ↳ QDP
                                                                                                                                                                                            ↳ Rewriting
                                                                                                                                                                                              ↳ QDP
                                                                                                                                                                                                ↳ DependencyGraphProof
                                                                                                                                                                                                  ↳ QDP
                                                                                                                                                                                                    ↳ Rewriting
                                                                                                                                                                                                      ↳ QDP
                                                                                                                                                                                                        ↳ DependencyGraphProof
                                                                                                                                                                                                          ↳ QDP
                                                                                                                                                                                                            ↳ Rewriting
                                                                                                                                                                                                              ↳ QDP
                                                                                                                                                                                                                ↳ Rewriting
                                                                                                                                                                                                                  ↳ QDP
                                                                                                                                                                                                                    ↳ QDPOrderProof
                                                                                                                                                                                                                      ↳ QDP
                                                                                                                                                                                                                        ↳ DependencyGraphProof
                                                                                                                                                                                                                          ↳ AND
                                                                                                                                                                                                                            ↳ QDP
                                                                                                                                                                                                                            ↳ QDP
                                                                                                                                                                                                                            ↳ QDP
                                                                                                                                                                                                                              ↳ QDPOrderProof
                                                                                                                                                                                                                                ↳ QDP
                                                                                                                                                                                                                                  ↳ DependencyGraphProof
                                                                                                                                                                                                                                    ↳ AND
                                                                                                                                                                                                                                      ↳ QDP
                                                                                                                                                                                                                                      ↳ QDP
                                                                                                                                                                                                                                        ↳ QDPOrderProof
                                                                                                                                                                                                                                          ↳ QDP
                                                                                                                                                                                                                                            ↳ DependencyGraphProof
                                                                                                                                                                                                                                              ↳ AND
                                                                                                                                                                                                                                                ↳ QDP
                                                                                                                                                                                                                                                ↳ QDP
                                                                                                                                                                                                                                                  ↳ UsableRulesProof
                                                                                                                                                                                                                                                    ↳ QDP
                                                                                                                                                                                                                                                      ↳ QReductionProof
                                                                                                                                                                                                                                                        ↳ QDP
                                                                                                                                                                                                                                                          ↳ QDPSizeChangeProof
                                                                                                                                                                                                                            ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP

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

new_mkVBalBranch3MkVBalBranch125(zzz1337, zzz1338, zzz1339, zzz1340, zzz1341, zzz1342, zzz1343, zzz1344, zzz1345, zzz1346, zzz1347, Succ(zzz13480), Succ(zzz13490), bb) → new_mkVBalBranch3MkVBalBranch125(zzz1337, zzz1338, zzz1339, zzz1340, zzz1341, zzz1342, zzz1343, zzz1344, zzz1345, zzz1346, zzz1347, zzz13480, zzz13490, 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
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                    ↳ DependencyGraphProof
                                      ↳ QDP
                                        ↳ Rewriting
                                          ↳ QDP
                                            ↳ Rewriting
                                              ↳ QDP
                                                ↳ Rewriting
                                                  ↳ QDP
                                                    ↳ Rewriting
                                                      ↳ QDP
                                                        ↳ Rewriting
                                                          ↳ QDP
                                                            ↳ Rewriting
                                                              ↳ QDP
                                                                ↳ Rewriting
                                                                  ↳ QDP
                                                                    ↳ Rewriting
                                                                      ↳ QDP
                                                                        ↳ Rewriting
                                                                          ↳ QDP
                                                                            ↳ Rewriting
                                                                              ↳ QDP
                                                                                ↳ UsableRulesProof
                                                                                  ↳ QDP
                                                                                    ↳ QReductionProof
                                                                                      ↳ QDP
                                                                                        ↳ Rewriting
                                                                                          ↳ QDP
                                                                                            ↳ Rewriting
                                                                                              ↳ QDP
                                                                                                ↳ Rewriting
                                                                                                  ↳ QDP
                                                                                                    ↳ Rewriting
                                                                                                      ↳ QDP
                                                                                                        ↳ Rewriting
                                                                                                          ↳ QDP
                                                                                                            ↳ Rewriting
                                                                                                              ↳ QDP
                                                                                                                ↳ Rewriting
                                                                                                                  ↳ QDP
                                                                                                                    ↳ Rewriting
                                                                                                                      ↳ QDP
                                                                                                                        ↳ Rewriting
                                                                                                                          ↳ QDP
                                                                                                                            ↳ Rewriting
                                                                                                                              ↳ QDP
                                                                                                                                ↳ UsableRulesProof
                                                                                                                                  ↳ QDP
                                                                                                                                    ↳ QReductionProof
                                                                                                                                      ↳ QDP
                                                                                                                                        ↳ Rewriting
                                                                                                                                          ↳ QDP
                                                                                                                                            ↳ Rewriting
                                                                                                                                              ↳ QDP
                                                                                                                                                ↳ Rewriting
                                                                                                                                                  ↳ QDP
                                                                                                                                                    ↳ DependencyGraphProof
                                                                                                                                                      ↳ QDP
                                                                                                                                                        ↳ Rewriting
                                                                                                                                                          ↳ QDP
                                                                                                                                                            ↳ Rewriting
                                                                                                                                                              ↳ QDP
                                                                                                                                                                ↳ DependencyGraphProof
                                                                                                                                                                  ↳ QDP
                                                                                                                                                                    ↳ Rewriting
                                                                                                                                                                      ↳ QDP
                                                                                                                                                                        ↳ Rewriting
                                                                                                                                                                          ↳ QDP
                                                                                                                                                                            ↳ Rewriting
                                                                                                                                                                              ↳ QDP
                                                                                                                                                                                ↳ Rewriting
                                                                                                                                                                                  ↳ QDP
                                                                                                                                                                                    ↳ Rewriting
                                                                                                                                                                                      ↳ QDP
                                                                                                                                                                                        ↳ Rewriting
                                                                                                                                                                                          ↳ QDP
                                                                                                                                                                                            ↳ Rewriting
                                                                                                                                                                                              ↳ QDP
                                                                                                                                                                                                ↳ DependencyGraphProof
                                                                                                                                                                                                  ↳ QDP
                                                                                                                                                                                                    ↳ Rewriting
                                                                                                                                                                                                      ↳ QDP
                                                                                                                                                                                                        ↳ DependencyGraphProof
                                                                                                                                                                                                          ↳ QDP
                                                                                                                                                                                                            ↳ Rewriting
                                                                                                                                                                                                              ↳ QDP
                                                                                                                                                                                                                ↳ Rewriting
                                                                                                                                                                                                                  ↳ QDP
                                                                                                                                                                                                                    ↳ QDPOrderProof
                                                                                                                                                                                                                      ↳ QDP
                                                                                                                                                                                                                        ↳ DependencyGraphProof
                                                                                                                                                                                                                          ↳ AND
                                                                                                                                                                                                                            ↳ QDP
                                                                                                                                                                                                                            ↳ QDP
                                                                                                                                                                                                                            ↳ QDP
                                                                                                                                                                                                                            ↳ QDP
                                                                                                                                                                                                                              ↳ UsableRulesProof
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP

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

new_mkVBalBranch3MkVBalBranch129(zzz1851, zzz1852, zzz1853, zzz1854, zzz1855, zzz1856, zzz1857, zzz1858, zzz1859, zzz1860, zzz1861, Succ(zzz18620), Succ(zzz18630), bd) → new_mkVBalBranch3MkVBalBranch129(zzz1851, zzz1852, zzz1853, zzz1854, zzz1855, zzz1856, zzz1857, zzz1858, zzz1859, zzz1860, zzz1861, zzz18620, zzz18630, bd)

The TRS R consists of the following rules:

new_primPlusNat1(Zero) → Zero
new_primPlusNat1(Succ(zzz62000)) → Succ(Succ(new_primPlusNat1(zzz62000)))
new_primPlusNat3(zzz90, Succ(zzz910)) → Succ(Succ(new_primPlusNat2(zzz90, zzz910)))
new_primPlusNat3(zzz90, Zero) → Succ(zzz90)
new_primPlusNat2(Succ(zzz900), Succ(zzz9100)) → Succ(Succ(new_primPlusNat2(zzz900, zzz9100)))
new_primPlusNat2(Succ(zzz900), Zero) → Succ(zzz900)
new_primPlusNat2(Zero, Succ(zzz9100)) → Succ(zzz9100)
new_primPlusNat2(Zero, Zero) → Zero

The set Q consists of the following terms:

new_primPlusNat2(Zero, Succ(x0))
new_primPlusNat3(x0, Succ(x1))
new_primPlusNat2(Succ(x0), Succ(x1))
new_primPlusNat3(x0, Zero)
new_primPlusNat1(Zero)
new_primPlusNat2(Zero, Zero)
new_primPlusNat1(Succ(x0))
new_primPlusNat2(Succ(x0), Zero)

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

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

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

new_mkVBalBranch3MkVBalBranch129(zzz1851, zzz1852, zzz1853, zzz1854, zzz1855, zzz1856, zzz1857, zzz1858, zzz1859, zzz1860, zzz1861, Succ(zzz18620), Succ(zzz18630), bd) → new_mkVBalBranch3MkVBalBranch129(zzz1851, zzz1852, zzz1853, zzz1854, zzz1855, zzz1856, zzz1857, zzz1858, zzz1859, zzz1860, zzz1861, zzz18620, zzz18630, bd)

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

new_primPlusNat2(Zero, Succ(x0))
new_primPlusNat3(x0, Succ(x1))
new_primPlusNat2(Succ(x0), Succ(x1))
new_primPlusNat3(x0, Zero)
new_primPlusNat1(Zero)
new_primPlusNat2(Zero, Zero)
new_primPlusNat1(Succ(x0))
new_primPlusNat2(Succ(x0), Zero)

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

new_primPlusNat2(Zero, Succ(x0))
new_primPlusNat3(x0, Succ(x1))
new_primPlusNat2(Succ(x0), Succ(x1))
new_primPlusNat3(x0, Zero)
new_primPlusNat1(Zero)
new_primPlusNat2(Zero, Zero)
new_primPlusNat1(Succ(x0))
new_primPlusNat2(Succ(x0), 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
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                    ↳ DependencyGraphProof
                                      ↳ QDP
                                        ↳ Rewriting
                                          ↳ QDP
                                            ↳ Rewriting
                                              ↳ QDP
                                                ↳ Rewriting
                                                  ↳ QDP
                                                    ↳ Rewriting
                                                      ↳ QDP
                                                        ↳ Rewriting
                                                          ↳ QDP
                                                            ↳ Rewriting
                                                              ↳ QDP
                                                                ↳ Rewriting
                                                                  ↳ QDP
                                                                    ↳ Rewriting
                                                                      ↳ QDP
                                                                        ↳ Rewriting
                                                                          ↳ QDP
                                                                            ↳ Rewriting
                                                                              ↳ QDP
                                                                                ↳ UsableRulesProof
                                                                                  ↳ QDP
                                                                                    ↳ QReductionProof
                                                                                      ↳ QDP
                                                                                        ↳ Rewriting
                                                                                          ↳ QDP
                                                                                            ↳ Rewriting
                                                                                              ↳ QDP
                                                                                                ↳ Rewriting
                                                                                                  ↳ QDP
                                                                                                    ↳ Rewriting
                                                                                                      ↳ QDP
                                                                                                        ↳ Rewriting
                                                                                                          ↳ QDP
                                                                                                            ↳ Rewriting
                                                                                                              ↳ QDP
                                                                                                                ↳ Rewriting
                                                                                                                  ↳ QDP
                                                                                                                    ↳ Rewriting
                                                                                                                      ↳ QDP
                                                                                                                        ↳ Rewriting
                                                                                                                          ↳ QDP
                                                                                                                            ↳ Rewriting
                                                                                                                              ↳ QDP
                                                                                                                                ↳ UsableRulesProof
                                                                                                                                  ↳ QDP
                                                                                                                                    ↳ QReductionProof
                                                                                                                                      ↳ QDP
                                                                                                                                        ↳ Rewriting
                                                                                                                                          ↳ QDP
                                                                                                                                            ↳ Rewriting
                                                                                                                                              ↳ QDP
                                                                                                                                                ↳ Rewriting
                                                                                                                                                  ↳ QDP
                                                                                                                                                    ↳ DependencyGraphProof
                                                                                                                                                      ↳ QDP
                                                                                                                                                        ↳ Rewriting
                                                                                                                                                          ↳ QDP
                                                                                                                                                            ↳ Rewriting
                                                                                                                                                              ↳ QDP
                                                                                                                                                                ↳ DependencyGraphProof
                                                                                                                                                                  ↳ QDP
                                                                                                                                                                    ↳ Rewriting
                                                                                                                                                                      ↳ QDP
                                                                                                                                                                        ↳ Rewriting
                                                                                                                                                                          ↳ QDP
                                                                                                                                                                            ↳ Rewriting
                                                                                                                                                                              ↳ QDP
                                                                                                                                                                                ↳ Rewriting
                                                                                                                                                                                  ↳ QDP
                                                                                                                                                                                    ↳ Rewriting
                                                                                                                                                                                      ↳ QDP
                                                                                                                                                                                        ↳ Rewriting
                                                                                                                                                                                          ↳ QDP
                                                                                                                                                                                            ↳ Rewriting
                                                                                                                                                                                              ↳ QDP
                                                                                                                                                                                                ↳ DependencyGraphProof
                                                                                                                                                                                                  ↳ QDP
                                                                                                                                                                                                    ↳ Rewriting
                                                                                                                                                                                                      ↳ QDP
                                                                                                                                                                                                        ↳ DependencyGraphProof
                                                                                                                                                                                                          ↳ QDP
                                                                                                                                                                                                            ↳ Rewriting
                                                                                                                                                                                                              ↳ QDP
                                                                                                                                                                                                                ↳ Rewriting
                                                                                                                                                                                                                  ↳ QDP
                                                                                                                                                                                                                    ↳ QDPOrderProof
                                                                                                                                                                                                                      ↳ QDP
                                                                                                                                                                                                                        ↳ DependencyGraphProof
                                                                                                                                                                                                                          ↳ AND
                                                                                                                                                                                                                            ↳ QDP
                                                                                                                                                                                                                            ↳ QDP
                                                                                                                                                                                                                            ↳ QDP
                                                                                                                                                                                                                            ↳ QDP
                                                                                                                                                                                                                              ↳ UsableRulesProof
                                                                                                                                                                                                                                ↳ QDP
                                                                                                                                                                                                                                  ↳ QReductionProof
                                                                                                                                                                                                                                    ↳ QDP
                                                                                                                                                                                                                                      ↳ QDPSizeChangeProof
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP

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

new_mkVBalBranch3MkVBalBranch129(zzz1851, zzz1852, zzz1853, zzz1854, zzz1855, zzz1856, zzz1857, zzz1858, zzz1859, zzz1860, zzz1861, Succ(zzz18620), Succ(zzz18630), bd) → new_mkVBalBranch3MkVBalBranch129(zzz1851, zzz1852, zzz1853, zzz1854, zzz1855, zzz1856, zzz1857, zzz1858, zzz1859, zzz1860, zzz1861, zzz18620, zzz18630, bd)

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

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

new_splitLT0(Branch(EQ, zzz21291, zzz21292, zzz21293, zzz21294), h) → new_splitLT0(zzz21294, h)
new_splitLT0(Branch(LT, zzz21291, zzz21292, zzz21293, zzz21294), h) → new_splitLT0(zzz21294, 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
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                    ↳ DependencyGraphProof
                                  ↳ QDP

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

new_splitLT22(zzz76, zzz77, Branch(LT, zzz781, zzz782, zzz783, zzz784), zzz79, h) → new_splitLT1(zzz784, h)
new_splitLT22(zzz76, zzz77, Branch(GT, zzz781, zzz782, zzz783, zzz784), zzz79, h) → new_splitLT21(zzz781, zzz782, zzz783, zzz784, h)
new_splitLT21(zzz76, zzz77, Branch(GT, zzz781, zzz782, zzz783, zzz784), zzz79, h) → new_splitLT21(zzz781, zzz782, zzz783, zzz784, h)
new_splitLT1(Branch(GT, zzz781, zzz782, zzz783, zzz784), h) → new_splitLT21(zzz781, zzz782, zzz783, zzz784, h)
new_splitLT21(zzz76, zzz77, Branch(LT, zzz781, zzz782, zzz783, zzz784), zzz79, h) → new_splitLT1(zzz784, h)
new_splitLT1(Branch(LT, zzz781, zzz782, zzz783, zzz784), h) → new_splitLT1(zzz784, h)

R is empty.
Q is empty.
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
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                    ↳ DependencyGraphProof
                                      ↳ QDP
                                        ↳ QDPSizeChangeProof
                                  ↳ QDP

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

new_splitLT21(zzz76, zzz77, Branch(GT, zzz781, zzz782, zzz783, zzz784), zzz79, h) → new_splitLT21(zzz781, zzz782, zzz783, zzz784, h)
new_splitLT1(Branch(GT, zzz781, zzz782, zzz783, zzz784), h) → new_splitLT21(zzz781, zzz782, zzz783, zzz784, h)
new_splitLT21(zzz76, zzz77, Branch(LT, zzz781, zzz782, zzz783, zzz784), zzz79, h) → new_splitLT1(zzz784, h)
new_splitLT1(Branch(LT, zzz781, zzz782, zzz783, zzz784), h) → new_splitLT1(zzz784, 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
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                    ↳ DependencyGraphProof

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

new_intersectFM_C(Branch(GT, zzz31, zzz32, Branch(GT, zzz331, zzz332, Branch(GT, zzz3331, zzz3332, EmptyFM, zzz3334), zzz334), zzz34), Branch(EQ, zzz41, zzz42, zzz43, zzz44), h) → new_intersectFM_C(new_mkVBalBranch3(zzz31, new_splitGT9(zzz331, zzz332, Branch(GT, zzz3331, zzz3332, EmptyFM, zzz3334), zzz334, h), zzz34, h), zzz44, h)
new_intersectFM_C2IntersectFM_C16(zzz2208, zzz2209, zzz2210, zzz2211, zzz2212, zzz2213, zzz2214, zzz2215, GT, zzz2217, zzz2218, zzz2219, zzz2220, ca, cb) → new_intersectFM_C2IntersectFM_C18(Branch(LT, zzz2208, zzz2209, zzz2210, zzz2211), zzz2212, zzz2213, zzz2214, zzz2215, zzz2217, zzz2218, zzz2219, zzz2220, ca, cb)
new_intersectFM_C2IntersectFM_C10(zzz869, zzz870, zzz871, zzz872, zzz873, zzz874, zzz875, zzz876, EQ, zzz878, zzz879, EmptyFM, zzz881, bc, bd) → new_intersectFM_C(new_intersectFM_C2Lts1(zzz869, zzz870, zzz871, zzz872, bc), zzz875, bc)
new_intersectFM_C2IntersectFM_C11(zzz883, zzz884, zzz885, zzz886, zzz887, zzz888, zzz889, zzz890, EQ, zzz892, zzz893, zzz894, zzz895, be, bf) → new_intersectFM_C(new_intersectFM_C2Gts2(zzz883, zzz884, zzz885, zzz886, be), zzz890, be)
new_intersectFM_C(Branch(GT, zzz31, zzz32, Branch(GT, zzz331, zzz332, Branch(EQ, zzz3331, zzz3332, zzz3333, zzz3334), zzz334), zzz34), Branch(EQ, zzz41, zzz42, zzz43, zzz44), h) → new_intersectFM_C(new_splitGT24(zzz31, zzz32, Branch(GT, zzz331, zzz332, Branch(EQ, zzz3331, zzz3332, zzz3333, zzz3334), zzz334), zzz34, h), zzz44, h)
new_intersectFM_C(Branch(LT, zzz31, zzz32, zzz33, EmptyFM), Branch(GT, zzz41, zzz42, zzz43, zzz44), h) → new_intersectFM_C(new_splitGT10(zzz31, zzz32, zzz33, h), zzz44, h)
new_intersectFM_C2IntersectFM_C10(zzz869, zzz870, zzz871, zzz872, zzz873, zzz874, zzz875, zzz876, LT, zzz878, zzz879, zzz880, zzz881, bc, bd) → new_intersectFM_C(new_intersectFM_C2Lts1(zzz869, zzz870, zzz871, zzz872, bc), zzz875, bc)
new_intersectFM_C(Branch(EQ, zzz31, zzz32, EmptyFM, zzz34), Branch(LT, zzz41, zzz42, zzz43, zzz44), h) → new_intersectFM_C(new_splitGT4(zzz31, zzz32, zzz34, h), zzz44, h)
new_intersectFM_C2IntersectFM_C114(zzz2223, zzz2224, zzz2225, zzz2226, zzz2227, zzz2228, zzz2229, zzz2230, EmptyFM, ce, cf) → new_intersectFM_C(new_intersectFM_C2Lts3(Branch(EQ, zzz2223, zzz2224, zzz2225, zzz2226), ce), zzz2229, ce)
new_intersectFM_C2IntersectFM_C112(zzz76, zzz77, zzz78, zzz79, zzz80, zzz81, zzz82, zzz83, Branch(LT, zzz871, zzz872, zzz873, zzz874), bg, bh) → new_intersectFM_C2IntersectFM_C12(zzz76, zzz77, zzz78, zzz79, zzz80, zzz81, zzz82, zzz83, zzz871, zzz872, zzz873, zzz874, bg, bh)
new_intersectFM_C(Branch(LT, zzz31, zzz32, zzz33, Branch(zzz340, zzz341, zzz342, zzz343, zzz344)), Branch(GT, zzz41, zzz42, zzz43, zzz44), h) → new_intersectFM_C2IntersectFM_C16(zzz31, zzz32, zzz33, Branch(zzz340, zzz341, zzz342, zzz343, zzz344), zzz41, zzz42, zzz43, zzz44, zzz340, zzz341, zzz342, zzz343, zzz344, h, h)
new_intersectFM_C(Branch(GT, zzz31, zzz32, Branch(GT, zzz331, zzz332, Branch(GT, zzz3331, zzz3332, Branch(EQ, zzz33331, zzz33332, zzz33333, zzz33334), zzz3334), zzz334), zzz34), Branch(EQ, zzz41, zzz42, zzz43, zzz44), h) → new_intersectFM_C(new_intersectFM_C2Gts(zzz31, zzz32, Branch(GT, zzz331, zzz332, Branch(GT, zzz3331, zzz3332, Branch(EQ, zzz33331, zzz33332, zzz33333, zzz33334), zzz3334), zzz334), zzz34, h), zzz44, h)
new_intersectFM_C(Branch(LT, zzz31, zzz32, zzz33, EmptyFM), Branch(GT, zzz41, zzz42, zzz43, zzz44), h) → new_intersectFM_C(new_splitLT10(zzz31, zzz32, zzz33, h), zzz43, h)
new_intersectFM_C(Branch(EQ, zzz31, zzz32, zzz33, zzz34), Branch(EQ, zzz41, zzz42, zzz43, zzz44), h) → new_intersectFM_C(new_splitLT7(zzz31, zzz32, zzz33, zzz34, h), zzz43, h)
new_intersectFM_C(Branch(EQ, zzz31, zzz32, zzz33, EmptyFM), Branch(GT, zzz41, zzz42, zzz43, zzz44), h) → new_intersectFM_C(new_splitGT11(zzz31, zzz32, zzz33, h), zzz44, h)
new_intersectFM_C(Branch(EQ, zzz31, zzz32, zzz33, zzz34), Branch(EQ, zzz41, zzz42, zzz43, zzz44), h) → new_intersectFM_C(new_splitGT7(zzz31, zzz32, zzz33, zzz34, h), zzz44, h)
new_intersectFM_C2IntersectFM_C111(zzz883, zzz884, zzz885, zzz886, zzz887, zzz888, zzz889, zzz890, EmptyFM, be, bf) → new_intersectFM_C(new_intersectFM_C2Lts2(zzz883, zzz884, zzz885, zzz886, be), zzz889, be)
new_intersectFM_C2IntersectFM_C17(zzz2223, zzz2224, zzz2225, zzz2226, zzz2227, zzz2228, zzz2229, zzz2230, LT, zzz2232, zzz2233, zzz2234, EmptyFM, ce, cf) → new_intersectFM_C(new_intersectFM_C2Lts3(Branch(EQ, zzz2223, zzz2224, zzz2225, zzz2226), ce), zzz2229, ce)
new_intersectFM_C2IntersectFM_C19(zzz854, zzz855, zzz856, zzz857, zzz858, zzz859, zzz860, zzz861, EmptyFM, ba, bb) → new_intersectFM_C(new_intersectFM_C2Gts0(zzz854, zzz855, zzz856, zzz857, ba), zzz861, ba)
new_intersectFM_C2IntersectFM_C14(zzz76, zzz77, zzz78, zzz79, zzz80, zzz81, zzz82, zzz83, zzz871, zzz872, zzz873, zzz874, bg, bh) → new_intersectFM_C(new_intersectFM_C2Lts(zzz76, zzz77, zzz78, zzz79, bg), zzz82, bg)
new_intersectFM_C(Branch(GT, zzz31, zzz32, Branch(GT, zzz331, zzz332, Branch(EQ, zzz3331, zzz3332, zzz3333, zzz3334), zzz334), zzz34), Branch(EQ, zzz41, zzz42, zzz43, zzz44), h) → new_intersectFM_C(new_splitLT23(zzz31, zzz32, Branch(GT, zzz331, zzz332, Branch(EQ, zzz3331, zzz3332, zzz3333, zzz3334), zzz334), zzz34, h), zzz43, h)
new_intersectFM_C(Branch(LT, zzz31, zzz32, zzz33, EmptyFM), Branch(EQ, zzz41, zzz42, zzz43, zzz44), h) → new_intersectFM_C(new_mkVBalBranch2(zzz31, zzz33, new_splitLT6(h), h), zzz43, h)
new_intersectFM_C(Branch(EQ, zzz31, zzz32, zzz33, EmptyFM), Branch(GT, zzz41, zzz42, zzz43, zzz44), h) → new_intersectFM_C(new_splitLT11(zzz31, zzz32, zzz33, h), zzz43, h)
new_intersectFM_C(Branch(LT, zzz31, zzz32, zzz33, EmptyFM), Branch(EQ, zzz41, zzz42, zzz43, zzz44), h) → new_intersectFM_C(new_splitGT6(h), zzz44, h)
new_intersectFM_C2IntersectFM_C10(zzz869, zzz870, zzz871, zzz872, zzz873, zzz874, zzz875, zzz876, EQ, zzz878, zzz879, Branch(zzz8800, zzz8801, zzz8802, zzz8803, zzz8804), zzz881, bc, bd) → new_intersectFM_C2IntersectFM_C10(zzz869, zzz870, zzz871, zzz872, zzz873, zzz874, zzz875, zzz876, zzz8800, zzz8801, zzz8802, zzz8803, zzz8804, bc, bd)
new_intersectFM_C(Branch(GT, zzz31, zzz32, Branch(EQ, zzz331, zzz332, zzz333, zzz334), zzz34), Branch(EQ, zzz41, zzz42, zzz43, zzz44), h) → new_intersectFM_C(new_splitLT7(zzz331, zzz332, zzz333, zzz334, h), zzz43, h)
new_intersectFM_C2IntersectFM_C18(zzz2129, zzz2130, zzz2131, zzz2132, zzz2133, zzz2134, zzz2135, zzz2136, zzz2137, cc, cd) → new_intersectFM_C(new_intersectFM_C2Gts3(zzz2129, cc), zzz2133, cc)
new_intersectFM_C2IntersectFM_C10(zzz869, zzz870, zzz871, zzz872, zzz873, zzz874, zzz875, zzz876, LT, zzz878, zzz879, zzz880, zzz881, bc, bd) → new_intersectFM_C(new_intersectFM_C2Gts1(zzz869, zzz870, zzz871, zzz872, bc), zzz876, bc)
new_intersectFM_C2IntersectFM_C112(zzz76, zzz77, zzz78, zzz79, zzz80, zzz81, zzz82, zzz83, Branch(GT, zzz871, zzz872, zzz873, zzz874), bg, bh) → new_intersectFM_C2IntersectFM_C112(zzz76, zzz77, zzz78, zzz79, zzz80, zzz81, zzz82, zzz83, zzz873, bg, bh)
new_intersectFM_C2IntersectFM_C11(zzz883, zzz884, zzz885, zzz886, zzz887, zzz888, zzz889, zzz890, GT, zzz892, zzz893, Branch(zzz8940, zzz8941, zzz8942, zzz8943, zzz8944), zzz895, be, bf) → new_intersectFM_C2IntersectFM_C11(zzz883, zzz884, zzz885, zzz886, zzz887, zzz888, zzz889, zzz890, zzz8940, zzz8941, zzz8942, zzz8943, zzz8944, be, bf)
new_intersectFM_C2IntersectFM_C19(zzz854, zzz855, zzz856, zzz857, zzz858, zzz859, zzz860, zzz861, EmptyFM, ba, bb) → new_intersectFM_C(new_intersectFM_C2Lts0(zzz854, zzz855, zzz856, zzz857, ba), zzz860, ba)
new_intersectFM_C2IntersectFM_C13(zzz76, zzz77, zzz78, zzz79, zzz80, zzz81, zzz82, zzz83, zzz871, zzz872, zzz873, zzz874, bg, bh) → new_intersectFM_C2IntersectFM_C12(zzz76, zzz77, zzz78, zzz79, zzz80, zzz81, zzz82, zzz83, zzz871, zzz872, zzz873, zzz874, bg, bh)
new_intersectFM_C2IntersectFM_C111(zzz883, zzz884, zzz885, zzz886, zzz887, zzz888, zzz889, zzz890, Branch(zzz8940, zzz8941, zzz8942, zzz8943, zzz8944), be, bf) → new_intersectFM_C2IntersectFM_C11(zzz883, zzz884, zzz885, zzz886, zzz887, zzz888, zzz889, zzz890, zzz8940, zzz8941, zzz8942, zzz8943, zzz8944, be, bf)
new_intersectFM_C(Branch(GT, zzz31, zzz32, Branch(GT, zzz331, zzz332, Branch(GT, zzz3331, zzz3332, Branch(GT, zzz33331, zzz33332, EmptyFM, zzz33334), zzz3334), zzz334), zzz34), Branch(EQ, zzz41, zzz42, zzz43, zzz44), h) → new_intersectFM_C(new_intersectFM_C2Gts(zzz31, zzz32, Branch(GT, zzz331, zzz332, Branch(GT, zzz3331, zzz3332, Branch(GT, zzz33331, zzz33332, EmptyFM, zzz33334), zzz3334), zzz334), zzz34, h), zzz44, h)
new_intersectFM_C2IntersectFM_C17(zzz2223, zzz2224, zzz2225, zzz2226, zzz2227, zzz2228, zzz2229, zzz2230, LT, zzz2232, zzz2233, zzz2234, EmptyFM, ce, cf) → new_intersectFM_C(new_intersectFM_C2Gts3(Branch(EQ, zzz2223, zzz2224, zzz2225, zzz2226), ce), zzz2230, ce)
new_intersectFM_C(Branch(GT, zzz31, zzz32, Branch(GT, zzz331, zzz332, Branch(GT, zzz3331, zzz3332, Branch(LT, zzz33331, zzz33332, zzz33333, zzz33334), zzz3334), zzz334), zzz34), Branch(EQ, zzz41, zzz42, zzz43, zzz44), h) → new_intersectFM_C2IntersectFM_C12(zzz31, zzz32, Branch(GT, zzz331, zzz332, Branch(GT, zzz3331, zzz3332, Branch(LT, zzz33331, zzz33332, zzz33333, zzz33334), zzz3334), zzz334), zzz34, zzz41, zzz42, zzz43, zzz44, zzz33331, zzz33332, zzz33333, zzz33334, h, h)
new_intersectFM_C(Branch(GT, zzz31, zzz32, EmptyFM, zzz34), Branch(EQ, zzz41, zzz42, zzz43, zzz44), h) → new_intersectFM_C(new_splitGT8(zzz31, zzz32, zzz34, h), zzz44, h)
new_intersectFM_C2IntersectFM_C10(zzz869, zzz870, zzz871, zzz872, zzz873, zzz874, zzz875, zzz876, EQ, zzz878, zzz879, EmptyFM, zzz881, bc, bd) → new_intersectFM_C(new_intersectFM_C2Gts1(zzz869, zzz870, zzz871, zzz872, bc), zzz876, bc)
new_intersectFM_C(Branch(GT, zzz31, zzz32, Branch(GT, zzz331, zzz332, Branch(GT, zzz3331, zzz3332, Branch(GT, zzz33331, zzz33332, Branch(LT, zzz333331, zzz333332, zzz333333, zzz333334), zzz33334), zzz3334), zzz334), zzz34), Branch(EQ, zzz41, zzz42, zzz43, zzz44), h) → new_intersectFM_C2IntersectFM_C13(zzz31, zzz32, Branch(GT, zzz331, zzz332, Branch(GT, zzz3331, zzz3332, Branch(GT, zzz33331, zzz33332, Branch(LT, zzz333331, zzz333332, zzz333333, zzz333334), zzz33334), zzz3334), zzz334), zzz34, zzz41, zzz42, zzz43, zzz44, zzz333331, zzz333332, zzz333333, zzz333334, h, h)
new_intersectFM_C2IntersectFM_C16(zzz2208, zzz2209, zzz2210, zzz2211, zzz2212, zzz2213, zzz2214, zzz2215, LT, zzz2217, zzz2218, zzz2219, EmptyFM, ca, cb) → new_intersectFM_C(new_intersectFM_C2Gts3(Branch(LT, zzz2208, zzz2209, zzz2210, zzz2211), ca), zzz2215, ca)
new_intersectFM_C(Branch(LT, zzz31, zzz32, zzz33, zzz34), Branch(LT, zzz41, zzz42, zzz43, zzz44), h) → new_intersectFM_C(new_splitLT3(zzz31, zzz32, zzz33, zzz34, h), zzz43, h)
new_intersectFM_C2IntersectFM_C14(zzz76, zzz77, zzz78, zzz79, zzz80, zzz81, zzz82, zzz83, zzz871, zzz872, zzz873, zzz874, bg, bh) → new_intersectFM_C(new_intersectFM_C2Gts(zzz76, zzz77, zzz78, zzz79, bg), zzz83, bg)
new_intersectFM_C(Branch(GT, zzz31, zzz32, Branch(GT, zzz331, zzz332, Branch(LT, zzz3331, zzz3332, zzz3333, zzz3334), zzz334), zzz34), Branch(EQ, zzz41, zzz42, zzz43, zzz44), h) → new_intersectFM_C2IntersectFM_C12(zzz31, zzz32, Branch(GT, zzz331, zzz332, Branch(LT, zzz3331, zzz3332, zzz3333, zzz3334), zzz334), zzz34, zzz41, zzz42, zzz43, zzz44, zzz3331, zzz3332, zzz3333, zzz3334, h, h)
new_intersectFM_C2IntersectFM_C17(zzz2223, zzz2224, zzz2225, zzz2226, zzz2227, zzz2228, zzz2229, zzz2230, LT, zzz2232, zzz2233, zzz2234, Branch(zzz22350, zzz22351, zzz22352, zzz22353, zzz22354), ce, cf) → new_intersectFM_C2IntersectFM_C17(zzz2223, zzz2224, zzz2225, zzz2226, zzz2227, zzz2228, zzz2229, zzz2230, zzz22350, zzz22351, zzz22352, zzz22353, zzz22354, ce, cf)
new_intersectFM_C2IntersectFM_C12(zzz76, zzz77, zzz78, zzz79, zzz80, zzz81, zzz82, zzz83, zzz84, zzz85, zzz86, EmptyFM, bg, bh) → new_intersectFM_C(new_intersectFM_C2Lts(zzz76, zzz77, zzz78, zzz79, bg), zzz82, bg)
new_intersectFM_C2IntersectFM_C16(zzz2208, zzz2209, zzz2210, zzz2211, zzz2212, zzz2213, zzz2214, zzz2215, LT, zzz2217, zzz2218, zzz2219, EmptyFM, ca, cb) → new_intersectFM_C(new_intersectFM_C2Lts3(Branch(LT, zzz2208, zzz2209, zzz2210, zzz2211), ca), zzz2214, ca)
new_intersectFM_C2IntersectFM_C112(zzz76, zzz77, zzz78, zzz79, zzz80, zzz81, zzz82, zzz83, EmptyFM, bg, bh) → new_intersectFM_C(new_intersectFM_C2Gts(zzz76, zzz77, zzz78, zzz79, bg), zzz83, bg)
new_intersectFM_C(Branch(EQ, zzz31, zzz32, EmptyFM, zzz34), Branch(LT, zzz41, zzz42, zzz43, zzz44), h) → new_intersectFM_C(new_splitLT4(zzz31, zzz32, zzz34, h), zzz43, h)
new_intersectFM_C2IntersectFM_C110(zzz869, zzz870, zzz871, zzz872, zzz873, zzz874, zzz875, zzz876, EmptyFM, bc, bd) → new_intersectFM_C(new_intersectFM_C2Lts1(zzz869, zzz870, zzz871, zzz872, bc), zzz875, bc)
new_intersectFM_C2IntersectFM_C113(zzz2208, zzz2209, zzz2210, zzz2211, zzz2212, zzz2213, zzz2214, zzz2215, Branch(zzz22200, zzz22201, zzz22202, zzz22203, zzz22204), ca, cb) → new_intersectFM_C2IntersectFM_C16(zzz2208, zzz2209, zzz2210, zzz2211, zzz2212, zzz2213, zzz2214, zzz2215, zzz22200, zzz22201, zzz22202, zzz22203, zzz22204, ca, cb)
new_intersectFM_C2IntersectFM_C16(zzz2208, zzz2209, zzz2210, zzz2211, zzz2212, zzz2213, zzz2214, zzz2215, EQ, zzz2217, zzz2218, zzz2219, zzz2220, ca, cb) → new_intersectFM_C2IntersectFM_C113(zzz2208, zzz2209, zzz2210, zzz2211, zzz2212, zzz2213, zzz2214, zzz2215, zzz2220, ca, cb)
new_intersectFM_C2IntersectFM_C12(zzz76, zzz77, zzz78, zzz79, zzz80, zzz81, zzz82, zzz83, zzz84, zzz85, zzz86, Branch(EQ, zzz871, zzz872, zzz873, zzz874), bg, bh) → new_intersectFM_C(new_intersectFM_C2Gts(zzz76, zzz77, zzz78, zzz79, bg), zzz83, bg)
new_intersectFM_C(Branch(GT, zzz31, zzz32, Branch(GT, zzz331, zzz332, Branch(GT, zzz3331, zzz3332, Branch(GT, zzz33331, zzz33332, Branch(EQ, zzz333331, zzz333332, zzz333333, zzz333334), zzz33334), zzz3334), zzz334), zzz34), Branch(EQ, zzz41, zzz42, zzz43, zzz44), h) → new_intersectFM_C2IntersectFM_C14(zzz31, zzz32, Branch(GT, zzz331, zzz332, Branch(GT, zzz3331, zzz3332, Branch(GT, zzz33331, zzz33332, Branch(EQ, zzz333331, zzz333332, zzz333333, zzz333334), zzz33334), zzz3334), zzz334), zzz34, zzz41, zzz42, zzz43, zzz44, zzz333331, zzz333332, zzz333333, zzz333334, h, h)
new_intersectFM_C2IntersectFM_C11(zzz883, zzz884, zzz885, zzz886, zzz887, zzz888, zzz889, zzz890, GT, zzz892, zzz893, EmptyFM, zzz895, be, bf) → new_intersectFM_C(new_intersectFM_C2Lts2(zzz883, zzz884, zzz885, zzz886, be), zzz889, be)
new_intersectFM_C(Branch(GT, zzz31, zzz32, Branch(GT, zzz331, zzz332, Branch(GT, zzz3331, zzz3332, EmptyFM, zzz3334), zzz334), zzz34), Branch(EQ, zzz41, zzz42, zzz43, zzz44), h) → new_intersectFM_C(new_splitLT9(zzz331, zzz332, Branch(GT, zzz3331, zzz3332, EmptyFM, zzz3334), zzz334, h), zzz43, h)
new_intersectFM_C(Branch(GT, zzz31, zzz32, Branch(LT, zzz331, zzz332, zzz333, zzz334), zzz34), Branch(EQ, zzz41, zzz42, zzz43, zzz44), h) → new_intersectFM_C2IntersectFM_C12(zzz31, zzz32, Branch(LT, zzz331, zzz332, zzz333, zzz334), zzz34, zzz41, zzz42, zzz43, zzz44, zzz331, zzz332, zzz333, zzz334, h, h)
new_intersectFM_C(Branch(GT, zzz31, zzz32, Branch(zzz330, zzz331, zzz332, zzz333, zzz334), zzz34), Branch(LT, zzz41, zzz42, zzz43, zzz44), h) → new_intersectFM_C2IntersectFM_C10(zzz31, zzz32, Branch(zzz330, zzz331, zzz332, zzz333, zzz334), zzz34, zzz41, zzz42, zzz43, zzz44, zzz330, zzz331, zzz332, zzz333, zzz334, h, h)
new_intersectFM_C(Branch(GT, zzz31, zzz32, Branch(GT, zzz331, zzz332, Branch(GT, zzz3331, zzz3332, Branch(EQ, zzz33331, zzz33332, zzz33333, zzz33334), zzz3334), zzz334), zzz34), Branch(EQ, zzz41, zzz42, zzz43, zzz44), h) → new_intersectFM_C(new_intersectFM_C2Lts(zzz31, zzz32, Branch(GT, zzz331, zzz332, Branch(GT, zzz3331, zzz3332, Branch(EQ, zzz33331, zzz33332, zzz33333, zzz33334), zzz3334), zzz334), zzz34, h), zzz43, h)
new_intersectFM_C2IntersectFM_C113(zzz2208, zzz2209, zzz2210, zzz2211, zzz2212, zzz2213, zzz2214, zzz2215, EmptyFM, ca, cb) → new_intersectFM_C(new_intersectFM_C2Lts3(Branch(LT, zzz2208, zzz2209, zzz2210, zzz2211), ca), zzz2214, ca)
new_intersectFM_C(Branch(GT, zzz31, zzz32, Branch(GT, zzz331, zzz332, Branch(GT, zzz3331, zzz3332, Branch(GT, zzz33331, zzz33332, Branch(GT, zzz333331, zzz333332, zzz333333, zzz333334), zzz33334), zzz3334), zzz334), zzz34), Branch(EQ, zzz41, zzz42, zzz43, zzz44), h) → new_intersectFM_C2IntersectFM_C15(zzz31, zzz32, Branch(GT, zzz331, zzz332, Branch(GT, zzz3331, zzz3332, Branch(GT, zzz33331, zzz33332, Branch(GT, zzz333331, zzz333332, zzz333333, zzz333334), zzz33334), zzz3334), zzz334), zzz34, zzz41, zzz42, zzz43, zzz44, zzz333331, zzz333332, zzz333333, zzz333334, h, h)
new_intersectFM_C2IntersectFM_C12(zzz76, zzz77, zzz78, zzz79, zzz80, zzz81, zzz82, zzz83, zzz84, zzz85, zzz86, Branch(LT, zzz871, zzz872, zzz873, zzz874), bg, bh) → new_intersectFM_C2IntersectFM_C12(zzz76, zzz77, zzz78, zzz79, zzz80, zzz81, zzz82, zzz83, zzz871, zzz872, zzz873, zzz874, bg, bh)
new_intersectFM_C2IntersectFM_C17(zzz2223, zzz2224, zzz2225, zzz2226, zzz2227, zzz2228, zzz2229, zzz2230, GT, zzz2232, zzz2233, zzz2234, zzz2235, ce, cf) → new_intersectFM_C2IntersectFM_C18(Branch(EQ, zzz2223, zzz2224, zzz2225, zzz2226), zzz2227, zzz2228, zzz2229, zzz2230, zzz2232, zzz2233, zzz2234, zzz2235, ce, cf)
new_intersectFM_C(Branch(EQ, zzz31, zzz32, Branch(zzz330, zzz331, zzz332, zzz333, zzz334), zzz34), Branch(LT, zzz41, zzz42, zzz43, zzz44), h) → new_intersectFM_C2IntersectFM_C1(zzz31, zzz32, Branch(zzz330, zzz331, zzz332, zzz333, zzz334), zzz34, zzz41, zzz42, zzz43, zzz44, zzz330, zzz331, zzz332, zzz333, zzz334, h, h)
new_intersectFM_C2IntersectFM_C110(zzz869, zzz870, zzz871, zzz872, zzz873, zzz874, zzz875, zzz876, Branch(zzz8800, zzz8801, zzz8802, zzz8803, zzz8804), bc, bd) → new_intersectFM_C2IntersectFM_C10(zzz869, zzz870, zzz871, zzz872, zzz873, zzz874, zzz875, zzz876, zzz8800, zzz8801, zzz8802, zzz8803, zzz8804, bc, bd)
new_intersectFM_C2IntersectFM_C114(zzz2223, zzz2224, zzz2225, zzz2226, zzz2227, zzz2228, zzz2229, zzz2230, Branch(zzz22350, zzz22351, zzz22352, zzz22353, zzz22354), ce, cf) → new_intersectFM_C2IntersectFM_C17(zzz2223, zzz2224, zzz2225, zzz2226, zzz2227, zzz2228, zzz2229, zzz2230, zzz22350, zzz22351, zzz22352, zzz22353, zzz22354, ce, cf)
new_intersectFM_C2IntersectFM_C11(zzz883, zzz884, zzz885, zzz886, zzz887, zzz888, zzz889, zzz890, EQ, zzz892, zzz893, zzz894, zzz895, be, bf) → new_intersectFM_C(new_intersectFM_C2Lts2(zzz883, zzz884, zzz885, zzz886, be), zzz889, be)
new_intersectFM_C(Branch(EQ, zzz31, zzz32, zzz33, Branch(zzz340, zzz341, zzz342, zzz343, zzz344)), Branch(GT, zzz41, zzz42, zzz43, zzz44), h) → new_intersectFM_C2IntersectFM_C17(zzz31, zzz32, zzz33, Branch(zzz340, zzz341, zzz342, zzz343, zzz344), zzz41, zzz42, zzz43, zzz44, zzz340, zzz341, zzz342, zzz343, zzz344, h, h)
new_intersectFM_C2IntersectFM_C112(zzz76, zzz77, zzz78, zzz79, zzz80, zzz81, zzz82, zzz83, EmptyFM, bg, bh) → new_intersectFM_C(new_intersectFM_C2Lts(zzz76, zzz77, zzz78, zzz79, bg), zzz82, bg)
new_intersectFM_C2IntersectFM_C10(zzz869, zzz870, zzz871, zzz872, zzz873, zzz874, zzz875, zzz876, GT, zzz878, zzz879, zzz880, zzz881, bc, bd) → new_intersectFM_C2IntersectFM_C110(zzz869, zzz870, zzz871, zzz872, zzz873, zzz874, zzz875, zzz876, zzz880, bc, bd)
new_intersectFM_C2IntersectFM_C110(zzz869, zzz870, zzz871, zzz872, zzz873, zzz874, zzz875, zzz876, EmptyFM, bc, bd) → new_intersectFM_C(new_intersectFM_C2Gts1(zzz869, zzz870, zzz871, zzz872, bc), zzz876, bc)
new_intersectFM_C(Branch(GT, zzz31, zzz32, EmptyFM, zzz34), Branch(LT, zzz41, zzz42, zzz43, zzz44), h) → new_intersectFM_C(new_splitGT5(zzz31, zzz32, zzz34, h), zzz44, h)
new_intersectFM_C2IntersectFM_C112(zzz76, zzz77, zzz78, zzz79, zzz80, zzz81, zzz82, zzz83, Branch(EQ, zzz871, zzz872, zzz873, zzz874), bg, bh) → new_intersectFM_C(new_intersectFM_C2Lts(zzz76, zzz77, zzz78, zzz79, bg), zzz82, bg)
new_intersectFM_C2IntersectFM_C114(zzz2223, zzz2224, zzz2225, zzz2226, zzz2227, zzz2228, zzz2229, zzz2230, EmptyFM, ce, cf) → new_intersectFM_C(new_intersectFM_C2Gts3(Branch(EQ, zzz2223, zzz2224, zzz2225, zzz2226), ce), zzz2230, ce)
new_intersectFM_C(Branch(GT, zzz31, zzz32, zzz33, zzz34), Branch(GT, zzz41, zzz42, zzz43, zzz44), h) → new_intersectFM_C2IntersectFM_C18(Branch(GT, zzz31, zzz32, zzz33, zzz34), zzz41, zzz42, zzz43, zzz44, zzz31, zzz32, zzz33, zzz34, h, h)
new_intersectFM_C(Branch(LT, zzz31, zzz32, zzz33, Branch(zzz340, zzz341, zzz342, zzz343, zzz344)), Branch(EQ, zzz41, zzz42, zzz43, zzz44), h) → new_intersectFM_C2IntersectFM_C11(zzz31, zzz32, zzz33, Branch(zzz340, zzz341, zzz342, zzz343, zzz344), zzz41, zzz42, zzz43, zzz44, zzz340, zzz341, zzz342, zzz343, zzz344, h, h)
new_intersectFM_C2IntersectFM_C1(zzz854, zzz855, zzz856, zzz857, zzz858, zzz859, zzz860, zzz861, EQ, zzz863, zzz864, Branch(zzz8650, zzz8651, zzz8652, zzz8653, zzz8654), zzz866, ba, bb) → new_intersectFM_C2IntersectFM_C1(zzz854, zzz855, zzz856, zzz857, zzz858, zzz859, zzz860, zzz861, zzz8650, zzz8651, zzz8652, zzz8653, zzz8654, ba, bb)
new_intersectFM_C2IntersectFM_C11(zzz883, zzz884, zzz885, zzz886, zzz887, zzz888, zzz889, zzz890, GT, zzz892, zzz893, EmptyFM, zzz895, be, bf) → new_intersectFM_C(new_intersectFM_C2Gts2(zzz883, zzz884, zzz885, zzz886, be), zzz890, be)
new_intersectFM_C2IntersectFM_C111(zzz883, zzz884, zzz885, zzz886, zzz887, zzz888, zzz889, zzz890, EmptyFM, be, bf) → new_intersectFM_C(new_intersectFM_C2Gts2(zzz883, zzz884, zzz885, zzz886, be), zzz890, be)
new_intersectFM_C2IntersectFM_C12(zzz76, zzz77, zzz78, zzz79, zzz80, zzz81, zzz82, zzz83, zzz84, zzz85, zzz86, EmptyFM, bg, bh) → new_intersectFM_C(new_intersectFM_C2Gts(zzz76, zzz77, zzz78, zzz79, bg), zzz83, bg)
new_intersectFM_C2IntersectFM_C112(zzz76, zzz77, zzz78, zzz79, zzz80, zzz81, zzz82, zzz83, Branch(EQ, zzz871, zzz872, zzz873, zzz874), bg, bh) → new_intersectFM_C(new_intersectFM_C2Gts(zzz76, zzz77, zzz78, zzz79, bg), zzz83, bg)
new_intersectFM_C2IntersectFM_C18(zzz2129, zzz2130, zzz2131, zzz2132, zzz2133, zzz2134, zzz2135, zzz2136, zzz2137, cc, cd) → new_intersectFM_C(new_intersectFM_C2Lts3(zzz2129, cc), zzz2132, cc)
new_intersectFM_C2IntersectFM_C1(zzz854, zzz855, zzz856, zzz857, zzz858, zzz859, zzz860, zzz861, EQ, zzz863, zzz864, EmptyFM, zzz866, ba, bb) → new_intersectFM_C(new_intersectFM_C2Gts0(zzz854, zzz855, zzz856, zzz857, ba), zzz861, ba)
new_intersectFM_C(Branch(GT, zzz31, zzz32, Branch(GT, zzz331, zzz332, Branch(GT, zzz3331, zzz3332, Branch(GT, zzz33331, zzz33332, EmptyFM, zzz33334), zzz3334), zzz334), zzz34), Branch(EQ, zzz41, zzz42, zzz43, zzz44), h) → new_intersectFM_C(new_intersectFM_C2Lts(zzz31, zzz32, Branch(GT, zzz331, zzz332, Branch(GT, zzz3331, zzz3332, Branch(GT, zzz33331, zzz33332, EmptyFM, zzz33334), zzz3334), zzz334), zzz34, h), zzz43, h)
new_intersectFM_C2IntersectFM_C17(zzz2223, zzz2224, zzz2225, zzz2226, zzz2227, zzz2228, zzz2229, zzz2230, EQ, zzz2232, zzz2233, zzz2234, zzz2235, ce, cf) → new_intersectFM_C2IntersectFM_C114(zzz2223, zzz2224, zzz2225, zzz2226, zzz2227, zzz2228, zzz2229, zzz2230, zzz2235, ce, cf)
new_intersectFM_C2IntersectFM_C11(zzz883, zzz884, zzz885, zzz886, zzz887, zzz888, zzz889, zzz890, LT, zzz892, zzz893, zzz894, zzz895, be, bf) → new_intersectFM_C2IntersectFM_C111(zzz883, zzz884, zzz885, zzz886, zzz887, zzz888, zzz889, zzz890, zzz895, be, bf)
new_intersectFM_C2IntersectFM_C1(zzz854, zzz855, zzz856, zzz857, zzz858, zzz859, zzz860, zzz861, LT, zzz863, zzz864, zzz865, zzz866, ba, bb) → new_intersectFM_C(new_intersectFM_C2Lts0(zzz854, zzz855, zzz856, zzz857, ba), zzz860, ba)
new_intersectFM_C2IntersectFM_C1(zzz854, zzz855, zzz856, zzz857, zzz858, zzz859, zzz860, zzz861, LT, zzz863, zzz864, zzz865, zzz866, ba, bb) → new_intersectFM_C(new_intersectFM_C2Gts0(zzz854, zzz855, zzz856, zzz857, ba), zzz861, ba)
new_intersectFM_C(Branch(GT, zzz31, zzz32, EmptyFM, zzz34), Branch(LT, zzz41, zzz42, zzz43, zzz44), h) → new_intersectFM_C(new_splitLT5(zzz31, zzz32, zzz34, h), zzz43, h)
new_intersectFM_C2IntersectFM_C19(zzz854, zzz855, zzz856, zzz857, zzz858, zzz859, zzz860, zzz861, Branch(zzz8650, zzz8651, zzz8652, zzz8653, zzz8654), ba, bb) → new_intersectFM_C2IntersectFM_C1(zzz854, zzz855, zzz856, zzz857, zzz858, zzz859, zzz860, zzz861, zzz8650, zzz8651, zzz8652, zzz8653, zzz8654, ba, bb)
new_intersectFM_C2IntersectFM_C113(zzz2208, zzz2209, zzz2210, zzz2211, zzz2212, zzz2213, zzz2214, zzz2215, EmptyFM, ca, cb) → new_intersectFM_C(new_intersectFM_C2Gts3(Branch(LT, zzz2208, zzz2209, zzz2210, zzz2211), ca), zzz2215, ca)
new_intersectFM_C2IntersectFM_C1(zzz854, zzz855, zzz856, zzz857, zzz858, zzz859, zzz860, zzz861, EQ, zzz863, zzz864, EmptyFM, zzz866, ba, bb) → new_intersectFM_C(new_intersectFM_C2Lts0(zzz854, zzz855, zzz856, zzz857, ba), zzz860, ba)
new_intersectFM_C2IntersectFM_C16(zzz2208, zzz2209, zzz2210, zzz2211, zzz2212, zzz2213, zzz2214, zzz2215, LT, zzz2217, zzz2218, zzz2219, Branch(zzz22200, zzz22201, zzz22202, zzz22203, zzz22204), ca, cb) → new_intersectFM_C2IntersectFM_C16(zzz2208, zzz2209, zzz2210, zzz2211, zzz2212, zzz2213, zzz2214, zzz2215, zzz22200, zzz22201, zzz22202, zzz22203, zzz22204, ca, cb)
new_intersectFM_C(Branch(LT, zzz31, zzz32, zzz33, zzz34), Branch(LT, zzz41, zzz42, zzz43, zzz44), h) → new_intersectFM_C(new_splitGT3(zzz31, zzz32, zzz33, zzz34, h), zzz44, h)
new_intersectFM_C(Branch(GT, zzz31, zzz32, Branch(GT, zzz331, zzz332, EmptyFM, zzz334), zzz34), Branch(EQ, zzz41, zzz42, zzz43, zzz44), h) → new_intersectFM_C(new_mkVBalBranch3(zzz31, new_splitGT8(zzz331, zzz332, zzz334, h), zzz34, h), zzz44, h)
new_intersectFM_C(Branch(GT, zzz31, zzz32, EmptyFM, zzz34), Branch(EQ, zzz41, zzz42, zzz43, zzz44), h) → new_intersectFM_C(new_splitLT8(zzz31, zzz32, zzz34, h), zzz43, h)
new_intersectFM_C(Branch(GT, zzz31, zzz32, Branch(GT, zzz331, zzz332, EmptyFM, zzz334), zzz34), Branch(EQ, zzz41, zzz42, zzz43, zzz44), h) → new_intersectFM_C(new_splitLT8(zzz331, zzz332, zzz334, h), zzz43, h)
new_intersectFM_C2IntersectFM_C12(zzz76, zzz77, zzz78, zzz79, zzz80, zzz81, zzz82, zzz83, zzz84, zzz85, zzz86, Branch(GT, zzz871, zzz872, zzz873, zzz874), bg, bh) → new_intersectFM_C2IntersectFM_C112(zzz76, zzz77, zzz78, zzz79, zzz80, zzz81, zzz82, zzz83, zzz873, bg, bh)
new_intersectFM_C2IntersectFM_C15(zzz76, zzz77, zzz78, zzz79, zzz80, zzz81, zzz82, zzz83, zzz871, zzz872, zzz873, zzz874, bg, bh) → new_intersectFM_C2IntersectFM_C112(zzz76, zzz77, zzz78, zzz79, zzz80, zzz81, zzz82, zzz83, zzz873, bg, bh)
new_intersectFM_C(Branch(GT, zzz31, zzz32, Branch(EQ, zzz331, zzz332, zzz333, zzz334), zzz34), Branch(EQ, zzz41, zzz42, zzz43, zzz44), h) → new_intersectFM_C(new_mkVBalBranch3(zzz31, new_splitGT7(zzz331, zzz332, zzz333, zzz334, h), zzz34, h), zzz44, h)
new_intersectFM_C2IntersectFM_C12(zzz76, zzz77, zzz78, zzz79, zzz80, zzz81, zzz82, zzz83, zzz84, zzz85, zzz86, Branch(EQ, zzz871, zzz872, zzz873, zzz874), bg, bh) → new_intersectFM_C(new_intersectFM_C2Lts(zzz76, zzz77, zzz78, zzz79, bg), zzz82, bg)
new_intersectFM_C2IntersectFM_C1(zzz854, zzz855, zzz856, zzz857, zzz858, zzz859, zzz860, zzz861, GT, zzz863, zzz864, zzz865, zzz866, ba, bb) → new_intersectFM_C2IntersectFM_C19(zzz854, zzz855, zzz856, zzz857, zzz858, zzz859, zzz860, zzz861, zzz865, ba, bb)

The TRS R consists of the following rules:

new_mkVBalBranch3MkVBalBranch133(zzz340, zzz341, zzz34200, zzz343, zzz344, zzz510, zzz511, zzz513, zzz514, zzz31, Succ(zzz1240), h) → new_mkBalBranch(zzz510, zzz511, zzz513, new_mkVBalBranch4(zzz31, zzz514, Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), h), ty_Ordering, h)
new_mkBalBranch6MkBalBranch111(zzz2934, zzz21270, zzz21271, zzz21272, zzz21273, zzz21274, zzz2930, zzz2931, zzz226200, Succ(zzz22700), da, db) → new_mkBalBranch6MkBalBranch1113(zzz2934, zzz21270, zzz21271, zzz21272, zzz21273, zzz21274, zzz2930, zzz2931, zzz226200, zzz22700, da, db)
new_mkVBalBranch3MkVBalBranch285(zzz340, zzz341, zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, h) → new_mkBalBranch(zzz510, zzz511, zzz513, new_mkVBalBranch4(zzz31, zzz514, Branch(zzz340, zzz341, Pos(Zero), zzz343, zzz344), h), ty_Ordering, h)
new_mkVBalBranch3MkVBalBranch162(zzz1986, zzz1987, zzz1988, zzz1989, zzz1990, zzz1991, zzz1992, zzz1993, zzz1994, zzz1995, zzz1996, Succ(zzz19970), Zero, dh) → new_mkVBalBranch3MkVBalBranch142(zzz1986, zzz1987, zzz1988, zzz1989, zzz1990, zzz1991, zzz1992, zzz1993, zzz1994, zzz1995, zzz1996, dh)
new_primPlusInt(Pos(zzz22720), zzz2268, zzz2269, zzz2266, ec, ed) → new_primPlusInt0(zzz22720, new_sizeFM(zzz2269, ec, ed))
new_mkBalBranch6MkBalBranch48(zzz2934, zzz2127, zzz2930, zzz2931, Zero, da, db) → new_mkBalBranch6MkBalBranch40(zzz2934, zzz2127, zzz2930, zzz2931, da, db)
new_splitLT12(EmptyFM, ba) → new_splitLT42(ba)
new_mkVBalBranch3MkVBalBranch281(zzz340, zzz341, Neg(Succ(Zero)), zzz343, zzz344, zzz510, zzz511, Zero, zzz513, zzz514, zzz31, Zero, h) → new_mkVBalBranch3MkVBalBranch157(zzz340, zzz341, Zero, zzz343, zzz344, zzz510, zzz511, zzz513, zzz514, zzz31, new_primMulNat1(Zero), h)
new_mkBalBranch6MkBalBranch014(zzz29340, zzz29341, zzz29342, zzz29343, zzz29344, zzz2127, zzz2930, zzz2931, Zero, Zero, da, db) → new_mkBalBranch6MkBalBranch012(zzz29340, zzz29341, zzz29342, zzz29343, zzz29344, zzz2127, zzz2930, zzz2931, da, db)
new_splitLT14(Branch(LT, zzz21291, zzz21292, zzz21293, zzz21294), cc) → new_mkVBalBranch2(zzz21291, zzz21293, new_splitLT14(zzz21294, cc), cc)
new_mkVBalBranch3MkVBalBranch275(zzz958, zzz959, zzz960, zzz961, zzz962, zzz963, zzz964, zzz965, zzz966, zzz967, zzz968, Zero, Zero, fa) → new_mkVBalBranch3MkVBalBranch276(zzz958, zzz959, zzz960, zzz961, zzz962, zzz963, zzz964, zzz965, zzz966, zzz967, zzz968, fa)
new_addToFM_C2(EmptyFM, zzz31, h) → Branch(LT, zzz31, Pos(Succ(Zero)), new_emptyFM(h), new_emptyFM(h))
new_mkVBalBranch3MkVBalBranch255(zzz537, zzz538, zzz539, zzz540, zzz541, zzz542, zzz543, zzz544, zzz545, zzz546, zzz547, Succ(zzz5480), Zero, dg) → new_mkVBalBranch3MkVBalBranch256(zzz537, zzz538, zzz539, zzz540, zzz541, zzz542, zzz543, zzz544, zzz545, zzz546, zzz547, dg)
new_mkBalBranch6MkBalBranch117(zzz2934, zzz21270, zzz21271, zzz21272, zzz21273, zzz21274, zzz2930, zzz2931, Zero, da, db) → new_mkBalBranch6MkBalBranch112(zzz2934, zzz21270, zzz21271, zzz21272, zzz21273, zzz21274, zzz2930, zzz2931, da, db)
new_mkVBalBranch3MkVBalBranch253(zzz929, zzz930, zzz931, zzz932, zzz933, zzz934, zzz935, zzz936, zzz937, zzz938, zzz939, dc) → new_mkVBalBranch3MkVBalBranch131(zzz929, zzz930, zzz931, zzz932, zzz933, zzz934, zzz935, zzz936, zzz937, zzz938, zzz939, new_primMulNat1(zzz931), dc)
new_mkVBalBranch3MkVBalBranch167(zzz340, zzz341, zzz34200, zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, Zero, h) → new_mkVBalBranch3MkVBalBranch160(zzz340, zzz341, zzz34200, zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, h)
new_mkVBalBranch3MkVBalBranch280(zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, zzz1125, zzz1126, zzz1127, zzz1128, zzz1129, Zero, Succ(zzz11310), ff) → new_mkVBalBranch3MkVBalBranch257(zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, zzz1125, zzz1126, zzz1127, zzz1128, zzz1129, ff)
new_splitLT16(h) → new_splitLT42(h)
new_mkVBalBranch3MkVBalBranch258(zzz340, zzz341, zzz3420, zzz343, zzz344, zzz520, zzz521, zzz52200, zzz523, zzz524, zzz31, h) → new_mkBalBranch(zzz340, zzz341, new_mkVBalBranch3(zzz31, Branch(zzz520, zzz521, Neg(Succ(zzz52200)), zzz523, zzz524), zzz343, h), zzz344, ty_Ordering, h)
new_splitGT12(Branch(LT, zzz8561, zzz8562, zzz8563, zzz8564), ba) → new_splitGT210(zzz8561, zzz8562, zzz8563, zzz8564, ba)
new_mkBalBranch6MkBalBranch310(zzz2934, zzz2127, zzz2930, zzz2931, Pos(Zero), Neg(zzz22450), da, db) → new_mkBalBranch6MkBalBranch315(zzz2934, zzz2127, zzz2930, zzz2931, new_primMulNat(zzz22450), da, db)
new_addToFM_C2(Branch(GT, zzz3171, zzz3172, zzz3173, zzz3174), zzz31, h) → new_mkBalBranch(GT, zzz3171, new_addToFM_C2(zzz3173, zzz31, h), zzz3174, ty_Ordering, h)
new_mkVBalBranch3MkVBalBranch149(zzz2050, zzz2051, zzz2052, zzz2053, zzz2054, zzz2055, zzz2056, zzz2057, zzz2058, zzz2059, zzz2060, Zero, Zero, ef) → new_mkVBalBranch3MkVBalBranch150(zzz2050, zzz2051, zzz2052, zzz2053, zzz2054, zzz2055, zzz2056, zzz2057, zzz2058, zzz2059, zzz2060, ef)
new_mkVBalBranch3MkVBalBranch278(zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, zzz1125, zzz1126, zzz1127, zzz1128, zzz1129, ff) → new_mkVBalBranch3MkVBalBranch159(zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, zzz1125, zzz1126, zzz1127, zzz1128, zzz1129, new_primMulNat1(zzz1121), ff)
new_mkVBalBranch3MkVBalBranch277(zzz1133, zzz1134, zzz1135, zzz1136, zzz1137, zzz1138, zzz1139, zzz1140, zzz1141, zzz1142, Succ(zzz11430), Succ(zzz11440), fd) → new_mkVBalBranch3MkVBalBranch277(zzz1133, zzz1134, zzz1135, zzz1136, zzz1137, zzz1138, zzz1139, zzz1140, zzz1141, zzz1142, zzz11430, zzz11440, fd)
new_mkVBalBranch3MkVBalBranch145(zzz3170, zzz3171, zzz317200, zzz3173, zzz3174, zzz330, zzz331, zzz333, zzz334, zzz31, Zero, h) → new_mkBranch(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))), LT, zzz31, Branch(zzz330, zzz331, Pos(Zero), zzz333, zzz334), Branch(zzz3170, zzz3171, Neg(Succ(zzz317200)), zzz3173, zzz3174), ty_Ordering, h)
new_mkVBalBranch3MkVBalBranch143(zzz818, zzz819, zzz820, zzz821, zzz822, zzz823, zzz824, zzz825, zzz826, zzz827, Zero, eb) → new_mkVBalBranch3MkVBalBranch144(zzz818, zzz819, zzz820, zzz821, zzz822, zzz823, zzz824, Zero, zzz825, zzz826, zzz827, Succ(Zero), Zero, eb)
new_mkVBalBranch3MkVBalBranch255(zzz537, zzz538, zzz539, zzz540, zzz541, zzz542, zzz543, zzz544, zzz545, zzz546, zzz547, Zero, Zero, dg) → new_mkVBalBranch3MkVBalBranch256(zzz537, zzz538, zzz539, zzz540, zzz541, zzz542, zzz543, zzz544, zzz545, zzz546, zzz547, dg)
new_mkVBalBranch3MkVBalBranch288(zzz340, zzz341, Pos(Succ(Succ(zzz342000))), zzz343, zzz344, zzz510, zzz511, Succ(zzz512000), zzz513, zzz514, zzz31, Zero, h) → new_mkVBalBranch3MkVBalBranch289(zzz340, zzz341, Succ(zzz342000), zzz343, zzz344, zzz510, zzz511, zzz512000, zzz513, zzz514, zzz31, zzz512000, zzz342000, h)
new_mkVBalBranch3MkVBalBranch154(zzz340, zzz341, zzz34200, zzz343, zzz344, zzz520, zzz521, zzz523, zzz524, zzz31, Zero, h) → new_mkBranch(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))), GT, zzz31, Branch(zzz520, zzz521, Pos(Zero), zzz523, zzz524), Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), ty_Ordering, h)
new_mkBalBranch6MkBalBranch1111(zzz2934, zzz21270, zzz21271, zzz21272, zzz21273, zzz21274, zzz2930, zzz2931, Succ(zzz22760), zzz226200, da, db) → new_mkBalBranch6MkBalBranch1113(zzz2934, zzz21270, zzz21271, zzz21272, zzz21273, zzz21274, zzz2930, zzz2931, zzz22760, zzz226200, da, db)
new_mkVBalBranch3MkVBalBranch148(zzz340, zzz341, zzz34200, zzz343, zzz344, zzz520, zzz521, zzz52200, zzz523, zzz524, zzz31, h) → new_mkBalBranch(zzz520, zzz521, zzz523, new_mkVBalBranch3(zzz31, zzz524, Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), h), ty_Ordering, h)
new_mkVBalBranch3MkVBalBranch136(zzz461, zzz462, zzz463, zzz464, zzz465, zzz466, zzz467, zzz468, zzz469, zzz470, zzz471, de) → new_mkVBalBranch3MkVBalBranch137(zzz461, zzz462, zzz463, zzz464, zzz465, zzz466, zzz467, zzz468, zzz469, zzz470, zzz471, new_primMulNat1(zzz463), de)
new_splitGT14(EmptyFM, be) → new_splitGT42(be)
new_splitGT28(zzz869, zzz870, zzz871, zzz872, bc) → new_mkVBalBranch3(zzz869, new_splitGT12(zzz871, bc), zzz872, bc)
new_mkVBalBranch3MkVBalBranch271(zzz473, zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, zzz481, zzz482, eh) → new_mkVBalBranch3MkVBalBranch164(zzz473, zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, zzz481, zzz482, new_primMulNat1(zzz475), eh)
new_mkVBalBranch3MkVBalBranch270(zzz473, zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, zzz481, zzz482, Succ(zzz4830), Succ(zzz4840), eh) → new_mkVBalBranch3MkVBalBranch270(zzz473, zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, zzz481, zzz482, zzz4830, zzz4840, eh)
new_mkVBalBranch3MkVBalBranch270(zzz473, zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, zzz481, zzz482, Zero, Zero, eh) → new_mkVBalBranch3MkVBalBranch271(zzz473, zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, zzz481, zzz482, eh)
new_mkVBalBranch3MkVBalBranch156(zzz958, zzz959, zzz960, zzz961, zzz962, zzz963, zzz964, zzz965, zzz966, zzz967, zzz968, Succ(zzz10180), fa) → new_mkVBalBranch3MkVBalBranch152(zzz958, zzz959, zzz960, zzz961, zzz962, zzz963, zzz964, zzz965, zzz966, zzz967, zzz968, Succ(zzz10180), Succ(zzz965), fa)
new_splitGT29(zzz883, zzz884, zzz885, zzz886, be) → new_splitGT14(zzz886, be)
new_mkVBalBranch3MkVBalBranch288(zzz340, zzz341, Neg(zzz3420), zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, Zero, h) → new_mkVBalBranch3MkVBalBranch284(zzz340, zzz341, zzz3420, zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, h)
new_primPlusNat3(zzz90, Succ(zzz910)) → Succ(Succ(new_primPlusNat2(zzz90, zzz910)))
new_addToFM_C2(Branch(EQ, zzz3171, zzz3172, zzz3173, zzz3174), zzz31, h) → new_mkBalBranch(EQ, zzz3171, new_addToFM_C2(zzz3173, zzz31, h), zzz3174, ty_Ordering, h)
new_splitLT14(EmptyFM, cc) → new_splitLT40(cc)
new_mkVBalBranch3MkVBalBranch288(zzz340, zzz341, Pos(Succ(Zero)), zzz343, zzz344, zzz510, zzz511, Succ(zzz512000), zzz513, zzz514, zzz31, Zero, h) → new_mkVBalBranch3MkVBalBranch283(zzz340, zzz341, Zero, zzz343, zzz344, zzz510, zzz511, zzz512000, zzz513, zzz514, zzz31, h)
new_splitGT24(zzz76, zzz77, zzz78, zzz79, bg) → new_mkVBalBranch3(zzz76, new_splitGT14(zzz78, bg), zzz79, bg)
new_mkVBalBranch3MkVBalBranch281(zzz340, zzz341, Neg(Succ(Succ(Zero))), zzz343, zzz344, zzz510, zzz511, Zero, zzz513, zzz514, zzz31, Succ(Succ(zzz6700)), h) → new_mkVBalBranch3MkVBalBranch263(zzz340, zzz341, Succ(Zero), zzz343, zzz344, zzz510, zzz511, zzz513, zzz514, zzz31, Zero, Succ(zzz6700), h)
new_addToFM_C4(EmptyFM, zzz31, h) → Branch(EQ, zzz31, Pos(Succ(Zero)), new_emptyFM(h), new_emptyFM(h))
new_mkVBalBranch3MkVBalBranch281(zzz340, zzz341, Neg(Zero), zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, Succ(zzz670), h) → new_mkVBalBranch3MkVBalBranch266(zzz340, zzz341, zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, h)
new_mkVBalBranch3MkVBalBranch246(zzz972, zzz973, zzz974, zzz975, zzz976, zzz977, zzz978, zzz979, zzz980, zzz981, zzz982, Zero, Zero, cg) → new_mkVBalBranch3MkVBalBranch247(zzz972, zzz973, zzz974, zzz975, zzz976, zzz977, zzz978, zzz979, zzz980, zzz981, zzz982, cg)
new_mkVBalBranch3MkVBalBranch247(zzz972, zzz973, zzz974, zzz975, zzz976, zzz977, zzz978, zzz979, zzz980, zzz981, zzz982, cg) → new_mkVBalBranch3MkVBalBranch141(zzz972, zzz973, zzz974, zzz975, zzz976, zzz977, zzz978, zzz979, zzz980, zzz981, zzz982, new_primMulNat1(zzz974), cg)
new_mkVBalBranch3MkVBalBranch131(zzz929, zzz930, zzz931, zzz932, zzz933, zzz934, zzz935, zzz936, zzz937, zzz938, zzz939, Succ(zzz10020), dc) → new_mkVBalBranch3MkVBalBranch132(zzz929, zzz930, zzz931, zzz932, zzz933, zzz934, zzz935, zzz936, zzz937, zzz938, zzz939, Succ(zzz10020), Succ(zzz936), dc)
new_mkVBalBranch3MkVBalBranch145(zzz3170, zzz3171, zzz317200, zzz3173, zzz3174, zzz330, zzz331, zzz333, zzz334, zzz31, Succ(zzz5350), h) → new_mkBalBranch(zzz330, zzz331, zzz333, new_mkVBalBranch2(zzz31, zzz334, Branch(zzz3170, zzz3171, Neg(Succ(zzz317200)), zzz3173, zzz3174), h), ty_Ordering, h)
new_primPlusNat2(Succ(zzz900), Succ(zzz9100)) → Succ(Succ(new_primPlusNat2(zzz900, zzz9100)))
new_mkVBalBranch3MkVBalBranch282(zzz461, zzz462, zzz463, zzz464, zzz465, zzz466, zzz467, zzz468, zzz469, zzz470, zzz471, de) → new_mkVBalBranch3MkVBalBranch165(zzz461, zzz462, zzz463, zzz464, zzz465, zzz466, zzz467, zzz468, zzz469, zzz470, zzz471, de)
new_mkVBalBranch3MkVBalBranch255(zzz537, zzz538, zzz539, zzz540, zzz541, zzz542, zzz543, zzz544, zzz545, zzz546, zzz547, Succ(zzz5480), Succ(zzz5490), dg) → new_mkVBalBranch3MkVBalBranch255(zzz537, zzz538, zzz539, zzz540, zzz541, zzz542, zzz543, zzz544, zzz545, zzz546, zzz547, zzz5480, zzz5490, dg)
new_splitLT27(zzz76, zzz77, zzz78, zzz79, bg) → new_splitLT23(zzz76, zzz77, zzz78, zzz79, bg)
new_mkVBalBranch3MkVBalBranch272(zzz340, zzz341, Neg(Zero), zzz343, zzz344, zzz520, zzz521, zzz52200, zzz523, zzz524, zzz31, Succ(zzz690), h) → new_mkVBalBranch3MkVBalBranch245(zzz340, zzz341, zzz343, zzz344, zzz520, zzz521, zzz52200, zzz523, zzz524, zzz31, h)
new_mkVBalBranch3MkVBalBranch281(zzz340, zzz341, Neg(Succ(Succ(zzz342000))), zzz343, zzz344, zzz510, zzz511, Zero, zzz513, zzz514, zzz31, Zero, h) → new_mkVBalBranch3MkVBalBranch249(zzz340, zzz341, zzz342000, zzz343, zzz344, zzz510, zzz511, zzz513, zzz514, zzz31, h)
new_mkBalBranch6MkBalBranch413(zzz2934, zzz2127, zzz2930, zzz2931, Zero, da, db) → new_mkBalBranch6MkBalBranch40(zzz2934, zzz2127, zzz2930, zzz2931, da, db)
new_primPlusNat1(Succ(zzz62000)) → Succ(Succ(new_primPlusNat1(zzz62000)))
new_mkBalBranch6MkBalBranch39(zzz2934, zzz2127, zzz2930, zzz2931, Succ(zzz2244000), Zero, da, db) → new_mkBalBranch6MkBalBranch33(zzz2934, zzz2127, zzz2930, zzz2931, da, db)
new_mkVBalBranch3MkVBalBranch269(zzz340, zzz341, Succ(zzz34200), zzz343, zzz344, zzz520, zzz521, zzz52200, zzz523, zzz524, zzz31, h) → new_mkVBalBranch3MkVBalBranch147(zzz340, zzz341, zzz34200, zzz343, zzz344, zzz520, zzz521, zzz52200, zzz523, zzz524, zzz31, new_primPlusNat2(new_primMulNat0(zzz34200), Succ(zzz34200)), h)
new_mkVBalBranch3MkVBalBranch149(zzz2050, zzz2051, zzz2052, zzz2053, zzz2054, zzz2055, zzz2056, zzz2057, zzz2058, zzz2059, zzz2060, Succ(zzz20610), Succ(zzz20620), ef) → new_mkVBalBranch3MkVBalBranch149(zzz2050, zzz2051, zzz2052, zzz2053, zzz2054, zzz2055, zzz2056, zzz2057, zzz2058, zzz2059, zzz2060, zzz20610, zzz20620, ef)
new_splitLT6(h) → new_splitLT41(h)
new_primMulNat2(Succ(zzz224700)) → new_primPlusNat2(new_primPlusNat2(Zero, Succ(zzz224700)), Succ(zzz224700))
new_mkBalBranch6MkBalBranch310(zzz2934, zzz2127, zzz2930, zzz2931, Neg(Zero), Pos(zzz22450), da, db) → new_mkBalBranch6MkBalBranch30(zzz2934, zzz2127, zzz2930, zzz2931, new_primMulNat(zzz22450), da, db)
new_mkBalBranch6MkBalBranch412(zzz2934, zzz2127, zzz2930, zzz2931, Succ(zzz2221000), Zero, da, db) → new_mkBalBranch6MkBalBranch49(zzz2934, zzz2127, zzz2930, zzz2931, da, db)
new_mkBalBranch6MkBalBranch014(zzz29340, zzz29341, zzz29342, zzz29343, zzz29344, zzz2127, zzz2930, zzz2931, Succ(zzz2246000), Succ(zzz226000), da, db) → new_mkBalBranch6MkBalBranch014(zzz29340, zzz29341, zzz29342, zzz29343, zzz29344, zzz2127, zzz2930, zzz2931, zzz2246000, zzz226000, da, db)
new_mkVBalBranch3MkVBalBranch132(zzz2033, zzz2034, zzz2035, zzz2036, zzz2037, zzz2038, zzz2039, zzz2040, zzz2041, zzz2042, zzz2043, Zero, Succ(zzz20450), fg) → new_mkBalBranch(zzz2038, zzz2039, zzz2041, new_mkVBalBranch3(zzz2043, zzz2042, Branch(zzz2033, zzz2034, Pos(Succ(zzz2035)), zzz2036, zzz2037), fg), ty_Ordering, fg)
new_mkVBalBranch3MkVBalBranch138(zzz1702, zzz1703, zzz1704, zzz1705, zzz1706, zzz1707, zzz1708, zzz1709, zzz1710, zzz1711, zzz1712, df) → new_mkBranch(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))), GT, zzz1712, Branch(zzz1707, zzz1708, Neg(Succ(zzz1709)), zzz1710, zzz1711), Branch(zzz1702, zzz1703, Neg(Succ(zzz1704)), zzz1705, zzz1706), ty_Ordering, df)
new_addToFM2(zzz34, zzz31, h) → new_addToFM_C4(zzz34, zzz31, h)
new_mkBalBranch6MkBalBranch113(zzz2934, zzz21270, zzz21271, zzz21272, zzz21273, zzz21274, zzz2930, zzz2931, Pos(Zero), Pos(zzz22630), da, db) → new_mkBalBranch6MkBalBranch116(zzz2934, zzz21270, zzz21271, zzz21272, zzz21273, zzz21274, zzz2930, zzz2931, new_primMulNat2(zzz22630), da, db)
new_mkVBalBranch3MkVBalBranch261(zzz3170, zzz3171, Pos(Succ(zzz317200)), zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, Succ(zzz4170), h) → new_mkVBalBranch3MkVBalBranch275(zzz3170, zzz3171, zzz317200, zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, zzz4170, zzz317200, h)
new_mkVBalBranch3MkVBalBranch143(zzz818, zzz819, zzz820, zzz821, zzz822, zzz823, zzz824, zzz825, zzz826, zzz827, Succ(zzz8960), eb) → new_mkVBalBranch3MkVBalBranch144(zzz818, zzz819, zzz820, zzz821, zzz822, zzz823, zzz824, Zero, zzz825, zzz826, zzz827, Succ(Zero), Succ(zzz8960), eb)
new_mkBalBranch6MkBalBranch411(zzz2934, zzz2127, zzz2930, zzz2931, Neg(Zero), Pos(zzz22060), da, db) → new_mkBalBranch6MkBalBranch416(zzz2934, zzz2127, zzz2930, zzz2931, new_primMulNat(zzz22060), da, db)
new_mkBalBranch6MkBalBranch36(zzz2934, zzz2127, zzz2930, zzz2931, Succ(zzz22530), zzz224400, da, db) → new_mkBalBranch6MkBalBranch39(zzz2934, zzz2127, zzz2930, zzz2931, zzz22530, zzz224400, da, db)
new_primPlusNat1(Zero) → Zero
new_mkBalBranch6MkBalBranch018(zzz29340, zzz29341, zzz29342, zzz29343, zzz29344, zzz2127, zzz2930, zzz2931, Succ(zzz22610), zzz224600, da, db) → new_mkBalBranch6MkBalBranch014(zzz29340, zzz29341, zzz29342, zzz29343, zzz29344, zzz2127, zzz2930, zzz2931, zzz22610, zzz224600, da, db)
new_mkVBalBranch3MkVBalBranch139(zzz3170, zzz3171, zzz317200, zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, Succ(zzz5620), h) → new_mkVBalBranch3MkVBalBranch140(zzz3170, zzz3171, zzz317200, zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, h)
new_mkVBalBranch3MkVBalBranch140(zzz3170, zzz3171, zzz317200, zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, h) → new_mkBalBranch(zzz330, zzz331, zzz333, new_mkVBalBranch2(zzz31, zzz334, Branch(zzz3170, zzz3171, Neg(Succ(zzz317200)), zzz3173, zzz3174), h), ty_Ordering, h)
new_splitGT210(zzz31, zzz32, zzz33, zzz34, h) → zzz34
new_splitGT14(Branch(GT, zzz8861, zzz8862, zzz8863, zzz8864), be) → new_splitGT26(zzz8861, zzz8862, zzz8863, zzz8864, be)
new_primPlusInt2(Pos(zzz21410), zzz2934, zzz2127, zzz2930, zzz2931, db, da) → new_primPlusInt0(zzz21410, new_sizeFM(zzz2934, da, db))
new_mkBalBranch6MkBalBranch111(zzz2934, zzz21270, zzz21271, zzz21272, zzz21273, zzz21274, zzz2930, zzz2931, zzz226200, Zero, da, db) → new_mkBalBranch6MkBalBranch1114(zzz2934, zzz21270, zzz21271, zzz21272, zzz21273, zzz21274, zzz2930, zzz2931, da, db)
new_mkVBalBranch2(zzz31, Branch(zzz330, zzz331, Neg(Succ(zzz33200)), zzz333, zzz334), Branch(zzz3170, zzz3171, zzz3172, zzz3173, zzz3174), h) → new_mkVBalBranch3MkVBalBranch262(zzz3170, zzz3171, zzz3172, zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, new_primPlusNat2(new_primMulNat0(zzz33200), Succ(zzz33200)), h)
new_mkVBalBranch3MkVBalBranch142(zzz1986, zzz1987, zzz1988, zzz1989, zzz1990, zzz1991, zzz1992, zzz1993, zzz1994, zzz1995, zzz1996, dh) → new_mkBranch(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))), EQ, zzz1996, Branch(zzz1991, zzz1992, Pos(Succ(zzz1993)), zzz1994, zzz1995), Branch(zzz1986, zzz1987, Pos(Succ(zzz1988)), zzz1989, zzz1990), ty_Ordering, dh)
new_mkVBalBranch3MkVBalBranch159(zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, zzz1125, zzz1126, zzz1127, zzz1128, zzz1129, Succ(zzz12130), ff) → new_mkVBalBranch3MkVBalBranch149(zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, zzz1125, Succ(zzz1126), zzz1127, zzz1128, zzz1129, Succ(Succ(zzz1126)), Succ(zzz12130), ff)
new_splitGT10(zzz31, zzz32, zzz33, h) → new_splitGT16(h)
new_mkVBalBranch3(zzz31, Branch(zzz520, zzz521, Neg(Zero), zzz523, zzz524), Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), h) → new_mkVBalBranch3MkVBalBranch155(zzz340, zzz341, zzz34200, zzz343, zzz344, zzz520, zzz521, zzz523, zzz524, zzz31, new_primMulNat1(zzz34200), h)
new_mkVBalBranch3MkVBalBranch270(zzz473, zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, zzz481, zzz482, Succ(zzz4830), Zero, eh) → new_mkVBalBranch3MkVBalBranch271(zzz473, zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, zzz481, zzz482, eh)
new_mkVBalBranch3(zzz31, Branch(zzz520, zzz521, Pos(Zero), zzz523, zzz524), Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), h) → new_mkVBalBranch3MkVBalBranch154(zzz340, zzz341, zzz34200, zzz343, zzz344, zzz520, zzz521, zzz523, zzz524, zzz31, new_primMulNat1(zzz34200), h)
new_primPlusInt(Neg(zzz22720), zzz2268, zzz2269, zzz2266, ec, ed) → new_primPlusInt1(zzz22720, new_sizeFM(zzz2269, ec, ed))
new_splitGT16(h) → new_splitGT40(h)
new_mkVBalBranch3MkVBalBranch152(zzz1337, zzz1338, zzz1339, zzz1340, zzz1341, zzz1342, zzz1343, zzz1344, zzz1345, zzz1346, zzz1347, Zero, Succ(zzz13490), eg) → new_mkBalBranch(zzz1342, zzz1343, zzz1345, new_mkVBalBranch2(zzz1347, zzz1346, Branch(zzz1337, zzz1338, Pos(Succ(zzz1339)), zzz1340, zzz1341), eg), ty_Ordering, eg)
new_mkBalBranch6MkBalBranch010(zzz29340, zzz29341, zzz29342, zzz29343, zzz29344, zzz2127, zzz2930, zzz2931, Zero, da, db) → new_mkBalBranch6MkBalBranch012(zzz29340, zzz29341, zzz29342, zzz29343, zzz29344, zzz2127, zzz2930, zzz2931, da, db)
new_addToFM_C4(Branch(GT, zzz341, zzz342, zzz343, zzz344), zzz31, h) → new_mkBalBranch(GT, zzz341, new_addToFM_C4(zzz343, zzz31, h), zzz344, ty_Ordering, h)
new_mkVBalBranch3MkVBalBranch162(zzz1986, zzz1987, zzz1988, zzz1989, zzz1990, zzz1991, zzz1992, zzz1993, zzz1994, zzz1995, zzz1996, Succ(zzz19970), Succ(zzz19980), dh) → new_mkVBalBranch3MkVBalBranch162(zzz1986, zzz1987, zzz1988, zzz1989, zzz1990, zzz1991, zzz1992, zzz1993, zzz1994, zzz1995, zzz1996, zzz19970, zzz19980, dh)
new_splitGT40(h) → new_emptyFM(h)
new_mkVBalBranch3MkVBalBranch288(zzz340, zzz341, Pos(Succ(Succ(zzz342000))), zzz343, zzz344, zzz510, zzz511, Zero, zzz513, zzz514, zzz31, Zero, h) → new_mkVBalBranch3MkVBalBranch290(zzz340, zzz341, zzz342000, zzz343, zzz344, zzz510, zzz511, zzz513, zzz514, zzz31, h)
new_mkBalBranch6MkBalBranch113(zzz2934, zzz21270, zzz21271, zzz21272, zzz21273, zzz21274, zzz2930, zzz2931, Neg(Zero), Neg(zzz22630), da, db) → new_mkBalBranch6MkBalBranch110(zzz2934, zzz21270, zzz21271, zzz21272, zzz21273, zzz21274, zzz2930, zzz2931, new_primMulNat2(zzz22630), da, db)
new_mkBalBranch6MkBalBranch411(zzz2934, zzz2127, zzz2930, zzz2931, Neg(Zero), Neg(zzz22060), da, db) → new_mkBalBranch6MkBalBranch413(zzz2934, zzz2127, zzz2930, zzz2931, new_primMulNat(zzz22060), da, db)
new_mkVBalBranch3(zzz31, Branch(zzz520, zzz521, zzz522, zzz523, zzz524), EmptyFM, h) → new_addToFM(Branch(zzz520, zzz521, zzz522, zzz523, zzz524), zzz31, h)
new_mkVBalBranch3MkVBalBranch269(zzz340, zzz341, Zero, zzz343, zzz344, zzz520, zzz521, zzz52200, zzz523, zzz524, zzz31, h) → new_mkBalBranch(zzz520, zzz521, zzz523, new_mkVBalBranch3(zzz31, zzz524, Branch(zzz340, zzz341, Neg(Zero), zzz343, zzz344), h), ty_Ordering, h)
new_mkBalBranch6MkBalBranch47(zzz2934, zzz2127, zzz2930, zzz2931, Zero, zzz222100, da, db) → new_mkBalBranch6MkBalBranch43(zzz2934, zzz2127, zzz2930, zzz2931, da, db)
new_mkBalBranch6MkBalBranch5(zzz2934, zzz2127, zzz2930, zzz2931, Neg(Succ(zzz213900)), da, db) → new_mkBalBranch6MkBalBranch51(zzz2934, zzz2127, zzz2930, zzz2931, da, db)
new_primPlusInt1(zzz13120, Pos(zzz13150)) → new_primMinusNat0(zzz13150, zzz13120)
new_splitGT3(zzz31, zzz32, zzz33, zzz34, h) → new_splitGT210(zzz31, zzz32, zzz33, zzz34, h)
new_mkVBalBranch3MkVBalBranch263(zzz498, zzz499, zzz500, zzz501, zzz502, zzz503, zzz504, zzz505, zzz506, zzz507, Succ(zzz5080), Succ(zzz5090), ee) → new_mkVBalBranch3MkVBalBranch263(zzz498, zzz499, zzz500, zzz501, zzz502, zzz503, zzz504, zzz505, zzz506, zzz507, zzz5080, zzz5090, ee)
new_mkVBalBranch3MkVBalBranch167(zzz340, zzz341, zzz34200, zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, Succ(zzz1410), h) → new_mkVBalBranch3MkVBalBranch160(zzz340, zzz341, zzz34200, zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, h)
new_mkVBalBranch3(zzz31, EmptyFM, zzz34, h) → new_addToFM(zzz34, zzz31, h)
new_mkVBalBranch3MkVBalBranch267(zzz340, zzz341, Pos(Zero), zzz343, zzz344, zzz520, zzz521, zzz52200, zzz523, zzz524, zzz31, Succ(zzz680), h) → new_mkVBalBranch3MkVBalBranch268(zzz340, zzz341, zzz343, zzz344, zzz520, zzz521, zzz52200, zzz523, zzz524, zzz31, h)
new_mkVBalBranch3MkVBalBranch155(zzz340, zzz341, zzz34200, zzz343, zzz344, zzz520, zzz521, zzz523, zzz524, zzz31, Succ(zzz1290), h) → new_mkBalBranch(zzz520, zzz521, zzz523, new_mkVBalBranch3(zzz31, zzz524, Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), h), ty_Ordering, h)
new_mkVBalBranch3MkVBalBranch144(zzz1702, zzz1703, zzz1704, zzz1705, zzz1706, zzz1707, zzz1708, zzz1709, zzz1710, zzz1711, zzz1712, Zero, Succ(zzz17140), df) → new_mkBalBranch(zzz1707, zzz1708, zzz1710, new_mkVBalBranch3(zzz1712, zzz1711, Branch(zzz1702, zzz1703, Neg(Succ(zzz1704)), zzz1705, zzz1706), df), ty_Ordering, df)
new_mkBalBranch6MkBalBranch1113(zzz2934, zzz21270, zzz21271, zzz21272, zzz21273, zzz21274, zzz2930, zzz2931, Succ(zzz2262000), Succ(zzz227000), da, db) → new_mkBalBranch6MkBalBranch1113(zzz2934, zzz21270, zzz21271, zzz21272, zzz21273, zzz21274, zzz2930, zzz2931, zzz2262000, zzz227000, da, db)
new_mkVBalBranch3MkVBalBranch134(zzz1851, zzz1852, zzz1853, zzz1854, zzz1855, zzz1856, zzz1857, zzz1858, zzz1859, zzz1860, zzz1861, Zero, Succ(zzz18630), dd) → new_mkBalBranch(zzz1856, zzz1857, zzz1859, new_mkVBalBranch2(zzz1861, zzz1860, Branch(zzz1851, zzz1852, Neg(Succ(zzz1853)), zzz1854, zzz1855), dd), ty_Ordering, dd)
new_mkVBalBranch3MkVBalBranch152(zzz1337, zzz1338, zzz1339, zzz1340, zzz1341, zzz1342, zzz1343, zzz1344, zzz1345, zzz1346, zzz1347, Succ(zzz13480), Zero, eg) → new_mkVBalBranch3MkVBalBranch151(zzz1337, zzz1338, zzz1339, zzz1340, zzz1341, zzz1342, zzz1343, zzz1344, zzz1345, zzz1346, zzz1347, eg)
new_mkVBalBranch3MkVBalBranch268(zzz340, zzz341, zzz343, zzz344, zzz520, zzz521, zzz52200, zzz523, zzz524, zzz31, h) → new_mkBalBranch(zzz520, zzz521, zzz523, new_mkVBalBranch3(zzz31, zzz524, Branch(zzz340, zzz341, Pos(Zero), zzz343, zzz344), h), ty_Ordering, h)
new_splitGT8(zzz31, zzz32, zzz34, h) → new_mkVBalBranch3(zzz31, new_splitGT6(h), zzz34, h)
new_mkBalBranch6MkBalBranch5(zzz2934, zzz2127, zzz2930, zzz2931, Pos(Succ(Succ(Zero))), da, db) → new_mkBalBranch6MkBalBranch50(zzz2934, zzz2127, zzz2930, zzz2931, da, db)
new_mkVBalBranch3MkVBalBranch272(zzz340, zzz341, Neg(Succ(Succ(Zero))), zzz343, zzz344, zzz520, zzz521, Zero, zzz523, zzz524, zzz31, Succ(Zero), h) → new_mkVBalBranch3MkVBalBranch277(zzz340, zzz341, Succ(Zero), zzz343, zzz344, zzz520, zzz521, zzz523, zzz524, zzz31, Zero, Zero, h)
new_mkBalBranch6MkBalBranch1110(zzz2934, zzz21270, zzz21271, zzz21272, zzz21273, zzz21274, zzz2930, zzz2931, Zero, da, db) → new_mkBalBranch6MkBalBranch112(zzz2934, zzz21270, zzz21271, zzz21272, zzz21273, zzz21274, zzz2930, zzz2931, da, db)
new_mkVBalBranch3MkVBalBranch162(zzz1986, zzz1987, zzz1988, zzz1989, zzz1990, zzz1991, zzz1992, zzz1993, zzz1994, zzz1995, zzz1996, Zero, Zero, dh) → new_mkVBalBranch3MkVBalBranch142(zzz1986, zzz1987, zzz1988, zzz1989, zzz1990, zzz1991, zzz1992, zzz1993, zzz1994, zzz1995, zzz1996, dh)
new_mkVBalBranch3MkVBalBranch287(zzz340, zzz341, zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, h) → new_mkVBalBranch3MkVBalBranch161(zzz340, zzz341, zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, new_primMulNat1(Zero), h)
new_mkVBalBranch3MkVBalBranch270(zzz473, zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, zzz481, zzz482, Zero, Succ(zzz4840), eh) → new_mkBalBranch(zzz473, zzz474, new_mkVBalBranch4(zzz482, Branch(zzz478, zzz479, Pos(Succ(Zero)), zzz480, zzz481), zzz476, eh), zzz477, ty_Ordering, eh)
new_mkVBalBranch3MkVBalBranch281(zzz340, zzz341, Neg(Succ(Succ(Succ(zzz3420000)))), zzz343, zzz344, zzz510, zzz511, Succ(zzz512000), zzz513, zzz514, zzz31, Succ(Zero), h) → new_mkVBalBranch3MkVBalBranch280(zzz340, zzz341, Succ(Succ(zzz3420000)), zzz343, zzz344, zzz510, zzz511, zzz512000, zzz513, zzz514, zzz31, Succ(zzz3420000), Succ(zzz512000), h)
new_mkVBalBranch3MkVBalBranch288(zzz340, zzz341, Pos(Succ(Succ(zzz342000))), zzz343, zzz344, zzz510, zzz511, Zero, zzz513, zzz514, zzz31, Succ(Succ(zzz6600)), h) → new_mkVBalBranch3MkVBalBranch270(zzz340, zzz341, Succ(zzz342000), zzz343, zzz344, zzz510, zzz511, zzz513, zzz514, zzz31, Succ(zzz6600), zzz342000, h)
new_intersectFM_C2Gts0(zzz854, zzz855, zzz856, zzz857, ba) → new_splitGT25(zzz854, zzz855, zzz856, zzz857, ba)
new_mkVBalBranch3MkVBalBranch281(zzz340, zzz341, Neg(Succ(Succ(Zero))), zzz343, zzz344, zzz510, zzz511, Zero, zzz513, zzz514, zzz31, Succ(Zero), h) → new_mkVBalBranch3MkVBalBranch263(zzz340, zzz341, Succ(Zero), zzz343, zzz344, zzz510, zzz511, zzz513, zzz514, zzz31, Zero, Zero, h)
new_mkVBalBranch3MkVBalBranch260(zzz340, zzz341, zzz342000, zzz343, zzz344, zzz520, zzz521, zzz523, zzz524, zzz31, h) → new_mkVBalBranch3MkVBalBranch143(zzz340, zzz341, Succ(zzz342000), zzz343, zzz344, zzz520, zzz521, zzz523, zzz524, zzz31, new_primMulNat1(Succ(zzz342000)), h)
new_mkVBalBranch4(zzz31, EmptyFM, zzz34, h) → new_addToFM2(zzz34, zzz31, h)
new_mkBalBranch6MkBalBranch110(zzz2934, zzz21270, zzz21271, zzz21272, zzz21273, zzz21274, zzz2930, zzz2931, Zero, da, db) → new_mkBalBranch6MkBalBranch112(zzz2934, zzz21270, zzz21271, zzz21272, zzz21273, zzz21274, zzz2930, zzz2931, da, db)
new_intersectFM_C2Gts3(zzz2129, cc) → new_splitGT15(zzz2129, cc)
new_mkVBalBranch3MkVBalBranch283(zzz461, zzz462, zzz463, zzz464, zzz465, zzz466, zzz467, zzz468, zzz469, zzz470, zzz471, de) → new_mkVBalBranch3MkVBalBranch282(zzz461, zzz462, zzz463, zzz464, zzz465, zzz466, zzz467, zzz468, zzz469, zzz470, zzz471, de)
new_mkVBalBranch3(zzz31, Branch(zzz520, zzz521, Pos(Zero), zzz523, zzz524), Branch(zzz340, zzz341, Pos(Succ(zzz34200)), zzz343, zzz344), h) → new_mkBalBranch(zzz340, zzz341, new_mkVBalBranch3(zzz31, Branch(zzz520, zzz521, Pos(Zero), zzz523, zzz524), zzz343, h), zzz344, ty_Ordering, h)
new_mkVBalBranch3MkVBalBranch281(zzz340, zzz341, Neg(Succ(Zero)), zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, Succ(zzz670), h) → new_mkBalBranch(zzz340, zzz341, new_mkVBalBranch4(zzz31, Branch(zzz510, zzz511, Neg(Succ(zzz51200)), zzz513, zzz514), zzz343, h), zzz344, ty_Ordering, h)
new_splitLT12(Branch(LT, zzz8561, zzz8562, zzz8563, zzz8564), ba) → new_splitLT28(zzz8561, zzz8562, zzz8563, zzz8564, ba)
new_mkBalBranch6MkBalBranch0110(zzz29340, zzz29341, zzz29342, zzz29343, zzz29344, zzz2127, zzz2930, zzz2931, Zero, da, db) → new_mkBalBranch6MkBalBranch012(zzz29340, zzz29341, zzz29342, zzz29343, zzz29344, zzz2127, zzz2930, zzz2931, da, db)
new_addToFM(zzz34, zzz31, h) → new_addToFM_C3(zzz34, zzz31, h)
new_mkVBalBranch3MkVBalBranch252(zzz929, zzz930, zzz931, zzz932, zzz933, zzz934, zzz935, zzz936, zzz937, zzz938, zzz939, Zero, Zero, dc) → new_mkVBalBranch3MkVBalBranch253(zzz929, zzz930, zzz931, zzz932, zzz933, zzz934, zzz935, zzz936, zzz937, zzz938, zzz939, dc)
new_mkVBalBranch3MkVBalBranch137(zzz461, zzz462, zzz463, zzz464, zzz465, zzz466, zzz467, zzz468, zzz469, zzz470, zzz471, Zero, de) → new_mkVBalBranch3MkVBalBranch162(zzz461, zzz462, zzz463, zzz464, zzz465, zzz466, zzz467, Succ(zzz468), zzz469, zzz470, zzz471, Zero, Succ(Succ(zzz468)), de)
new_mkVBalBranch3MkVBalBranch273(zzz818, zzz819, zzz820, zzz821, zzz822, zzz823, zzz824, zzz825, zzz826, zzz827, eb) → new_mkVBalBranch3MkVBalBranch274(zzz818, zzz819, zzz820, zzz821, zzz822, zzz823, zzz824, zzz825, zzz826, zzz827, eb)
new_mkVBalBranch3MkVBalBranch275(zzz958, zzz959, zzz960, zzz961, zzz962, zzz963, zzz964, zzz965, zzz966, zzz967, zzz968, Succ(zzz9690), Succ(zzz9700), fa) → new_mkVBalBranch3MkVBalBranch275(zzz958, zzz959, zzz960, zzz961, zzz962, zzz963, zzz964, zzz965, zzz966, zzz967, zzz968, zzz9690, zzz9700, fa)
new_mkVBalBranch3MkVBalBranch288(zzz340, zzz341, Neg(zzz3420), zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, Succ(zzz660), h) → new_mkVBalBranch3MkVBalBranch284(zzz340, zzz341, zzz3420, zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, h)
new_mkBalBranch6MkBalBranch30(zzz2934, zzz2127, zzz2930, zzz2931, Succ(zzz22540), da, db) → new_mkBalBranch6MkBalBranch31(zzz2934, zzz2127, zzz2930, zzz2931, da, db)
new_mkVBalBranch3MkVBalBranch261(zzz3170, zzz3171, Pos(Zero), zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, Succ(zzz4170), h) → new_mkVBalBranch3MkVBalBranch279(zzz3170, zzz3171, zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, h)
new_mkVBalBranch3MkVBalBranch288(zzz340, zzz341, Pos(Zero), zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, Succ(zzz660), h) → new_mkVBalBranch3MkVBalBranch285(zzz340, zzz341, zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, h)
new_mkVBalBranch2(zzz31, EmptyFM, zzz317, h) → new_addToFM1(zzz317, zzz31, h)
new_splitLT25(zzz869, zzz870, zzz871, zzz872, bc) → new_splitLT12(zzz871, bc)
new_splitGT4(zzz31, zzz32, zzz34, h) → new_mkVBalBranch4(zzz31, new_splitGT13(h), zzz34, h)
new_mkBalBranch6MkBalBranch116(zzz2934, zzz21270, zzz21271, zzz21272, zzz21273, zzz21274, zzz2930, zzz2931, Succ(zzz22730), da, db) → new_mkBalBranch6MkBalBranch1111(zzz2934, zzz21270, zzz21271, zzz21272, zzz21273, zzz21274, zzz2930, zzz2931, Zero, zzz22730, da, db)
new_mkBalBranch6MkBalBranch017(zzz29340, zzz29341, zzz29342, zzz29343, zzz29344, zzz2127, zzz2930, zzz2931, Neg(Zero), Pos(zzz22470), da, db) → new_mkBalBranch6MkBalBranch010(zzz29340, zzz29341, zzz29342, zzz29343, zzz29344, zzz2127, zzz2930, zzz2931, new_primMulNat2(zzz22470), da, db)
new_mkVBalBranch3MkVBalBranch281(zzz340, zzz341, Neg(Succ(Succ(Succ(zzz3420000)))), zzz343, zzz344, zzz510, zzz511, Zero, zzz513, zzz514, zzz31, Succ(Succ(zzz6700)), h) → new_mkVBalBranch3MkVBalBranch263(zzz340, zzz341, Succ(Succ(zzz3420000)), zzz343, zzz344, zzz510, zzz511, zzz513, zzz514, zzz31, Succ(zzz3420000), Succ(zzz6700), h)
new_mkBalBranch6MkBalBranch113(zzz2934, zzz21270, zzz21271, zzz21272, zzz21273, zzz21274, zzz2930, zzz2931, Neg(Succ(zzz226200)), Pos(zzz22630), da, db) → new_mkBalBranch6MkBalBranch118(zzz2934, zzz21270, zzz21271, zzz21272, zzz21273, zzz21274, zzz2930, zzz2931, zzz226200, new_primMulNat2(zzz22630), da, db)
new_mkVBalBranch3MkVBalBranch272(zzz340, zzz341, Neg(Succ(Succ(Succ(zzz3420000)))), zzz343, zzz344, zzz520, zzz521, Zero, zzz523, zzz524, zzz31, Succ(Zero), h) → new_mkVBalBranch3MkVBalBranch277(zzz340, zzz341, Succ(Succ(zzz3420000)), zzz343, zzz344, zzz520, zzz521, zzz523, zzz524, zzz31, Succ(zzz3420000), Zero, h)
new_mkVBalBranch3MkVBalBranch272(zzz340, zzz341, Pos(zzz3420), zzz343, zzz344, zzz520, zzz521, zzz52200, zzz523, zzz524, zzz31, Zero, h) → new_mkVBalBranch3MkVBalBranch258(zzz340, zzz341, zzz3420, zzz343, zzz344, zzz520, zzz521, zzz52200, zzz523, zzz524, zzz31, h)
new_mkBalBranch6MkBalBranch39(zzz2934, zzz2127, zzz2930, zzz2931, Succ(zzz2244000), Succ(zzz224800), da, db) → new_mkBalBranch6MkBalBranch39(zzz2934, zzz2127, zzz2930, zzz2931, zzz2244000, zzz224800, da, db)
new_mkVBalBranch3MkVBalBranch154(zzz340, zzz341, zzz34200, zzz343, zzz344, zzz520, zzz521, zzz523, zzz524, zzz31, Succ(zzz1250), h) → new_mkBalBranch(zzz520, zzz521, zzz523, new_mkVBalBranch3(zzz31, zzz524, Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), h), ty_Ordering, h)
new_splitGT15(Branch(EQ, zzz21291, zzz21292, zzz21293, zzz21294), cc) → new_splitGT15(zzz21294, cc)
new_mkVBalBranch4(zzz31, Branch(zzz510, zzz511, Pos(Zero), zzz513, zzz514), Branch(zzz340, zzz341, Pos(Zero), zzz343, zzz344), h) → new_mkBranch(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))), EQ, zzz31, Branch(zzz510, zzz511, Pos(Zero), zzz513, zzz514), Branch(zzz340, zzz341, Pos(Zero), zzz343, zzz344), ty_Ordering, h)
new_mkVBalBranch3MkVBalBranch281(zzz340, zzz341, Neg(Succ(Zero)), zzz343, zzz344, zzz510, zzz511, Succ(zzz512000), zzz513, zzz514, zzz31, Zero, h) → new_mkVBalBranch3MkVBalBranch257(zzz340, zzz341, Zero, zzz343, zzz344, zzz510, zzz511, zzz512000, zzz513, zzz514, zzz31, h)
new_splitLT15(Branch(GT, zzz781, zzz782, zzz783, zzz784), bg) → new_splitLT27(zzz781, zzz782, zzz783, zzz784, bg)
new_splitLT40(h) → new_emptyFM(h)
new_mkVBalBranch3MkVBalBranch280(zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, zzz1125, zzz1126, zzz1127, zzz1128, zzz1129, Succ(zzz11300), Zero, ff) → new_mkVBalBranch3MkVBalBranch278(zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, zzz1125, zzz1126, zzz1127, zzz1128, zzz1129, ff)
new_mkVBalBranch3MkVBalBranch272(zzz340, zzz341, Neg(Succ(Succ(Zero))), zzz343, zzz344, zzz520, zzz521, Zero, zzz523, zzz524, zzz31, Succ(Succ(zzz6900)), h) → new_mkVBalBranch3MkVBalBranch277(zzz340, zzz341, Succ(Zero), zzz343, zzz344, zzz520, zzz521, zzz523, zzz524, zzz31, Zero, Succ(zzz6900), h)
new_intersectFM_C2Gts1(zzz869, zzz870, zzz871, zzz872, bc) → new_splitGT28(zzz869, zzz870, zzz871, zzz872, bc)
new_mkVBalBranch3MkVBalBranch281(zzz340, zzz341, Neg(Succ(Succ(zzz342000))), zzz343, zzz344, zzz510, zzz511, Succ(zzz512000), zzz513, zzz514, zzz31, Zero, h) → new_mkVBalBranch3MkVBalBranch280(zzz340, zzz341, Succ(zzz342000), zzz343, zzz344, zzz510, zzz511, zzz512000, zzz513, zzz514, zzz31, zzz342000, zzz512000, h)
new_addToFM_C2(Branch(LT, zzz3171, zzz3172, zzz3173, zzz3174), zzz31, h) → Branch(LT, new_addToFM0(zzz3171, zzz31, h), zzz3172, zzz3173, zzz3174)
new_mkBalBranch6MkBalBranch018(zzz29340, zzz29341, zzz29342, zzz29343, zzz29344, zzz2127, zzz2930, zzz2931, Zero, zzz224600, da, db) → new_mkBalBranch6MkBalBranch011(zzz29340, zzz29341, zzz29342, zzz29343, zzz29344, zzz2127, zzz2930, zzz2931, da, db)
new_mkVBalBranch3MkVBalBranch246(zzz972, zzz973, zzz974, zzz975, zzz976, zzz977, zzz978, zzz979, zzz980, zzz981, zzz982, Zero, Succ(zzz9840), cg) → new_mkBalBranch(zzz972, zzz973, new_mkVBalBranch2(zzz982, Branch(zzz977, zzz978, Neg(Succ(zzz979)), zzz980, zzz981), zzz975, cg), zzz976, ty_Ordering, cg)
new_mkBalBranch6MkBalBranch411(zzz2934, zzz2127, zzz2930, zzz2931, Pos(Succ(zzz222100)), Neg(zzz22060), da, db) → new_mkBalBranch6MkBalBranch415(zzz2934, zzz2127, zzz2930, zzz2931, zzz222100, new_primMulNat(zzz22060), da, db)
new_mkVBalBranch4(zzz31, Branch(zzz510, zzz511, Pos(Zero), zzz513, zzz514), Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), h) → new_mkVBalBranch3MkVBalBranch168(zzz340, zzz341, zzz34200, zzz343, zzz344, zzz510, zzz511, zzz513, zzz514, zzz31, new_primMulNat1(zzz34200), h)
new_mkVBalBranch3MkVBalBranch162(zzz1986, zzz1987, zzz1988, zzz1989, zzz1990, zzz1991, zzz1992, zzz1993, zzz1994, zzz1995, zzz1996, Zero, Succ(zzz19980), dh) → new_mkBalBranch(zzz1991, zzz1992, zzz1994, new_mkVBalBranch4(zzz1996, zzz1995, Branch(zzz1986, zzz1987, Pos(Succ(zzz1988)), zzz1989, zzz1990), dh), ty_Ordering, dh)
new_addToFM0(zzz71, zzz13, h) → zzz13
new_mkVBalBranch3MkVBalBranch288(zzz340, zzz341, Pos(Succ(Succ(zzz342000))), zzz343, zzz344, zzz510, zzz511, Succ(zzz512000), zzz513, zzz514, zzz31, Succ(Zero), h) → new_mkVBalBranch3MkVBalBranch289(zzz340, zzz341, Succ(zzz342000), zzz343, zzz344, zzz510, zzz511, zzz512000, zzz513, zzz514, zzz31, Succ(zzz512000), zzz342000, h)
new_mkBalBranch(zzz2930, zzz2931, zzz2127, zzz2934, da, db) → new_mkBalBranch6MkBalBranch5(zzz2934, zzz2127, zzz2930, zzz2931, new_primPlusInt2(new_mkBalBranch6Size_l(zzz2934, zzz2127, zzz2930, zzz2931, db, da), zzz2934, zzz2127, zzz2930, zzz2931, db, da), da, db)
new_mkBalBranch6MkBalBranch37(zzz2934, zzz2127, zzz2930, zzz2931, zzz224400, zzz2253, da, db) → new_mkBalBranch6MkBalBranch36(zzz2934, zzz2127, zzz2930, zzz2931, zzz2253, zzz224400, da, db)
new_mkVBalBranch3MkVBalBranch281(zzz340, zzz341, Neg(Succ(Succ(Succ(zzz3420000)))), zzz343, zzz344, zzz510, zzz511, Succ(zzz512000), zzz513, zzz514, zzz31, Succ(Succ(zzz6700)), h) → new_mkVBalBranch3MkVBalBranch280(zzz340, zzz341, Succ(Succ(zzz3420000)), zzz343, zzz344, zzz510, zzz511, zzz512000, zzz513, zzz514, zzz31, Succ(zzz3420000), Succ(Succ(new_primPlusNat2(zzz6700, zzz512000))), h)
new_splitGT42(h) → new_emptyFM(h)
new_mkBalBranch6MkBalBranch114(zzz2934, zzz21270, zzz21271, zzz21272, zzz21273, zzz21274, zzz2930, zzz2931, zzz226200, zzz2270, da, db) → new_mkBalBranch6MkBalBranch111(zzz2934, zzz21270, zzz21271, zzz21272, zzz21273, zzz21274, zzz2930, zzz2931, zzz226200, zzz2270, da, db)
new_mkVBalBranch3MkVBalBranch264(zzz498, zzz499, zzz500, zzz501, zzz502, zzz503, zzz504, zzz505, zzz506, zzz507, ee) → new_mkVBalBranch3MkVBalBranch157(zzz498, zzz499, zzz500, zzz501, zzz502, zzz503, zzz504, zzz505, zzz506, zzz507, new_primMulNat1(zzz500), ee)
new_splitGT9(zzz76, zzz77, zzz78, zzz79, bg) → new_splitGT26(zzz76, zzz77, zzz78, zzz79, bg)
new_mkVBalBranch3MkVBalBranch166(zzz2033, zzz2034, zzz2035, zzz2036, zzz2037, zzz2038, zzz2039, zzz2040, zzz2041, zzz2042, zzz2043, fg) → new_mkBranch(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))), GT, zzz2043, Branch(zzz2038, zzz2039, Pos(Succ(zzz2040)), zzz2041, zzz2042), Branch(zzz2033, zzz2034, Pos(Succ(zzz2035)), zzz2036, zzz2037), ty_Ordering, fg)
new_intersectFM_C2Gts(zzz76, zzz77, zzz78, zzz79, bg) → new_splitGT9(zzz76, zzz77, zzz78, zzz79, bg)
new_mkVBalBranch4(zzz31, Branch(zzz510, zzz511, Neg(Zero), zzz513, zzz514), Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), h) → new_mkVBalBranch3MkVBalBranch133(zzz340, zzz341, zzz34200, zzz343, zzz344, zzz510, zzz511, zzz513, zzz514, zzz31, new_primMulNat1(zzz34200), h)
new_mkBalBranch6MkBalBranch015(zzz29340, zzz29341, zzz29342, zzz29343, zzz29344, zzz2127, zzz2930, zzz2931, da, db) → new_mkBalBranch6MkBalBranch016(zzz29340, zzz29341, zzz29342, zzz29343, zzz29344, zzz2127, zzz2930, zzz2931, da, db)
new_splitLT15(Branch(EQ, zzz781, zzz782, zzz783, zzz784), bg) → new_splitLT26(zzz781, zzz782, zzz783, zzz784, bg)
new_mkVBalBranch3MkVBalBranch272(zzz340, zzz341, Neg(Succ(Zero)), zzz343, zzz344, zzz520, zzz521, zzz52200, zzz523, zzz524, zzz31, Succ(zzz690), h) → new_mkVBalBranch3MkVBalBranch254(zzz340, zzz341, zzz343, zzz344, zzz520, zzz521, zzz52200, zzz523, zzz524, zzz31, h)
new_mkVBalBranch3MkVBalBranch277(zzz1133, zzz1134, zzz1135, zzz1136, zzz1137, zzz1138, zzz1139, zzz1140, zzz1141, zzz1142, Zero, Zero, fd) → new_mkVBalBranch3MkVBalBranch273(zzz1133, zzz1134, zzz1135, zzz1136, zzz1137, zzz1138, zzz1139, zzz1140, zzz1141, zzz1142, fd)
new_mkVBalBranch3MkVBalBranch161(zzz340, zzz341, zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, Zero, h) → new_mkVBalBranch3MkVBalBranch162(zzz340, zzz341, Zero, zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, Zero, Succ(zzz51200), h)
new_mkVBalBranch3MkVBalBranch252(zzz929, zzz930, zzz931, zzz932, zzz933, zzz934, zzz935, zzz936, zzz937, zzz938, zzz939, Zero, Succ(zzz9410), dc) → new_mkBalBranch(zzz929, zzz930, new_mkVBalBranch3(zzz939, Branch(zzz934, zzz935, Pos(Succ(zzz936)), zzz937, zzz938), zzz932, dc), zzz933, ty_Ordering, dc)
new_primPlusInt0(zzz1311, Neg(zzz13130)) → new_primMinusNat0(zzz1311, zzz13130)
new_mkBalBranch6MkBalBranch34(zzz2934, zzz2127, zzz2930, zzz2931, zzz224400, zzz2252, da, db) → new_mkBalBranch6MkBalBranch31(zzz2934, zzz2127, zzz2930, zzz2931, da, db)
new_mkBalBranch6MkBalBranch39(zzz2934, zzz2127, zzz2930, zzz2931, Zero, Succ(zzz224800), da, db) → new_mkBalBranch6MkBalBranch31(zzz2934, zzz2127, zzz2930, zzz2931, da, db)
new_splitGT7(zzz31, zzz32, zzz33, zzz34, h) → new_splitGT27(zzz31, zzz32, zzz33, zzz34, h)
new_mkVBalBranch3MkVBalBranch272(zzz340, zzz341, Neg(Succ(Succ(zzz342000))), zzz343, zzz344, zzz520, zzz521, Succ(zzz522000), zzz523, zzz524, zzz31, Zero, h) → new_mkVBalBranch3MkVBalBranch255(zzz340, zzz341, Succ(zzz342000), zzz343, zzz344, zzz520, zzz521, zzz522000, zzz523, zzz524, zzz31, zzz342000, zzz522000, h)
new_splitGT41(h) → new_emptyFM(h)
new_mkBalBranch6MkBalBranch44(zzz2934, zzz2127, zzz2930, zzz2931, zzz222100, zzz2236, da, db) → new_mkBalBranch6MkBalBranch45(zzz2934, zzz2127, zzz2930, zzz2931, zzz222100, zzz2236, da, db)
new_mkBalBranch6MkBalBranch412(zzz2934, zzz2127, zzz2930, zzz2931, Zero, Succ(zzz223600), da, db) → new_mkBalBranch6MkBalBranch43(zzz2934, zzz2127, zzz2930, zzz2931, da, db)
new_mkVBalBranch3MkVBalBranch272(zzz340, zzz341, Neg(Zero), zzz343, zzz344, zzz520, zzz521, zzz52200, zzz523, zzz524, zzz31, Zero, h) → new_mkVBalBranch3MkVBalBranch245(zzz340, zzz341, zzz343, zzz344, zzz520, zzz521, zzz52200, zzz523, zzz524, zzz31, h)
new_mkVBalBranch3MkVBalBranch275(zzz958, zzz959, zzz960, zzz961, zzz962, zzz963, zzz964, zzz965, zzz966, zzz967, zzz968, Zero, Succ(zzz9700), fa) → new_mkBalBranch(zzz958, zzz959, new_mkVBalBranch2(zzz968, Branch(zzz963, zzz964, Pos(Succ(zzz965)), zzz966, zzz967), zzz961, fa), zzz962, ty_Ordering, fa)
new_mkVBalBranch3MkVBalBranch272(zzz340, zzz341, Neg(Succ(Succ(Zero))), zzz343, zzz344, zzz520, zzz521, Succ(zzz522000), zzz523, zzz524, zzz31, Succ(Zero), h) → new_mkVBalBranch3MkVBalBranch255(zzz340, zzz341, Succ(Zero), zzz343, zzz344, zzz520, zzz521, zzz522000, zzz523, zzz524, zzz31, Zero, Succ(zzz522000), h)
new_mkBranch(zzz2265, zzz2266, zzz2267, zzz2268, zzz2269, ec, ed) → Branch(zzz2266, zzz2267, new_primPlusInt(new_primPlusInt0(Succ(Zero), new_sizeFM(zzz2268, ec, ed)), zzz2268, zzz2269, zzz2266, ec, ed), zzz2268, zzz2269)
new_mkVBalBranch3MkVBalBranch262(zzz3170, zzz3171, Neg(Zero), zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, Zero, h) → new_mkBranch(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))), LT, zzz31, Branch(zzz330, zzz331, Neg(Succ(zzz33200)), zzz333, zzz334), Branch(zzz3170, zzz3171, Neg(Zero), zzz3173, zzz3174), ty_Ordering, h)
new_mkBalBranch6MkBalBranch016(zzz29340, zzz29341, zzz29342, EmptyFM, zzz29344, zzz2127, zzz2930, zzz2931, da, db) → error([])
new_mkBalBranch6MkBalBranch47(zzz2934, zzz2127, zzz2930, zzz2931, Succ(zzz22410), zzz222100, da, db) → new_mkBalBranch6MkBalBranch412(zzz2934, zzz2127, zzz2930, zzz2931, zzz22410, zzz222100, da, db)
new_mkVBalBranch3MkVBalBranch279(zzz3170, zzz3171, zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, h) → new_mkBalBranch(zzz330, zzz331, zzz333, new_mkVBalBranch2(zzz31, zzz334, Branch(zzz3170, zzz3171, Pos(Zero), zzz3173, zzz3174), h), ty_Ordering, h)
new_primMinusNat0(Succ(zzz100100), Zero) → Pos(Succ(zzz100100))
new_sizeFM(EmptyFM, fb, fc) → Pos(Zero)
new_mkBalBranch6MkBalBranch1114(zzz2934, zzz21270, zzz21271, zzz21272, zzz21273, zzz21274, zzz2930, zzz2931, da, db) → new_mkBalBranch6MkBalBranch1115(zzz2934, zzz21270, zzz21271, zzz21272, zzz21273, zzz21274, zzz2930, zzz2931, da, db)
new_mkVBalBranch3MkVBalBranch245(zzz340, zzz341, zzz343, zzz344, zzz520, zzz521, zzz52200, zzz523, zzz524, zzz31, h) → new_mkBalBranch(zzz340, zzz341, new_mkVBalBranch3(zzz31, Branch(zzz520, zzz521, Neg(Succ(zzz52200)), zzz523, zzz524), zzz343, h), zzz344, ty_Ordering, h)
new_mkVBalBranch3MkVBalBranch152(zzz1337, zzz1338, zzz1339, zzz1340, zzz1341, zzz1342, zzz1343, zzz1344, zzz1345, zzz1346, zzz1347, Succ(zzz13480), Succ(zzz13490), eg) → new_mkVBalBranch3MkVBalBranch152(zzz1337, zzz1338, zzz1339, zzz1340, zzz1341, zzz1342, zzz1343, zzz1344, zzz1345, zzz1346, zzz1347, zzz13480, zzz13490, eg)
new_mkVBalBranch3MkVBalBranch141(zzz972, zzz973, zzz974, zzz975, zzz976, zzz977, zzz978, zzz979, zzz980, zzz981, zzz982, Succ(zzz10190), cg) → new_mkVBalBranch3MkVBalBranch134(zzz972, zzz973, zzz974, zzz975, zzz976, zzz977, zzz978, zzz979, zzz980, zzz981, zzz982, Succ(zzz979), Succ(zzz10190), cg)
new_mkVBalBranch3MkVBalBranch135(zzz1851, zzz1852, zzz1853, zzz1854, zzz1855, zzz1856, zzz1857, zzz1858, zzz1859, zzz1860, zzz1861, dd) → new_mkBranch(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))), LT, zzz1861, Branch(zzz1856, zzz1857, Neg(Succ(zzz1858)), zzz1859, zzz1860), Branch(zzz1851, zzz1852, Neg(Succ(zzz1853)), zzz1854, zzz1855), ty_Ordering, dd)
new_mkBalBranch6MkBalBranch38(zzz2934, zzz2127, zzz2930, zzz2931, zzz224400, Succ(zzz22480), da, db) → new_mkBalBranch6MkBalBranch39(zzz2934, zzz2127, zzz2930, zzz2931, zzz224400, zzz22480, da, db)
new_mkVBalBranch3MkVBalBranch134(zzz1851, zzz1852, zzz1853, zzz1854, zzz1855, zzz1856, zzz1857, zzz1858, zzz1859, zzz1860, zzz1861, Succ(zzz18620), Succ(zzz18630), dd) → new_mkVBalBranch3MkVBalBranch134(zzz1851, zzz1852, zzz1853, zzz1854, zzz1855, zzz1856, zzz1857, zzz1858, zzz1859, zzz1860, zzz1861, zzz18620, zzz18630, dd)
new_mkVBalBranch3MkVBalBranch267(zzz340, zzz341, Neg(zzz3420), zzz343, zzz344, zzz520, zzz521, zzz52200, zzz523, zzz524, zzz31, Zero, h) → new_mkVBalBranch3MkVBalBranch269(zzz340, zzz341, zzz3420, zzz343, zzz344, zzz520, zzz521, zzz52200, zzz523, zzz524, zzz31, h)
new_mkVBalBranch3MkVBalBranch262(zzz3170, zzz3171, Pos(Zero), zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, Zero, h) → new_mkBranch(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))), LT, zzz31, Branch(zzz330, zzz331, Neg(Succ(zzz33200)), zzz333, zzz334), Branch(zzz3170, zzz3171, Pos(Zero), zzz3173, zzz3174), ty_Ordering, h)
new_mkBalBranch6MkBalBranch113(zzz2934, zzz21270, zzz21271, zzz21272, zzz21273, zzz21274, zzz2930, zzz2931, Pos(Zero), Neg(zzz22630), da, db) → new_mkBalBranch6MkBalBranch117(zzz2934, zzz21270, zzz21271, zzz21272, zzz21273, zzz21274, zzz2930, zzz2931, new_primMulNat2(zzz22630), da, db)
new_mkVBalBranch3MkVBalBranch250(zzz340, zzz341, zzz342000, zzz343, zzz344, zzz510, zzz511, zzz513, zzz514, zzz31, h) → new_mkVBalBranch3MkVBalBranch157(zzz340, zzz341, Succ(zzz342000), zzz343, zzz344, zzz510, zzz511, zzz513, zzz514, zzz31, new_primMulNat1(Succ(zzz342000)), h)
new_mkVBalBranch4(zzz31, Branch(zzz510, zzz511, Neg(Zero), zzz513, zzz514), Branch(zzz340, zzz341, Neg(Zero), zzz343, zzz344), h) → new_mkBranch(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))), EQ, zzz31, Branch(zzz510, zzz511, Neg(Zero), zzz513, zzz514), Branch(zzz340, zzz341, Neg(Zero), zzz343, zzz344), ty_Ordering, h)
new_mkBalBranch6MkBalBranch1113(zzz2934, zzz21270, zzz21271, zzz21272, zzz21273, zzz21274, zzz2930, zzz2931, Zero, Zero, da, db) → new_mkBalBranch6MkBalBranch112(zzz2934, zzz21270, zzz21271, zzz21272, zzz21273, zzz21274, zzz2930, zzz2931, da, db)
new_mkBalBranch6MkBalBranch40(zzz2934, zzz2127, zzz2930, zzz2931, da, db) → new_mkBalBranch6MkBalBranch41(zzz2934, zzz2127, zzz2930, zzz2931, da, db)
new_mkVBalBranch3MkVBalBranch272(zzz340, zzz341, Pos(zzz3420), zzz343, zzz344, zzz520, zzz521, zzz52200, zzz523, zzz524, zzz31, Succ(zzz690), h) → new_mkVBalBranch3MkVBalBranch258(zzz340, zzz341, zzz3420, zzz343, zzz344, zzz520, zzz521, zzz52200, zzz523, zzz524, zzz31, h)
new_mkVBalBranch3MkVBalBranch149(zzz2050, zzz2051, zzz2052, zzz2053, zzz2054, zzz2055, zzz2056, zzz2057, zzz2058, zzz2059, zzz2060, Succ(zzz20610), Zero, ef) → new_mkVBalBranch3MkVBalBranch150(zzz2050, zzz2051, zzz2052, zzz2053, zzz2054, zzz2055, zzz2056, zzz2057, zzz2058, zzz2059, zzz2060, ef)
new_mkVBalBranch3MkVBalBranch134(zzz1851, zzz1852, zzz1853, zzz1854, zzz1855, zzz1856, zzz1857, zzz1858, zzz1859, zzz1860, zzz1861, Succ(zzz18620), Zero, dd) → new_mkVBalBranch3MkVBalBranch135(zzz1851, zzz1852, zzz1853, zzz1854, zzz1855, zzz1856, zzz1857, zzz1858, zzz1859, zzz1860, zzz1861, dd)
new_mkVBalBranch3MkVBalBranch249(zzz340, zzz341, zzz342000, zzz343, zzz344, zzz510, zzz511, zzz513, zzz514, zzz31, h) → new_mkVBalBranch3MkVBalBranch250(zzz340, zzz341, zzz342000, zzz343, zzz344, zzz510, zzz511, zzz513, zzz514, zzz31, h)
new_addToFM_C3(Branch(EQ, zzz341, zzz342, zzz343, zzz344), zzz31, h) → new_mkBalBranch(EQ, zzz341, zzz343, new_addToFM_C3(zzz344, zzz31, h), ty_Ordering, h)
new_mkVBalBranch3MkVBalBranch272(zzz340, zzz341, Neg(Succ(Succ(Succ(zzz3420000)))), zzz343, zzz344, zzz520, zzz521, Succ(zzz522000), zzz523, zzz524, zzz31, Succ(Succ(zzz6900)), h) → new_mkVBalBranch3MkVBalBranch255(zzz340, zzz341, Succ(Succ(zzz3420000)), zzz343, zzz344, zzz520, zzz521, zzz522000, zzz523, zzz524, zzz31, Succ(zzz3420000), Succ(Succ(new_primPlusNat2(zzz6900, zzz522000))), h)
new_mkBalBranch6MkBalBranch017(zzz29340, zzz29341, zzz29342, zzz29343, zzz29344, zzz2127, zzz2930, zzz2931, Pos(Zero), Neg(zzz22470), da, db) → new_mkBalBranch6MkBalBranch0111(zzz29340, zzz29341, zzz29342, zzz29343, zzz29344, zzz2127, zzz2930, zzz2931, new_primMulNat2(zzz22470), da, db)
new_primMulNat2(Zero) → Zero
new_mkBalBranch6MkBalBranch5(zzz2934, zzz2127, zzz2930, zzz2931, Pos(Succ(Zero)), da, db) → new_mkBalBranch6MkBalBranch51(zzz2934, zzz2127, zzz2930, zzz2931, da, db)
new_mkVBalBranch3MkVBalBranch263(zzz498, zzz499, zzz500, zzz501, zzz502, zzz503, zzz504, zzz505, zzz506, zzz507, Zero, Zero, ee) → new_mkVBalBranch3MkVBalBranch264(zzz498, zzz499, zzz500, zzz501, zzz502, zzz503, zzz504, zzz505, zzz506, zzz507, ee)
new_mkVBalBranch3MkVBalBranch261(zzz3170, zzz3171, Pos(Succ(zzz317200)), zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, Zero, h) → new_mkVBalBranch3MkVBalBranch275(zzz3170, zzz3171, zzz317200, zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, Zero, Succ(zzz317200), h)
new_mkVBalBranch3MkVBalBranch158(zzz461, zzz462, zzz463, zzz464, zzz465, zzz466, zzz467, zzz468, zzz469, zzz470, zzz471, de) → new_mkVBalBranch3MkVBalBranch136(zzz461, zzz462, zzz463, zzz464, zzz465, zzz466, zzz467, zzz468, zzz469, zzz470, zzz471, de)
new_mkBalBranch6MkBalBranch31(zzz2934, zzz2127, zzz2930, zzz2931, da, db) → new_mkBalBranch6MkBalBranch313(zzz2934, zzz2127, zzz2930, zzz2931, da, db)
new_mkBalBranch6MkBalBranch39(zzz2934, zzz2127, zzz2930, zzz2931, Zero, Zero, da, db) → new_mkBalBranch6MkBalBranch32(zzz2934, zzz2127, zzz2930, zzz2931, da, db)
new_mkBalBranch6MkBalBranch313(zzz2934, zzz2127, zzz2930, zzz2931, da, db) → new_mkBranch(Succ(Zero), zzz2930, zzz2931, zzz2127, zzz2934, da, db)
new_mkBalBranch6MkBalBranch310(zzz2934, zzz2127, zzz2930, zzz2931, Neg(Zero), Neg(zzz22450), da, db) → new_mkBalBranch6MkBalBranch314(zzz2934, zzz2127, zzz2930, zzz2931, new_primMulNat(zzz22450), da, db)
new_mkVBalBranch3MkVBalBranch288(zzz340, zzz341, Pos(Succ(Succ(zzz342000))), zzz343, zzz344, zzz510, zzz511, Succ(zzz512000), zzz513, zzz514, zzz31, Succ(Succ(zzz6600)), h) → new_mkVBalBranch3MkVBalBranch289(zzz340, zzz341, Succ(zzz342000), zzz343, zzz344, zzz510, zzz511, zzz512000, zzz513, zzz514, zzz31, Succ(Succ(new_primPlusNat2(zzz6600, zzz512000))), zzz342000, h)
new_splitGT14(Branch(LT, zzz8861, zzz8862, zzz8863, zzz8864), be) → new_splitGT29(zzz8861, zzz8862, zzz8863, zzz8864, be)
new_intersectFM_C2Lts0(zzz854, zzz855, zzz856, zzz857, ba) → new_splitLT24(zzz854, zzz855, zzz856, zzz857, ba)
new_primPlusNat3(zzz90, Zero) → Succ(zzz90)
new_splitLT8(zzz31, zzz32, zzz34, h) → new_splitLT6(h)
new_splitGT12(Branch(EQ, zzz8561, zzz8562, zzz8563, zzz8564), ba) → new_splitGT25(zzz8561, zzz8562, zzz8563, zzz8564, ba)
new_mkVBalBranch3MkVBalBranch256(zzz537, zzz538, zzz539, zzz540, zzz541, zzz542, zzz543, zzz544, zzz545, zzz546, zzz547, dg) → new_mkVBalBranch3MkVBalBranch153(zzz537, zzz538, zzz539, zzz540, zzz541, zzz542, zzz543, zzz544, zzz545, zzz546, zzz547, new_primMulNat1(zzz539), dg)
new_mkVBalBranch3MkVBalBranch261(zzz3170, zzz3171, Pos(Zero), zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, Zero, h) → new_mkVBalBranch3MkVBalBranch279(zzz3170, zzz3171, zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, h)
new_mkVBalBranch4(zzz31, Branch(zzz510, zzz511, zzz512, zzz513, zzz514), EmptyFM, h) → new_addToFM2(Branch(zzz510, zzz511, zzz512, zzz513, zzz514), zzz31, h)
new_mkVBalBranch4(zzz31, Branch(zzz510, zzz511, Neg(Succ(zzz51200)), zzz513, zzz514), Branch(zzz340, zzz341, zzz342, zzz343, zzz344), h) → new_mkVBalBranch3MkVBalBranch281(zzz340, zzz341, zzz342, zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, new_primMulNat0(zzz51200), h)
new_mkBalBranch6MkBalBranch017(zzz29340, zzz29341, zzz29342, zzz29343, zzz29344, zzz2127, zzz2930, zzz2931, Neg(Succ(zzz224600)), Neg(zzz22470), da, db) → new_mkBalBranch6MkBalBranch018(zzz29340, zzz29341, zzz29342, zzz29343, zzz29344, zzz2127, zzz2930, zzz2931, new_primMulNat2(zzz22470), zzz224600, da, db)
new_mkBalBranch6MkBalBranch33(zzz2934, Branch(zzz21270, zzz21271, zzz21272, zzz21273, zzz21274), zzz2930, zzz2931, da, db) → new_mkBalBranch6MkBalBranch113(zzz2934, zzz21270, zzz21271, zzz21272, zzz21273, zzz21274, zzz2930, zzz2931, new_sizeFM(zzz21274, da, db), new_sizeFM(zzz21273, da, db), da, db)
new_mkVBalBranch3MkVBalBranch259(zzz340, zzz341, zzz342000, zzz343, zzz344, zzz520, zzz521, zzz523, zzz524, zzz31, h) → new_mkVBalBranch3MkVBalBranch260(zzz340, zzz341, zzz342000, zzz343, zzz344, zzz520, zzz521, zzz523, zzz524, zzz31, h)
new_mkVBalBranch3MkVBalBranch266(zzz340, zzz341, zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, h) → new_mkBalBranch(zzz340, zzz341, new_mkVBalBranch4(zzz31, Branch(zzz510, zzz511, Neg(Succ(zzz51200)), zzz513, zzz514), zzz343, h), zzz344, ty_Ordering, h)
new_mkBalBranch6MkBalBranch46(zzz2934, zzz2127, zzz2930, zzz2931, zzz222100, zzz2241, da, db) → new_mkBalBranch6MkBalBranch47(zzz2934, zzz2127, zzz2930, zzz2931, zzz2241, zzz222100, da, db)
new_mkVBalBranch3MkVBalBranch289(zzz1105, zzz1106, zzz1107, zzz1108, zzz1109, zzz1110, zzz1111, zzz1112, zzz1113, zzz1114, zzz1115, Succ(zzz11160), Succ(zzz11170), fh) → new_mkVBalBranch3MkVBalBranch289(zzz1105, zzz1106, zzz1107, zzz1108, zzz1109, zzz1110, zzz1111, zzz1112, zzz1113, zzz1114, zzz1115, zzz11160, zzz11170, fh)
new_mkBalBranch6MkBalBranch314(zzz2934, zzz2127, zzz2930, zzz2931, Succ(zzz22550), da, db) → new_mkBalBranch6MkBalBranch38(zzz2934, zzz2127, zzz2930, zzz2931, zzz22550, Zero, da, db)
new_mkVBalBranch3MkVBalBranch262(zzz3170, zzz3171, Pos(Succ(zzz317200)), zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, Zero, h) → new_mkVBalBranch3MkVBalBranch251(zzz3170, zzz3171, Succ(zzz317200), zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, h)
new_primMulNat(Zero) → Zero
new_mkBalBranch6MkBalBranch51(zzz2934, zzz2127, zzz2930, zzz2931, da, db) → new_mkBranch(Zero, zzz2930, zzz2931, zzz2127, zzz2934, da, db)
new_mkBalBranch6MkBalBranch411(zzz2934, zzz2127, zzz2930, zzz2931, Pos(Zero), Pos(zzz22060), da, db) → new_mkBalBranch6MkBalBranch414(zzz2934, zzz2127, zzz2930, zzz2931, new_primMulNat(zzz22060), da, db)
new_mkVBalBranch2(zzz31, Branch(zzz330, zzz331, Neg(Zero), zzz333, zzz334), Branch(zzz3170, zzz3171, Pos(Succ(zzz317200)), zzz3173, zzz3174), h) → new_mkBalBranch(zzz3170, zzz3171, new_mkVBalBranch2(zzz31, Branch(zzz330, zzz331, Neg(Zero), zzz333, zzz334), zzz3173, h), zzz3174, ty_Ordering, h)
new_mkVBalBranch3MkVBalBranch265(zzz3170, zzz3171, Zero, zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, h) → new_mkBalBranch(zzz330, zzz331, zzz333, new_mkVBalBranch2(zzz31, zzz334, Branch(zzz3170, zzz3171, Neg(Zero), zzz3173, zzz3174), h), ty_Ordering, h)
new_mkVBalBranch3MkVBalBranch164(zzz473, zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, zzz481, zzz482, Succ(zzz7390), eh) → new_mkVBalBranch3MkVBalBranch162(zzz473, zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, Zero, zzz480, zzz481, zzz482, Succ(zzz7390), Succ(Zero), eh)
new_splitLT15(Branch(LT, zzz781, zzz782, zzz783, zzz784), bg) → new_mkVBalBranch2(zzz781, zzz783, new_splitLT15(zzz784, bg), bg)
new_splitLT15(EmptyFM, bg) → new_splitLT41(bg)
new_mkBalBranch6MkBalBranch1110(zzz2934, zzz21270, zzz21271, zzz21272, zzz21273, zzz21274, zzz2930, zzz2931, Succ(zzz22770), da, db) → new_mkBalBranch6MkBalBranch1112(zzz2934, zzz21270, zzz21271, zzz21272, zzz21273, zzz21274, zzz2930, zzz2931, da, db)
new_mkBalBranch6MkBalBranch32(zzz2934, zzz2127, zzz2930, zzz2931, da, db) → new_mkBalBranch6MkBalBranch313(zzz2934, zzz2127, zzz2930, zzz2931, da, db)
new_mkVBalBranch3MkVBalBranch286(zzz3170, zzz3171, zzz31720, zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, h) → new_mkVBalBranch3MkVBalBranch265(zzz3170, zzz3171, zzz31720, zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, h)
new_mkVBalBranch3MkVBalBranch263(zzz498, zzz499, zzz500, zzz501, zzz502, zzz503, zzz504, zzz505, zzz506, zzz507, Zero, Succ(zzz5090), ee) → new_mkBalBranch(zzz498, zzz499, new_mkVBalBranch4(zzz507, Branch(zzz503, zzz504, Neg(Succ(Zero)), zzz505, zzz506), zzz501, ee), zzz502, ty_Ordering, ee)
new_mkVBalBranch3(zzz31, Branch(zzz520, zzz521, Neg(Zero), zzz523, zzz524), Branch(zzz340, zzz341, Pos(Zero), zzz343, zzz344), h) → new_mkBranch(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))), GT, zzz31, Branch(zzz520, zzz521, Neg(Zero), zzz523, zzz524), Branch(zzz340, zzz341, Pos(Zero), zzz343, zzz344), ty_Ordering, h)
new_mkVBalBranch3(zzz31, Branch(zzz520, zzz521, Pos(Zero), zzz523, zzz524), Branch(zzz340, zzz341, Neg(Zero), zzz343, zzz344), h) → new_mkBranch(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))), GT, zzz31, Branch(zzz520, zzz521, Pos(Zero), zzz523, zzz524), Branch(zzz340, zzz341, Neg(Zero), zzz343, zzz344), ty_Ordering, h)
new_addToFM_C4(Branch(LT, zzz341, zzz342, zzz343, zzz344), zzz31, h) → new_mkBalBranch(LT, zzz341, zzz343, new_addToFM_C4(zzz344, zzz31, h), ty_Ordering, h)
new_mkBalBranch6MkBalBranch35(zzz2934, zzz2127, zzz2930, zzz2931, Succ(zzz22500), da, db) → new_mkBalBranch6MkBalBranch36(zzz2934, zzz2127, zzz2930, zzz2931, Zero, zzz22500, da, db)
new_mkVBalBranch3MkVBalBranch159(zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, zzz1125, zzz1126, zzz1127, zzz1128, zzz1129, Zero, ff) → new_mkVBalBranch3MkVBalBranch149(zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, zzz1125, Succ(zzz1126), zzz1127, zzz1128, zzz1129, Succ(Succ(zzz1126)), Zero, ff)
new_mkVBalBranch3MkVBalBranch132(zzz2033, zzz2034, zzz2035, zzz2036, zzz2037, zzz2038, zzz2039, zzz2040, zzz2041, zzz2042, zzz2043, Zero, Zero, fg) → new_mkVBalBranch3MkVBalBranch166(zzz2033, zzz2034, zzz2035, zzz2036, zzz2037, zzz2038, zzz2039, zzz2040, zzz2041, zzz2042, zzz2043, fg)
new_mkVBalBranch3MkVBalBranch157(zzz498, zzz499, zzz500, zzz501, zzz502, zzz503, zzz504, zzz505, zzz506, zzz507, Succ(zzz8040), ee) → new_mkVBalBranch3MkVBalBranch149(zzz498, zzz499, zzz500, zzz501, zzz502, zzz503, zzz504, Zero, zzz505, zzz506, zzz507, Succ(Zero), Succ(zzz8040), ee)
new_mkVBalBranch3MkVBalBranch156(zzz958, zzz959, zzz960, zzz961, zzz962, zzz963, zzz964, zzz965, zzz966, zzz967, zzz968, Zero, fa) → new_mkVBalBranch3MkVBalBranch152(zzz958, zzz959, zzz960, zzz961, zzz962, zzz963, zzz964, zzz965, zzz966, zzz967, zzz968, Zero, Succ(zzz965), fa)
new_mkBalBranch6MkBalBranch310(zzz2934, zzz2127, zzz2930, zzz2931, Neg(Succ(zzz224400)), Neg(zzz22450), da, db) → new_mkBalBranch6MkBalBranch37(zzz2934, zzz2127, zzz2930, zzz2931, zzz224400, new_primMulNat(zzz22450), da, db)
new_mkVBalBranch3MkVBalBranch132(zzz2033, zzz2034, zzz2035, zzz2036, zzz2037, zzz2038, zzz2039, zzz2040, zzz2041, zzz2042, zzz2043, Succ(zzz20440), Zero, fg) → new_mkVBalBranch3MkVBalBranch166(zzz2033, zzz2034, zzz2035, zzz2036, zzz2037, zzz2038, zzz2039, zzz2040, zzz2041, zzz2042, zzz2043, fg)
new_splitGT15(Branch(LT, zzz21291, zzz21292, zzz21293, zzz21294), cc) → new_splitGT15(zzz21294, cc)
new_mkBalBranch6MkBalBranch415(zzz2934, zzz2127, zzz2930, zzz2931, zzz222100, zzz2237, da, db) → new_mkBalBranch6MkBalBranch49(zzz2934, zzz2127, zzz2930, zzz2931, da, db)
new_mkVBalBranch3MkVBalBranch263(zzz498, zzz499, zzz500, zzz501, zzz502, zzz503, zzz504, zzz505, zzz506, zzz507, Succ(zzz5080), Zero, ee) → new_mkVBalBranch3MkVBalBranch264(zzz498, zzz499, zzz500, zzz501, zzz502, zzz503, zzz504, zzz505, zzz506, zzz507, ee)
new_intersectFM_C2Gts2(zzz883, zzz884, zzz885, zzz886, be) → new_splitGT29(zzz883, zzz884, zzz885, zzz886, be)
new_mkBalBranch6MkBalBranch017(zzz29340, zzz29341, zzz29342, zzz29343, zzz29344, zzz2127, zzz2930, zzz2931, Neg(Succ(zzz224600)), Pos(zzz22470), da, db) → new_mkBalBranch6MkBalBranch011(zzz29340, zzz29341, zzz29342, zzz29343, zzz29344, zzz2127, zzz2930, zzz2931, da, db)
new_mkBalBranch6MkBalBranch013(zzz29340, zzz29341, zzz29342, zzz29343, zzz29344, zzz2127, zzz2930, zzz2931, zzz224600, Zero, da, db) → new_mkBalBranch6MkBalBranch015(zzz29340, zzz29341, zzz29342, zzz29343, zzz29344, zzz2127, zzz2930, zzz2931, da, db)
new_mkVBalBranch3MkVBalBranch168(zzz340, zzz341, zzz34200, zzz343, zzz344, zzz510, zzz511, zzz513, zzz514, zzz31, Zero, h) → new_mkBranch(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))), EQ, zzz31, Branch(zzz510, zzz511, Pos(Zero), zzz513, zzz514), Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), ty_Ordering, h)
new_mkVBalBranch3MkVBalBranch275(zzz958, zzz959, zzz960, zzz961, zzz962, zzz963, zzz964, zzz965, zzz966, zzz967, zzz968, Succ(zzz9690), Zero, fa) → new_mkVBalBranch3MkVBalBranch276(zzz958, zzz959, zzz960, zzz961, zzz962, zzz963, zzz964, zzz965, zzz966, zzz967, zzz968, fa)
new_splitLT24(zzz854, zzz855, zzz856, zzz857, ba) → new_splitLT12(zzz856, ba)
new_mkVBalBranch3MkVBalBranch160(zzz340, zzz341, zzz34200, zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, h) → new_mkBalBranch(zzz510, zzz511, zzz513, new_mkVBalBranch4(zzz31, zzz514, Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), h), ty_Ordering, h)
new_mkVBalBranch3MkVBalBranch274(zzz818, zzz819, zzz820, zzz821, zzz822, zzz823, zzz824, zzz825, zzz826, zzz827, eb) → new_mkVBalBranch3MkVBalBranch143(zzz818, zzz819, zzz820, zzz821, zzz822, zzz823, zzz824, zzz825, zzz826, zzz827, new_primMulNat1(zzz820), eb)
new_mkVBalBranch3MkVBalBranch261(zzz3170, zzz3171, Neg(Succ(zzz317200)), zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, Zero, h) → new_mkVBalBranch3MkVBalBranch286(zzz3170, zzz3171, Succ(zzz317200), zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, h)
new_splitGT6(h) → new_splitGT42(h)
new_splitGT13(h) → new_splitGT41(h)
new_mkBalBranch6MkBalBranch30(zzz2934, zzz2127, zzz2930, zzz2931, Zero, da, db) → new_mkBalBranch6MkBalBranch32(zzz2934, zzz2127, zzz2930, zzz2931, da, db)
new_addToFM1(zzz317, zzz31, h) → new_addToFM_C2(zzz317, zzz31, h)
new_mkVBalBranch3MkVBalBranch272(zzz340, zzz341, Neg(Succ(Succ(Succ(zzz3420000)))), zzz343, zzz344, zzz520, zzz521, Succ(zzz522000), zzz523, zzz524, zzz31, Succ(Zero), h) → new_mkVBalBranch3MkVBalBranch255(zzz340, zzz341, Succ(Succ(zzz3420000)), zzz343, zzz344, zzz520, zzz521, zzz522000, zzz523, zzz524, zzz31, Succ(zzz3420000), Succ(zzz522000), h)
new_splitGT12(EmptyFM, ba) → new_splitGT41(ba)
new_mkBalBranch6MkBalBranch0110(zzz29340, zzz29341, zzz29342, zzz29343, zzz29344, zzz2127, zzz2930, zzz2931, Succ(zzz22560), da, db) → new_mkBalBranch6MkBalBranch018(zzz29340, zzz29341, zzz29342, zzz29343, zzz29344, zzz2127, zzz2930, zzz2931, Zero, zzz22560, da, db)
new_mkVBalBranch3MkVBalBranch281(zzz340, zzz341, Neg(Zero), zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, Zero, h) → new_mkVBalBranch3MkVBalBranch266(zzz340, zzz341, zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, h)
new_mkBalBranch6MkBalBranch1111(zzz2934, zzz21270, zzz21271, zzz21272, zzz21273, zzz21274, zzz2930, zzz2931, Zero, zzz226200, da, db) → new_mkBalBranch6MkBalBranch1112(zzz2934, zzz21270, zzz21271, zzz21272, zzz21273, zzz21274, zzz2930, zzz2931, da, db)
new_mkVBalBranch3MkVBalBranch131(zzz929, zzz930, zzz931, zzz932, zzz933, zzz934, zzz935, zzz936, zzz937, zzz938, zzz939, Zero, dc) → new_mkVBalBranch3MkVBalBranch132(zzz929, zzz930, zzz931, zzz932, zzz933, zzz934, zzz935, zzz936, zzz937, zzz938, zzz939, Zero, Succ(zzz936), dc)
new_intersectFM_C2Lts(zzz76, zzz77, zzz78, zzz79, bg) → new_splitLT9(zzz76, zzz77, zzz78, zzz79, bg)
new_primPlusInt0(zzz1311, Pos(zzz13130)) → Pos(new_primPlusNat2(zzz1311, zzz13130))
new_mkBalBranch6MkBalBranch115(zzz2934, zzz21270, zzz21271, zzz21272, zzz21273, zzz21274, zzz2930, zzz2931, zzz226200, zzz2271, da, db) → new_mkBalBranch6MkBalBranch1114(zzz2934, zzz21270, zzz21271, zzz21272, zzz21273, zzz21274, zzz2930, zzz2931, da, db)
new_mkVBalBranch3MkVBalBranch289(zzz1105, zzz1106, zzz1107, zzz1108, zzz1109, zzz1110, zzz1111, zzz1112, zzz1113, zzz1114, zzz1115, Zero, Succ(zzz11170), fh) → new_mkBalBranch(zzz1105, zzz1106, new_mkVBalBranch4(zzz1115, Branch(zzz1110, zzz1111, Pos(Succ(Succ(zzz1112))), zzz1113, zzz1114), zzz1108, fh), zzz1109, ty_Ordering, fh)
new_mkVBalBranch3MkVBalBranch168(zzz340, zzz341, zzz34200, zzz343, zzz344, zzz510, zzz511, zzz513, zzz514, zzz31, Succ(zzz1200), h) → new_mkBalBranch(zzz510, zzz511, zzz513, new_mkVBalBranch4(zzz31, zzz514, Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), h), ty_Ordering, h)
new_mkVBalBranch3MkVBalBranch281(zzz340, zzz341, Pos(zzz3420), zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, Zero, h) → new_mkVBalBranch3MkVBalBranch248(zzz340, zzz341, zzz3420, zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, h)
new_mkVBalBranch3MkVBalBranch281(zzz340, zzz341, Pos(zzz3420), zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, Succ(zzz670), h) → new_mkVBalBranch3MkVBalBranch248(zzz340, zzz341, zzz3420, zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, h)
new_mkBalBranch6MkBalBranch5(zzz2934, zzz2127, zzz2930, zzz2931, Neg(Zero), da, db) → new_mkBalBranch6MkBalBranch51(zzz2934, zzz2127, zzz2930, zzz2931, da, db)
new_mkVBalBranch3MkVBalBranch262(zzz3170, zzz3171, Pos(zzz31720), zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, Succ(zzz4190), h) → new_mkVBalBranch3MkVBalBranch251(zzz3170, zzz3171, zzz31720, zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, h)
new_mkBalBranch6MkBalBranch017(zzz29340, zzz29341, zzz29342, zzz29343, zzz29344, zzz2127, zzz2930, zzz2931, Pos(Succ(zzz224600)), Neg(zzz22470), da, db) → new_mkBalBranch6MkBalBranch015(zzz29340, zzz29341, zzz29342, zzz29343, zzz29344, zzz2127, zzz2930, zzz2931, da, db)
new_intersectFM_C2Lts1(zzz869, zzz870, zzz871, zzz872, bc) → new_splitLT25(zzz869, zzz870, zzz871, zzz872, bc)
new_mkVBalBranch3MkVBalBranch288(zzz340, zzz341, Pos(Zero), zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, Zero, h) → new_mkVBalBranch3MkVBalBranch285(zzz340, zzz341, zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, h)
new_mkVBalBranch4(zzz31, Branch(zzz510, zzz511, Pos(Zero), zzz513, zzz514), Branch(zzz340, zzz341, Neg(Zero), zzz343, zzz344), h) → new_mkBranch(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))), EQ, zzz31, Branch(zzz510, zzz511, Pos(Zero), zzz513, zzz514), Branch(zzz340, zzz341, Neg(Zero), zzz343, zzz344), ty_Ordering, h)
new_mkVBalBranch4(zzz31, Branch(zzz510, zzz511, Neg(Zero), zzz513, zzz514), Branch(zzz340, zzz341, Pos(Zero), zzz343, zzz344), h) → new_mkBranch(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))), EQ, zzz31, Branch(zzz510, zzz511, Neg(Zero), zzz513, zzz514), Branch(zzz340, zzz341, Pos(Zero), zzz343, zzz344), ty_Ordering, h)
new_mkBalBranch6Size_l(zzz2934, zzz2127, zzz2930, zzz2931, db, da) → new_sizeFM(zzz2127, da, db)
new_mkBalBranch6Size_r(zzz2934, zzz2127, zzz2930, zzz2931, db, da) → new_sizeFM(zzz2934, da, db)
new_mkVBalBranch3MkVBalBranch288(zzz340, zzz341, Pos(Succ(Succ(zzz342000))), zzz343, zzz344, zzz510, zzz511, Zero, zzz513, zzz514, zzz31, Succ(Zero), h) → new_mkVBalBranch3MkVBalBranch270(zzz340, zzz341, Succ(zzz342000), zzz343, zzz344, zzz510, zzz511, zzz513, zzz514, zzz31, Zero, zzz342000, h)
new_mkVBalBranch3MkVBalBranch147(zzz340, zzz341, zzz34200, zzz343, zzz344, zzz520, zzz521, zzz52200, zzz523, zzz524, zzz31, Succ(zzz1430), h) → new_mkVBalBranch3MkVBalBranch148(zzz340, zzz341, zzz34200, zzz343, zzz344, zzz520, zzz521, zzz52200, zzz523, zzz524, zzz31, h)
new_mkBalBranch6MkBalBranch416(zzz2934, zzz2127, zzz2930, zzz2931, Succ(zzz22420), da, db) → new_mkBalBranch6MkBalBranch43(zzz2934, zzz2127, zzz2930, zzz2931, da, db)
new_mkBalBranch6MkBalBranch012(zzz29340, zzz29341, zzz29342, zzz29343, zzz29344, zzz2127, zzz2930, zzz2931, da, db) → new_mkBalBranch6MkBalBranch016(zzz29340, zzz29341, zzz29342, zzz29343, zzz29344, zzz2127, zzz2930, zzz2931, da, db)
new_mkBalBranch6MkBalBranch1113(zzz2934, zzz21270, zzz21271, zzz21272, zzz21273, zzz21274, zzz2930, zzz2931, Succ(zzz2262000), Zero, da, db) → new_mkBalBranch6MkBalBranch1114(zzz2934, zzz21270, zzz21271, zzz21272, zzz21273, zzz21274, zzz2930, zzz2931, da, db)
new_mkBalBranch6MkBalBranch017(zzz29340, zzz29341, zzz29342, zzz29343, zzz29344, zzz2127, zzz2930, zzz2931, Neg(Zero), Neg(zzz22470), da, db) → new_mkBalBranch6MkBalBranch019(zzz29340, zzz29341, zzz29342, zzz29343, zzz29344, zzz2127, zzz2930, zzz2931, new_primMulNat2(zzz22470), da, db)
new_splitLT12(Branch(GT, zzz8561, zzz8562, zzz8563, zzz8564), ba) → new_splitLT25(zzz8561, zzz8562, zzz8563, zzz8564, ba)
new_splitGT26(zzz76, zzz77, zzz78, zzz79, bg) → new_splitGT24(zzz76, zzz77, zzz78, zzz79, bg)
new_mkVBalBranch3MkVBalBranch281(zzz340, zzz341, Neg(Succ(Succ(Succ(zzz3420000)))), zzz343, zzz344, zzz510, zzz511, Zero, zzz513, zzz514, zzz31, Succ(Zero), h) → new_mkVBalBranch3MkVBalBranch263(zzz340, zzz341, Succ(Succ(zzz3420000)), zzz343, zzz344, zzz510, zzz511, zzz513, zzz514, zzz31, Succ(zzz3420000), Zero, h)
new_mkVBalBranch3MkVBalBranch152(zzz1337, zzz1338, zzz1339, zzz1340, zzz1341, zzz1342, zzz1343, zzz1344, zzz1345, zzz1346, zzz1347, Zero, Zero, eg) → new_mkVBalBranch3MkVBalBranch151(zzz1337, zzz1338, zzz1339, zzz1340, zzz1341, zzz1342, zzz1343, zzz1344, zzz1345, zzz1346, zzz1347, eg)
new_mkVBalBranch3MkVBalBranch267(zzz340, zzz341, Pos(Zero), zzz343, zzz344, zzz520, zzz521, zzz52200, zzz523, zzz524, zzz31, Zero, h) → new_mkVBalBranch3MkVBalBranch268(zzz340, zzz341, zzz343, zzz344, zzz520, zzz521, zzz52200, zzz523, zzz524, zzz31, h)
new_mkVBalBranch2(zzz31, Branch(zzz330, zzz331, zzz332, zzz333, zzz334), EmptyFM, h) → new_addToFM1(Branch(zzz330, zzz331, zzz332, zzz333, zzz334), zzz31, h)
new_mkBalBranch6MkBalBranch113(zzz2934, zzz21270, zzz21271, zzz21272, zzz21273, zzz21274, zzz2930, zzz2931, Neg(Zero), Pos(zzz22630), da, db) → new_mkBalBranch6MkBalBranch1110(zzz2934, zzz21270, zzz21271, zzz21272, zzz21273, zzz21274, zzz2930, zzz2931, new_primMulNat2(zzz22630), da, db)
new_intersectFM_C2Lts2(zzz883, zzz884, zzz885, zzz886, be) → new_splitLT15(Branch(LT, zzz883, zzz884, zzz885, zzz886), be)
new_mkVBalBranch3MkVBalBranch164(zzz473, zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, zzz481, zzz482, Zero, eh) → new_mkVBalBranch3MkVBalBranch162(zzz473, zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, Zero, zzz480, zzz481, zzz482, Zero, Succ(Zero), eh)
new_mkVBalBranch3MkVBalBranch165(zzz461, zzz462, zzz463, zzz464, zzz465, zzz466, zzz467, zzz468, zzz469, zzz470, zzz471, de) → new_mkVBalBranch3MkVBalBranch163(zzz461, zzz462, zzz463, zzz464, zzz465, zzz466, zzz467, zzz468, zzz469, zzz470, zzz471, de)
new_mkVBalBranch3(zzz31, Branch(zzz520, zzz521, Pos(Zero), zzz523, zzz524), Branch(zzz340, zzz341, Pos(Zero), zzz343, zzz344), h) → new_mkBranch(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))), GT, zzz31, Branch(zzz520, zzz521, Pos(Zero), zzz523, zzz524), Branch(zzz340, zzz341, Pos(Zero), zzz343, zzz344), ty_Ordering, h)
new_mkBalBranch6MkBalBranch113(zzz2934, zzz21270, zzz21271, zzz21272, zzz21273, zzz21274, zzz2930, zzz2931, Pos(Succ(zzz226200)), Pos(zzz22630), da, db) → new_mkBalBranch6MkBalBranch114(zzz2934, zzz21270, zzz21271, zzz21272, zzz21273, zzz21274, zzz2930, zzz2931, zzz226200, new_primMulNat2(zzz22630), da, db)
new_mkVBalBranch3MkVBalBranch272(zzz340, zzz341, Neg(Succ(Succ(Succ(zzz3420000)))), zzz343, zzz344, zzz520, zzz521, Zero, zzz523, zzz524, zzz31, Succ(Succ(zzz6900)), h) → new_mkVBalBranch3MkVBalBranch277(zzz340, zzz341, Succ(Succ(zzz3420000)), zzz343, zzz344, zzz520, zzz521, zzz523, zzz524, zzz31, Succ(zzz3420000), Succ(zzz6900), h)
new_mkBalBranch6MkBalBranch113(zzz2934, zzz21270, zzz21271, zzz21272, zzz21273, zzz21274, zzz2930, zzz2931, Pos(Succ(zzz226200)), Neg(zzz22630), da, db) → new_mkBalBranch6MkBalBranch115(zzz2934, zzz21270, zzz21271, zzz21272, zzz21273, zzz21274, zzz2930, zzz2931, zzz226200, new_primMulNat2(zzz22630), da, db)
new_splitGT27(zzz31, zzz32, zzz33, zzz34, h) → zzz34
new_mkBalBranch6MkBalBranch42(zzz2934, zzz2127, zzz2930, zzz2931, zzz222100, zzz2240, da, db) → new_mkBalBranch6MkBalBranch43(zzz2934, zzz2127, zzz2930, zzz2931, da, db)
new_primMulNat1(zzz34200) → new_primPlusNat2(new_primMulNat0(zzz34200), Succ(zzz34200))
new_mkBalBranch6MkBalBranch1112(zzz2934, zzz21270, zzz21271, zzz21272, zzz21273, zzz21274, zzz2930, zzz2931, da, db) → new_mkBranch(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))), zzz21270, zzz21271, zzz21273, new_mkBranch(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))), zzz2930, zzz2931, zzz21274, zzz2934, da, db), da, db)
new_mkVBalBranch3MkVBalBranch281(zzz340, zzz341, Neg(Succ(Succ(Zero))), zzz343, zzz344, zzz510, zzz511, Succ(zzz512000), zzz513, zzz514, zzz31, Succ(Succ(zzz6700)), h) → new_mkVBalBranch3MkVBalBranch280(zzz340, zzz341, Succ(Zero), zzz343, zzz344, zzz510, zzz511, zzz512000, zzz513, zzz514, zzz31, Zero, Succ(Succ(new_primPlusNat2(zzz6700, zzz512000))), h)
new_mkBalBranch6MkBalBranch010(zzz29340, zzz29341, zzz29342, zzz29343, zzz29344, zzz2127, zzz2930, zzz2931, Succ(zzz22580), da, db) → new_mkBalBranch6MkBalBranch011(zzz29340, zzz29341, zzz29342, zzz29343, zzz29344, zzz2127, zzz2930, zzz2931, da, db)
new_mkVBalBranch3MkVBalBranch163(zzz461, zzz462, zzz463, zzz464, zzz465, zzz466, zzz467, zzz468, zzz469, zzz470, zzz471, de) → new_mkVBalBranch3MkVBalBranch158(zzz461, zzz462, zzz463, zzz464, zzz465, zzz466, zzz467, zzz468, zzz469, zzz470, zzz471, de)
new_addToFM_C3(Branch(LT, zzz341, zzz342, zzz343, zzz344), zzz31, h) → new_mkBalBranch(LT, zzz341, zzz343, new_addToFM_C3(zzz344, zzz31, h), ty_Ordering, h)
new_splitGT14(Branch(EQ, zzz8861, zzz8862, zzz8863, zzz8864), be) → new_splitGT27(zzz8861, zzz8862, zzz8863, zzz8864, be)
new_splitLT3(zzz31, zzz32, zzz33, zzz34, h) → new_splitLT28(zzz31, zzz32, zzz33, zzz34, h)
new_mkVBalBranch3MkVBalBranch248(zzz340, zzz341, zzz3420, zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, h) → new_mkBalBranch(zzz340, zzz341, new_mkVBalBranch4(zzz31, Branch(zzz510, zzz511, Neg(Succ(zzz51200)), zzz513, zzz514), zzz343, h), zzz344, ty_Ordering, h)
new_mkVBalBranch3MkVBalBranch267(zzz340, zzz341, Neg(zzz3420), zzz343, zzz344, zzz520, zzz521, zzz52200, zzz523, zzz524, zzz31, Succ(zzz680), h) → new_mkVBalBranch3MkVBalBranch269(zzz340, zzz341, zzz3420, zzz343, zzz344, zzz520, zzz521, zzz52200, zzz523, zzz524, zzz31, h)
new_sizeFM(Branch(zzz13040, zzz13041, zzz13042, zzz13043, zzz13044), fb, fc) → zzz13042
new_mkBalBranch6MkBalBranch35(zzz2934, zzz2127, zzz2930, zzz2931, Zero, da, db) → new_mkBalBranch6MkBalBranch32(zzz2934, zzz2127, zzz2930, zzz2931, da, db)
new_mkVBalBranch2(zzz31, Branch(zzz330, zzz331, Neg(Zero), zzz333, zzz334), Branch(zzz3170, zzz3171, Neg(Zero), zzz3173, zzz3174), h) → new_mkBranch(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))), LT, zzz31, Branch(zzz330, zzz331, Neg(Zero), zzz333, zzz334), Branch(zzz3170, zzz3171, Neg(Zero), zzz3173, zzz3174), ty_Ordering, h)
new_mkBalBranch6MkBalBranch116(zzz2934, zzz21270, zzz21271, zzz21272, zzz21273, zzz21274, zzz2930, zzz2931, Zero, da, db) → new_mkBalBranch6MkBalBranch112(zzz2934, zzz21270, zzz21271, zzz21272, zzz21273, zzz21274, zzz2930, zzz2931, da, db)
new_mkVBalBranch3MkVBalBranch281(zzz340, zzz341, Neg(Succ(Succ(Zero))), zzz343, zzz344, zzz510, zzz511, Succ(zzz512000), zzz513, zzz514, zzz31, Succ(Zero), h) → new_mkVBalBranch3MkVBalBranch280(zzz340, zzz341, Succ(Zero), zzz343, zzz344, zzz510, zzz511, zzz512000, zzz513, zzz514, zzz31, Zero, Succ(zzz512000), h)
new_mkVBalBranch3MkVBalBranch262(zzz3170, zzz3171, Neg(Succ(zzz317200)), zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, Zero, h) → new_mkVBalBranch3MkVBalBranch246(zzz3170, zzz3171, zzz317200, zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, Succ(zzz317200), Zero, h)
new_mkBalBranch6MkBalBranch118(zzz2934, zzz21270, zzz21271, zzz21272, zzz21273, zzz21274, zzz2930, zzz2931, zzz226200, zzz2275, da, db) → new_mkBalBranch6MkBalBranch1112(zzz2934, zzz21270, zzz21271, zzz21272, zzz21273, zzz21274, zzz2930, zzz2931, da, db)
new_primMinusNat0(Zero, Zero) → Pos(Zero)
new_mkBalBranch6MkBalBranch117(zzz2934, zzz21270, zzz21271, zzz21272, zzz21273, zzz21274, zzz2930, zzz2931, Succ(zzz22740), da, db) → new_mkBalBranch6MkBalBranch1114(zzz2934, zzz21270, zzz21271, zzz21272, zzz21273, zzz21274, zzz2930, zzz2931, da, db)
new_mkVBalBranch3(zzz31, Branch(zzz520, zzz521, Neg(Succ(zzz52200)), zzz523, zzz524), Branch(zzz340, zzz341, zzz342, zzz343, zzz344), h) → new_mkVBalBranch3MkVBalBranch272(zzz340, zzz341, zzz342, zzz343, zzz344, zzz520, zzz521, zzz52200, zzz523, zzz524, zzz31, new_primMulNat0(zzz52200), h)
new_mkBalBranch6MkBalBranch119(zzz2934, zzz21270, zzz21271, zzz21272, zzz21273, zzz21274, zzz2930, zzz2931, zzz226200, zzz2276, da, db) → new_mkBalBranch6MkBalBranch1111(zzz2934, zzz21270, zzz21271, zzz21272, zzz21273, zzz21274, zzz2930, zzz2931, zzz2276, zzz226200, da, db)
new_mkBalBranch6MkBalBranch110(zzz2934, zzz21270, zzz21271, zzz21272, zzz21273, zzz21274, zzz2930, zzz2931, Succ(zzz22780), da, db) → new_mkBalBranch6MkBalBranch111(zzz2934, zzz21270, zzz21271, zzz21272, zzz21273, zzz21274, zzz2930, zzz2931, zzz22780, Zero, da, db)
new_mkBalBranch6MkBalBranch414(zzz2934, zzz2127, zzz2930, zzz2931, Succ(zzz22380), da, db) → new_mkBalBranch6MkBalBranch47(zzz2934, zzz2127, zzz2930, zzz2931, Zero, zzz22380, da, db)
new_mkVBalBranch3MkVBalBranch262(zzz3170, zzz3171, Neg(Zero), zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, Succ(zzz4190), h) → new_mkBalBranch(zzz3170, zzz3171, new_mkVBalBranch2(zzz31, Branch(zzz330, zzz331, Neg(Succ(zzz33200)), zzz333, zzz334), zzz3173, h), zzz3174, ty_Ordering, h)
new_mkVBalBranch3MkVBalBranch261(zzz3170, zzz3171, Neg(Zero), zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, Zero, h) → new_mkVBalBranch3MkVBalBranch265(zzz3170, zzz3171, Zero, zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, h)
new_mkVBalBranch3MkVBalBranch137(zzz461, zzz462, zzz463, zzz464, zzz465, zzz466, zzz467, zzz468, zzz469, zzz470, zzz471, Succ(zzz5800), de) → new_mkVBalBranch3MkVBalBranch162(zzz461, zzz462, zzz463, zzz464, zzz465, zzz466, zzz467, Succ(zzz468), zzz469, zzz470, zzz471, Succ(zzz5800), Succ(Succ(zzz468)), de)
new_mkVBalBranch3MkVBalBranch267(zzz340, zzz341, Pos(Succ(zzz34200)), zzz343, zzz344, zzz520, zzz521, zzz52200, zzz523, zzz524, zzz31, Zero, h) → new_mkVBalBranch3MkVBalBranch252(zzz340, zzz341, zzz34200, zzz343, zzz344, zzz520, zzz521, zzz52200, zzz523, zzz524, zzz31, zzz52200, zzz34200, h)
new_splitLT26(zzz31, zzz32, zzz33, zzz34, h) → zzz33
new_mkBalBranch6MkBalBranch014(zzz29340, zzz29341, zzz29342, zzz29343, zzz29344, zzz2127, zzz2930, zzz2931, Succ(zzz2246000), Zero, da, db) → new_mkBalBranch6MkBalBranch015(zzz29340, zzz29341, zzz29342, zzz29343, zzz29344, zzz2127, zzz2930, zzz2931, da, db)
new_mkVBalBranch3MkVBalBranch267(zzz340, zzz341, Pos(Succ(zzz34200)), zzz343, zzz344, zzz520, zzz521, zzz52200, zzz523, zzz524, zzz31, Succ(zzz680), h) → new_mkVBalBranch3MkVBalBranch252(zzz340, zzz341, zzz34200, zzz343, zzz344, zzz520, zzz521, zzz52200, zzz523, zzz524, zzz31, Succ(new_primPlusNat2(zzz680, zzz52200)), zzz34200, h)
new_mkBalBranch6MkBalBranch1115(zzz2934, zzz21270, zzz21271, zzz21272, zzz21273, EmptyFM, zzz2930, zzz2931, da, db) → error([])
new_mkBalBranch6MkBalBranch0111(zzz29340, zzz29341, zzz29342, zzz29343, zzz29344, zzz2127, zzz2930, zzz2931, Succ(zzz22570), da, db) → new_mkBalBranch6MkBalBranch015(zzz29340, zzz29341, zzz29342, zzz29343, zzz29344, zzz2127, zzz2930, zzz2931, da, db)
new_splitLT12(Branch(EQ, zzz8561, zzz8562, zzz8563, zzz8564), ba) → new_splitLT24(zzz8561, zzz8562, zzz8563, zzz8564, ba)
new_mkVBalBranch3MkVBalBranch272(zzz340, zzz341, Neg(Succ(Zero)), zzz343, zzz344, zzz520, zzz521, Zero, zzz523, zzz524, zzz31, Zero, h) → new_mkVBalBranch3MkVBalBranch273(zzz340, zzz341, Zero, zzz343, zzz344, zzz520, zzz521, zzz523, zzz524, zzz31, h)
new_mkVBalBranch3MkVBalBranch262(zzz3170, zzz3171, Neg(Succ(zzz317200)), zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, Succ(zzz4190), h) → new_mkVBalBranch3MkVBalBranch246(zzz3170, zzz3171, zzz317200, zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, zzz317200, zzz4190, h)
new_mkBalBranch6MkBalBranch315(zzz2934, zzz2127, zzz2930, zzz2931, Zero, da, db) → new_mkBalBranch6MkBalBranch32(zzz2934, zzz2127, zzz2930, zzz2931, da, db)
new_primMulNat0(zzz6200) → new_primPlusNat3(Succ(new_primPlusNat3(new_primPlusNat1(zzz6200), zzz6200)), Succ(zzz6200))
new_mkVBalBranch3MkVBalBranch146(zzz3170, zzz3171, zzz317200, zzz3173, zzz3174, zzz330, zzz331, zzz333, zzz334, zzz31, Succ(zzz5500), h) → new_mkBalBranch(zzz330, zzz331, zzz333, new_mkVBalBranch2(zzz31, zzz334, Branch(zzz3170, zzz3171, Neg(Succ(zzz317200)), zzz3173, zzz3174), h), ty_Ordering, h)
new_mkBalBranch6MkBalBranch411(zzz2934, zzz2127, zzz2930, zzz2931, Pos(Succ(zzz222100)), Pos(zzz22060), da, db) → new_mkBalBranch6MkBalBranch44(zzz2934, zzz2127, zzz2930, zzz2931, zzz222100, new_primMulNat(zzz22060), da, db)
new_mkBalBranch6MkBalBranch1113(zzz2934, zzz21270, zzz21271, zzz21272, zzz21273, zzz21274, zzz2930, zzz2931, Zero, Succ(zzz227000), da, db) → new_mkBalBranch6MkBalBranch1112(zzz2934, zzz21270, zzz21271, zzz21272, zzz21273, zzz21274, zzz2930, zzz2931, da, db)
new_mkVBalBranch3MkVBalBranch272(zzz340, zzz341, Neg(Succ(Zero)), zzz343, zzz344, zzz520, zzz521, Succ(zzz522000), zzz523, zzz524, zzz31, Zero, h) → new_mkVBalBranch3MkVBalBranch254(zzz340, zzz341, zzz343, zzz344, zzz520, zzz521, Succ(zzz522000), zzz523, zzz524, zzz31, h)
new_mkVBalBranch2(zzz31, Branch(zzz330, zzz331, Pos(Succ(zzz33200)), zzz333, zzz334), Branch(zzz3170, zzz3171, zzz3172, zzz3173, zzz3174), h) → new_mkVBalBranch3MkVBalBranch261(zzz3170, zzz3171, zzz3172, zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, new_primPlusNat2(new_primMulNat0(zzz33200), Succ(zzz33200)), h)
new_mkVBalBranch3MkVBalBranch139(zzz3170, zzz3171, zzz317200, zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, Zero, h) → new_mkVBalBranch3MkVBalBranch140(zzz3170, zzz3171, zzz317200, zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, h)
new_mkVBalBranch3MkVBalBranch251(zzz3170, zzz3171, zzz31720, zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, h) → new_mkBalBranch(zzz3170, zzz3171, new_mkVBalBranch2(zzz31, Branch(zzz330, zzz331, Neg(Succ(zzz33200)), zzz333, zzz334), zzz3173, h), zzz3174, ty_Ordering, h)
new_mkBalBranch6MkBalBranch314(zzz2934, zzz2127, zzz2930, zzz2931, Zero, da, db) → new_mkBalBranch6MkBalBranch32(zzz2934, zzz2127, zzz2930, zzz2931, da, db)
new_addToFM_C3(EmptyFM, zzz31, h) → Branch(GT, zzz31, Pos(Succ(Zero)), new_emptyFM(h), new_emptyFM(h))
new_splitLT42(h) → new_emptyFM(h)
new_emptyFM(h) → EmptyFM
new_mkBalBranch6MkBalBranch411(zzz2934, zzz2127, zzz2930, zzz2931, Neg(Succ(zzz222100)), Neg(zzz22060), da, db) → new_mkBalBranch6MkBalBranch46(zzz2934, zzz2127, zzz2930, zzz2931, zzz222100, new_primMulNat(zzz22060), da, db)
new_splitLT7(zzz31, zzz32, zzz33, zzz34, h) → new_splitLT26(zzz31, zzz32, zzz33, zzz34, h)
new_mkVBalBranch3MkVBalBranch280(zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, zzz1125, zzz1126, zzz1127, zzz1128, zzz1129, Zero, Zero, ff) → new_mkVBalBranch3MkVBalBranch278(zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, zzz1125, zzz1126, zzz1127, zzz1128, zzz1129, ff)
new_mkVBalBranch3MkVBalBranch280(zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, zzz1125, zzz1126, zzz1127, zzz1128, zzz1129, Succ(zzz11300), Succ(zzz11310), ff) → new_mkVBalBranch3MkVBalBranch280(zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, zzz1125, zzz1126, zzz1127, zzz1128, zzz1129, zzz11300, zzz11310, ff)
new_mkBalBranch6MkBalBranch311(zzz2934, zzz2127, zzz2930, zzz2931, zzz224400, zzz2248, da, db) → new_mkBalBranch6MkBalBranch38(zzz2934, zzz2127, zzz2930, zzz2931, zzz224400, zzz2248, da, db)
new_mkBalBranch6MkBalBranch011(zzz29340, zzz29341, zzz29342, zzz29343, zzz29344, zzz2127, zzz2930, zzz2931, da, db) → new_mkBranch(Succ(Succ(Zero)), zzz29340, zzz29341, new_mkBranch(Succ(Succ(Succ(Zero))), zzz2930, zzz2931, zzz2127, zzz29343, da, db), zzz29344, da, db)
new_mkBalBranch6MkBalBranch43(zzz2934, zzz2127, zzz2930, zzz2931, da, db) → new_mkBalBranch6MkBalBranch41(zzz2934, zzz2127, zzz2930, zzz2931, da, db)
new_mkBalBranch6MkBalBranch414(zzz2934, zzz2127, zzz2930, zzz2931, Zero, da, db) → new_mkBalBranch6MkBalBranch40(zzz2934, zzz2127, zzz2930, zzz2931, da, db)
new_mkVBalBranch3(zzz31, Branch(zzz520, zzz521, Neg(Zero), zzz523, zzz524), Branch(zzz340, zzz341, Pos(Succ(zzz34200)), zzz343, zzz344), h) → new_mkBalBranch(zzz340, zzz341, new_mkVBalBranch3(zzz31, Branch(zzz520, zzz521, Neg(Zero), zzz523, zzz524), zzz343, h), zzz344, ty_Ordering, h)
new_mkBalBranch6MkBalBranch411(zzz2934, zzz2127, zzz2930, zzz2931, Pos(Zero), Neg(zzz22060), da, db) → new_mkBalBranch6MkBalBranch48(zzz2934, zzz2127, zzz2930, zzz2931, new_primMulNat(zzz22060), da, db)
new_mkVBalBranch3MkVBalBranch133(zzz340, zzz341, zzz34200, zzz343, zzz344, zzz510, zzz511, zzz513, zzz514, zzz31, Zero, h) → new_mkBranch(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))), EQ, zzz31, Branch(zzz510, zzz511, Neg(Zero), zzz513, zzz514), Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), ty_Ordering, h)
new_mkBalBranch6MkBalBranch410(zzz2934, zzz2127, zzz2930, zzz2931, zzz2206, da, db) → new_mkBalBranch6MkBalBranch411(zzz2934, zzz2127, zzz2930, zzz2931, new_mkBalBranch6Size_r(zzz2934, zzz2127, zzz2930, zzz2931, db, da), zzz2206, da, db)
new_mkVBalBranch3MkVBalBranch246(zzz972, zzz973, zzz974, zzz975, zzz976, zzz977, zzz978, zzz979, zzz980, zzz981, zzz982, Succ(zzz9830), Succ(zzz9840), cg) → new_mkVBalBranch3MkVBalBranch246(zzz972, zzz973, zzz974, zzz975, zzz976, zzz977, zzz978, zzz979, zzz980, zzz981, zzz982, zzz9830, zzz9840, cg)
new_mkBalBranch6MkBalBranch113(zzz2934, zzz21270, zzz21271, zzz21272, zzz21273, zzz21274, zzz2930, zzz2931, Neg(Succ(zzz226200)), Neg(zzz22630), da, db) → new_mkBalBranch6MkBalBranch119(zzz2934, zzz21270, zzz21271, zzz21272, zzz21273, zzz21274, zzz2930, zzz2931, zzz226200, new_primMulNat2(zzz22630), da, db)
new_mkBalBranch6MkBalBranch017(zzz29340, zzz29341, zzz29342, zzz29343, zzz29344, zzz2127, zzz2930, zzz2931, Pos(Zero), Pos(zzz22470), da, db) → new_mkBalBranch6MkBalBranch0110(zzz29340, zzz29341, zzz29342, zzz29343, zzz29344, zzz2127, zzz2930, zzz2931, new_primMulNat2(zzz22470), da, db)
new_mkVBalBranch3MkVBalBranch272(zzz340, zzz341, Neg(Succ(Succ(Zero))), zzz343, zzz344, zzz520, zzz521, Succ(zzz522000), zzz523, zzz524, zzz31, Succ(Succ(zzz6900)), h) → new_mkVBalBranch3MkVBalBranch255(zzz340, zzz341, Succ(Zero), zzz343, zzz344, zzz520, zzz521, zzz522000, zzz523, zzz524, zzz31, Zero, Succ(Succ(new_primPlusNat2(zzz6900, zzz522000))), h)
new_mkBalBranch6MkBalBranch016(zzz29340, zzz29341, zzz29342, Branch(zzz293430, zzz293431, zzz293432, zzz293433, zzz293434), zzz29344, zzz2127, zzz2930, zzz2931, da, db) → new_mkBranch(Succ(Succ(Succ(Succ(Zero)))), zzz293430, zzz293431, new_mkBranch(Succ(Succ(Succ(Succ(Succ(Zero))))), zzz2930, zzz2931, zzz2127, zzz293433, da, db), new_mkBranch(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))), zzz29340, zzz29341, zzz293434, zzz29344, da, db), da, db)
new_mkVBalBranch3MkVBalBranch246(zzz972, zzz973, zzz974, zzz975, zzz976, zzz977, zzz978, zzz979, zzz980, zzz981, zzz982, Succ(zzz9830), Zero, cg) → new_mkVBalBranch3MkVBalBranch247(zzz972, zzz973, zzz974, zzz975, zzz976, zzz977, zzz978, zzz979, zzz980, zzz981, zzz982, cg)
new_mkVBalBranch3MkVBalBranch153(zzz537, zzz538, zzz539, zzz540, zzz541, zzz542, zzz543, zzz544, zzz545, zzz546, zzz547, Zero, dg) → new_mkVBalBranch3MkVBalBranch144(zzz537, zzz538, zzz539, zzz540, zzz541, zzz542, zzz543, Succ(zzz544), zzz545, zzz546, zzz547, Succ(Succ(zzz544)), Zero, dg)
new_mkVBalBranch3MkVBalBranch252(zzz929, zzz930, zzz931, zzz932, zzz933, zzz934, zzz935, zzz936, zzz937, zzz938, zzz939, Succ(zzz9400), Succ(zzz9410), dc) → new_mkVBalBranch3MkVBalBranch252(zzz929, zzz930, zzz931, zzz932, zzz933, zzz934, zzz935, zzz936, zzz937, zzz938, zzz939, zzz9400, zzz9410, dc)
new_splitGT12(Branch(GT, zzz8561, zzz8562, zzz8563, zzz8564), ba) → new_splitGT28(zzz8561, zzz8562, zzz8563, zzz8564, ba)
new_splitLT5(zzz31, zzz32, zzz34, h) → new_splitLT16(h)
new_splitLT4(zzz31, zzz32, zzz34, h) → new_splitLT16(h)
new_mkVBalBranch3MkVBalBranch161(zzz340, zzz341, zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, Succ(zzz1480), h) → new_mkVBalBranch3MkVBalBranch162(zzz340, zzz341, Zero, zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, Succ(zzz1480), Succ(zzz51200), h)
new_mkVBalBranch4(zzz31, Branch(zzz510, zzz511, Pos(Zero), zzz513, zzz514), Branch(zzz340, zzz341, Pos(Succ(zzz34200)), zzz343, zzz344), h) → new_mkBalBranch(zzz340, zzz341, new_mkVBalBranch4(zzz31, Branch(zzz510, zzz511, Pos(Zero), zzz513, zzz514), zzz343, h), zzz344, ty_Ordering, h)
new_mkVBalBranch3MkVBalBranch149(zzz2050, zzz2051, zzz2052, zzz2053, zzz2054, zzz2055, zzz2056, zzz2057, zzz2058, zzz2059, zzz2060, Zero, Succ(zzz20620), ef) → new_mkBalBranch(zzz2055, zzz2056, zzz2058, new_mkVBalBranch4(zzz2060, zzz2059, Branch(zzz2050, zzz2051, Neg(Succ(zzz2052)), zzz2053, zzz2054), ef), ty_Ordering, ef)
new_mkVBalBranch4(zzz31, Branch(zzz510, zzz511, Pos(Succ(zzz51200)), zzz513, zzz514), Branch(zzz340, zzz341, zzz342, zzz343, zzz344), h) → new_mkVBalBranch3MkVBalBranch288(zzz340, zzz341, zzz342, zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, new_primMulNat0(zzz51200), h)
new_mkVBalBranch3(zzz31, Branch(zzz520, zzz521, Pos(Succ(zzz52200)), zzz523, zzz524), Branch(zzz340, zzz341, zzz342, zzz343, zzz344), h) → new_mkVBalBranch3MkVBalBranch267(zzz340, zzz341, zzz342, zzz343, zzz344, zzz520, zzz521, zzz52200, zzz523, zzz524, zzz31, new_primMulNat0(zzz52200), h)
new_primPlusNat2(Zero, Succ(zzz9100)) → Succ(zzz9100)
new_primPlusNat2(Succ(zzz900), Zero) → Succ(zzz900)
new_mkVBalBranch3MkVBalBranch289(zzz1105, zzz1106, zzz1107, zzz1108, zzz1109, zzz1110, zzz1111, zzz1112, zzz1113, zzz1114, zzz1115, Zero, Zero, fh) → new_mkVBalBranch3MkVBalBranch282(zzz1105, zzz1106, zzz1107, zzz1108, zzz1109, zzz1110, zzz1111, zzz1112, zzz1113, zzz1114, zzz1115, fh)
new_addToFM_C3(Branch(GT, zzz341, zzz342, zzz343, zzz344), zzz31, h) → Branch(GT, new_addToFM0(zzz341, zzz31, h), zzz342, zzz343, zzz344)
new_splitLT14(Branch(EQ, zzz21291, zzz21292, zzz21293, zzz21294), cc) → new_mkVBalBranch4(zzz21291, zzz21293, new_splitLT14(zzz21294, cc), cc)
new_primPlusInt2(Neg(zzz21410), zzz2934, zzz2127, zzz2930, zzz2931, db, da) → new_primPlusInt1(zzz21410, new_sizeFM(zzz2934, da, db))
new_mkVBalBranch3MkVBalBranch150(zzz2050, zzz2051, zzz2052, zzz2053, zzz2054, zzz2055, zzz2056, zzz2057, zzz2058, zzz2059, zzz2060, ef) → new_mkBranch(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))), EQ, zzz2060, Branch(zzz2055, zzz2056, Neg(Succ(zzz2057)), zzz2058, zzz2059), Branch(zzz2050, zzz2051, Neg(Succ(zzz2052)), zzz2053, zzz2054), ty_Ordering, ef)
new_primMinusNat0(Zero, Succ(zzz542000)) → Neg(Succ(zzz542000))
new_mkBalBranch6MkBalBranch49(Branch(zzz29340, zzz29341, zzz29342, zzz29343, zzz29344), zzz2127, zzz2930, zzz2931, da, db) → new_mkBalBranch6MkBalBranch017(zzz29340, zzz29341, zzz29342, zzz29343, zzz29344, zzz2127, zzz2930, zzz2931, new_sizeFM(zzz29343, da, db), new_sizeFM(zzz29344, da, db), da, db)
new_mkBalBranch6MkBalBranch312(zzz2934, zzz2127, zzz2930, zzz2931, zzz224400, zzz2249, da, db) → new_mkBalBranch6MkBalBranch33(zzz2934, zzz2127, zzz2930, zzz2931, da, db)
new_mkBalBranch6MkBalBranch310(zzz2934, zzz2127, zzz2930, zzz2931, Pos(Succ(zzz224400)), Neg(zzz22450), da, db) → new_mkBalBranch6MkBalBranch312(zzz2934, zzz2127, zzz2930, zzz2931, zzz224400, new_primMulNat(zzz22450), da, db)
new_primPlusInt1(zzz13120, Neg(zzz13150)) → Neg(new_primPlusNat2(zzz13120, zzz13150))
new_splitLT11(zzz31, zzz32, zzz33, h) → new_mkVBalBranch4(zzz31, zzz33, new_splitLT13(h), h)
new_mkVBalBranch3MkVBalBranch290(zzz340, zzz341, zzz342000, zzz343, zzz344, zzz510, zzz511, zzz513, zzz514, zzz31, h) → new_mkBalBranch(zzz340, zzz341, new_mkVBalBranch4(zzz31, Branch(zzz510, zzz511, Pos(Succ(Zero)), zzz513, zzz514), zzz343, h), zzz344, ty_Ordering, h)
new_mkVBalBranch3MkVBalBranch254(zzz340, zzz341, zzz343, zzz344, zzz520, zzz521, zzz52200, zzz523, zzz524, zzz31, h) → new_mkBalBranch(zzz340, zzz341, new_mkVBalBranch3(zzz31, Branch(zzz520, zzz521, Neg(Succ(zzz52200)), zzz523, zzz524), zzz343, h), zzz344, ty_Ordering, h)
new_splitLT28(zzz31, zzz32, zzz33, zzz34, h) → zzz33
new_splitLT13(h) → new_splitLT40(h)
new_splitLT10(zzz31, zzz32, zzz33, h) → new_mkVBalBranch2(zzz31, zzz33, new_splitLT13(h), h)
new_mkVBalBranch3MkVBalBranch257(zzz486, zzz487, zzz488, zzz489, zzz490, zzz491, zzz492, zzz493, zzz494, zzz495, zzz496, ea) → new_mkBalBranch(zzz486, zzz487, new_mkVBalBranch4(zzz496, Branch(zzz491, zzz492, Neg(Succ(Succ(zzz493))), zzz494, zzz495), zzz489, ea), zzz490, ty_Ordering, ea)
new_primPlusNat2(Zero, Zero) → Zero
new_mkBalBranch6MkBalBranch5(zzz2934, zzz2127, zzz2930, zzz2931, Pos(Succ(Succ(Succ(zzz21390000)))), da, db) → new_mkBalBranch6MkBalBranch50(zzz2934, zzz2127, zzz2930, zzz2931, da, db)
new_splitGT5(zzz31, zzz32, zzz34, h) → new_mkVBalBranch3(zzz31, new_splitGT13(h), zzz34, h)
new_mkVBalBranch3MkVBalBranch265(zzz3170, zzz3171, Succ(zzz317200), zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, h) → new_mkVBalBranch3MkVBalBranch139(zzz3170, zzz3171, zzz317200, zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, new_primPlusNat2(new_primMulNat0(zzz317200), Succ(zzz317200)), h)
new_splitLT9(zzz76, zzz77, zzz78, zzz79, bg) → new_splitLT27(zzz76, zzz77, zzz78, zzz79, bg)
new_mkVBalBranch3MkVBalBranch284(zzz340, zzz341, Succ(zzz34200), zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, h) → new_mkVBalBranch3MkVBalBranch167(zzz340, zzz341, zzz34200, zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, new_primPlusNat2(new_primMulNat0(zzz34200), Succ(zzz34200)), h)
new_mkVBalBranch3MkVBalBranch147(zzz340, zzz341, zzz34200, zzz343, zzz344, zzz520, zzz521, zzz52200, zzz523, zzz524, zzz31, Zero, h) → new_mkVBalBranch3MkVBalBranch148(zzz340, zzz341, zzz34200, zzz343, zzz344, zzz520, zzz521, zzz52200, zzz523, zzz524, zzz31, h)
new_mkBalBranch6MkBalBranch013(zzz29340, zzz29341, zzz29342, zzz29343, zzz29344, zzz2127, zzz2930, zzz2931, zzz224600, Succ(zzz22600), da, db) → new_mkBalBranch6MkBalBranch014(zzz29340, zzz29341, zzz29342, zzz29343, zzz29344, zzz2127, zzz2930, zzz2931, zzz224600, zzz22600, da, db)
new_mkBalBranch6MkBalBranch112(zzz2934, zzz21270, zzz21271, zzz21272, zzz21273, zzz21274, zzz2930, zzz2931, da, db) → new_mkBalBranch6MkBalBranch1115(zzz2934, zzz21270, zzz21271, zzz21272, zzz21273, zzz21274, zzz2930, zzz2931, da, db)
new_mkBalBranch6MkBalBranch38(zzz2934, zzz2127, zzz2930, zzz2931, zzz224400, Zero, da, db) → new_mkBalBranch6MkBalBranch33(zzz2934, zzz2127, zzz2930, zzz2931, da, db)
new_mkBalBranch6MkBalBranch014(zzz29340, zzz29341, zzz29342, zzz29343, zzz29344, zzz2127, zzz2930, zzz2931, Zero, Succ(zzz226000), da, db) → new_mkBalBranch6MkBalBranch011(zzz29340, zzz29341, zzz29342, zzz29343, zzz29344, zzz2127, zzz2930, zzz2931, da, db)
new_mkVBalBranch3MkVBalBranch261(zzz3170, zzz3171, Neg(zzz31720), zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, Succ(zzz4170), h) → new_mkVBalBranch3MkVBalBranch286(zzz3170, zzz3171, zzz31720, zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, h)
new_mkVBalBranch3MkVBalBranch288(zzz340, zzz341, Pos(Succ(Zero)), zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, Succ(zzz660), h) → new_mkVBalBranch3MkVBalBranch287(zzz340, zzz341, zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, h)
new_mkBalBranch6MkBalBranch48(zzz2934, zzz2127, zzz2930, zzz2931, Succ(zzz22390), da, db) → new_mkBalBranch6MkBalBranch49(zzz2934, zzz2127, zzz2930, zzz2931, da, db)
new_splitGT11(zzz31, zzz32, zzz33, h) → new_splitGT16(h)
new_mkBalBranch6MkBalBranch310(zzz2934, zzz2127, zzz2930, zzz2931, Neg(Succ(zzz224400)), Pos(zzz22450), da, db) → new_mkBalBranch6MkBalBranch34(zzz2934, zzz2127, zzz2930, zzz2931, zzz224400, new_primMulNat(zzz22450), da, db)
new_mkBalBranch6MkBalBranch45(zzz2934, zzz2127, zzz2930, zzz2931, zzz222100, Succ(zzz22360), da, db) → new_mkBalBranch6MkBalBranch412(zzz2934, zzz2127, zzz2930, zzz2931, zzz222100, zzz22360, da, db)
new_mkVBalBranch3MkVBalBranch157(zzz498, zzz499, zzz500, zzz501, zzz502, zzz503, zzz504, zzz505, zzz506, zzz507, Zero, ee) → new_mkVBalBranch3MkVBalBranch149(zzz498, zzz499, zzz500, zzz501, zzz502, zzz503, zzz504, Zero, zzz505, zzz506, zzz507, Succ(Zero), Zero, ee)
new_intersectFM_C2Lts3(zzz2129, cc) → new_splitLT14(zzz2129, cc)
new_mkVBalBranch3MkVBalBranch272(zzz340, zzz341, Neg(Succ(Succ(zzz342000))), zzz343, zzz344, zzz520, zzz521, Zero, zzz523, zzz524, zzz31, Zero, h) → new_mkVBalBranch3MkVBalBranch259(zzz340, zzz341, zzz342000, zzz343, zzz344, zzz520, zzz521, zzz523, zzz524, zzz31, h)
new_splitLT23(zzz76, zzz77, zzz78, zzz79, bg) → new_splitLT15(zzz78, bg)
new_mkVBalBranch4(zzz31, Branch(zzz510, zzz511, Neg(Zero), zzz513, zzz514), Branch(zzz340, zzz341, Pos(Succ(zzz34200)), zzz343, zzz344), h) → new_mkBalBranch(zzz340, zzz341, new_mkVBalBranch4(zzz31, Branch(zzz510, zzz511, Neg(Zero), zzz513, zzz514), zzz343, h), zzz344, ty_Ordering, h)
new_mkVBalBranch3(zzz31, Branch(zzz520, zzz521, Neg(Zero), zzz523, zzz524), Branch(zzz340, zzz341, Neg(Zero), zzz343, zzz344), h) → new_mkBranch(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))), GT, zzz31, Branch(zzz520, zzz521, Neg(Zero), zzz523, zzz524), Branch(zzz340, zzz341, Neg(Zero), zzz343, zzz344), ty_Ordering, h)
new_mkBalBranch6MkBalBranch019(zzz29340, zzz29341, zzz29342, zzz29343, zzz29344, zzz2127, zzz2930, zzz2931, Zero, da, db) → new_mkBalBranch6MkBalBranch012(zzz29340, zzz29341, zzz29342, zzz29343, zzz29344, zzz2127, zzz2930, zzz2931, da, db)
new_mkVBalBranch2(zzz31, Branch(zzz330, zzz331, Neg(Zero), zzz333, zzz334), Branch(zzz3170, zzz3171, Neg(Succ(zzz317200)), zzz3173, zzz3174), h) → new_mkVBalBranch3MkVBalBranch146(zzz3170, zzz3171, zzz317200, zzz3173, zzz3174, zzz330, zzz331, zzz333, zzz334, zzz31, new_primMulNat1(zzz317200), h)
new_mkVBalBranch3MkVBalBranch289(zzz1105, zzz1106, zzz1107, zzz1108, zzz1109, zzz1110, zzz1111, zzz1112, zzz1113, zzz1114, zzz1115, Succ(zzz11160), Zero, fh) → new_mkVBalBranch3MkVBalBranch283(zzz1105, zzz1106, zzz1107, zzz1108, zzz1109, zzz1110, zzz1111, zzz1112, zzz1113, zzz1114, zzz1115, fh)
new_mkVBalBranch3MkVBalBranch277(zzz1133, zzz1134, zzz1135, zzz1136, zzz1137, zzz1138, zzz1139, zzz1140, zzz1141, zzz1142, Zero, Succ(zzz11440), fd) → new_mkBalBranch(zzz1133, zzz1134, new_mkVBalBranch3(zzz1142, Branch(zzz1138, zzz1139, Neg(Succ(Zero)), zzz1140, zzz1141), zzz1136, fd), zzz1137, ty_Ordering, fd)
new_mkVBalBranch3MkVBalBranch146(zzz3170, zzz3171, zzz317200, zzz3173, zzz3174, zzz330, zzz331, zzz333, zzz334, zzz31, Zero, h) → new_mkBranch(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))), LT, zzz31, Branch(zzz330, zzz331, Neg(Zero), zzz333, zzz334), Branch(zzz3170, zzz3171, Neg(Succ(zzz317200)), zzz3173, zzz3174), ty_Ordering, h)
new_mkVBalBranch2(zzz31, Branch(zzz330, zzz331, Pos(Zero), zzz333, zzz334), Branch(zzz3170, zzz3171, Neg(Zero), zzz3173, zzz3174), h) → new_mkBranch(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))), LT, zzz31, Branch(zzz330, zzz331, Pos(Zero), zzz333, zzz334), Branch(zzz3170, zzz3171, Neg(Zero), zzz3173, zzz3174), ty_Ordering, h)
new_mkVBalBranch2(zzz31, Branch(zzz330, zzz331, Neg(Zero), zzz333, zzz334), Branch(zzz3170, zzz3171, Pos(Zero), zzz3173, zzz3174), h) → new_mkBranch(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))), LT, zzz31, Branch(zzz330, zzz331, Neg(Zero), zzz333, zzz334), Branch(zzz3170, zzz3171, Pos(Zero), zzz3173, zzz3174), ty_Ordering, h)
new_mkVBalBranch3MkVBalBranch277(zzz1133, zzz1134, zzz1135, zzz1136, zzz1137, zzz1138, zzz1139, zzz1140, zzz1141, zzz1142, Succ(zzz11430), Zero, fd) → new_mkVBalBranch3MkVBalBranch274(zzz1133, zzz1134, zzz1135, zzz1136, zzz1137, zzz1138, zzz1139, zzz1140, zzz1141, zzz1142, fd)
new_mkBalBranch6MkBalBranch0111(zzz29340, zzz29341, zzz29342, zzz29343, zzz29344, zzz2127, zzz2930, zzz2931, Zero, da, db) → new_mkBalBranch6MkBalBranch012(zzz29340, zzz29341, zzz29342, zzz29343, zzz29344, zzz2127, zzz2930, zzz2931, da, db)
new_mkBalBranch6MkBalBranch50(zzz2934, zzz2127, zzz2930, zzz2931, da, db) → new_mkBalBranch6MkBalBranch410(zzz2934, zzz2127, zzz2930, zzz2931, new_mkBalBranch6Size_l(zzz2934, zzz2127, zzz2930, zzz2931, db, da), da, db)
new_mkVBalBranch2(zzz31, Branch(zzz330, zzz331, Pos(Zero), zzz333, zzz334), Branch(zzz3170, zzz3171, Pos(Zero), zzz3173, zzz3174), h) → new_mkBranch(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))), LT, zzz31, Branch(zzz330, zzz331, Pos(Zero), zzz333, zzz334), Branch(zzz3170, zzz3171, Pos(Zero), zzz3173, zzz3174), ty_Ordering, h)
new_mkBalBranch6MkBalBranch412(zzz2934, zzz2127, zzz2930, zzz2931, Zero, Zero, da, db) → new_mkBalBranch6MkBalBranch40(zzz2934, zzz2127, zzz2930, zzz2931, da, db)
new_mkVBalBranch3MkVBalBranch144(zzz1702, zzz1703, zzz1704, zzz1705, zzz1706, zzz1707, zzz1708, zzz1709, zzz1710, zzz1711, zzz1712, Succ(zzz17130), Succ(zzz17140), df) → new_mkVBalBranch3MkVBalBranch144(zzz1702, zzz1703, zzz1704, zzz1705, zzz1706, zzz1707, zzz1708, zzz1709, zzz1710, zzz1711, zzz1712, zzz17130, zzz17140, df)
new_splitLT14(Branch(GT, zzz21291, zzz21292, zzz21293, zzz21294), cc) → zzz21293
new_mkVBalBranch3MkVBalBranch276(zzz958, zzz959, zzz960, zzz961, zzz962, zzz963, zzz964, zzz965, zzz966, zzz967, zzz968, fa) → new_mkVBalBranch3MkVBalBranch156(zzz958, zzz959, zzz960, zzz961, zzz962, zzz963, zzz964, zzz965, zzz966, zzz967, zzz968, new_primMulNat1(zzz960), fa)
new_mkBalBranch6MkBalBranch45(zzz2934, zzz2127, zzz2930, zzz2931, zzz222100, Zero, da, db) → new_mkBalBranch6MkBalBranch49(zzz2934, zzz2127, zzz2930, zzz2931, da, db)
new_mkVBalBranch3MkVBalBranch252(zzz929, zzz930, zzz931, zzz932, zzz933, zzz934, zzz935, zzz936, zzz937, zzz938, zzz939, Succ(zzz9400), Zero, dc) → new_mkVBalBranch3MkVBalBranch253(zzz929, zzz930, zzz931, zzz932, zzz933, zzz934, zzz935, zzz936, zzz937, zzz938, zzz939, dc)
new_mkBalBranch6MkBalBranch315(zzz2934, zzz2127, zzz2930, zzz2931, Succ(zzz22510), da, db) → new_mkBalBranch6MkBalBranch33(zzz2934, zzz2127, zzz2930, zzz2931, da, db)
new_mkVBalBranch3MkVBalBranch155(zzz340, zzz341, zzz34200, zzz343, zzz344, zzz520, zzz521, zzz523, zzz524, zzz31, Zero, h) → new_mkBranch(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))), GT, zzz31, Branch(zzz520, zzz521, Neg(Zero), zzz523, zzz524), Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), ty_Ordering, h)
new_mkBalBranch6MkBalBranch412(zzz2934, zzz2127, zzz2930, zzz2931, Succ(zzz2221000), Succ(zzz223600), da, db) → new_mkBalBranch6MkBalBranch412(zzz2934, zzz2127, zzz2930, zzz2931, zzz2221000, zzz223600, da, db)
new_mkVBalBranch3MkVBalBranch132(zzz2033, zzz2034, zzz2035, zzz2036, zzz2037, zzz2038, zzz2039, zzz2040, zzz2041, zzz2042, zzz2043, Succ(zzz20440), Succ(zzz20450), fg) → new_mkVBalBranch3MkVBalBranch132(zzz2033, zzz2034, zzz2035, zzz2036, zzz2037, zzz2038, zzz2039, zzz2040, zzz2041, zzz2042, zzz2043, zzz20440, zzz20450, fg)
new_mkVBalBranch2(zzz31, Branch(zzz330, zzz331, Pos(Zero), zzz333, zzz334), Branch(zzz3170, zzz3171, Pos(Succ(zzz317200)), zzz3173, zzz3174), h) → new_mkBalBranch(zzz3170, zzz3171, new_mkVBalBranch2(zzz31, Branch(zzz330, zzz331, Pos(Zero), zzz333, zzz334), zzz3173, h), zzz3174, ty_Ordering, h)
new_mkVBalBranch2(zzz31, Branch(zzz330, zzz331, Pos(Zero), zzz333, zzz334), Branch(zzz3170, zzz3171, Neg(Succ(zzz317200)), zzz3173, zzz3174), h) → new_mkVBalBranch3MkVBalBranch145(zzz3170, zzz3171, zzz317200, zzz3173, zzz3174, zzz330, zzz331, zzz333, zzz334, zzz31, new_primMulNat1(zzz317200), h)
new_mkVBalBranch3MkVBalBranch144(zzz1702, zzz1703, zzz1704, zzz1705, zzz1706, zzz1707, zzz1708, zzz1709, zzz1710, zzz1711, zzz1712, Succ(zzz17130), Zero, df) → new_mkVBalBranch3MkVBalBranch138(zzz1702, zzz1703, zzz1704, zzz1705, zzz1706, zzz1707, zzz1708, zzz1709, zzz1710, zzz1711, zzz1712, df)
new_mkBalBranch6MkBalBranch41(zzz2934, zzz2127, zzz2930, zzz2931, da, db) → new_mkBalBranch6MkBalBranch310(zzz2934, zzz2127, zzz2930, zzz2931, new_mkBalBranch6Size_l(zzz2934, zzz2127, zzz2930, zzz2931, db, da), new_mkBalBranch6Size_r(zzz2934, zzz2127, zzz2930, zzz2931, db, da), da, db)
new_mkVBalBranch3MkVBalBranch153(zzz537, zzz538, zzz539, zzz540, zzz541, zzz542, zzz543, zzz544, zzz545, zzz546, zzz547, Succ(zzz6990), dg) → new_mkVBalBranch3MkVBalBranch144(zzz537, zzz538, zzz539, zzz540, zzz541, zzz542, zzz543, Succ(zzz544), zzz545, zzz546, zzz547, Succ(Succ(zzz544)), Succ(zzz6990), dg)
new_mkBalBranch6MkBalBranch416(zzz2934, zzz2127, zzz2930, zzz2931, Zero, da, db) → new_mkBalBranch6MkBalBranch40(zzz2934, zzz2127, zzz2930, zzz2931, da, db)
new_mkBalBranch6MkBalBranch33(zzz2934, EmptyFM, zzz2930, zzz2931, da, db) → error([])
new_mkVBalBranch3MkVBalBranch284(zzz340, zzz341, Zero, zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, h) → new_mkBalBranch(zzz510, zzz511, zzz513, new_mkVBalBranch4(zzz31, zzz514, Branch(zzz340, zzz341, Neg(Zero), zzz343, zzz344), h), ty_Ordering, h)
new_splitLT41(h) → new_emptyFM(h)
new_mkBalBranch6MkBalBranch5(zzz2934, zzz2127, zzz2930, zzz2931, Pos(Zero), da, db) → new_mkBalBranch6MkBalBranch51(zzz2934, zzz2127, zzz2930, zzz2931, da, db)
new_mkBalBranch6MkBalBranch310(zzz2934, zzz2127, zzz2930, zzz2931, Pos(Zero), Pos(zzz22450), da, db) → new_mkBalBranch6MkBalBranch35(zzz2934, zzz2127, zzz2930, zzz2931, new_primMulNat(zzz22450), da, db)
new_splitGT15(EmptyFM, cc) → new_splitGT40(cc)
new_mkBalBranch6MkBalBranch1115(zzz2934, zzz21270, zzz21271, zzz21272, zzz21273, Branch(zzz212740, zzz212741, zzz212742, zzz212743, zzz212744), zzz2930, zzz2931, da, db) → new_mkBranch(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))), zzz212740, zzz212741, new_mkBranch(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))), zzz21270, zzz21271, zzz21273, zzz212743, da, db), new_mkBranch(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))), zzz2930, zzz2931, zzz212744, zzz2934, da, db), da, db)
new_primMulNat(Succ(zzz206300)) → new_primPlusNat2(new_primMulNat0(zzz206300), Succ(zzz206300))
new_addToFM_C4(Branch(EQ, zzz341, zzz342, zzz343, zzz344), zzz31, h) → Branch(EQ, new_addToFM0(zzz341, zzz31, h), zzz342, zzz343, zzz344)
new_mkBalBranch6MkBalBranch019(zzz29340, zzz29341, zzz29342, zzz29343, zzz29344, zzz2127, zzz2930, zzz2931, Succ(zzz22590), da, db) → new_mkBalBranch6MkBalBranch013(zzz29340, zzz29341, zzz29342, zzz29343, zzz29344, zzz2127, zzz2930, zzz2931, zzz22590, Zero, da, db)
new_mkBalBranch6MkBalBranch413(zzz2934, zzz2127, zzz2930, zzz2931, Succ(zzz22430), da, db) → new_mkBalBranch6MkBalBranch45(zzz2934, zzz2127, zzz2930, zzz2931, zzz22430, Zero, da, db)
new_mkBalBranch6MkBalBranch36(zzz2934, zzz2127, zzz2930, zzz2931, Zero, zzz224400, da, db) → new_mkBalBranch6MkBalBranch31(zzz2934, zzz2127, zzz2930, zzz2931, da, db)
new_mkBalBranch6MkBalBranch49(EmptyFM, zzz2127, zzz2930, zzz2931, da, db) → error([])
new_mkVBalBranch3MkVBalBranch141(zzz972, zzz973, zzz974, zzz975, zzz976, zzz977, zzz978, zzz979, zzz980, zzz981, zzz982, Zero, cg) → new_mkVBalBranch3MkVBalBranch134(zzz972, zzz973, zzz974, zzz975, zzz976, zzz977, zzz978, zzz979, zzz980, zzz981, zzz982, Succ(zzz979), Zero, cg)
new_mkVBalBranch3MkVBalBranch134(zzz1851, zzz1852, zzz1853, zzz1854, zzz1855, zzz1856, zzz1857, zzz1858, zzz1859, zzz1860, zzz1861, Zero, Zero, dd) → new_mkVBalBranch3MkVBalBranch135(zzz1851, zzz1852, zzz1853, zzz1854, zzz1855, zzz1856, zzz1857, zzz1858, zzz1859, zzz1860, zzz1861, dd)
new_mkBalBranch6MkBalBranch411(zzz2934, zzz2127, zzz2930, zzz2931, Neg(Succ(zzz222100)), Pos(zzz22060), da, db) → new_mkBalBranch6MkBalBranch42(zzz2934, zzz2127, zzz2930, zzz2931, zzz222100, new_primMulNat(zzz22060), da, db)
new_mkVBalBranch3MkVBalBranch255(zzz537, zzz538, zzz539, zzz540, zzz541, zzz542, zzz543, zzz544, zzz545, zzz546, zzz547, Zero, Succ(zzz5490), dg) → new_mkBalBranch(zzz537, zzz538, new_mkVBalBranch3(zzz547, Branch(zzz542, zzz543, Neg(Succ(Succ(zzz544))), zzz545, zzz546), zzz540, dg), zzz541, ty_Ordering, dg)
new_mkVBalBranch3MkVBalBranch151(zzz1337, zzz1338, zzz1339, zzz1340, zzz1341, zzz1342, zzz1343, zzz1344, zzz1345, zzz1346, zzz1347, eg) → new_mkBranch(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))), LT, zzz1347, Branch(zzz1342, zzz1343, Pos(Succ(zzz1344)), zzz1345, zzz1346), Branch(zzz1337, zzz1338, Pos(Succ(zzz1339)), zzz1340, zzz1341), ty_Ordering, eg)
new_splitGT15(Branch(GT, zzz21291, zzz21292, zzz21293, zzz21294), cc) → zzz21294
new_splitGT25(zzz854, zzz855, zzz856, zzz857, ba) → new_mkVBalBranch4(zzz854, new_splitGT12(zzz856, ba), zzz857, ba)
new_mkVBalBranch3MkVBalBranch144(zzz1702, zzz1703, zzz1704, zzz1705, zzz1706, zzz1707, zzz1708, zzz1709, zzz1710, zzz1711, zzz1712, Zero, Zero, df) → new_mkVBalBranch3MkVBalBranch138(zzz1702, zzz1703, zzz1704, zzz1705, zzz1706, zzz1707, zzz1708, zzz1709, zzz1710, zzz1711, zzz1712, df)
new_mkVBalBranch3MkVBalBranch288(zzz340, zzz341, Pos(Succ(Zero)), zzz343, zzz344, zzz510, zzz511, Zero, zzz513, zzz514, zzz31, Zero, h) → new_mkVBalBranch3MkVBalBranch287(zzz340, zzz341, zzz343, zzz344, zzz510, zzz511, Zero, zzz513, zzz514, zzz31, h)
new_mkBalBranch6MkBalBranch017(zzz29340, zzz29341, zzz29342, zzz29343, zzz29344, zzz2127, zzz2930, zzz2931, Pos(Succ(zzz224600)), Pos(zzz22470), da, db) → new_mkBalBranch6MkBalBranch013(zzz29340, zzz29341, zzz29342, zzz29343, zzz29344, zzz2127, zzz2930, zzz2931, zzz224600, new_primMulNat2(zzz22470), da, db)
new_mkBalBranch6MkBalBranch310(zzz2934, zzz2127, zzz2930, zzz2931, Pos(Succ(zzz224400)), Pos(zzz22450), da, db) → new_mkBalBranch6MkBalBranch311(zzz2934, zzz2127, zzz2930, zzz2931, zzz224400, new_primMulNat(zzz22450), da, db)
new_primMinusNat0(Succ(zzz100100), Succ(zzz542000)) → new_primMinusNat0(zzz100100, zzz542000)

The set Q consists of the following terms:

new_mkVBalBranch3MkVBalBranch281(x0, x1, Neg(Succ(Succ(Succ(x2)))), x3, x4, x5, x6, Succ(x7), x8, x9, x10, Succ(Succ(x11)), x12)
new_mkBalBranch6MkBalBranch35(x0, x1, x2, x3, Zero, x4, x5)
new_mkVBalBranch2(x0, Branch(x1, x2, Pos(Zero), x3, x4), Branch(x5, x6, Pos(Zero), x7, x8), x9)
new_mkVBalBranch3MkVBalBranch159(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, Zero, x11)
new_addToFM_C2(Branch(LT, x0, x1, x2, x3), x4, x5)
new_primMulNat1(x0)
new_primMinusNat0(Zero, Zero)
new_mkVBalBranch3MkVBalBranch281(x0, x1, Neg(Zero), x2, x3, x4, x5, x6, x7, x8, x9, Succ(x10), x11)
new_mkVBalBranch3MkVBalBranch263(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, Succ(x10), Succ(x11), x12)
new_mkVBalBranch3MkVBalBranch163(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11)
new_primPlusInt(Pos(x0), x1, x2, x3, x4, x5)
new_primMulNat0(x0)
new_mkBalBranch6MkBalBranch116(x0, x1, x2, x3, x4, x5, x6, x7, Succ(x8), x9, x10)
new_mkVBalBranch3(x0, EmptyFM, x1, x2)
new_mkVBalBranch3MkVBalBranch281(x0, x1, Neg(Succ(Succ(x2))), x3, x4, x5, x6, Zero, x7, x8, x9, Zero, x10)
new_mkBalBranch6MkBalBranch411(x0, x1, x2, x3, Pos(Succ(x4)), Pos(x5), x6, x7)
new_mkBalBranch6MkBalBranch1113(x0, x1, x2, x3, x4, x5, x6, x7, Zero, Succ(x8), x9, x10)
new_mkVBalBranch3MkVBalBranch157(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, Succ(x10), x11)
new_mkVBalBranch3MkVBalBranch278(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11)
new_mkVBalBranch3MkVBalBranch281(x0, x1, Neg(Zero), x2, x3, x4, x5, x6, x7, x8, x9, Zero, x10)
new_mkVBalBranch3MkVBalBranch281(x0, x1, Neg(Succ(Succ(x2))), x3, x4, x5, x6, Succ(x7), x8, x9, x10, Zero, x11)
new_mkVBalBranch3MkVBalBranch269(x0, x1, Succ(x2), x3, x4, x5, x6, x7, x8, x9, x10, x11)
new_mkVBalBranch4(x0, Branch(x1, x2, Pos(Zero), x3, x4), Branch(x5, x6, Pos(Succ(x7)), x8, x9), x10)
new_mkVBalBranch3MkVBalBranch247(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11)
new_mkBalBranch6MkBalBranch315(x0, x1, x2, x3, Succ(x4), x5, x6)
new_mkVBalBranch3MkVBalBranch272(x0, x1, Neg(Succ(Zero)), x2, x3, x4, x5, Succ(x6), x7, x8, x9, Zero, x10)
new_mkVBalBranch3(x0, Branch(x1, x2, Neg(Succ(x3)), x4, x5), Branch(x6, x7, x8, x9, x10), x11)
new_addToFM_C3(Branch(EQ, x0, x1, x2, x3), x4, x5)
new_mkVBalBranch3MkVBalBranch158(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11)
new_mkVBalBranch3MkVBalBranch270(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, Succ(x10), Zero, x11)
new_mkVBalBranch3MkVBalBranch159(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, Succ(x11), x12)
new_splitGT4(x0, x1, x2, x3)
new_mkVBalBranch3MkVBalBranch261(x0, x1, Pos(Succ(x2)), x3, x4, x5, x6, x7, x8, x9, x10, Succ(x11), x12)
new_mkVBalBranch3MkVBalBranch137(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, Succ(x11), x12)
new_mkBalBranch6MkBalBranch45(x0, x1, x2, x3, x4, Zero, x5, x6)
new_mkBalBranch6MkBalBranch014(x0, x1, x2, x3, x4, x5, x6, x7, Zero, Zero, x8, x9)
new_mkBalBranch6MkBalBranch111(x0, x1, x2, x3, x4, x5, x6, x7, x8, Zero, x9, x10)
new_mkVBalBranch3(x0, Branch(x1, x2, Neg(Zero), x3, x4), Branch(x5, x6, Neg(Succ(x7)), x8, x9), x10)
new_mkBalBranch6MkBalBranch116(x0, x1, x2, x3, x4, x5, x6, x7, Zero, x8, x9)
new_mkBalBranch6MkBalBranch015(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9)
new_mkBalBranch6MkBalBranch5(x0, x1, x2, x3, Pos(Succ(Succ(Zero))), x4, x5)
new_mkBalBranch6MkBalBranch49(EmptyFM, x0, x1, x2, x3, x4)
new_primMinusNat0(Succ(x0), Zero)
new_mkVBalBranch3MkVBalBranch157(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, Zero, x10)
new_mkBalBranch6MkBalBranch33(x0, Branch(x1, x2, x3, x4, x5), x6, x7, x8, x9)
new_mkVBalBranch3MkVBalBranch266(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10)
new_addToFM_C2(Branch(EQ, x0, x1, x2, x3), x4, x5)
new_mkVBalBranch3MkVBalBranch263(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, Zero, Succ(x10), x11)
new_mkBalBranch6MkBalBranch51(x0, x1, x2, x3, x4, x5)
new_mkVBalBranch3MkVBalBranch287(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10)
new_mkBalBranch6MkBalBranch013(x0, x1, x2, x3, x4, x5, x6, x7, x8, Zero, x9, x10)
new_mkBalBranch6MkBalBranch312(x0, x1, x2, x3, x4, x5, x6, x7)
new_mkVBalBranch3MkVBalBranch267(x0, x1, Pos(Zero), x2, x3, x4, x5, x6, x7, x8, x9, Succ(x10), x11)
new_addToFM2(x0, x1, x2)
new_mkVBalBranch3MkVBalBranch155(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, Zero, x10)
new_splitLT11(x0, x1, x2, x3)
new_mkVBalBranch3MkVBalBranch272(x0, x1, Neg(Succ(Succ(Zero))), x2, x3, x4, x5, Zero, x6, x7, x8, Succ(Succ(x9)), x10)
new_mkVBalBranch3MkVBalBranch281(x0, x1, Neg(Succ(Zero)), x2, x3, x4, x5, Succ(x6), x7, x8, x9, Zero, x10)
new_splitLT6(x0)
new_mkVBalBranch3MkVBalBranch161(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, Zero, x10)
new_mkVBalBranch3MkVBalBranch134(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, Succ(x11), Zero, x12)
new_mkBalBranch6MkBalBranch39(x0, x1, x2, x3, Zero, Zero, x4, x5)
new_splitLT24(x0, x1, x2, x3, x4)
new_mkVBalBranch3MkVBalBranch288(x0, x1, Pos(Zero), x2, x3, x4, x5, x6, x7, x8, x9, Zero, x10)
new_mkBalBranch6MkBalBranch310(x0, x1, x2, x3, Pos(Zero), Neg(x4), x5, x6)
new_mkBalBranch6MkBalBranch310(x0, x1, x2, x3, Neg(Zero), Pos(x4), x5, x6)
new_mkVBalBranch3MkVBalBranch285(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10)
new_mkVBalBranch2(x0, Branch(x1, x2, x3, x4, x5), EmptyFM, x6)
new_mkVBalBranch3MkVBalBranch272(x0, x1, Neg(Succ(Succ(Zero))), x2, x3, x4, x5, Zero, x6, x7, x8, Succ(Zero), x9)
new_mkVBalBranch3MkVBalBranch141(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, Succ(x11), x12)
new_splitLT15(Branch(GT, x0, x1, x2, x3), x4)
new_mkVBalBranch3MkVBalBranch265(x0, x1, Zero, x2, x3, x4, x5, x6, x7, x8, x9, x10)
new_mkVBalBranch3MkVBalBranch267(x0, x1, Pos(Succ(x2)), x3, x4, x5, x6, x7, x8, x9, x10, Zero, x11)
new_mkBalBranch6MkBalBranch017(x0, x1, x2, x3, x4, x5, x6, x7, Pos(Succ(x8)), Pos(x9), x10, x11)
new_mkBalBranch6MkBalBranch412(x0, x1, x2, x3, Zero, Zero, x4, x5)
new_mkVBalBranch3MkVBalBranch288(x0, x1, Pos(Succ(Succ(x2))), x3, x4, x5, x6, Succ(x7), x8, x9, x10, Zero, x11)
new_splitGT41(x0)
new_mkBalBranch6MkBalBranch110(x0, x1, x2, x3, x4, x5, x6, x7, Succ(x8), x9, x10)
new_mkBalBranch6MkBalBranch416(x0, x1, x2, x3, Zero, x4, x5)
new_splitGT15(Branch(GT, x0, x1, x2, x3), x4)
new_mkVBalBranch3MkVBalBranch277(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, Zero, Succ(x10), x11)
new_mkBalBranch6MkBalBranch017(x0, x1, x2, x3, x4, x5, x6, x7, Pos(Zero), Pos(x8), x9, x10)
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_mkBalBranch6MkBalBranch310(x0, x1, x2, x3, Neg(Succ(x4)), Pos(x5), x6, x7)
new_mkBalBranch6MkBalBranch310(x0, x1, x2, x3, Pos(Succ(x4)), Neg(x5), x6, x7)
new_mkVBalBranch2(x0, Branch(x1, x2, Pos(Zero), x3, x4), Branch(x5, x6, Neg(Zero), x7, x8), x9)
new_mkVBalBranch2(x0, Branch(x1, x2, Neg(Zero), x3, x4), Branch(x5, x6, Pos(Zero), x7, x8), x9)
new_mkVBalBranch3MkVBalBranch289(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, Succ(x11), Succ(x12), x13)
new_mkBalBranch6MkBalBranch310(x0, x1, x2, x3, Neg(Succ(x4)), Neg(x5), x6, x7)
new_mkVBalBranch3MkVBalBranch139(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, Succ(x11), x12)
new_splitGT26(x0, x1, x2, x3, x4)
new_mkBalBranch6MkBalBranch1113(x0, x1, x2, x3, x4, x5, x6, x7, Succ(x8), Zero, x9, x10)
new_primPlusNat2(Zero, Zero)
new_mkVBalBranch3MkVBalBranch143(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, Zero, x10)
new_mkVBalBranch3MkVBalBranch277(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, Succ(x10), Zero, x11)
new_splitGT14(Branch(EQ, x0, x1, x2, x3), x4)
new_splitLT10(x0, x1, x2, x3)
new_mkVBalBranch4(x0, Branch(x1, x2, Pos(Succ(x3)), x4, x5), Branch(x6, x7, x8, x9, x10), x11)
new_addToFM_C2(EmptyFM, x0, x1)
new_mkVBalBranch3MkVBalBranch156(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, Zero, x11)
new_mkVBalBranch3MkVBalBranch262(x0, x1, Pos(Succ(x2)), x3, x4, x5, x6, x7, x8, x9, x10, Zero, x11)
new_splitLT12(EmptyFM, x0)
new_mkVBalBranch3MkVBalBranch271(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10)
new_mkVBalBranch4(x0, Branch(x1, x2, x3, x4, x5), EmptyFM, x6)
new_intersectFM_C2Gts1(x0, x1, x2, x3, x4)
new_mkVBalBranch3MkVBalBranch155(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, Succ(x10), x11)
new_mkVBalBranch3MkVBalBranch272(x0, x1, Neg(Succ(Succ(Succ(x2)))), x3, x4, x5, x6, Succ(x7), x8, x9, x10, Succ(Zero), x11)
new_mkBalBranch6MkBalBranch41(x0, x1, x2, x3, x4, x5)
new_mkVBalBranch4(x0, Branch(x1, x2, Neg(Zero), x3, x4), Branch(x5, x6, Neg(Zero), x7, x8), x9)
new_mkVBalBranch3(x0, Branch(x1, x2, Pos(Zero), x3, x4), Branch(x5, x6, Pos(Zero), x7, x8), x9)
new_mkVBalBranch3MkVBalBranch156(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, Succ(x11), x12)
new_mkBalBranch6MkBalBranch018(x0, x1, x2, x3, x4, x5, x6, x7, Succ(x8), x9, x10, x11)
new_mkBalBranch6MkBalBranch1111(x0, x1, x2, x3, x4, x5, x6, x7, Zero, x8, x9, x10)
new_mkVBalBranch3MkVBalBranch270(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, Zero, Succ(x10), x11)
new_primPlusNat2(Zero, Succ(x0))
new_mkBalBranch6MkBalBranch113(x0, x1, x2, x3, x4, x5, x6, x7, Neg(Succ(x8)), Neg(x9), x10, x11)
new_mkVBalBranch3MkVBalBranch272(x0, x1, Neg(Succ(Zero)), x2, x3, x4, x5, Zero, x6, x7, x8, Zero, x9)
new_mkVBalBranch3MkVBalBranch261(x0, x1, Neg(x2), x3, x4, x5, x6, x7, x8, x9, x10, Succ(x11), x12)
new_addToFM1(x0, x1, x2)
new_mkVBalBranch3MkVBalBranch284(x0, x1, Zero, x2, x3, x4, x5, x6, x7, x8, x9, x10)
new_mkVBalBranch3MkVBalBranch136(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11)
new_splitLT15(EmptyFM, x0)
new_mkBalBranch6MkBalBranch013(x0, x1, x2, x3, x4, x5, x6, x7, x8, Succ(x9), x10, x11)
new_mkVBalBranch3MkVBalBranch166(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11)
new_mkVBalBranch3MkVBalBranch144(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, Zero, Zero, x11)
new_splitLT41(x0)
new_mkBalBranch6MkBalBranch5(x0, x1, x2, x3, Neg(Succ(x4)), x5, x6)
new_splitLT4(x0, x1, x2, x3)
new_splitLT14(Branch(GT, x0, x1, x2, x3), x4)
new_mkBalBranch6MkBalBranch010(x0, x1, x2, x3, x4, x5, x6, x7, Zero, x8, x9)
new_primPlusNat3(x0, Zero)
new_mkVBalBranch3MkVBalBranch255(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, Zero, Succ(x11), x12)
new_mkVBalBranch3MkVBalBranch272(x0, x1, Pos(x2), x3, x4, x5, x6, x7, x8, x9, x10, Zero, x11)
new_splitGT25(x0, x1, x2, x3, x4)
new_mkBalBranch6MkBalBranch35(x0, x1, x2, x3, Succ(x4), x5, x6)
new_splitLT12(Branch(LT, x0, x1, x2, x3), x4)
new_intersectFM_C2Gts0(x0, x1, x2, x3, x4)
new_primMulNat(Zero)
new_primPlusNat1(Succ(x0))
new_mkVBalBranch3MkVBalBranch273(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10)
new_mkVBalBranch3MkVBalBranch152(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, Zero, Zero, x11)
new_splitGT15(Branch(EQ, x0, x1, x2, x3), x4)
new_mkVBalBranch3MkVBalBranch262(x0, x1, Pos(x2), x3, x4, x5, x6, x7, x8, x9, x10, Succ(x11), x12)
new_mkBalBranch6MkBalBranch017(x0, x1, x2, x3, x4, x5, x6, x7, Neg(Zero), Pos(x8), x9, x10)
new_primPlusInt2(Pos(x0), x1, x2, x3, x4, x5, x6)
new_mkBalBranch6MkBalBranch017(x0, x1, x2, x3, x4, x5, x6, x7, Pos(Zero), Neg(x8), x9, x10)
new_mkVBalBranch3MkVBalBranch275(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, Succ(x11), Zero, x12)
new_mkVBalBranch3MkVBalBranch255(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, Zero, Zero, x11)
new_addToFM_C2(Branch(GT, x0, x1, x2, x3), x4, x5)
new_splitGT10(x0, x1, x2, x3)
new_mkVBalBranch3MkVBalBranch149(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, Zero, Zero, x11)
new_mkVBalBranch3MkVBalBranch245(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10)
new_mkBalBranch6MkBalBranch39(x0, x1, x2, x3, Zero, Succ(x4), x5, x6)
new_mkVBalBranch3MkVBalBranch289(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, Zero, Zero, x11)
new_mkVBalBranch3MkVBalBranch276(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11)
new_mkVBalBranch3MkVBalBranch275(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, Zero, Zero, x11)
new_mkVBalBranch3MkVBalBranch277(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, Succ(x10), Succ(x11), x12)
new_splitLT7(x0, x1, x2, x3, x4)
new_mkVBalBranch3MkVBalBranch261(x0, x1, Neg(Zero), x2, x3, x4, x5, x6, x7, x8, x9, Zero, x10)
new_splitGT12(Branch(EQ, x0, x1, x2, x3), x4)
new_intersectFM_C2Gts(x0, x1, x2, x3, x4)
new_mkVBalBranch3MkVBalBranch289(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, Zero, Succ(x11), x12)
new_mkVBalBranch3MkVBalBranch281(x0, x1, Neg(Succ(Zero)), x2, x3, x4, x5, x6, x7, x8, x9, Succ(x10), x11)
new_mkBalBranch6MkBalBranch413(x0, x1, x2, x3, Zero, x4, x5)
new_addToFM_C4(Branch(GT, x0, x1, x2, x3), x4, x5)
new_mkBalBranch6MkBalBranch413(x0, x1, x2, x3, Succ(x4), x5, x6)
new_mkVBalBranch3MkVBalBranch281(x0, x1, Neg(Succ(Succ(Succ(x2)))), x3, x4, x5, x6, Succ(x7), x8, x9, x10, Succ(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_mkBalBranch6MkBalBranch34(x0, x1, x2, x3, x4, x5, x6, x7)
new_mkVBalBranch3MkVBalBranch265(x0, x1, Succ(x2), x3, x4, x5, x6, x7, x8, x9, x10, x11)
new_intersectFM_C2Lts3(x0, x1)
new_mkBalBranch6MkBalBranch314(x0, x1, x2, x3, Zero, x4, x5)
new_mkVBalBranch3MkVBalBranch145(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, Succ(x10), x11)
new_splitLT9(x0, x1, x2, x3, x4)
new_mkBalBranch6Size_r(x0, x1, x2, x3, x4, x5)
new_mkBalBranch6MkBalBranch43(x0, x1, x2, x3, x4, x5)
new_mkVBalBranch3MkVBalBranch283(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11)
new_splitGT29(x0, x1, x2, x3, x4)
new_mkBalBranch6MkBalBranch30(x0, x1, x2, x3, Zero, x4, x5)
new_mkVBalBranch3MkVBalBranch146(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, Zero, x10)
new_sizeFM(EmptyFM, x0, x1)
new_mkVBalBranch3MkVBalBranch281(x0, x1, Neg(Succ(Zero)), x2, x3, x4, x5, Zero, x6, x7, x8, Zero, x9)
new_mkVBalBranch3MkVBalBranch281(x0, x1, Neg(Succ(Succ(Succ(x2)))), x3, x4, x5, x6, Zero, x7, x8, x9, Succ(Succ(x10)), x11)
new_mkVBalBranch3MkVBalBranch152(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, Succ(x11), Zero, x12)
new_mkVBalBranch3MkVBalBranch288(x0, x1, Pos(Succ(Succ(x2))), x3, x4, x5, x6, Zero, x7, x8, x9, Succ(Zero), x10)
new_mkVBalBranch3MkVBalBranch249(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10)
new_mkVBalBranch3MkVBalBranch135(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11)
new_mkVBalBranch3MkVBalBranch254(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10)
new_splitLT28(x0, x1, x2, x3, x4)
new_mkBalBranch6MkBalBranch47(x0, x1, x2, x3, Succ(x4), x5, x6, x7)
new_mkBalBranch6MkBalBranch014(x0, x1, x2, x3, x4, x5, x6, x7, Succ(x8), Succ(x9), x10, x11)
new_mkVBalBranch2(x0, Branch(x1, x2, Pos(Zero), x3, x4), Branch(x5, x6, Neg(Succ(x7)), x8, x9), x10)
new_mkVBalBranch2(x0, Branch(x1, x2, Neg(Zero), x3, x4), Branch(x5, x6, Pos(Succ(x7)), x8, x9), x10)
new_addToFM_C4(EmptyFM, x0, x1)
new_mkBalBranch6MkBalBranch313(x0, x1, x2, x3, x4, x5)
new_mkVBalBranch3MkVBalBranch267(x0, x1, Pos(Zero), x2, x3, x4, x5, x6, x7, x8, x9, Zero, x10)
new_mkVBalBranch3MkVBalBranch248(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11)
new_splitGT14(EmptyFM, x0)
new_mkVBalBranch3MkVBalBranch132(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, Succ(x11), Zero, x12)
new_mkVBalBranch3MkVBalBranch144(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, Succ(x11), Succ(x12), x13)
new_mkVBalBranch3MkVBalBranch261(x0, x1, Neg(Succ(x2)), x3, x4, x5, x6, x7, x8, x9, x10, Zero, x11)
new_mkBalBranch6MkBalBranch410(x0, x1, x2, x3, x4, x5, x6)
new_mkVBalBranch2(x0, Branch(x1, x2, Pos(Succ(x3)), x4, x5), Branch(x6, x7, x8, x9, x10), x11)
new_mkBalBranch6MkBalBranch019(x0, x1, x2, x3, x4, x5, x6, x7, Zero, x8, x9)
new_mkVBalBranch3MkVBalBranch280(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, Zero, Succ(x11), x12)
new_mkBalBranch6MkBalBranch014(x0, x1, x2, x3, x4, x5, x6, x7, Succ(x8), Zero, x9, x10)
new_mkVBalBranch3MkVBalBranch272(x0, x1, Neg(Succ(Succ(Zero))), x2, x3, x4, x5, Succ(x6), x7, x8, x9, Succ(Succ(x10)), x11)
new_mkVBalBranch3MkVBalBranch134(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, Zero, Zero, x11)
new_mkVBalBranch3(x0, Branch(x1, x2, Neg(Zero), x3, x4), Branch(x5, x6, Neg(Zero), x7, x8), x9)
new_mkVBalBranch3MkVBalBranch280(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, Succ(x11), Succ(x12), x13)
new_primPlusNat2(Succ(x0), Succ(x1))
new_splitGT12(Branch(GT, x0, x1, x2, x3), x4)
new_mkVBalBranch3MkVBalBranch145(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, Zero, x10)
new_mkVBalBranch3MkVBalBranch272(x0, x1, Neg(Succ(Zero)), x2, x3, x4, x5, x6, x7, x8, x9, Succ(x10), x11)
new_mkVBalBranch3MkVBalBranch288(x0, x1, Pos(Succ(Succ(x2))), x3, x4, x5, x6, Succ(x7), x8, x9, x10, Succ(Succ(x11)), x12)
new_mkVBalBranch3MkVBalBranch262(x0, x1, Neg(Zero), x2, x3, x4, x5, x6, x7, x8, x9, Succ(x10), x11)
new_mkBalBranch6MkBalBranch414(x0, x1, x2, x3, Zero, x4, x5)
new_mkVBalBranch4(x0, Branch(x1, x2, Neg(Zero), x3, x4), Branch(x5, x6, Pos(Zero), x7, x8), x9)
new_mkVBalBranch4(x0, Branch(x1, x2, Pos(Zero), x3, x4), Branch(x5, x6, Neg(Zero), x7, x8), x9)
new_splitGT12(Branch(LT, x0, x1, x2, x3), x4)
new_mkVBalBranch3MkVBalBranch270(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, Zero, Zero, x10)
new_mkVBalBranch3MkVBalBranch288(x0, x1, Pos(Succ(Succ(x2))), x3, x4, x5, x6, Succ(x7), x8, x9, x10, Succ(Zero), x11)
new_splitLT12(Branch(GT, x0, x1, x2, x3), x4)
new_mkVBalBranch3MkVBalBranch282(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11)
new_mkVBalBranch3MkVBalBranch272(x0, x1, Neg(Succ(Succ(Zero))), x2, x3, x4, x5, Succ(x6), x7, x8, x9, Succ(Zero), x10)
new_mkBalBranch6MkBalBranch315(x0, x1, x2, x3, Zero, x4, x5)
new_primPlusInt(Neg(x0), x1, x2, x3, x4, x5)
new_mkVBalBranch3MkVBalBranch272(x0, x1, Pos(x2), x3, x4, x5, x6, x7, x8, x9, x10, Succ(x11), x12)
new_mkVBalBranch3MkVBalBranch149(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, Zero, Succ(x11), x12)
new_mkBalBranch6MkBalBranch019(x0, x1, x2, x3, x4, x5, x6, x7, Succ(x8), x9, x10)
new_mkVBalBranch3MkVBalBranch252(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, Succ(x11), Zero, x12)
new_mkVBalBranch3MkVBalBranch153(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, Zero, x11)
new_mkBalBranch6MkBalBranch32(x0, x1, x2, x3, x4, x5)
new_mkVBalBranch3MkVBalBranch280(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, Zero, Zero, x11)
new_splitGT3(x0, x1, x2, x3, x4)
new_splitLT25(x0, x1, x2, x3, x4)
new_mkBalBranch6MkBalBranch111(x0, x1, x2, x3, x4, x5, x6, x7, x8, Succ(x9), x10, x11)
new_mkVBalBranch3MkVBalBranch164(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, Zero, x10)
new_mkBalBranch6MkBalBranch117(x0, x1, x2, x3, x4, x5, x6, x7, Succ(x8), x9, x10)
new_mkVBalBranch3MkVBalBranch132(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, Zero, Succ(x11), x12)
new_splitGT210(x0, x1, x2, x3, x4)
new_mkBalBranch6MkBalBranch30(x0, x1, x2, x3, Succ(x4), x5, x6)
new_mkVBalBranch3MkVBalBranch165(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11)
new_mkBalBranch6MkBalBranch31(x0, x1, x2, x3, x4, x5)
new_mkVBalBranch3MkVBalBranch133(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, Zero, x10)
new_mkVBalBranch3MkVBalBranch167(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, Succ(x11), x12)
new_mkVBalBranch3MkVBalBranch144(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, Zero, Succ(x11), x12)
new_splitGT8(x0, x1, x2, x3)
new_splitGT9(x0, x1, x2, x3, x4)
new_mkVBalBranch3MkVBalBranch256(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11)
new_intersectFM_C2Gts2(x0, x1, x2, x3, x4)
new_splitGT16(x0)
new_mkVBalBranch3MkVBalBranch260(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10)
new_splitLT42(x0)
new_splitGT15(Branch(LT, x0, x1, x2, x3), x4)
new_splitLT14(EmptyFM, x0)
new_splitLT14(Branch(LT, x0, x1, x2, x3), x4)
new_addToFM_C4(Branch(EQ, x0, x1, x2, x3), x4, x5)
new_mkBalBranch6MkBalBranch1113(x0, x1, x2, x3, x4, x5, x6, x7, Succ(x8), Succ(x9), x10, x11)
new_mkBalBranch6MkBalBranch415(x0, x1, x2, x3, x4, x5, x6, x7)
new_mkBalBranch6MkBalBranch0110(x0, x1, x2, x3, x4, x5, x6, x7, Zero, x8, x9)
new_mkVBalBranch3MkVBalBranch151(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11)
new_mkVBalBranch3MkVBalBranch262(x0, x1, Pos(Zero), x2, x3, x4, x5, x6, x7, x8, x9, Zero, x10)
new_mkVBalBranch3(x0, Branch(x1, x2, Pos(Zero), x3, x4), Branch(x5, x6, Neg(Zero), x7, x8), x9)
new_mkVBalBranch3(x0, Branch(x1, x2, Neg(Zero), x3, x4), Branch(x5, x6, Pos(Zero), x7, x8), x9)
new_splitGT11(x0, x1, x2, x3)
new_mkVBalBranch2(x0, Branch(x1, x2, Neg(Zero), x3, x4), Branch(x5, x6, Neg(Zero), x7, x8), x9)
new_mkVBalBranch3(x0, Branch(x1, x2, x3, x4, x5), EmptyFM, x6)
new_mkVBalBranch3MkVBalBranch263(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, Zero, Zero, x10)
new_mkVBalBranch3(x0, Branch(x1, x2, Pos(Zero), x3, x4), Branch(x5, x6, Pos(Succ(x7)), x8, x9), x10)
new_mkBalBranch6MkBalBranch310(x0, x1, x2, x3, Neg(Zero), Neg(x4), x5, x6)
new_mkVBalBranch3MkVBalBranch147(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, Succ(x11), x12)
new_mkBalBranch6MkBalBranch42(x0, x1, x2, x3, x4, x5, x6, x7)
new_mkBalBranch6MkBalBranch310(x0, x1, x2, x3, Pos(Succ(x4)), Pos(x5), x6, x7)
new_mkVBalBranch3MkVBalBranch275(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, Succ(x11), Succ(x12), x13)
new_splitGT24(x0, x1, x2, x3, x4)
new_mkVBalBranch3MkVBalBranch153(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, Succ(x11), x12)
new_mkVBalBranch3MkVBalBranch288(x0, x1, Pos(Succ(Zero)), x2, x3, x4, x5, Zero, x6, x7, x8, Zero, x9)
new_mkVBalBranch4(x0, Branch(x1, x2, Pos(Zero), x3, x4), Branch(x5, x6, Pos(Zero), x7, x8), x9)
new_mkBalBranch6MkBalBranch1110(x0, x1, x2, x3, x4, x5, x6, x7, Succ(x8), x9, x10)
new_splitGT28(x0, x1, x2, x3, x4)
new_mkBalBranch6MkBalBranch48(x0, x1, x2, x3, Succ(x4), x5, x6)
new_mkVBalBranch3MkVBalBranch275(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, Zero, Succ(x11), x12)
new_mkVBalBranch3MkVBalBranch284(x0, x1, Succ(x2), x3, x4, x5, x6, x7, x8, x9, x10, x11)
new_mkVBalBranch3MkVBalBranch267(x0, x1, Neg(x2), x3, x4, x5, x6, x7, x8, x9, x10, Zero, x11)
new_mkBalBranch6MkBalBranch016(x0, x1, x2, EmptyFM, x3, x4, x5, x6, x7, x8)
new_intersectFM_C2Lts1(x0, x1, x2, x3, x4)
new_mkBalBranch6MkBalBranch416(x0, x1, x2, x3, Succ(x4), x5, x6)
new_mkVBalBranch3MkVBalBranch252(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, Succ(x11), Succ(x12), x13)
new_mkVBalBranch3MkVBalBranch149(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, Succ(x11), Zero, x12)
new_mkVBalBranch3MkVBalBranch146(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, Succ(x10), x11)
new_mkVBalBranch3MkVBalBranch148(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11)
new_mkBalBranch6MkBalBranch113(x0, x1, x2, x3, x4, x5, x6, x7, Pos(Zero), Pos(x8), x9, x10)
new_mkBalBranch6MkBalBranch411(x0, x1, x2, x3, Pos(Zero), Neg(x4), x5, x6)
new_mkBalBranch6MkBalBranch411(x0, x1, x2, x3, Neg(Zero), Pos(x4), x5, x6)
new_mkVBalBranch4(x0, EmptyFM, x1, x2)
new_splitGT13(x0)
new_mkBalBranch6MkBalBranch1115(x0, x1, x2, x3, x4, EmptyFM, x5, x6, x7, x8)
new_splitLT27(x0, x1, x2, x3, x4)
new_mkBalBranch6MkBalBranch5(x0, x1, x2, x3, Pos(Succ(Zero)), x4, x5)
new_primMinusNat0(Zero, Succ(x0))
new_mkBalBranch6MkBalBranch5(x0, x1, x2, x3, Pos(Zero), x4, x5)
new_splitGT12(EmptyFM, x0)
new_mkVBalBranch3MkVBalBranch288(x0, x1, Pos(Succ(Zero)), x2, x3, x4, x5, Succ(x6), x7, x8, x9, Zero, x10)
new_mkBalBranch6MkBalBranch39(x0, x1, x2, x3, Succ(x4), Zero, x5, x6)
new_mkVBalBranch3MkVBalBranch274(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10)
new_mkVBalBranch3MkVBalBranch288(x0, x1, Pos(Succ(Succ(x2))), x3, x4, x5, x6, Zero, x7, x8, x9, Zero, x10)
new_mkBalBranch6MkBalBranch310(x0, x1, x2, x3, Pos(Zero), Pos(x4), x5, x6)
new_mkBalBranch6MkBalBranch411(x0, x1, x2, x3, Neg(Succ(x4)), Neg(x5), x6, x7)
new_mkVBalBranch3MkVBalBranch272(x0, x1, Neg(Succ(Succ(Succ(x2)))), x3, x4, x5, x6, Zero, x7, x8, x9, Succ(Zero), x10)
new_primPlusNat1(Zero)
new_mkVBalBranch3MkVBalBranch263(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, Succ(x10), Zero, x11)
new_mkVBalBranch2(x0, Branch(x1, x2, Pos(Zero), x3, x4), Branch(x5, x6, Pos(Succ(x7)), x8, x9), x10)
new_mkBalBranch6MkBalBranch50(x0, x1, x2, x3, x4, x5)
new_mkBalBranch(x0, x1, x2, x3, x4, x5)
new_mkVBalBranch3MkVBalBranch132(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, Zero, Zero, x11)
new_mkBalBranch6MkBalBranch5(x0, x1, x2, x3, Neg(Zero), x4, x5)
new_mkVBalBranch3MkVBalBranch272(x0, x1, Neg(Zero), x2, x3, x4, x5, x6, x7, x8, x9, Zero, x10)
new_sizeFM(Branch(x0, x1, x2, x3, x4), x5, x6)
new_mkVBalBranch3MkVBalBranch288(x0, x1, Pos(Succ(Zero)), x2, x3, x4, x5, x6, x7, x8, x9, Succ(x10), x11)
new_mkVBalBranch3MkVBalBranch252(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, Zero, Succ(x11), x12)
new_splitLT13(x0)
new_splitGT7(x0, x1, x2, x3, x4)
new_primPlusInt1(x0, Neg(x1))
new_mkBalBranch6MkBalBranch110(x0, x1, x2, x3, x4, x5, x6, x7, Zero, x8, x9)
new_mkBalBranch6MkBalBranch45(x0, x1, x2, x3, x4, Succ(x5), x6, x7)
new_splitLT14(Branch(EQ, x0, x1, x2, x3), x4)
new_mkVBalBranch3MkVBalBranch154(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, Zero, x10)
new_mkVBalBranch3MkVBalBranch264(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10)
new_mkBalBranch6MkBalBranch411(x0, x1, x2, x3, Neg(Zero), Neg(x4), x5, x6)
new_mkBalBranch6MkBalBranch40(x0, x1, x2, x3, x4, x5)
new_mkVBalBranch3MkVBalBranch251(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11)
new_addToFM_C3(Branch(GT, x0, x1, x2, x3), x4, x5)
new_mkBalBranch6MkBalBranch017(x0, x1, x2, x3, x4, x5, x6, x7, Neg(Zero), Neg(x8), x9, x10)
new_mkBalBranch6MkBalBranch112(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9)
new_mkVBalBranch3MkVBalBranch281(x0, x1, Neg(Succ(Succ(Zero))), x2, x3, x4, x5, Succ(x6), x7, x8, x9, Succ(Succ(x10)), x11)
new_mkBalBranch6MkBalBranch411(x0, x1, x2, x3, Neg(Succ(x4)), Pos(x5), x6, x7)
new_mkBalBranch6MkBalBranch411(x0, x1, x2, x3, Pos(Succ(x4)), Neg(x5), x6, x7)
new_mkBalBranch6MkBalBranch012(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9)
new_mkVBalBranch3MkVBalBranch250(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10)
new_mkVBalBranch3MkVBalBranch255(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, Succ(x11), Succ(x12), x13)
new_addToFM0(x0, x1, x2)
new_mkVBalBranch3MkVBalBranch259(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10)
new_mkVBalBranch3MkVBalBranch279(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10)
new_mkVBalBranch3MkVBalBranch281(x0, x1, Neg(Succ(Succ(Succ(x2)))), x3, x4, x5, x6, Zero, x7, x8, x9, Succ(Zero), x10)
new_mkBalBranch6MkBalBranch36(x0, x1, x2, x3, Succ(x4), x5, x6, x7)
new_splitLT23(x0, x1, x2, x3, x4)
new_mkBalBranch6MkBalBranch1111(x0, x1, x2, x3, x4, x5, x6, x7, Succ(x8), x9, x10, x11)
new_mkBalBranch6MkBalBranch0111(x0, x1, x2, x3, x4, x5, x6, x7, Zero, x8, x9)
new_addToFM_C3(EmptyFM, x0, x1)
new_splitGT15(EmptyFM, x0)
new_mkBalBranch6MkBalBranch011(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9)
new_mkVBalBranch3MkVBalBranch143(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, Succ(x10), x11)
new_mkVBalBranch3MkVBalBranch162(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, Zero, Zero, x11)
new_mkVBalBranch3MkVBalBranch134(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, Zero, Succ(x11), x12)
new_mkVBalBranch3MkVBalBranch246(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, Zero, Zero, x11)
new_mkVBalBranch3MkVBalBranch162(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, Succ(x11), Zero, x12)
new_mkVBalBranch3MkVBalBranch289(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, Succ(x11), Zero, x12)
new_mkVBalBranch3MkVBalBranch133(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, Succ(x10), x11)
new_mkVBalBranch3MkVBalBranch141(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, Zero, x11)
new_mkVBalBranch3MkVBalBranch272(x0, x1, Neg(Zero), x2, x3, x4, x5, x6, x7, x8, x9, Succ(x10), x11)
new_primPlusNat2(Succ(x0), Zero)
new_mkBalBranch6MkBalBranch119(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11)
new_mkBalBranch6MkBalBranch38(x0, x1, x2, x3, x4, Succ(x5), x6, x7)
new_mkBalBranch6MkBalBranch33(x0, EmptyFM, x1, x2, x3, x4)
new_splitLT8(x0, x1, x2, x3)
new_mkBalBranch6MkBalBranch46(x0, x1, x2, x3, x4, x5, x6, x7)
new_mkVBalBranch3MkVBalBranch267(x0, x1, Pos(Succ(x2)), x3, x4, x5, x6, x7, x8, x9, x10, Succ(x11), x12)
new_mkVBalBranch3MkVBalBranch152(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, Zero, Succ(x11), x12)
new_mkVBalBranch3MkVBalBranch281(x0, x1, Pos(x2), x3, x4, x5, x6, x7, x8, x9, x10, Zero, x11)
new_mkVBalBranch3MkVBalBranch281(x0, x1, Pos(x2), x3, x4, x5, x6, x7, x8, x9, x10, Succ(x11), x12)
new_mkVBalBranch3MkVBalBranch272(x0, x1, Neg(Succ(Succ(Succ(x2)))), x3, x4, x5, x6, Succ(x7), x8, x9, x10, Succ(Succ(x11)), x12)
new_mkVBalBranch3MkVBalBranch288(x0, x1, Neg(x2), x3, x4, x5, x6, x7, x8, x9, x10, Succ(x11), x12)
new_splitLT40(x0)
new_mkBalBranch6MkBalBranch44(x0, x1, x2, x3, x4, x5, x6, x7)
new_mkVBalBranch3MkVBalBranch138(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11)
new_mkBalBranch6MkBalBranch414(x0, x1, x2, x3, Succ(x4), x5, x6)
new_mkBalBranch6MkBalBranch115(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11)
new_mkVBalBranch3MkVBalBranch253(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11)
new_mkVBalBranch2(x0, Branch(x1, x2, Neg(Zero), x3, x4), Branch(x5, x6, Neg(Succ(x7)), x8, x9), x10)
new_mkBalBranch6MkBalBranch412(x0, x1, x2, x3, Zero, Succ(x4), x5, x6)
new_mkVBalBranch3MkVBalBranch288(x0, x1, Neg(x2), x3, x4, x5, x6, x7, x8, x9, x10, Zero, x11)
new_mkVBalBranch3(x0, Branch(x1, x2, Neg(Zero), x3, x4), Branch(x5, x6, Pos(Succ(x7)), x8, x9), x10)
new_mkVBalBranch3(x0, Branch(x1, x2, Pos(Zero), x3, x4), Branch(x5, x6, Neg(Succ(x7)), x8, x9), x10)
new_mkVBalBranch3MkVBalBranch272(x0, x1, Neg(Succ(Succ(x2))), x3, x4, x5, x6, Succ(x7), x8, x9, x10, Zero, x11)
new_mkVBalBranch3MkVBalBranch286(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11)
new_splitLT12(Branch(EQ, x0, x1, x2, x3), x4)
new_splitLT15(Branch(EQ, x0, x1, x2, x3), x4)
new_mkVBalBranch3MkVBalBranch268(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10)
new_mkVBalBranch3MkVBalBranch270(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, Succ(x10), Succ(x11), x12)
new_mkBalBranch6MkBalBranch314(x0, x1, x2, x3, Succ(x4), x5, x6)
new_mkBalBranch6MkBalBranch49(Branch(x0, x1, x2, x3, x4), x5, x6, x7, x8, x9)
new_mkVBalBranch3MkVBalBranch281(x0, x1, Neg(Succ(Succ(Zero))), x2, x3, x4, x5, Zero, x6, x7, x8, Succ(Zero), x9)
new_mkVBalBranch3MkVBalBranch144(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, Succ(x11), Zero, x12)
new_mkBalBranch6MkBalBranch1113(x0, x1, x2, x3, x4, x5, x6, x7, Zero, Zero, x8, x9)
new_splitLT5(x0, x1, x2, x3)
new_primPlusInt1(x0, Pos(x1))
new_mkBalBranch6MkBalBranch48(x0, x1, x2, x3, Zero, x4, x5)
new_mkVBalBranch3MkVBalBranch149(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, Succ(x11), Succ(x12), x13)
new_mkBalBranch6MkBalBranch412(x0, x1, x2, x3, Succ(x4), Zero, x5, x6)
new_mkBalBranch6MkBalBranch412(x0, x1, x2, x3, Succ(x4), Succ(x5), x6, x7)
new_splitLT15(Branch(LT, x0, x1, x2, x3), x4)
new_mkVBalBranch3MkVBalBranch272(x0, x1, Neg(Succ(Succ(Succ(x2)))), x3, x4, x5, x6, Zero, x7, x8, x9, Succ(Succ(x10)), x11)
new_mkVBalBranch3MkVBalBranch167(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, Zero, x11)
new_mkVBalBranch3MkVBalBranch267(x0, x1, Neg(x2), x3, x4, x5, x6, x7, x8, x9, x10, Succ(x11), x12)
new_mkVBalBranch3MkVBalBranch137(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, Zero, x11)
new_mkBalBranch6MkBalBranch1115(x0, x1, x2, x3, x4, Branch(x5, x6, x7, x8, x9), x10, x11, x12, x13)
new_mkVBalBranch3MkVBalBranch140(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11)
new_mkVBalBranch3MkVBalBranch257(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11)
new_splitGT14(Branch(LT, x0, x1, x2, x3), x4)
new_mkBalBranch6MkBalBranch014(x0, x1, x2, x3, x4, x5, x6, x7, Zero, Succ(x8), x9, x10)
new_mkVBalBranch3MkVBalBranch246(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, Succ(x11), Zero, x12)
new_intersectFM_C2Lts(x0, x1, x2, x3, x4)
new_mkVBalBranch3(x0, Branch(x1, x2, Pos(Succ(x3)), x4, x5), Branch(x6, x7, x8, x9, x10), x11)
new_splitGT14(Branch(GT, x0, x1, x2, x3), x4)
new_mkVBalBranch3MkVBalBranch261(x0, x1, Pos(Zero), x2, x3, x4, x5, x6, x7, x8, x9, Succ(x10), x11)
new_mkVBalBranch3MkVBalBranch131(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, Zero, x11)
new_mkVBalBranch3MkVBalBranch246(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, Zero, Succ(x11), x12)
new_mkBalBranch6MkBalBranch1112(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9)
new_mkVBalBranch3MkVBalBranch261(x0, x1, Pos(Succ(x2)), x3, x4, x5, x6, x7, x8, x9, x10, Zero, x11)
new_mkBalBranch6MkBalBranch113(x0, x1, x2, x3, x4, x5, x6, x7, Pos(Succ(x8)), Pos(x9), x10, x11)
new_mkBalBranch6MkBalBranch018(x0, x1, x2, x3, x4, x5, x6, x7, Zero, x8, x9, x10)
new_mkBalBranch6MkBalBranch5(x0, x1, x2, x3, Pos(Succ(Succ(Succ(x4)))), x5, x6)
new_splitGT40(x0)
new_mkVBalBranch3MkVBalBranch255(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, Succ(x11), Zero, x12)
new_mkVBalBranch3MkVBalBranch262(x0, x1, Neg(Zero), x2, x3, x4, x5, x6, x7, x8, x9, Zero, x10)
new_mkVBalBranch3MkVBalBranch290(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10)
new_addToFM(x0, x1, x2)
new_mkVBalBranch4(x0, Branch(x1, x2, Neg(Zero), x3, x4), Branch(x5, x6, Neg(Succ(x7)), x8, x9), x10)
new_mkVBalBranch3MkVBalBranch288(x0, x1, Pos(Succ(Succ(x2))), x3, x4, x5, x6, Zero, x7, x8, x9, Succ(Succ(x10)), x11)
new_mkVBalBranch3MkVBalBranch164(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, Succ(x10), x11)
new_mkBalBranch6MkBalBranch1114(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9)
new_mkVBalBranch3MkVBalBranch272(x0, x1, Neg(Succ(Succ(x2))), x3, x4, x5, x6, Zero, x7, x8, x9, Zero, x10)
new_mkBalBranch6MkBalBranch113(x0, x1, x2, x3, x4, x5, x6, x7, Neg(Zero), Neg(x8), x9, x10)
new_mkBalBranch6MkBalBranch39(x0, x1, x2, x3, Succ(x4), Succ(x5), x6, x7)
new_mkVBalBranch3MkVBalBranch277(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, Zero, Zero, x10)
new_mkVBalBranch3MkVBalBranch288(x0, x1, Pos(Zero), x2, x3, x4, x5, x6, x7, x8, x9, Succ(x10), x11)
new_mkVBalBranch4(x0, Branch(x1, x2, Neg(Succ(x3)), x4, x5), Branch(x6, x7, x8, x9, x10), x11)
new_mkVBalBranch3MkVBalBranch132(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, Succ(x11), Succ(x12), x13)
new_mkBalBranch6MkBalBranch016(x0, x1, x2, Branch(x3, x4, x5, x6, x7), x8, x9, x10, x11, x12, x13)
new_mkVBalBranch3MkVBalBranch134(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, Succ(x11), Succ(x12), x13)
new_mkVBalBranch3MkVBalBranch154(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, Succ(x10), x11)
new_mkVBalBranch3MkVBalBranch258(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11)
new_intersectFM_C2Lts2(x0, x1, x2, x3, x4)
new_mkVBalBranch2(x0, Branch(x1, x2, Neg(Succ(x3)), x4, x5), Branch(x6, x7, x8, x9, x10), x11)
new_emptyFM(x0)
new_primPlusInt0(x0, Neg(x1))
new_intersectFM_C2Gts3(x0, x1)
new_mkBalBranch6MkBalBranch411(x0, x1, x2, x3, Pos(Zero), Pos(x4), x5, x6)
new_mkVBalBranch3MkVBalBranch281(x0, x1, Neg(Succ(Succ(Zero))), x2, x3, x4, x5, Succ(x6), x7, x8, x9, Succ(Zero), x10)
new_splitGT6(x0)
new_primPlusNat3(x0, Succ(x1))
new_mkVBalBranch3MkVBalBranch168(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, Succ(x10), x11)
new_mkBalBranch6MkBalBranch118(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11)
new_mkVBalBranch3MkVBalBranch280(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, Succ(x11), Zero, x12)
new_mkVBalBranch3MkVBalBranch142(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11)
new_primMulNat(Succ(x0))
new_mkVBalBranch3MkVBalBranch161(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, Succ(x10), x11)
new_mkVBalBranch2(x0, EmptyFM, x1, x2)
new_mkBalBranch6MkBalBranch37(x0, x1, x2, x3, x4, x5, x6, x7)
new_primPlusInt2(Neg(x0), x1, x2, x3, x4, x5, x6)
new_mkVBalBranch3MkVBalBranch162(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, Succ(x11), Succ(x12), x13)
new_mkVBalBranch3MkVBalBranch139(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, Zero, x11)
new_mkVBalBranch3MkVBalBranch281(x0, x1, Neg(Succ(Succ(Zero))), x2, x3, x4, x5, Zero, x6, x7, x8, Succ(Succ(x9)), x10)
new_mkBalBranch6MkBalBranch117(x0, x1, x2, x3, x4, x5, x6, x7, Zero, x8, x9)
new_splitLT3(x0, x1, x2, x3, x4)
new_addToFM_C4(Branch(LT, x0, x1, x2, x3), x4, x5)
new_mkVBalBranch3MkVBalBranch252(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, Zero, Zero, x11)
new_mkVBalBranch3MkVBalBranch246(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, Succ(x11), Succ(x12), x13)
new_mkVBalBranch3MkVBalBranch262(x0, x1, Neg(Succ(x2)), x3, x4, x5, x6, x7, x8, x9, x10, Zero, x11)
new_mkBranch(x0, x1, x2, x3, x4, x5, x6)
new_mkBalBranch6MkBalBranch0111(x0, x1, x2, x3, x4, x5, x6, x7, Succ(x8), x9, x10)
new_mkBalBranch6MkBalBranch38(x0, x1, x2, x3, x4, Zero, x5, x6)
new_primMulNat2(Zero)
new_mkBalBranch6MkBalBranch010(x0, x1, x2, x3, x4, x5, x6, x7, Succ(x8), x9, x10)
new_mkBalBranch6MkBalBranch36(x0, x1, x2, x3, Zero, x4, x5, x6)
new_mkBalBranch6MkBalBranch017(x0, x1, x2, x3, x4, x5, x6, x7, Neg(Succ(x8)), Neg(x9), x10, x11)
new_addToFM_C3(Branch(LT, x0, x1, x2, x3), x4, x5)
new_splitLT26(x0, x1, x2, x3, x4)
new_mkVBalBranch3MkVBalBranch168(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, Zero, x10)
new_mkBalBranch6MkBalBranch0110(x0, x1, x2, x3, x4, x5, x6, x7, Succ(x8), x9, x10)
new_mkBalBranch6MkBalBranch114(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11)
new_mkVBalBranch3MkVBalBranch150(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11)
new_splitGT42(x0)
new_mkBalBranch6MkBalBranch47(x0, x1, x2, x3, Zero, x4, x5, x6)
new_mkVBalBranch3MkVBalBranch261(x0, x1, Pos(Zero), x2, x3, x4, x5, x6, x7, x8, x9, Zero, x10)
new_mkBalBranch6MkBalBranch017(x0, x1, x2, x3, x4, x5, x6, x7, Neg(Succ(x8)), Pos(x9), x10, x11)
new_mkBalBranch6MkBalBranch017(x0, x1, x2, x3, x4, x5, x6, x7, Pos(Succ(x8)), Neg(x9), x10, x11)
new_mkBalBranch6MkBalBranch1110(x0, x1, x2, x3, x4, x5, x6, x7, Zero, x8, x9)
new_mkVBalBranch3MkVBalBranch131(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, Succ(x11), x12)
new_mkVBalBranch4(x0, Branch(x1, x2, Neg(Zero), x3, x4), Branch(x5, x6, Pos(Succ(x7)), x8, x9), x10)
new_mkVBalBranch4(x0, Branch(x1, x2, Pos(Zero), x3, x4), Branch(x5, x6, Neg(Succ(x7)), x8, x9), x10)
new_mkVBalBranch3MkVBalBranch262(x0, x1, Neg(Succ(x2)), x3, x4, x5, x6, x7, x8, x9, x10, Succ(x11), x12)
new_primPlusInt0(x0, Pos(x1))
new_mkVBalBranch3MkVBalBranch162(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, Zero, Succ(x11), x12)
new_mkVBalBranch3MkVBalBranch147(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, Zero, x11)
new_primMulNat2(Succ(x0))
new_intersectFM_C2Lts0(x0, x1, x2, x3, x4)
new_mkVBalBranch3MkVBalBranch269(x0, x1, Zero, x2, x3, x4, x5, x6, x7, x8, x9, x10)
new_splitGT27(x0, x1, x2, x3, x4)
new_splitLT16(x0)
new_mkVBalBranch3MkVBalBranch152(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, Succ(x11), Succ(x12), x13)
new_mkBalBranch6Size_l(x0, x1, x2, x3, x4, x5)
new_mkBalBranch6MkBalBranch311(x0, x1, x2, x3, x4, x5, x6, x7)
new_splitGT5(x0, x1, x2, x3)
new_mkVBalBranch3MkVBalBranch160(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11)
new_primMinusNat0(Succ(x0), Succ(x1))

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
                                  ↳ 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_C(Branch(GT, zzz31, zzz32, Branch(GT, zzz331, zzz332, Branch(GT, zzz3331, zzz3332, EmptyFM, zzz3334), zzz334), zzz34), Branch(EQ, zzz41, zzz42, zzz43, zzz44), h) → new_intersectFM_C(new_mkVBalBranch3(zzz31, new_splitGT9(zzz331, zzz332, Branch(GT, zzz3331, zzz3332, EmptyFM, zzz3334), zzz334, h), zzz34, h), zzz44, h)
new_intersectFM_C(Branch(LT, zzz31, zzz32, zzz33, zzz34), Branch(LT, zzz41, zzz42, zzz43, zzz44), h) → new_intersectFM_C(new_splitLT3(zzz31, zzz32, zzz33, zzz34, h), zzz43, h)
new_intersectFM_C2IntersectFM_C16(zzz2208, zzz2209, zzz2210, zzz2211, zzz2212, zzz2213, zzz2214, zzz2215, GT, zzz2217, zzz2218, zzz2219, zzz2220, ca, cb) → new_intersectFM_C2IntersectFM_C18(Branch(LT, zzz2208, zzz2209, zzz2210, zzz2211), zzz2212, zzz2213, zzz2214, zzz2215, zzz2217, zzz2218, zzz2219, zzz2220, ca, cb)
new_intersectFM_C2IntersectFM_C10(zzz869, zzz870, zzz871, zzz872, zzz873, zzz874, zzz875, zzz876, EQ, zzz878, zzz879, EmptyFM, zzz881, bc, bd) → new_intersectFM_C(new_intersectFM_C2Lts1(zzz869, zzz870, zzz871, zzz872, bc), zzz875, bc)
new_intersectFM_C(Branch(GT, zzz31, zzz32, Branch(GT, zzz331, zzz332, Branch(EQ, zzz3331, zzz3332, zzz3333, zzz3334), zzz334), zzz34), Branch(EQ, zzz41, zzz42, zzz43, zzz44), h) → new_intersectFM_C(new_splitGT24(zzz31, zzz32, Branch(GT, zzz331, zzz332, Branch(EQ, zzz3331, zzz3332, zzz3333, zzz3334), zzz334), zzz34, h), zzz44, h)
new_intersectFM_C2IntersectFM_C11(zzz883, zzz884, zzz885, zzz886, zzz887, zzz888, zzz889, zzz890, EQ, zzz892, zzz893, zzz894, zzz895, be, bf) → new_intersectFM_C(new_intersectFM_C2Gts2(zzz883, zzz884, zzz885, zzz886, be), zzz890, be)
new_intersectFM_C2IntersectFM_C14(zzz76, zzz77, zzz78, zzz79, zzz80, zzz81, zzz82, zzz83, zzz871, zzz872, zzz873, zzz874, bg, bh) → new_intersectFM_C(new_intersectFM_C2Gts(zzz76, zzz77, zzz78, zzz79, bg), zzz83, bg)
new_intersectFM_C(Branch(GT, zzz31, zzz32, Branch(GT, zzz331, zzz332, Branch(LT, zzz3331, zzz3332, zzz3333, zzz3334), zzz334), zzz34), Branch(EQ, zzz41, zzz42, zzz43, zzz44), h) → new_intersectFM_C2IntersectFM_C12(zzz31, zzz32, Branch(GT, zzz331, zzz332, Branch(LT, zzz3331, zzz3332, zzz3333, zzz3334), zzz334), zzz34, zzz41, zzz42, zzz43, zzz44, zzz3331, zzz3332, zzz3333, zzz3334, h, h)
new_intersectFM_C2IntersectFM_C17(zzz2223, zzz2224, zzz2225, zzz2226, zzz2227, zzz2228, zzz2229, zzz2230, LT, zzz2232, zzz2233, zzz2234, Branch(zzz22350, zzz22351, zzz22352, zzz22353, zzz22354), ce, cf) → new_intersectFM_C2IntersectFM_C17(zzz2223, zzz2224, zzz2225, zzz2226, zzz2227, zzz2228, zzz2229, zzz2230, zzz22350, zzz22351, zzz22352, zzz22353, zzz22354, ce, cf)
new_intersectFM_C2IntersectFM_C10(zzz869, zzz870, zzz871, zzz872, zzz873, zzz874, zzz875, zzz876, LT, zzz878, zzz879, zzz880, zzz881, bc, bd) → new_intersectFM_C(new_intersectFM_C2Lts1(zzz869, zzz870, zzz871, zzz872, bc), zzz875, bc)
new_intersectFM_C(Branch(EQ, zzz31, zzz32, EmptyFM, zzz34), Branch(LT, zzz41, zzz42, zzz43, zzz44), h) → new_intersectFM_C(new_splitGT4(zzz31, zzz32, zzz34, h), zzz44, h)
new_intersectFM_C2IntersectFM_C114(zzz2223, zzz2224, zzz2225, zzz2226, zzz2227, zzz2228, zzz2229, zzz2230, EmptyFM, ce, cf) → new_intersectFM_C(new_intersectFM_C2Lts3(Branch(EQ, zzz2223, zzz2224, zzz2225, zzz2226), ce), zzz2229, ce)
new_intersectFM_C2IntersectFM_C12(zzz76, zzz77, zzz78, zzz79, zzz80, zzz81, zzz82, zzz83, zzz84, zzz85, zzz86, EmptyFM, bg, bh) → new_intersectFM_C(new_intersectFM_C2Lts(zzz76, zzz77, zzz78, zzz79, bg), zzz82, bg)
new_intersectFM_C2IntersectFM_C112(zzz76, zzz77, zzz78, zzz79, zzz80, zzz81, zzz82, zzz83, Branch(LT, zzz871, zzz872, zzz873, zzz874), bg, bh) → new_intersectFM_C2IntersectFM_C12(zzz76, zzz77, zzz78, zzz79, zzz80, zzz81, zzz82, zzz83, zzz871, zzz872, zzz873, zzz874, bg, bh)
new_intersectFM_C2IntersectFM_C16(zzz2208, zzz2209, zzz2210, zzz2211, zzz2212, zzz2213, zzz2214, zzz2215, LT, zzz2217, zzz2218, zzz2219, EmptyFM, ca, cb) → new_intersectFM_C(new_intersectFM_C2Lts3(Branch(LT, zzz2208, zzz2209, zzz2210, zzz2211), ca), zzz2214, ca)
new_intersectFM_C(Branch(LT, zzz31, zzz32, zzz33, Branch(zzz340, zzz341, zzz342, zzz343, zzz344)), Branch(GT, zzz41, zzz42, zzz43, zzz44), h) → new_intersectFM_C2IntersectFM_C16(zzz31, zzz32, zzz33, Branch(zzz340, zzz341, zzz342, zzz343, zzz344), zzz41, zzz42, zzz43, zzz44, zzz340, zzz341, zzz342, zzz343, zzz344, h, h)
new_intersectFM_C(Branch(GT, zzz31, zzz32, Branch(GT, zzz331, zzz332, Branch(GT, zzz3331, zzz3332, Branch(EQ, zzz33331, zzz33332, zzz33333, zzz33334), zzz3334), zzz334), zzz34), Branch(EQ, zzz41, zzz42, zzz43, zzz44), h) → new_intersectFM_C(new_intersectFM_C2Gts(zzz31, zzz32, Branch(GT, zzz331, zzz332, Branch(GT, zzz3331, zzz3332, Branch(EQ, zzz33331, zzz33332, zzz33333, zzz33334), zzz3334), zzz334), zzz34, h), zzz44, h)
new_intersectFM_C2IntersectFM_C112(zzz76, zzz77, zzz78, zzz79, zzz80, zzz81, zzz82, zzz83, EmptyFM, bg, bh) → new_intersectFM_C(new_intersectFM_C2Gts(zzz76, zzz77, zzz78, zzz79, bg), zzz83, bg)
new_intersectFM_C2IntersectFM_C110(zzz869, zzz870, zzz871, zzz872, zzz873, zzz874, zzz875, zzz876, EmptyFM, bc, bd) → new_intersectFM_C(new_intersectFM_C2Lts1(zzz869, zzz870, zzz871, zzz872, bc), zzz875, bc)
new_intersectFM_C2IntersectFM_C113(zzz2208, zzz2209, zzz2210, zzz2211, zzz2212, zzz2213, zzz2214, zzz2215, Branch(zzz22200, zzz22201, zzz22202, zzz22203, zzz22204), ca, cb) → new_intersectFM_C2IntersectFM_C16(zzz2208, zzz2209, zzz2210, zzz2211, zzz2212, zzz2213, zzz2214, zzz2215, zzz22200, zzz22201, zzz22202, zzz22203, zzz22204, ca, cb)
new_intersectFM_C(Branch(LT, zzz31, zzz32, zzz33, EmptyFM), Branch(GT, zzz41, zzz42, zzz43, zzz44), h) → new_intersectFM_C(new_splitLT10(zzz31, zzz32, zzz33, h), zzz43, h)
new_intersectFM_C2IntersectFM_C16(zzz2208, zzz2209, zzz2210, zzz2211, zzz2212, zzz2213, zzz2214, zzz2215, EQ, zzz2217, zzz2218, zzz2219, zzz2220, ca, cb) → new_intersectFM_C2IntersectFM_C113(zzz2208, zzz2209, zzz2210, zzz2211, zzz2212, zzz2213, zzz2214, zzz2215, zzz2220, ca, cb)
new_intersectFM_C2IntersectFM_C12(zzz76, zzz77, zzz78, zzz79, zzz80, zzz81, zzz82, zzz83, zzz84, zzz85, zzz86, Branch(EQ, zzz871, zzz872, zzz873, zzz874), bg, bh) → new_intersectFM_C(new_intersectFM_C2Gts(zzz76, zzz77, zzz78, zzz79, bg), zzz83, bg)
new_intersectFM_C2IntersectFM_C11(zzz883, zzz884, zzz885, zzz886, zzz887, zzz888, zzz889, zzz890, GT, zzz892, zzz893, EmptyFM, zzz895, be, bf) → new_intersectFM_C(new_intersectFM_C2Lts2(zzz883, zzz884, zzz885, zzz886, be), zzz889, be)
new_intersectFM_C(Branch(EQ, zzz31, zzz32, zzz33, zzz34), Branch(EQ, zzz41, zzz42, zzz43, zzz44), h) → new_intersectFM_C(new_splitLT7(zzz31, zzz32, zzz33, zzz34, h), zzz43, h)
new_intersectFM_C(Branch(GT, zzz31, zzz32, Branch(GT, zzz331, zzz332, Branch(GT, zzz3331, zzz3332, Branch(GT, zzz33331, zzz33332, Branch(EQ, zzz333331, zzz333332, zzz333333, zzz333334), zzz33334), zzz3334), zzz334), zzz34), Branch(EQ, zzz41, zzz42, zzz43, zzz44), h) → new_intersectFM_C2IntersectFM_C14(zzz31, zzz32, Branch(GT, zzz331, zzz332, Branch(GT, zzz3331, zzz3332, Branch(GT, zzz33331, zzz33332, Branch(EQ, zzz333331, zzz333332, zzz333333, zzz333334), zzz33334), zzz3334), zzz334), zzz34, zzz41, zzz42, zzz43, zzz44, zzz333331, zzz333332, zzz333333, zzz333334, h, h)
new_intersectFM_C(Branch(GT, zzz31, zzz32, Branch(GT, zzz331, zzz332, Branch(GT, zzz3331, zzz3332, EmptyFM, zzz3334), zzz334), zzz34), Branch(EQ, zzz41, zzz42, zzz43, zzz44), h) → new_intersectFM_C(new_splitLT9(zzz331, zzz332, Branch(GT, zzz3331, zzz3332, EmptyFM, zzz3334), zzz334, h), zzz43, h)
new_intersectFM_C(Branch(EQ, zzz31, zzz32, zzz33, zzz34), Branch(EQ, zzz41, zzz42, zzz43, zzz44), h) → new_intersectFM_C(new_splitGT7(zzz31, zzz32, zzz33, zzz34, h), zzz44, h)
new_intersectFM_C(Branch(GT, zzz31, zzz32, Branch(LT, zzz331, zzz332, zzz333, zzz334), zzz34), Branch(EQ, zzz41, zzz42, zzz43, zzz44), h) → new_intersectFM_C2IntersectFM_C12(zzz31, zzz32, Branch(LT, zzz331, zzz332, zzz333, zzz334), zzz34, zzz41, zzz42, zzz43, zzz44, zzz331, zzz332, zzz333, zzz334, h, h)
new_intersectFM_C(Branch(GT, zzz31, zzz32, Branch(zzz330, zzz331, zzz332, zzz333, zzz334), zzz34), Branch(LT, zzz41, zzz42, zzz43, zzz44), h) → new_intersectFM_C2IntersectFM_C10(zzz31, zzz32, Branch(zzz330, zzz331, zzz332, zzz333, zzz334), zzz34, zzz41, zzz42, zzz43, zzz44, zzz330, zzz331, zzz332, zzz333, zzz334, h, h)
new_intersectFM_C2IntersectFM_C111(zzz883, zzz884, zzz885, zzz886, zzz887, zzz888, zzz889, zzz890, EmptyFM, be, bf) → new_intersectFM_C(new_intersectFM_C2Lts2(zzz883, zzz884, zzz885, zzz886, be), zzz889, be)
new_intersectFM_C2IntersectFM_C17(zzz2223, zzz2224, zzz2225, zzz2226, zzz2227, zzz2228, zzz2229, zzz2230, LT, zzz2232, zzz2233, zzz2234, EmptyFM, ce, cf) → new_intersectFM_C(new_intersectFM_C2Lts3(Branch(EQ, zzz2223, zzz2224, zzz2225, zzz2226), ce), zzz2229, ce)
new_intersectFM_C2IntersectFM_C19(zzz854, zzz855, zzz856, zzz857, zzz858, zzz859, zzz860, zzz861, EmptyFM, ba, bb) → new_intersectFM_C(new_intersectFM_C2Gts0(zzz854, zzz855, zzz856, zzz857, ba), zzz861, ba)
new_intersectFM_C(Branch(GT, zzz31, zzz32, Branch(GT, zzz331, zzz332, Branch(GT, zzz3331, zzz3332, Branch(EQ, zzz33331, zzz33332, zzz33333, zzz33334), zzz3334), zzz334), zzz34), Branch(EQ, zzz41, zzz42, zzz43, zzz44), h) → new_intersectFM_C(new_intersectFM_C2Lts(zzz31, zzz32, Branch(GT, zzz331, zzz332, Branch(GT, zzz3331, zzz3332, Branch(EQ, zzz33331, zzz33332, zzz33333, zzz33334), zzz3334), zzz334), zzz34, h), zzz43, h)
new_intersectFM_C2IntersectFM_C113(zzz2208, zzz2209, zzz2210, zzz2211, zzz2212, zzz2213, zzz2214, zzz2215, EmptyFM, ca, cb) → new_intersectFM_C(new_intersectFM_C2Lts3(Branch(LT, zzz2208, zzz2209, zzz2210, zzz2211), ca), zzz2214, ca)
new_intersectFM_C(Branch(GT, zzz31, zzz32, Branch(GT, zzz331, zzz332, Branch(GT, zzz3331, zzz3332, Branch(GT, zzz33331, zzz33332, Branch(GT, zzz333331, zzz333332, zzz333333, zzz333334), zzz33334), zzz3334), zzz334), zzz34), Branch(EQ, zzz41, zzz42, zzz43, zzz44), h) → new_intersectFM_C2IntersectFM_C15(zzz31, zzz32, Branch(GT, zzz331, zzz332, Branch(GT, zzz3331, zzz3332, Branch(GT, zzz33331, zzz33332, Branch(GT, zzz333331, zzz333332, zzz333333, zzz333334), zzz33334), zzz3334), zzz334), zzz34, zzz41, zzz42, zzz43, zzz44, zzz333331, zzz333332, zzz333333, zzz333334, h, h)
new_intersectFM_C2IntersectFM_C14(zzz76, zzz77, zzz78, zzz79, zzz80, zzz81, zzz82, zzz83, zzz871, zzz872, zzz873, zzz874, bg, bh) → new_intersectFM_C(new_intersectFM_C2Lts(zzz76, zzz77, zzz78, zzz79, bg), zzz82, bg)
new_intersectFM_C2IntersectFM_C12(zzz76, zzz77, zzz78, zzz79, zzz80, zzz81, zzz82, zzz83, zzz84, zzz85, zzz86, Branch(LT, zzz871, zzz872, zzz873, zzz874), bg, bh) → new_intersectFM_C2IntersectFM_C12(zzz76, zzz77, zzz78, zzz79, zzz80, zzz81, zzz82, zzz83, zzz871, zzz872, zzz873, zzz874, bg, bh)
new_intersectFM_C(Branch(GT, zzz31, zzz32, Branch(GT, zzz331, zzz332, Branch(EQ, zzz3331, zzz3332, zzz3333, zzz3334), zzz334), zzz34), Branch(EQ, zzz41, zzz42, zzz43, zzz44), h) → new_intersectFM_C(new_splitLT23(zzz31, zzz32, Branch(GT, zzz331, zzz332, Branch(EQ, zzz3331, zzz3332, zzz3333, zzz3334), zzz334), zzz34, h), zzz43, h)
new_intersectFM_C(Branch(LT, zzz31, zzz32, zzz33, EmptyFM), Branch(EQ, zzz41, zzz42, zzz43, zzz44), h) → new_intersectFM_C(new_mkVBalBranch2(zzz31, zzz33, new_splitLT6(h), h), zzz43, h)
new_intersectFM_C(Branch(EQ, zzz31, zzz32, zzz33, EmptyFM), Branch(GT, zzz41, zzz42, zzz43, zzz44), h) → new_intersectFM_C(new_splitLT11(zzz31, zzz32, zzz33, h), zzz43, h)
new_intersectFM_C2IntersectFM_C10(zzz869, zzz870, zzz871, zzz872, zzz873, zzz874, zzz875, zzz876, EQ, zzz878, zzz879, Branch(zzz8800, zzz8801, zzz8802, zzz8803, zzz8804), zzz881, bc, bd) → new_intersectFM_C2IntersectFM_C10(zzz869, zzz870, zzz871, zzz872, zzz873, zzz874, zzz875, zzz876, zzz8800, zzz8801, zzz8802, zzz8803, zzz8804, bc, bd)
new_intersectFM_C2IntersectFM_C17(zzz2223, zzz2224, zzz2225, zzz2226, zzz2227, zzz2228, zzz2229, zzz2230, GT, zzz2232, zzz2233, zzz2234, zzz2235, ce, cf) → new_intersectFM_C2IntersectFM_C18(Branch(EQ, zzz2223, zzz2224, zzz2225, zzz2226), zzz2227, zzz2228, zzz2229, zzz2230, zzz2232, zzz2233, zzz2234, zzz2235, ce, cf)
new_intersectFM_C2IntersectFM_C110(zzz869, zzz870, zzz871, zzz872, zzz873, zzz874, zzz875, zzz876, Branch(zzz8800, zzz8801, zzz8802, zzz8803, zzz8804), bc, bd) → new_intersectFM_C2IntersectFM_C10(zzz869, zzz870, zzz871, zzz872, zzz873, zzz874, zzz875, zzz876, zzz8800, zzz8801, zzz8802, zzz8803, zzz8804, bc, bd)
new_intersectFM_C(Branch(GT, zzz31, zzz32, Branch(EQ, zzz331, zzz332, zzz333, zzz334), zzz34), Branch(EQ, zzz41, zzz42, zzz43, zzz44), h) → new_intersectFM_C(new_splitLT7(zzz331, zzz332, zzz333, zzz334, h), zzz43, h)
new_intersectFM_C(Branch(EQ, zzz31, zzz32, Branch(zzz330, zzz331, zzz332, zzz333, zzz334), zzz34), Branch(LT, zzz41, zzz42, zzz43, zzz44), h) → new_intersectFM_C2IntersectFM_C1(zzz31, zzz32, Branch(zzz330, zzz331, zzz332, zzz333, zzz334), zzz34, zzz41, zzz42, zzz43, zzz44, zzz330, zzz331, zzz332, zzz333, zzz334, h, h)
new_intersectFM_C2IntersectFM_C114(zzz2223, zzz2224, zzz2225, zzz2226, zzz2227, zzz2228, zzz2229, zzz2230, Branch(zzz22350, zzz22351, zzz22352, zzz22353, zzz22354), ce, cf) → new_intersectFM_C2IntersectFM_C17(zzz2223, zzz2224, zzz2225, zzz2226, zzz2227, zzz2228, zzz2229, zzz2230, zzz22350, zzz22351, zzz22352, zzz22353, zzz22354, ce, cf)
new_intersectFM_C2IntersectFM_C11(zzz883, zzz884, zzz885, zzz886, zzz887, zzz888, zzz889, zzz890, EQ, zzz892, zzz893, zzz894, zzz895, be, bf) → new_intersectFM_C(new_intersectFM_C2Lts2(zzz883, zzz884, zzz885, zzz886, be), zzz889, be)
new_intersectFM_C2IntersectFM_C18(zzz2129, zzz2130, zzz2131, zzz2132, zzz2133, zzz2134, zzz2135, zzz2136, zzz2137, cc, cd) → new_intersectFM_C(new_intersectFM_C2Gts3(zzz2129, cc), zzz2133, cc)
new_intersectFM_C2IntersectFM_C10(zzz869, zzz870, zzz871, zzz872, zzz873, zzz874, zzz875, zzz876, LT, zzz878, zzz879, zzz880, zzz881, bc, bd) → new_intersectFM_C(new_intersectFM_C2Gts1(zzz869, zzz870, zzz871, zzz872, bc), zzz876, bc)
new_intersectFM_C2IntersectFM_C112(zzz76, zzz77, zzz78, zzz79, zzz80, zzz81, zzz82, zzz83, EmptyFM, bg, bh) → new_intersectFM_C(new_intersectFM_C2Lts(zzz76, zzz77, zzz78, zzz79, bg), zzz82, bg)
new_intersectFM_C(Branch(EQ, zzz31, zzz32, zzz33, Branch(zzz340, zzz341, zzz342, zzz343, zzz344)), Branch(GT, zzz41, zzz42, zzz43, zzz44), h) → new_intersectFM_C2IntersectFM_C17(zzz31, zzz32, zzz33, Branch(zzz340, zzz341, zzz342, zzz343, zzz344), zzz41, zzz42, zzz43, zzz44, zzz340, zzz341, zzz342, zzz343, zzz344, h, h)
new_intersectFM_C2IntersectFM_C110(zzz869, zzz870, zzz871, zzz872, zzz873, zzz874, zzz875, zzz876, EmptyFM, bc, bd) → new_intersectFM_C(new_intersectFM_C2Gts1(zzz869, zzz870, zzz871, zzz872, bc), zzz876, bc)
new_intersectFM_C2IntersectFM_C10(zzz869, zzz870, zzz871, zzz872, zzz873, zzz874, zzz875, zzz876, GT, zzz878, zzz879, zzz880, zzz881, bc, bd) → new_intersectFM_C2IntersectFM_C110(zzz869, zzz870, zzz871, zzz872, zzz873, zzz874, zzz875, zzz876, zzz880, bc, bd)
new_intersectFM_C2IntersectFM_C11(zzz883, zzz884, zzz885, zzz886, zzz887, zzz888, zzz889, zzz890, GT, zzz892, zzz893, Branch(zzz8940, zzz8941, zzz8942, zzz8943, zzz8944), zzz895, be, bf) → new_intersectFM_C2IntersectFM_C11(zzz883, zzz884, zzz885, zzz886, zzz887, zzz888, zzz889, zzz890, zzz8940, zzz8941, zzz8942, zzz8943, zzz8944, be, bf)
new_intersectFM_C2IntersectFM_C112(zzz76, zzz77, zzz78, zzz79, zzz80, zzz81, zzz82, zzz83, Branch(GT, zzz871, zzz872, zzz873, zzz874), bg, bh) → new_intersectFM_C2IntersectFM_C112(zzz76, zzz77, zzz78, zzz79, zzz80, zzz81, zzz82, zzz83, zzz873, bg, bh)
new_intersectFM_C(Branch(GT, zzz31, zzz32, EmptyFM, zzz34), Branch(LT, zzz41, zzz42, zzz43, zzz44), h) → new_intersectFM_C(new_splitGT5(zzz31, zzz32, zzz34, h), zzz44, h)
new_intersectFM_C2IntersectFM_C112(zzz76, zzz77, zzz78, zzz79, zzz80, zzz81, zzz82, zzz83, Branch(EQ, zzz871, zzz872, zzz873, zzz874), bg, bh) → new_intersectFM_C(new_intersectFM_C2Lts(zzz76, zzz77, zzz78, zzz79, bg), zzz82, bg)
new_intersectFM_C2IntersectFM_C19(zzz854, zzz855, zzz856, zzz857, zzz858, zzz859, zzz860, zzz861, EmptyFM, ba, bb) → new_intersectFM_C(new_intersectFM_C2Lts0(zzz854, zzz855, zzz856, zzz857, ba), zzz860, ba)
new_intersectFM_C2IntersectFM_C114(zzz2223, zzz2224, zzz2225, zzz2226, zzz2227, zzz2228, zzz2229, zzz2230, EmptyFM, ce, cf) → new_intersectFM_C(new_intersectFM_C2Gts3(Branch(EQ, zzz2223, zzz2224, zzz2225, zzz2226), ce), zzz2230, ce)
new_intersectFM_C(Branch(GT, zzz31, zzz32, zzz33, zzz34), Branch(GT, zzz41, zzz42, zzz43, zzz44), h) → new_intersectFM_C2IntersectFM_C18(Branch(GT, zzz31, zzz32, zzz33, zzz34), zzz41, zzz42, zzz43, zzz44, zzz31, zzz32, zzz33, zzz34, h, h)
new_intersectFM_C(Branch(LT, zzz31, zzz32, zzz33, Branch(zzz340, zzz341, zzz342, zzz343, zzz344)), Branch(EQ, zzz41, zzz42, zzz43, zzz44), h) → new_intersectFM_C2IntersectFM_C11(zzz31, zzz32, zzz33, Branch(zzz340, zzz341, zzz342, zzz343, zzz344), zzz41, zzz42, zzz43, zzz44, zzz340, zzz341, zzz342, zzz343, zzz344, h, h)
new_intersectFM_C2IntersectFM_C11(zzz883, zzz884, zzz885, zzz886, zzz887, zzz888, zzz889, zzz890, GT, zzz892, zzz893, EmptyFM, zzz895, be, bf) → new_intersectFM_C(new_intersectFM_C2Gts2(zzz883, zzz884, zzz885, zzz886, be), zzz890, be)
new_intersectFM_C2IntersectFM_C1(zzz854, zzz855, zzz856, zzz857, zzz858, zzz859, zzz860, zzz861, EQ, zzz863, zzz864, Branch(zzz8650, zzz8651, zzz8652, zzz8653, zzz8654), zzz866, ba, bb) → new_intersectFM_C2IntersectFM_C1(zzz854, zzz855, zzz856, zzz857, zzz858, zzz859, zzz860, zzz861, zzz8650, zzz8651, zzz8652, zzz8653, zzz8654, ba, bb)
new_intersectFM_C2IntersectFM_C13(zzz76, zzz77, zzz78, zzz79, zzz80, zzz81, zzz82, zzz83, zzz871, zzz872, zzz873, zzz874, bg, bh) → new_intersectFM_C2IntersectFM_C12(zzz76, zzz77, zzz78, zzz79, zzz80, zzz81, zzz82, zzz83, zzz871, zzz872, zzz873, zzz874, bg, bh)
new_intersectFM_C2IntersectFM_C112(zzz76, zzz77, zzz78, zzz79, zzz80, zzz81, zzz82, zzz83, Branch(EQ, zzz871, zzz872, zzz873, zzz874), bg, bh) → new_intersectFM_C(new_intersectFM_C2Gts(zzz76, zzz77, zzz78, zzz79, bg), zzz83, bg)
new_intersectFM_C2IntersectFM_C111(zzz883, zzz884, zzz885, zzz886, zzz887, zzz888, zzz889, zzz890, EmptyFM, be, bf) → new_intersectFM_C(new_intersectFM_C2Gts2(zzz883, zzz884, zzz885, zzz886, be), zzz890, be)
new_intersectFM_C2IntersectFM_C12(zzz76, zzz77, zzz78, zzz79, zzz80, zzz81, zzz82, zzz83, zzz84, zzz85, zzz86, EmptyFM, bg, bh) → new_intersectFM_C(new_intersectFM_C2Gts(zzz76, zzz77, zzz78, zzz79, bg), zzz83, bg)
new_intersectFM_C2IntersectFM_C18(zzz2129, zzz2130, zzz2131, zzz2132, zzz2133, zzz2134, zzz2135, zzz2136, zzz2137, cc, cd) → new_intersectFM_C(new_intersectFM_C2Lts3(zzz2129, cc), zzz2132, cc)
new_intersectFM_C2IntersectFM_C111(zzz883, zzz884, zzz885, zzz886, zzz887, zzz888, zzz889, zzz890, Branch(zzz8940, zzz8941, zzz8942, zzz8943, zzz8944), be, bf) → new_intersectFM_C2IntersectFM_C11(zzz883, zzz884, zzz885, zzz886, zzz887, zzz888, zzz889, zzz890, zzz8940, zzz8941, zzz8942, zzz8943, zzz8944, be, bf)
new_intersectFM_C2IntersectFM_C1(zzz854, zzz855, zzz856, zzz857, zzz858, zzz859, zzz860, zzz861, EQ, zzz863, zzz864, EmptyFM, zzz866, ba, bb) → new_intersectFM_C(new_intersectFM_C2Gts0(zzz854, zzz855, zzz856, zzz857, ba), zzz861, ba)
new_intersectFM_C2IntersectFM_C17(zzz2223, zzz2224, zzz2225, zzz2226, zzz2227, zzz2228, zzz2229, zzz2230, EQ, zzz2232, zzz2233, zzz2234, zzz2235, ce, cf) → new_intersectFM_C2IntersectFM_C114(zzz2223, zzz2224, zzz2225, zzz2226, zzz2227, zzz2228, zzz2229, zzz2230, zzz2235, ce, cf)
new_intersectFM_C(Branch(GT, zzz31, zzz32, Branch(GT, zzz331, zzz332, Branch(GT, zzz3331, zzz3332, Branch(GT, zzz33331, zzz33332, EmptyFM, zzz33334), zzz3334), zzz334), zzz34), Branch(EQ, zzz41, zzz42, zzz43, zzz44), h) → new_intersectFM_C(new_intersectFM_C2Lts(zzz31, zzz32, Branch(GT, zzz331, zzz332, Branch(GT, zzz3331, zzz3332, Branch(GT, zzz33331, zzz33332, EmptyFM, zzz33334), zzz3334), zzz334), zzz34, h), zzz43, h)
new_intersectFM_C2IntersectFM_C11(zzz883, zzz884, zzz885, zzz886, zzz887, zzz888, zzz889, zzz890, LT, zzz892, zzz893, zzz894, zzz895, be, bf) → new_intersectFM_C2IntersectFM_C111(zzz883, zzz884, zzz885, zzz886, zzz887, zzz888, zzz889, zzz890, zzz895, be, bf)
new_intersectFM_C2IntersectFM_C1(zzz854, zzz855, zzz856, zzz857, zzz858, zzz859, zzz860, zzz861, LT, zzz863, zzz864, zzz865, zzz866, ba, bb) → new_intersectFM_C(new_intersectFM_C2Lts0(zzz854, zzz855, zzz856, zzz857, ba), zzz860, ba)
new_intersectFM_C2IntersectFM_C1(zzz854, zzz855, zzz856, zzz857, zzz858, zzz859, zzz860, zzz861, LT, zzz863, zzz864, zzz865, zzz866, ba, bb) → new_intersectFM_C(new_intersectFM_C2Gts0(zzz854, zzz855, zzz856, zzz857, ba), zzz861, ba)
new_intersectFM_C2IntersectFM_C113(zzz2208, zzz2209, zzz2210, zzz2211, zzz2212, zzz2213, zzz2214, zzz2215, EmptyFM, ca, cb) → new_intersectFM_C(new_intersectFM_C2Gts3(Branch(LT, zzz2208, zzz2209, zzz2210, zzz2211), ca), zzz2215, ca)
new_intersectFM_C2IntersectFM_C19(zzz854, zzz855, zzz856, zzz857, zzz858, zzz859, zzz860, zzz861, Branch(zzz8650, zzz8651, zzz8652, zzz8653, zzz8654), ba, bb) → new_intersectFM_C2IntersectFM_C1(zzz854, zzz855, zzz856, zzz857, zzz858, zzz859, zzz860, zzz861, zzz8650, zzz8651, zzz8652, zzz8653, zzz8654, ba, bb)
new_intersectFM_C(Branch(GT, zzz31, zzz32, Branch(GT, zzz331, zzz332, Branch(GT, zzz3331, zzz3332, Branch(GT, zzz33331, zzz33332, EmptyFM, zzz33334), zzz3334), zzz334), zzz34), Branch(EQ, zzz41, zzz42, zzz43, zzz44), h) → new_intersectFM_C(new_intersectFM_C2Gts(zzz31, zzz32, Branch(GT, zzz331, zzz332, Branch(GT, zzz3331, zzz3332, Branch(GT, zzz33331, zzz33332, EmptyFM, zzz33334), zzz3334), zzz334), zzz34, h), zzz44, h)
new_intersectFM_C2IntersectFM_C16(zzz2208, zzz2209, zzz2210, zzz2211, zzz2212, zzz2213, zzz2214, zzz2215, LT, zzz2217, zzz2218, zzz2219, Branch(zzz22200, zzz22201, zzz22202, zzz22203, zzz22204), ca, cb) → new_intersectFM_C2IntersectFM_C16(zzz2208, zzz2209, zzz2210, zzz2211, zzz2212, zzz2213, zzz2214, zzz2215, zzz22200, zzz22201, zzz22202, zzz22203, zzz22204, ca, cb)
new_intersectFM_C2IntersectFM_C1(zzz854, zzz855, zzz856, zzz857, zzz858, zzz859, zzz860, zzz861, EQ, zzz863, zzz864, EmptyFM, zzz866, ba, bb) → new_intersectFM_C(new_intersectFM_C2Lts0(zzz854, zzz855, zzz856, zzz857, ba), zzz860, ba)
new_intersectFM_C(Branch(GT, zzz31, zzz32, Branch(GT, zzz331, zzz332, EmptyFM, zzz334), zzz34), Branch(EQ, zzz41, zzz42, zzz43, zzz44), h) → new_intersectFM_C(new_mkVBalBranch3(zzz31, new_splitGT8(zzz331, zzz332, zzz334, h), zzz34, h), zzz44, h)
new_intersectFM_C(Branch(LT, zzz31, zzz32, zzz33, zzz34), Branch(LT, zzz41, zzz42, zzz43, zzz44), h) → new_intersectFM_C(new_splitGT3(zzz31, zzz32, zzz33, zzz34, h), zzz44, h)
new_intersectFM_C2IntersectFM_C17(zzz2223, zzz2224, zzz2225, zzz2226, zzz2227, zzz2228, zzz2229, zzz2230, LT, zzz2232, zzz2233, zzz2234, EmptyFM, ce, cf) → new_intersectFM_C(new_intersectFM_C2Gts3(Branch(EQ, zzz2223, zzz2224, zzz2225, zzz2226), ce), zzz2230, ce)
new_intersectFM_C2IntersectFM_C12(zzz76, zzz77, zzz78, zzz79, zzz80, zzz81, zzz82, zzz83, zzz84, zzz85, zzz86, Branch(GT, zzz871, zzz872, zzz873, zzz874), bg, bh) → new_intersectFM_C2IntersectFM_C112(zzz76, zzz77, zzz78, zzz79, zzz80, zzz81, zzz82, zzz83, zzz873, bg, bh)
new_intersectFM_C(Branch(GT, zzz31, zzz32, Branch(GT, zzz331, zzz332, Branch(GT, zzz3331, zzz3332, Branch(LT, zzz33331, zzz33332, zzz33333, zzz33334), zzz3334), zzz334), zzz34), Branch(EQ, zzz41, zzz42, zzz43, zzz44), h) → new_intersectFM_C2IntersectFM_C12(zzz31, zzz32, Branch(GT, zzz331, zzz332, Branch(GT, zzz3331, zzz3332, Branch(LT, zzz33331, zzz33332, zzz33333, zzz33334), zzz3334), zzz334), zzz34, zzz41, zzz42, zzz43, zzz44, zzz33331, zzz33332, zzz33333, zzz33334, h, h)
new_intersectFM_C(Branch(GT, zzz31, zzz32, EmptyFM, zzz34), Branch(EQ, zzz41, zzz42, zzz43, zzz44), h) → new_intersectFM_C(new_splitGT8(zzz31, zzz32, zzz34, h), zzz44, h)
new_intersectFM_C2IntersectFM_C10(zzz869, zzz870, zzz871, zzz872, zzz873, zzz874, zzz875, zzz876, EQ, zzz878, zzz879, EmptyFM, zzz881, bc, bd) → new_intersectFM_C(new_intersectFM_C2Gts1(zzz869, zzz870, zzz871, zzz872, bc), zzz876, bc)
new_intersectFM_C(Branch(GT, zzz31, zzz32, Branch(GT, zzz331, zzz332, Branch(GT, zzz3331, zzz3332, Branch(GT, zzz33331, zzz33332, Branch(LT, zzz333331, zzz333332, zzz333333, zzz333334), zzz33334), zzz3334), zzz334), zzz34), Branch(EQ, zzz41, zzz42, zzz43, zzz44), h) → new_intersectFM_C2IntersectFM_C13(zzz31, zzz32, Branch(GT, zzz331, zzz332, Branch(GT, zzz3331, zzz3332, Branch(GT, zzz33331, zzz33332, Branch(LT, zzz333331, zzz333332, zzz333333, zzz333334), zzz33334), zzz3334), zzz334), zzz34, zzz41, zzz42, zzz43, zzz44, zzz333331, zzz333332, zzz333333, zzz333334, h, h)
new_intersectFM_C2IntersectFM_C15(zzz76, zzz77, zzz78, zzz79, zzz80, zzz81, zzz82, zzz83, zzz871, zzz872, zzz873, zzz874, bg, bh) → new_intersectFM_C2IntersectFM_C112(zzz76, zzz77, zzz78, zzz79, zzz80, zzz81, zzz82, zzz83, zzz873, bg, bh)
new_intersectFM_C2IntersectFM_C16(zzz2208, zzz2209, zzz2210, zzz2211, zzz2212, zzz2213, zzz2214, zzz2215, LT, zzz2217, zzz2218, zzz2219, EmptyFM, ca, cb) → new_intersectFM_C(new_intersectFM_C2Gts3(Branch(LT, zzz2208, zzz2209, zzz2210, zzz2211), ca), zzz2215, ca)
new_intersectFM_C(Branch(GT, zzz31, zzz32, Branch(EQ, zzz331, zzz332, zzz333, zzz334), zzz34), Branch(EQ, zzz41, zzz42, zzz43, zzz44), h) → new_intersectFM_C(new_mkVBalBranch3(zzz31, new_splitGT7(zzz331, zzz332, zzz333, zzz334, h), zzz34, h), zzz44, h)
new_intersectFM_C2IntersectFM_C1(zzz854, zzz855, zzz856, zzz857, zzz858, zzz859, zzz860, zzz861, GT, zzz863, zzz864, zzz865, zzz866, ba, bb) → new_intersectFM_C2IntersectFM_C19(zzz854, zzz855, zzz856, zzz857, zzz858, zzz859, zzz860, zzz861, zzz865, ba, bb)
new_intersectFM_C2IntersectFM_C12(zzz76, zzz77, zzz78, zzz79, zzz80, zzz81, zzz82, zzz83, zzz84, zzz85, zzz86, Branch(EQ, zzz871, zzz872, zzz873, zzz874), bg, bh) → new_intersectFM_C(new_intersectFM_C2Lts(zzz76, zzz77, zzz78, zzz79, bg), zzz82, bg)

The TRS R consists of the following rules:

new_mkVBalBranch3MkVBalBranch133(zzz340, zzz341, zzz34200, zzz343, zzz344, zzz510, zzz511, zzz513, zzz514, zzz31, Succ(zzz1240), h) → new_mkBalBranch(zzz510, zzz511, zzz513, new_mkVBalBranch4(zzz31, zzz514, Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), h), ty_Ordering, h)
new_mkBalBranch6MkBalBranch111(zzz2934, zzz21270, zzz21271, zzz21272, zzz21273, zzz21274, zzz2930, zzz2931, zzz226200, Succ(zzz22700), da, db) → new_mkBalBranch6MkBalBranch1113(zzz2934, zzz21270, zzz21271, zzz21272, zzz21273, zzz21274, zzz2930, zzz2931, zzz226200, zzz22700, da, db)
new_mkVBalBranch3MkVBalBranch285(zzz340, zzz341, zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, h) → new_mkBalBranch(zzz510, zzz511, zzz513, new_mkVBalBranch4(zzz31, zzz514, Branch(zzz340, zzz341, Pos(Zero), zzz343, zzz344), h), ty_Ordering, h)
new_mkVBalBranch3MkVBalBranch162(zzz1986, zzz1987, zzz1988, zzz1989, zzz1990, zzz1991, zzz1992, zzz1993, zzz1994, zzz1995, zzz1996, Succ(zzz19970), Zero, dh) → new_mkVBalBranch3MkVBalBranch142(zzz1986, zzz1987, zzz1988, zzz1989, zzz1990, zzz1991, zzz1992, zzz1993, zzz1994, zzz1995, zzz1996, dh)
new_primPlusInt(Pos(zzz22720), zzz2268, zzz2269, zzz2266, ec, ed) → new_primPlusInt0(zzz22720, new_sizeFM(zzz2269, ec, ed))
new_mkBalBranch6MkBalBranch48(zzz2934, zzz2127, zzz2930, zzz2931, Zero, da, db) → new_mkBalBranch6MkBalBranch40(zzz2934, zzz2127, zzz2930, zzz2931, da, db)
new_splitLT12(EmptyFM, ba) → new_splitLT42(ba)
new_mkVBalBranch3MkVBalBranch281(zzz340, zzz341, Neg(Succ(Zero)), zzz343, zzz344, zzz510, zzz511, Zero, zzz513, zzz514, zzz31, Zero, h) → new_mkVBalBranch3MkVBalBranch157(zzz340, zzz341, Zero, zzz343, zzz344, zzz510, zzz511, zzz513, zzz514, zzz31, new_primMulNat1(Zero), h)
new_mkBalBranch6MkBalBranch014(zzz29340, zzz29341, zzz29342, zzz29343, zzz29344, zzz2127, zzz2930, zzz2931, Zero, Zero, da, db) → new_mkBalBranch6MkBalBranch012(zzz29340, zzz29341, zzz29342, zzz29343, zzz29344, zzz2127, zzz2930, zzz2931, da, db)
new_splitLT14(Branch(LT, zzz21291, zzz21292, zzz21293, zzz21294), cc) → new_mkVBalBranch2(zzz21291, zzz21293, new_splitLT14(zzz21294, cc), cc)
new_mkVBalBranch3MkVBalBranch275(zzz958, zzz959, zzz960, zzz961, zzz962, zzz963, zzz964, zzz965, zzz966, zzz967, zzz968, Zero, Zero, fa) → new_mkVBalBranch3MkVBalBranch276(zzz958, zzz959, zzz960, zzz961, zzz962, zzz963, zzz964, zzz965, zzz966, zzz967, zzz968, fa)
new_addToFM_C2(EmptyFM, zzz31, h) → Branch(LT, zzz31, Pos(Succ(Zero)), new_emptyFM(h), new_emptyFM(h))
new_mkVBalBranch3MkVBalBranch255(zzz537, zzz538, zzz539, zzz540, zzz541, zzz542, zzz543, zzz544, zzz545, zzz546, zzz547, Succ(zzz5480), Zero, dg) → new_mkVBalBranch3MkVBalBranch256(zzz537, zzz538, zzz539, zzz540, zzz541, zzz542, zzz543, zzz544, zzz545, zzz546, zzz547, dg)
new_mkBalBranch6MkBalBranch117(zzz2934, zzz21270, zzz21271, zzz21272, zzz21273, zzz21274, zzz2930, zzz2931, Zero, da, db) → new_mkBalBranch6MkBalBranch112(zzz2934, zzz21270, zzz21271, zzz21272, zzz21273, zzz21274, zzz2930, zzz2931, da, db)
new_mkVBalBranch3MkVBalBranch253(zzz929, zzz930, zzz931, zzz932, zzz933, zzz934, zzz935, zzz936, zzz937, zzz938, zzz939, dc) → new_mkVBalBranch3MkVBalBranch131(zzz929, zzz930, zzz931, zzz932, zzz933, zzz934, zzz935, zzz936, zzz937, zzz938, zzz939, new_primMulNat1(zzz931), dc)
new_mkVBalBranch3MkVBalBranch167(zzz340, zzz341, zzz34200, zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, Zero, h) → new_mkVBalBranch3MkVBalBranch160(zzz340, zzz341, zzz34200, zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, h)
new_mkVBalBranch3MkVBalBranch280(zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, zzz1125, zzz1126, zzz1127, zzz1128, zzz1129, Zero, Succ(zzz11310), ff) → new_mkVBalBranch3MkVBalBranch257(zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, zzz1125, zzz1126, zzz1127, zzz1128, zzz1129, ff)
new_splitLT16(h) → new_splitLT42(h)
new_mkVBalBranch3MkVBalBranch258(zzz340, zzz341, zzz3420, zzz343, zzz344, zzz520, zzz521, zzz52200, zzz523, zzz524, zzz31, h) → new_mkBalBranch(zzz340, zzz341, new_mkVBalBranch3(zzz31, Branch(zzz520, zzz521, Neg(Succ(zzz52200)), zzz523, zzz524), zzz343, h), zzz344, ty_Ordering, h)
new_splitGT12(Branch(LT, zzz8561, zzz8562, zzz8563, zzz8564), ba) → new_splitGT210(zzz8561, zzz8562, zzz8563, zzz8564, ba)
new_mkBalBranch6MkBalBranch310(zzz2934, zzz2127, zzz2930, zzz2931, Pos(Zero), Neg(zzz22450), da, db) → new_mkBalBranch6MkBalBranch315(zzz2934, zzz2127, zzz2930, zzz2931, new_primMulNat(zzz22450), da, db)
new_addToFM_C2(Branch(GT, zzz3171, zzz3172, zzz3173, zzz3174), zzz31, h) → new_mkBalBranch(GT, zzz3171, new_addToFM_C2(zzz3173, zzz31, h), zzz3174, ty_Ordering, h)
new_mkVBalBranch3MkVBalBranch149(zzz2050, zzz2051, zzz2052, zzz2053, zzz2054, zzz2055, zzz2056, zzz2057, zzz2058, zzz2059, zzz2060, Zero, Zero, ef) → new_mkVBalBranch3MkVBalBranch150(zzz2050, zzz2051, zzz2052, zzz2053, zzz2054, zzz2055, zzz2056, zzz2057, zzz2058, zzz2059, zzz2060, ef)
new_mkVBalBranch3MkVBalBranch278(zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, zzz1125, zzz1126, zzz1127, zzz1128, zzz1129, ff) → new_mkVBalBranch3MkVBalBranch159(zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, zzz1125, zzz1126, zzz1127, zzz1128, zzz1129, new_primMulNat1(zzz1121), ff)
new_mkVBalBranch3MkVBalBranch277(zzz1133, zzz1134, zzz1135, zzz1136, zzz1137, zzz1138, zzz1139, zzz1140, zzz1141, zzz1142, Succ(zzz11430), Succ(zzz11440), fd) → new_mkVBalBranch3MkVBalBranch277(zzz1133, zzz1134, zzz1135, zzz1136, zzz1137, zzz1138, zzz1139, zzz1140, zzz1141, zzz1142, zzz11430, zzz11440, fd)
new_mkVBalBranch3MkVBalBranch145(zzz3170, zzz3171, zzz317200, zzz3173, zzz3174, zzz330, zzz331, zzz333, zzz334, zzz31, Zero, h) → new_mkBranch(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))), LT, zzz31, Branch(zzz330, zzz331, Pos(Zero), zzz333, zzz334), Branch(zzz3170, zzz3171, Neg(Succ(zzz317200)), zzz3173, zzz3174), ty_Ordering, h)
new_mkVBalBranch3MkVBalBranch143(zzz818, zzz819, zzz820, zzz821, zzz822, zzz823, zzz824, zzz825, zzz826, zzz827, Zero, eb) → new_mkVBalBranch3MkVBalBranch144(zzz818, zzz819, zzz820, zzz821, zzz822, zzz823, zzz824, Zero, zzz825, zzz826, zzz827, Succ(Zero), Zero, eb)
new_mkVBalBranch3MkVBalBranch255(zzz537, zzz538, zzz539, zzz540, zzz541, zzz542, zzz543, zzz544, zzz545, zzz546, zzz547, Zero, Zero, dg) → new_mkVBalBranch3MkVBalBranch256(zzz537, zzz538, zzz539, zzz540, zzz541, zzz542, zzz543, zzz544, zzz545, zzz546, zzz547, dg)
new_mkVBalBranch3MkVBalBranch288(zzz340, zzz341, Pos(Succ(Succ(zzz342000))), zzz343, zzz344, zzz510, zzz511, Succ(zzz512000), zzz513, zzz514, zzz31, Zero, h) → new_mkVBalBranch3MkVBalBranch289(zzz340, zzz341, Succ(zzz342000), zzz343, zzz344, zzz510, zzz511, zzz512000, zzz513, zzz514, zzz31, zzz512000, zzz342000, h)
new_mkVBalBranch3MkVBalBranch154(zzz340, zzz341, zzz34200, zzz343, zzz344, zzz520, zzz521, zzz523, zzz524, zzz31, Zero, h) → new_mkBranch(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))), GT, zzz31, Branch(zzz520, zzz521, Pos(Zero), zzz523, zzz524), Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), ty_Ordering, h)
new_mkBalBranch6MkBalBranch1111(zzz2934, zzz21270, zzz21271, zzz21272, zzz21273, zzz21274, zzz2930, zzz2931, Succ(zzz22760), zzz226200, da, db) → new_mkBalBranch6MkBalBranch1113(zzz2934, zzz21270, zzz21271, zzz21272, zzz21273, zzz21274, zzz2930, zzz2931, zzz22760, zzz226200, da, db)
new_mkVBalBranch3MkVBalBranch148(zzz340, zzz341, zzz34200, zzz343, zzz344, zzz520, zzz521, zzz52200, zzz523, zzz524, zzz31, h) → new_mkBalBranch(zzz520, zzz521, zzz523, new_mkVBalBranch3(zzz31, zzz524, Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), h), ty_Ordering, h)
new_mkVBalBranch3MkVBalBranch136(zzz461, zzz462, zzz463, zzz464, zzz465, zzz466, zzz467, zzz468, zzz469, zzz470, zzz471, de) → new_mkVBalBranch3MkVBalBranch137(zzz461, zzz462, zzz463, zzz464, zzz465, zzz466, zzz467, zzz468, zzz469, zzz470, zzz471, new_primMulNat1(zzz463), de)
new_splitGT14(EmptyFM, be) → new_splitGT42(be)
new_splitGT28(zzz869, zzz870, zzz871, zzz872, bc) → new_mkVBalBranch3(zzz869, new_splitGT12(zzz871, bc), zzz872, bc)
new_mkVBalBranch3MkVBalBranch271(zzz473, zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, zzz481, zzz482, eh) → new_mkVBalBranch3MkVBalBranch164(zzz473, zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, zzz481, zzz482, new_primMulNat1(zzz475), eh)
new_mkVBalBranch3MkVBalBranch270(zzz473, zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, zzz481, zzz482, Succ(zzz4830), Succ(zzz4840), eh) → new_mkVBalBranch3MkVBalBranch270(zzz473, zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, zzz481, zzz482, zzz4830, zzz4840, eh)
new_mkVBalBranch3MkVBalBranch270(zzz473, zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, zzz481, zzz482, Zero, Zero, eh) → new_mkVBalBranch3MkVBalBranch271(zzz473, zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, zzz481, zzz482, eh)
new_mkVBalBranch3MkVBalBranch156(zzz958, zzz959, zzz960, zzz961, zzz962, zzz963, zzz964, zzz965, zzz966, zzz967, zzz968, Succ(zzz10180), fa) → new_mkVBalBranch3MkVBalBranch152(zzz958, zzz959, zzz960, zzz961, zzz962, zzz963, zzz964, zzz965, zzz966, zzz967, zzz968, Succ(zzz10180), Succ(zzz965), fa)
new_splitGT29(zzz883, zzz884, zzz885, zzz886, be) → new_splitGT14(zzz886, be)
new_mkVBalBranch3MkVBalBranch288(zzz340, zzz341, Neg(zzz3420), zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, Zero, h) → new_mkVBalBranch3MkVBalBranch284(zzz340, zzz341, zzz3420, zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, h)
new_primPlusNat3(zzz90, Succ(zzz910)) → Succ(Succ(new_primPlusNat2(zzz90, zzz910)))
new_addToFM_C2(Branch(EQ, zzz3171, zzz3172, zzz3173, zzz3174), zzz31, h) → new_mkBalBranch(EQ, zzz3171, new_addToFM_C2(zzz3173, zzz31, h), zzz3174, ty_Ordering, h)
new_splitLT14(EmptyFM, cc) → new_splitLT40(cc)
new_mkVBalBranch3MkVBalBranch288(zzz340, zzz341, Pos(Succ(Zero)), zzz343, zzz344, zzz510, zzz511, Succ(zzz512000), zzz513, zzz514, zzz31, Zero, h) → new_mkVBalBranch3MkVBalBranch283(zzz340, zzz341, Zero, zzz343, zzz344, zzz510, zzz511, zzz512000, zzz513, zzz514, zzz31, h)
new_splitGT24(zzz76, zzz77, zzz78, zzz79, bg) → new_mkVBalBranch3(zzz76, new_splitGT14(zzz78, bg), zzz79, bg)
new_mkVBalBranch3MkVBalBranch281(zzz340, zzz341, Neg(Succ(Succ(Zero))), zzz343, zzz344, zzz510, zzz511, Zero, zzz513, zzz514, zzz31, Succ(Succ(zzz6700)), h) → new_mkVBalBranch3MkVBalBranch263(zzz340, zzz341, Succ(Zero), zzz343, zzz344, zzz510, zzz511, zzz513, zzz514, zzz31, Zero, Succ(zzz6700), h)
new_addToFM_C4(EmptyFM, zzz31, h) → Branch(EQ, zzz31, Pos(Succ(Zero)), new_emptyFM(h), new_emptyFM(h))
new_mkVBalBranch3MkVBalBranch281(zzz340, zzz341, Neg(Zero), zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, Succ(zzz670), h) → new_mkVBalBranch3MkVBalBranch266(zzz340, zzz341, zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, h)
new_mkVBalBranch3MkVBalBranch246(zzz972, zzz973, zzz974, zzz975, zzz976, zzz977, zzz978, zzz979, zzz980, zzz981, zzz982, Zero, Zero, cg) → new_mkVBalBranch3MkVBalBranch247(zzz972, zzz973, zzz974, zzz975, zzz976, zzz977, zzz978, zzz979, zzz980, zzz981, zzz982, cg)
new_mkVBalBranch3MkVBalBranch247(zzz972, zzz973, zzz974, zzz975, zzz976, zzz977, zzz978, zzz979, zzz980, zzz981, zzz982, cg) → new_mkVBalBranch3MkVBalBranch141(zzz972, zzz973, zzz974, zzz975, zzz976, zzz977, zzz978, zzz979, zzz980, zzz981, zzz982, new_primMulNat1(zzz974), cg)
new_mkVBalBranch3MkVBalBranch131(zzz929, zzz930, zzz931, zzz932, zzz933, zzz934, zzz935, zzz936, zzz937, zzz938, zzz939, Succ(zzz10020), dc) → new_mkVBalBranch3MkVBalBranch132(zzz929, zzz930, zzz931, zzz932, zzz933, zzz934, zzz935, zzz936, zzz937, zzz938, zzz939, Succ(zzz10020), Succ(zzz936), dc)
new_mkVBalBranch3MkVBalBranch145(zzz3170, zzz3171, zzz317200, zzz3173, zzz3174, zzz330, zzz331, zzz333, zzz334, zzz31, Succ(zzz5350), h) → new_mkBalBranch(zzz330, zzz331, zzz333, new_mkVBalBranch2(zzz31, zzz334, Branch(zzz3170, zzz3171, Neg(Succ(zzz317200)), zzz3173, zzz3174), h), ty_Ordering, h)
new_primPlusNat2(Succ(zzz900), Succ(zzz9100)) → Succ(Succ(new_primPlusNat2(zzz900, zzz9100)))
new_mkVBalBranch3MkVBalBranch282(zzz461, zzz462, zzz463, zzz464, zzz465, zzz466, zzz467, zzz468, zzz469, zzz470, zzz471, de) → new_mkVBalBranch3MkVBalBranch165(zzz461, zzz462, zzz463, zzz464, zzz465, zzz466, zzz467, zzz468, zzz469, zzz470, zzz471, de)
new_mkVBalBranch3MkVBalBranch255(zzz537, zzz538, zzz539, zzz540, zzz541, zzz542, zzz543, zzz544, zzz545, zzz546, zzz547, Succ(zzz5480), Succ(zzz5490), dg) → new_mkVBalBranch3MkVBalBranch255(zzz537, zzz538, zzz539, zzz540, zzz541, zzz542, zzz543, zzz544, zzz545, zzz546, zzz547, zzz5480, zzz5490, dg)
new_splitLT27(zzz76, zzz77, zzz78, zzz79, bg) → new_splitLT23(zzz76, zzz77, zzz78, zzz79, bg)
new_mkVBalBranch3MkVBalBranch272(zzz340, zzz341, Neg(Zero), zzz343, zzz344, zzz520, zzz521, zzz52200, zzz523, zzz524, zzz31, Succ(zzz690), h) → new_mkVBalBranch3MkVBalBranch245(zzz340, zzz341, zzz343, zzz344, zzz520, zzz521, zzz52200, zzz523, zzz524, zzz31, h)
new_mkVBalBranch3MkVBalBranch281(zzz340, zzz341, Neg(Succ(Succ(zzz342000))), zzz343, zzz344, zzz510, zzz511, Zero, zzz513, zzz514, zzz31, Zero, h) → new_mkVBalBranch3MkVBalBranch249(zzz340, zzz341, zzz342000, zzz343, zzz344, zzz510, zzz511, zzz513, zzz514, zzz31, h)
new_mkBalBranch6MkBalBranch413(zzz2934, zzz2127, zzz2930, zzz2931, Zero, da, db) → new_mkBalBranch6MkBalBranch40(zzz2934, zzz2127, zzz2930, zzz2931, da, db)
new_primPlusNat1(Succ(zzz62000)) → Succ(Succ(new_primPlusNat1(zzz62000)))
new_mkBalBranch6MkBalBranch39(zzz2934, zzz2127, zzz2930, zzz2931, Succ(zzz2244000), Zero, da, db) → new_mkBalBranch6MkBalBranch33(zzz2934, zzz2127, zzz2930, zzz2931, da, db)
new_mkVBalBranch3MkVBalBranch269(zzz340, zzz341, Succ(zzz34200), zzz343, zzz344, zzz520, zzz521, zzz52200, zzz523, zzz524, zzz31, h) → new_mkVBalBranch3MkVBalBranch147(zzz340, zzz341, zzz34200, zzz343, zzz344, zzz520, zzz521, zzz52200, zzz523, zzz524, zzz31, new_primPlusNat2(new_primMulNat0(zzz34200), Succ(zzz34200)), h)
new_mkVBalBranch3MkVBalBranch149(zzz2050, zzz2051, zzz2052, zzz2053, zzz2054, zzz2055, zzz2056, zzz2057, zzz2058, zzz2059, zzz2060, Succ(zzz20610), Succ(zzz20620), ef) → new_mkVBalBranch3MkVBalBranch149(zzz2050, zzz2051, zzz2052, zzz2053, zzz2054, zzz2055, zzz2056, zzz2057, zzz2058, zzz2059, zzz2060, zzz20610, zzz20620, ef)
new_splitLT6(h) → new_splitLT41(h)
new_primMulNat2(Succ(zzz224700)) → new_primPlusNat2(new_primPlusNat2(Zero, Succ(zzz224700)), Succ(zzz224700))
new_mkBalBranch6MkBalBranch310(zzz2934, zzz2127, zzz2930, zzz2931, Neg(Zero), Pos(zzz22450), da, db) → new_mkBalBranch6MkBalBranch30(zzz2934, zzz2127, zzz2930, zzz2931, new_primMulNat(zzz22450), da, db)
new_mkBalBranch6MkBalBranch412(zzz2934, zzz2127, zzz2930, zzz2931, Succ(zzz2221000), Zero, da, db) → new_mkBalBranch6MkBalBranch49(zzz2934, zzz2127, zzz2930, zzz2931, da, db)
new_mkBalBranch6MkBalBranch014(zzz29340, zzz29341, zzz29342, zzz29343, zzz29344, zzz2127, zzz2930, zzz2931, Succ(zzz2246000), Succ(zzz226000), da, db) → new_mkBalBranch6MkBalBranch014(zzz29340, zzz29341, zzz29342, zzz29343, zzz29344, zzz2127, zzz2930, zzz2931, zzz2246000, zzz226000, da, db)
new_mkVBalBranch3MkVBalBranch132(zzz2033, zzz2034, zzz2035, zzz2036, zzz2037, zzz2038, zzz2039, zzz2040, zzz2041, zzz2042, zzz2043, Zero, Succ(zzz20450), fg) → new_mkBalBranch(zzz2038, zzz2039, zzz2041, new_mkVBalBranch3(zzz2043, zzz2042, Branch(zzz2033, zzz2034, Pos(Succ(zzz2035)), zzz2036, zzz2037), fg), ty_Ordering, fg)
new_mkVBalBranch3MkVBalBranch138(zzz1702, zzz1703, zzz1704, zzz1705, zzz1706, zzz1707, zzz1708, zzz1709, zzz1710, zzz1711, zzz1712, df) → new_mkBranch(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))), GT, zzz1712, Branch(zzz1707, zzz1708, Neg(Succ(zzz1709)), zzz1710, zzz1711), Branch(zzz1702, zzz1703, Neg(Succ(zzz1704)), zzz1705, zzz1706), ty_Ordering, df)
new_addToFM2(zzz34, zzz31, h) → new_addToFM_C4(zzz34, zzz31, h)
new_mkBalBranch6MkBalBranch113(zzz2934, zzz21270, zzz21271, zzz21272, zzz21273, zzz21274, zzz2930, zzz2931, Pos(Zero), Pos(zzz22630), da, db) → new_mkBalBranch6MkBalBranch116(zzz2934, zzz21270, zzz21271, zzz21272, zzz21273, zzz21274, zzz2930, zzz2931, new_primMulNat2(zzz22630), da, db)
new_mkVBalBranch3MkVBalBranch261(zzz3170, zzz3171, Pos(Succ(zzz317200)), zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, Succ(zzz4170), h) → new_mkVBalBranch3MkVBalBranch275(zzz3170, zzz3171, zzz317200, zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, zzz4170, zzz317200, h)
new_mkVBalBranch3MkVBalBranch143(zzz818, zzz819, zzz820, zzz821, zzz822, zzz823, zzz824, zzz825, zzz826, zzz827, Succ(zzz8960), eb) → new_mkVBalBranch3MkVBalBranch144(zzz818, zzz819, zzz820, zzz821, zzz822, zzz823, zzz824, Zero, zzz825, zzz826, zzz827, Succ(Zero), Succ(zzz8960), eb)
new_mkBalBranch6MkBalBranch411(zzz2934, zzz2127, zzz2930, zzz2931, Neg(Zero), Pos(zzz22060), da, db) → new_mkBalBranch6MkBalBranch416(zzz2934, zzz2127, zzz2930, zzz2931, new_primMulNat(zzz22060), da, db)
new_mkBalBranch6MkBalBranch36(zzz2934, zzz2127, zzz2930, zzz2931, Succ(zzz22530), zzz224400, da, db) → new_mkBalBranch6MkBalBranch39(zzz2934, zzz2127, zzz2930, zzz2931, zzz22530, zzz224400, da, db)
new_primPlusNat1(Zero) → Zero
new_mkBalBranch6MkBalBranch018(zzz29340, zzz29341, zzz29342, zzz29343, zzz29344, zzz2127, zzz2930, zzz2931, Succ(zzz22610), zzz224600, da, db) → new_mkBalBranch6MkBalBranch014(zzz29340, zzz29341, zzz29342, zzz29343, zzz29344, zzz2127, zzz2930, zzz2931, zzz22610, zzz224600, da, db)
new_mkVBalBranch3MkVBalBranch139(zzz3170, zzz3171, zzz317200, zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, Succ(zzz5620), h) → new_mkVBalBranch3MkVBalBranch140(zzz3170, zzz3171, zzz317200, zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, h)
new_mkVBalBranch3MkVBalBranch140(zzz3170, zzz3171, zzz317200, zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, h) → new_mkBalBranch(zzz330, zzz331, zzz333, new_mkVBalBranch2(zzz31, zzz334, Branch(zzz3170, zzz3171, Neg(Succ(zzz317200)), zzz3173, zzz3174), h), ty_Ordering, h)
new_splitGT210(zzz31, zzz32, zzz33, zzz34, h) → zzz34
new_splitGT14(Branch(GT, zzz8861, zzz8862, zzz8863, zzz8864), be) → new_splitGT26(zzz8861, zzz8862, zzz8863, zzz8864, be)
new_primPlusInt2(Pos(zzz21410), zzz2934, zzz2127, zzz2930, zzz2931, db, da) → new_primPlusInt0(zzz21410, new_sizeFM(zzz2934, da, db))
new_mkBalBranch6MkBalBranch111(zzz2934, zzz21270, zzz21271, zzz21272, zzz21273, zzz21274, zzz2930, zzz2931, zzz226200, Zero, da, db) → new_mkBalBranch6MkBalBranch1114(zzz2934, zzz21270, zzz21271, zzz21272, zzz21273, zzz21274, zzz2930, zzz2931, da, db)
new_mkVBalBranch2(zzz31, Branch(zzz330, zzz331, Neg(Succ(zzz33200)), zzz333, zzz334), Branch(zzz3170, zzz3171, zzz3172, zzz3173, zzz3174), h) → new_mkVBalBranch3MkVBalBranch262(zzz3170, zzz3171, zzz3172, zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, new_primPlusNat2(new_primMulNat0(zzz33200), Succ(zzz33200)), h)
new_mkVBalBranch3MkVBalBranch142(zzz1986, zzz1987, zzz1988, zzz1989, zzz1990, zzz1991, zzz1992, zzz1993, zzz1994, zzz1995, zzz1996, dh) → new_mkBranch(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))), EQ, zzz1996, Branch(zzz1991, zzz1992, Pos(Succ(zzz1993)), zzz1994, zzz1995), Branch(zzz1986, zzz1987, Pos(Succ(zzz1988)), zzz1989, zzz1990), ty_Ordering, dh)
new_mkVBalBranch3MkVBalBranch159(zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, zzz1125, zzz1126, zzz1127, zzz1128, zzz1129, Succ(zzz12130), ff) → new_mkVBalBranch3MkVBalBranch149(zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, zzz1125, Succ(zzz1126), zzz1127, zzz1128, zzz1129, Succ(Succ(zzz1126)), Succ(zzz12130), ff)
new_splitGT10(zzz31, zzz32, zzz33, h) → new_splitGT16(h)
new_mkVBalBranch3(zzz31, Branch(zzz520, zzz521, Neg(Zero), zzz523, zzz524), Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), h) → new_mkVBalBranch3MkVBalBranch155(zzz340, zzz341, zzz34200, zzz343, zzz344, zzz520, zzz521, zzz523, zzz524, zzz31, new_primMulNat1(zzz34200), h)
new_mkVBalBranch3MkVBalBranch270(zzz473, zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, zzz481, zzz482, Succ(zzz4830), Zero, eh) → new_mkVBalBranch3MkVBalBranch271(zzz473, zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, zzz481, zzz482, eh)
new_mkVBalBranch3(zzz31, Branch(zzz520, zzz521, Pos(Zero), zzz523, zzz524), Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), h) → new_mkVBalBranch3MkVBalBranch154(zzz340, zzz341, zzz34200, zzz343, zzz344, zzz520, zzz521, zzz523, zzz524, zzz31, new_primMulNat1(zzz34200), h)
new_primPlusInt(Neg(zzz22720), zzz2268, zzz2269, zzz2266, ec, ed) → new_primPlusInt1(zzz22720, new_sizeFM(zzz2269, ec, ed))
new_splitGT16(h) → new_splitGT40(h)
new_mkVBalBranch3MkVBalBranch152(zzz1337, zzz1338, zzz1339, zzz1340, zzz1341, zzz1342, zzz1343, zzz1344, zzz1345, zzz1346, zzz1347, Zero, Succ(zzz13490), eg) → new_mkBalBranch(zzz1342, zzz1343, zzz1345, new_mkVBalBranch2(zzz1347, zzz1346, Branch(zzz1337, zzz1338, Pos(Succ(zzz1339)), zzz1340, zzz1341), eg), ty_Ordering, eg)
new_mkBalBranch6MkBalBranch010(zzz29340, zzz29341, zzz29342, zzz29343, zzz29344, zzz2127, zzz2930, zzz2931, Zero, da, db) → new_mkBalBranch6MkBalBranch012(zzz29340, zzz29341, zzz29342, zzz29343, zzz29344, zzz2127, zzz2930, zzz2931, da, db)
new_addToFM_C4(Branch(GT, zzz341, zzz342, zzz343, zzz344), zzz31, h) → new_mkBalBranch(GT, zzz341, new_addToFM_C4(zzz343, zzz31, h), zzz344, ty_Ordering, h)
new_mkVBalBranch3MkVBalBranch162(zzz1986, zzz1987, zzz1988, zzz1989, zzz1990, zzz1991, zzz1992, zzz1993, zzz1994, zzz1995, zzz1996, Succ(zzz19970), Succ(zzz19980), dh) → new_mkVBalBranch3MkVBalBranch162(zzz1986, zzz1987, zzz1988, zzz1989, zzz1990, zzz1991, zzz1992, zzz1993, zzz1994, zzz1995, zzz1996, zzz19970, zzz19980, dh)
new_splitGT40(h) → new_emptyFM(h)
new_mkVBalBranch3MkVBalBranch288(zzz340, zzz341, Pos(Succ(Succ(zzz342000))), zzz343, zzz344, zzz510, zzz511, Zero, zzz513, zzz514, zzz31, Zero, h) → new_mkVBalBranch3MkVBalBranch290(zzz340, zzz341, zzz342000, zzz343, zzz344, zzz510, zzz511, zzz513, zzz514, zzz31, h)
new_mkBalBranch6MkBalBranch113(zzz2934, zzz21270, zzz21271, zzz21272, zzz21273, zzz21274, zzz2930, zzz2931, Neg(Zero), Neg(zzz22630), da, db) → new_mkBalBranch6MkBalBranch110(zzz2934, zzz21270, zzz21271, zzz21272, zzz21273, zzz21274, zzz2930, zzz2931, new_primMulNat2(zzz22630), da, db)
new_mkBalBranch6MkBalBranch411(zzz2934, zzz2127, zzz2930, zzz2931, Neg(Zero), Neg(zzz22060), da, db) → new_mkBalBranch6MkBalBranch413(zzz2934, zzz2127, zzz2930, zzz2931, new_primMulNat(zzz22060), da, db)
new_mkVBalBranch3(zzz31, Branch(zzz520, zzz521, zzz522, zzz523, zzz524), EmptyFM, h) → new_addToFM(Branch(zzz520, zzz521, zzz522, zzz523, zzz524), zzz31, h)
new_mkVBalBranch3MkVBalBranch269(zzz340, zzz341, Zero, zzz343, zzz344, zzz520, zzz521, zzz52200, zzz523, zzz524, zzz31, h) → new_mkBalBranch(zzz520, zzz521, zzz523, new_mkVBalBranch3(zzz31, zzz524, Branch(zzz340, zzz341, Neg(Zero), zzz343, zzz344), h), ty_Ordering, h)
new_mkBalBranch6MkBalBranch47(zzz2934, zzz2127, zzz2930, zzz2931, Zero, zzz222100, da, db) → new_mkBalBranch6MkBalBranch43(zzz2934, zzz2127, zzz2930, zzz2931, da, db)
new_mkBalBranch6MkBalBranch5(zzz2934, zzz2127, zzz2930, zzz2931, Neg(Succ(zzz213900)), da, db) → new_mkBalBranch6MkBalBranch51(zzz2934, zzz2127, zzz2930, zzz2931, da, db)
new_primPlusInt1(zzz13120, Pos(zzz13150)) → new_primMinusNat0(zzz13150, zzz13120)
new_splitGT3(zzz31, zzz32, zzz33, zzz34, h) → new_splitGT210(zzz31, zzz32, zzz33, zzz34, h)
new_mkVBalBranch3MkVBalBranch263(zzz498, zzz499, zzz500, zzz501, zzz502, zzz503, zzz504, zzz505, zzz506, zzz507, Succ(zzz5080), Succ(zzz5090), ee) → new_mkVBalBranch3MkVBalBranch263(zzz498, zzz499, zzz500, zzz501, zzz502, zzz503, zzz504, zzz505, zzz506, zzz507, zzz5080, zzz5090, ee)
new_mkVBalBranch3MkVBalBranch167(zzz340, zzz341, zzz34200, zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, Succ(zzz1410), h) → new_mkVBalBranch3MkVBalBranch160(zzz340, zzz341, zzz34200, zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, h)
new_mkVBalBranch3(zzz31, EmptyFM, zzz34, h) → new_addToFM(zzz34, zzz31, h)
new_mkVBalBranch3MkVBalBranch267(zzz340, zzz341, Pos(Zero), zzz343, zzz344, zzz520, zzz521, zzz52200, zzz523, zzz524, zzz31, Succ(zzz680), h) → new_mkVBalBranch3MkVBalBranch268(zzz340, zzz341, zzz343, zzz344, zzz520, zzz521, zzz52200, zzz523, zzz524, zzz31, h)
new_mkVBalBranch3MkVBalBranch155(zzz340, zzz341, zzz34200, zzz343, zzz344, zzz520, zzz521, zzz523, zzz524, zzz31, Succ(zzz1290), h) → new_mkBalBranch(zzz520, zzz521, zzz523, new_mkVBalBranch3(zzz31, zzz524, Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), h), ty_Ordering, h)
new_mkVBalBranch3MkVBalBranch144(zzz1702, zzz1703, zzz1704, zzz1705, zzz1706, zzz1707, zzz1708, zzz1709, zzz1710, zzz1711, zzz1712, Zero, Succ(zzz17140), df) → new_mkBalBranch(zzz1707, zzz1708, zzz1710, new_mkVBalBranch3(zzz1712, zzz1711, Branch(zzz1702, zzz1703, Neg(Succ(zzz1704)), zzz1705, zzz1706), df), ty_Ordering, df)
new_mkBalBranch6MkBalBranch1113(zzz2934, zzz21270, zzz21271, zzz21272, zzz21273, zzz21274, zzz2930, zzz2931, Succ(zzz2262000), Succ(zzz227000), da, db) → new_mkBalBranch6MkBalBranch1113(zzz2934, zzz21270, zzz21271, zzz21272, zzz21273, zzz21274, zzz2930, zzz2931, zzz2262000, zzz227000, da, db)
new_mkVBalBranch3MkVBalBranch134(zzz1851, zzz1852, zzz1853, zzz1854, zzz1855, zzz1856, zzz1857, zzz1858, zzz1859, zzz1860, zzz1861, Zero, Succ(zzz18630), dd) → new_mkBalBranch(zzz1856, zzz1857, zzz1859, new_mkVBalBranch2(zzz1861, zzz1860, Branch(zzz1851, zzz1852, Neg(Succ(zzz1853)), zzz1854, zzz1855), dd), ty_Ordering, dd)
new_mkVBalBranch3MkVBalBranch152(zzz1337, zzz1338, zzz1339, zzz1340, zzz1341, zzz1342, zzz1343, zzz1344, zzz1345, zzz1346, zzz1347, Succ(zzz13480), Zero, eg) → new_mkVBalBranch3MkVBalBranch151(zzz1337, zzz1338, zzz1339, zzz1340, zzz1341, zzz1342, zzz1343, zzz1344, zzz1345, zzz1346, zzz1347, eg)
new_mkVBalBranch3MkVBalBranch268(zzz340, zzz341, zzz343, zzz344, zzz520, zzz521, zzz52200, zzz523, zzz524, zzz31, h) → new_mkBalBranch(zzz520, zzz521, zzz523, new_mkVBalBranch3(zzz31, zzz524, Branch(zzz340, zzz341, Pos(Zero), zzz343, zzz344), h), ty_Ordering, h)
new_splitGT8(zzz31, zzz32, zzz34, h) → new_mkVBalBranch3(zzz31, new_splitGT6(h), zzz34, h)
new_mkBalBranch6MkBalBranch5(zzz2934, zzz2127, zzz2930, zzz2931, Pos(Succ(Succ(Zero))), da, db) → new_mkBalBranch6MkBalBranch50(zzz2934, zzz2127, zzz2930, zzz2931, da, db)
new_mkVBalBranch3MkVBalBranch272(zzz340, zzz341, Neg(Succ(Succ(Zero))), zzz343, zzz344, zzz520, zzz521, Zero, zzz523, zzz524, zzz31, Succ(Zero), h) → new_mkVBalBranch3MkVBalBranch277(zzz340, zzz341, Succ(Zero), zzz343, zzz344, zzz520, zzz521, zzz523, zzz524, zzz31, Zero, Zero, h)
new_mkBalBranch6MkBalBranch1110(zzz2934, zzz21270, zzz21271, zzz21272, zzz21273, zzz21274, zzz2930, zzz2931, Zero, da, db) → new_mkBalBranch6MkBalBranch112(zzz2934, zzz21270, zzz21271, zzz21272, zzz21273, zzz21274, zzz2930, zzz2931, da, db)
new_mkVBalBranch3MkVBalBranch162(zzz1986, zzz1987, zzz1988, zzz1989, zzz1990, zzz1991, zzz1992, zzz1993, zzz1994, zzz1995, zzz1996, Zero, Zero, dh) → new_mkVBalBranch3MkVBalBranch142(zzz1986, zzz1987, zzz1988, zzz1989, zzz1990, zzz1991, zzz1992, zzz1993, zzz1994, zzz1995, zzz1996, dh)
new_mkVBalBranch3MkVBalBranch287(zzz340, zzz341, zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, h) → new_mkVBalBranch3MkVBalBranch161(zzz340, zzz341, zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, new_primMulNat1(Zero), h)
new_mkVBalBranch3MkVBalBranch270(zzz473, zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, zzz481, zzz482, Zero, Succ(zzz4840), eh) → new_mkBalBranch(zzz473, zzz474, new_mkVBalBranch4(zzz482, Branch(zzz478, zzz479, Pos(Succ(Zero)), zzz480, zzz481), zzz476, eh), zzz477, ty_Ordering, eh)
new_mkVBalBranch3MkVBalBranch281(zzz340, zzz341, Neg(Succ(Succ(Succ(zzz3420000)))), zzz343, zzz344, zzz510, zzz511, Succ(zzz512000), zzz513, zzz514, zzz31, Succ(Zero), h) → new_mkVBalBranch3MkVBalBranch280(zzz340, zzz341, Succ(Succ(zzz3420000)), zzz343, zzz344, zzz510, zzz511, zzz512000, zzz513, zzz514, zzz31, Succ(zzz3420000), Succ(zzz512000), h)
new_mkVBalBranch3MkVBalBranch288(zzz340, zzz341, Pos(Succ(Succ(zzz342000))), zzz343, zzz344, zzz510, zzz511, Zero, zzz513, zzz514, zzz31, Succ(Succ(zzz6600)), h) → new_mkVBalBranch3MkVBalBranch270(zzz340, zzz341, Succ(zzz342000), zzz343, zzz344, zzz510, zzz511, zzz513, zzz514, zzz31, Succ(zzz6600), zzz342000, h)
new_intersectFM_C2Gts0(zzz854, zzz855, zzz856, zzz857, ba) → new_splitGT25(zzz854, zzz855, zzz856, zzz857, ba)
new_mkVBalBranch3MkVBalBranch281(zzz340, zzz341, Neg(Succ(Succ(Zero))), zzz343, zzz344, zzz510, zzz511, Zero, zzz513, zzz514, zzz31, Succ(Zero), h) → new_mkVBalBranch3MkVBalBranch263(zzz340, zzz341, Succ(Zero), zzz343, zzz344, zzz510, zzz511, zzz513, zzz514, zzz31, Zero, Zero, h)
new_mkVBalBranch3MkVBalBranch260(zzz340, zzz341, zzz342000, zzz343, zzz344, zzz520, zzz521, zzz523, zzz524, zzz31, h) → new_mkVBalBranch3MkVBalBranch143(zzz340, zzz341, Succ(zzz342000), zzz343, zzz344, zzz520, zzz521, zzz523, zzz524, zzz31, new_primMulNat1(Succ(zzz342000)), h)
new_mkVBalBranch4(zzz31, EmptyFM, zzz34, h) → new_addToFM2(zzz34, zzz31, h)
new_mkBalBranch6MkBalBranch110(zzz2934, zzz21270, zzz21271, zzz21272, zzz21273, zzz21274, zzz2930, zzz2931, Zero, da, db) → new_mkBalBranch6MkBalBranch112(zzz2934, zzz21270, zzz21271, zzz21272, zzz21273, zzz21274, zzz2930, zzz2931, da, db)
new_intersectFM_C2Gts3(zzz2129, cc) → new_splitGT15(zzz2129, cc)
new_mkVBalBranch3MkVBalBranch283(zzz461, zzz462, zzz463, zzz464, zzz465, zzz466, zzz467, zzz468, zzz469, zzz470, zzz471, de) → new_mkVBalBranch3MkVBalBranch282(zzz461, zzz462, zzz463, zzz464, zzz465, zzz466, zzz467, zzz468, zzz469, zzz470, zzz471, de)
new_mkVBalBranch3(zzz31, Branch(zzz520, zzz521, Pos(Zero), zzz523, zzz524), Branch(zzz340, zzz341, Pos(Succ(zzz34200)), zzz343, zzz344), h) → new_mkBalBranch(zzz340, zzz341, new_mkVBalBranch3(zzz31, Branch(zzz520, zzz521, Pos(Zero), zzz523, zzz524), zzz343, h), zzz344, ty_Ordering, h)
new_mkVBalBranch3MkVBalBranch281(zzz340, zzz341, Neg(Succ(Zero)), zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, Succ(zzz670), h) → new_mkBalBranch(zzz340, zzz341, new_mkVBalBranch4(zzz31, Branch(zzz510, zzz511, Neg(Succ(zzz51200)), zzz513, zzz514), zzz343, h), zzz344, ty_Ordering, h)
new_splitLT12(Branch(LT, zzz8561, zzz8562, zzz8563, zzz8564), ba) → new_splitLT28(zzz8561, zzz8562, zzz8563, zzz8564, ba)
new_mkBalBranch6MkBalBranch0110(zzz29340, zzz29341, zzz29342, zzz29343, zzz29344, zzz2127, zzz2930, zzz2931, Zero, da, db) → new_mkBalBranch6MkBalBranch012(zzz29340, zzz29341, zzz29342, zzz29343, zzz29344, zzz2127, zzz2930, zzz2931, da, db)
new_addToFM(zzz34, zzz31, h) → new_addToFM_C3(zzz34, zzz31, h)
new_mkVBalBranch3MkVBalBranch252(zzz929, zzz930, zzz931, zzz932, zzz933, zzz934, zzz935, zzz936, zzz937, zzz938, zzz939, Zero, Zero, dc) → new_mkVBalBranch3MkVBalBranch253(zzz929, zzz930, zzz931, zzz932, zzz933, zzz934, zzz935, zzz936, zzz937, zzz938, zzz939, dc)
new_mkVBalBranch3MkVBalBranch137(zzz461, zzz462, zzz463, zzz464, zzz465, zzz466, zzz467, zzz468, zzz469, zzz470, zzz471, Zero, de) → new_mkVBalBranch3MkVBalBranch162(zzz461, zzz462, zzz463, zzz464, zzz465, zzz466, zzz467, Succ(zzz468), zzz469, zzz470, zzz471, Zero, Succ(Succ(zzz468)), de)
new_mkVBalBranch3MkVBalBranch273(zzz818, zzz819, zzz820, zzz821, zzz822, zzz823, zzz824, zzz825, zzz826, zzz827, eb) → new_mkVBalBranch3MkVBalBranch274(zzz818, zzz819, zzz820, zzz821, zzz822, zzz823, zzz824, zzz825, zzz826, zzz827, eb)
new_mkVBalBranch3MkVBalBranch275(zzz958, zzz959, zzz960, zzz961, zzz962, zzz963, zzz964, zzz965, zzz966, zzz967, zzz968, Succ(zzz9690), Succ(zzz9700), fa) → new_mkVBalBranch3MkVBalBranch275(zzz958, zzz959, zzz960, zzz961, zzz962, zzz963, zzz964, zzz965, zzz966, zzz967, zzz968, zzz9690, zzz9700, fa)
new_mkVBalBranch3MkVBalBranch288(zzz340, zzz341, Neg(zzz3420), zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, Succ(zzz660), h) → new_mkVBalBranch3MkVBalBranch284(zzz340, zzz341, zzz3420, zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, h)
new_mkBalBranch6MkBalBranch30(zzz2934, zzz2127, zzz2930, zzz2931, Succ(zzz22540), da, db) → new_mkBalBranch6MkBalBranch31(zzz2934, zzz2127, zzz2930, zzz2931, da, db)
new_mkVBalBranch3MkVBalBranch261(zzz3170, zzz3171, Pos(Zero), zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, Succ(zzz4170), h) → new_mkVBalBranch3MkVBalBranch279(zzz3170, zzz3171, zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, h)
new_mkVBalBranch3MkVBalBranch288(zzz340, zzz341, Pos(Zero), zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, Succ(zzz660), h) → new_mkVBalBranch3MkVBalBranch285(zzz340, zzz341, zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, h)
new_mkVBalBranch2(zzz31, EmptyFM, zzz317, h) → new_addToFM1(zzz317, zzz31, h)
new_splitLT25(zzz869, zzz870, zzz871, zzz872, bc) → new_splitLT12(zzz871, bc)
new_splitGT4(zzz31, zzz32, zzz34, h) → new_mkVBalBranch4(zzz31, new_splitGT13(h), zzz34, h)
new_mkBalBranch6MkBalBranch116(zzz2934, zzz21270, zzz21271, zzz21272, zzz21273, zzz21274, zzz2930, zzz2931, Succ(zzz22730), da, db) → new_mkBalBranch6MkBalBranch1111(zzz2934, zzz21270, zzz21271, zzz21272, zzz21273, zzz21274, zzz2930, zzz2931, Zero, zzz22730, da, db)
new_mkBalBranch6MkBalBranch017(zzz29340, zzz29341, zzz29342, zzz29343, zzz29344, zzz2127, zzz2930, zzz2931, Neg(Zero), Pos(zzz22470), da, db) → new_mkBalBranch6MkBalBranch010(zzz29340, zzz29341, zzz29342, zzz29343, zzz29344, zzz2127, zzz2930, zzz2931, new_primMulNat2(zzz22470), da, db)
new_mkVBalBranch3MkVBalBranch281(zzz340, zzz341, Neg(Succ(Succ(Succ(zzz3420000)))), zzz343, zzz344, zzz510, zzz511, Zero, zzz513, zzz514, zzz31, Succ(Succ(zzz6700)), h) → new_mkVBalBranch3MkVBalBranch263(zzz340, zzz341, Succ(Succ(zzz3420000)), zzz343, zzz344, zzz510, zzz511, zzz513, zzz514, zzz31, Succ(zzz3420000), Succ(zzz6700), h)
new_mkBalBranch6MkBalBranch113(zzz2934, zzz21270, zzz21271, zzz21272, zzz21273, zzz21274, zzz2930, zzz2931, Neg(Succ(zzz226200)), Pos(zzz22630), da, db) → new_mkBalBranch6MkBalBranch118(zzz2934, zzz21270, zzz21271, zzz21272, zzz21273, zzz21274, zzz2930, zzz2931, zzz226200, new_primMulNat2(zzz22630), da, db)
new_mkVBalBranch3MkVBalBranch272(zzz340, zzz341, Neg(Succ(Succ(Succ(zzz3420000)))), zzz343, zzz344, zzz520, zzz521, Zero, zzz523, zzz524, zzz31, Succ(Zero), h) → new_mkVBalBranch3MkVBalBranch277(zzz340, zzz341, Succ(Succ(zzz3420000)), zzz343, zzz344, zzz520, zzz521, zzz523, zzz524, zzz31, Succ(zzz3420000), Zero, h)
new_mkVBalBranch3MkVBalBranch272(zzz340, zzz341, Pos(zzz3420), zzz343, zzz344, zzz520, zzz521, zzz52200, zzz523, zzz524, zzz31, Zero, h) → new_mkVBalBranch3MkVBalBranch258(zzz340, zzz341, zzz3420, zzz343, zzz344, zzz520, zzz521, zzz52200, zzz523, zzz524, zzz31, h)
new_mkBalBranch6MkBalBranch39(zzz2934, zzz2127, zzz2930, zzz2931, Succ(zzz2244000), Succ(zzz224800), da, db) → new_mkBalBranch6MkBalBranch39(zzz2934, zzz2127, zzz2930, zzz2931, zzz2244000, zzz224800, da, db)
new_mkVBalBranch3MkVBalBranch154(zzz340, zzz341, zzz34200, zzz343, zzz344, zzz520, zzz521, zzz523, zzz524, zzz31, Succ(zzz1250), h) → new_mkBalBranch(zzz520, zzz521, zzz523, new_mkVBalBranch3(zzz31, zzz524, Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), h), ty_Ordering, h)
new_splitGT15(Branch(EQ, zzz21291, zzz21292, zzz21293, zzz21294), cc) → new_splitGT15(zzz21294, cc)
new_mkVBalBranch4(zzz31, Branch(zzz510, zzz511, Pos(Zero), zzz513, zzz514), Branch(zzz340, zzz341, Pos(Zero), zzz343, zzz344), h) → new_mkBranch(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))), EQ, zzz31, Branch(zzz510, zzz511, Pos(Zero), zzz513, zzz514), Branch(zzz340, zzz341, Pos(Zero), zzz343, zzz344), ty_Ordering, h)
new_mkVBalBranch3MkVBalBranch281(zzz340, zzz341, Neg(Succ(Zero)), zzz343, zzz344, zzz510, zzz511, Succ(zzz512000), zzz513, zzz514, zzz31, Zero, h) → new_mkVBalBranch3MkVBalBranch257(zzz340, zzz341, Zero, zzz343, zzz344, zzz510, zzz511, zzz512000, zzz513, zzz514, zzz31, h)
new_splitLT15(Branch(GT, zzz781, zzz782, zzz783, zzz784), bg) → new_splitLT27(zzz781, zzz782, zzz783, zzz784, bg)
new_splitLT40(h) → new_emptyFM(h)
new_mkVBalBranch3MkVBalBranch280(zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, zzz1125, zzz1126, zzz1127, zzz1128, zzz1129, Succ(zzz11300), Zero, ff) → new_mkVBalBranch3MkVBalBranch278(zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, zzz1125, zzz1126, zzz1127, zzz1128, zzz1129, ff)
new_mkVBalBranch3MkVBalBranch272(zzz340, zzz341, Neg(Succ(Succ(Zero))), zzz343, zzz344, zzz520, zzz521, Zero, zzz523, zzz524, zzz31, Succ(Succ(zzz6900)), h) → new_mkVBalBranch3MkVBalBranch277(zzz340, zzz341, Succ(Zero), zzz343, zzz344, zzz520, zzz521, zzz523, zzz524, zzz31, Zero, Succ(zzz6900), h)
new_intersectFM_C2Gts1(zzz869, zzz870, zzz871, zzz872, bc) → new_splitGT28(zzz869, zzz870, zzz871, zzz872, bc)
new_mkVBalBranch3MkVBalBranch281(zzz340, zzz341, Neg(Succ(Succ(zzz342000))), zzz343, zzz344, zzz510, zzz511, Succ(zzz512000), zzz513, zzz514, zzz31, Zero, h) → new_mkVBalBranch3MkVBalBranch280(zzz340, zzz341, Succ(zzz342000), zzz343, zzz344, zzz510, zzz511, zzz512000, zzz513, zzz514, zzz31, zzz342000, zzz512000, h)
new_addToFM_C2(Branch(LT, zzz3171, zzz3172, zzz3173, zzz3174), zzz31, h) → Branch(LT, new_addToFM0(zzz3171, zzz31, h), zzz3172, zzz3173, zzz3174)
new_mkBalBranch6MkBalBranch018(zzz29340, zzz29341, zzz29342, zzz29343, zzz29344, zzz2127, zzz2930, zzz2931, Zero, zzz224600, da, db) → new_mkBalBranch6MkBalBranch011(zzz29340, zzz29341, zzz29342, zzz29343, zzz29344, zzz2127, zzz2930, zzz2931, da, db)
new_mkVBalBranch3MkVBalBranch246(zzz972, zzz973, zzz974, zzz975, zzz976, zzz977, zzz978, zzz979, zzz980, zzz981, zzz982, Zero, Succ(zzz9840), cg) → new_mkBalBranch(zzz972, zzz973, new_mkVBalBranch2(zzz982, Branch(zzz977, zzz978, Neg(Succ(zzz979)), zzz980, zzz981), zzz975, cg), zzz976, ty_Ordering, cg)
new_mkBalBranch6MkBalBranch411(zzz2934, zzz2127, zzz2930, zzz2931, Pos(Succ(zzz222100)), Neg(zzz22060), da, db) → new_mkBalBranch6MkBalBranch415(zzz2934, zzz2127, zzz2930, zzz2931, zzz222100, new_primMulNat(zzz22060), da, db)
new_mkVBalBranch4(zzz31, Branch(zzz510, zzz511, Pos(Zero), zzz513, zzz514), Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), h) → new_mkVBalBranch3MkVBalBranch168(zzz340, zzz341, zzz34200, zzz343, zzz344, zzz510, zzz511, zzz513, zzz514, zzz31, new_primMulNat1(zzz34200), h)
new_mkVBalBranch3MkVBalBranch162(zzz1986, zzz1987, zzz1988, zzz1989, zzz1990, zzz1991, zzz1992, zzz1993, zzz1994, zzz1995, zzz1996, Zero, Succ(zzz19980), dh) → new_mkBalBranch(zzz1991, zzz1992, zzz1994, new_mkVBalBranch4(zzz1996, zzz1995, Branch(zzz1986, zzz1987, Pos(Succ(zzz1988)), zzz1989, zzz1990), dh), ty_Ordering, dh)
new_addToFM0(zzz71, zzz13, h) → zzz13
new_mkVBalBranch3MkVBalBranch288(zzz340, zzz341, Pos(Succ(Succ(zzz342000))), zzz343, zzz344, zzz510, zzz511, Succ(zzz512000), zzz513, zzz514, zzz31, Succ(Zero), h) → new_mkVBalBranch3MkVBalBranch289(zzz340, zzz341, Succ(zzz342000), zzz343, zzz344, zzz510, zzz511, zzz512000, zzz513, zzz514, zzz31, Succ(zzz512000), zzz342000, h)
new_mkBalBranch(zzz2930, zzz2931, zzz2127, zzz2934, da, db) → new_mkBalBranch6MkBalBranch5(zzz2934, zzz2127, zzz2930, zzz2931, new_primPlusInt2(new_mkBalBranch6Size_l(zzz2934, zzz2127, zzz2930, zzz2931, db, da), zzz2934, zzz2127, zzz2930, zzz2931, db, da), da, db)
new_mkBalBranch6MkBalBranch37(zzz2934, zzz2127, zzz2930, zzz2931, zzz224400, zzz2253, da, db) → new_mkBalBranch6MkBalBranch36(zzz2934, zzz2127, zzz2930, zzz2931, zzz2253, zzz224400, da, db)
new_mkVBalBranch3MkVBalBranch281(zzz340, zzz341, Neg(Succ(Succ(Succ(zzz3420000)))), zzz343, zzz344, zzz510, zzz511, Succ(zzz512000), zzz513, zzz514, zzz31, Succ(Succ(zzz6700)), h) → new_mkVBalBranch3MkVBalBranch280(zzz340, zzz341, Succ(Succ(zzz3420000)), zzz343, zzz344, zzz510, zzz511, zzz512000, zzz513, zzz514, zzz31, Succ(zzz3420000), Succ(Succ(new_primPlusNat2(zzz6700, zzz512000))), h)
new_splitGT42(h) → new_emptyFM(h)
new_mkBalBranch6MkBalBranch114(zzz2934, zzz21270, zzz21271, zzz21272, zzz21273, zzz21274, zzz2930, zzz2931, zzz226200, zzz2270, da, db) → new_mkBalBranch6MkBalBranch111(zzz2934, zzz21270, zzz21271, zzz21272, zzz21273, zzz21274, zzz2930, zzz2931, zzz226200, zzz2270, da, db)
new_mkVBalBranch3MkVBalBranch264(zzz498, zzz499, zzz500, zzz501, zzz502, zzz503, zzz504, zzz505, zzz506, zzz507, ee) → new_mkVBalBranch3MkVBalBranch157(zzz498, zzz499, zzz500, zzz501, zzz502, zzz503, zzz504, zzz505, zzz506, zzz507, new_primMulNat1(zzz500), ee)
new_splitGT9(zzz76, zzz77, zzz78, zzz79, bg) → new_splitGT26(zzz76, zzz77, zzz78, zzz79, bg)
new_mkVBalBranch3MkVBalBranch166(zzz2033, zzz2034, zzz2035, zzz2036, zzz2037, zzz2038, zzz2039, zzz2040, zzz2041, zzz2042, zzz2043, fg) → new_mkBranch(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))), GT, zzz2043, Branch(zzz2038, zzz2039, Pos(Succ(zzz2040)), zzz2041, zzz2042), Branch(zzz2033, zzz2034, Pos(Succ(zzz2035)), zzz2036, zzz2037), ty_Ordering, fg)
new_intersectFM_C2Gts(zzz76, zzz77, zzz78, zzz79, bg) → new_splitGT9(zzz76, zzz77, zzz78, zzz79, bg)
new_mkVBalBranch4(zzz31, Branch(zzz510, zzz511, Neg(Zero), zzz513, zzz514), Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), h) → new_mkVBalBranch3MkVBalBranch133(zzz340, zzz341, zzz34200, zzz343, zzz344, zzz510, zzz511, zzz513, zzz514, zzz31, new_primMulNat1(zzz34200), h)
new_mkBalBranch6MkBalBranch015(zzz29340, zzz29341, zzz29342, zzz29343, zzz29344, zzz2127, zzz2930, zzz2931, da, db) → new_mkBalBranch6MkBalBranch016(zzz29340, zzz29341, zzz29342, zzz29343, zzz29344, zzz2127, zzz2930, zzz2931, da, db)
new_splitLT15(Branch(EQ, zzz781, zzz782, zzz783, zzz784), bg) → new_splitLT26(zzz781, zzz782, zzz783, zzz784, bg)
new_mkVBalBranch3MkVBalBranch272(zzz340, zzz341, Neg(Succ(Zero)), zzz343, zzz344, zzz520, zzz521, zzz52200, zzz523, zzz524, zzz31, Succ(zzz690), h) → new_mkVBalBranch3MkVBalBranch254(zzz340, zzz341, zzz343, zzz344, zzz520, zzz521, zzz52200, zzz523, zzz524, zzz31, h)
new_mkVBalBranch3MkVBalBranch277(zzz1133, zzz1134, zzz1135, zzz1136, zzz1137, zzz1138, zzz1139, zzz1140, zzz1141, zzz1142, Zero, Zero, fd) → new_mkVBalBranch3MkVBalBranch273(zzz1133, zzz1134, zzz1135, zzz1136, zzz1137, zzz1138, zzz1139, zzz1140, zzz1141, zzz1142, fd)
new_mkVBalBranch3MkVBalBranch161(zzz340, zzz341, zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, Zero, h) → new_mkVBalBranch3MkVBalBranch162(zzz340, zzz341, Zero, zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, Zero, Succ(zzz51200), h)
new_mkVBalBranch3MkVBalBranch252(zzz929, zzz930, zzz931, zzz932, zzz933, zzz934, zzz935, zzz936, zzz937, zzz938, zzz939, Zero, Succ(zzz9410), dc) → new_mkBalBranch(zzz929, zzz930, new_mkVBalBranch3(zzz939, Branch(zzz934, zzz935, Pos(Succ(zzz936)), zzz937, zzz938), zzz932, dc), zzz933, ty_Ordering, dc)
new_primPlusInt0(zzz1311, Neg(zzz13130)) → new_primMinusNat0(zzz1311, zzz13130)
new_mkBalBranch6MkBalBranch34(zzz2934, zzz2127, zzz2930, zzz2931, zzz224400, zzz2252, da, db) → new_mkBalBranch6MkBalBranch31(zzz2934, zzz2127, zzz2930, zzz2931, da, db)
new_mkBalBranch6MkBalBranch39(zzz2934, zzz2127, zzz2930, zzz2931, Zero, Succ(zzz224800), da, db) → new_mkBalBranch6MkBalBranch31(zzz2934, zzz2127, zzz2930, zzz2931, da, db)
new_splitGT7(zzz31, zzz32, zzz33, zzz34, h) → new_splitGT27(zzz31, zzz32, zzz33, zzz34, h)
new_mkVBalBranch3MkVBalBranch272(zzz340, zzz341, Neg(Succ(Succ(zzz342000))), zzz343, zzz344, zzz520, zzz521, Succ(zzz522000), zzz523, zzz524, zzz31, Zero, h) → new_mkVBalBranch3MkVBalBranch255(zzz340, zzz341, Succ(zzz342000), zzz343, zzz344, zzz520, zzz521, zzz522000, zzz523, zzz524, zzz31, zzz342000, zzz522000, h)
new_splitGT41(h) → new_emptyFM(h)
new_mkBalBranch6MkBalBranch44(zzz2934, zzz2127, zzz2930, zzz2931, zzz222100, zzz2236, da, db) → new_mkBalBranch6MkBalBranch45(zzz2934, zzz2127, zzz2930, zzz2931, zzz222100, zzz2236, da, db)
new_mkBalBranch6MkBalBranch412(zzz2934, zzz2127, zzz2930, zzz2931, Zero, Succ(zzz223600), da, db) → new_mkBalBranch6MkBalBranch43(zzz2934, zzz2127, zzz2930, zzz2931, da, db)
new_mkVBalBranch3MkVBalBranch272(zzz340, zzz341, Neg(Zero), zzz343, zzz344, zzz520, zzz521, zzz52200, zzz523, zzz524, zzz31, Zero, h) → new_mkVBalBranch3MkVBalBranch245(zzz340, zzz341, zzz343, zzz344, zzz520, zzz521, zzz52200, zzz523, zzz524, zzz31, h)
new_mkVBalBranch3MkVBalBranch275(zzz958, zzz959, zzz960, zzz961, zzz962, zzz963, zzz964, zzz965, zzz966, zzz967, zzz968, Zero, Succ(zzz9700), fa) → new_mkBalBranch(zzz958, zzz959, new_mkVBalBranch2(zzz968, Branch(zzz963, zzz964, Pos(Succ(zzz965)), zzz966, zzz967), zzz961, fa), zzz962, ty_Ordering, fa)
new_mkVBalBranch3MkVBalBranch272(zzz340, zzz341, Neg(Succ(Succ(Zero))), zzz343, zzz344, zzz520, zzz521, Succ(zzz522000), zzz523, zzz524, zzz31, Succ(Zero), h) → new_mkVBalBranch3MkVBalBranch255(zzz340, zzz341, Succ(Zero), zzz343, zzz344, zzz520, zzz521, zzz522000, zzz523, zzz524, zzz31, Zero, Succ(zzz522000), h)
new_mkBranch(zzz2265, zzz2266, zzz2267, zzz2268, zzz2269, ec, ed) → Branch(zzz2266, zzz2267, new_primPlusInt(new_primPlusInt0(Succ(Zero), new_sizeFM(zzz2268, ec, ed)), zzz2268, zzz2269, zzz2266, ec, ed), zzz2268, zzz2269)
new_mkVBalBranch3MkVBalBranch262(zzz3170, zzz3171, Neg(Zero), zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, Zero, h) → new_mkBranch(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))), LT, zzz31, Branch(zzz330, zzz331, Neg(Succ(zzz33200)), zzz333, zzz334), Branch(zzz3170, zzz3171, Neg(Zero), zzz3173, zzz3174), ty_Ordering, h)
new_mkBalBranch6MkBalBranch016(zzz29340, zzz29341, zzz29342, EmptyFM, zzz29344, zzz2127, zzz2930, zzz2931, da, db) → error([])
new_mkBalBranch6MkBalBranch47(zzz2934, zzz2127, zzz2930, zzz2931, Succ(zzz22410), zzz222100, da, db) → new_mkBalBranch6MkBalBranch412(zzz2934, zzz2127, zzz2930, zzz2931, zzz22410, zzz222100, da, db)
new_mkVBalBranch3MkVBalBranch279(zzz3170, zzz3171, zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, h) → new_mkBalBranch(zzz330, zzz331, zzz333, new_mkVBalBranch2(zzz31, zzz334, Branch(zzz3170, zzz3171, Pos(Zero), zzz3173, zzz3174), h), ty_Ordering, h)
new_primMinusNat0(Succ(zzz100100), Zero) → Pos(Succ(zzz100100))
new_sizeFM(EmptyFM, fb, fc) → Pos(Zero)
new_mkBalBranch6MkBalBranch1114(zzz2934, zzz21270, zzz21271, zzz21272, zzz21273, zzz21274, zzz2930, zzz2931, da, db) → new_mkBalBranch6MkBalBranch1115(zzz2934, zzz21270, zzz21271, zzz21272, zzz21273, zzz21274, zzz2930, zzz2931, da, db)
new_mkVBalBranch3MkVBalBranch245(zzz340, zzz341, zzz343, zzz344, zzz520, zzz521, zzz52200, zzz523, zzz524, zzz31, h) → new_mkBalBranch(zzz340, zzz341, new_mkVBalBranch3(zzz31, Branch(zzz520, zzz521, Neg(Succ(zzz52200)), zzz523, zzz524), zzz343, h), zzz344, ty_Ordering, h)
new_mkVBalBranch3MkVBalBranch152(zzz1337, zzz1338, zzz1339, zzz1340, zzz1341, zzz1342, zzz1343, zzz1344, zzz1345, zzz1346, zzz1347, Succ(zzz13480), Succ(zzz13490), eg) → new_mkVBalBranch3MkVBalBranch152(zzz1337, zzz1338, zzz1339, zzz1340, zzz1341, zzz1342, zzz1343, zzz1344, zzz1345, zzz1346, zzz1347, zzz13480, zzz13490, eg)
new_mkVBalBranch3MkVBalBranch141(zzz972, zzz973, zzz974, zzz975, zzz976, zzz977, zzz978, zzz979, zzz980, zzz981, zzz982, Succ(zzz10190), cg) → new_mkVBalBranch3MkVBalBranch134(zzz972, zzz973, zzz974, zzz975, zzz976, zzz977, zzz978, zzz979, zzz980, zzz981, zzz982, Succ(zzz979), Succ(zzz10190), cg)
new_mkVBalBranch3MkVBalBranch135(zzz1851, zzz1852, zzz1853, zzz1854, zzz1855, zzz1856, zzz1857, zzz1858, zzz1859, zzz1860, zzz1861, dd) → new_mkBranch(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))), LT, zzz1861, Branch(zzz1856, zzz1857, Neg(Succ(zzz1858)), zzz1859, zzz1860), Branch(zzz1851, zzz1852, Neg(Succ(zzz1853)), zzz1854, zzz1855), ty_Ordering, dd)
new_mkBalBranch6MkBalBranch38(zzz2934, zzz2127, zzz2930, zzz2931, zzz224400, Succ(zzz22480), da, db) → new_mkBalBranch6MkBalBranch39(zzz2934, zzz2127, zzz2930, zzz2931, zzz224400, zzz22480, da, db)
new_mkVBalBranch3MkVBalBranch134(zzz1851, zzz1852, zzz1853, zzz1854, zzz1855, zzz1856, zzz1857, zzz1858, zzz1859, zzz1860, zzz1861, Succ(zzz18620), Succ(zzz18630), dd) → new_mkVBalBranch3MkVBalBranch134(zzz1851, zzz1852, zzz1853, zzz1854, zzz1855, zzz1856, zzz1857, zzz1858, zzz1859, zzz1860, zzz1861, zzz18620, zzz18630, dd)
new_mkVBalBranch3MkVBalBranch267(zzz340, zzz341, Neg(zzz3420), zzz343, zzz344, zzz520, zzz521, zzz52200, zzz523, zzz524, zzz31, Zero, h) → new_mkVBalBranch3MkVBalBranch269(zzz340, zzz341, zzz3420, zzz343, zzz344, zzz520, zzz521, zzz52200, zzz523, zzz524, zzz31, h)
new_mkVBalBranch3MkVBalBranch262(zzz3170, zzz3171, Pos(Zero), zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, Zero, h) → new_mkBranch(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))), LT, zzz31, Branch(zzz330, zzz331, Neg(Succ(zzz33200)), zzz333, zzz334), Branch(zzz3170, zzz3171, Pos(Zero), zzz3173, zzz3174), ty_Ordering, h)
new_mkBalBranch6MkBalBranch113(zzz2934, zzz21270, zzz21271, zzz21272, zzz21273, zzz21274, zzz2930, zzz2931, Pos(Zero), Neg(zzz22630), da, db) → new_mkBalBranch6MkBalBranch117(zzz2934, zzz21270, zzz21271, zzz21272, zzz21273, zzz21274, zzz2930, zzz2931, new_primMulNat2(zzz22630), da, db)
new_mkVBalBranch3MkVBalBranch250(zzz340, zzz341, zzz342000, zzz343, zzz344, zzz510, zzz511, zzz513, zzz514, zzz31, h) → new_mkVBalBranch3MkVBalBranch157(zzz340, zzz341, Succ(zzz342000), zzz343, zzz344, zzz510, zzz511, zzz513, zzz514, zzz31, new_primMulNat1(Succ(zzz342000)), h)
new_mkVBalBranch4(zzz31, Branch(zzz510, zzz511, Neg(Zero), zzz513, zzz514), Branch(zzz340, zzz341, Neg(Zero), zzz343, zzz344), h) → new_mkBranch(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))), EQ, zzz31, Branch(zzz510, zzz511, Neg(Zero), zzz513, zzz514), Branch(zzz340, zzz341, Neg(Zero), zzz343, zzz344), ty_Ordering, h)
new_mkBalBranch6MkBalBranch1113(zzz2934, zzz21270, zzz21271, zzz21272, zzz21273, zzz21274, zzz2930, zzz2931, Zero, Zero, da, db) → new_mkBalBranch6MkBalBranch112(zzz2934, zzz21270, zzz21271, zzz21272, zzz21273, zzz21274, zzz2930, zzz2931, da, db)
new_mkBalBranch6MkBalBranch40(zzz2934, zzz2127, zzz2930, zzz2931, da, db) → new_mkBalBranch6MkBalBranch41(zzz2934, zzz2127, zzz2930, zzz2931, da, db)
new_mkVBalBranch3MkVBalBranch272(zzz340, zzz341, Pos(zzz3420), zzz343, zzz344, zzz520, zzz521, zzz52200, zzz523, zzz524, zzz31, Succ(zzz690), h) → new_mkVBalBranch3MkVBalBranch258(zzz340, zzz341, zzz3420, zzz343, zzz344, zzz520, zzz521, zzz52200, zzz523, zzz524, zzz31, h)
new_mkVBalBranch3MkVBalBranch149(zzz2050, zzz2051, zzz2052, zzz2053, zzz2054, zzz2055, zzz2056, zzz2057, zzz2058, zzz2059, zzz2060, Succ(zzz20610), Zero, ef) → new_mkVBalBranch3MkVBalBranch150(zzz2050, zzz2051, zzz2052, zzz2053, zzz2054, zzz2055, zzz2056, zzz2057, zzz2058, zzz2059, zzz2060, ef)
new_mkVBalBranch3MkVBalBranch134(zzz1851, zzz1852, zzz1853, zzz1854, zzz1855, zzz1856, zzz1857, zzz1858, zzz1859, zzz1860, zzz1861, Succ(zzz18620), Zero, dd) → new_mkVBalBranch3MkVBalBranch135(zzz1851, zzz1852, zzz1853, zzz1854, zzz1855, zzz1856, zzz1857, zzz1858, zzz1859, zzz1860, zzz1861, dd)
new_mkVBalBranch3MkVBalBranch249(zzz340, zzz341, zzz342000, zzz343, zzz344, zzz510, zzz511, zzz513, zzz514, zzz31, h) → new_mkVBalBranch3MkVBalBranch250(zzz340, zzz341, zzz342000, zzz343, zzz344, zzz510, zzz511, zzz513, zzz514, zzz31, h)
new_addToFM_C3(Branch(EQ, zzz341, zzz342, zzz343, zzz344), zzz31, h) → new_mkBalBranch(EQ, zzz341, zzz343, new_addToFM_C3(zzz344, zzz31, h), ty_Ordering, h)
new_mkVBalBranch3MkVBalBranch272(zzz340, zzz341, Neg(Succ(Succ(Succ(zzz3420000)))), zzz343, zzz344, zzz520, zzz521, Succ(zzz522000), zzz523, zzz524, zzz31, Succ(Succ(zzz6900)), h) → new_mkVBalBranch3MkVBalBranch255(zzz340, zzz341, Succ(Succ(zzz3420000)), zzz343, zzz344, zzz520, zzz521, zzz522000, zzz523, zzz524, zzz31, Succ(zzz3420000), Succ(Succ(new_primPlusNat2(zzz6900, zzz522000))), h)
new_mkBalBranch6MkBalBranch017(zzz29340, zzz29341, zzz29342, zzz29343, zzz29344, zzz2127, zzz2930, zzz2931, Pos(Zero), Neg(zzz22470), da, db) → new_mkBalBranch6MkBalBranch0111(zzz29340, zzz29341, zzz29342, zzz29343, zzz29344, zzz2127, zzz2930, zzz2931, new_primMulNat2(zzz22470), da, db)
new_primMulNat2(Zero) → Zero
new_mkBalBranch6MkBalBranch5(zzz2934, zzz2127, zzz2930, zzz2931, Pos(Succ(Zero)), da, db) → new_mkBalBranch6MkBalBranch51(zzz2934, zzz2127, zzz2930, zzz2931, da, db)
new_mkVBalBranch3MkVBalBranch263(zzz498, zzz499, zzz500, zzz501, zzz502, zzz503, zzz504, zzz505, zzz506, zzz507, Zero, Zero, ee) → new_mkVBalBranch3MkVBalBranch264(zzz498, zzz499, zzz500, zzz501, zzz502, zzz503, zzz504, zzz505, zzz506, zzz507, ee)
new_mkVBalBranch3MkVBalBranch261(zzz3170, zzz3171, Pos(Succ(zzz317200)), zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, Zero, h) → new_mkVBalBranch3MkVBalBranch275(zzz3170, zzz3171, zzz317200, zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, Zero, Succ(zzz317200), h)
new_mkVBalBranch3MkVBalBranch158(zzz461, zzz462, zzz463, zzz464, zzz465, zzz466, zzz467, zzz468, zzz469, zzz470, zzz471, de) → new_mkVBalBranch3MkVBalBranch136(zzz461, zzz462, zzz463, zzz464, zzz465, zzz466, zzz467, zzz468, zzz469, zzz470, zzz471, de)
new_mkBalBranch6MkBalBranch31(zzz2934, zzz2127, zzz2930, zzz2931, da, db) → new_mkBalBranch6MkBalBranch313(zzz2934, zzz2127, zzz2930, zzz2931, da, db)
new_mkBalBranch6MkBalBranch39(zzz2934, zzz2127, zzz2930, zzz2931, Zero, Zero, da, db) → new_mkBalBranch6MkBalBranch32(zzz2934, zzz2127, zzz2930, zzz2931, da, db)
new_mkBalBranch6MkBalBranch313(zzz2934, zzz2127, zzz2930, zzz2931, da, db) → new_mkBranch(Succ(Zero), zzz2930, zzz2931, zzz2127, zzz2934, da, db)
new_mkBalBranch6MkBalBranch310(zzz2934, zzz2127, zzz2930, zzz2931, Neg(Zero), Neg(zzz22450), da, db) → new_mkBalBranch6MkBalBranch314(zzz2934, zzz2127, zzz2930, zzz2931, new_primMulNat(zzz22450), da, db)
new_mkVBalBranch3MkVBalBranch288(zzz340, zzz341, Pos(Succ(Succ(zzz342000))), zzz343, zzz344, zzz510, zzz511, Succ(zzz512000), zzz513, zzz514, zzz31, Succ(Succ(zzz6600)), h) → new_mkVBalBranch3MkVBalBranch289(zzz340, zzz341, Succ(zzz342000), zzz343, zzz344, zzz510, zzz511, zzz512000, zzz513, zzz514, zzz31, Succ(Succ(new_primPlusNat2(zzz6600, zzz512000))), zzz342000, h)
new_splitGT14(Branch(LT, zzz8861, zzz8862, zzz8863, zzz8864), be) → new_splitGT29(zzz8861, zzz8862, zzz8863, zzz8864, be)
new_intersectFM_C2Lts0(zzz854, zzz855, zzz856, zzz857, ba) → new_splitLT24(zzz854, zzz855, zzz856, zzz857, ba)
new_primPlusNat3(zzz90, Zero) → Succ(zzz90)
new_splitLT8(zzz31, zzz32, zzz34, h) → new_splitLT6(h)
new_splitGT12(Branch(EQ, zzz8561, zzz8562, zzz8563, zzz8564), ba) → new_splitGT25(zzz8561, zzz8562, zzz8563, zzz8564, ba)
new_mkVBalBranch3MkVBalBranch256(zzz537, zzz538, zzz539, zzz540, zzz541, zzz542, zzz543, zzz544, zzz545, zzz546, zzz547, dg) → new_mkVBalBranch3MkVBalBranch153(zzz537, zzz538, zzz539, zzz540, zzz541, zzz542, zzz543, zzz544, zzz545, zzz546, zzz547, new_primMulNat1(zzz539), dg)
new_mkVBalBranch3MkVBalBranch261(zzz3170, zzz3171, Pos(Zero), zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, Zero, h) → new_mkVBalBranch3MkVBalBranch279(zzz3170, zzz3171, zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, h)
new_mkVBalBranch4(zzz31, Branch(zzz510, zzz511, zzz512, zzz513, zzz514), EmptyFM, h) → new_addToFM2(Branch(zzz510, zzz511, zzz512, zzz513, zzz514), zzz31, h)
new_mkVBalBranch4(zzz31, Branch(zzz510, zzz511, Neg(Succ(zzz51200)), zzz513, zzz514), Branch(zzz340, zzz341, zzz342, zzz343, zzz344), h) → new_mkVBalBranch3MkVBalBranch281(zzz340, zzz341, zzz342, zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, new_primMulNat0(zzz51200), h)
new_mkBalBranch6MkBalBranch017(zzz29340, zzz29341, zzz29342, zzz29343, zzz29344, zzz2127, zzz2930, zzz2931, Neg(Succ(zzz224600)), Neg(zzz22470), da, db) → new_mkBalBranch6MkBalBranch018(zzz29340, zzz29341, zzz29342, zzz29343, zzz29344, zzz2127, zzz2930, zzz2931, new_primMulNat2(zzz22470), zzz224600, da, db)
new_mkBalBranch6MkBalBranch33(zzz2934, Branch(zzz21270, zzz21271, zzz21272, zzz21273, zzz21274), zzz2930, zzz2931, da, db) → new_mkBalBranch6MkBalBranch113(zzz2934, zzz21270, zzz21271, zzz21272, zzz21273, zzz21274, zzz2930, zzz2931, new_sizeFM(zzz21274, da, db), new_sizeFM(zzz21273, da, db), da, db)
new_mkVBalBranch3MkVBalBranch259(zzz340, zzz341, zzz342000, zzz343, zzz344, zzz520, zzz521, zzz523, zzz524, zzz31, h) → new_mkVBalBranch3MkVBalBranch260(zzz340, zzz341, zzz342000, zzz343, zzz344, zzz520, zzz521, zzz523, zzz524, zzz31, h)
new_mkVBalBranch3MkVBalBranch266(zzz340, zzz341, zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, h) → new_mkBalBranch(zzz340, zzz341, new_mkVBalBranch4(zzz31, Branch(zzz510, zzz511, Neg(Succ(zzz51200)), zzz513, zzz514), zzz343, h), zzz344, ty_Ordering, h)
new_mkBalBranch6MkBalBranch46(zzz2934, zzz2127, zzz2930, zzz2931, zzz222100, zzz2241, da, db) → new_mkBalBranch6MkBalBranch47(zzz2934, zzz2127, zzz2930, zzz2931, zzz2241, zzz222100, da, db)
new_mkVBalBranch3MkVBalBranch289(zzz1105, zzz1106, zzz1107, zzz1108, zzz1109, zzz1110, zzz1111, zzz1112, zzz1113, zzz1114, zzz1115, Succ(zzz11160), Succ(zzz11170), fh) → new_mkVBalBranch3MkVBalBranch289(zzz1105, zzz1106, zzz1107, zzz1108, zzz1109, zzz1110, zzz1111, zzz1112, zzz1113, zzz1114, zzz1115, zzz11160, zzz11170, fh)
new_mkBalBranch6MkBalBranch314(zzz2934, zzz2127, zzz2930, zzz2931, Succ(zzz22550), da, db) → new_mkBalBranch6MkBalBranch38(zzz2934, zzz2127, zzz2930, zzz2931, zzz22550, Zero, da, db)
new_mkVBalBranch3MkVBalBranch262(zzz3170, zzz3171, Pos(Succ(zzz317200)), zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, Zero, h) → new_mkVBalBranch3MkVBalBranch251(zzz3170, zzz3171, Succ(zzz317200), zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, h)
new_primMulNat(Zero) → Zero
new_mkBalBranch6MkBalBranch51(zzz2934, zzz2127, zzz2930, zzz2931, da, db) → new_mkBranch(Zero, zzz2930, zzz2931, zzz2127, zzz2934, da, db)
new_mkBalBranch6MkBalBranch411(zzz2934, zzz2127, zzz2930, zzz2931, Pos(Zero), Pos(zzz22060), da, db) → new_mkBalBranch6MkBalBranch414(zzz2934, zzz2127, zzz2930, zzz2931, new_primMulNat(zzz22060), da, db)
new_mkVBalBranch2(zzz31, Branch(zzz330, zzz331, Neg(Zero), zzz333, zzz334), Branch(zzz3170, zzz3171, Pos(Succ(zzz317200)), zzz3173, zzz3174), h) → new_mkBalBranch(zzz3170, zzz3171, new_mkVBalBranch2(zzz31, Branch(zzz330, zzz331, Neg(Zero), zzz333, zzz334), zzz3173, h), zzz3174, ty_Ordering, h)
new_mkVBalBranch3MkVBalBranch265(zzz3170, zzz3171, Zero, zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, h) → new_mkBalBranch(zzz330, zzz331, zzz333, new_mkVBalBranch2(zzz31, zzz334, Branch(zzz3170, zzz3171, Neg(Zero), zzz3173, zzz3174), h), ty_Ordering, h)
new_mkVBalBranch3MkVBalBranch164(zzz473, zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, zzz481, zzz482, Succ(zzz7390), eh) → new_mkVBalBranch3MkVBalBranch162(zzz473, zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, Zero, zzz480, zzz481, zzz482, Succ(zzz7390), Succ(Zero), eh)
new_splitLT15(Branch(LT, zzz781, zzz782, zzz783, zzz784), bg) → new_mkVBalBranch2(zzz781, zzz783, new_splitLT15(zzz784, bg), bg)
new_splitLT15(EmptyFM, bg) → new_splitLT41(bg)
new_mkBalBranch6MkBalBranch1110(zzz2934, zzz21270, zzz21271, zzz21272, zzz21273, zzz21274, zzz2930, zzz2931, Succ(zzz22770), da, db) → new_mkBalBranch6MkBalBranch1112(zzz2934, zzz21270, zzz21271, zzz21272, zzz21273, zzz21274, zzz2930, zzz2931, da, db)
new_mkBalBranch6MkBalBranch32(zzz2934, zzz2127, zzz2930, zzz2931, da, db) → new_mkBalBranch6MkBalBranch313(zzz2934, zzz2127, zzz2930, zzz2931, da, db)
new_mkVBalBranch3MkVBalBranch286(zzz3170, zzz3171, zzz31720, zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, h) → new_mkVBalBranch3MkVBalBranch265(zzz3170, zzz3171, zzz31720, zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, h)
new_mkVBalBranch3MkVBalBranch263(zzz498, zzz499, zzz500, zzz501, zzz502, zzz503, zzz504, zzz505, zzz506, zzz507, Zero, Succ(zzz5090), ee) → new_mkBalBranch(zzz498, zzz499, new_mkVBalBranch4(zzz507, Branch(zzz503, zzz504, Neg(Succ(Zero)), zzz505, zzz506), zzz501, ee), zzz502, ty_Ordering, ee)
new_mkVBalBranch3(zzz31, Branch(zzz520, zzz521, Neg(Zero), zzz523, zzz524), Branch(zzz340, zzz341, Pos(Zero), zzz343, zzz344), h) → new_mkBranch(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))), GT, zzz31, Branch(zzz520, zzz521, Neg(Zero), zzz523, zzz524), Branch(zzz340, zzz341, Pos(Zero), zzz343, zzz344), ty_Ordering, h)
new_mkVBalBranch3(zzz31, Branch(zzz520, zzz521, Pos(Zero), zzz523, zzz524), Branch(zzz340, zzz341, Neg(Zero), zzz343, zzz344), h) → new_mkBranch(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))), GT, zzz31, Branch(zzz520, zzz521, Pos(Zero), zzz523, zzz524), Branch(zzz340, zzz341, Neg(Zero), zzz343, zzz344), ty_Ordering, h)
new_addToFM_C4(Branch(LT, zzz341, zzz342, zzz343, zzz344), zzz31, h) → new_mkBalBranch(LT, zzz341, zzz343, new_addToFM_C4(zzz344, zzz31, h), ty_Ordering, h)
new_mkBalBranch6MkBalBranch35(zzz2934, zzz2127, zzz2930, zzz2931, Succ(zzz22500), da, db) → new_mkBalBranch6MkBalBranch36(zzz2934, zzz2127, zzz2930, zzz2931, Zero, zzz22500, da, db)
new_mkVBalBranch3MkVBalBranch159(zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, zzz1125, zzz1126, zzz1127, zzz1128, zzz1129, Zero, ff) → new_mkVBalBranch3MkVBalBranch149(zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, zzz1125, Succ(zzz1126), zzz1127, zzz1128, zzz1129, Succ(Succ(zzz1126)), Zero, ff)
new_mkVBalBranch3MkVBalBranch132(zzz2033, zzz2034, zzz2035, zzz2036, zzz2037, zzz2038, zzz2039, zzz2040, zzz2041, zzz2042, zzz2043, Zero, Zero, fg) → new_mkVBalBranch3MkVBalBranch166(zzz2033, zzz2034, zzz2035, zzz2036, zzz2037, zzz2038, zzz2039, zzz2040, zzz2041, zzz2042, zzz2043, fg)
new_mkVBalBranch3MkVBalBranch157(zzz498, zzz499, zzz500, zzz501, zzz502, zzz503, zzz504, zzz505, zzz506, zzz507, Succ(zzz8040), ee) → new_mkVBalBranch3MkVBalBranch149(zzz498, zzz499, zzz500, zzz501, zzz502, zzz503, zzz504, Zero, zzz505, zzz506, zzz507, Succ(Zero), Succ(zzz8040), ee)
new_mkVBalBranch3MkVBalBranch156(zzz958, zzz959, zzz960, zzz961, zzz962, zzz963, zzz964, zzz965, zzz966, zzz967, zzz968, Zero, fa) → new_mkVBalBranch3MkVBalBranch152(zzz958, zzz959, zzz960, zzz961, zzz962, zzz963, zzz964, zzz965, zzz966, zzz967, zzz968, Zero, Succ(zzz965), fa)
new_mkBalBranch6MkBalBranch310(zzz2934, zzz2127, zzz2930, zzz2931, Neg(Succ(zzz224400)), Neg(zzz22450), da, db) → new_mkBalBranch6MkBalBranch37(zzz2934, zzz2127, zzz2930, zzz2931, zzz224400, new_primMulNat(zzz22450), da, db)
new_mkVBalBranch3MkVBalBranch132(zzz2033, zzz2034, zzz2035, zzz2036, zzz2037, zzz2038, zzz2039, zzz2040, zzz2041, zzz2042, zzz2043, Succ(zzz20440), Zero, fg) → new_mkVBalBranch3MkVBalBranch166(zzz2033, zzz2034, zzz2035, zzz2036, zzz2037, zzz2038, zzz2039, zzz2040, zzz2041, zzz2042, zzz2043, fg)
new_splitGT15(Branch(LT, zzz21291, zzz21292, zzz21293, zzz21294), cc) → new_splitGT15(zzz21294, cc)
new_mkBalBranch6MkBalBranch415(zzz2934, zzz2127, zzz2930, zzz2931, zzz222100, zzz2237, da, db) → new_mkBalBranch6MkBalBranch49(zzz2934, zzz2127, zzz2930, zzz2931, da, db)
new_mkVBalBranch3MkVBalBranch263(zzz498, zzz499, zzz500, zzz501, zzz502, zzz503, zzz504, zzz505, zzz506, zzz507, Succ(zzz5080), Zero, ee) → new_mkVBalBranch3MkVBalBranch264(zzz498, zzz499, zzz500, zzz501, zzz502, zzz503, zzz504, zzz505, zzz506, zzz507, ee)
new_intersectFM_C2Gts2(zzz883, zzz884, zzz885, zzz886, be) → new_splitGT29(zzz883, zzz884, zzz885, zzz886, be)
new_mkBalBranch6MkBalBranch017(zzz29340, zzz29341, zzz29342, zzz29343, zzz29344, zzz2127, zzz2930, zzz2931, Neg(Succ(zzz224600)), Pos(zzz22470), da, db) → new_mkBalBranch6MkBalBranch011(zzz29340, zzz29341, zzz29342, zzz29343, zzz29344, zzz2127, zzz2930, zzz2931, da, db)
new_mkBalBranch6MkBalBranch013(zzz29340, zzz29341, zzz29342, zzz29343, zzz29344, zzz2127, zzz2930, zzz2931, zzz224600, Zero, da, db) → new_mkBalBranch6MkBalBranch015(zzz29340, zzz29341, zzz29342, zzz29343, zzz29344, zzz2127, zzz2930, zzz2931, da, db)
new_mkVBalBranch3MkVBalBranch168(zzz340, zzz341, zzz34200, zzz343, zzz344, zzz510, zzz511, zzz513, zzz514, zzz31, Zero, h) → new_mkBranch(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))), EQ, zzz31, Branch(zzz510, zzz511, Pos(Zero), zzz513, zzz514), Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), ty_Ordering, h)
new_mkVBalBranch3MkVBalBranch275(zzz958, zzz959, zzz960, zzz961, zzz962, zzz963, zzz964, zzz965, zzz966, zzz967, zzz968, Succ(zzz9690), Zero, fa) → new_mkVBalBranch3MkVBalBranch276(zzz958, zzz959, zzz960, zzz961, zzz962, zzz963, zzz964, zzz965, zzz966, zzz967, zzz968, fa)
new_splitLT24(zzz854, zzz855, zzz856, zzz857, ba) → new_splitLT12(zzz856, ba)
new_mkVBalBranch3MkVBalBranch160(zzz340, zzz341, zzz34200, zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, h) → new_mkBalBranch(zzz510, zzz511, zzz513, new_mkVBalBranch4(zzz31, zzz514, Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), h), ty_Ordering, h)
new_mkVBalBranch3MkVBalBranch274(zzz818, zzz819, zzz820, zzz821, zzz822, zzz823, zzz824, zzz825, zzz826, zzz827, eb) → new_mkVBalBranch3MkVBalBranch143(zzz818, zzz819, zzz820, zzz821, zzz822, zzz823, zzz824, zzz825, zzz826, zzz827, new_primMulNat1(zzz820), eb)
new_mkVBalBranch3MkVBalBranch261(zzz3170, zzz3171, Neg(Succ(zzz317200)), zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, Zero, h) → new_mkVBalBranch3MkVBalBranch286(zzz3170, zzz3171, Succ(zzz317200), zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, h)
new_splitGT6(h) → new_splitGT42(h)
new_splitGT13(h) → new_splitGT41(h)
new_mkBalBranch6MkBalBranch30(zzz2934, zzz2127, zzz2930, zzz2931, Zero, da, db) → new_mkBalBranch6MkBalBranch32(zzz2934, zzz2127, zzz2930, zzz2931, da, db)
new_addToFM1(zzz317, zzz31, h) → new_addToFM_C2(zzz317, zzz31, h)
new_mkVBalBranch3MkVBalBranch272(zzz340, zzz341, Neg(Succ(Succ(Succ(zzz3420000)))), zzz343, zzz344, zzz520, zzz521, Succ(zzz522000), zzz523, zzz524, zzz31, Succ(Zero), h) → new_mkVBalBranch3MkVBalBranch255(zzz340, zzz341, Succ(Succ(zzz3420000)), zzz343, zzz344, zzz520, zzz521, zzz522000, zzz523, zzz524, zzz31, Succ(zzz3420000), Succ(zzz522000), h)
new_splitGT12(EmptyFM, ba) → new_splitGT41(ba)
new_mkBalBranch6MkBalBranch0110(zzz29340, zzz29341, zzz29342, zzz29343, zzz29344, zzz2127, zzz2930, zzz2931, Succ(zzz22560), da, db) → new_mkBalBranch6MkBalBranch018(zzz29340, zzz29341, zzz29342, zzz29343, zzz29344, zzz2127, zzz2930, zzz2931, Zero, zzz22560, da, db)
new_mkVBalBranch3MkVBalBranch281(zzz340, zzz341, Neg(Zero), zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, Zero, h) → new_mkVBalBranch3MkVBalBranch266(zzz340, zzz341, zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, h)
new_mkBalBranch6MkBalBranch1111(zzz2934, zzz21270, zzz21271, zzz21272, zzz21273, zzz21274, zzz2930, zzz2931, Zero, zzz226200, da, db) → new_mkBalBranch6MkBalBranch1112(zzz2934, zzz21270, zzz21271, zzz21272, zzz21273, zzz21274, zzz2930, zzz2931, da, db)
new_mkVBalBranch3MkVBalBranch131(zzz929, zzz930, zzz931, zzz932, zzz933, zzz934, zzz935, zzz936, zzz937, zzz938, zzz939, Zero, dc) → new_mkVBalBranch3MkVBalBranch132(zzz929, zzz930, zzz931, zzz932, zzz933, zzz934, zzz935, zzz936, zzz937, zzz938, zzz939, Zero, Succ(zzz936), dc)
new_intersectFM_C2Lts(zzz76, zzz77, zzz78, zzz79, bg) → new_splitLT9(zzz76, zzz77, zzz78, zzz79, bg)
new_primPlusInt0(zzz1311, Pos(zzz13130)) → Pos(new_primPlusNat2(zzz1311, zzz13130))
new_mkBalBranch6MkBalBranch115(zzz2934, zzz21270, zzz21271, zzz21272, zzz21273, zzz21274, zzz2930, zzz2931, zzz226200, zzz2271, da, db) → new_mkBalBranch6MkBalBranch1114(zzz2934, zzz21270, zzz21271, zzz21272, zzz21273, zzz21274, zzz2930, zzz2931, da, db)
new_mkVBalBranch3MkVBalBranch289(zzz1105, zzz1106, zzz1107, zzz1108, zzz1109, zzz1110, zzz1111, zzz1112, zzz1113, zzz1114, zzz1115, Zero, Succ(zzz11170), fh) → new_mkBalBranch(zzz1105, zzz1106, new_mkVBalBranch4(zzz1115, Branch(zzz1110, zzz1111, Pos(Succ(Succ(zzz1112))), zzz1113, zzz1114), zzz1108, fh), zzz1109, ty_Ordering, fh)
new_mkVBalBranch3MkVBalBranch168(zzz340, zzz341, zzz34200, zzz343, zzz344, zzz510, zzz511, zzz513, zzz514, zzz31, Succ(zzz1200), h) → new_mkBalBranch(zzz510, zzz511, zzz513, new_mkVBalBranch4(zzz31, zzz514, Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), h), ty_Ordering, h)
new_mkVBalBranch3MkVBalBranch281(zzz340, zzz341, Pos(zzz3420), zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, Zero, h) → new_mkVBalBranch3MkVBalBranch248(zzz340, zzz341, zzz3420, zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, h)
new_mkVBalBranch3MkVBalBranch281(zzz340, zzz341, Pos(zzz3420), zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, Succ(zzz670), h) → new_mkVBalBranch3MkVBalBranch248(zzz340, zzz341, zzz3420, zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, h)
new_mkBalBranch6MkBalBranch5(zzz2934, zzz2127, zzz2930, zzz2931, Neg(Zero), da, db) → new_mkBalBranch6MkBalBranch51(zzz2934, zzz2127, zzz2930, zzz2931, da, db)
new_mkVBalBranch3MkVBalBranch262(zzz3170, zzz3171, Pos(zzz31720), zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, Succ(zzz4190), h) → new_mkVBalBranch3MkVBalBranch251(zzz3170, zzz3171, zzz31720, zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, h)
new_mkBalBranch6MkBalBranch017(zzz29340, zzz29341, zzz29342, zzz29343, zzz29344, zzz2127, zzz2930, zzz2931, Pos(Succ(zzz224600)), Neg(zzz22470), da, db) → new_mkBalBranch6MkBalBranch015(zzz29340, zzz29341, zzz29342, zzz29343, zzz29344, zzz2127, zzz2930, zzz2931, da, db)
new_intersectFM_C2Lts1(zzz869, zzz870, zzz871, zzz872, bc) → new_splitLT25(zzz869, zzz870, zzz871, zzz872, bc)
new_mkVBalBranch3MkVBalBranch288(zzz340, zzz341, Pos(Zero), zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, Zero, h) → new_mkVBalBranch3MkVBalBranch285(zzz340, zzz341, zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, h)
new_mkVBalBranch4(zzz31, Branch(zzz510, zzz511, Pos(Zero), zzz513, zzz514), Branch(zzz340, zzz341, Neg(Zero), zzz343, zzz344), h) → new_mkBranch(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))), EQ, zzz31, Branch(zzz510, zzz511, Pos(Zero), zzz513, zzz514), Branch(zzz340, zzz341, Neg(Zero), zzz343, zzz344), ty_Ordering, h)
new_mkVBalBranch4(zzz31, Branch(zzz510, zzz511, Neg(Zero), zzz513, zzz514), Branch(zzz340, zzz341, Pos(Zero), zzz343, zzz344), h) → new_mkBranch(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))), EQ, zzz31, Branch(zzz510, zzz511, Neg(Zero), zzz513, zzz514), Branch(zzz340, zzz341, Pos(Zero), zzz343, zzz344), ty_Ordering, h)
new_mkBalBranch6Size_l(zzz2934, zzz2127, zzz2930, zzz2931, db, da) → new_sizeFM(zzz2127, da, db)
new_mkBalBranch6Size_r(zzz2934, zzz2127, zzz2930, zzz2931, db, da) → new_sizeFM(zzz2934, da, db)
new_mkVBalBranch3MkVBalBranch288(zzz340, zzz341, Pos(Succ(Succ(zzz342000))), zzz343, zzz344, zzz510, zzz511, Zero, zzz513, zzz514, zzz31, Succ(Zero), h) → new_mkVBalBranch3MkVBalBranch270(zzz340, zzz341, Succ(zzz342000), zzz343, zzz344, zzz510, zzz511, zzz513, zzz514, zzz31, Zero, zzz342000, h)
new_mkVBalBranch3MkVBalBranch147(zzz340, zzz341, zzz34200, zzz343, zzz344, zzz520, zzz521, zzz52200, zzz523, zzz524, zzz31, Succ(zzz1430), h) → new_mkVBalBranch3MkVBalBranch148(zzz340, zzz341, zzz34200, zzz343, zzz344, zzz520, zzz521, zzz52200, zzz523, zzz524, zzz31, h)
new_mkBalBranch6MkBalBranch416(zzz2934, zzz2127, zzz2930, zzz2931, Succ(zzz22420), da, db) → new_mkBalBranch6MkBalBranch43(zzz2934, zzz2127, zzz2930, zzz2931, da, db)
new_mkBalBranch6MkBalBranch012(zzz29340, zzz29341, zzz29342, zzz29343, zzz29344, zzz2127, zzz2930, zzz2931, da, db) → new_mkBalBranch6MkBalBranch016(zzz29340, zzz29341, zzz29342, zzz29343, zzz29344, zzz2127, zzz2930, zzz2931, da, db)
new_mkBalBranch6MkBalBranch1113(zzz2934, zzz21270, zzz21271, zzz21272, zzz21273, zzz21274, zzz2930, zzz2931, Succ(zzz2262000), Zero, da, db) → new_mkBalBranch6MkBalBranch1114(zzz2934, zzz21270, zzz21271, zzz21272, zzz21273, zzz21274, zzz2930, zzz2931, da, db)
new_mkBalBranch6MkBalBranch017(zzz29340, zzz29341, zzz29342, zzz29343, zzz29344, zzz2127, zzz2930, zzz2931, Neg(Zero), Neg(zzz22470), da, db) → new_mkBalBranch6MkBalBranch019(zzz29340, zzz29341, zzz29342, zzz29343, zzz29344, zzz2127, zzz2930, zzz2931, new_primMulNat2(zzz22470), da, db)
new_splitLT12(Branch(GT, zzz8561, zzz8562, zzz8563, zzz8564), ba) → new_splitLT25(zzz8561, zzz8562, zzz8563, zzz8564, ba)
new_splitGT26(zzz76, zzz77, zzz78, zzz79, bg) → new_splitGT24(zzz76, zzz77, zzz78, zzz79, bg)
new_mkVBalBranch3MkVBalBranch281(zzz340, zzz341, Neg(Succ(Succ(Succ(zzz3420000)))), zzz343, zzz344, zzz510, zzz511, Zero, zzz513, zzz514, zzz31, Succ(Zero), h) → new_mkVBalBranch3MkVBalBranch263(zzz340, zzz341, Succ(Succ(zzz3420000)), zzz343, zzz344, zzz510, zzz511, zzz513, zzz514, zzz31, Succ(zzz3420000), Zero, h)
new_mkVBalBranch3MkVBalBranch152(zzz1337, zzz1338, zzz1339, zzz1340, zzz1341, zzz1342, zzz1343, zzz1344, zzz1345, zzz1346, zzz1347, Zero, Zero, eg) → new_mkVBalBranch3MkVBalBranch151(zzz1337, zzz1338, zzz1339, zzz1340, zzz1341, zzz1342, zzz1343, zzz1344, zzz1345, zzz1346, zzz1347, eg)
new_mkVBalBranch3MkVBalBranch267(zzz340, zzz341, Pos(Zero), zzz343, zzz344, zzz520, zzz521, zzz52200, zzz523, zzz524, zzz31, Zero, h) → new_mkVBalBranch3MkVBalBranch268(zzz340, zzz341, zzz343, zzz344, zzz520, zzz521, zzz52200, zzz523, zzz524, zzz31, h)
new_mkVBalBranch2(zzz31, Branch(zzz330, zzz331, zzz332, zzz333, zzz334), EmptyFM, h) → new_addToFM1(Branch(zzz330, zzz331, zzz332, zzz333, zzz334), zzz31, h)
new_mkBalBranch6MkBalBranch113(zzz2934, zzz21270, zzz21271, zzz21272, zzz21273, zzz21274, zzz2930, zzz2931, Neg(Zero), Pos(zzz22630), da, db) → new_mkBalBranch6MkBalBranch1110(zzz2934, zzz21270, zzz21271, zzz21272, zzz21273, zzz21274, zzz2930, zzz2931, new_primMulNat2(zzz22630), da, db)
new_intersectFM_C2Lts2(zzz883, zzz884, zzz885, zzz886, be) → new_splitLT15(Branch(LT, zzz883, zzz884, zzz885, zzz886), be)
new_mkVBalBranch3MkVBalBranch164(zzz473, zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, zzz481, zzz482, Zero, eh) → new_mkVBalBranch3MkVBalBranch162(zzz473, zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, Zero, zzz480, zzz481, zzz482, Zero, Succ(Zero), eh)
new_mkVBalBranch3MkVBalBranch165(zzz461, zzz462, zzz463, zzz464, zzz465, zzz466, zzz467, zzz468, zzz469, zzz470, zzz471, de) → new_mkVBalBranch3MkVBalBranch163(zzz461, zzz462, zzz463, zzz464, zzz465, zzz466, zzz467, zzz468, zzz469, zzz470, zzz471, de)
new_mkVBalBranch3(zzz31, Branch(zzz520, zzz521, Pos(Zero), zzz523, zzz524), Branch(zzz340, zzz341, Pos(Zero), zzz343, zzz344), h) → new_mkBranch(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))), GT, zzz31, Branch(zzz520, zzz521, Pos(Zero), zzz523, zzz524), Branch(zzz340, zzz341, Pos(Zero), zzz343, zzz344), ty_Ordering, h)
new_mkBalBranch6MkBalBranch113(zzz2934, zzz21270, zzz21271, zzz21272, zzz21273, zzz21274, zzz2930, zzz2931, Pos(Succ(zzz226200)), Pos(zzz22630), da, db) → new_mkBalBranch6MkBalBranch114(zzz2934, zzz21270, zzz21271, zzz21272, zzz21273, zzz21274, zzz2930, zzz2931, zzz226200, new_primMulNat2(zzz22630), da, db)
new_mkVBalBranch3MkVBalBranch272(zzz340, zzz341, Neg(Succ(Succ(Succ(zzz3420000)))), zzz343, zzz344, zzz520, zzz521, Zero, zzz523, zzz524, zzz31, Succ(Succ(zzz6900)), h) → new_mkVBalBranch3MkVBalBranch277(zzz340, zzz341, Succ(Succ(zzz3420000)), zzz343, zzz344, zzz520, zzz521, zzz523, zzz524, zzz31, Succ(zzz3420000), Succ(zzz6900), h)
new_mkBalBranch6MkBalBranch113(zzz2934, zzz21270, zzz21271, zzz21272, zzz21273, zzz21274, zzz2930, zzz2931, Pos(Succ(zzz226200)), Neg(zzz22630), da, db) → new_mkBalBranch6MkBalBranch115(zzz2934, zzz21270, zzz21271, zzz21272, zzz21273, zzz21274, zzz2930, zzz2931, zzz226200, new_primMulNat2(zzz22630), da, db)
new_splitGT27(zzz31, zzz32, zzz33, zzz34, h) → zzz34
new_mkBalBranch6MkBalBranch42(zzz2934, zzz2127, zzz2930, zzz2931, zzz222100, zzz2240, da, db) → new_mkBalBranch6MkBalBranch43(zzz2934, zzz2127, zzz2930, zzz2931, da, db)
new_primMulNat1(zzz34200) → new_primPlusNat2(new_primMulNat0(zzz34200), Succ(zzz34200))
new_mkBalBranch6MkBalBranch1112(zzz2934, zzz21270, zzz21271, zzz21272, zzz21273, zzz21274, zzz2930, zzz2931, da, db) → new_mkBranch(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))), zzz21270, zzz21271, zzz21273, new_mkBranch(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))), zzz2930, zzz2931, zzz21274, zzz2934, da, db), da, db)
new_mkVBalBranch3MkVBalBranch281(zzz340, zzz341, Neg(Succ(Succ(Zero))), zzz343, zzz344, zzz510, zzz511, Succ(zzz512000), zzz513, zzz514, zzz31, Succ(Succ(zzz6700)), h) → new_mkVBalBranch3MkVBalBranch280(zzz340, zzz341, Succ(Zero), zzz343, zzz344, zzz510, zzz511, zzz512000, zzz513, zzz514, zzz31, Zero, Succ(Succ(new_primPlusNat2(zzz6700, zzz512000))), h)
new_mkBalBranch6MkBalBranch010(zzz29340, zzz29341, zzz29342, zzz29343, zzz29344, zzz2127, zzz2930, zzz2931, Succ(zzz22580), da, db) → new_mkBalBranch6MkBalBranch011(zzz29340, zzz29341, zzz29342, zzz29343, zzz29344, zzz2127, zzz2930, zzz2931, da, db)
new_mkVBalBranch3MkVBalBranch163(zzz461, zzz462, zzz463, zzz464, zzz465, zzz466, zzz467, zzz468, zzz469, zzz470, zzz471, de) → new_mkVBalBranch3MkVBalBranch158(zzz461, zzz462, zzz463, zzz464, zzz465, zzz466, zzz467, zzz468, zzz469, zzz470, zzz471, de)
new_addToFM_C3(Branch(LT, zzz341, zzz342, zzz343, zzz344), zzz31, h) → new_mkBalBranch(LT, zzz341, zzz343, new_addToFM_C3(zzz344, zzz31, h), ty_Ordering, h)
new_splitGT14(Branch(EQ, zzz8861, zzz8862, zzz8863, zzz8864), be) → new_splitGT27(zzz8861, zzz8862, zzz8863, zzz8864, be)
new_splitLT3(zzz31, zzz32, zzz33, zzz34, h) → new_splitLT28(zzz31, zzz32, zzz33, zzz34, h)
new_mkVBalBranch3MkVBalBranch248(zzz340, zzz341, zzz3420, zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, h) → new_mkBalBranch(zzz340, zzz341, new_mkVBalBranch4(zzz31, Branch(zzz510, zzz511, Neg(Succ(zzz51200)), zzz513, zzz514), zzz343, h), zzz344, ty_Ordering, h)
new_mkVBalBranch3MkVBalBranch267(zzz340, zzz341, Neg(zzz3420), zzz343, zzz344, zzz520, zzz521, zzz52200, zzz523, zzz524, zzz31, Succ(zzz680), h) → new_mkVBalBranch3MkVBalBranch269(zzz340, zzz341, zzz3420, zzz343, zzz344, zzz520, zzz521, zzz52200, zzz523, zzz524, zzz31, h)
new_sizeFM(Branch(zzz13040, zzz13041, zzz13042, zzz13043, zzz13044), fb, fc) → zzz13042
new_mkBalBranch6MkBalBranch35(zzz2934, zzz2127, zzz2930, zzz2931, Zero, da, db) → new_mkBalBranch6MkBalBranch32(zzz2934, zzz2127, zzz2930, zzz2931, da, db)
new_mkVBalBranch2(zzz31, Branch(zzz330, zzz331, Neg(Zero), zzz333, zzz334), Branch(zzz3170, zzz3171, Neg(Zero), zzz3173, zzz3174), h) → new_mkBranch(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))), LT, zzz31, Branch(zzz330, zzz331, Neg(Zero), zzz333, zzz334), Branch(zzz3170, zzz3171, Neg(Zero), zzz3173, zzz3174), ty_Ordering, h)
new_mkBalBranch6MkBalBranch116(zzz2934, zzz21270, zzz21271, zzz21272, zzz21273, zzz21274, zzz2930, zzz2931, Zero, da, db) → new_mkBalBranch6MkBalBranch112(zzz2934, zzz21270, zzz21271, zzz21272, zzz21273, zzz21274, zzz2930, zzz2931, da, db)
new_mkVBalBranch3MkVBalBranch281(zzz340, zzz341, Neg(Succ(Succ(Zero))), zzz343, zzz344, zzz510, zzz511, Succ(zzz512000), zzz513, zzz514, zzz31, Succ(Zero), h) → new_mkVBalBranch3MkVBalBranch280(zzz340, zzz341, Succ(Zero), zzz343, zzz344, zzz510, zzz511, zzz512000, zzz513, zzz514, zzz31, Zero, Succ(zzz512000), h)
new_mkVBalBranch3MkVBalBranch262(zzz3170, zzz3171, Neg(Succ(zzz317200)), zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, Zero, h) → new_mkVBalBranch3MkVBalBranch246(zzz3170, zzz3171, zzz317200, zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, Succ(zzz317200), Zero, h)
new_mkBalBranch6MkBalBranch118(zzz2934, zzz21270, zzz21271, zzz21272, zzz21273, zzz21274, zzz2930, zzz2931, zzz226200, zzz2275, da, db) → new_mkBalBranch6MkBalBranch1112(zzz2934, zzz21270, zzz21271, zzz21272, zzz21273, zzz21274, zzz2930, zzz2931, da, db)
new_primMinusNat0(Zero, Zero) → Pos(Zero)
new_mkBalBranch6MkBalBranch117(zzz2934, zzz21270, zzz21271, zzz21272, zzz21273, zzz21274, zzz2930, zzz2931, Succ(zzz22740), da, db) → new_mkBalBranch6MkBalBranch1114(zzz2934, zzz21270, zzz21271, zzz21272, zzz21273, zzz21274, zzz2930, zzz2931, da, db)
new_mkVBalBranch3(zzz31, Branch(zzz520, zzz521, Neg(Succ(zzz52200)), zzz523, zzz524), Branch(zzz340, zzz341, zzz342, zzz343, zzz344), h) → new_mkVBalBranch3MkVBalBranch272(zzz340, zzz341, zzz342, zzz343, zzz344, zzz520, zzz521, zzz52200, zzz523, zzz524, zzz31, new_primMulNat0(zzz52200), h)
new_mkBalBranch6MkBalBranch119(zzz2934, zzz21270, zzz21271, zzz21272, zzz21273, zzz21274, zzz2930, zzz2931, zzz226200, zzz2276, da, db) → new_mkBalBranch6MkBalBranch1111(zzz2934, zzz21270, zzz21271, zzz21272, zzz21273, zzz21274, zzz2930, zzz2931, zzz2276, zzz226200, da, db)
new_mkBalBranch6MkBalBranch110(zzz2934, zzz21270, zzz21271, zzz21272, zzz21273, zzz21274, zzz2930, zzz2931, Succ(zzz22780), da, db) → new_mkBalBranch6MkBalBranch111(zzz2934, zzz21270, zzz21271, zzz21272, zzz21273, zzz21274, zzz2930, zzz2931, zzz22780, Zero, da, db)
new_mkBalBranch6MkBalBranch414(zzz2934, zzz2127, zzz2930, zzz2931, Succ(zzz22380), da, db) → new_mkBalBranch6MkBalBranch47(zzz2934, zzz2127, zzz2930, zzz2931, Zero, zzz22380, da, db)
new_mkVBalBranch3MkVBalBranch262(zzz3170, zzz3171, Neg(Zero), zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, Succ(zzz4190), h) → new_mkBalBranch(zzz3170, zzz3171, new_mkVBalBranch2(zzz31, Branch(zzz330, zzz331, Neg(Succ(zzz33200)), zzz333, zzz334), zzz3173, h), zzz3174, ty_Ordering, h)
new_mkVBalBranch3MkVBalBranch261(zzz3170, zzz3171, Neg(Zero), zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, Zero, h) → new_mkVBalBranch3MkVBalBranch265(zzz3170, zzz3171, Zero, zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, h)
new_mkVBalBranch3MkVBalBranch137(zzz461, zzz462, zzz463, zzz464, zzz465, zzz466, zzz467, zzz468, zzz469, zzz470, zzz471, Succ(zzz5800), de) → new_mkVBalBranch3MkVBalBranch162(zzz461, zzz462, zzz463, zzz464, zzz465, zzz466, zzz467, Succ(zzz468), zzz469, zzz470, zzz471, Succ(zzz5800), Succ(Succ(zzz468)), de)
new_mkVBalBranch3MkVBalBranch267(zzz340, zzz341, Pos(Succ(zzz34200)), zzz343, zzz344, zzz520, zzz521, zzz52200, zzz523, zzz524, zzz31, Zero, h) → new_mkVBalBranch3MkVBalBranch252(zzz340, zzz341, zzz34200, zzz343, zzz344, zzz520, zzz521, zzz52200, zzz523, zzz524, zzz31, zzz52200, zzz34200, h)
new_splitLT26(zzz31, zzz32, zzz33, zzz34, h) → zzz33
new_mkBalBranch6MkBalBranch014(zzz29340, zzz29341, zzz29342, zzz29343, zzz29344, zzz2127, zzz2930, zzz2931, Succ(zzz2246000), Zero, da, db) → new_mkBalBranch6MkBalBranch015(zzz29340, zzz29341, zzz29342, zzz29343, zzz29344, zzz2127, zzz2930, zzz2931, da, db)
new_mkVBalBranch3MkVBalBranch267(zzz340, zzz341, Pos(Succ(zzz34200)), zzz343, zzz344, zzz520, zzz521, zzz52200, zzz523, zzz524, zzz31, Succ(zzz680), h) → new_mkVBalBranch3MkVBalBranch252(zzz340, zzz341, zzz34200, zzz343, zzz344, zzz520, zzz521, zzz52200, zzz523, zzz524, zzz31, Succ(new_primPlusNat2(zzz680, zzz52200)), zzz34200, h)
new_mkBalBranch6MkBalBranch1115(zzz2934, zzz21270, zzz21271, zzz21272, zzz21273, EmptyFM, zzz2930, zzz2931, da, db) → error([])
new_mkBalBranch6MkBalBranch0111(zzz29340, zzz29341, zzz29342, zzz29343, zzz29344, zzz2127, zzz2930, zzz2931, Succ(zzz22570), da, db) → new_mkBalBranch6MkBalBranch015(zzz29340, zzz29341, zzz29342, zzz29343, zzz29344, zzz2127, zzz2930, zzz2931, da, db)
new_splitLT12(Branch(EQ, zzz8561, zzz8562, zzz8563, zzz8564), ba) → new_splitLT24(zzz8561, zzz8562, zzz8563, zzz8564, ba)
new_mkVBalBranch3MkVBalBranch272(zzz340, zzz341, Neg(Succ(Zero)), zzz343, zzz344, zzz520, zzz521, Zero, zzz523, zzz524, zzz31, Zero, h) → new_mkVBalBranch3MkVBalBranch273(zzz340, zzz341, Zero, zzz343, zzz344, zzz520, zzz521, zzz523, zzz524, zzz31, h)
new_mkVBalBranch3MkVBalBranch262(zzz3170, zzz3171, Neg(Succ(zzz317200)), zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, Succ(zzz4190), h) → new_mkVBalBranch3MkVBalBranch246(zzz3170, zzz3171, zzz317200, zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, zzz317200, zzz4190, h)
new_mkBalBranch6MkBalBranch315(zzz2934, zzz2127, zzz2930, zzz2931, Zero, da, db) → new_mkBalBranch6MkBalBranch32(zzz2934, zzz2127, zzz2930, zzz2931, da, db)
new_primMulNat0(zzz6200) → new_primPlusNat3(Succ(new_primPlusNat3(new_primPlusNat1(zzz6200), zzz6200)), Succ(zzz6200))
new_mkVBalBranch3MkVBalBranch146(zzz3170, zzz3171, zzz317200, zzz3173, zzz3174, zzz330, zzz331, zzz333, zzz334, zzz31, Succ(zzz5500), h) → new_mkBalBranch(zzz330, zzz331, zzz333, new_mkVBalBranch2(zzz31, zzz334, Branch(zzz3170, zzz3171, Neg(Succ(zzz317200)), zzz3173, zzz3174), h), ty_Ordering, h)
new_mkBalBranch6MkBalBranch411(zzz2934, zzz2127, zzz2930, zzz2931, Pos(Succ(zzz222100)), Pos(zzz22060), da, db) → new_mkBalBranch6MkBalBranch44(zzz2934, zzz2127, zzz2930, zzz2931, zzz222100, new_primMulNat(zzz22060), da, db)
new_mkBalBranch6MkBalBranch1113(zzz2934, zzz21270, zzz21271, zzz21272, zzz21273, zzz21274, zzz2930, zzz2931, Zero, Succ(zzz227000), da, db) → new_mkBalBranch6MkBalBranch1112(zzz2934, zzz21270, zzz21271, zzz21272, zzz21273, zzz21274, zzz2930, zzz2931, da, db)
new_mkVBalBranch3MkVBalBranch272(zzz340, zzz341, Neg(Succ(Zero)), zzz343, zzz344, zzz520, zzz521, Succ(zzz522000), zzz523, zzz524, zzz31, Zero, h) → new_mkVBalBranch3MkVBalBranch254(zzz340, zzz341, zzz343, zzz344, zzz520, zzz521, Succ(zzz522000), zzz523, zzz524, zzz31, h)
new_mkVBalBranch2(zzz31, Branch(zzz330, zzz331, Pos(Succ(zzz33200)), zzz333, zzz334), Branch(zzz3170, zzz3171, zzz3172, zzz3173, zzz3174), h) → new_mkVBalBranch3MkVBalBranch261(zzz3170, zzz3171, zzz3172, zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, new_primPlusNat2(new_primMulNat0(zzz33200), Succ(zzz33200)), h)
new_mkVBalBranch3MkVBalBranch139(zzz3170, zzz3171, zzz317200, zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, Zero, h) → new_mkVBalBranch3MkVBalBranch140(zzz3170, zzz3171, zzz317200, zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, h)
new_mkVBalBranch3MkVBalBranch251(zzz3170, zzz3171, zzz31720, zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, h) → new_mkBalBranch(zzz3170, zzz3171, new_mkVBalBranch2(zzz31, Branch(zzz330, zzz331, Neg(Succ(zzz33200)), zzz333, zzz334), zzz3173, h), zzz3174, ty_Ordering, h)
new_mkBalBranch6MkBalBranch314(zzz2934, zzz2127, zzz2930, zzz2931, Zero, da, db) → new_mkBalBranch6MkBalBranch32(zzz2934, zzz2127, zzz2930, zzz2931, da, db)
new_addToFM_C3(EmptyFM, zzz31, h) → Branch(GT, zzz31, Pos(Succ(Zero)), new_emptyFM(h), new_emptyFM(h))
new_splitLT42(h) → new_emptyFM(h)
new_emptyFM(h) → EmptyFM
new_mkBalBranch6MkBalBranch411(zzz2934, zzz2127, zzz2930, zzz2931, Neg(Succ(zzz222100)), Neg(zzz22060), da, db) → new_mkBalBranch6MkBalBranch46(zzz2934, zzz2127, zzz2930, zzz2931, zzz222100, new_primMulNat(zzz22060), da, db)
new_splitLT7(zzz31, zzz32, zzz33, zzz34, h) → new_splitLT26(zzz31, zzz32, zzz33, zzz34, h)
new_mkVBalBranch3MkVBalBranch280(zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, zzz1125, zzz1126, zzz1127, zzz1128, zzz1129, Zero, Zero, ff) → new_mkVBalBranch3MkVBalBranch278(zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, zzz1125, zzz1126, zzz1127, zzz1128, zzz1129, ff)
new_mkVBalBranch3MkVBalBranch280(zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, zzz1125, zzz1126, zzz1127, zzz1128, zzz1129, Succ(zzz11300), Succ(zzz11310), ff) → new_mkVBalBranch3MkVBalBranch280(zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, zzz1125, zzz1126, zzz1127, zzz1128, zzz1129, zzz11300, zzz11310, ff)
new_mkBalBranch6MkBalBranch311(zzz2934, zzz2127, zzz2930, zzz2931, zzz224400, zzz2248, da, db) → new_mkBalBranch6MkBalBranch38(zzz2934, zzz2127, zzz2930, zzz2931, zzz224400, zzz2248, da, db)
new_mkBalBranch6MkBalBranch011(zzz29340, zzz29341, zzz29342, zzz29343, zzz29344, zzz2127, zzz2930, zzz2931, da, db) → new_mkBranch(Succ(Succ(Zero)), zzz29340, zzz29341, new_mkBranch(Succ(Succ(Succ(Zero))), zzz2930, zzz2931, zzz2127, zzz29343, da, db), zzz29344, da, db)
new_mkBalBranch6MkBalBranch43(zzz2934, zzz2127, zzz2930, zzz2931, da, db) → new_mkBalBranch6MkBalBranch41(zzz2934, zzz2127, zzz2930, zzz2931, da, db)
new_mkBalBranch6MkBalBranch414(zzz2934, zzz2127, zzz2930, zzz2931, Zero, da, db) → new_mkBalBranch6MkBalBranch40(zzz2934, zzz2127, zzz2930, zzz2931, da, db)
new_mkVBalBranch3(zzz31, Branch(zzz520, zzz521, Neg(Zero), zzz523, zzz524), Branch(zzz340, zzz341, Pos(Succ(zzz34200)), zzz343, zzz344), h) → new_mkBalBranch(zzz340, zzz341, new_mkVBalBranch3(zzz31, Branch(zzz520, zzz521, Neg(Zero), zzz523, zzz524), zzz343, h), zzz344, ty_Ordering, h)
new_mkBalBranch6MkBalBranch411(zzz2934, zzz2127, zzz2930, zzz2931, Pos(Zero), Neg(zzz22060), da, db) → new_mkBalBranch6MkBalBranch48(zzz2934, zzz2127, zzz2930, zzz2931, new_primMulNat(zzz22060), da, db)
new_mkVBalBranch3MkVBalBranch133(zzz340, zzz341, zzz34200, zzz343, zzz344, zzz510, zzz511, zzz513, zzz514, zzz31, Zero, h) → new_mkBranch(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))), EQ, zzz31, Branch(zzz510, zzz511, Neg(Zero), zzz513, zzz514), Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), ty_Ordering, h)
new_mkBalBranch6MkBalBranch410(zzz2934, zzz2127, zzz2930, zzz2931, zzz2206, da, db) → new_mkBalBranch6MkBalBranch411(zzz2934, zzz2127, zzz2930, zzz2931, new_mkBalBranch6Size_r(zzz2934, zzz2127, zzz2930, zzz2931, db, da), zzz2206, da, db)
new_mkVBalBranch3MkVBalBranch246(zzz972, zzz973, zzz974, zzz975, zzz976, zzz977, zzz978, zzz979, zzz980, zzz981, zzz982, Succ(zzz9830), Succ(zzz9840), cg) → new_mkVBalBranch3MkVBalBranch246(zzz972, zzz973, zzz974, zzz975, zzz976, zzz977, zzz978, zzz979, zzz980, zzz981, zzz982, zzz9830, zzz9840, cg)
new_mkBalBranch6MkBalBranch113(zzz2934, zzz21270, zzz21271, zzz21272, zzz21273, zzz21274, zzz2930, zzz2931, Neg(Succ(zzz226200)), Neg(zzz22630), da, db) → new_mkBalBranch6MkBalBranch119(zzz2934, zzz21270, zzz21271, zzz21272, zzz21273, zzz21274, zzz2930, zzz2931, zzz226200, new_primMulNat2(zzz22630), da, db)
new_mkBalBranch6MkBalBranch017(zzz29340, zzz29341, zzz29342, zzz29343, zzz29344, zzz2127, zzz2930, zzz2931, Pos(Zero), Pos(zzz22470), da, db) → new_mkBalBranch6MkBalBranch0110(zzz29340, zzz29341, zzz29342, zzz29343, zzz29344, zzz2127, zzz2930, zzz2931, new_primMulNat2(zzz22470), da, db)
new_mkVBalBranch3MkVBalBranch272(zzz340, zzz341, Neg(Succ(Succ(Zero))), zzz343, zzz344, zzz520, zzz521, Succ(zzz522000), zzz523, zzz524, zzz31, Succ(Succ(zzz6900)), h) → new_mkVBalBranch3MkVBalBranch255(zzz340, zzz341, Succ(Zero), zzz343, zzz344, zzz520, zzz521, zzz522000, zzz523, zzz524, zzz31, Zero, Succ(Succ(new_primPlusNat2(zzz6900, zzz522000))), h)
new_mkBalBranch6MkBalBranch016(zzz29340, zzz29341, zzz29342, Branch(zzz293430, zzz293431, zzz293432, zzz293433, zzz293434), zzz29344, zzz2127, zzz2930, zzz2931, da, db) → new_mkBranch(Succ(Succ(Succ(Succ(Zero)))), zzz293430, zzz293431, new_mkBranch(Succ(Succ(Succ(Succ(Succ(Zero))))), zzz2930, zzz2931, zzz2127, zzz293433, da, db), new_mkBranch(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))), zzz29340, zzz29341, zzz293434, zzz29344, da, db), da, db)
new_mkVBalBranch3MkVBalBranch246(zzz972, zzz973, zzz974, zzz975, zzz976, zzz977, zzz978, zzz979, zzz980, zzz981, zzz982, Succ(zzz9830), Zero, cg) → new_mkVBalBranch3MkVBalBranch247(zzz972, zzz973, zzz974, zzz975, zzz976, zzz977, zzz978, zzz979, zzz980, zzz981, zzz982, cg)
new_mkVBalBranch3MkVBalBranch153(zzz537, zzz538, zzz539, zzz540, zzz541, zzz542, zzz543, zzz544, zzz545, zzz546, zzz547, Zero, dg) → new_mkVBalBranch3MkVBalBranch144(zzz537, zzz538, zzz539, zzz540, zzz541, zzz542, zzz543, Succ(zzz544), zzz545, zzz546, zzz547, Succ(Succ(zzz544)), Zero, dg)
new_mkVBalBranch3MkVBalBranch252(zzz929, zzz930, zzz931, zzz932, zzz933, zzz934, zzz935, zzz936, zzz937, zzz938, zzz939, Succ(zzz9400), Succ(zzz9410), dc) → new_mkVBalBranch3MkVBalBranch252(zzz929, zzz930, zzz931, zzz932, zzz933, zzz934, zzz935, zzz936, zzz937, zzz938, zzz939, zzz9400, zzz9410, dc)
new_splitGT12(Branch(GT, zzz8561, zzz8562, zzz8563, zzz8564), ba) → new_splitGT28(zzz8561, zzz8562, zzz8563, zzz8564, ba)
new_splitLT5(zzz31, zzz32, zzz34, h) → new_splitLT16(h)
new_splitLT4(zzz31, zzz32, zzz34, h) → new_splitLT16(h)
new_mkVBalBranch3MkVBalBranch161(zzz340, zzz341, zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, Succ(zzz1480), h) → new_mkVBalBranch3MkVBalBranch162(zzz340, zzz341, Zero, zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, Succ(zzz1480), Succ(zzz51200), h)
new_mkVBalBranch4(zzz31, Branch(zzz510, zzz511, Pos(Zero), zzz513, zzz514), Branch(zzz340, zzz341, Pos(Succ(zzz34200)), zzz343, zzz344), h) → new_mkBalBranch(zzz340, zzz341, new_mkVBalBranch4(zzz31, Branch(zzz510, zzz511, Pos(Zero), zzz513, zzz514), zzz343, h), zzz344, ty_Ordering, h)
new_mkVBalBranch3MkVBalBranch149(zzz2050, zzz2051, zzz2052, zzz2053, zzz2054, zzz2055, zzz2056, zzz2057, zzz2058, zzz2059, zzz2060, Zero, Succ(zzz20620), ef) → new_mkBalBranch(zzz2055, zzz2056, zzz2058, new_mkVBalBranch4(zzz2060, zzz2059, Branch(zzz2050, zzz2051, Neg(Succ(zzz2052)), zzz2053, zzz2054), ef), ty_Ordering, ef)
new_mkVBalBranch4(zzz31, Branch(zzz510, zzz511, Pos(Succ(zzz51200)), zzz513, zzz514), Branch(zzz340, zzz341, zzz342, zzz343, zzz344), h) → new_mkVBalBranch3MkVBalBranch288(zzz340, zzz341, zzz342, zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, new_primMulNat0(zzz51200), h)
new_mkVBalBranch3(zzz31, Branch(zzz520, zzz521, Pos(Succ(zzz52200)), zzz523, zzz524), Branch(zzz340, zzz341, zzz342, zzz343, zzz344), h) → new_mkVBalBranch3MkVBalBranch267(zzz340, zzz341, zzz342, zzz343, zzz344, zzz520, zzz521, zzz52200, zzz523, zzz524, zzz31, new_primMulNat0(zzz52200), h)
new_primPlusNat2(Zero, Succ(zzz9100)) → Succ(zzz9100)
new_primPlusNat2(Succ(zzz900), Zero) → Succ(zzz900)
new_mkVBalBranch3MkVBalBranch289(zzz1105, zzz1106, zzz1107, zzz1108, zzz1109, zzz1110, zzz1111, zzz1112, zzz1113, zzz1114, zzz1115, Zero, Zero, fh) → new_mkVBalBranch3MkVBalBranch282(zzz1105, zzz1106, zzz1107, zzz1108, zzz1109, zzz1110, zzz1111, zzz1112, zzz1113, zzz1114, zzz1115, fh)
new_addToFM_C3(Branch(GT, zzz341, zzz342, zzz343, zzz344), zzz31, h) → Branch(GT, new_addToFM0(zzz341, zzz31, h), zzz342, zzz343, zzz344)
new_splitLT14(Branch(EQ, zzz21291, zzz21292, zzz21293, zzz21294), cc) → new_mkVBalBranch4(zzz21291, zzz21293, new_splitLT14(zzz21294, cc), cc)
new_primPlusInt2(Neg(zzz21410), zzz2934, zzz2127, zzz2930, zzz2931, db, da) → new_primPlusInt1(zzz21410, new_sizeFM(zzz2934, da, db))
new_mkVBalBranch3MkVBalBranch150(zzz2050, zzz2051, zzz2052, zzz2053, zzz2054, zzz2055, zzz2056, zzz2057, zzz2058, zzz2059, zzz2060, ef) → new_mkBranch(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))), EQ, zzz2060, Branch(zzz2055, zzz2056, Neg(Succ(zzz2057)), zzz2058, zzz2059), Branch(zzz2050, zzz2051, Neg(Succ(zzz2052)), zzz2053, zzz2054), ty_Ordering, ef)
new_primMinusNat0(Zero, Succ(zzz542000)) → Neg(Succ(zzz542000))
new_mkBalBranch6MkBalBranch49(Branch(zzz29340, zzz29341, zzz29342, zzz29343, zzz29344), zzz2127, zzz2930, zzz2931, da, db) → new_mkBalBranch6MkBalBranch017(zzz29340, zzz29341, zzz29342, zzz29343, zzz29344, zzz2127, zzz2930, zzz2931, new_sizeFM(zzz29343, da, db), new_sizeFM(zzz29344, da, db), da, db)
new_mkBalBranch6MkBalBranch312(zzz2934, zzz2127, zzz2930, zzz2931, zzz224400, zzz2249, da, db) → new_mkBalBranch6MkBalBranch33(zzz2934, zzz2127, zzz2930, zzz2931, da, db)
new_mkBalBranch6MkBalBranch310(zzz2934, zzz2127, zzz2930, zzz2931, Pos(Succ(zzz224400)), Neg(zzz22450), da, db) → new_mkBalBranch6MkBalBranch312(zzz2934, zzz2127, zzz2930, zzz2931, zzz224400, new_primMulNat(zzz22450), da, db)
new_primPlusInt1(zzz13120, Neg(zzz13150)) → Neg(new_primPlusNat2(zzz13120, zzz13150))
new_splitLT11(zzz31, zzz32, zzz33, h) → new_mkVBalBranch4(zzz31, zzz33, new_splitLT13(h), h)
new_mkVBalBranch3MkVBalBranch290(zzz340, zzz341, zzz342000, zzz343, zzz344, zzz510, zzz511, zzz513, zzz514, zzz31, h) → new_mkBalBranch(zzz340, zzz341, new_mkVBalBranch4(zzz31, Branch(zzz510, zzz511, Pos(Succ(Zero)), zzz513, zzz514), zzz343, h), zzz344, ty_Ordering, h)
new_mkVBalBranch3MkVBalBranch254(zzz340, zzz341, zzz343, zzz344, zzz520, zzz521, zzz52200, zzz523, zzz524, zzz31, h) → new_mkBalBranch(zzz340, zzz341, new_mkVBalBranch3(zzz31, Branch(zzz520, zzz521, Neg(Succ(zzz52200)), zzz523, zzz524), zzz343, h), zzz344, ty_Ordering, h)
new_splitLT28(zzz31, zzz32, zzz33, zzz34, h) → zzz33
new_splitLT13(h) → new_splitLT40(h)
new_splitLT10(zzz31, zzz32, zzz33, h) → new_mkVBalBranch2(zzz31, zzz33, new_splitLT13(h), h)
new_mkVBalBranch3MkVBalBranch257(zzz486, zzz487, zzz488, zzz489, zzz490, zzz491, zzz492, zzz493, zzz494, zzz495, zzz496, ea) → new_mkBalBranch(zzz486, zzz487, new_mkVBalBranch4(zzz496, Branch(zzz491, zzz492, Neg(Succ(Succ(zzz493))), zzz494, zzz495), zzz489, ea), zzz490, ty_Ordering, ea)
new_primPlusNat2(Zero, Zero) → Zero
new_mkBalBranch6MkBalBranch5(zzz2934, zzz2127, zzz2930, zzz2931, Pos(Succ(Succ(Succ(zzz21390000)))), da, db) → new_mkBalBranch6MkBalBranch50(zzz2934, zzz2127, zzz2930, zzz2931, da, db)
new_splitGT5(zzz31, zzz32, zzz34, h) → new_mkVBalBranch3(zzz31, new_splitGT13(h), zzz34, h)
new_mkVBalBranch3MkVBalBranch265(zzz3170, zzz3171, Succ(zzz317200), zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, h) → new_mkVBalBranch3MkVBalBranch139(zzz3170, zzz3171, zzz317200, zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, new_primPlusNat2(new_primMulNat0(zzz317200), Succ(zzz317200)), h)
new_splitLT9(zzz76, zzz77, zzz78, zzz79, bg) → new_splitLT27(zzz76, zzz77, zzz78, zzz79, bg)
new_mkVBalBranch3MkVBalBranch284(zzz340, zzz341, Succ(zzz34200), zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, h) → new_mkVBalBranch3MkVBalBranch167(zzz340, zzz341, zzz34200, zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, new_primPlusNat2(new_primMulNat0(zzz34200), Succ(zzz34200)), h)
new_mkVBalBranch3MkVBalBranch147(zzz340, zzz341, zzz34200, zzz343, zzz344, zzz520, zzz521, zzz52200, zzz523, zzz524, zzz31, Zero, h) → new_mkVBalBranch3MkVBalBranch148(zzz340, zzz341, zzz34200, zzz343, zzz344, zzz520, zzz521, zzz52200, zzz523, zzz524, zzz31, h)
new_mkBalBranch6MkBalBranch013(zzz29340, zzz29341, zzz29342, zzz29343, zzz29344, zzz2127, zzz2930, zzz2931, zzz224600, Succ(zzz22600), da, db) → new_mkBalBranch6MkBalBranch014(zzz29340, zzz29341, zzz29342, zzz29343, zzz29344, zzz2127, zzz2930, zzz2931, zzz224600, zzz22600, da, db)
new_mkBalBranch6MkBalBranch112(zzz2934, zzz21270, zzz21271, zzz21272, zzz21273, zzz21274, zzz2930, zzz2931, da, db) → new_mkBalBranch6MkBalBranch1115(zzz2934, zzz21270, zzz21271, zzz21272, zzz21273, zzz21274, zzz2930, zzz2931, da, db)
new_mkBalBranch6MkBalBranch38(zzz2934, zzz2127, zzz2930, zzz2931, zzz224400, Zero, da, db) → new_mkBalBranch6MkBalBranch33(zzz2934, zzz2127, zzz2930, zzz2931, da, db)
new_mkBalBranch6MkBalBranch014(zzz29340, zzz29341, zzz29342, zzz29343, zzz29344, zzz2127, zzz2930, zzz2931, Zero, Succ(zzz226000), da, db) → new_mkBalBranch6MkBalBranch011(zzz29340, zzz29341, zzz29342, zzz29343, zzz29344, zzz2127, zzz2930, zzz2931, da, db)
new_mkVBalBranch3MkVBalBranch261(zzz3170, zzz3171, Neg(zzz31720), zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, Succ(zzz4170), h) → new_mkVBalBranch3MkVBalBranch286(zzz3170, zzz3171, zzz31720, zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, h)
new_mkVBalBranch3MkVBalBranch288(zzz340, zzz341, Pos(Succ(Zero)), zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, Succ(zzz660), h) → new_mkVBalBranch3MkVBalBranch287(zzz340, zzz341, zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, h)
new_mkBalBranch6MkBalBranch48(zzz2934, zzz2127, zzz2930, zzz2931, Succ(zzz22390), da, db) → new_mkBalBranch6MkBalBranch49(zzz2934, zzz2127, zzz2930, zzz2931, da, db)
new_splitGT11(zzz31, zzz32, zzz33, h) → new_splitGT16(h)
new_mkBalBranch6MkBalBranch310(zzz2934, zzz2127, zzz2930, zzz2931, Neg(Succ(zzz224400)), Pos(zzz22450), da, db) → new_mkBalBranch6MkBalBranch34(zzz2934, zzz2127, zzz2930, zzz2931, zzz224400, new_primMulNat(zzz22450), da, db)
new_mkBalBranch6MkBalBranch45(zzz2934, zzz2127, zzz2930, zzz2931, zzz222100, Succ(zzz22360), da, db) → new_mkBalBranch6MkBalBranch412(zzz2934, zzz2127, zzz2930, zzz2931, zzz222100, zzz22360, da, db)
new_mkVBalBranch3MkVBalBranch157(zzz498, zzz499, zzz500, zzz501, zzz502, zzz503, zzz504, zzz505, zzz506, zzz507, Zero, ee) → new_mkVBalBranch3MkVBalBranch149(zzz498, zzz499, zzz500, zzz501, zzz502, zzz503, zzz504, Zero, zzz505, zzz506, zzz507, Succ(Zero), Zero, ee)
new_intersectFM_C2Lts3(zzz2129, cc) → new_splitLT14(zzz2129, cc)
new_mkVBalBranch3MkVBalBranch272(zzz340, zzz341, Neg(Succ(Succ(zzz342000))), zzz343, zzz344, zzz520, zzz521, Zero, zzz523, zzz524, zzz31, Zero, h) → new_mkVBalBranch3MkVBalBranch259(zzz340, zzz341, zzz342000, zzz343, zzz344, zzz520, zzz521, zzz523, zzz524, zzz31, h)
new_splitLT23(zzz76, zzz77, zzz78, zzz79, bg) → new_splitLT15(zzz78, bg)
new_mkVBalBranch4(zzz31, Branch(zzz510, zzz511, Neg(Zero), zzz513, zzz514), Branch(zzz340, zzz341, Pos(Succ(zzz34200)), zzz343, zzz344), h) → new_mkBalBranch(zzz340, zzz341, new_mkVBalBranch4(zzz31, Branch(zzz510, zzz511, Neg(Zero), zzz513, zzz514), zzz343, h), zzz344, ty_Ordering, h)
new_mkVBalBranch3(zzz31, Branch(zzz520, zzz521, Neg(Zero), zzz523, zzz524), Branch(zzz340, zzz341, Neg(Zero), zzz343, zzz344), h) → new_mkBranch(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))), GT, zzz31, Branch(zzz520, zzz521, Neg(Zero), zzz523, zzz524), Branch(zzz340, zzz341, Neg(Zero), zzz343, zzz344), ty_Ordering, h)
new_mkBalBranch6MkBalBranch019(zzz29340, zzz29341, zzz29342, zzz29343, zzz29344, zzz2127, zzz2930, zzz2931, Zero, da, db) → new_mkBalBranch6MkBalBranch012(zzz29340, zzz29341, zzz29342, zzz29343, zzz29344, zzz2127, zzz2930, zzz2931, da, db)
new_mkVBalBranch2(zzz31, Branch(zzz330, zzz331, Neg(Zero), zzz333, zzz334), Branch(zzz3170, zzz3171, Neg(Succ(zzz317200)), zzz3173, zzz3174), h) → new_mkVBalBranch3MkVBalBranch146(zzz3170, zzz3171, zzz317200, zzz3173, zzz3174, zzz330, zzz331, zzz333, zzz334, zzz31, new_primMulNat1(zzz317200), h)
new_mkVBalBranch3MkVBalBranch289(zzz1105, zzz1106, zzz1107, zzz1108, zzz1109, zzz1110, zzz1111, zzz1112, zzz1113, zzz1114, zzz1115, Succ(zzz11160), Zero, fh) → new_mkVBalBranch3MkVBalBranch283(zzz1105, zzz1106, zzz1107, zzz1108, zzz1109, zzz1110, zzz1111, zzz1112, zzz1113, zzz1114, zzz1115, fh)
new_mkVBalBranch3MkVBalBranch277(zzz1133, zzz1134, zzz1135, zzz1136, zzz1137, zzz1138, zzz1139, zzz1140, zzz1141, zzz1142, Zero, Succ(zzz11440), fd) → new_mkBalBranch(zzz1133, zzz1134, new_mkVBalBranch3(zzz1142, Branch(zzz1138, zzz1139, Neg(Succ(Zero)), zzz1140, zzz1141), zzz1136, fd), zzz1137, ty_Ordering, fd)
new_mkVBalBranch3MkVBalBranch146(zzz3170, zzz3171, zzz317200, zzz3173, zzz3174, zzz330, zzz331, zzz333, zzz334, zzz31, Zero, h) → new_mkBranch(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))), LT, zzz31, Branch(zzz330, zzz331, Neg(Zero), zzz333, zzz334), Branch(zzz3170, zzz3171, Neg(Succ(zzz317200)), zzz3173, zzz3174), ty_Ordering, h)
new_mkVBalBranch2(zzz31, Branch(zzz330, zzz331, Pos(Zero), zzz333, zzz334), Branch(zzz3170, zzz3171, Neg(Zero), zzz3173, zzz3174), h) → new_mkBranch(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))), LT, zzz31, Branch(zzz330, zzz331, Pos(Zero), zzz333, zzz334), Branch(zzz3170, zzz3171, Neg(Zero), zzz3173, zzz3174), ty_Ordering, h)
new_mkVBalBranch2(zzz31, Branch(zzz330, zzz331, Neg(Zero), zzz333, zzz334), Branch(zzz3170, zzz3171, Pos(Zero), zzz3173, zzz3174), h) → new_mkBranch(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))), LT, zzz31, Branch(zzz330, zzz331, Neg(Zero), zzz333, zzz334), Branch(zzz3170, zzz3171, Pos(Zero), zzz3173, zzz3174), ty_Ordering, h)
new_mkVBalBranch3MkVBalBranch277(zzz1133, zzz1134, zzz1135, zzz1136, zzz1137, zzz1138, zzz1139, zzz1140, zzz1141, zzz1142, Succ(zzz11430), Zero, fd) → new_mkVBalBranch3MkVBalBranch274(zzz1133, zzz1134, zzz1135, zzz1136, zzz1137, zzz1138, zzz1139, zzz1140, zzz1141, zzz1142, fd)
new_mkBalBranch6MkBalBranch0111(zzz29340, zzz29341, zzz29342, zzz29343, zzz29344, zzz2127, zzz2930, zzz2931, Zero, da, db) → new_mkBalBranch6MkBalBranch012(zzz29340, zzz29341, zzz29342, zzz29343, zzz29344, zzz2127, zzz2930, zzz2931, da, db)
new_mkBalBranch6MkBalBranch50(zzz2934, zzz2127, zzz2930, zzz2931, da, db) → new_mkBalBranch6MkBalBranch410(zzz2934, zzz2127, zzz2930, zzz2931, new_mkBalBranch6Size_l(zzz2934, zzz2127, zzz2930, zzz2931, db, da), da, db)
new_mkVBalBranch2(zzz31, Branch(zzz330, zzz331, Pos(Zero), zzz333, zzz334), Branch(zzz3170, zzz3171, Pos(Zero), zzz3173, zzz3174), h) → new_mkBranch(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))), LT, zzz31, Branch(zzz330, zzz331, Pos(Zero), zzz333, zzz334), Branch(zzz3170, zzz3171, Pos(Zero), zzz3173, zzz3174), ty_Ordering, h)
new_mkBalBranch6MkBalBranch412(zzz2934, zzz2127, zzz2930, zzz2931, Zero, Zero, da, db) → new_mkBalBranch6MkBalBranch40(zzz2934, zzz2127, zzz2930, zzz2931, da, db)
new_mkVBalBranch3MkVBalBranch144(zzz1702, zzz1703, zzz1704, zzz1705, zzz1706, zzz1707, zzz1708, zzz1709, zzz1710, zzz1711, zzz1712, Succ(zzz17130), Succ(zzz17140), df) → new_mkVBalBranch3MkVBalBranch144(zzz1702, zzz1703, zzz1704, zzz1705, zzz1706, zzz1707, zzz1708, zzz1709, zzz1710, zzz1711, zzz1712, zzz17130, zzz17140, df)
new_splitLT14(Branch(GT, zzz21291, zzz21292, zzz21293, zzz21294), cc) → zzz21293
new_mkVBalBranch3MkVBalBranch276(zzz958, zzz959, zzz960, zzz961, zzz962, zzz963, zzz964, zzz965, zzz966, zzz967, zzz968, fa) → new_mkVBalBranch3MkVBalBranch156(zzz958, zzz959, zzz960, zzz961, zzz962, zzz963, zzz964, zzz965, zzz966, zzz967, zzz968, new_primMulNat1(zzz960), fa)
new_mkBalBranch6MkBalBranch45(zzz2934, zzz2127, zzz2930, zzz2931, zzz222100, Zero, da, db) → new_mkBalBranch6MkBalBranch49(zzz2934, zzz2127, zzz2930, zzz2931, da, db)
new_mkVBalBranch3MkVBalBranch252(zzz929, zzz930, zzz931, zzz932, zzz933, zzz934, zzz935, zzz936, zzz937, zzz938, zzz939, Succ(zzz9400), Zero, dc) → new_mkVBalBranch3MkVBalBranch253(zzz929, zzz930, zzz931, zzz932, zzz933, zzz934, zzz935, zzz936, zzz937, zzz938, zzz939, dc)
new_mkBalBranch6MkBalBranch315(zzz2934, zzz2127, zzz2930, zzz2931, Succ(zzz22510), da, db) → new_mkBalBranch6MkBalBranch33(zzz2934, zzz2127, zzz2930, zzz2931, da, db)
new_mkVBalBranch3MkVBalBranch155(zzz340, zzz341, zzz34200, zzz343, zzz344, zzz520, zzz521, zzz523, zzz524, zzz31, Zero, h) → new_mkBranch(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))), GT, zzz31, Branch(zzz520, zzz521, Neg(Zero), zzz523, zzz524), Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), ty_Ordering, h)
new_mkBalBranch6MkBalBranch412(zzz2934, zzz2127, zzz2930, zzz2931, Succ(zzz2221000), Succ(zzz223600), da, db) → new_mkBalBranch6MkBalBranch412(zzz2934, zzz2127, zzz2930, zzz2931, zzz2221000, zzz223600, da, db)
new_mkVBalBranch3MkVBalBranch132(zzz2033, zzz2034, zzz2035, zzz2036, zzz2037, zzz2038, zzz2039, zzz2040, zzz2041, zzz2042, zzz2043, Succ(zzz20440), Succ(zzz20450), fg) → new_mkVBalBranch3MkVBalBranch132(zzz2033, zzz2034, zzz2035, zzz2036, zzz2037, zzz2038, zzz2039, zzz2040, zzz2041, zzz2042, zzz2043, zzz20440, zzz20450, fg)
new_mkVBalBranch2(zzz31, Branch(zzz330, zzz331, Pos(Zero), zzz333, zzz334), Branch(zzz3170, zzz3171, Pos(Succ(zzz317200)), zzz3173, zzz3174), h) → new_mkBalBranch(zzz3170, zzz3171, new_mkVBalBranch2(zzz31, Branch(zzz330, zzz331, Pos(Zero), zzz333, zzz334), zzz3173, h), zzz3174, ty_Ordering, h)
new_mkVBalBranch2(zzz31, Branch(zzz330, zzz331, Pos(Zero), zzz333, zzz334), Branch(zzz3170, zzz3171, Neg(Succ(zzz317200)), zzz3173, zzz3174), h) → new_mkVBalBranch3MkVBalBranch145(zzz3170, zzz3171, zzz317200, zzz3173, zzz3174, zzz330, zzz331, zzz333, zzz334, zzz31, new_primMulNat1(zzz317200), h)
new_mkVBalBranch3MkVBalBranch144(zzz1702, zzz1703, zzz1704, zzz1705, zzz1706, zzz1707, zzz1708, zzz1709, zzz1710, zzz1711, zzz1712, Succ(zzz17130), Zero, df) → new_mkVBalBranch3MkVBalBranch138(zzz1702, zzz1703, zzz1704, zzz1705, zzz1706, zzz1707, zzz1708, zzz1709, zzz1710, zzz1711, zzz1712, df)
new_mkBalBranch6MkBalBranch41(zzz2934, zzz2127, zzz2930, zzz2931, da, db) → new_mkBalBranch6MkBalBranch310(zzz2934, zzz2127, zzz2930, zzz2931, new_mkBalBranch6Size_l(zzz2934, zzz2127, zzz2930, zzz2931, db, da), new_mkBalBranch6Size_r(zzz2934, zzz2127, zzz2930, zzz2931, db, da), da, db)
new_mkVBalBranch3MkVBalBranch153(zzz537, zzz538, zzz539, zzz540, zzz541, zzz542, zzz543, zzz544, zzz545, zzz546, zzz547, Succ(zzz6990), dg) → new_mkVBalBranch3MkVBalBranch144(zzz537, zzz538, zzz539, zzz540, zzz541, zzz542, zzz543, Succ(zzz544), zzz545, zzz546, zzz547, Succ(Succ(zzz544)), Succ(zzz6990), dg)
new_mkBalBranch6MkBalBranch416(zzz2934, zzz2127, zzz2930, zzz2931, Zero, da, db) → new_mkBalBranch6MkBalBranch40(zzz2934, zzz2127, zzz2930, zzz2931, da, db)
new_mkBalBranch6MkBalBranch33(zzz2934, EmptyFM, zzz2930, zzz2931, da, db) → error([])
new_mkVBalBranch3MkVBalBranch284(zzz340, zzz341, Zero, zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, h) → new_mkBalBranch(zzz510, zzz511, zzz513, new_mkVBalBranch4(zzz31, zzz514, Branch(zzz340, zzz341, Neg(Zero), zzz343, zzz344), h), ty_Ordering, h)
new_splitLT41(h) → new_emptyFM(h)
new_mkBalBranch6MkBalBranch5(zzz2934, zzz2127, zzz2930, zzz2931, Pos(Zero), da, db) → new_mkBalBranch6MkBalBranch51(zzz2934, zzz2127, zzz2930, zzz2931, da, db)
new_mkBalBranch6MkBalBranch310(zzz2934, zzz2127, zzz2930, zzz2931, Pos(Zero), Pos(zzz22450), da, db) → new_mkBalBranch6MkBalBranch35(zzz2934, zzz2127, zzz2930, zzz2931, new_primMulNat(zzz22450), da, db)
new_splitGT15(EmptyFM, cc) → new_splitGT40(cc)
new_mkBalBranch6MkBalBranch1115(zzz2934, zzz21270, zzz21271, zzz21272, zzz21273, Branch(zzz212740, zzz212741, zzz212742, zzz212743, zzz212744), zzz2930, zzz2931, da, db) → new_mkBranch(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))), zzz212740, zzz212741, new_mkBranch(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))), zzz21270, zzz21271, zzz21273, zzz212743, da, db), new_mkBranch(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))), zzz2930, zzz2931, zzz212744, zzz2934, da, db), da, db)
new_primMulNat(Succ(zzz206300)) → new_primPlusNat2(new_primMulNat0(zzz206300), Succ(zzz206300))
new_addToFM_C4(Branch(EQ, zzz341, zzz342, zzz343, zzz344), zzz31, h) → Branch(EQ, new_addToFM0(zzz341, zzz31, h), zzz342, zzz343, zzz344)
new_mkBalBranch6MkBalBranch019(zzz29340, zzz29341, zzz29342, zzz29343, zzz29344, zzz2127, zzz2930, zzz2931, Succ(zzz22590), da, db) → new_mkBalBranch6MkBalBranch013(zzz29340, zzz29341, zzz29342, zzz29343, zzz29344, zzz2127, zzz2930, zzz2931, zzz22590, Zero, da, db)
new_mkBalBranch6MkBalBranch413(zzz2934, zzz2127, zzz2930, zzz2931, Succ(zzz22430), da, db) → new_mkBalBranch6MkBalBranch45(zzz2934, zzz2127, zzz2930, zzz2931, zzz22430, Zero, da, db)
new_mkBalBranch6MkBalBranch36(zzz2934, zzz2127, zzz2930, zzz2931, Zero, zzz224400, da, db) → new_mkBalBranch6MkBalBranch31(zzz2934, zzz2127, zzz2930, zzz2931, da, db)
new_mkBalBranch6MkBalBranch49(EmptyFM, zzz2127, zzz2930, zzz2931, da, db) → error([])
new_mkVBalBranch3MkVBalBranch141(zzz972, zzz973, zzz974, zzz975, zzz976, zzz977, zzz978, zzz979, zzz980, zzz981, zzz982, Zero, cg) → new_mkVBalBranch3MkVBalBranch134(zzz972, zzz973, zzz974, zzz975, zzz976, zzz977, zzz978, zzz979, zzz980, zzz981, zzz982, Succ(zzz979), Zero, cg)
new_mkVBalBranch3MkVBalBranch134(zzz1851, zzz1852, zzz1853, zzz1854, zzz1855, zzz1856, zzz1857, zzz1858, zzz1859, zzz1860, zzz1861, Zero, Zero, dd) → new_mkVBalBranch3MkVBalBranch135(zzz1851, zzz1852, zzz1853, zzz1854, zzz1855, zzz1856, zzz1857, zzz1858, zzz1859, zzz1860, zzz1861, dd)
new_mkBalBranch6MkBalBranch411(zzz2934, zzz2127, zzz2930, zzz2931, Neg(Succ(zzz222100)), Pos(zzz22060), da, db) → new_mkBalBranch6MkBalBranch42(zzz2934, zzz2127, zzz2930, zzz2931, zzz222100, new_primMulNat(zzz22060), da, db)
new_mkVBalBranch3MkVBalBranch255(zzz537, zzz538, zzz539, zzz540, zzz541, zzz542, zzz543, zzz544, zzz545, zzz546, zzz547, Zero, Succ(zzz5490), dg) → new_mkBalBranch(zzz537, zzz538, new_mkVBalBranch3(zzz547, Branch(zzz542, zzz543, Neg(Succ(Succ(zzz544))), zzz545, zzz546), zzz540, dg), zzz541, ty_Ordering, dg)
new_mkVBalBranch3MkVBalBranch151(zzz1337, zzz1338, zzz1339, zzz1340, zzz1341, zzz1342, zzz1343, zzz1344, zzz1345, zzz1346, zzz1347, eg) → new_mkBranch(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))), LT, zzz1347, Branch(zzz1342, zzz1343, Pos(Succ(zzz1344)), zzz1345, zzz1346), Branch(zzz1337, zzz1338, Pos(Succ(zzz1339)), zzz1340, zzz1341), ty_Ordering, eg)
new_splitGT15(Branch(GT, zzz21291, zzz21292, zzz21293, zzz21294), cc) → zzz21294
new_splitGT25(zzz854, zzz855, zzz856, zzz857, ba) → new_mkVBalBranch4(zzz854, new_splitGT12(zzz856, ba), zzz857, ba)
new_mkVBalBranch3MkVBalBranch144(zzz1702, zzz1703, zzz1704, zzz1705, zzz1706, zzz1707, zzz1708, zzz1709, zzz1710, zzz1711, zzz1712, Zero, Zero, df) → new_mkVBalBranch3MkVBalBranch138(zzz1702, zzz1703, zzz1704, zzz1705, zzz1706, zzz1707, zzz1708, zzz1709, zzz1710, zzz1711, zzz1712, df)
new_mkVBalBranch3MkVBalBranch288(zzz340, zzz341, Pos(Succ(Zero)), zzz343, zzz344, zzz510, zzz511, Zero, zzz513, zzz514, zzz31, Zero, h) → new_mkVBalBranch3MkVBalBranch287(zzz340, zzz341, zzz343, zzz344, zzz510, zzz511, Zero, zzz513, zzz514, zzz31, h)
new_mkBalBranch6MkBalBranch017(zzz29340, zzz29341, zzz29342, zzz29343, zzz29344, zzz2127, zzz2930, zzz2931, Pos(Succ(zzz224600)), Pos(zzz22470), da, db) → new_mkBalBranch6MkBalBranch013(zzz29340, zzz29341, zzz29342, zzz29343, zzz29344, zzz2127, zzz2930, zzz2931, zzz224600, new_primMulNat2(zzz22470), da, db)
new_mkBalBranch6MkBalBranch310(zzz2934, zzz2127, zzz2930, zzz2931, Pos(Succ(zzz224400)), Pos(zzz22450), da, db) → new_mkBalBranch6MkBalBranch311(zzz2934, zzz2127, zzz2930, zzz2931, zzz224400, new_primMulNat(zzz22450), da, db)
new_primMinusNat0(Succ(zzz100100), Succ(zzz542000)) → new_primMinusNat0(zzz100100, zzz542000)

The set Q consists of the following terms:

new_mkVBalBranch3MkVBalBranch281(x0, x1, Neg(Succ(Succ(Succ(x2)))), x3, x4, x5, x6, Succ(x7), x8, x9, x10, Succ(Succ(x11)), x12)
new_mkBalBranch6MkBalBranch35(x0, x1, x2, x3, Zero, x4, x5)
new_mkVBalBranch2(x0, Branch(x1, x2, Pos(Zero), x3, x4), Branch(x5, x6, Pos(Zero), x7, x8), x9)
new_mkVBalBranch3MkVBalBranch159(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, Zero, x11)
new_addToFM_C2(Branch(LT, x0, x1, x2, x3), x4, x5)
new_primMulNat1(x0)
new_primMinusNat0(Zero, Zero)
new_mkVBalBranch3MkVBalBranch281(x0, x1, Neg(Zero), x2, x3, x4, x5, x6, x7, x8, x9, Succ(x10), x11)
new_mkVBalBranch3MkVBalBranch263(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, Succ(x10), Succ(x11), x12)
new_mkVBalBranch3MkVBalBranch163(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11)
new_primPlusInt(Pos(x0), x1, x2, x3, x4, x5)
new_primMulNat0(x0)
new_mkBalBranch6MkBalBranch116(x0, x1, x2, x3, x4, x5, x6, x7, Succ(x8), x9, x10)
new_mkVBalBranch3(x0, EmptyFM, x1, x2)
new_mkVBalBranch3MkVBalBranch281(x0, x1, Neg(Succ(Succ(x2))), x3, x4, x5, x6, Zero, x7, x8, x9, Zero, x10)
new_mkBalBranch6MkBalBranch411(x0, x1, x2, x3, Pos(Succ(x4)), Pos(x5), x6, x7)
new_mkBalBranch6MkBalBranch1113(x0, x1, x2, x3, x4, x5, x6, x7, Zero, Succ(x8), x9, x10)
new_mkVBalBranch3MkVBalBranch157(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, Succ(x10), x11)
new_mkVBalBranch3MkVBalBranch278(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11)
new_mkVBalBranch3MkVBalBranch281(x0, x1, Neg(Zero), x2, x3, x4, x5, x6, x7, x8, x9, Zero, x10)
new_mkVBalBranch3MkVBalBranch281(x0, x1, Neg(Succ(Succ(x2))), x3, x4, x5, x6, Succ(x7), x8, x9, x10, Zero, x11)
new_mkVBalBranch3MkVBalBranch269(x0, x1, Succ(x2), x3, x4, x5, x6, x7, x8, x9, x10, x11)
new_mkVBalBranch4(x0, Branch(x1, x2, Pos(Zero), x3, x4), Branch(x5, x6, Pos(Succ(x7)), x8, x9), x10)
new_mkVBalBranch3MkVBalBranch247(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11)
new_mkBalBranch6MkBalBranch315(x0, x1, x2, x3, Succ(x4), x5, x6)
new_mkVBalBranch3MkVBalBranch272(x0, x1, Neg(Succ(Zero)), x2, x3, x4, x5, Succ(x6), x7, x8, x9, Zero, x10)
new_mkVBalBranch3(x0, Branch(x1, x2, Neg(Succ(x3)), x4, x5), Branch(x6, x7, x8, x9, x10), x11)
new_addToFM_C3(Branch(EQ, x0, x1, x2, x3), x4, x5)
new_mkVBalBranch3MkVBalBranch158(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11)
new_mkVBalBranch3MkVBalBranch270(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, Succ(x10), Zero, x11)
new_mkVBalBranch3MkVBalBranch159(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, Succ(x11), x12)
new_splitGT4(x0, x1, x2, x3)
new_mkVBalBranch3MkVBalBranch261(x0, x1, Pos(Succ(x2)), x3, x4, x5, x6, x7, x8, x9, x10, Succ(x11), x12)
new_mkVBalBranch3MkVBalBranch137(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, Succ(x11), x12)
new_mkBalBranch6MkBalBranch45(x0, x1, x2, x3, x4, Zero, x5, x6)
new_mkBalBranch6MkBalBranch014(x0, x1, x2, x3, x4, x5, x6, x7, Zero, Zero, x8, x9)
new_mkBalBranch6MkBalBranch111(x0, x1, x2, x3, x4, x5, x6, x7, x8, Zero, x9, x10)
new_mkVBalBranch3(x0, Branch(x1, x2, Neg(Zero), x3, x4), Branch(x5, x6, Neg(Succ(x7)), x8, x9), x10)
new_mkBalBranch6MkBalBranch116(x0, x1, x2, x3, x4, x5, x6, x7, Zero, x8, x9)
new_mkBalBranch6MkBalBranch015(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9)
new_mkBalBranch6MkBalBranch5(x0, x1, x2, x3, Pos(Succ(Succ(Zero))), x4, x5)
new_mkBalBranch6MkBalBranch49(EmptyFM, x0, x1, x2, x3, x4)
new_primMinusNat0(Succ(x0), Zero)
new_mkVBalBranch3MkVBalBranch157(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, Zero, x10)
new_mkBalBranch6MkBalBranch33(x0, Branch(x1, x2, x3, x4, x5), x6, x7, x8, x9)
new_mkVBalBranch3MkVBalBranch266(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10)
new_addToFM_C2(Branch(EQ, x0, x1, x2, x3), x4, x5)
new_mkVBalBranch3MkVBalBranch263(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, Zero, Succ(x10), x11)
new_mkBalBranch6MkBalBranch51(x0, x1, x2, x3, x4, x5)
new_mkVBalBranch3MkVBalBranch287(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10)
new_mkBalBranch6MkBalBranch013(x0, x1, x2, x3, x4, x5, x6, x7, x8, Zero, x9, x10)
new_mkBalBranch6MkBalBranch312(x0, x1, x2, x3, x4, x5, x6, x7)
new_mkVBalBranch3MkVBalBranch267(x0, x1, Pos(Zero), x2, x3, x4, x5, x6, x7, x8, x9, Succ(x10), x11)
new_addToFM2(x0, x1, x2)
new_mkVBalBranch3MkVBalBranch155(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, Zero, x10)
new_splitLT11(x0, x1, x2, x3)
new_mkVBalBranch3MkVBalBranch272(x0, x1, Neg(Succ(Succ(Zero))), x2, x3, x4, x5, Zero, x6, x7, x8, Succ(Succ(x9)), x10)
new_mkVBalBranch3MkVBalBranch281(x0, x1, Neg(Succ(Zero)), x2, x3, x4, x5, Succ(x6), x7, x8, x9, Zero, x10)
new_splitLT6(x0)
new_mkVBalBranch3MkVBalBranch161(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, Zero, x10)
new_mkVBalBranch3MkVBalBranch134(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, Succ(x11), Zero, x12)
new_mkBalBranch6MkBalBranch39(x0, x1, x2, x3, Zero, Zero, x4, x5)
new_splitLT24(x0, x1, x2, x3, x4)
new_mkVBalBranch3MkVBalBranch288(x0, x1, Pos(Zero), x2, x3, x4, x5, x6, x7, x8, x9, Zero, x10)
new_mkBalBranch6MkBalBranch310(x0, x1, x2, x3, Pos(Zero), Neg(x4), x5, x6)
new_mkBalBranch6MkBalBranch310(x0, x1, x2, x3, Neg(Zero), Pos(x4), x5, x6)
new_mkVBalBranch3MkVBalBranch285(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10)
new_mkVBalBranch2(x0, Branch(x1, x2, x3, x4, x5), EmptyFM, x6)
new_mkVBalBranch3MkVBalBranch272(x0, x1, Neg(Succ(Succ(Zero))), x2, x3, x4, x5, Zero, x6, x7, x8, Succ(Zero), x9)
new_mkVBalBranch3MkVBalBranch141(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, Succ(x11), x12)
new_splitLT15(Branch(GT, x0, x1, x2, x3), x4)
new_mkVBalBranch3MkVBalBranch265(x0, x1, Zero, x2, x3, x4, x5, x6, x7, x8, x9, x10)
new_mkVBalBranch3MkVBalBranch267(x0, x1, Pos(Succ(x2)), x3, x4, x5, x6, x7, x8, x9, x10, Zero, x11)
new_mkBalBranch6MkBalBranch017(x0, x1, x2, x3, x4, x5, x6, x7, Pos(Succ(x8)), Pos(x9), x10, x11)
new_mkBalBranch6MkBalBranch412(x0, x1, x2, x3, Zero, Zero, x4, x5)
new_mkVBalBranch3MkVBalBranch288(x0, x1, Pos(Succ(Succ(x2))), x3, x4, x5, x6, Succ(x7), x8, x9, x10, Zero, x11)
new_splitGT41(x0)
new_mkBalBranch6MkBalBranch110(x0, x1, x2, x3, x4, x5, x6, x7, Succ(x8), x9, x10)
new_mkBalBranch6MkBalBranch416(x0, x1, x2, x3, Zero, x4, x5)
new_splitGT15(Branch(GT, x0, x1, x2, x3), x4)
new_mkVBalBranch3MkVBalBranch277(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, Zero, Succ(x10), x11)
new_mkBalBranch6MkBalBranch017(x0, x1, x2, x3, x4, x5, x6, x7, Pos(Zero), Pos(x8), x9, x10)
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_mkBalBranch6MkBalBranch310(x0, x1, x2, x3, Neg(Succ(x4)), Pos(x5), x6, x7)
new_mkBalBranch6MkBalBranch310(x0, x1, x2, x3, Pos(Succ(x4)), Neg(x5), x6, x7)
new_mkVBalBranch2(x0, Branch(x1, x2, Pos(Zero), x3, x4), Branch(x5, x6, Neg(Zero), x7, x8), x9)
new_mkVBalBranch2(x0, Branch(x1, x2, Neg(Zero), x3, x4), Branch(x5, x6, Pos(Zero), x7, x8), x9)
new_mkVBalBranch3MkVBalBranch289(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, Succ(x11), Succ(x12), x13)
new_mkBalBranch6MkBalBranch310(x0, x1, x2, x3, Neg(Succ(x4)), Neg(x5), x6, x7)
new_mkVBalBranch3MkVBalBranch139(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, Succ(x11), x12)
new_splitGT26(x0, x1, x2, x3, x4)
new_mkBalBranch6MkBalBranch1113(x0, x1, x2, x3, x4, x5, x6, x7, Succ(x8), Zero, x9, x10)
new_primPlusNat2(Zero, Zero)
new_mkVBalBranch3MkVBalBranch143(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, Zero, x10)
new_mkVBalBranch3MkVBalBranch277(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, Succ(x10), Zero, x11)
new_splitGT14(Branch(EQ, x0, x1, x2, x3), x4)
new_splitLT10(x0, x1, x2, x3)
new_mkVBalBranch4(x0, Branch(x1, x2, Pos(Succ(x3)), x4, x5), Branch(x6, x7, x8, x9, x10), x11)
new_addToFM_C2(EmptyFM, x0, x1)
new_mkVBalBranch3MkVBalBranch156(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, Zero, x11)
new_mkVBalBranch3MkVBalBranch262(x0, x1, Pos(Succ(x2)), x3, x4, x5, x6, x7, x8, x9, x10, Zero, x11)
new_splitLT12(EmptyFM, x0)
new_mkVBalBranch3MkVBalBranch271(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10)
new_mkVBalBranch4(x0, Branch(x1, x2, x3, x4, x5), EmptyFM, x6)
new_intersectFM_C2Gts1(x0, x1, x2, x3, x4)
new_mkVBalBranch3MkVBalBranch155(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, Succ(x10), x11)
new_mkVBalBranch3MkVBalBranch272(x0, x1, Neg(Succ(Succ(Succ(x2)))), x3, x4, x5, x6, Succ(x7), x8, x9, x10, Succ(Zero), x11)
new_mkBalBranch6MkBalBranch41(x0, x1, x2, x3, x4, x5)
new_mkVBalBranch4(x0, Branch(x1, x2, Neg(Zero), x3, x4), Branch(x5, x6, Neg(Zero), x7, x8), x9)
new_mkVBalBranch3(x0, Branch(x1, x2, Pos(Zero), x3, x4), Branch(x5, x6, Pos(Zero), x7, x8), x9)
new_mkVBalBranch3MkVBalBranch156(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, Succ(x11), x12)
new_mkBalBranch6MkBalBranch018(x0, x1, x2, x3, x4, x5, x6, x7, Succ(x8), x9, x10, x11)
new_mkBalBranch6MkBalBranch1111(x0, x1, x2, x3, x4, x5, x6, x7, Zero, x8, x9, x10)
new_mkVBalBranch3MkVBalBranch270(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, Zero, Succ(x10), x11)
new_primPlusNat2(Zero, Succ(x0))
new_mkBalBranch6MkBalBranch113(x0, x1, x2, x3, x4, x5, x6, x7, Neg(Succ(x8)), Neg(x9), x10, x11)
new_mkVBalBranch3MkVBalBranch272(x0, x1, Neg(Succ(Zero)), x2, x3, x4, x5, Zero, x6, x7, x8, Zero, x9)
new_mkVBalBranch3MkVBalBranch261(x0, x1, Neg(x2), x3, x4, x5, x6, x7, x8, x9, x10, Succ(x11), x12)
new_addToFM1(x0, x1, x2)
new_mkVBalBranch3MkVBalBranch284(x0, x1, Zero, x2, x3, x4, x5, x6, x7, x8, x9, x10)
new_mkVBalBranch3MkVBalBranch136(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11)
new_splitLT15(EmptyFM, x0)
new_mkBalBranch6MkBalBranch013(x0, x1, x2, x3, x4, x5, x6, x7, x8, Succ(x9), x10, x11)
new_mkVBalBranch3MkVBalBranch166(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11)
new_mkVBalBranch3MkVBalBranch144(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, Zero, Zero, x11)
new_splitLT41(x0)
new_mkBalBranch6MkBalBranch5(x0, x1, x2, x3, Neg(Succ(x4)), x5, x6)
new_splitLT4(x0, x1, x2, x3)
new_splitLT14(Branch(GT, x0, x1, x2, x3), x4)
new_mkBalBranch6MkBalBranch010(x0, x1, x2, x3, x4, x5, x6, x7, Zero, x8, x9)
new_primPlusNat3(x0, Zero)
new_mkVBalBranch3MkVBalBranch255(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, Zero, Succ(x11), x12)
new_mkVBalBranch3MkVBalBranch272(x0, x1, Pos(x2), x3, x4, x5, x6, x7, x8, x9, x10, Zero, x11)
new_splitGT25(x0, x1, x2, x3, x4)
new_mkBalBranch6MkBalBranch35(x0, x1, x2, x3, Succ(x4), x5, x6)
new_splitLT12(Branch(LT, x0, x1, x2, x3), x4)
new_intersectFM_C2Gts0(x0, x1, x2, x3, x4)
new_primMulNat(Zero)
new_primPlusNat1(Succ(x0))
new_mkVBalBranch3MkVBalBranch273(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10)
new_mkVBalBranch3MkVBalBranch152(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, Zero, Zero, x11)
new_splitGT15(Branch(EQ, x0, x1, x2, x3), x4)
new_mkVBalBranch3MkVBalBranch262(x0, x1, Pos(x2), x3, x4, x5, x6, x7, x8, x9, x10, Succ(x11), x12)
new_mkBalBranch6MkBalBranch017(x0, x1, x2, x3, x4, x5, x6, x7, Neg(Zero), Pos(x8), x9, x10)
new_primPlusInt2(Pos(x0), x1, x2, x3, x4, x5, x6)
new_mkBalBranch6MkBalBranch017(x0, x1, x2, x3, x4, x5, x6, x7, Pos(Zero), Neg(x8), x9, x10)
new_mkVBalBranch3MkVBalBranch275(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, Succ(x11), Zero, x12)
new_mkVBalBranch3MkVBalBranch255(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, Zero, Zero, x11)
new_addToFM_C2(Branch(GT, x0, x1, x2, x3), x4, x5)
new_splitGT10(x0, x1, x2, x3)
new_mkVBalBranch3MkVBalBranch149(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, Zero, Zero, x11)
new_mkVBalBranch3MkVBalBranch245(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10)
new_mkBalBranch6MkBalBranch39(x0, x1, x2, x3, Zero, Succ(x4), x5, x6)
new_mkVBalBranch3MkVBalBranch289(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, Zero, Zero, x11)
new_mkVBalBranch3MkVBalBranch276(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11)
new_mkVBalBranch3MkVBalBranch275(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, Zero, Zero, x11)
new_mkVBalBranch3MkVBalBranch277(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, Succ(x10), Succ(x11), x12)
new_splitLT7(x0, x1, x2, x3, x4)
new_mkVBalBranch3MkVBalBranch261(x0, x1, Neg(Zero), x2, x3, x4, x5, x6, x7, x8, x9, Zero, x10)
new_splitGT12(Branch(EQ, x0, x1, x2, x3), x4)
new_intersectFM_C2Gts(x0, x1, x2, x3, x4)
new_mkVBalBranch3MkVBalBranch289(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, Zero, Succ(x11), x12)
new_mkVBalBranch3MkVBalBranch281(x0, x1, Neg(Succ(Zero)), x2, x3, x4, x5, x6, x7, x8, x9, Succ(x10), x11)
new_mkBalBranch6MkBalBranch413(x0, x1, x2, x3, Zero, x4, x5)
new_addToFM_C4(Branch(GT, x0, x1, x2, x3), x4, x5)
new_mkBalBranch6MkBalBranch413(x0, x1, x2, x3, Succ(x4), x5, x6)
new_mkVBalBranch3MkVBalBranch281(x0, x1, Neg(Succ(Succ(Succ(x2)))), x3, x4, x5, x6, Succ(x7), x8, x9, x10, Succ(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_mkBalBranch6MkBalBranch34(x0, x1, x2, x3, x4, x5, x6, x7)
new_mkVBalBranch3MkVBalBranch265(x0, x1, Succ(x2), x3, x4, x5, x6, x7, x8, x9, x10, x11)
new_intersectFM_C2Lts3(x0, x1)
new_mkBalBranch6MkBalBranch314(x0, x1, x2, x3, Zero, x4, x5)
new_mkVBalBranch3MkVBalBranch145(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, Succ(x10), x11)
new_splitLT9(x0, x1, x2, x3, x4)
new_mkBalBranch6Size_r(x0, x1, x2, x3, x4, x5)
new_mkBalBranch6MkBalBranch43(x0, x1, x2, x3, x4, x5)
new_mkVBalBranch3MkVBalBranch283(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11)
new_splitGT29(x0, x1, x2, x3, x4)
new_mkBalBranch6MkBalBranch30(x0, x1, x2, x3, Zero, x4, x5)
new_mkVBalBranch3MkVBalBranch146(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, Zero, x10)
new_sizeFM(EmptyFM, x0, x1)
new_mkVBalBranch3MkVBalBranch281(x0, x1, Neg(Succ(Zero)), x2, x3, x4, x5, Zero, x6, x7, x8, Zero, x9)
new_mkVBalBranch3MkVBalBranch281(x0, x1, Neg(Succ(Succ(Succ(x2)))), x3, x4, x5, x6, Zero, x7, x8, x9, Succ(Succ(x10)), x11)
new_mkVBalBranch3MkVBalBranch152(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, Succ(x11), Zero, x12)
new_mkVBalBranch3MkVBalBranch288(x0, x1, Pos(Succ(Succ(x2))), x3, x4, x5, x6, Zero, x7, x8, x9, Succ(Zero), x10)
new_mkVBalBranch3MkVBalBranch249(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10)
new_mkVBalBranch3MkVBalBranch135(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11)
new_mkVBalBranch3MkVBalBranch254(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10)
new_splitLT28(x0, x1, x2, x3, x4)
new_mkBalBranch6MkBalBranch47(x0, x1, x2, x3, Succ(x4), x5, x6, x7)
new_mkBalBranch6MkBalBranch014(x0, x1, x2, x3, x4, x5, x6, x7, Succ(x8), Succ(x9), x10, x11)
new_mkVBalBranch2(x0, Branch(x1, x2, Pos(Zero), x3, x4), Branch(x5, x6, Neg(Succ(x7)), x8, x9), x10)
new_mkVBalBranch2(x0, Branch(x1, x2, Neg(Zero), x3, x4), Branch(x5, x6, Pos(Succ(x7)), x8, x9), x10)
new_addToFM_C4(EmptyFM, x0, x1)
new_mkBalBranch6MkBalBranch313(x0, x1, x2, x3, x4, x5)
new_mkVBalBranch3MkVBalBranch267(x0, x1, Pos(Zero), x2, x3, x4, x5, x6, x7, x8, x9, Zero, x10)
new_mkVBalBranch3MkVBalBranch248(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11)
new_splitGT14(EmptyFM, x0)
new_mkVBalBranch3MkVBalBranch132(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, Succ(x11), Zero, x12)
new_mkVBalBranch3MkVBalBranch144(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, Succ(x11), Succ(x12), x13)
new_mkVBalBranch3MkVBalBranch261(x0, x1, Neg(Succ(x2)), x3, x4, x5, x6, x7, x8, x9, x10, Zero, x11)
new_mkBalBranch6MkBalBranch410(x0, x1, x2, x3, x4, x5, x6)
new_mkVBalBranch2(x0, Branch(x1, x2, Pos(Succ(x3)), x4, x5), Branch(x6, x7, x8, x9, x10), x11)
new_mkBalBranch6MkBalBranch019(x0, x1, x2, x3, x4, x5, x6, x7, Zero, x8, x9)
new_mkVBalBranch3MkVBalBranch280(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, Zero, Succ(x11), x12)
new_mkBalBranch6MkBalBranch014(x0, x1, x2, x3, x4, x5, x6, x7, Succ(x8), Zero, x9, x10)
new_mkVBalBranch3MkVBalBranch272(x0, x1, Neg(Succ(Succ(Zero))), x2, x3, x4, x5, Succ(x6), x7, x8, x9, Succ(Succ(x10)), x11)
new_mkVBalBranch3MkVBalBranch134(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, Zero, Zero, x11)
new_mkVBalBranch3(x0, Branch(x1, x2, Neg(Zero), x3, x4), Branch(x5, x6, Neg(Zero), x7, x8), x9)
new_mkVBalBranch3MkVBalBranch280(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, Succ(x11), Succ(x12), x13)
new_primPlusNat2(Succ(x0), Succ(x1))
new_splitGT12(Branch(GT, x0, x1, x2, x3), x4)
new_mkVBalBranch3MkVBalBranch145(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, Zero, x10)
new_mkVBalBranch3MkVBalBranch272(x0, x1, Neg(Succ(Zero)), x2, x3, x4, x5, x6, x7, x8, x9, Succ(x10), x11)
new_mkVBalBranch3MkVBalBranch288(x0, x1, Pos(Succ(Succ(x2))), x3, x4, x5, x6, Succ(x7), x8, x9, x10, Succ(Succ(x11)), x12)
new_mkVBalBranch3MkVBalBranch262(x0, x1, Neg(Zero), x2, x3, x4, x5, x6, x7, x8, x9, Succ(x10), x11)
new_mkBalBranch6MkBalBranch414(x0, x1, x2, x3, Zero, x4, x5)
new_mkVBalBranch4(x0, Branch(x1, x2, Neg(Zero), x3, x4), Branch(x5, x6, Pos(Zero), x7, x8), x9)
new_mkVBalBranch4(x0, Branch(x1, x2, Pos(Zero), x3, x4), Branch(x5, x6, Neg(Zero), x7, x8), x9)
new_splitGT12(Branch(LT, x0, x1, x2, x3), x4)
new_mkVBalBranch3MkVBalBranch270(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, Zero, Zero, x10)
new_mkVBalBranch3MkVBalBranch288(x0, x1, Pos(Succ(Succ(x2))), x3, x4, x5, x6, Succ(x7), x8, x9, x10, Succ(Zero), x11)
new_splitLT12(Branch(GT, x0, x1, x2, x3), x4)
new_mkVBalBranch3MkVBalBranch282(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11)
new_mkVBalBranch3MkVBalBranch272(x0, x1, Neg(Succ(Succ(Zero))), x2, x3, x4, x5, Succ(x6), x7, x8, x9, Succ(Zero), x10)
new_mkBalBranch6MkBalBranch315(x0, x1, x2, x3, Zero, x4, x5)
new_primPlusInt(Neg(x0), x1, x2, x3, x4, x5)
new_mkVBalBranch3MkVBalBranch272(x0, x1, Pos(x2), x3, x4, x5, x6, x7, x8, x9, x10, Succ(x11), x12)
new_mkVBalBranch3MkVBalBranch149(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, Zero, Succ(x11), x12)
new_mkBalBranch6MkBalBranch019(x0, x1, x2, x3, x4, x5, x6, x7, Succ(x8), x9, x10)
new_mkVBalBranch3MkVBalBranch252(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, Succ(x11), Zero, x12)
new_mkVBalBranch3MkVBalBranch153(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, Zero, x11)
new_mkBalBranch6MkBalBranch32(x0, x1, x2, x3, x4, x5)
new_mkVBalBranch3MkVBalBranch280(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, Zero, Zero, x11)
new_splitGT3(x0, x1, x2, x3, x4)
new_splitLT25(x0, x1, x2, x3, x4)
new_mkBalBranch6MkBalBranch111(x0, x1, x2, x3, x4, x5, x6, x7, x8, Succ(x9), x10, x11)
new_mkVBalBranch3MkVBalBranch164(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, Zero, x10)
new_mkBalBranch6MkBalBranch117(x0, x1, x2, x3, x4, x5, x6, x7, Succ(x8), x9, x10)
new_mkVBalBranch3MkVBalBranch132(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, Zero, Succ(x11), x12)
new_splitGT210(x0, x1, x2, x3, x4)
new_mkBalBranch6MkBalBranch30(x0, x1, x2, x3, Succ(x4), x5, x6)
new_mkVBalBranch3MkVBalBranch165(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11)
new_mkBalBranch6MkBalBranch31(x0, x1, x2, x3, x4, x5)
new_mkVBalBranch3MkVBalBranch133(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, Zero, x10)
new_mkVBalBranch3MkVBalBranch167(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, Succ(x11), x12)
new_mkVBalBranch3MkVBalBranch144(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, Zero, Succ(x11), x12)
new_splitGT8(x0, x1, x2, x3)
new_splitGT9(x0, x1, x2, x3, x4)
new_mkVBalBranch3MkVBalBranch256(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11)
new_intersectFM_C2Gts2(x0, x1, x2, x3, x4)
new_splitGT16(x0)
new_mkVBalBranch3MkVBalBranch260(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10)
new_splitLT42(x0)
new_splitGT15(Branch(LT, x0, x1, x2, x3), x4)
new_splitLT14(EmptyFM, x0)
new_splitLT14(Branch(LT, x0, x1, x2, x3), x4)
new_addToFM_C4(Branch(EQ, x0, x1, x2, x3), x4, x5)
new_mkBalBranch6MkBalBranch1113(x0, x1, x2, x3, x4, x5, x6, x7, Succ(x8), Succ(x9), x10, x11)
new_mkBalBranch6MkBalBranch415(x0, x1, x2, x3, x4, x5, x6, x7)
new_mkBalBranch6MkBalBranch0110(x0, x1, x2, x3, x4, x5, x6, x7, Zero, x8, x9)
new_mkVBalBranch3MkVBalBranch151(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11)
new_mkVBalBranch3MkVBalBranch262(x0, x1, Pos(Zero), x2, x3, x4, x5, x6, x7, x8, x9, Zero, x10)
new_mkVBalBranch3(x0, Branch(x1, x2, Pos(Zero), x3, x4), Branch(x5, x6, Neg(Zero), x7, x8), x9)
new_mkVBalBranch3(x0, Branch(x1, x2, Neg(Zero), x3, x4), Branch(x5, x6, Pos(Zero), x7, x8), x9)
new_splitGT11(x0, x1, x2, x3)
new_mkVBalBranch2(x0, Branch(x1, x2, Neg(Zero), x3, x4), Branch(x5, x6, Neg(Zero), x7, x8), x9)
new_mkVBalBranch3(x0, Branch(x1, x2, x3, x4, x5), EmptyFM, x6)
new_mkVBalBranch3MkVBalBranch263(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, Zero, Zero, x10)
new_mkVBalBranch3(x0, Branch(x1, x2, Pos(Zero), x3, x4), Branch(x5, x6, Pos(Succ(x7)), x8, x9), x10)
new_mkBalBranch6MkBalBranch310(x0, x1, x2, x3, Neg(Zero), Neg(x4), x5, x6)
new_mkVBalBranch3MkVBalBranch147(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, Succ(x11), x12)
new_mkBalBranch6MkBalBranch42(x0, x1, x2, x3, x4, x5, x6, x7)
new_mkBalBranch6MkBalBranch310(x0, x1, x2, x3, Pos(Succ(x4)), Pos(x5), x6, x7)
new_mkVBalBranch3MkVBalBranch275(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, Succ(x11), Succ(x12), x13)
new_splitGT24(x0, x1, x2, x3, x4)
new_mkVBalBranch3MkVBalBranch153(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, Succ(x11), x12)
new_mkVBalBranch3MkVBalBranch288(x0, x1, Pos(Succ(Zero)), x2, x3, x4, x5, Zero, x6, x7, x8, Zero, x9)
new_mkVBalBranch4(x0, Branch(x1, x2, Pos(Zero), x3, x4), Branch(x5, x6, Pos(Zero), x7, x8), x9)
new_mkBalBranch6MkBalBranch1110(x0, x1, x2, x3, x4, x5, x6, x7, Succ(x8), x9, x10)
new_splitGT28(x0, x1, x2, x3, x4)
new_mkBalBranch6MkBalBranch48(x0, x1, x2, x3, Succ(x4), x5, x6)
new_mkVBalBranch3MkVBalBranch275(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, Zero, Succ(x11), x12)
new_mkVBalBranch3MkVBalBranch284(x0, x1, Succ(x2), x3, x4, x5, x6, x7, x8, x9, x10, x11)
new_mkVBalBranch3MkVBalBranch267(x0, x1, Neg(x2), x3, x4, x5, x6, x7, x8, x9, x10, Zero, x11)
new_mkBalBranch6MkBalBranch016(x0, x1, x2, EmptyFM, x3, x4, x5, x6, x7, x8)
new_intersectFM_C2Lts1(x0, x1, x2, x3, x4)
new_mkBalBranch6MkBalBranch416(x0, x1, x2, x3, Succ(x4), x5, x6)
new_mkVBalBranch3MkVBalBranch252(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, Succ(x11), Succ(x12), x13)
new_mkVBalBranch3MkVBalBranch149(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, Succ(x11), Zero, x12)
new_mkVBalBranch3MkVBalBranch146(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, Succ(x10), x11)
new_mkVBalBranch3MkVBalBranch148(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11)
new_mkBalBranch6MkBalBranch113(x0, x1, x2, x3, x4, x5, x6, x7, Pos(Zero), Pos(x8), x9, x10)
new_mkBalBranch6MkBalBranch411(x0, x1, x2, x3, Pos(Zero), Neg(x4), x5, x6)
new_mkBalBranch6MkBalBranch411(x0, x1, x2, x3, Neg(Zero), Pos(x4), x5, x6)
new_mkVBalBranch4(x0, EmptyFM, x1, x2)
new_splitGT13(x0)
new_mkBalBranch6MkBalBranch1115(x0, x1, x2, x3, x4, EmptyFM, x5, x6, x7, x8)
new_splitLT27(x0, x1, x2, x3, x4)
new_mkBalBranch6MkBalBranch5(x0, x1, x2, x3, Pos(Succ(Zero)), x4, x5)
new_primMinusNat0(Zero, Succ(x0))
new_mkBalBranch6MkBalBranch5(x0, x1, x2, x3, Pos(Zero), x4, x5)
new_splitGT12(EmptyFM, x0)
new_mkVBalBranch3MkVBalBranch288(x0, x1, Pos(Succ(Zero)), x2, x3, x4, x5, Succ(x6), x7, x8, x9, Zero, x10)
new_mkBalBranch6MkBalBranch39(x0, x1, x2, x3, Succ(x4), Zero, x5, x6)
new_mkVBalBranch3MkVBalBranch274(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10)
new_mkVBalBranch3MkVBalBranch288(x0, x1, Pos(Succ(Succ(x2))), x3, x4, x5, x6, Zero, x7, x8, x9, Zero, x10)
new_mkBalBranch6MkBalBranch310(x0, x1, x2, x3, Pos(Zero), Pos(x4), x5, x6)
new_mkBalBranch6MkBalBranch411(x0, x1, x2, x3, Neg(Succ(x4)), Neg(x5), x6, x7)
new_mkVBalBranch3MkVBalBranch272(x0, x1, Neg(Succ(Succ(Succ(x2)))), x3, x4, x5, x6, Zero, x7, x8, x9, Succ(Zero), x10)
new_primPlusNat1(Zero)
new_mkVBalBranch3MkVBalBranch263(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, Succ(x10), Zero, x11)
new_mkVBalBranch2(x0, Branch(x1, x2, Pos(Zero), x3, x4), Branch(x5, x6, Pos(Succ(x7)), x8, x9), x10)
new_mkBalBranch6MkBalBranch50(x0, x1, x2, x3, x4, x5)
new_mkBalBranch(x0, x1, x2, x3, x4, x5)
new_mkVBalBranch3MkVBalBranch132(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, Zero, Zero, x11)
new_mkBalBranch6MkBalBranch5(x0, x1, x2, x3, Neg(Zero), x4, x5)
new_mkVBalBranch3MkVBalBranch272(x0, x1, Neg(Zero), x2, x3, x4, x5, x6, x7, x8, x9, Zero, x10)
new_sizeFM(Branch(x0, x1, x2, x3, x4), x5, x6)
new_mkVBalBranch3MkVBalBranch288(x0, x1, Pos(Succ(Zero)), x2, x3, x4, x5, x6, x7, x8, x9, Succ(x10), x11)
new_mkVBalBranch3MkVBalBranch252(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, Zero, Succ(x11), x12)
new_splitLT13(x0)
new_splitGT7(x0, x1, x2, x3, x4)
new_primPlusInt1(x0, Neg(x1))
new_mkBalBranch6MkBalBranch110(x0, x1, x2, x3, x4, x5, x6, x7, Zero, x8, x9)
new_mkBalBranch6MkBalBranch45(x0, x1, x2, x3, x4, Succ(x5), x6, x7)
new_splitLT14(Branch(EQ, x0, x1, x2, x3), x4)
new_mkVBalBranch3MkVBalBranch154(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, Zero, x10)
new_mkVBalBranch3MkVBalBranch264(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10)
new_mkBalBranch6MkBalBranch411(x0, x1, x2, x3, Neg(Zero), Neg(x4), x5, x6)
new_mkBalBranch6MkBalBranch40(x0, x1, x2, x3, x4, x5)
new_mkVBalBranch3MkVBalBranch251(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11)
new_addToFM_C3(Branch(GT, x0, x1, x2, x3), x4, x5)
new_mkBalBranch6MkBalBranch017(x0, x1, x2, x3, x4, x5, x6, x7, Neg(Zero), Neg(x8), x9, x10)
new_mkBalBranch6MkBalBranch112(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9)
new_mkVBalBranch3MkVBalBranch281(x0, x1, Neg(Succ(Succ(Zero))), x2, x3, x4, x5, Succ(x6), x7, x8, x9, Succ(Succ(x10)), x11)
new_mkBalBranch6MkBalBranch411(x0, x1, x2, x3, Neg(Succ(x4)), Pos(x5), x6, x7)
new_mkBalBranch6MkBalBranch411(x0, x1, x2, x3, Pos(Succ(x4)), Neg(x5), x6, x7)
new_mkBalBranch6MkBalBranch012(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9)
new_mkVBalBranch3MkVBalBranch250(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10)
new_mkVBalBranch3MkVBalBranch255(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, Succ(x11), Succ(x12), x13)
new_addToFM0(x0, x1, x2)
new_mkVBalBranch3MkVBalBranch259(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10)
new_mkVBalBranch3MkVBalBranch279(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10)
new_mkVBalBranch3MkVBalBranch281(x0, x1, Neg(Succ(Succ(Succ(x2)))), x3, x4, x5, x6, Zero, x7, x8, x9, Succ(Zero), x10)
new_mkBalBranch6MkBalBranch36(x0, x1, x2, x3, Succ(x4), x5, x6, x7)
new_splitLT23(x0, x1, x2, x3, x4)
new_mkBalBranch6MkBalBranch1111(x0, x1, x2, x3, x4, x5, x6, x7, Succ(x8), x9, x10, x11)
new_mkBalBranch6MkBalBranch0111(x0, x1, x2, x3, x4, x5, x6, x7, Zero, x8, x9)
new_addToFM_C3(EmptyFM, x0, x1)
new_splitGT15(EmptyFM, x0)
new_mkBalBranch6MkBalBranch011(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9)
new_mkVBalBranch3MkVBalBranch143(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, Succ(x10), x11)
new_mkVBalBranch3MkVBalBranch162(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, Zero, Zero, x11)
new_mkVBalBranch3MkVBalBranch134(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, Zero, Succ(x11), x12)
new_mkVBalBranch3MkVBalBranch246(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, Zero, Zero, x11)
new_mkVBalBranch3MkVBalBranch162(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, Succ(x11), Zero, x12)
new_mkVBalBranch3MkVBalBranch289(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, Succ(x11), Zero, x12)
new_mkVBalBranch3MkVBalBranch133(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, Succ(x10), x11)
new_mkVBalBranch3MkVBalBranch141(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, Zero, x11)
new_mkVBalBranch3MkVBalBranch272(x0, x1, Neg(Zero), x2, x3, x4, x5, x6, x7, x8, x9, Succ(x10), x11)
new_primPlusNat2(Succ(x0), Zero)
new_mkBalBranch6MkBalBranch119(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11)
new_mkBalBranch6MkBalBranch38(x0, x1, x2, x3, x4, Succ(x5), x6, x7)
new_mkBalBranch6MkBalBranch33(x0, EmptyFM, x1, x2, x3, x4)
new_splitLT8(x0, x1, x2, x3)
new_mkBalBranch6MkBalBranch46(x0, x1, x2, x3, x4, x5, x6, x7)
new_mkVBalBranch3MkVBalBranch267(x0, x1, Pos(Succ(x2)), x3, x4, x5, x6, x7, x8, x9, x10, Succ(x11), x12)
new_mkVBalBranch3MkVBalBranch152(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, Zero, Succ(x11), x12)
new_mkVBalBranch3MkVBalBranch281(x0, x1, Pos(x2), x3, x4, x5, x6, x7, x8, x9, x10, Zero, x11)
new_mkVBalBranch3MkVBalBranch281(x0, x1, Pos(x2), x3, x4, x5, x6, x7, x8, x9, x10, Succ(x11), x12)
new_mkVBalBranch3MkVBalBranch272(x0, x1, Neg(Succ(Succ(Succ(x2)))), x3, x4, x5, x6, Succ(x7), x8, x9, x10, Succ(Succ(x11)), x12)
new_mkVBalBranch3MkVBalBranch288(x0, x1, Neg(x2), x3, x4, x5, x6, x7, x8, x9, x10, Succ(x11), x12)
new_splitLT40(x0)
new_mkBalBranch6MkBalBranch44(x0, x1, x2, x3, x4, x5, x6, x7)
new_mkVBalBranch3MkVBalBranch138(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11)
new_mkBalBranch6MkBalBranch414(x0, x1, x2, x3, Succ(x4), x5, x6)
new_mkBalBranch6MkBalBranch115(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11)
new_mkVBalBranch3MkVBalBranch253(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11)
new_mkVBalBranch2(x0, Branch(x1, x2, Neg(Zero), x3, x4), Branch(x5, x6, Neg(Succ(x7)), x8, x9), x10)
new_mkBalBranch6MkBalBranch412(x0, x1, x2, x3, Zero, Succ(x4), x5, x6)
new_mkVBalBranch3MkVBalBranch288(x0, x1, Neg(x2), x3, x4, x5, x6, x7, x8, x9, x10, Zero, x11)
new_mkVBalBranch3(x0, Branch(x1, x2, Neg(Zero), x3, x4), Branch(x5, x6, Pos(Succ(x7)), x8, x9), x10)
new_mkVBalBranch3(x0, Branch(x1, x2, Pos(Zero), x3, x4), Branch(x5, x6, Neg(Succ(x7)), x8, x9), x10)
new_mkVBalBranch3MkVBalBranch272(x0, x1, Neg(Succ(Succ(x2))), x3, x4, x5, x6, Succ(x7), x8, x9, x10, Zero, x11)
new_mkVBalBranch3MkVBalBranch286(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11)
new_splitLT12(Branch(EQ, x0, x1, x2, x3), x4)
new_splitLT15(Branch(EQ, x0, x1, x2, x3), x4)
new_mkVBalBranch3MkVBalBranch268(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10)
new_mkVBalBranch3MkVBalBranch270(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, Succ(x10), Succ(x11), x12)
new_mkBalBranch6MkBalBranch314(x0, x1, x2, x3, Succ(x4), x5, x6)
new_mkBalBranch6MkBalBranch49(Branch(x0, x1, x2, x3, x4), x5, x6, x7, x8, x9)
new_mkVBalBranch3MkVBalBranch281(x0, x1, Neg(Succ(Succ(Zero))), x2, x3, x4, x5, Zero, x6, x7, x8, Succ(Zero), x9)
new_mkVBalBranch3MkVBalBranch144(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, Succ(x11), Zero, x12)
new_mkBalBranch6MkBalBranch1113(x0, x1, x2, x3, x4, x5, x6, x7, Zero, Zero, x8, x9)
new_splitLT5(x0, x1, x2, x3)
new_primPlusInt1(x0, Pos(x1))
new_mkBalBranch6MkBalBranch48(x0, x1, x2, x3, Zero, x4, x5)
new_mkVBalBranch3MkVBalBranch149(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, Succ(x11), Succ(x12), x13)
new_mkBalBranch6MkBalBranch412(x0, x1, x2, x3, Succ(x4), Zero, x5, x6)
new_mkBalBranch6MkBalBranch412(x0, x1, x2, x3, Succ(x4), Succ(x5), x6, x7)
new_splitLT15(Branch(LT, x0, x1, x2, x3), x4)
new_mkVBalBranch3MkVBalBranch272(x0, x1, Neg(Succ(Succ(Succ(x2)))), x3, x4, x5, x6, Zero, x7, x8, x9, Succ(Succ(x10)), x11)
new_mkVBalBranch3MkVBalBranch167(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, Zero, x11)
new_mkVBalBranch3MkVBalBranch267(x0, x1, Neg(x2), x3, x4, x5, x6, x7, x8, x9, x10, Succ(x11), x12)
new_mkVBalBranch3MkVBalBranch137(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, Zero, x11)
new_mkBalBranch6MkBalBranch1115(x0, x1, x2, x3, x4, Branch(x5, x6, x7, x8, x9), x10, x11, x12, x13)
new_mkVBalBranch3MkVBalBranch140(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11)
new_mkVBalBranch3MkVBalBranch257(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11)
new_splitGT14(Branch(LT, x0, x1, x2, x3), x4)
new_mkBalBranch6MkBalBranch014(x0, x1, x2, x3, x4, x5, x6, x7, Zero, Succ(x8), x9, x10)
new_mkVBalBranch3MkVBalBranch246(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, Succ(x11), Zero, x12)
new_intersectFM_C2Lts(x0, x1, x2, x3, x4)
new_mkVBalBranch3(x0, Branch(x1, x2, Pos(Succ(x3)), x4, x5), Branch(x6, x7, x8, x9, x10), x11)
new_splitGT14(Branch(GT, x0, x1, x2, x3), x4)
new_mkVBalBranch3MkVBalBranch261(x0, x1, Pos(Zero), x2, x3, x4, x5, x6, x7, x8, x9, Succ(x10), x11)
new_mkVBalBranch3MkVBalBranch131(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, Zero, x11)
new_mkVBalBranch3MkVBalBranch246(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, Zero, Succ(x11), x12)
new_mkBalBranch6MkBalBranch1112(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9)
new_mkVBalBranch3MkVBalBranch261(x0, x1, Pos(Succ(x2)), x3, x4, x5, x6, x7, x8, x9, x10, Zero, x11)
new_mkBalBranch6MkBalBranch113(x0, x1, x2, x3, x4, x5, x6, x7, Pos(Succ(x8)), Pos(x9), x10, x11)
new_mkBalBranch6MkBalBranch018(x0, x1, x2, x3, x4, x5, x6, x7, Zero, x8, x9, x10)
new_mkBalBranch6MkBalBranch5(x0, x1, x2, x3, Pos(Succ(Succ(Succ(x4)))), x5, x6)
new_splitGT40(x0)
new_mkVBalBranch3MkVBalBranch255(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, Succ(x11), Zero, x12)
new_mkVBalBranch3MkVBalBranch262(x0, x1, Neg(Zero), x2, x3, x4, x5, x6, x7, x8, x9, Zero, x10)
new_mkVBalBranch3MkVBalBranch290(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10)
new_addToFM(x0, x1, x2)
new_mkVBalBranch4(x0, Branch(x1, x2, Neg(Zero), x3, x4), Branch(x5, x6, Neg(Succ(x7)), x8, x9), x10)
new_mkVBalBranch3MkVBalBranch288(x0, x1, Pos(Succ(Succ(x2))), x3, x4, x5, x6, Zero, x7, x8, x9, Succ(Succ(x10)), x11)
new_mkVBalBranch3MkVBalBranch164(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, Succ(x10), x11)
new_mkBalBranch6MkBalBranch1114(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9)
new_mkVBalBranch3MkVBalBranch272(x0, x1, Neg(Succ(Succ(x2))), x3, x4, x5, x6, Zero, x7, x8, x9, Zero, x10)
new_mkBalBranch6MkBalBranch113(x0, x1, x2, x3, x4, x5, x6, x7, Neg(Zero), Neg(x8), x9, x10)
new_mkBalBranch6MkBalBranch39(x0, x1, x2, x3, Succ(x4), Succ(x5), x6, x7)
new_mkVBalBranch3MkVBalBranch277(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, Zero, Zero, x10)
new_mkVBalBranch3MkVBalBranch288(x0, x1, Pos(Zero), x2, x3, x4, x5, x6, x7, x8, x9, Succ(x10), x11)
new_mkVBalBranch4(x0, Branch(x1, x2, Neg(Succ(x3)), x4, x5), Branch(x6, x7, x8, x9, x10), x11)
new_mkVBalBranch3MkVBalBranch132(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, Succ(x11), Succ(x12), x13)
new_mkBalBranch6MkBalBranch016(x0, x1, x2, Branch(x3, x4, x5, x6, x7), x8, x9, x10, x11, x12, x13)
new_mkVBalBranch3MkVBalBranch134(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, Succ(x11), Succ(x12), x13)
new_mkVBalBranch3MkVBalBranch154(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, Succ(x10), x11)
new_mkVBalBranch3MkVBalBranch258(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11)
new_intersectFM_C2Lts2(x0, x1, x2, x3, x4)
new_mkVBalBranch2(x0, Branch(x1, x2, Neg(Succ(x3)), x4, x5), Branch(x6, x7, x8, x9, x10), x11)
new_emptyFM(x0)
new_primPlusInt0(x0, Neg(x1))
new_intersectFM_C2Gts3(x0, x1)
new_mkBalBranch6MkBalBranch411(x0, x1, x2, x3, Pos(Zero), Pos(x4), x5, x6)
new_mkVBalBranch3MkVBalBranch281(x0, x1, Neg(Succ(Succ(Zero))), x2, x3, x4, x5, Succ(x6), x7, x8, x9, Succ(Zero), x10)
new_splitGT6(x0)
new_primPlusNat3(x0, Succ(x1))
new_mkVBalBranch3MkVBalBranch168(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, Succ(x10), x11)
new_mkBalBranch6MkBalBranch118(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11)
new_mkVBalBranch3MkVBalBranch280(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, Succ(x11), Zero, x12)
new_mkVBalBranch3MkVBalBranch142(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11)
new_primMulNat(Succ(x0))
new_mkVBalBranch3MkVBalBranch161(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, Succ(x10), x11)
new_mkVBalBranch2(x0, EmptyFM, x1, x2)
new_mkBalBranch6MkBalBranch37(x0, x1, x2, x3, x4, x5, x6, x7)
new_primPlusInt2(Neg(x0), x1, x2, x3, x4, x5, x6)
new_mkVBalBranch3MkVBalBranch162(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, Succ(x11), Succ(x12), x13)
new_mkVBalBranch3MkVBalBranch139(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, Zero, x11)
new_mkVBalBranch3MkVBalBranch281(x0, x1, Neg(Succ(Succ(Zero))), x2, x3, x4, x5, Zero, x6, x7, x8, Succ(Succ(x9)), x10)
new_mkBalBranch6MkBalBranch117(x0, x1, x2, x3, x4, x5, x6, x7, Zero, x8, x9)
new_splitLT3(x0, x1, x2, x3, x4)
new_addToFM_C4(Branch(LT, x0, x1, x2, x3), x4, x5)
new_mkVBalBranch3MkVBalBranch252(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, Zero, Zero, x11)
new_mkVBalBranch3MkVBalBranch246(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, Succ(x11), Succ(x12), x13)
new_mkVBalBranch3MkVBalBranch262(x0, x1, Neg(Succ(x2)), x3, x4, x5, x6, x7, x8, x9, x10, Zero, x11)
new_mkBranch(x0, x1, x2, x3, x4, x5, x6)
new_mkBalBranch6MkBalBranch0111(x0, x1, x2, x3, x4, x5, x6, x7, Succ(x8), x9, x10)
new_mkBalBranch6MkBalBranch38(x0, x1, x2, x3, x4, Zero, x5, x6)
new_primMulNat2(Zero)
new_mkBalBranch6MkBalBranch010(x0, x1, x2, x3, x4, x5, x6, x7, Succ(x8), x9, x10)
new_mkBalBranch6MkBalBranch36(x0, x1, x2, x3, Zero, x4, x5, x6)
new_mkBalBranch6MkBalBranch017(x0, x1, x2, x3, x4, x5, x6, x7, Neg(Succ(x8)), Neg(x9), x10, x11)
new_addToFM_C3(Branch(LT, x0, x1, x2, x3), x4, x5)
new_splitLT26(x0, x1, x2, x3, x4)
new_mkVBalBranch3MkVBalBranch168(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, Zero, x10)
new_mkBalBranch6MkBalBranch0110(x0, x1, x2, x3, x4, x5, x6, x7, Succ(x8), x9, x10)
new_mkBalBranch6MkBalBranch114(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11)
new_mkVBalBranch3MkVBalBranch150(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11)
new_splitGT42(x0)
new_mkBalBranch6MkBalBranch47(x0, x1, x2, x3, Zero, x4, x5, x6)
new_mkVBalBranch3MkVBalBranch261(x0, x1, Pos(Zero), x2, x3, x4, x5, x6, x7, x8, x9, Zero, x10)
new_mkBalBranch6MkBalBranch017(x0, x1, x2, x3, x4, x5, x6, x7, Neg(Succ(x8)), Pos(x9), x10, x11)
new_mkBalBranch6MkBalBranch017(x0, x1, x2, x3, x4, x5, x6, x7, Pos(Succ(x8)), Neg(x9), x10, x11)
new_mkBalBranch6MkBalBranch1110(x0, x1, x2, x3, x4, x5, x6, x7, Zero, x8, x9)
new_mkVBalBranch3MkVBalBranch131(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, Succ(x11), x12)
new_mkVBalBranch4(x0, Branch(x1, x2, Neg(Zero), x3, x4), Branch(x5, x6, Pos(Succ(x7)), x8, x9), x10)
new_mkVBalBranch4(x0, Branch(x1, x2, Pos(Zero), x3, x4), Branch(x5, x6, Neg(Succ(x7)), x8, x9), x10)
new_mkVBalBranch3MkVBalBranch262(x0, x1, Neg(Succ(x2)), x3, x4, x5, x6, x7, x8, x9, x10, Succ(x11), x12)
new_primPlusInt0(x0, Pos(x1))
new_mkVBalBranch3MkVBalBranch162(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, Zero, Succ(x11), x12)
new_mkVBalBranch3MkVBalBranch147(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, Zero, x11)
new_primMulNat2(Succ(x0))
new_intersectFM_C2Lts0(x0, x1, x2, x3, x4)
new_mkVBalBranch3MkVBalBranch269(x0, x1, Zero, x2, x3, x4, x5, x6, x7, x8, x9, x10)
new_splitGT27(x0, x1, x2, x3, x4)
new_splitLT16(x0)
new_mkVBalBranch3MkVBalBranch152(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, Succ(x11), Succ(x12), x13)
new_mkBalBranch6Size_l(x0, x1, x2, x3, x4, x5)
new_mkBalBranch6MkBalBranch311(x0, x1, x2, x3, x4, x5, x6, x7)
new_splitGT5(x0, x1, x2, x3)
new_mkVBalBranch3MkVBalBranch160(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11)
new_primMinusNat0(Succ(x0), Succ(x1))

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

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

new_intersectFM_C(Branch(GT, zzz31, zzz32, Branch(GT, zzz331, zzz332, Branch(GT, zzz3331, zzz3332, EmptyFM, zzz3334), zzz334), zzz34), Branch(EQ, zzz41, zzz42, zzz43, zzz44), h) → new_intersectFM_C(new_mkVBalBranch3(zzz31, new_splitGT9(zzz331, zzz332, Branch(GT, zzz3331, zzz3332, EmptyFM, zzz3334), zzz334, h), zzz34, h), zzz44, h)
new_intersectFM_C(Branch(LT, zzz31, zzz32, zzz33, zzz34), Branch(LT, zzz41, zzz42, zzz43, zzz44), h) → new_intersectFM_C(new_splitLT3(zzz31, zzz32, zzz33, zzz34, h), zzz43, h)
new_intersectFM_C2IntersectFM_C16(zzz2208, zzz2209, zzz2210, zzz2211, zzz2212, zzz2213, zzz2214, zzz2215, GT, zzz2217, zzz2218, zzz2219, zzz2220, ca, cb) → new_intersectFM_C2IntersectFM_C18(Branch(LT, zzz2208, zzz2209, zzz2210, zzz2211), zzz2212, zzz2213, zzz2214, zzz2215, zzz2217, zzz2218, zzz2219, zzz2220, ca, cb)
new_intersectFM_C2IntersectFM_C10(zzz869, zzz870, zzz871, zzz872, zzz873, zzz874, zzz875, zzz876, EQ, zzz878, zzz879, EmptyFM, zzz881, bc, bd) → new_intersectFM_C(new_intersectFM_C2Lts1(zzz869, zzz870, zzz871, zzz872, bc), zzz875, bc)
new_intersectFM_C(Branch(GT, zzz31, zzz32, Branch(GT, zzz331, zzz332, Branch(EQ, zzz3331, zzz3332, zzz3333, zzz3334), zzz334), zzz34), Branch(EQ, zzz41, zzz42, zzz43, zzz44), h) → new_intersectFM_C(new_splitGT24(zzz31, zzz32, Branch(GT, zzz331, zzz332, Branch(EQ, zzz3331, zzz3332, zzz3333, zzz3334), zzz334), zzz34, h), zzz44, h)
new_intersectFM_C2IntersectFM_C11(zzz883, zzz884, zzz885, zzz886, zzz887, zzz888, zzz889, zzz890, EQ, zzz892, zzz893, zzz894, zzz895, be, bf) → new_intersectFM_C(new_intersectFM_C2Gts2(zzz883, zzz884, zzz885, zzz886, be), zzz890, be)
new_intersectFM_C2IntersectFM_C14(zzz76, zzz77, zzz78, zzz79, zzz80, zzz81, zzz82, zzz83, zzz871, zzz872, zzz873, zzz874, bg, bh) → new_intersectFM_C(new_intersectFM_C2Gts(zzz76, zzz77, zzz78, zzz79, bg), zzz83, bg)
new_intersectFM_C(Branch(GT, zzz31, zzz32, Branch(GT, zzz331, zzz332, Branch(LT, zzz3331, zzz3332, zzz3333, zzz3334), zzz334), zzz34), Branch(EQ, zzz41, zzz42, zzz43, zzz44), h) → new_intersectFM_C2IntersectFM_C12(zzz31, zzz32, Branch(GT, zzz331, zzz332, Branch(LT, zzz3331, zzz3332, zzz3333, zzz3334), zzz334), zzz34, zzz41, zzz42, zzz43, zzz44, zzz3331, zzz3332, zzz3333, zzz3334, h, h)
new_intersectFM_C2IntersectFM_C17(zzz2223, zzz2224, zzz2225, zzz2226, zzz2227, zzz2228, zzz2229, zzz2230, LT, zzz2232, zzz2233, zzz2234, Branch(zzz22350, zzz22351, zzz22352, zzz22353, zzz22354), ce, cf) → new_intersectFM_C2IntersectFM_C17(zzz2223, zzz2224, zzz2225, zzz2226, zzz2227, zzz2228, zzz2229, zzz2230, zzz22350, zzz22351, zzz22352, zzz22353, zzz22354, ce, cf)
new_intersectFM_C2IntersectFM_C10(zzz869, zzz870, zzz871, zzz872, zzz873, zzz874, zzz875, zzz876, LT, zzz878, zzz879, zzz880, zzz881, bc, bd) → new_intersectFM_C(new_intersectFM_C2Lts1(zzz869, zzz870, zzz871, zzz872, bc), zzz875, bc)
new_intersectFM_C(Branch(EQ, zzz31, zzz32, EmptyFM, zzz34), Branch(LT, zzz41, zzz42, zzz43, zzz44), h) → new_intersectFM_C(new_splitGT4(zzz31, zzz32, zzz34, h), zzz44, h)
new_intersectFM_C2IntersectFM_C114(zzz2223, zzz2224, zzz2225, zzz2226, zzz2227, zzz2228, zzz2229, zzz2230, EmptyFM, ce, cf) → new_intersectFM_C(new_intersectFM_C2Lts3(Branch(EQ, zzz2223, zzz2224, zzz2225, zzz2226), ce), zzz2229, ce)
new_intersectFM_C2IntersectFM_C12(zzz76, zzz77, zzz78, zzz79, zzz80, zzz81, zzz82, zzz83, zzz84, zzz85, zzz86, EmptyFM, bg, bh) → new_intersectFM_C(new_intersectFM_C2Lts(zzz76, zzz77, zzz78, zzz79, bg), zzz82, bg)
new_intersectFM_C2IntersectFM_C112(zzz76, zzz77, zzz78, zzz79, zzz80, zzz81, zzz82, zzz83, Branch(LT, zzz871, zzz872, zzz873, zzz874), bg, bh) → new_intersectFM_C2IntersectFM_C12(zzz76, zzz77, zzz78, zzz79, zzz80, zzz81, zzz82, zzz83, zzz871, zzz872, zzz873, zzz874, bg, bh)
new_intersectFM_C2IntersectFM_C16(zzz2208, zzz2209, zzz2210, zzz2211, zzz2212, zzz2213, zzz2214, zzz2215, LT, zzz2217, zzz2218, zzz2219, EmptyFM, ca, cb) → new_intersectFM_C(new_intersectFM_C2Lts3(Branch(LT, zzz2208, zzz2209, zzz2210, zzz2211), ca), zzz2214, ca)
new_intersectFM_C(Branch(LT, zzz31, zzz32, zzz33, Branch(zzz340, zzz341, zzz342, zzz343, zzz344)), Branch(GT, zzz41, zzz42, zzz43, zzz44), h) → new_intersectFM_C2IntersectFM_C16(zzz31, zzz32, zzz33, Branch(zzz340, zzz341, zzz342, zzz343, zzz344), zzz41, zzz42, zzz43, zzz44, zzz340, zzz341, zzz342, zzz343, zzz344, h, h)
new_intersectFM_C(Branch(GT, zzz31, zzz32, Branch(GT, zzz331, zzz332, Branch(GT, zzz3331, zzz3332, Branch(EQ, zzz33331, zzz33332, zzz33333, zzz33334), zzz3334), zzz334), zzz34), Branch(EQ, zzz41, zzz42, zzz43, zzz44), h) → new_intersectFM_C(new_intersectFM_C2Gts(zzz31, zzz32, Branch(GT, zzz331, zzz332, Branch(GT, zzz3331, zzz3332, Branch(EQ, zzz33331, zzz33332, zzz33333, zzz33334), zzz3334), zzz334), zzz34, h), zzz44, h)
new_intersectFM_C2IntersectFM_C112(zzz76, zzz77, zzz78, zzz79, zzz80, zzz81, zzz82, zzz83, EmptyFM, bg, bh) → new_intersectFM_C(new_intersectFM_C2Gts(zzz76, zzz77, zzz78, zzz79, bg), zzz83, bg)
new_intersectFM_C2IntersectFM_C110(zzz869, zzz870, zzz871, zzz872, zzz873, zzz874, zzz875, zzz876, EmptyFM, bc, bd) → new_intersectFM_C(new_intersectFM_C2Lts1(zzz869, zzz870, zzz871, zzz872, bc), zzz875, bc)
new_intersectFM_C2IntersectFM_C113(zzz2208, zzz2209, zzz2210, zzz2211, zzz2212, zzz2213, zzz2214, zzz2215, Branch(zzz22200, zzz22201, zzz22202, zzz22203, zzz22204), ca, cb) → new_intersectFM_C2IntersectFM_C16(zzz2208, zzz2209, zzz2210, zzz2211, zzz2212, zzz2213, zzz2214, zzz2215, zzz22200, zzz22201, zzz22202, zzz22203, zzz22204, ca, cb)
new_intersectFM_C(Branch(LT, zzz31, zzz32, zzz33, EmptyFM), Branch(GT, zzz41, zzz42, zzz43, zzz44), h) → new_intersectFM_C(new_splitLT10(zzz31, zzz32, zzz33, h), zzz43, h)
new_intersectFM_C2IntersectFM_C16(zzz2208, zzz2209, zzz2210, zzz2211, zzz2212, zzz2213, zzz2214, zzz2215, EQ, zzz2217, zzz2218, zzz2219, zzz2220, ca, cb) → new_intersectFM_C2IntersectFM_C113(zzz2208, zzz2209, zzz2210, zzz2211, zzz2212, zzz2213, zzz2214, zzz2215, zzz2220, ca, cb)
new_intersectFM_C2IntersectFM_C12(zzz76, zzz77, zzz78, zzz79, zzz80, zzz81, zzz82, zzz83, zzz84, zzz85, zzz86, Branch(EQ, zzz871, zzz872, zzz873, zzz874), bg, bh) → new_intersectFM_C(new_intersectFM_C2Gts(zzz76, zzz77, zzz78, zzz79, bg), zzz83, bg)
new_intersectFM_C2IntersectFM_C11(zzz883, zzz884, zzz885, zzz886, zzz887, zzz888, zzz889, zzz890, GT, zzz892, zzz893, EmptyFM, zzz895, be, bf) → new_intersectFM_C(new_intersectFM_C2Lts2(zzz883, zzz884, zzz885, zzz886, be), zzz889, be)
new_intersectFM_C(Branch(EQ, zzz31, zzz32, zzz33, zzz34), Branch(EQ, zzz41, zzz42, zzz43, zzz44), h) → new_intersectFM_C(new_splitLT7(zzz31, zzz32, zzz33, zzz34, h), zzz43, h)
new_intersectFM_C(Branch(GT, zzz31, zzz32, Branch(GT, zzz331, zzz332, Branch(GT, zzz3331, zzz3332, Branch(GT, zzz33331, zzz33332, Branch(EQ, zzz333331, zzz333332, zzz333333, zzz333334), zzz33334), zzz3334), zzz334), zzz34), Branch(EQ, zzz41, zzz42, zzz43, zzz44), h) → new_intersectFM_C2IntersectFM_C14(zzz31, zzz32, Branch(GT, zzz331, zzz332, Branch(GT, zzz3331, zzz3332, Branch(GT, zzz33331, zzz33332, Branch(EQ, zzz333331, zzz333332, zzz333333, zzz333334), zzz33334), zzz3334), zzz334), zzz34, zzz41, zzz42, zzz43, zzz44, zzz333331, zzz333332, zzz333333, zzz333334, h, h)
new_intersectFM_C(Branch(GT, zzz31, zzz32, Branch(GT, zzz331, zzz332, Branch(GT, zzz3331, zzz3332, EmptyFM, zzz3334), zzz334), zzz34), Branch(EQ, zzz41, zzz42, zzz43, zzz44), h) → new_intersectFM_C(new_splitLT9(zzz331, zzz332, Branch(GT, zzz3331, zzz3332, EmptyFM, zzz3334), zzz334, h), zzz43, h)
new_intersectFM_C(Branch(EQ, zzz31, zzz32, zzz33, zzz34), Branch(EQ, zzz41, zzz42, zzz43, zzz44), h) → new_intersectFM_C(new_splitGT7(zzz31, zzz32, zzz33, zzz34, h), zzz44, h)
new_intersectFM_C(Branch(GT, zzz31, zzz32, Branch(LT, zzz331, zzz332, zzz333, zzz334), zzz34), Branch(EQ, zzz41, zzz42, zzz43, zzz44), h) → new_intersectFM_C2IntersectFM_C12(zzz31, zzz32, Branch(LT, zzz331, zzz332, zzz333, zzz334), zzz34, zzz41, zzz42, zzz43, zzz44, zzz331, zzz332, zzz333, zzz334, h, h)
new_intersectFM_C(Branch(GT, zzz31, zzz32, Branch(zzz330, zzz331, zzz332, zzz333, zzz334), zzz34), Branch(LT, zzz41, zzz42, zzz43, zzz44), h) → new_intersectFM_C2IntersectFM_C10(zzz31, zzz32, Branch(zzz330, zzz331, zzz332, zzz333, zzz334), zzz34, zzz41, zzz42, zzz43, zzz44, zzz330, zzz331, zzz332, zzz333, zzz334, h, h)
new_intersectFM_C2IntersectFM_C111(zzz883, zzz884, zzz885, zzz886, zzz887, zzz888, zzz889, zzz890, EmptyFM, be, bf) → new_intersectFM_C(new_intersectFM_C2Lts2(zzz883, zzz884, zzz885, zzz886, be), zzz889, be)
new_intersectFM_C2IntersectFM_C17(zzz2223, zzz2224, zzz2225, zzz2226, zzz2227, zzz2228, zzz2229, zzz2230, LT, zzz2232, zzz2233, zzz2234, EmptyFM, ce, cf) → new_intersectFM_C(new_intersectFM_C2Lts3(Branch(EQ, zzz2223, zzz2224, zzz2225, zzz2226), ce), zzz2229, ce)
new_intersectFM_C2IntersectFM_C19(zzz854, zzz855, zzz856, zzz857, zzz858, zzz859, zzz860, zzz861, EmptyFM, ba, bb) → new_intersectFM_C(new_intersectFM_C2Gts0(zzz854, zzz855, zzz856, zzz857, ba), zzz861, ba)
new_intersectFM_C(Branch(GT, zzz31, zzz32, Branch(GT, zzz331, zzz332, Branch(GT, zzz3331, zzz3332, Branch(EQ, zzz33331, zzz33332, zzz33333, zzz33334), zzz3334), zzz334), zzz34), Branch(EQ, zzz41, zzz42, zzz43, zzz44), h) → new_intersectFM_C(new_intersectFM_C2Lts(zzz31, zzz32, Branch(GT, zzz331, zzz332, Branch(GT, zzz3331, zzz3332, Branch(EQ, zzz33331, zzz33332, zzz33333, zzz33334), zzz3334), zzz334), zzz34, h), zzz43, h)
new_intersectFM_C2IntersectFM_C113(zzz2208, zzz2209, zzz2210, zzz2211, zzz2212, zzz2213, zzz2214, zzz2215, EmptyFM, ca, cb) → new_intersectFM_C(new_intersectFM_C2Lts3(Branch(LT, zzz2208, zzz2209, zzz2210, zzz2211), ca), zzz2214, ca)
new_intersectFM_C(Branch(GT, zzz31, zzz32, Branch(GT, zzz331, zzz332, Branch(GT, zzz3331, zzz3332, Branch(GT, zzz33331, zzz33332, Branch(GT, zzz333331, zzz333332, zzz333333, zzz333334), zzz33334), zzz3334), zzz334), zzz34), Branch(EQ, zzz41, zzz42, zzz43, zzz44), h) → new_intersectFM_C2IntersectFM_C15(zzz31, zzz32, Branch(GT, zzz331, zzz332, Branch(GT, zzz3331, zzz3332, Branch(GT, zzz33331, zzz33332, Branch(GT, zzz333331, zzz333332, zzz333333, zzz333334), zzz33334), zzz3334), zzz334), zzz34, zzz41, zzz42, zzz43, zzz44, zzz333331, zzz333332, zzz333333, zzz333334, h, h)
new_intersectFM_C2IntersectFM_C14(zzz76, zzz77, zzz78, zzz79, zzz80, zzz81, zzz82, zzz83, zzz871, zzz872, zzz873, zzz874, bg, bh) → new_intersectFM_C(new_intersectFM_C2Lts(zzz76, zzz77, zzz78, zzz79, bg), zzz82, bg)
new_intersectFM_C2IntersectFM_C12(zzz76, zzz77, zzz78, zzz79, zzz80, zzz81, zzz82, zzz83, zzz84, zzz85, zzz86, Branch(LT, zzz871, zzz872, zzz873, zzz874), bg, bh) → new_intersectFM_C2IntersectFM_C12(zzz76, zzz77, zzz78, zzz79, zzz80, zzz81, zzz82, zzz83, zzz871, zzz872, zzz873, zzz874, bg, bh)
new_intersectFM_C(Branch(GT, zzz31, zzz32, Branch(GT, zzz331, zzz332, Branch(EQ, zzz3331, zzz3332, zzz3333, zzz3334), zzz334), zzz34), Branch(EQ, zzz41, zzz42, zzz43, zzz44), h) → new_intersectFM_C(new_splitLT23(zzz31, zzz32, Branch(GT, zzz331, zzz332, Branch(EQ, zzz3331, zzz3332, zzz3333, zzz3334), zzz334), zzz34, h), zzz43, h)
new_intersectFM_C(Branch(LT, zzz31, zzz32, zzz33, EmptyFM), Branch(EQ, zzz41, zzz42, zzz43, zzz44), h) → new_intersectFM_C(new_mkVBalBranch2(zzz31, zzz33, new_splitLT6(h), h), zzz43, h)
new_intersectFM_C(Branch(EQ, zzz31, zzz32, zzz33, EmptyFM), Branch(GT, zzz41, zzz42, zzz43, zzz44), h) → new_intersectFM_C(new_splitLT11(zzz31, zzz32, zzz33, h), zzz43, h)
new_intersectFM_C2IntersectFM_C10(zzz869, zzz870, zzz871, zzz872, zzz873, zzz874, zzz875, zzz876, EQ, zzz878, zzz879, Branch(zzz8800, zzz8801, zzz8802, zzz8803, zzz8804), zzz881, bc, bd) → new_intersectFM_C2IntersectFM_C10(zzz869, zzz870, zzz871, zzz872, zzz873, zzz874, zzz875, zzz876, zzz8800, zzz8801, zzz8802, zzz8803, zzz8804, bc, bd)
new_intersectFM_C2IntersectFM_C17(zzz2223, zzz2224, zzz2225, zzz2226, zzz2227, zzz2228, zzz2229, zzz2230, GT, zzz2232, zzz2233, zzz2234, zzz2235, ce, cf) → new_intersectFM_C2IntersectFM_C18(Branch(EQ, zzz2223, zzz2224, zzz2225, zzz2226), zzz2227, zzz2228, zzz2229, zzz2230, zzz2232, zzz2233, zzz2234, zzz2235, ce, cf)
new_intersectFM_C2IntersectFM_C110(zzz869, zzz870, zzz871, zzz872, zzz873, zzz874, zzz875, zzz876, Branch(zzz8800, zzz8801, zzz8802, zzz8803, zzz8804), bc, bd) → new_intersectFM_C2IntersectFM_C10(zzz869, zzz870, zzz871, zzz872, zzz873, zzz874, zzz875, zzz876, zzz8800, zzz8801, zzz8802, zzz8803, zzz8804, bc, bd)
new_intersectFM_C(Branch(GT, zzz31, zzz32, Branch(EQ, zzz331, zzz332, zzz333, zzz334), zzz34), Branch(EQ, zzz41, zzz42, zzz43, zzz44), h) → new_intersectFM_C(new_splitLT7(zzz331, zzz332, zzz333, zzz334, h), zzz43, h)
new_intersectFM_C(Branch(EQ, zzz31, zzz32, Branch(zzz330, zzz331, zzz332, zzz333, zzz334), zzz34), Branch(LT, zzz41, zzz42, zzz43, zzz44), h) → new_intersectFM_C2IntersectFM_C1(zzz31, zzz32, Branch(zzz330, zzz331, zzz332, zzz333, zzz334), zzz34, zzz41, zzz42, zzz43, zzz44, zzz330, zzz331, zzz332, zzz333, zzz334, h, h)
new_intersectFM_C2IntersectFM_C114(zzz2223, zzz2224, zzz2225, zzz2226, zzz2227, zzz2228, zzz2229, zzz2230, Branch(zzz22350, zzz22351, zzz22352, zzz22353, zzz22354), ce, cf) → new_intersectFM_C2IntersectFM_C17(zzz2223, zzz2224, zzz2225, zzz2226, zzz2227, zzz2228, zzz2229, zzz2230, zzz22350, zzz22351, zzz22352, zzz22353, zzz22354, ce, cf)
new_intersectFM_C2IntersectFM_C11(zzz883, zzz884, zzz885, zzz886, zzz887, zzz888, zzz889, zzz890, EQ, zzz892, zzz893, zzz894, zzz895, be, bf) → new_intersectFM_C(new_intersectFM_C2Lts2(zzz883, zzz884, zzz885, zzz886, be), zzz889, be)
new_intersectFM_C2IntersectFM_C18(zzz2129, zzz2130, zzz2131, zzz2132, zzz2133, zzz2134, zzz2135, zzz2136, zzz2137, cc, cd) → new_intersectFM_C(new_intersectFM_C2Gts3(zzz2129, cc), zzz2133, cc)
new_intersectFM_C2IntersectFM_C10(zzz869, zzz870, zzz871, zzz872, zzz873, zzz874, zzz875, zzz876, LT, zzz878, zzz879, zzz880, zzz881, bc, bd) → new_intersectFM_C(new_intersectFM_C2Gts1(zzz869, zzz870, zzz871, zzz872, bc), zzz876, bc)
new_intersectFM_C2IntersectFM_C112(zzz76, zzz77, zzz78, zzz79, zzz80, zzz81, zzz82, zzz83, EmptyFM, bg, bh) → new_intersectFM_C(new_intersectFM_C2Lts(zzz76, zzz77, zzz78, zzz79, bg), zzz82, bg)
new_intersectFM_C(Branch(EQ, zzz31, zzz32, zzz33, Branch(zzz340, zzz341, zzz342, zzz343, zzz344)), Branch(GT, zzz41, zzz42, zzz43, zzz44), h) → new_intersectFM_C2IntersectFM_C17(zzz31, zzz32, zzz33, Branch(zzz340, zzz341, zzz342, zzz343, zzz344), zzz41, zzz42, zzz43, zzz44, zzz340, zzz341, zzz342, zzz343, zzz344, h, h)
new_intersectFM_C2IntersectFM_C110(zzz869, zzz870, zzz871, zzz872, zzz873, zzz874, zzz875, zzz876, EmptyFM, bc, bd) → new_intersectFM_C(new_intersectFM_C2Gts1(zzz869, zzz870, zzz871, zzz872, bc), zzz876, bc)
new_intersectFM_C2IntersectFM_C10(zzz869, zzz870, zzz871, zzz872, zzz873, zzz874, zzz875, zzz876, GT, zzz878, zzz879, zzz880, zzz881, bc, bd) → new_intersectFM_C2IntersectFM_C110(zzz869, zzz870, zzz871, zzz872, zzz873, zzz874, zzz875, zzz876, zzz880, bc, bd)
new_intersectFM_C2IntersectFM_C11(zzz883, zzz884, zzz885, zzz886, zzz887, zzz888, zzz889, zzz890, GT, zzz892, zzz893, Branch(zzz8940, zzz8941, zzz8942, zzz8943, zzz8944), zzz895, be, bf) → new_intersectFM_C2IntersectFM_C11(zzz883, zzz884, zzz885, zzz886, zzz887, zzz888, zzz889, zzz890, zzz8940, zzz8941, zzz8942, zzz8943, zzz8944, be, bf)
new_intersectFM_C2IntersectFM_C112(zzz76, zzz77, zzz78, zzz79, zzz80, zzz81, zzz82, zzz83, Branch(GT, zzz871, zzz872, zzz873, zzz874), bg, bh) → new_intersectFM_C2IntersectFM_C112(zzz76, zzz77, zzz78, zzz79, zzz80, zzz81, zzz82, zzz83, zzz873, bg, bh)
new_intersectFM_C(Branch(GT, zzz31, zzz32, EmptyFM, zzz34), Branch(LT, zzz41, zzz42, zzz43, zzz44), h) → new_intersectFM_C(new_splitGT5(zzz31, zzz32, zzz34, h), zzz44, h)
new_intersectFM_C2IntersectFM_C112(zzz76, zzz77, zzz78, zzz79, zzz80, zzz81, zzz82, zzz83, Branch(EQ, zzz871, zzz872, zzz873, zzz874), bg, bh) → new_intersectFM_C(new_intersectFM_C2Lts(zzz76, zzz77, zzz78, zzz79, bg), zzz82, bg)
new_intersectFM_C2IntersectFM_C19(zzz854, zzz855, zzz856, zzz857, zzz858, zzz859, zzz860, zzz861, EmptyFM, ba, bb) → new_intersectFM_C(new_intersectFM_C2Lts0(zzz854, zzz855, zzz856, zzz857, ba), zzz860, ba)
new_intersectFM_C2IntersectFM_C114(zzz2223, zzz2224, zzz2225, zzz2226, zzz2227, zzz2228, zzz2229, zzz2230, EmptyFM, ce, cf) → new_intersectFM_C(new_intersectFM_C2Gts3(Branch(EQ, zzz2223, zzz2224, zzz2225, zzz2226), ce), zzz2230, ce)
new_intersectFM_C(Branch(GT, zzz31, zzz32, zzz33, zzz34), Branch(GT, zzz41, zzz42, zzz43, zzz44), h) → new_intersectFM_C2IntersectFM_C18(Branch(GT, zzz31, zzz32, zzz33, zzz34), zzz41, zzz42, zzz43, zzz44, zzz31, zzz32, zzz33, zzz34, h, h)
new_intersectFM_C(Branch(LT, zzz31, zzz32, zzz33, Branch(zzz340, zzz341, zzz342, zzz343, zzz344)), Branch(EQ, zzz41, zzz42, zzz43, zzz44), h) → new_intersectFM_C2IntersectFM_C11(zzz31, zzz32, zzz33, Branch(zzz340, zzz341, zzz342, zzz343, zzz344), zzz41, zzz42, zzz43, zzz44, zzz340, zzz341, zzz342, zzz343, zzz344, h, h)
new_intersectFM_C2IntersectFM_C11(zzz883, zzz884, zzz885, zzz886, zzz887, zzz888, zzz889, zzz890, GT, zzz892, zzz893, EmptyFM, zzz895, be, bf) → new_intersectFM_C(new_intersectFM_C2Gts2(zzz883, zzz884, zzz885, zzz886, be), zzz890, be)
new_intersectFM_C2IntersectFM_C1(zzz854, zzz855, zzz856, zzz857, zzz858, zzz859, zzz860, zzz861, EQ, zzz863, zzz864, Branch(zzz8650, zzz8651, zzz8652, zzz8653, zzz8654), zzz866, ba, bb) → new_intersectFM_C2IntersectFM_C1(zzz854, zzz855, zzz856, zzz857, zzz858, zzz859, zzz860, zzz861, zzz8650, zzz8651, zzz8652, zzz8653, zzz8654, ba, bb)
new_intersectFM_C2IntersectFM_C13(zzz76, zzz77, zzz78, zzz79, zzz80, zzz81, zzz82, zzz83, zzz871, zzz872, zzz873, zzz874, bg, bh) → new_intersectFM_C2IntersectFM_C12(zzz76, zzz77, zzz78, zzz79, zzz80, zzz81, zzz82, zzz83, zzz871, zzz872, zzz873, zzz874, bg, bh)
new_intersectFM_C2IntersectFM_C112(zzz76, zzz77, zzz78, zzz79, zzz80, zzz81, zzz82, zzz83, Branch(EQ, zzz871, zzz872, zzz873, zzz874), bg, bh) → new_intersectFM_C(new_intersectFM_C2Gts(zzz76, zzz77, zzz78, zzz79, bg), zzz83, bg)
new_intersectFM_C2IntersectFM_C111(zzz883, zzz884, zzz885, zzz886, zzz887, zzz888, zzz889, zzz890, EmptyFM, be, bf) → new_intersectFM_C(new_intersectFM_C2Gts2(zzz883, zzz884, zzz885, zzz886, be), zzz890, be)
new_intersectFM_C2IntersectFM_C12(zzz76, zzz77, zzz78, zzz79, zzz80, zzz81, zzz82, zzz83, zzz84, zzz85, zzz86, EmptyFM, bg, bh) → new_intersectFM_C(new_intersectFM_C2Gts(zzz76, zzz77, zzz78, zzz79, bg), zzz83, bg)
new_intersectFM_C2IntersectFM_C18(zzz2129, zzz2130, zzz2131, zzz2132, zzz2133, zzz2134, zzz2135, zzz2136, zzz2137, cc, cd) → new_intersectFM_C(new_intersectFM_C2Lts3(zzz2129, cc), zzz2132, cc)
new_intersectFM_C2IntersectFM_C111(zzz883, zzz884, zzz885, zzz886, zzz887, zzz888, zzz889, zzz890, Branch(zzz8940, zzz8941, zzz8942, zzz8943, zzz8944), be, bf) → new_intersectFM_C2IntersectFM_C11(zzz883, zzz884, zzz885, zzz886, zzz887, zzz888, zzz889, zzz890, zzz8940, zzz8941, zzz8942, zzz8943, zzz8944, be, bf)
new_intersectFM_C2IntersectFM_C1(zzz854, zzz855, zzz856, zzz857, zzz858, zzz859, zzz860, zzz861, EQ, zzz863, zzz864, EmptyFM, zzz866, ba, bb) → new_intersectFM_C(new_intersectFM_C2Gts0(zzz854, zzz855, zzz856, zzz857, ba), zzz861, ba)
new_intersectFM_C2IntersectFM_C17(zzz2223, zzz2224, zzz2225, zzz2226, zzz2227, zzz2228, zzz2229, zzz2230, EQ, zzz2232, zzz2233, zzz2234, zzz2235, ce, cf) → new_intersectFM_C2IntersectFM_C114(zzz2223, zzz2224, zzz2225, zzz2226, zzz2227, zzz2228, zzz2229, zzz2230, zzz2235, ce, cf)
new_intersectFM_C(Branch(GT, zzz31, zzz32, Branch(GT, zzz331, zzz332, Branch(GT, zzz3331, zzz3332, Branch(GT, zzz33331, zzz33332, EmptyFM, zzz33334), zzz3334), zzz334), zzz34), Branch(EQ, zzz41, zzz42, zzz43, zzz44), h) → new_intersectFM_C(new_intersectFM_C2Lts(zzz31, zzz32, Branch(GT, zzz331, zzz332, Branch(GT, zzz3331, zzz3332, Branch(GT, zzz33331, zzz33332, EmptyFM, zzz33334), zzz3334), zzz334), zzz34, h), zzz43, h)
new_intersectFM_C2IntersectFM_C11(zzz883, zzz884, zzz885, zzz886, zzz887, zzz888, zzz889, zzz890, LT, zzz892, zzz893, zzz894, zzz895, be, bf) → new_intersectFM_C2IntersectFM_C111(zzz883, zzz884, zzz885, zzz886, zzz887, zzz888, zzz889, zzz890, zzz895, be, bf)
new_intersectFM_C2IntersectFM_C1(zzz854, zzz855, zzz856, zzz857, zzz858, zzz859, zzz860, zzz861, LT, zzz863, zzz864, zzz865, zzz866, ba, bb) → new_intersectFM_C(new_intersectFM_C2Lts0(zzz854, zzz855, zzz856, zzz857, ba), zzz860, ba)
new_intersectFM_C2IntersectFM_C1(zzz854, zzz855, zzz856, zzz857, zzz858, zzz859, zzz860, zzz861, LT, zzz863, zzz864, zzz865, zzz866, ba, bb) → new_intersectFM_C(new_intersectFM_C2Gts0(zzz854, zzz855, zzz856, zzz857, ba), zzz861, ba)
new_intersectFM_C2IntersectFM_C113(zzz2208, zzz2209, zzz2210, zzz2211, zzz2212, zzz2213, zzz2214, zzz2215, EmptyFM, ca, cb) → new_intersectFM_C(new_intersectFM_C2Gts3(Branch(LT, zzz2208, zzz2209, zzz2210, zzz2211), ca), zzz2215, ca)
new_intersectFM_C2IntersectFM_C19(zzz854, zzz855, zzz856, zzz857, zzz858, zzz859, zzz860, zzz861, Branch(zzz8650, zzz8651, zzz8652, zzz8653, zzz8654), ba, bb) → new_intersectFM_C2IntersectFM_C1(zzz854, zzz855, zzz856, zzz857, zzz858, zzz859, zzz860, zzz861, zzz8650, zzz8651, zzz8652, zzz8653, zzz8654, ba, bb)
new_intersectFM_C(Branch(GT, zzz31, zzz32, Branch(GT, zzz331, zzz332, Branch(GT, zzz3331, zzz3332, Branch(GT, zzz33331, zzz33332, EmptyFM, zzz33334), zzz3334), zzz334), zzz34), Branch(EQ, zzz41, zzz42, zzz43, zzz44), h) → new_intersectFM_C(new_intersectFM_C2Gts(zzz31, zzz32, Branch(GT, zzz331, zzz332, Branch(GT, zzz3331, zzz3332, Branch(GT, zzz33331, zzz33332, EmptyFM, zzz33334), zzz3334), zzz334), zzz34, h), zzz44, h)
new_intersectFM_C2IntersectFM_C16(zzz2208, zzz2209, zzz2210, zzz2211, zzz2212, zzz2213, zzz2214, zzz2215, LT, zzz2217, zzz2218, zzz2219, Branch(zzz22200, zzz22201, zzz22202, zzz22203, zzz22204), ca, cb) → new_intersectFM_C2IntersectFM_C16(zzz2208, zzz2209, zzz2210, zzz2211, zzz2212, zzz2213, zzz2214, zzz2215, zzz22200, zzz22201, zzz22202, zzz22203, zzz22204, ca, cb)
new_intersectFM_C2IntersectFM_C1(zzz854, zzz855, zzz856, zzz857, zzz858, zzz859, zzz860, zzz861, EQ, zzz863, zzz864, EmptyFM, zzz866, ba, bb) → new_intersectFM_C(new_intersectFM_C2Lts0(zzz854, zzz855, zzz856, zzz857, ba), zzz860, ba)
new_intersectFM_C(Branch(GT, zzz31, zzz32, Branch(GT, zzz331, zzz332, EmptyFM, zzz334), zzz34), Branch(EQ, zzz41, zzz42, zzz43, zzz44), h) → new_intersectFM_C(new_mkVBalBranch3(zzz31, new_splitGT8(zzz331, zzz332, zzz334, h), zzz34, h), zzz44, h)
new_intersectFM_C(Branch(LT, zzz31, zzz32, zzz33, zzz34), Branch(LT, zzz41, zzz42, zzz43, zzz44), h) → new_intersectFM_C(new_splitGT3(zzz31, zzz32, zzz33, zzz34, h), zzz44, h)
new_intersectFM_C2IntersectFM_C17(zzz2223, zzz2224, zzz2225, zzz2226, zzz2227, zzz2228, zzz2229, zzz2230, LT, zzz2232, zzz2233, zzz2234, EmptyFM, ce, cf) → new_intersectFM_C(new_intersectFM_C2Gts3(Branch(EQ, zzz2223, zzz2224, zzz2225, zzz2226), ce), zzz2230, ce)
new_intersectFM_C2IntersectFM_C12(zzz76, zzz77, zzz78, zzz79, zzz80, zzz81, zzz82, zzz83, zzz84, zzz85, zzz86, Branch(GT, zzz871, zzz872, zzz873, zzz874), bg, bh) → new_intersectFM_C2IntersectFM_C112(zzz76, zzz77, zzz78, zzz79, zzz80, zzz81, zzz82, zzz83, zzz873, bg, bh)
new_intersectFM_C(Branch(GT, zzz31, zzz32, Branch(GT, zzz331, zzz332, Branch(GT, zzz3331, zzz3332, Branch(LT, zzz33331, zzz33332, zzz33333, zzz33334), zzz3334), zzz334), zzz34), Branch(EQ, zzz41, zzz42, zzz43, zzz44), h) → new_intersectFM_C2IntersectFM_C12(zzz31, zzz32, Branch(GT, zzz331, zzz332, Branch(GT, zzz3331, zzz3332, Branch(LT, zzz33331, zzz33332, zzz33333, zzz33334), zzz3334), zzz334), zzz34, zzz41, zzz42, zzz43, zzz44, zzz33331, zzz33332, zzz33333, zzz33334, h, h)
new_intersectFM_C(Branch(GT, zzz31, zzz32, EmptyFM, zzz34), Branch(EQ, zzz41, zzz42, zzz43, zzz44), h) → new_intersectFM_C(new_splitGT8(zzz31, zzz32, zzz34, h), zzz44, h)
new_intersectFM_C2IntersectFM_C10(zzz869, zzz870, zzz871, zzz872, zzz873, zzz874, zzz875, zzz876, EQ, zzz878, zzz879, EmptyFM, zzz881, bc, bd) → new_intersectFM_C(new_intersectFM_C2Gts1(zzz869, zzz870, zzz871, zzz872, bc), zzz876, bc)
new_intersectFM_C(Branch(GT, zzz31, zzz32, Branch(GT, zzz331, zzz332, Branch(GT, zzz3331, zzz3332, Branch(GT, zzz33331, zzz33332, Branch(LT, zzz333331, zzz333332, zzz333333, zzz333334), zzz33334), zzz3334), zzz334), zzz34), Branch(EQ, zzz41, zzz42, zzz43, zzz44), h) → new_intersectFM_C2IntersectFM_C13(zzz31, zzz32, Branch(GT, zzz331, zzz332, Branch(GT, zzz3331, zzz3332, Branch(GT, zzz33331, zzz33332, Branch(LT, zzz333331, zzz333332, zzz333333, zzz333334), zzz33334), zzz3334), zzz334), zzz34, zzz41, zzz42, zzz43, zzz44, zzz333331, zzz333332, zzz333333, zzz333334, h, h)
new_intersectFM_C2IntersectFM_C15(zzz76, zzz77, zzz78, zzz79, zzz80, zzz81, zzz82, zzz83, zzz871, zzz872, zzz873, zzz874, bg, bh) → new_intersectFM_C2IntersectFM_C112(zzz76, zzz77, zzz78, zzz79, zzz80, zzz81, zzz82, zzz83, zzz873, bg, bh)
new_intersectFM_C2IntersectFM_C16(zzz2208, zzz2209, zzz2210, zzz2211, zzz2212, zzz2213, zzz2214, zzz2215, LT, zzz2217, zzz2218, zzz2219, EmptyFM, ca, cb) → new_intersectFM_C(new_intersectFM_C2Gts3(Branch(LT, zzz2208, zzz2209, zzz2210, zzz2211), ca), zzz2215, ca)
new_intersectFM_C(Branch(GT, zzz31, zzz32, Branch(EQ, zzz331, zzz332, zzz333, zzz334), zzz34), Branch(EQ, zzz41, zzz42, zzz43, zzz44), h) → new_intersectFM_C(new_mkVBalBranch3(zzz31, new_splitGT7(zzz331, zzz332, zzz333, zzz334, h), zzz34, h), zzz44, h)
new_intersectFM_C2IntersectFM_C1(zzz854, zzz855, zzz856, zzz857, zzz858, zzz859, zzz860, zzz861, GT, zzz863, zzz864, zzz865, zzz866, ba, bb) → new_intersectFM_C2IntersectFM_C19(zzz854, zzz855, zzz856, zzz857, zzz858, zzz859, zzz860, zzz861, zzz865, ba, bb)
new_intersectFM_C2IntersectFM_C12(zzz76, zzz77, zzz78, zzz79, zzz80, zzz81, zzz82, zzz83, zzz84, zzz85, zzz86, Branch(EQ, zzz871, zzz872, zzz873, zzz874), bg, bh) → new_intersectFM_C(new_intersectFM_C2Lts(zzz76, zzz77, zzz78, zzz79, bg), zzz82, bg)

The TRS R consists of the following rules:

new_splitGT24(zzz76, zzz77, zzz78, zzz79, bg) → new_mkVBalBranch3(zzz76, new_splitGT14(zzz78, bg), zzz79, bg)
new_splitGT14(EmptyFM, be) → new_splitGT42(be)
new_splitGT14(Branch(GT, zzz8861, zzz8862, zzz8863, zzz8864), be) → new_splitGT26(zzz8861, zzz8862, zzz8863, zzz8864, be)
new_splitGT14(Branch(LT, zzz8861, zzz8862, zzz8863, zzz8864), be) → new_splitGT29(zzz8861, zzz8862, zzz8863, zzz8864, be)
new_splitGT29(zzz883, zzz884, zzz885, zzz886, be) → new_splitGT14(zzz886, be)
new_splitGT14(Branch(EQ, zzz8861, zzz8862, zzz8863, zzz8864), be) → new_splitGT27(zzz8861, zzz8862, zzz8863, zzz8864, be)
new_mkVBalBranch3(zzz31, Branch(zzz520, zzz521, Neg(Zero), zzz523, zzz524), Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), h) → new_mkVBalBranch3MkVBalBranch155(zzz340, zzz341, zzz34200, zzz343, zzz344, zzz520, zzz521, zzz523, zzz524, zzz31, new_primMulNat1(zzz34200), h)
new_mkVBalBranch3(zzz31, Branch(zzz520, zzz521, Pos(Zero), zzz523, zzz524), Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), h) → new_mkVBalBranch3MkVBalBranch154(zzz340, zzz341, zzz34200, zzz343, zzz344, zzz520, zzz521, zzz523, zzz524, zzz31, new_primMulNat1(zzz34200), h)
new_mkVBalBranch3(zzz31, Branch(zzz520, zzz521, zzz522, zzz523, zzz524), EmptyFM, h) → new_addToFM(Branch(zzz520, zzz521, zzz522, zzz523, zzz524), zzz31, h)
new_mkVBalBranch3(zzz31, EmptyFM, zzz34, h) → new_addToFM(zzz34, zzz31, h)
new_mkVBalBranch3(zzz31, Branch(zzz520, zzz521, Pos(Zero), zzz523, zzz524), Branch(zzz340, zzz341, Pos(Succ(zzz34200)), zzz343, zzz344), h) → new_mkBalBranch(zzz340, zzz341, new_mkVBalBranch3(zzz31, Branch(zzz520, zzz521, Pos(Zero), zzz523, zzz524), zzz343, h), zzz344, ty_Ordering, h)
new_mkVBalBranch3(zzz31, Branch(zzz520, zzz521, Neg(Zero), zzz523, zzz524), Branch(zzz340, zzz341, Pos(Zero), zzz343, zzz344), h) → new_mkBranch(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))), GT, zzz31, Branch(zzz520, zzz521, Neg(Zero), zzz523, zzz524), Branch(zzz340, zzz341, Pos(Zero), zzz343, zzz344), ty_Ordering, h)
new_mkVBalBranch3(zzz31, Branch(zzz520, zzz521, Pos(Zero), zzz523, zzz524), Branch(zzz340, zzz341, Neg(Zero), zzz343, zzz344), h) → new_mkBranch(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))), GT, zzz31, Branch(zzz520, zzz521, Pos(Zero), zzz523, zzz524), Branch(zzz340, zzz341, Neg(Zero), zzz343, zzz344), ty_Ordering, h)
new_mkVBalBranch3(zzz31, Branch(zzz520, zzz521, Pos(Zero), zzz523, zzz524), Branch(zzz340, zzz341, Pos(Zero), zzz343, zzz344), h) → new_mkBranch(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))), GT, zzz31, Branch(zzz520, zzz521, Pos(Zero), zzz523, zzz524), Branch(zzz340, zzz341, Pos(Zero), zzz343, zzz344), ty_Ordering, h)
new_mkVBalBranch3(zzz31, Branch(zzz520, zzz521, Neg(Succ(zzz52200)), zzz523, zzz524), Branch(zzz340, zzz341, zzz342, zzz343, zzz344), h) → new_mkVBalBranch3MkVBalBranch272(zzz340, zzz341, zzz342, zzz343, zzz344, zzz520, zzz521, zzz52200, zzz523, zzz524, zzz31, new_primMulNat0(zzz52200), h)
new_mkVBalBranch3(zzz31, Branch(zzz520, zzz521, Neg(Zero), zzz523, zzz524), Branch(zzz340, zzz341, Pos(Succ(zzz34200)), zzz343, zzz344), h) → new_mkBalBranch(zzz340, zzz341, new_mkVBalBranch3(zzz31, Branch(zzz520, zzz521, Neg(Zero), zzz523, zzz524), zzz343, h), zzz344, ty_Ordering, h)
new_mkVBalBranch3(zzz31, Branch(zzz520, zzz521, Pos(Succ(zzz52200)), zzz523, zzz524), Branch(zzz340, zzz341, zzz342, zzz343, zzz344), h) → new_mkVBalBranch3MkVBalBranch267(zzz340, zzz341, zzz342, zzz343, zzz344, zzz520, zzz521, zzz52200, zzz523, zzz524, zzz31, new_primMulNat0(zzz52200), h)
new_mkVBalBranch3(zzz31, Branch(zzz520, zzz521, Neg(Zero), zzz523, zzz524), Branch(zzz340, zzz341, Neg(Zero), zzz343, zzz344), h) → new_mkBranch(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))), GT, zzz31, Branch(zzz520, zzz521, Neg(Zero), zzz523, zzz524), Branch(zzz340, zzz341, Neg(Zero), zzz343, zzz344), ty_Ordering, h)
new_mkBranch(zzz2265, zzz2266, zzz2267, zzz2268, zzz2269, ec, ed) → Branch(zzz2266, zzz2267, new_primPlusInt(new_primPlusInt0(Succ(Zero), new_sizeFM(zzz2268, ec, ed)), zzz2268, zzz2269, zzz2266, ec, ed), zzz2268, zzz2269)
new_sizeFM(EmptyFM, fb, fc) → Pos(Zero)
new_sizeFM(Branch(zzz13040, zzz13041, zzz13042, zzz13043, zzz13044), fb, fc) → zzz13042
new_primPlusInt0(zzz1311, Neg(zzz13130)) → new_primMinusNat0(zzz1311, zzz13130)
new_primPlusInt0(zzz1311, Pos(zzz13130)) → Pos(new_primPlusNat2(zzz1311, zzz13130))
new_primPlusInt(Pos(zzz22720), zzz2268, zzz2269, zzz2266, ec, ed) → new_primPlusInt0(zzz22720, new_sizeFM(zzz2269, ec, ed))
new_primPlusInt(Neg(zzz22720), zzz2268, zzz2269, zzz2266, ec, ed) → new_primPlusInt1(zzz22720, new_sizeFM(zzz2269, ec, ed))
new_primPlusInt1(zzz13120, Pos(zzz13150)) → new_primMinusNat0(zzz13150, zzz13120)
new_primPlusInt1(zzz13120, Neg(zzz13150)) → Neg(new_primPlusNat2(zzz13120, zzz13150))
new_primPlusNat2(Succ(zzz900), Succ(zzz9100)) → Succ(Succ(new_primPlusNat2(zzz900, zzz9100)))
new_primPlusNat2(Zero, Succ(zzz9100)) → Succ(zzz9100)
new_primPlusNat2(Succ(zzz900), Zero) → Succ(zzz900)
new_primPlusNat2(Zero, Zero) → Zero
new_primMinusNat0(Succ(zzz100100), Zero) → Pos(Succ(zzz100100))
new_primMinusNat0(Zero, Zero) → Pos(Zero)
new_primMinusNat0(Zero, Succ(zzz542000)) → Neg(Succ(zzz542000))
new_primMinusNat0(Succ(zzz100100), Succ(zzz542000)) → new_primMinusNat0(zzz100100, zzz542000)
new_primMulNat0(zzz6200) → new_primPlusNat3(Succ(new_primPlusNat3(new_primPlusNat1(zzz6200), zzz6200)), Succ(zzz6200))
new_mkVBalBranch3MkVBalBranch267(zzz340, zzz341, Pos(Zero), zzz343, zzz344, zzz520, zzz521, zzz52200, zzz523, zzz524, zzz31, Succ(zzz680), h) → new_mkVBalBranch3MkVBalBranch268(zzz340, zzz341, zzz343, zzz344, zzz520, zzz521, zzz52200, zzz523, zzz524, zzz31, h)
new_mkVBalBranch3MkVBalBranch267(zzz340, zzz341, Neg(zzz3420), zzz343, zzz344, zzz520, zzz521, zzz52200, zzz523, zzz524, zzz31, Zero, h) → new_mkVBalBranch3MkVBalBranch269(zzz340, zzz341, zzz3420, zzz343, zzz344, zzz520, zzz521, zzz52200, zzz523, zzz524, zzz31, h)
new_mkVBalBranch3MkVBalBranch267(zzz340, zzz341, Pos(Zero), zzz343, zzz344, zzz520, zzz521, zzz52200, zzz523, zzz524, zzz31, Zero, h) → new_mkVBalBranch3MkVBalBranch268(zzz340, zzz341, zzz343, zzz344, zzz520, zzz521, zzz52200, zzz523, zzz524, zzz31, h)
new_mkVBalBranch3MkVBalBranch267(zzz340, zzz341, Neg(zzz3420), zzz343, zzz344, zzz520, zzz521, zzz52200, zzz523, zzz524, zzz31, Succ(zzz680), h) → new_mkVBalBranch3MkVBalBranch269(zzz340, zzz341, zzz3420, zzz343, zzz344, zzz520, zzz521, zzz52200, zzz523, zzz524, zzz31, h)
new_mkVBalBranch3MkVBalBranch267(zzz340, zzz341, Pos(Succ(zzz34200)), zzz343, zzz344, zzz520, zzz521, zzz52200, zzz523, zzz524, zzz31, Zero, h) → new_mkVBalBranch3MkVBalBranch252(zzz340, zzz341, zzz34200, zzz343, zzz344, zzz520, zzz521, zzz52200, zzz523, zzz524, zzz31, zzz52200, zzz34200, h)
new_mkVBalBranch3MkVBalBranch267(zzz340, zzz341, Pos(Succ(zzz34200)), zzz343, zzz344, zzz520, zzz521, zzz52200, zzz523, zzz524, zzz31, Succ(zzz680), h) → new_mkVBalBranch3MkVBalBranch252(zzz340, zzz341, zzz34200, zzz343, zzz344, zzz520, zzz521, zzz52200, zzz523, zzz524, zzz31, Succ(new_primPlusNat2(zzz680, zzz52200)), zzz34200, h)
new_mkVBalBranch3MkVBalBranch252(zzz929, zzz930, zzz931, zzz932, zzz933, zzz934, zzz935, zzz936, zzz937, zzz938, zzz939, Succ(zzz9400), Succ(zzz9410), dc) → new_mkVBalBranch3MkVBalBranch252(zzz929, zzz930, zzz931, zzz932, zzz933, zzz934, zzz935, zzz936, zzz937, zzz938, zzz939, zzz9400, zzz9410, dc)
new_mkVBalBranch3MkVBalBranch252(zzz929, zzz930, zzz931, zzz932, zzz933, zzz934, zzz935, zzz936, zzz937, zzz938, zzz939, Succ(zzz9400), Zero, dc) → new_mkVBalBranch3MkVBalBranch253(zzz929, zzz930, zzz931, zzz932, zzz933, zzz934, zzz935, zzz936, zzz937, zzz938, zzz939, dc)
new_mkVBalBranch3MkVBalBranch253(zzz929, zzz930, zzz931, zzz932, zzz933, zzz934, zzz935, zzz936, zzz937, zzz938, zzz939, dc) → new_mkVBalBranch3MkVBalBranch131(zzz929, zzz930, zzz931, zzz932, zzz933, zzz934, zzz935, zzz936, zzz937, zzz938, zzz939, new_primMulNat1(zzz931), dc)
new_primMulNat1(zzz34200) → new_primPlusNat2(new_primMulNat0(zzz34200), Succ(zzz34200))
new_mkVBalBranch3MkVBalBranch131(zzz929, zzz930, zzz931, zzz932, zzz933, zzz934, zzz935, zzz936, zzz937, zzz938, zzz939, Succ(zzz10020), dc) → new_mkVBalBranch3MkVBalBranch132(zzz929, zzz930, zzz931, zzz932, zzz933, zzz934, zzz935, zzz936, zzz937, zzz938, zzz939, Succ(zzz10020), Succ(zzz936), dc)
new_mkVBalBranch3MkVBalBranch131(zzz929, zzz930, zzz931, zzz932, zzz933, zzz934, zzz935, zzz936, zzz937, zzz938, zzz939, Zero, dc) → new_mkVBalBranch3MkVBalBranch132(zzz929, zzz930, zzz931, zzz932, zzz933, zzz934, zzz935, zzz936, zzz937, zzz938, zzz939, Zero, Succ(zzz936), dc)
new_mkVBalBranch3MkVBalBranch132(zzz2033, zzz2034, zzz2035, zzz2036, zzz2037, zzz2038, zzz2039, zzz2040, zzz2041, zzz2042, zzz2043, Zero, Succ(zzz20450), fg) → new_mkBalBranch(zzz2038, zzz2039, zzz2041, new_mkVBalBranch3(zzz2043, zzz2042, Branch(zzz2033, zzz2034, Pos(Succ(zzz2035)), zzz2036, zzz2037), fg), ty_Ordering, fg)
new_mkBalBranch(zzz2930, zzz2931, zzz2127, zzz2934, da, db) → new_mkBalBranch6MkBalBranch5(zzz2934, zzz2127, zzz2930, zzz2931, new_primPlusInt2(new_mkBalBranch6Size_l(zzz2934, zzz2127, zzz2930, zzz2931, db, da), zzz2934, zzz2127, zzz2930, zzz2931, db, da), da, db)
new_mkBalBranch6Size_l(zzz2934, zzz2127, zzz2930, zzz2931, db, da) → new_sizeFM(zzz2127, da, db)
new_primPlusInt2(Pos(zzz21410), zzz2934, zzz2127, zzz2930, zzz2931, db, da) → new_primPlusInt0(zzz21410, new_sizeFM(zzz2934, da, db))
new_primPlusInt2(Neg(zzz21410), zzz2934, zzz2127, zzz2930, zzz2931, db, da) → new_primPlusInt1(zzz21410, new_sizeFM(zzz2934, da, db))
new_mkBalBranch6MkBalBranch5(zzz2934, zzz2127, zzz2930, zzz2931, Neg(Succ(zzz213900)), da, db) → new_mkBalBranch6MkBalBranch51(zzz2934, zzz2127, zzz2930, zzz2931, da, db)
new_mkBalBranch6MkBalBranch5(zzz2934, zzz2127, zzz2930, zzz2931, Pos(Succ(Succ(Zero))), da, db) → new_mkBalBranch6MkBalBranch50(zzz2934, zzz2127, zzz2930, zzz2931, da, db)
new_mkBalBranch6MkBalBranch5(zzz2934, zzz2127, zzz2930, zzz2931, Pos(Succ(Zero)), da, db) → new_mkBalBranch6MkBalBranch51(zzz2934, zzz2127, zzz2930, zzz2931, da, db)
new_mkBalBranch6MkBalBranch5(zzz2934, zzz2127, zzz2930, zzz2931, Neg(Zero), da, db) → new_mkBalBranch6MkBalBranch51(zzz2934, zzz2127, zzz2930, zzz2931, da, db)
new_mkBalBranch6MkBalBranch5(zzz2934, zzz2127, zzz2930, zzz2931, Pos(Succ(Succ(Succ(zzz21390000)))), da, db) → new_mkBalBranch6MkBalBranch50(zzz2934, zzz2127, zzz2930, zzz2931, da, db)
new_mkBalBranch6MkBalBranch5(zzz2934, zzz2127, zzz2930, zzz2931, Pos(Zero), da, db) → new_mkBalBranch6MkBalBranch51(zzz2934, zzz2127, zzz2930, zzz2931, da, db)
new_mkBalBranch6MkBalBranch51(zzz2934, zzz2127, zzz2930, zzz2931, da, db) → new_mkBranch(Zero, zzz2930, zzz2931, zzz2127, zzz2934, da, db)
new_mkBalBranch6MkBalBranch50(zzz2934, zzz2127, zzz2930, zzz2931, da, db) → new_mkBalBranch6MkBalBranch410(zzz2934, zzz2127, zzz2930, zzz2931, new_mkBalBranch6Size_l(zzz2934, zzz2127, zzz2930, zzz2931, db, da), da, db)
new_mkBalBranch6MkBalBranch410(zzz2934, zzz2127, zzz2930, zzz2931, zzz2206, da, db) → new_mkBalBranch6MkBalBranch411(zzz2934, zzz2127, zzz2930, zzz2931, new_mkBalBranch6Size_r(zzz2934, zzz2127, zzz2930, zzz2931, db, da), zzz2206, da, db)
new_mkBalBranch6Size_r(zzz2934, zzz2127, zzz2930, zzz2931, db, da) → new_sizeFM(zzz2934, da, db)
new_mkBalBranch6MkBalBranch411(zzz2934, zzz2127, zzz2930, zzz2931, Neg(Zero), Pos(zzz22060), da, db) → new_mkBalBranch6MkBalBranch416(zzz2934, zzz2127, zzz2930, zzz2931, new_primMulNat(zzz22060), da, db)
new_mkBalBranch6MkBalBranch411(zzz2934, zzz2127, zzz2930, zzz2931, Neg(Zero), Neg(zzz22060), da, db) → new_mkBalBranch6MkBalBranch413(zzz2934, zzz2127, zzz2930, zzz2931, new_primMulNat(zzz22060), da, db)
new_mkBalBranch6MkBalBranch411(zzz2934, zzz2127, zzz2930, zzz2931, Pos(Succ(zzz222100)), Neg(zzz22060), da, db) → new_mkBalBranch6MkBalBranch415(zzz2934, zzz2127, zzz2930, zzz2931, zzz222100, new_primMulNat(zzz22060), da, db)
new_mkBalBranch6MkBalBranch411(zzz2934, zzz2127, zzz2930, zzz2931, Pos(Zero), Pos(zzz22060), da, db) → new_mkBalBranch6MkBalBranch414(zzz2934, zzz2127, zzz2930, zzz2931, new_primMulNat(zzz22060), da, db)
new_mkBalBranch6MkBalBranch411(zzz2934, zzz2127, zzz2930, zzz2931, Pos(Succ(zzz222100)), Pos(zzz22060), da, db) → new_mkBalBranch6MkBalBranch44(zzz2934, zzz2127, zzz2930, zzz2931, zzz222100, new_primMulNat(zzz22060), da, db)
new_mkBalBranch6MkBalBranch411(zzz2934, zzz2127, zzz2930, zzz2931, Neg(Succ(zzz222100)), Neg(zzz22060), da, db) → new_mkBalBranch6MkBalBranch46(zzz2934, zzz2127, zzz2930, zzz2931, zzz222100, new_primMulNat(zzz22060), da, db)
new_mkBalBranch6MkBalBranch411(zzz2934, zzz2127, zzz2930, zzz2931, Pos(Zero), Neg(zzz22060), da, db) → new_mkBalBranch6MkBalBranch48(zzz2934, zzz2127, zzz2930, zzz2931, new_primMulNat(zzz22060), da, db)
new_mkBalBranch6MkBalBranch411(zzz2934, zzz2127, zzz2930, zzz2931, Neg(Succ(zzz222100)), Pos(zzz22060), da, db) → new_mkBalBranch6MkBalBranch42(zzz2934, zzz2127, zzz2930, zzz2931, zzz222100, new_primMulNat(zzz22060), da, db)
new_primMulNat(Zero) → Zero
new_primMulNat(Succ(zzz206300)) → new_primPlusNat2(new_primMulNat0(zzz206300), Succ(zzz206300))
new_mkBalBranch6MkBalBranch42(zzz2934, zzz2127, zzz2930, zzz2931, zzz222100, zzz2240, da, db) → new_mkBalBranch6MkBalBranch43(zzz2934, zzz2127, zzz2930, zzz2931, da, db)
new_mkBalBranch6MkBalBranch43(zzz2934, zzz2127, zzz2930, zzz2931, da, db) → new_mkBalBranch6MkBalBranch41(zzz2934, zzz2127, zzz2930, zzz2931, da, db)
new_mkBalBranch6MkBalBranch41(zzz2934, zzz2127, zzz2930, zzz2931, da, db) → new_mkBalBranch6MkBalBranch310(zzz2934, zzz2127, zzz2930, zzz2931, new_mkBalBranch6Size_l(zzz2934, zzz2127, zzz2930, zzz2931, db, da), new_mkBalBranch6Size_r(zzz2934, zzz2127, zzz2930, zzz2931, db, da), da, db)
new_mkBalBranch6MkBalBranch310(zzz2934, zzz2127, zzz2930, zzz2931, Pos(Zero), Neg(zzz22450), da, db) → new_mkBalBranch6MkBalBranch315(zzz2934, zzz2127, zzz2930, zzz2931, new_primMulNat(zzz22450), da, db)
new_mkBalBranch6MkBalBranch310(zzz2934, zzz2127, zzz2930, zzz2931, Neg(Zero), Pos(zzz22450), da, db) → new_mkBalBranch6MkBalBranch30(zzz2934, zzz2127, zzz2930, zzz2931, new_primMulNat(zzz22450), da, db)
new_mkBalBranch6MkBalBranch310(zzz2934, zzz2127, zzz2930, zzz2931, Neg(Zero), Neg(zzz22450), da, db) → new_mkBalBranch6MkBalBranch314(zzz2934, zzz2127, zzz2930, zzz2931, new_primMulNat(zzz22450), da, db)
new_mkBalBranch6MkBalBranch310(zzz2934, zzz2127, zzz2930, zzz2931, Neg(Succ(zzz224400)), Neg(zzz22450), da, db) → new_mkBalBranch6MkBalBranch37(zzz2934, zzz2127, zzz2930, zzz2931, zzz224400, new_primMulNat(zzz22450), da, db)
new_mkBalBranch6MkBalBranch310(zzz2934, zzz2127, zzz2930, zzz2931, Pos(Succ(zzz224400)), Neg(zzz22450), da, db) → new_mkBalBranch6MkBalBranch312(zzz2934, zzz2127, zzz2930, zzz2931, zzz224400, new_primMulNat(zzz22450), da, db)
new_mkBalBranch6MkBalBranch310(zzz2934, zzz2127, zzz2930, zzz2931, Neg(Succ(zzz224400)), Pos(zzz22450), da, db) → new_mkBalBranch6MkBalBranch34(zzz2934, zzz2127, zzz2930, zzz2931, zzz224400, new_primMulNat(zzz22450), da, db)
new_mkBalBranch6MkBalBranch310(zzz2934, zzz2127, zzz2930, zzz2931, Pos(Zero), Pos(zzz22450), da, db) → new_mkBalBranch6MkBalBranch35(zzz2934, zzz2127, zzz2930, zzz2931, new_primMulNat(zzz22450), da, db)
new_mkBalBranch6MkBalBranch310(zzz2934, zzz2127, zzz2930, zzz2931, Pos(Succ(zzz224400)), Pos(zzz22450), da, db) → new_mkBalBranch6MkBalBranch311(zzz2934, zzz2127, zzz2930, zzz2931, zzz224400, new_primMulNat(zzz22450), da, db)
new_mkBalBranch6MkBalBranch311(zzz2934, zzz2127, zzz2930, zzz2931, zzz224400, zzz2248, da, db) → new_mkBalBranch6MkBalBranch38(zzz2934, zzz2127, zzz2930, zzz2931, zzz224400, zzz2248, da, db)
new_mkBalBranch6MkBalBranch38(zzz2934, zzz2127, zzz2930, zzz2931, zzz224400, Succ(zzz22480), da, db) → new_mkBalBranch6MkBalBranch39(zzz2934, zzz2127, zzz2930, zzz2931, zzz224400, zzz22480, da, db)
new_mkBalBranch6MkBalBranch38(zzz2934, zzz2127, zzz2930, zzz2931, zzz224400, Zero, da, db) → new_mkBalBranch6MkBalBranch33(zzz2934, zzz2127, zzz2930, zzz2931, da, db)
new_mkBalBranch6MkBalBranch33(zzz2934, Branch(zzz21270, zzz21271, zzz21272, zzz21273, zzz21274), zzz2930, zzz2931, da, db) → new_mkBalBranch6MkBalBranch113(zzz2934, zzz21270, zzz21271, zzz21272, zzz21273, zzz21274, zzz2930, zzz2931, new_sizeFM(zzz21274, da, db), new_sizeFM(zzz21273, da, db), da, db)
new_mkBalBranch6MkBalBranch33(zzz2934, EmptyFM, zzz2930, zzz2931, da, db) → error([])
new_mkBalBranch6MkBalBranch113(zzz2934, zzz21270, zzz21271, zzz21272, zzz21273, zzz21274, zzz2930, zzz2931, Pos(Zero), Pos(zzz22630), da, db) → new_mkBalBranch6MkBalBranch116(zzz2934, zzz21270, zzz21271, zzz21272, zzz21273, zzz21274, zzz2930, zzz2931, new_primMulNat2(zzz22630), da, db)
new_mkBalBranch6MkBalBranch113(zzz2934, zzz21270, zzz21271, zzz21272, zzz21273, zzz21274, zzz2930, zzz2931, Neg(Zero), Neg(zzz22630), da, db) → new_mkBalBranch6MkBalBranch110(zzz2934, zzz21270, zzz21271, zzz21272, zzz21273, zzz21274, zzz2930, zzz2931, new_primMulNat2(zzz22630), da, db)
new_mkBalBranch6MkBalBranch113(zzz2934, zzz21270, zzz21271, zzz21272, zzz21273, zzz21274, zzz2930, zzz2931, Neg(Succ(zzz226200)), Pos(zzz22630), da, db) → new_mkBalBranch6MkBalBranch118(zzz2934, zzz21270, zzz21271, zzz21272, zzz21273, zzz21274, zzz2930, zzz2931, zzz226200, new_primMulNat2(zzz22630), da, db)
new_mkBalBranch6MkBalBranch113(zzz2934, zzz21270, zzz21271, zzz21272, zzz21273, zzz21274, zzz2930, zzz2931, Pos(Zero), Neg(zzz22630), da, db) → new_mkBalBranch6MkBalBranch117(zzz2934, zzz21270, zzz21271, zzz21272, zzz21273, zzz21274, zzz2930, zzz2931, new_primMulNat2(zzz22630), da, db)
new_mkBalBranch6MkBalBranch113(zzz2934, zzz21270, zzz21271, zzz21272, zzz21273, zzz21274, zzz2930, zzz2931, Neg(Zero), Pos(zzz22630), da, db) → new_mkBalBranch6MkBalBranch1110(zzz2934, zzz21270, zzz21271, zzz21272, zzz21273, zzz21274, zzz2930, zzz2931, new_primMulNat2(zzz22630), da, db)
new_mkBalBranch6MkBalBranch113(zzz2934, zzz21270, zzz21271, zzz21272, zzz21273, zzz21274, zzz2930, zzz2931, Pos(Succ(zzz226200)), Pos(zzz22630), da, db) → new_mkBalBranch6MkBalBranch114(zzz2934, zzz21270, zzz21271, zzz21272, zzz21273, zzz21274, zzz2930, zzz2931, zzz226200, new_primMulNat2(zzz22630), da, db)
new_mkBalBranch6MkBalBranch113(zzz2934, zzz21270, zzz21271, zzz21272, zzz21273, zzz21274, zzz2930, zzz2931, Pos(Succ(zzz226200)), Neg(zzz22630), da, db) → new_mkBalBranch6MkBalBranch115(zzz2934, zzz21270, zzz21271, zzz21272, zzz21273, zzz21274, zzz2930, zzz2931, zzz226200, new_primMulNat2(zzz22630), da, db)
new_mkBalBranch6MkBalBranch113(zzz2934, zzz21270, zzz21271, zzz21272, zzz21273, zzz21274, zzz2930, zzz2931, Neg(Succ(zzz226200)), Neg(zzz22630), da, db) → new_mkBalBranch6MkBalBranch119(zzz2934, zzz21270, zzz21271, zzz21272, zzz21273, zzz21274, zzz2930, zzz2931, zzz226200, new_primMulNat2(zzz22630), da, db)
new_primMulNat2(Succ(zzz224700)) → new_primPlusNat2(new_primPlusNat2(Zero, Succ(zzz224700)), Succ(zzz224700))
new_primMulNat2(Zero) → Zero
new_mkBalBranch6MkBalBranch119(zzz2934, zzz21270, zzz21271, zzz21272, zzz21273, zzz21274, zzz2930, zzz2931, zzz226200, zzz2276, da, db) → new_mkBalBranch6MkBalBranch1111(zzz2934, zzz21270, zzz21271, zzz21272, zzz21273, zzz21274, zzz2930, zzz2931, zzz2276, zzz226200, da, db)
new_mkBalBranch6MkBalBranch1111(zzz2934, zzz21270, zzz21271, zzz21272, zzz21273, zzz21274, zzz2930, zzz2931, Succ(zzz22760), zzz226200, da, db) → new_mkBalBranch6MkBalBranch1113(zzz2934, zzz21270, zzz21271, zzz21272, zzz21273, zzz21274, zzz2930, zzz2931, zzz22760, zzz226200, da, db)
new_mkBalBranch6MkBalBranch1111(zzz2934, zzz21270, zzz21271, zzz21272, zzz21273, zzz21274, zzz2930, zzz2931, Zero, zzz226200, da, db) → new_mkBalBranch6MkBalBranch1112(zzz2934, zzz21270, zzz21271, zzz21272, zzz21273, zzz21274, zzz2930, zzz2931, da, db)
new_mkBalBranch6MkBalBranch1112(zzz2934, zzz21270, zzz21271, zzz21272, zzz21273, zzz21274, zzz2930, zzz2931, da, db) → new_mkBranch(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))), zzz21270, zzz21271, zzz21273, new_mkBranch(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))), zzz2930, zzz2931, zzz21274, zzz2934, da, db), da, db)
new_mkBalBranch6MkBalBranch1113(zzz2934, zzz21270, zzz21271, zzz21272, zzz21273, zzz21274, zzz2930, zzz2931, Succ(zzz2262000), Succ(zzz227000), da, db) → new_mkBalBranch6MkBalBranch1113(zzz2934, zzz21270, zzz21271, zzz21272, zzz21273, zzz21274, zzz2930, zzz2931, zzz2262000, zzz227000, da, db)
new_mkBalBranch6MkBalBranch1113(zzz2934, zzz21270, zzz21271, zzz21272, zzz21273, zzz21274, zzz2930, zzz2931, Zero, Zero, da, db) → new_mkBalBranch6MkBalBranch112(zzz2934, zzz21270, zzz21271, zzz21272, zzz21273, zzz21274, zzz2930, zzz2931, da, db)
new_mkBalBranch6MkBalBranch1113(zzz2934, zzz21270, zzz21271, zzz21272, zzz21273, zzz21274, zzz2930, zzz2931, Succ(zzz2262000), Zero, da, db) → new_mkBalBranch6MkBalBranch1114(zzz2934, zzz21270, zzz21271, zzz21272, zzz21273, zzz21274, zzz2930, zzz2931, da, db)
new_mkBalBranch6MkBalBranch1113(zzz2934, zzz21270, zzz21271, zzz21272, zzz21273, zzz21274, zzz2930, zzz2931, Zero, Succ(zzz227000), da, db) → new_mkBalBranch6MkBalBranch1112(zzz2934, zzz21270, zzz21271, zzz21272, zzz21273, zzz21274, zzz2930, zzz2931, da, db)
new_mkBalBranch6MkBalBranch1114(zzz2934, zzz21270, zzz21271, zzz21272, zzz21273, zzz21274, zzz2930, zzz2931, da, db) → new_mkBalBranch6MkBalBranch1115(zzz2934, zzz21270, zzz21271, zzz21272, zzz21273, zzz21274, zzz2930, zzz2931, da, db)
new_mkBalBranch6MkBalBranch1115(zzz2934, zzz21270, zzz21271, zzz21272, zzz21273, EmptyFM, zzz2930, zzz2931, da, db) → error([])
new_mkBalBranch6MkBalBranch1115(zzz2934, zzz21270, zzz21271, zzz21272, zzz21273, Branch(zzz212740, zzz212741, zzz212742, zzz212743, zzz212744), zzz2930, zzz2931, da, db) → new_mkBranch(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))), zzz212740, zzz212741, new_mkBranch(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))), zzz21270, zzz21271, zzz21273, zzz212743, da, db), new_mkBranch(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))), zzz2930, zzz2931, zzz212744, zzz2934, da, db), da, db)
new_mkBalBranch6MkBalBranch112(zzz2934, zzz21270, zzz21271, zzz21272, zzz21273, zzz21274, zzz2930, zzz2931, da, db) → new_mkBalBranch6MkBalBranch1115(zzz2934, zzz21270, zzz21271, zzz21272, zzz21273, zzz21274, zzz2930, zzz2931, da, db)
new_mkBalBranch6MkBalBranch115(zzz2934, zzz21270, zzz21271, zzz21272, zzz21273, zzz21274, zzz2930, zzz2931, zzz226200, zzz2271, da, db) → new_mkBalBranch6MkBalBranch1114(zzz2934, zzz21270, zzz21271, zzz21272, zzz21273, zzz21274, zzz2930, zzz2931, da, db)
new_mkBalBranch6MkBalBranch114(zzz2934, zzz21270, zzz21271, zzz21272, zzz21273, zzz21274, zzz2930, zzz2931, zzz226200, zzz2270, da, db) → new_mkBalBranch6MkBalBranch111(zzz2934, zzz21270, zzz21271, zzz21272, zzz21273, zzz21274, zzz2930, zzz2931, zzz226200, zzz2270, da, db)
new_mkBalBranch6MkBalBranch111(zzz2934, zzz21270, zzz21271, zzz21272, zzz21273, zzz21274, zzz2930, zzz2931, zzz226200, Succ(zzz22700), da, db) → new_mkBalBranch6MkBalBranch1113(zzz2934, zzz21270, zzz21271, zzz21272, zzz21273, zzz21274, zzz2930, zzz2931, zzz226200, zzz22700, da, db)
new_mkBalBranch6MkBalBranch111(zzz2934, zzz21270, zzz21271, zzz21272, zzz21273, zzz21274, zzz2930, zzz2931, zzz226200, Zero, da, db) → new_mkBalBranch6MkBalBranch1114(zzz2934, zzz21270, zzz21271, zzz21272, zzz21273, zzz21274, zzz2930, zzz2931, da, db)
new_mkBalBranch6MkBalBranch1110(zzz2934, zzz21270, zzz21271, zzz21272, zzz21273, zzz21274, zzz2930, zzz2931, Zero, da, db) → new_mkBalBranch6MkBalBranch112(zzz2934, zzz21270, zzz21271, zzz21272, zzz21273, zzz21274, zzz2930, zzz2931, da, db)
new_mkBalBranch6MkBalBranch1110(zzz2934, zzz21270, zzz21271, zzz21272, zzz21273, zzz21274, zzz2930, zzz2931, Succ(zzz22770), da, db) → new_mkBalBranch6MkBalBranch1112(zzz2934, zzz21270, zzz21271, zzz21272, zzz21273, zzz21274, zzz2930, zzz2931, da, db)
new_mkBalBranch6MkBalBranch117(zzz2934, zzz21270, zzz21271, zzz21272, zzz21273, zzz21274, zzz2930, zzz2931, Zero, da, db) → new_mkBalBranch6MkBalBranch112(zzz2934, zzz21270, zzz21271, zzz21272, zzz21273, zzz21274, zzz2930, zzz2931, da, db)
new_mkBalBranch6MkBalBranch117(zzz2934, zzz21270, zzz21271, zzz21272, zzz21273, zzz21274, zzz2930, zzz2931, Succ(zzz22740), da, db) → new_mkBalBranch6MkBalBranch1114(zzz2934, zzz21270, zzz21271, zzz21272, zzz21273, zzz21274, zzz2930, zzz2931, da, db)
new_mkBalBranch6MkBalBranch118(zzz2934, zzz21270, zzz21271, zzz21272, zzz21273, zzz21274, zzz2930, zzz2931, zzz226200, zzz2275, da, db) → new_mkBalBranch6MkBalBranch1112(zzz2934, zzz21270, zzz21271, zzz21272, zzz21273, zzz21274, zzz2930, zzz2931, da, db)
new_mkBalBranch6MkBalBranch110(zzz2934, zzz21270, zzz21271, zzz21272, zzz21273, zzz21274, zzz2930, zzz2931, Zero, da, db) → new_mkBalBranch6MkBalBranch112(zzz2934, zzz21270, zzz21271, zzz21272, zzz21273, zzz21274, zzz2930, zzz2931, da, db)
new_mkBalBranch6MkBalBranch110(zzz2934, zzz21270, zzz21271, zzz21272, zzz21273, zzz21274, zzz2930, zzz2931, Succ(zzz22780), da, db) → new_mkBalBranch6MkBalBranch111(zzz2934, zzz21270, zzz21271, zzz21272, zzz21273, zzz21274, zzz2930, zzz2931, zzz22780, Zero, da, db)
new_mkBalBranch6MkBalBranch116(zzz2934, zzz21270, zzz21271, zzz21272, zzz21273, zzz21274, zzz2930, zzz2931, Succ(zzz22730), da, db) → new_mkBalBranch6MkBalBranch1111(zzz2934, zzz21270, zzz21271, zzz21272, zzz21273, zzz21274, zzz2930, zzz2931, Zero, zzz22730, da, db)
new_mkBalBranch6MkBalBranch116(zzz2934, zzz21270, zzz21271, zzz21272, zzz21273, zzz21274, zzz2930, zzz2931, Zero, da, db) → new_mkBalBranch6MkBalBranch112(zzz2934, zzz21270, zzz21271, zzz21272, zzz21273, zzz21274, zzz2930, zzz2931, da, db)
new_mkBalBranch6MkBalBranch39(zzz2934, zzz2127, zzz2930, zzz2931, Succ(zzz2244000), Zero, da, db) → new_mkBalBranch6MkBalBranch33(zzz2934, zzz2127, zzz2930, zzz2931, da, db)
new_mkBalBranch6MkBalBranch39(zzz2934, zzz2127, zzz2930, zzz2931, Succ(zzz2244000), Succ(zzz224800), da, db) → new_mkBalBranch6MkBalBranch39(zzz2934, zzz2127, zzz2930, zzz2931, zzz2244000, zzz224800, da, db)
new_mkBalBranch6MkBalBranch39(zzz2934, zzz2127, zzz2930, zzz2931, Zero, Succ(zzz224800), da, db) → new_mkBalBranch6MkBalBranch31(zzz2934, zzz2127, zzz2930, zzz2931, da, db)
new_mkBalBranch6MkBalBranch39(zzz2934, zzz2127, zzz2930, zzz2931, Zero, Zero, da, db) → new_mkBalBranch6MkBalBranch32(zzz2934, zzz2127, zzz2930, zzz2931, da, db)
new_mkBalBranch6MkBalBranch32(zzz2934, zzz2127, zzz2930, zzz2931, da, db) → new_mkBalBranch6MkBalBranch313(zzz2934, zzz2127, zzz2930, zzz2931, da, db)
new_mkBalBranch6MkBalBranch313(zzz2934, zzz2127, zzz2930, zzz2931, da, db) → new_mkBranch(Succ(Zero), zzz2930, zzz2931, zzz2127, zzz2934, da, db)
new_mkBalBranch6MkBalBranch31(zzz2934, zzz2127, zzz2930, zzz2931, da, db) → new_mkBalBranch6MkBalBranch313(zzz2934, zzz2127, zzz2930, zzz2931, da, db)
new_mkBalBranch6MkBalBranch35(zzz2934, zzz2127, zzz2930, zzz2931, Succ(zzz22500), da, db) → new_mkBalBranch6MkBalBranch36(zzz2934, zzz2127, zzz2930, zzz2931, Zero, zzz22500, da, db)
new_mkBalBranch6MkBalBranch35(zzz2934, zzz2127, zzz2930, zzz2931, Zero, da, db) → new_mkBalBranch6MkBalBranch32(zzz2934, zzz2127, zzz2930, zzz2931, da, db)
new_mkBalBranch6MkBalBranch36(zzz2934, zzz2127, zzz2930, zzz2931, Zero, zzz224400, da, db) → new_mkBalBranch6MkBalBranch31(zzz2934, zzz2127, zzz2930, zzz2931, da, db)
new_mkBalBranch6MkBalBranch34(zzz2934, zzz2127, zzz2930, zzz2931, zzz224400, zzz2252, da, db) → new_mkBalBranch6MkBalBranch31(zzz2934, zzz2127, zzz2930, zzz2931, da, db)
new_mkBalBranch6MkBalBranch312(zzz2934, zzz2127, zzz2930, zzz2931, zzz224400, zzz2249, da, db) → new_mkBalBranch6MkBalBranch33(zzz2934, zzz2127, zzz2930, zzz2931, da, db)
new_mkBalBranch6MkBalBranch37(zzz2934, zzz2127, zzz2930, zzz2931, zzz224400, zzz2253, da, db) → new_mkBalBranch6MkBalBranch36(zzz2934, zzz2127, zzz2930, zzz2931, zzz2253, zzz224400, da, db)
new_mkBalBranch6MkBalBranch36(zzz2934, zzz2127, zzz2930, zzz2931, Succ(zzz22530), zzz224400, da, db) → new_mkBalBranch6MkBalBranch39(zzz2934, zzz2127, zzz2930, zzz2931, zzz22530, zzz224400, da, db)
new_mkBalBranch6MkBalBranch314(zzz2934, zzz2127, zzz2930, zzz2931, Succ(zzz22550), da, db) → new_mkBalBranch6MkBalBranch38(zzz2934, zzz2127, zzz2930, zzz2931, zzz22550, Zero, da, db)
new_mkBalBranch6MkBalBranch314(zzz2934, zzz2127, zzz2930, zzz2931, Zero, da, db) → new_mkBalBranch6MkBalBranch32(zzz2934, zzz2127, zzz2930, zzz2931, da, db)
new_mkBalBranch6MkBalBranch30(zzz2934, zzz2127, zzz2930, zzz2931, Succ(zzz22540), da, db) → new_mkBalBranch6MkBalBranch31(zzz2934, zzz2127, zzz2930, zzz2931, da, db)
new_mkBalBranch6MkBalBranch30(zzz2934, zzz2127, zzz2930, zzz2931, Zero, da, db) → new_mkBalBranch6MkBalBranch32(zzz2934, zzz2127, zzz2930, zzz2931, da, db)
new_mkBalBranch6MkBalBranch315(zzz2934, zzz2127, zzz2930, zzz2931, Zero, da, db) → new_mkBalBranch6MkBalBranch32(zzz2934, zzz2127, zzz2930, zzz2931, da, db)
new_mkBalBranch6MkBalBranch315(zzz2934, zzz2127, zzz2930, zzz2931, Succ(zzz22510), da, db) → new_mkBalBranch6MkBalBranch33(zzz2934, zzz2127, zzz2930, zzz2931, da, db)
new_mkBalBranch6MkBalBranch48(zzz2934, zzz2127, zzz2930, zzz2931, Zero, da, db) → new_mkBalBranch6MkBalBranch40(zzz2934, zzz2127, zzz2930, zzz2931, da, db)
new_mkBalBranch6MkBalBranch48(zzz2934, zzz2127, zzz2930, zzz2931, Succ(zzz22390), da, db) → new_mkBalBranch6MkBalBranch49(zzz2934, zzz2127, zzz2930, zzz2931, da, db)
new_mkBalBranch6MkBalBranch49(Branch(zzz29340, zzz29341, zzz29342, zzz29343, zzz29344), zzz2127, zzz2930, zzz2931, da, db) → new_mkBalBranch6MkBalBranch017(zzz29340, zzz29341, zzz29342, zzz29343, zzz29344, zzz2127, zzz2930, zzz2931, new_sizeFM(zzz29343, da, db), new_sizeFM(zzz29344, da, db), da, db)
new_mkBalBranch6MkBalBranch49(EmptyFM, zzz2127, zzz2930, zzz2931, da, db) → error([])
new_mkBalBranch6MkBalBranch017(zzz29340, zzz29341, zzz29342, zzz29343, zzz29344, zzz2127, zzz2930, zzz2931, Neg(Zero), Pos(zzz22470), da, db) → new_mkBalBranch6MkBalBranch010(zzz29340, zzz29341, zzz29342, zzz29343, zzz29344, zzz2127, zzz2930, zzz2931, new_primMulNat2(zzz22470), da, db)
new_mkBalBranch6MkBalBranch017(zzz29340, zzz29341, zzz29342, zzz29343, zzz29344, zzz2127, zzz2930, zzz2931, Pos(Zero), Neg(zzz22470), da, db) → new_mkBalBranch6MkBalBranch0111(zzz29340, zzz29341, zzz29342, zzz29343, zzz29344, zzz2127, zzz2930, zzz2931, new_primMulNat2(zzz22470), da, db)
new_mkBalBranch6MkBalBranch017(zzz29340, zzz29341, zzz29342, zzz29343, zzz29344, zzz2127, zzz2930, zzz2931, Neg(Succ(zzz224600)), Neg(zzz22470), da, db) → new_mkBalBranch6MkBalBranch018(zzz29340, zzz29341, zzz29342, zzz29343, zzz29344, zzz2127, zzz2930, zzz2931, new_primMulNat2(zzz22470), zzz224600, da, db)
new_mkBalBranch6MkBalBranch017(zzz29340, zzz29341, zzz29342, zzz29343, zzz29344, zzz2127, zzz2930, zzz2931, Neg(Succ(zzz224600)), Pos(zzz22470), da, db) → new_mkBalBranch6MkBalBranch011(zzz29340, zzz29341, zzz29342, zzz29343, zzz29344, zzz2127, zzz2930, zzz2931, da, db)
new_mkBalBranch6MkBalBranch017(zzz29340, zzz29341, zzz29342, zzz29343, zzz29344, zzz2127, zzz2930, zzz2931, Pos(Succ(zzz224600)), Neg(zzz22470), da, db) → new_mkBalBranch6MkBalBranch015(zzz29340, zzz29341, zzz29342, zzz29343, zzz29344, zzz2127, zzz2930, zzz2931, da, db)
new_mkBalBranch6MkBalBranch017(zzz29340, zzz29341, zzz29342, zzz29343, zzz29344, zzz2127, zzz2930, zzz2931, Neg(Zero), Neg(zzz22470), da, db) → new_mkBalBranch6MkBalBranch019(zzz29340, zzz29341, zzz29342, zzz29343, zzz29344, zzz2127, zzz2930, zzz2931, new_primMulNat2(zzz22470), da, db)
new_mkBalBranch6MkBalBranch017(zzz29340, zzz29341, zzz29342, zzz29343, zzz29344, zzz2127, zzz2930, zzz2931, Pos(Zero), Pos(zzz22470), da, db) → new_mkBalBranch6MkBalBranch0110(zzz29340, zzz29341, zzz29342, zzz29343, zzz29344, zzz2127, zzz2930, zzz2931, new_primMulNat2(zzz22470), da, db)
new_mkBalBranch6MkBalBranch017(zzz29340, zzz29341, zzz29342, zzz29343, zzz29344, zzz2127, zzz2930, zzz2931, Pos(Succ(zzz224600)), Pos(zzz22470), da, db) → new_mkBalBranch6MkBalBranch013(zzz29340, zzz29341, zzz29342, zzz29343, zzz29344, zzz2127, zzz2930, zzz2931, zzz224600, new_primMulNat2(zzz22470), da, db)
new_mkBalBranch6MkBalBranch013(zzz29340, zzz29341, zzz29342, zzz29343, zzz29344, zzz2127, zzz2930, zzz2931, zzz224600, Zero, da, db) → new_mkBalBranch6MkBalBranch015(zzz29340, zzz29341, zzz29342, zzz29343, zzz29344, zzz2127, zzz2930, zzz2931, da, db)
new_mkBalBranch6MkBalBranch013(zzz29340, zzz29341, zzz29342, zzz29343, zzz29344, zzz2127, zzz2930, zzz2931, zzz224600, Succ(zzz22600), da, db) → new_mkBalBranch6MkBalBranch014(zzz29340, zzz29341, zzz29342, zzz29343, zzz29344, zzz2127, zzz2930, zzz2931, zzz224600, zzz22600, da, db)
new_mkBalBranch6MkBalBranch014(zzz29340, zzz29341, zzz29342, zzz29343, zzz29344, zzz2127, zzz2930, zzz2931, Zero, Zero, da, db) → new_mkBalBranch6MkBalBranch012(zzz29340, zzz29341, zzz29342, zzz29343, zzz29344, zzz2127, zzz2930, zzz2931, da, db)
new_mkBalBranch6MkBalBranch014(zzz29340, zzz29341, zzz29342, zzz29343, zzz29344, zzz2127, zzz2930, zzz2931, Succ(zzz2246000), Succ(zzz226000), da, db) → new_mkBalBranch6MkBalBranch014(zzz29340, zzz29341, zzz29342, zzz29343, zzz29344, zzz2127, zzz2930, zzz2931, zzz2246000, zzz226000, da, db)
new_mkBalBranch6MkBalBranch014(zzz29340, zzz29341, zzz29342, zzz29343, zzz29344, zzz2127, zzz2930, zzz2931, Succ(zzz2246000), Zero, da, db) → new_mkBalBranch6MkBalBranch015(zzz29340, zzz29341, zzz29342, zzz29343, zzz29344, zzz2127, zzz2930, zzz2931, da, db)
new_mkBalBranch6MkBalBranch014(zzz29340, zzz29341, zzz29342, zzz29343, zzz29344, zzz2127, zzz2930, zzz2931, Zero, Succ(zzz226000), da, db) → new_mkBalBranch6MkBalBranch011(zzz29340, zzz29341, zzz29342, zzz29343, zzz29344, zzz2127, zzz2930, zzz2931, da, db)
new_mkBalBranch6MkBalBranch011(zzz29340, zzz29341, zzz29342, zzz29343, zzz29344, zzz2127, zzz2930, zzz2931, da, db) → new_mkBranch(Succ(Succ(Zero)), zzz29340, zzz29341, new_mkBranch(Succ(Succ(Succ(Zero))), zzz2930, zzz2931, zzz2127, zzz29343, da, db), zzz29344, da, db)
new_mkBalBranch6MkBalBranch015(zzz29340, zzz29341, zzz29342, zzz29343, zzz29344, zzz2127, zzz2930, zzz2931, da, db) → new_mkBalBranch6MkBalBranch016(zzz29340, zzz29341, zzz29342, zzz29343, zzz29344, zzz2127, zzz2930, zzz2931, da, db)
new_mkBalBranch6MkBalBranch016(zzz29340, zzz29341, zzz29342, EmptyFM, zzz29344, zzz2127, zzz2930, zzz2931, da, db) → error([])
new_mkBalBranch6MkBalBranch016(zzz29340, zzz29341, zzz29342, Branch(zzz293430, zzz293431, zzz293432, zzz293433, zzz293434), zzz29344, zzz2127, zzz2930, zzz2931, da, db) → new_mkBranch(Succ(Succ(Succ(Succ(Zero)))), zzz293430, zzz293431, new_mkBranch(Succ(Succ(Succ(Succ(Succ(Zero))))), zzz2930, zzz2931, zzz2127, zzz293433, da, db), new_mkBranch(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))), zzz29340, zzz29341, zzz293434, zzz29344, da, db), da, db)
new_mkBalBranch6MkBalBranch012(zzz29340, zzz29341, zzz29342, zzz29343, zzz29344, zzz2127, zzz2930, zzz2931, da, db) → new_mkBalBranch6MkBalBranch016(zzz29340, zzz29341, zzz29342, zzz29343, zzz29344, zzz2127, zzz2930, zzz2931, da, db)
new_mkBalBranch6MkBalBranch0110(zzz29340, zzz29341, zzz29342, zzz29343, zzz29344, zzz2127, zzz2930, zzz2931, Zero, da, db) → new_mkBalBranch6MkBalBranch012(zzz29340, zzz29341, zzz29342, zzz29343, zzz29344, zzz2127, zzz2930, zzz2931, da, db)
new_mkBalBranch6MkBalBranch0110(zzz29340, zzz29341, zzz29342, zzz29343, zzz29344, zzz2127, zzz2930, zzz2931, Succ(zzz22560), da, db) → new_mkBalBranch6MkBalBranch018(zzz29340, zzz29341, zzz29342, zzz29343, zzz29344, zzz2127, zzz2930, zzz2931, Zero, zzz22560, da, db)
new_mkBalBranch6MkBalBranch018(zzz29340, zzz29341, zzz29342, zzz29343, zzz29344, zzz2127, zzz2930, zzz2931, Zero, zzz224600, da, db) → new_mkBalBranch6MkBalBranch011(zzz29340, zzz29341, zzz29342, zzz29343, zzz29344, zzz2127, zzz2930, zzz2931, da, db)
new_mkBalBranch6MkBalBranch019(zzz29340, zzz29341, zzz29342, zzz29343, zzz29344, zzz2127, zzz2930, zzz2931, Zero, da, db) → new_mkBalBranch6MkBalBranch012(zzz29340, zzz29341, zzz29342, zzz29343, zzz29344, zzz2127, zzz2930, zzz2931, da, db)
new_mkBalBranch6MkBalBranch019(zzz29340, zzz29341, zzz29342, zzz29343, zzz29344, zzz2127, zzz2930, zzz2931, Succ(zzz22590), da, db) → new_mkBalBranch6MkBalBranch013(zzz29340, zzz29341, zzz29342, zzz29343, zzz29344, zzz2127, zzz2930, zzz2931, zzz22590, Zero, da, db)
new_mkBalBranch6MkBalBranch018(zzz29340, zzz29341, zzz29342, zzz29343, zzz29344, zzz2127, zzz2930, zzz2931, Succ(zzz22610), zzz224600, da, db) → new_mkBalBranch6MkBalBranch014(zzz29340, zzz29341, zzz29342, zzz29343, zzz29344, zzz2127, zzz2930, zzz2931, zzz22610, zzz224600, da, db)
new_mkBalBranch6MkBalBranch0111(zzz29340, zzz29341, zzz29342, zzz29343, zzz29344, zzz2127, zzz2930, zzz2931, Succ(zzz22570), da, db) → new_mkBalBranch6MkBalBranch015(zzz29340, zzz29341, zzz29342, zzz29343, zzz29344, zzz2127, zzz2930, zzz2931, da, db)
new_mkBalBranch6MkBalBranch0111(zzz29340, zzz29341, zzz29342, zzz29343, zzz29344, zzz2127, zzz2930, zzz2931, Zero, da, db) → new_mkBalBranch6MkBalBranch012(zzz29340, zzz29341, zzz29342, zzz29343, zzz29344, zzz2127, zzz2930, zzz2931, da, db)
new_mkBalBranch6MkBalBranch010(zzz29340, zzz29341, zzz29342, zzz29343, zzz29344, zzz2127, zzz2930, zzz2931, Zero, da, db) → new_mkBalBranch6MkBalBranch012(zzz29340, zzz29341, zzz29342, zzz29343, zzz29344, zzz2127, zzz2930, zzz2931, da, db)
new_mkBalBranch6MkBalBranch010(zzz29340, zzz29341, zzz29342, zzz29343, zzz29344, zzz2127, zzz2930, zzz2931, Succ(zzz22580), da, db) → new_mkBalBranch6MkBalBranch011(zzz29340, zzz29341, zzz29342, zzz29343, zzz29344, zzz2127, zzz2930, zzz2931, da, db)
new_mkBalBranch6MkBalBranch40(zzz2934, zzz2127, zzz2930, zzz2931, da, db) → new_mkBalBranch6MkBalBranch41(zzz2934, zzz2127, zzz2930, zzz2931, da, db)
new_mkBalBranch6MkBalBranch46(zzz2934, zzz2127, zzz2930, zzz2931, zzz222100, zzz2241, da, db) → new_mkBalBranch6MkBalBranch47(zzz2934, zzz2127, zzz2930, zzz2931, zzz2241, zzz222100, da, db)
new_mkBalBranch6MkBalBranch47(zzz2934, zzz2127, zzz2930, zzz2931, Zero, zzz222100, da, db) → new_mkBalBranch6MkBalBranch43(zzz2934, zzz2127, zzz2930, zzz2931, da, db)
new_mkBalBranch6MkBalBranch47(zzz2934, zzz2127, zzz2930, zzz2931, Succ(zzz22410), zzz222100, da, db) → new_mkBalBranch6MkBalBranch412(zzz2934, zzz2127, zzz2930, zzz2931, zzz22410, zzz222100, da, db)
new_mkBalBranch6MkBalBranch412(zzz2934, zzz2127, zzz2930, zzz2931, Succ(zzz2221000), Zero, da, db) → new_mkBalBranch6MkBalBranch49(zzz2934, zzz2127, zzz2930, zzz2931, da, db)
new_mkBalBranch6MkBalBranch412(zzz2934, zzz2127, zzz2930, zzz2931, Zero, Succ(zzz223600), da, db) → new_mkBalBranch6MkBalBranch43(zzz2934, zzz2127, zzz2930, zzz2931, da, db)
new_mkBalBranch6MkBalBranch412(zzz2934, zzz2127, zzz2930, zzz2931, Zero, Zero, da, db) → new_mkBalBranch6MkBalBranch40(zzz2934, zzz2127, zzz2930, zzz2931, da, db)
new_mkBalBranch6MkBalBranch412(zzz2934, zzz2127, zzz2930, zzz2931, Succ(zzz2221000), Succ(zzz223600), da, db) → new_mkBalBranch6MkBalBranch412(zzz2934, zzz2127, zzz2930, zzz2931, zzz2221000, zzz223600, da, db)
new_mkBalBranch6MkBalBranch44(zzz2934, zzz2127, zzz2930, zzz2931, zzz222100, zzz2236, da, db) → new_mkBalBranch6MkBalBranch45(zzz2934, zzz2127, zzz2930, zzz2931, zzz222100, zzz2236, da, db)
new_mkBalBranch6MkBalBranch45(zzz2934, zzz2127, zzz2930, zzz2931, zzz222100, Succ(zzz22360), da, db) → new_mkBalBranch6MkBalBranch412(zzz2934, zzz2127, zzz2930, zzz2931, zzz222100, zzz22360, da, db)
new_mkBalBranch6MkBalBranch45(zzz2934, zzz2127, zzz2930, zzz2931, zzz222100, Zero, da, db) → new_mkBalBranch6MkBalBranch49(zzz2934, zzz2127, zzz2930, zzz2931, da, db)
new_mkBalBranch6MkBalBranch414(zzz2934, zzz2127, zzz2930, zzz2931, Succ(zzz22380), da, db) → new_mkBalBranch6MkBalBranch47(zzz2934, zzz2127, zzz2930, zzz2931, Zero, zzz22380, da, db)
new_mkBalBranch6MkBalBranch414(zzz2934, zzz2127, zzz2930, zzz2931, Zero, da, db) → new_mkBalBranch6MkBalBranch40(zzz2934, zzz2127, zzz2930, zzz2931, da, db)
new_mkBalBranch6MkBalBranch415(zzz2934, zzz2127, zzz2930, zzz2931, zzz222100, zzz2237, da, db) → new_mkBalBranch6MkBalBranch49(zzz2934, zzz2127, zzz2930, zzz2931, da, db)
new_mkBalBranch6MkBalBranch413(zzz2934, zzz2127, zzz2930, zzz2931, Zero, da, db) → new_mkBalBranch6MkBalBranch40(zzz2934, zzz2127, zzz2930, zzz2931, da, db)
new_mkBalBranch6MkBalBranch413(zzz2934, zzz2127, zzz2930, zzz2931, Succ(zzz22430), da, db) → new_mkBalBranch6MkBalBranch45(zzz2934, zzz2127, zzz2930, zzz2931, zzz22430, Zero, da, db)
new_mkBalBranch6MkBalBranch416(zzz2934, zzz2127, zzz2930, zzz2931, Succ(zzz22420), da, db) → new_mkBalBranch6MkBalBranch43(zzz2934, zzz2127, zzz2930, zzz2931, da, db)
new_mkBalBranch6MkBalBranch416(zzz2934, zzz2127, zzz2930, zzz2931, Zero, da, db) → new_mkBalBranch6MkBalBranch40(zzz2934, zzz2127, zzz2930, zzz2931, da, db)
new_mkVBalBranch3MkVBalBranch132(zzz2033, zzz2034, zzz2035, zzz2036, zzz2037, zzz2038, zzz2039, zzz2040, zzz2041, zzz2042, zzz2043, Succ(zzz20440), Succ(zzz20450), fg) → new_mkVBalBranch3MkVBalBranch132(zzz2033, zzz2034, zzz2035, zzz2036, zzz2037, zzz2038, zzz2039, zzz2040, zzz2041, zzz2042, zzz2043, zzz20440, zzz20450, fg)
new_mkVBalBranch3MkVBalBranch132(zzz2033, zzz2034, zzz2035, zzz2036, zzz2037, zzz2038, zzz2039, zzz2040, zzz2041, zzz2042, zzz2043, Zero, Zero, fg) → new_mkVBalBranch3MkVBalBranch166(zzz2033, zzz2034, zzz2035, zzz2036, zzz2037, zzz2038, zzz2039, zzz2040, zzz2041, zzz2042, zzz2043, fg)
new_mkVBalBranch3MkVBalBranch132(zzz2033, zzz2034, zzz2035, zzz2036, zzz2037, zzz2038, zzz2039, zzz2040, zzz2041, zzz2042, zzz2043, Succ(zzz20440), Zero, fg) → new_mkVBalBranch3MkVBalBranch166(zzz2033, zzz2034, zzz2035, zzz2036, zzz2037, zzz2038, zzz2039, zzz2040, zzz2041, zzz2042, zzz2043, fg)
new_mkVBalBranch3MkVBalBranch166(zzz2033, zzz2034, zzz2035, zzz2036, zzz2037, zzz2038, zzz2039, zzz2040, zzz2041, zzz2042, zzz2043, fg) → new_mkBranch(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))), GT, zzz2043, Branch(zzz2038, zzz2039, Pos(Succ(zzz2040)), zzz2041, zzz2042), Branch(zzz2033, zzz2034, Pos(Succ(zzz2035)), zzz2036, zzz2037), ty_Ordering, fg)
new_mkVBalBranch3MkVBalBranch252(zzz929, zzz930, zzz931, zzz932, zzz933, zzz934, zzz935, zzz936, zzz937, zzz938, zzz939, Zero, Zero, dc) → new_mkVBalBranch3MkVBalBranch253(zzz929, zzz930, zzz931, zzz932, zzz933, zzz934, zzz935, zzz936, zzz937, zzz938, zzz939, dc)
new_mkVBalBranch3MkVBalBranch252(zzz929, zzz930, zzz931, zzz932, zzz933, zzz934, zzz935, zzz936, zzz937, zzz938, zzz939, Zero, Succ(zzz9410), dc) → new_mkBalBranch(zzz929, zzz930, new_mkVBalBranch3(zzz939, Branch(zzz934, zzz935, Pos(Succ(zzz936)), zzz937, zzz938), zzz932, dc), zzz933, ty_Ordering, dc)
new_mkVBalBranch3MkVBalBranch269(zzz340, zzz341, Succ(zzz34200), zzz343, zzz344, zzz520, zzz521, zzz52200, zzz523, zzz524, zzz31, h) → new_mkVBalBranch3MkVBalBranch147(zzz340, zzz341, zzz34200, zzz343, zzz344, zzz520, zzz521, zzz52200, zzz523, zzz524, zzz31, new_primPlusNat2(new_primMulNat0(zzz34200), Succ(zzz34200)), h)
new_mkVBalBranch3MkVBalBranch269(zzz340, zzz341, Zero, zzz343, zzz344, zzz520, zzz521, zzz52200, zzz523, zzz524, zzz31, h) → new_mkBalBranch(zzz520, zzz521, zzz523, new_mkVBalBranch3(zzz31, zzz524, Branch(zzz340, zzz341, Neg(Zero), zzz343, zzz344), h), ty_Ordering, h)
new_mkVBalBranch3MkVBalBranch147(zzz340, zzz341, zzz34200, zzz343, zzz344, zzz520, zzz521, zzz52200, zzz523, zzz524, zzz31, Succ(zzz1430), h) → new_mkVBalBranch3MkVBalBranch148(zzz340, zzz341, zzz34200, zzz343, zzz344, zzz520, zzz521, zzz52200, zzz523, zzz524, zzz31, h)
new_mkVBalBranch3MkVBalBranch147(zzz340, zzz341, zzz34200, zzz343, zzz344, zzz520, zzz521, zzz52200, zzz523, zzz524, zzz31, Zero, h) → new_mkVBalBranch3MkVBalBranch148(zzz340, zzz341, zzz34200, zzz343, zzz344, zzz520, zzz521, zzz52200, zzz523, zzz524, zzz31, h)
new_mkVBalBranch3MkVBalBranch148(zzz340, zzz341, zzz34200, zzz343, zzz344, zzz520, zzz521, zzz52200, zzz523, zzz524, zzz31, h) → new_mkBalBranch(zzz520, zzz521, zzz523, new_mkVBalBranch3(zzz31, zzz524, Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), h), ty_Ordering, h)
new_mkVBalBranch3MkVBalBranch268(zzz340, zzz341, zzz343, zzz344, zzz520, zzz521, zzz52200, zzz523, zzz524, zzz31, h) → new_mkBalBranch(zzz520, zzz521, zzz523, new_mkVBalBranch3(zzz31, zzz524, Branch(zzz340, zzz341, Pos(Zero), zzz343, zzz344), h), ty_Ordering, h)
new_primPlusNat1(Succ(zzz62000)) → Succ(Succ(new_primPlusNat1(zzz62000)))
new_primPlusNat1(Zero) → Zero
new_primPlusNat3(zzz90, Succ(zzz910)) → Succ(Succ(new_primPlusNat2(zzz90, zzz910)))
new_primPlusNat3(zzz90, Zero) → Succ(zzz90)
new_mkVBalBranch3MkVBalBranch272(zzz340, zzz341, Neg(Zero), zzz343, zzz344, zzz520, zzz521, zzz52200, zzz523, zzz524, zzz31, Succ(zzz690), h) → new_mkVBalBranch3MkVBalBranch245(zzz340, zzz341, zzz343, zzz344, zzz520, zzz521, zzz52200, zzz523, zzz524, zzz31, h)
new_mkVBalBranch3MkVBalBranch272(zzz340, zzz341, Neg(Succ(Succ(Zero))), zzz343, zzz344, zzz520, zzz521, Zero, zzz523, zzz524, zzz31, Succ(Zero), h) → new_mkVBalBranch3MkVBalBranch277(zzz340, zzz341, Succ(Zero), zzz343, zzz344, zzz520, zzz521, zzz523, zzz524, zzz31, Zero, Zero, h)
new_mkVBalBranch3MkVBalBranch272(zzz340, zzz341, Neg(Succ(Succ(Succ(zzz3420000)))), zzz343, zzz344, zzz520, zzz521, Zero, zzz523, zzz524, zzz31, Succ(Zero), h) → new_mkVBalBranch3MkVBalBranch277(zzz340, zzz341, Succ(Succ(zzz3420000)), zzz343, zzz344, zzz520, zzz521, zzz523, zzz524, zzz31, Succ(zzz3420000), Zero, h)
new_mkVBalBranch3MkVBalBranch272(zzz340, zzz341, Pos(zzz3420), zzz343, zzz344, zzz520, zzz521, zzz52200, zzz523, zzz524, zzz31, Zero, h) → new_mkVBalBranch3MkVBalBranch258(zzz340, zzz341, zzz3420, zzz343, zzz344, zzz520, zzz521, zzz52200, zzz523, zzz524, zzz31, h)
new_mkVBalBranch3MkVBalBranch272(zzz340, zzz341, Neg(Succ(Succ(Zero))), zzz343, zzz344, zzz520, zzz521, Zero, zzz523, zzz524, zzz31, Succ(Succ(zzz6900)), h) → new_mkVBalBranch3MkVBalBranch277(zzz340, zzz341, Succ(Zero), zzz343, zzz344, zzz520, zzz521, zzz523, zzz524, zzz31, Zero, Succ(zzz6900), h)
new_mkVBalBranch3MkVBalBranch272(zzz340, zzz341, Neg(Succ(Zero)), zzz343, zzz344, zzz520, zzz521, zzz52200, zzz523, zzz524, zzz31, Succ(zzz690), h) → new_mkVBalBranch3MkVBalBranch254(zzz340, zzz341, zzz343, zzz344, zzz520, zzz521, zzz52200, zzz523, zzz524, zzz31, h)
new_mkVBalBranch3MkVBalBranch272(zzz340, zzz341, Neg(Succ(Succ(zzz342000))), zzz343, zzz344, zzz520, zzz521, Succ(zzz522000), zzz523, zzz524, zzz31, Zero, h) → new_mkVBalBranch3MkVBalBranch255(zzz340, zzz341, Succ(zzz342000), zzz343, zzz344, zzz520, zzz521, zzz522000, zzz523, zzz524, zzz31, zzz342000, zzz522000, h)
new_mkVBalBranch3MkVBalBranch272(zzz340, zzz341, Neg(Zero), zzz343, zzz344, zzz520, zzz521, zzz52200, zzz523, zzz524, zzz31, Zero, h) → new_mkVBalBranch3MkVBalBranch245(zzz340, zzz341, zzz343, zzz344, zzz520, zzz521, zzz52200, zzz523, zzz524, zzz31, h)
new_mkVBalBranch3MkVBalBranch272(zzz340, zzz341, Neg(Succ(Succ(Zero))), zzz343, zzz344, zzz520, zzz521, Succ(zzz522000), zzz523, zzz524, zzz31, Succ(Zero), h) → new_mkVBalBranch3MkVBalBranch255(zzz340, zzz341, Succ(Zero), zzz343, zzz344, zzz520, zzz521, zzz522000, zzz523, zzz524, zzz31, Zero, Succ(zzz522000), h)
new_mkVBalBranch3MkVBalBranch272(zzz340, zzz341, Pos(zzz3420), zzz343, zzz344, zzz520, zzz521, zzz52200, zzz523, zzz524, zzz31, Succ(zzz690), h) → new_mkVBalBranch3MkVBalBranch258(zzz340, zzz341, zzz3420, zzz343, zzz344, zzz520, zzz521, zzz52200, zzz523, zzz524, zzz31, h)
new_mkVBalBranch3MkVBalBranch272(zzz340, zzz341, Neg(Succ(Succ(Succ(zzz3420000)))), zzz343, zzz344, zzz520, zzz521, Succ(zzz522000), zzz523, zzz524, zzz31, Succ(Succ(zzz6900)), h) → new_mkVBalBranch3MkVBalBranch255(zzz340, zzz341, Succ(Succ(zzz3420000)), zzz343, zzz344, zzz520, zzz521, zzz522000, zzz523, zzz524, zzz31, Succ(zzz3420000), Succ(Succ(new_primPlusNat2(zzz6900, zzz522000))), h)
new_mkVBalBranch3MkVBalBranch272(zzz340, zzz341, Neg(Succ(Succ(Succ(zzz3420000)))), zzz343, zzz344, zzz520, zzz521, Succ(zzz522000), zzz523, zzz524, zzz31, Succ(Zero), h) → new_mkVBalBranch3MkVBalBranch255(zzz340, zzz341, Succ(Succ(zzz3420000)), zzz343, zzz344, zzz520, zzz521, zzz522000, zzz523, zzz524, zzz31, Succ(zzz3420000), Succ(zzz522000), h)
new_mkVBalBranch3MkVBalBranch272(zzz340, zzz341, Neg(Succ(Succ(Succ(zzz3420000)))), zzz343, zzz344, zzz520, zzz521, Zero, zzz523, zzz524, zzz31, Succ(Succ(zzz6900)), h) → new_mkVBalBranch3MkVBalBranch277(zzz340, zzz341, Succ(Succ(zzz3420000)), zzz343, zzz344, zzz520, zzz521, zzz523, zzz524, zzz31, Succ(zzz3420000), Succ(zzz6900), h)
new_mkVBalBranch3MkVBalBranch272(zzz340, zzz341, Neg(Succ(Zero)), zzz343, zzz344, zzz520, zzz521, Zero, zzz523, zzz524, zzz31, Zero, h) → new_mkVBalBranch3MkVBalBranch273(zzz340, zzz341, Zero, zzz343, zzz344, zzz520, zzz521, zzz523, zzz524, zzz31, h)
new_mkVBalBranch3MkVBalBranch272(zzz340, zzz341, Neg(Succ(Zero)), zzz343, zzz344, zzz520, zzz521, Succ(zzz522000), zzz523, zzz524, zzz31, Zero, h) → new_mkVBalBranch3MkVBalBranch254(zzz340, zzz341, zzz343, zzz344, zzz520, zzz521, Succ(zzz522000), zzz523, zzz524, zzz31, h)
new_mkVBalBranch3MkVBalBranch272(zzz340, zzz341, Neg(Succ(Succ(Zero))), zzz343, zzz344, zzz520, zzz521, Succ(zzz522000), zzz523, zzz524, zzz31, Succ(Succ(zzz6900)), h) → new_mkVBalBranch3MkVBalBranch255(zzz340, zzz341, Succ(Zero), zzz343, zzz344, zzz520, zzz521, zzz522000, zzz523, zzz524, zzz31, Zero, Succ(Succ(new_primPlusNat2(zzz6900, zzz522000))), h)
new_mkVBalBranch3MkVBalBranch272(zzz340, zzz341, Neg(Succ(Succ(zzz342000))), zzz343, zzz344, zzz520, zzz521, Zero, zzz523, zzz524, zzz31, Zero, h) → new_mkVBalBranch3MkVBalBranch259(zzz340, zzz341, zzz342000, zzz343, zzz344, zzz520, zzz521, zzz523, zzz524, zzz31, h)
new_mkVBalBranch3MkVBalBranch259(zzz340, zzz341, zzz342000, zzz343, zzz344, zzz520, zzz521, zzz523, zzz524, zzz31, h) → new_mkVBalBranch3MkVBalBranch260(zzz340, zzz341, zzz342000, zzz343, zzz344, zzz520, zzz521, zzz523, zzz524, zzz31, h)
new_mkVBalBranch3MkVBalBranch260(zzz340, zzz341, zzz342000, zzz343, zzz344, zzz520, zzz521, zzz523, zzz524, zzz31, h) → new_mkVBalBranch3MkVBalBranch143(zzz340, zzz341, Succ(zzz342000), zzz343, zzz344, zzz520, zzz521, zzz523, zzz524, zzz31, new_primMulNat1(Succ(zzz342000)), h)
new_mkVBalBranch3MkVBalBranch143(zzz818, zzz819, zzz820, zzz821, zzz822, zzz823, zzz824, zzz825, zzz826, zzz827, Zero, eb) → new_mkVBalBranch3MkVBalBranch144(zzz818, zzz819, zzz820, zzz821, zzz822, zzz823, zzz824, Zero, zzz825, zzz826, zzz827, Succ(Zero), Zero, eb)
new_mkVBalBranch3MkVBalBranch143(zzz818, zzz819, zzz820, zzz821, zzz822, zzz823, zzz824, zzz825, zzz826, zzz827, Succ(zzz8960), eb) → new_mkVBalBranch3MkVBalBranch144(zzz818, zzz819, zzz820, zzz821, zzz822, zzz823, zzz824, Zero, zzz825, zzz826, zzz827, Succ(Zero), Succ(zzz8960), eb)
new_mkVBalBranch3MkVBalBranch144(zzz1702, zzz1703, zzz1704, zzz1705, zzz1706, zzz1707, zzz1708, zzz1709, zzz1710, zzz1711, zzz1712, Succ(zzz17130), Succ(zzz17140), df) → new_mkVBalBranch3MkVBalBranch144(zzz1702, zzz1703, zzz1704, zzz1705, zzz1706, zzz1707, zzz1708, zzz1709, zzz1710, zzz1711, zzz1712, zzz17130, zzz17140, df)
new_mkVBalBranch3MkVBalBranch144(zzz1702, zzz1703, zzz1704, zzz1705, zzz1706, zzz1707, zzz1708, zzz1709, zzz1710, zzz1711, zzz1712, Zero, Succ(zzz17140), df) → new_mkBalBranch(zzz1707, zzz1708, zzz1710, new_mkVBalBranch3(zzz1712, zzz1711, Branch(zzz1702, zzz1703, Neg(Succ(zzz1704)), zzz1705, zzz1706), df), ty_Ordering, df)
new_mkVBalBranch3MkVBalBranch144(zzz1702, zzz1703, zzz1704, zzz1705, zzz1706, zzz1707, zzz1708, zzz1709, zzz1710, zzz1711, zzz1712, Succ(zzz17130), Zero, df) → new_mkVBalBranch3MkVBalBranch138(zzz1702, zzz1703, zzz1704, zzz1705, zzz1706, zzz1707, zzz1708, zzz1709, zzz1710, zzz1711, zzz1712, df)
new_mkVBalBranch3MkVBalBranch144(zzz1702, zzz1703, zzz1704, zzz1705, zzz1706, zzz1707, zzz1708, zzz1709, zzz1710, zzz1711, zzz1712, Zero, Zero, df) → new_mkVBalBranch3MkVBalBranch138(zzz1702, zzz1703, zzz1704, zzz1705, zzz1706, zzz1707, zzz1708, zzz1709, zzz1710, zzz1711, zzz1712, df)
new_mkVBalBranch3MkVBalBranch138(zzz1702, zzz1703, zzz1704, zzz1705, zzz1706, zzz1707, zzz1708, zzz1709, zzz1710, zzz1711, zzz1712, df) → new_mkBranch(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))), GT, zzz1712, Branch(zzz1707, zzz1708, Neg(Succ(zzz1709)), zzz1710, zzz1711), Branch(zzz1702, zzz1703, Neg(Succ(zzz1704)), zzz1705, zzz1706), ty_Ordering, df)
new_mkVBalBranch3MkVBalBranch255(zzz537, zzz538, zzz539, zzz540, zzz541, zzz542, zzz543, zzz544, zzz545, zzz546, zzz547, Zero, Succ(zzz5490), dg) → new_mkBalBranch(zzz537, zzz538, new_mkVBalBranch3(zzz547, Branch(zzz542, zzz543, Neg(Succ(Succ(zzz544))), zzz545, zzz546), zzz540, dg), zzz541, ty_Ordering, dg)
new_mkVBalBranch3MkVBalBranch254(zzz340, zzz341, zzz343, zzz344, zzz520, zzz521, zzz52200, zzz523, zzz524, zzz31, h) → new_mkBalBranch(zzz340, zzz341, new_mkVBalBranch3(zzz31, Branch(zzz520, zzz521, Neg(Succ(zzz52200)), zzz523, zzz524), zzz343, h), zzz344, ty_Ordering, h)
new_mkVBalBranch3MkVBalBranch273(zzz818, zzz819, zzz820, zzz821, zzz822, zzz823, zzz824, zzz825, zzz826, zzz827, eb) → new_mkVBalBranch3MkVBalBranch274(zzz818, zzz819, zzz820, zzz821, zzz822, zzz823, zzz824, zzz825, zzz826, zzz827, eb)
new_mkVBalBranch3MkVBalBranch274(zzz818, zzz819, zzz820, zzz821, zzz822, zzz823, zzz824, zzz825, zzz826, zzz827, eb) → new_mkVBalBranch3MkVBalBranch143(zzz818, zzz819, zzz820, zzz821, zzz822, zzz823, zzz824, zzz825, zzz826, zzz827, new_primMulNat1(zzz820), eb)
new_mkVBalBranch3MkVBalBranch277(zzz1133, zzz1134, zzz1135, zzz1136, zzz1137, zzz1138, zzz1139, zzz1140, zzz1141, zzz1142, Succ(zzz11430), Succ(zzz11440), fd) → new_mkVBalBranch3MkVBalBranch277(zzz1133, zzz1134, zzz1135, zzz1136, zzz1137, zzz1138, zzz1139, zzz1140, zzz1141, zzz1142, zzz11430, zzz11440, fd)
new_mkVBalBranch3MkVBalBranch277(zzz1133, zzz1134, zzz1135, zzz1136, zzz1137, zzz1138, zzz1139, zzz1140, zzz1141, zzz1142, Zero, Zero, fd) → new_mkVBalBranch3MkVBalBranch273(zzz1133, zzz1134, zzz1135, zzz1136, zzz1137, zzz1138, zzz1139, zzz1140, zzz1141, zzz1142, fd)
new_mkVBalBranch3MkVBalBranch277(zzz1133, zzz1134, zzz1135, zzz1136, zzz1137, zzz1138, zzz1139, zzz1140, zzz1141, zzz1142, Zero, Succ(zzz11440), fd) → new_mkBalBranch(zzz1133, zzz1134, new_mkVBalBranch3(zzz1142, Branch(zzz1138, zzz1139, Neg(Succ(Zero)), zzz1140, zzz1141), zzz1136, fd), zzz1137, ty_Ordering, fd)
new_mkVBalBranch3MkVBalBranch277(zzz1133, zzz1134, zzz1135, zzz1136, zzz1137, zzz1138, zzz1139, zzz1140, zzz1141, zzz1142, Succ(zzz11430), Zero, fd) → new_mkVBalBranch3MkVBalBranch274(zzz1133, zzz1134, zzz1135, zzz1136, zzz1137, zzz1138, zzz1139, zzz1140, zzz1141, zzz1142, fd)
new_mkVBalBranch3MkVBalBranch255(zzz537, zzz538, zzz539, zzz540, zzz541, zzz542, zzz543, zzz544, zzz545, zzz546, zzz547, Succ(zzz5480), Succ(zzz5490), dg) → new_mkVBalBranch3MkVBalBranch255(zzz537, zzz538, zzz539, zzz540, zzz541, zzz542, zzz543, zzz544, zzz545, zzz546, zzz547, zzz5480, zzz5490, dg)
new_mkVBalBranch3MkVBalBranch255(zzz537, zzz538, zzz539, zzz540, zzz541, zzz542, zzz543, zzz544, zzz545, zzz546, zzz547, Succ(zzz5480), Zero, dg) → new_mkVBalBranch3MkVBalBranch256(zzz537, zzz538, zzz539, zzz540, zzz541, zzz542, zzz543, zzz544, zzz545, zzz546, zzz547, dg)
new_mkVBalBranch3MkVBalBranch255(zzz537, zzz538, zzz539, zzz540, zzz541, zzz542, zzz543, zzz544, zzz545, zzz546, zzz547, Zero, Zero, dg) → new_mkVBalBranch3MkVBalBranch256(zzz537, zzz538, zzz539, zzz540, zzz541, zzz542, zzz543, zzz544, zzz545, zzz546, zzz547, dg)
new_mkVBalBranch3MkVBalBranch256(zzz537, zzz538, zzz539, zzz540, zzz541, zzz542, zzz543, zzz544, zzz545, zzz546, zzz547, dg) → new_mkVBalBranch3MkVBalBranch153(zzz537, zzz538, zzz539, zzz540, zzz541, zzz542, zzz543, zzz544, zzz545, zzz546, zzz547, new_primMulNat1(zzz539), dg)
new_mkVBalBranch3MkVBalBranch153(zzz537, zzz538, zzz539, zzz540, zzz541, zzz542, zzz543, zzz544, zzz545, zzz546, zzz547, Zero, dg) → new_mkVBalBranch3MkVBalBranch144(zzz537, zzz538, zzz539, zzz540, zzz541, zzz542, zzz543, Succ(zzz544), zzz545, zzz546, zzz547, Succ(Succ(zzz544)), Zero, dg)
new_mkVBalBranch3MkVBalBranch153(zzz537, zzz538, zzz539, zzz540, zzz541, zzz542, zzz543, zzz544, zzz545, zzz546, zzz547, Succ(zzz6990), dg) → new_mkVBalBranch3MkVBalBranch144(zzz537, zzz538, zzz539, zzz540, zzz541, zzz542, zzz543, Succ(zzz544), zzz545, zzz546, zzz547, Succ(Succ(zzz544)), Succ(zzz6990), dg)
new_mkVBalBranch3MkVBalBranch258(zzz340, zzz341, zzz3420, zzz343, zzz344, zzz520, zzz521, zzz52200, zzz523, zzz524, zzz31, h) → new_mkBalBranch(zzz340, zzz341, new_mkVBalBranch3(zzz31, Branch(zzz520, zzz521, Neg(Succ(zzz52200)), zzz523, zzz524), zzz343, h), zzz344, ty_Ordering, h)
new_mkVBalBranch3MkVBalBranch245(zzz340, zzz341, zzz343, zzz344, zzz520, zzz521, zzz52200, zzz523, zzz524, zzz31, h) → new_mkBalBranch(zzz340, zzz341, new_mkVBalBranch3(zzz31, Branch(zzz520, zzz521, Neg(Succ(zzz52200)), zzz523, zzz524), zzz343, h), zzz344, ty_Ordering, h)
new_addToFM(zzz34, zzz31, h) → new_addToFM_C3(zzz34, zzz31, h)
new_addToFM_C3(Branch(EQ, zzz341, zzz342, zzz343, zzz344), zzz31, h) → new_mkBalBranch(EQ, zzz341, zzz343, new_addToFM_C3(zzz344, zzz31, h), ty_Ordering, h)
new_addToFM_C3(Branch(LT, zzz341, zzz342, zzz343, zzz344), zzz31, h) → new_mkBalBranch(LT, zzz341, zzz343, new_addToFM_C3(zzz344, zzz31, h), ty_Ordering, h)
new_addToFM_C3(EmptyFM, zzz31, h) → Branch(GT, zzz31, Pos(Succ(Zero)), new_emptyFM(h), new_emptyFM(h))
new_addToFM_C3(Branch(GT, zzz341, zzz342, zzz343, zzz344), zzz31, h) → Branch(GT, new_addToFM0(zzz341, zzz31, h), zzz342, zzz343, zzz344)
new_addToFM0(zzz71, zzz13, h) → zzz13
new_emptyFM(h) → EmptyFM
new_mkVBalBranch3MkVBalBranch154(zzz340, zzz341, zzz34200, zzz343, zzz344, zzz520, zzz521, zzz523, zzz524, zzz31, Zero, h) → new_mkBranch(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))), GT, zzz31, Branch(zzz520, zzz521, Pos(Zero), zzz523, zzz524), Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), ty_Ordering, h)
new_mkVBalBranch3MkVBalBranch154(zzz340, zzz341, zzz34200, zzz343, zzz344, zzz520, zzz521, zzz523, zzz524, zzz31, Succ(zzz1250), h) → new_mkBalBranch(zzz520, zzz521, zzz523, new_mkVBalBranch3(zzz31, zzz524, Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), h), ty_Ordering, h)
new_mkVBalBranch3MkVBalBranch155(zzz340, zzz341, zzz34200, zzz343, zzz344, zzz520, zzz521, zzz523, zzz524, zzz31, Succ(zzz1290), h) → new_mkBalBranch(zzz520, zzz521, zzz523, new_mkVBalBranch3(zzz31, zzz524, Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), h), ty_Ordering, h)
new_mkVBalBranch3MkVBalBranch155(zzz340, zzz341, zzz34200, zzz343, zzz344, zzz520, zzz521, zzz523, zzz524, zzz31, Zero, h) → new_mkBranch(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))), GT, zzz31, Branch(zzz520, zzz521, Neg(Zero), zzz523, zzz524), Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), ty_Ordering, h)
new_splitGT27(zzz31, zzz32, zzz33, zzz34, h) → zzz34
new_splitGT26(zzz76, zzz77, zzz78, zzz79, bg) → new_splitGT24(zzz76, zzz77, zzz78, zzz79, bg)
new_splitGT42(h) → new_emptyFM(h)
new_intersectFM_C2Gts0(zzz854, zzz855, zzz856, zzz857, ba) → new_splitGT25(zzz854, zzz855, zzz856, zzz857, ba)
new_splitGT25(zzz854, zzz855, zzz856, zzz857, ba) → new_mkVBalBranch4(zzz854, new_splitGT12(zzz856, ba), zzz857, ba)
new_splitGT12(Branch(LT, zzz8561, zzz8562, zzz8563, zzz8564), ba) → new_splitGT210(zzz8561, zzz8562, zzz8563, zzz8564, ba)
new_splitGT12(Branch(EQ, zzz8561, zzz8562, zzz8563, zzz8564), ba) → new_splitGT25(zzz8561, zzz8562, zzz8563, zzz8564, ba)
new_splitGT12(EmptyFM, ba) → new_splitGT41(ba)
new_splitGT12(Branch(GT, zzz8561, zzz8562, zzz8563, zzz8564), ba) → new_splitGT28(zzz8561, zzz8562, zzz8563, zzz8564, ba)
new_mkVBalBranch4(zzz31, EmptyFM, zzz34, h) → new_addToFM2(zzz34, zzz31, h)
new_mkVBalBranch4(zzz31, Branch(zzz510, zzz511, Pos(Zero), zzz513, zzz514), Branch(zzz340, zzz341, Pos(Zero), zzz343, zzz344), h) → new_mkBranch(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))), EQ, zzz31, Branch(zzz510, zzz511, Pos(Zero), zzz513, zzz514), Branch(zzz340, zzz341, Pos(Zero), zzz343, zzz344), ty_Ordering, h)
new_mkVBalBranch4(zzz31, Branch(zzz510, zzz511, Pos(Zero), zzz513, zzz514), Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), h) → new_mkVBalBranch3MkVBalBranch168(zzz340, zzz341, zzz34200, zzz343, zzz344, zzz510, zzz511, zzz513, zzz514, zzz31, new_primMulNat1(zzz34200), h)
new_mkVBalBranch4(zzz31, Branch(zzz510, zzz511, Neg(Zero), zzz513, zzz514), Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), h) → new_mkVBalBranch3MkVBalBranch133(zzz340, zzz341, zzz34200, zzz343, zzz344, zzz510, zzz511, zzz513, zzz514, zzz31, new_primMulNat1(zzz34200), h)
new_mkVBalBranch4(zzz31, Branch(zzz510, zzz511, Neg(Zero), zzz513, zzz514), Branch(zzz340, zzz341, Neg(Zero), zzz343, zzz344), h) → new_mkBranch(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))), EQ, zzz31, Branch(zzz510, zzz511, Neg(Zero), zzz513, zzz514), Branch(zzz340, zzz341, Neg(Zero), zzz343, zzz344), ty_Ordering, h)
new_mkVBalBranch4(zzz31, Branch(zzz510, zzz511, zzz512, zzz513, zzz514), EmptyFM, h) → new_addToFM2(Branch(zzz510, zzz511, zzz512, zzz513, zzz514), zzz31, h)
new_mkVBalBranch4(zzz31, Branch(zzz510, zzz511, Neg(Succ(zzz51200)), zzz513, zzz514), Branch(zzz340, zzz341, zzz342, zzz343, zzz344), h) → new_mkVBalBranch3MkVBalBranch281(zzz340, zzz341, zzz342, zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, new_primMulNat0(zzz51200), h)
new_mkVBalBranch4(zzz31, Branch(zzz510, zzz511, Pos(Zero), zzz513, zzz514), Branch(zzz340, zzz341, Neg(Zero), zzz343, zzz344), h) → new_mkBranch(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))), EQ, zzz31, Branch(zzz510, zzz511, Pos(Zero), zzz513, zzz514), Branch(zzz340, zzz341, Neg(Zero), zzz343, zzz344), ty_Ordering, h)
new_mkVBalBranch4(zzz31, Branch(zzz510, zzz511, Neg(Zero), zzz513, zzz514), Branch(zzz340, zzz341, Pos(Zero), zzz343, zzz344), h) → new_mkBranch(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))), EQ, zzz31, Branch(zzz510, zzz511, Neg(Zero), zzz513, zzz514), Branch(zzz340, zzz341, Pos(Zero), zzz343, zzz344), ty_Ordering, h)
new_mkVBalBranch4(zzz31, Branch(zzz510, zzz511, Pos(Zero), zzz513, zzz514), Branch(zzz340, zzz341, Pos(Succ(zzz34200)), zzz343, zzz344), h) → new_mkBalBranch(zzz340, zzz341, new_mkVBalBranch4(zzz31, Branch(zzz510, zzz511, Pos(Zero), zzz513, zzz514), zzz343, h), zzz344, ty_Ordering, h)
new_mkVBalBranch4(zzz31, Branch(zzz510, zzz511, Pos(Succ(zzz51200)), zzz513, zzz514), Branch(zzz340, zzz341, zzz342, zzz343, zzz344), h) → new_mkVBalBranch3MkVBalBranch288(zzz340, zzz341, zzz342, zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, new_primMulNat0(zzz51200), h)
new_mkVBalBranch4(zzz31, Branch(zzz510, zzz511, Neg(Zero), zzz513, zzz514), Branch(zzz340, zzz341, Pos(Succ(zzz34200)), zzz343, zzz344), h) → new_mkBalBranch(zzz340, zzz341, new_mkVBalBranch4(zzz31, Branch(zzz510, zzz511, Neg(Zero), zzz513, zzz514), zzz343, h), zzz344, ty_Ordering, h)
new_mkVBalBranch3MkVBalBranch288(zzz340, zzz341, Pos(Succ(Succ(zzz342000))), zzz343, zzz344, zzz510, zzz511, Succ(zzz512000), zzz513, zzz514, zzz31, Zero, h) → new_mkVBalBranch3MkVBalBranch289(zzz340, zzz341, Succ(zzz342000), zzz343, zzz344, zzz510, zzz511, zzz512000, zzz513, zzz514, zzz31, zzz512000, zzz342000, h)
new_mkVBalBranch3MkVBalBranch288(zzz340, zzz341, Neg(zzz3420), zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, Zero, h) → new_mkVBalBranch3MkVBalBranch284(zzz340, zzz341, zzz3420, zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, h)
new_mkVBalBranch3MkVBalBranch288(zzz340, zzz341, Pos(Succ(Zero)), zzz343, zzz344, zzz510, zzz511, Succ(zzz512000), zzz513, zzz514, zzz31, Zero, h) → new_mkVBalBranch3MkVBalBranch283(zzz340, zzz341, Zero, zzz343, zzz344, zzz510, zzz511, zzz512000, zzz513, zzz514, zzz31, h)
new_mkVBalBranch3MkVBalBranch288(zzz340, zzz341, Pos(Succ(Succ(zzz342000))), zzz343, zzz344, zzz510, zzz511, Zero, zzz513, zzz514, zzz31, Zero, h) → new_mkVBalBranch3MkVBalBranch290(zzz340, zzz341, zzz342000, zzz343, zzz344, zzz510, zzz511, zzz513, zzz514, zzz31, h)
new_mkVBalBranch3MkVBalBranch288(zzz340, zzz341, Pos(Succ(Succ(zzz342000))), zzz343, zzz344, zzz510, zzz511, Zero, zzz513, zzz514, zzz31, Succ(Succ(zzz6600)), h) → new_mkVBalBranch3MkVBalBranch270(zzz340, zzz341, Succ(zzz342000), zzz343, zzz344, zzz510, zzz511, zzz513, zzz514, zzz31, Succ(zzz6600), zzz342000, h)
new_mkVBalBranch3MkVBalBranch288(zzz340, zzz341, Neg(zzz3420), zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, Succ(zzz660), h) → new_mkVBalBranch3MkVBalBranch284(zzz340, zzz341, zzz3420, zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, h)
new_mkVBalBranch3MkVBalBranch288(zzz340, zzz341, Pos(Zero), zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, Succ(zzz660), h) → new_mkVBalBranch3MkVBalBranch285(zzz340, zzz341, zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, h)
new_mkVBalBranch3MkVBalBranch288(zzz340, zzz341, Pos(Succ(Succ(zzz342000))), zzz343, zzz344, zzz510, zzz511, Succ(zzz512000), zzz513, zzz514, zzz31, Succ(Zero), h) → new_mkVBalBranch3MkVBalBranch289(zzz340, zzz341, Succ(zzz342000), zzz343, zzz344, zzz510, zzz511, zzz512000, zzz513, zzz514, zzz31, Succ(zzz512000), zzz342000, h)
new_mkVBalBranch3MkVBalBranch288(zzz340, zzz341, Pos(Succ(Succ(zzz342000))), zzz343, zzz344, zzz510, zzz511, Succ(zzz512000), zzz513, zzz514, zzz31, Succ(Succ(zzz6600)), h) → new_mkVBalBranch3MkVBalBranch289(zzz340, zzz341, Succ(zzz342000), zzz343, zzz344, zzz510, zzz511, zzz512000, zzz513, zzz514, zzz31, Succ(Succ(new_primPlusNat2(zzz6600, zzz512000))), zzz342000, h)
new_mkVBalBranch3MkVBalBranch288(zzz340, zzz341, Pos(Zero), zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, Zero, h) → new_mkVBalBranch3MkVBalBranch285(zzz340, zzz341, zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, h)
new_mkVBalBranch3MkVBalBranch288(zzz340, zzz341, Pos(Succ(Succ(zzz342000))), zzz343, zzz344, zzz510, zzz511, Zero, zzz513, zzz514, zzz31, Succ(Zero), h) → new_mkVBalBranch3MkVBalBranch270(zzz340, zzz341, Succ(zzz342000), zzz343, zzz344, zzz510, zzz511, zzz513, zzz514, zzz31, Zero, zzz342000, h)
new_mkVBalBranch3MkVBalBranch288(zzz340, zzz341, Pos(Succ(Zero)), zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, Succ(zzz660), h) → new_mkVBalBranch3MkVBalBranch287(zzz340, zzz341, zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, h)
new_mkVBalBranch3MkVBalBranch288(zzz340, zzz341, Pos(Succ(Zero)), zzz343, zzz344, zzz510, zzz511, Zero, zzz513, zzz514, zzz31, Zero, h) → new_mkVBalBranch3MkVBalBranch287(zzz340, zzz341, zzz343, zzz344, zzz510, zzz511, Zero, zzz513, zzz514, zzz31, h)
new_mkVBalBranch3MkVBalBranch287(zzz340, zzz341, zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, h) → new_mkVBalBranch3MkVBalBranch161(zzz340, zzz341, zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, new_primMulNat1(Zero), h)
new_mkVBalBranch3MkVBalBranch161(zzz340, zzz341, zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, Zero, h) → new_mkVBalBranch3MkVBalBranch162(zzz340, zzz341, Zero, zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, Zero, Succ(zzz51200), h)
new_mkVBalBranch3MkVBalBranch161(zzz340, zzz341, zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, Succ(zzz1480), h) → new_mkVBalBranch3MkVBalBranch162(zzz340, zzz341, Zero, zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, Succ(zzz1480), Succ(zzz51200), h)
new_mkVBalBranch3MkVBalBranch162(zzz1986, zzz1987, zzz1988, zzz1989, zzz1990, zzz1991, zzz1992, zzz1993, zzz1994, zzz1995, zzz1996, Succ(zzz19970), Succ(zzz19980), dh) → new_mkVBalBranch3MkVBalBranch162(zzz1986, zzz1987, zzz1988, zzz1989, zzz1990, zzz1991, zzz1992, zzz1993, zzz1994, zzz1995, zzz1996, zzz19970, zzz19980, dh)
new_mkVBalBranch3MkVBalBranch162(zzz1986, zzz1987, zzz1988, zzz1989, zzz1990, zzz1991, zzz1992, zzz1993, zzz1994, zzz1995, zzz1996, Succ(zzz19970), Zero, dh) → new_mkVBalBranch3MkVBalBranch142(zzz1986, zzz1987, zzz1988, zzz1989, zzz1990, zzz1991, zzz1992, zzz1993, zzz1994, zzz1995, zzz1996, dh)
new_mkVBalBranch3MkVBalBranch162(zzz1986, zzz1987, zzz1988, zzz1989, zzz1990, zzz1991, zzz1992, zzz1993, zzz1994, zzz1995, zzz1996, Zero, Zero, dh) → new_mkVBalBranch3MkVBalBranch142(zzz1986, zzz1987, zzz1988, zzz1989, zzz1990, zzz1991, zzz1992, zzz1993, zzz1994, zzz1995, zzz1996, dh)
new_mkVBalBranch3MkVBalBranch162(zzz1986, zzz1987, zzz1988, zzz1989, zzz1990, zzz1991, zzz1992, zzz1993, zzz1994, zzz1995, zzz1996, Zero, Succ(zzz19980), dh) → new_mkBalBranch(zzz1991, zzz1992, zzz1994, new_mkVBalBranch4(zzz1996, zzz1995, Branch(zzz1986, zzz1987, Pos(Succ(zzz1988)), zzz1989, zzz1990), dh), ty_Ordering, dh)
new_mkVBalBranch3MkVBalBranch142(zzz1986, zzz1987, zzz1988, zzz1989, zzz1990, zzz1991, zzz1992, zzz1993, zzz1994, zzz1995, zzz1996, dh) → new_mkBranch(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))), EQ, zzz1996, Branch(zzz1991, zzz1992, Pos(Succ(zzz1993)), zzz1994, zzz1995), Branch(zzz1986, zzz1987, Pos(Succ(zzz1988)), zzz1989, zzz1990), ty_Ordering, dh)
new_mkVBalBranch3MkVBalBranch270(zzz473, zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, zzz481, zzz482, Zero, Zero, eh) → new_mkVBalBranch3MkVBalBranch271(zzz473, zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, zzz481, zzz482, eh)
new_mkVBalBranch3MkVBalBranch270(zzz473, zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, zzz481, zzz482, Zero, Succ(zzz4840), eh) → new_mkBalBranch(zzz473, zzz474, new_mkVBalBranch4(zzz482, Branch(zzz478, zzz479, Pos(Succ(Zero)), zzz480, zzz481), zzz476, eh), zzz477, ty_Ordering, eh)
new_mkVBalBranch3MkVBalBranch271(zzz473, zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, zzz481, zzz482, eh) → new_mkVBalBranch3MkVBalBranch164(zzz473, zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, zzz481, zzz482, new_primMulNat1(zzz475), eh)
new_mkVBalBranch3MkVBalBranch164(zzz473, zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, zzz481, zzz482, Succ(zzz7390), eh) → new_mkVBalBranch3MkVBalBranch162(zzz473, zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, Zero, zzz480, zzz481, zzz482, Succ(zzz7390), Succ(Zero), eh)
new_mkVBalBranch3MkVBalBranch164(zzz473, zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, zzz481, zzz482, Zero, eh) → new_mkVBalBranch3MkVBalBranch162(zzz473, zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, Zero, zzz480, zzz481, zzz482, Zero, Succ(Zero), eh)
new_mkVBalBranch3MkVBalBranch285(zzz340, zzz341, zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, h) → new_mkBalBranch(zzz510, zzz511, zzz513, new_mkVBalBranch4(zzz31, zzz514, Branch(zzz340, zzz341, Pos(Zero), zzz343, zzz344), h), ty_Ordering, h)
new_mkVBalBranch3MkVBalBranch289(zzz1105, zzz1106, zzz1107, zzz1108, zzz1109, zzz1110, zzz1111, zzz1112, zzz1113, zzz1114, zzz1115, Succ(zzz11160), Succ(zzz11170), fh) → new_mkVBalBranch3MkVBalBranch289(zzz1105, zzz1106, zzz1107, zzz1108, zzz1109, zzz1110, zzz1111, zzz1112, zzz1113, zzz1114, zzz1115, zzz11160, zzz11170, fh)
new_mkVBalBranch3MkVBalBranch289(zzz1105, zzz1106, zzz1107, zzz1108, zzz1109, zzz1110, zzz1111, zzz1112, zzz1113, zzz1114, zzz1115, Succ(zzz11160), Zero, fh) → new_mkVBalBranch3MkVBalBranch283(zzz1105, zzz1106, zzz1107, zzz1108, zzz1109, zzz1110, zzz1111, zzz1112, zzz1113, zzz1114, zzz1115, fh)
new_mkVBalBranch3MkVBalBranch283(zzz461, zzz462, zzz463, zzz464, zzz465, zzz466, zzz467, zzz468, zzz469, zzz470, zzz471, de) → new_mkVBalBranch3MkVBalBranch282(zzz461, zzz462, zzz463, zzz464, zzz465, zzz466, zzz467, zzz468, zzz469, zzz470, zzz471, de)
new_mkVBalBranch3MkVBalBranch282(zzz461, zzz462, zzz463, zzz464, zzz465, zzz466, zzz467, zzz468, zzz469, zzz470, zzz471, de) → new_mkVBalBranch3MkVBalBranch165(zzz461, zzz462, zzz463, zzz464, zzz465, zzz466, zzz467, zzz468, zzz469, zzz470, zzz471, de)
new_mkVBalBranch3MkVBalBranch165(zzz461, zzz462, zzz463, zzz464, zzz465, zzz466, zzz467, zzz468, zzz469, zzz470, zzz471, de) → new_mkVBalBranch3MkVBalBranch163(zzz461, zzz462, zzz463, zzz464, zzz465, zzz466, zzz467, zzz468, zzz469, zzz470, zzz471, de)
new_mkVBalBranch3MkVBalBranch163(zzz461, zzz462, zzz463, zzz464, zzz465, zzz466, zzz467, zzz468, zzz469, zzz470, zzz471, de) → new_mkVBalBranch3MkVBalBranch158(zzz461, zzz462, zzz463, zzz464, zzz465, zzz466, zzz467, zzz468, zzz469, zzz470, zzz471, de)
new_mkVBalBranch3MkVBalBranch158(zzz461, zzz462, zzz463, zzz464, zzz465, zzz466, zzz467, zzz468, zzz469, zzz470, zzz471, de) → new_mkVBalBranch3MkVBalBranch136(zzz461, zzz462, zzz463, zzz464, zzz465, zzz466, zzz467, zzz468, zzz469, zzz470, zzz471, de)
new_mkVBalBranch3MkVBalBranch136(zzz461, zzz462, zzz463, zzz464, zzz465, zzz466, zzz467, zzz468, zzz469, zzz470, zzz471, de) → new_mkVBalBranch3MkVBalBranch137(zzz461, zzz462, zzz463, zzz464, zzz465, zzz466, zzz467, zzz468, zzz469, zzz470, zzz471, new_primMulNat1(zzz463), de)
new_mkVBalBranch3MkVBalBranch137(zzz461, zzz462, zzz463, zzz464, zzz465, zzz466, zzz467, zzz468, zzz469, zzz470, zzz471, Zero, de) → new_mkVBalBranch3MkVBalBranch162(zzz461, zzz462, zzz463, zzz464, zzz465, zzz466, zzz467, Succ(zzz468), zzz469, zzz470, zzz471, Zero, Succ(Succ(zzz468)), de)
new_mkVBalBranch3MkVBalBranch137(zzz461, zzz462, zzz463, zzz464, zzz465, zzz466, zzz467, zzz468, zzz469, zzz470, zzz471, Succ(zzz5800), de) → new_mkVBalBranch3MkVBalBranch162(zzz461, zzz462, zzz463, zzz464, zzz465, zzz466, zzz467, Succ(zzz468), zzz469, zzz470, zzz471, Succ(zzz5800), Succ(Succ(zzz468)), de)
new_mkVBalBranch3MkVBalBranch289(zzz1105, zzz1106, zzz1107, zzz1108, zzz1109, zzz1110, zzz1111, zzz1112, zzz1113, zzz1114, zzz1115, Zero, Succ(zzz11170), fh) → new_mkBalBranch(zzz1105, zzz1106, new_mkVBalBranch4(zzz1115, Branch(zzz1110, zzz1111, Pos(Succ(Succ(zzz1112))), zzz1113, zzz1114), zzz1108, fh), zzz1109, ty_Ordering, fh)
new_mkVBalBranch3MkVBalBranch289(zzz1105, zzz1106, zzz1107, zzz1108, zzz1109, zzz1110, zzz1111, zzz1112, zzz1113, zzz1114, zzz1115, Zero, Zero, fh) → new_mkVBalBranch3MkVBalBranch282(zzz1105, zzz1106, zzz1107, zzz1108, zzz1109, zzz1110, zzz1111, zzz1112, zzz1113, zzz1114, zzz1115, fh)
new_mkVBalBranch3MkVBalBranch284(zzz340, zzz341, Succ(zzz34200), zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, h) → new_mkVBalBranch3MkVBalBranch167(zzz340, zzz341, zzz34200, zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, new_primPlusNat2(new_primMulNat0(zzz34200), Succ(zzz34200)), h)
new_mkVBalBranch3MkVBalBranch284(zzz340, zzz341, Zero, zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, h) → new_mkBalBranch(zzz510, zzz511, zzz513, new_mkVBalBranch4(zzz31, zzz514, Branch(zzz340, zzz341, Neg(Zero), zzz343, zzz344), h), ty_Ordering, h)
new_mkVBalBranch3MkVBalBranch167(zzz340, zzz341, zzz34200, zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, Zero, h) → new_mkVBalBranch3MkVBalBranch160(zzz340, zzz341, zzz34200, zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, h)
new_mkVBalBranch3MkVBalBranch167(zzz340, zzz341, zzz34200, zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, Succ(zzz1410), h) → new_mkVBalBranch3MkVBalBranch160(zzz340, zzz341, zzz34200, zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, h)
new_mkVBalBranch3MkVBalBranch160(zzz340, zzz341, zzz34200, zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, h) → new_mkBalBranch(zzz510, zzz511, zzz513, new_mkVBalBranch4(zzz31, zzz514, Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), h), ty_Ordering, h)
new_mkVBalBranch3MkVBalBranch270(zzz473, zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, zzz481, zzz482, Succ(zzz4830), Succ(zzz4840), eh) → new_mkVBalBranch3MkVBalBranch270(zzz473, zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, zzz481, zzz482, zzz4830, zzz4840, eh)
new_mkVBalBranch3MkVBalBranch270(zzz473, zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, zzz481, zzz482, Succ(zzz4830), Zero, eh) → new_mkVBalBranch3MkVBalBranch271(zzz473, zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, zzz481, zzz482, eh)
new_mkVBalBranch3MkVBalBranch290(zzz340, zzz341, zzz342000, zzz343, zzz344, zzz510, zzz511, zzz513, zzz514, zzz31, h) → new_mkBalBranch(zzz340, zzz341, new_mkVBalBranch4(zzz31, Branch(zzz510, zzz511, Pos(Succ(Zero)), zzz513, zzz514), zzz343, h), zzz344, ty_Ordering, h)
new_mkVBalBranch3MkVBalBranch281(zzz340, zzz341, Neg(Succ(Zero)), zzz343, zzz344, zzz510, zzz511, Zero, zzz513, zzz514, zzz31, Zero, h) → new_mkVBalBranch3MkVBalBranch157(zzz340, zzz341, Zero, zzz343, zzz344, zzz510, zzz511, zzz513, zzz514, zzz31, new_primMulNat1(Zero), h)
new_mkVBalBranch3MkVBalBranch281(zzz340, zzz341, Neg(Succ(Succ(Zero))), zzz343, zzz344, zzz510, zzz511, Zero, zzz513, zzz514, zzz31, Succ(Succ(zzz6700)), h) → new_mkVBalBranch3MkVBalBranch263(zzz340, zzz341, Succ(Zero), zzz343, zzz344, zzz510, zzz511, zzz513, zzz514, zzz31, Zero, Succ(zzz6700), h)
new_mkVBalBranch3MkVBalBranch281(zzz340, zzz341, Neg(Zero), zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, Succ(zzz670), h) → new_mkVBalBranch3MkVBalBranch266(zzz340, zzz341, zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, h)
new_mkVBalBranch3MkVBalBranch281(zzz340, zzz341, Neg(Succ(Succ(zzz342000))), zzz343, zzz344, zzz510, zzz511, Zero, zzz513, zzz514, zzz31, Zero, h) → new_mkVBalBranch3MkVBalBranch249(zzz340, zzz341, zzz342000, zzz343, zzz344, zzz510, zzz511, zzz513, zzz514, zzz31, h)
new_mkVBalBranch3MkVBalBranch281(zzz340, zzz341, Neg(Succ(Succ(Succ(zzz3420000)))), zzz343, zzz344, zzz510, zzz511, Succ(zzz512000), zzz513, zzz514, zzz31, Succ(Zero), h) → new_mkVBalBranch3MkVBalBranch280(zzz340, zzz341, Succ(Succ(zzz3420000)), zzz343, zzz344, zzz510, zzz511, zzz512000, zzz513, zzz514, zzz31, Succ(zzz3420000), Succ(zzz512000), h)
new_mkVBalBranch3MkVBalBranch281(zzz340, zzz341, Neg(Succ(Succ(Zero))), zzz343, zzz344, zzz510, zzz511, Zero, zzz513, zzz514, zzz31, Succ(Zero), h) → new_mkVBalBranch3MkVBalBranch263(zzz340, zzz341, Succ(Zero), zzz343, zzz344, zzz510, zzz511, zzz513, zzz514, zzz31, Zero, Zero, h)
new_mkVBalBranch3MkVBalBranch281(zzz340, zzz341, Neg(Succ(Zero)), zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, Succ(zzz670), h) → new_mkBalBranch(zzz340, zzz341, new_mkVBalBranch4(zzz31, Branch(zzz510, zzz511, Neg(Succ(zzz51200)), zzz513, zzz514), zzz343, h), zzz344, ty_Ordering, h)
new_mkVBalBranch3MkVBalBranch281(zzz340, zzz341, Neg(Succ(Succ(Succ(zzz3420000)))), zzz343, zzz344, zzz510, zzz511, Zero, zzz513, zzz514, zzz31, Succ(Succ(zzz6700)), h) → new_mkVBalBranch3MkVBalBranch263(zzz340, zzz341, Succ(Succ(zzz3420000)), zzz343, zzz344, zzz510, zzz511, zzz513, zzz514, zzz31, Succ(zzz3420000), Succ(zzz6700), h)
new_mkVBalBranch3MkVBalBranch281(zzz340, zzz341, Neg(Succ(Zero)), zzz343, zzz344, zzz510, zzz511, Succ(zzz512000), zzz513, zzz514, zzz31, Zero, h) → new_mkVBalBranch3MkVBalBranch257(zzz340, zzz341, Zero, zzz343, zzz344, zzz510, zzz511, zzz512000, zzz513, zzz514, zzz31, h)
new_mkVBalBranch3MkVBalBranch281(zzz340, zzz341, Neg(Succ(Succ(zzz342000))), zzz343, zzz344, zzz510, zzz511, Succ(zzz512000), zzz513, zzz514, zzz31, Zero, h) → new_mkVBalBranch3MkVBalBranch280(zzz340, zzz341, Succ(zzz342000), zzz343, zzz344, zzz510, zzz511, zzz512000, zzz513, zzz514, zzz31, zzz342000, zzz512000, h)
new_mkVBalBranch3MkVBalBranch281(zzz340, zzz341, Neg(Succ(Succ(Succ(zzz3420000)))), zzz343, zzz344, zzz510, zzz511, Succ(zzz512000), zzz513, zzz514, zzz31, Succ(Succ(zzz6700)), h) → new_mkVBalBranch3MkVBalBranch280(zzz340, zzz341, Succ(Succ(zzz3420000)), zzz343, zzz344, zzz510, zzz511, zzz512000, zzz513, zzz514, zzz31, Succ(zzz3420000), Succ(Succ(new_primPlusNat2(zzz6700, zzz512000))), h)
new_mkVBalBranch3MkVBalBranch281(zzz340, zzz341, Neg(Zero), zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, Zero, h) → new_mkVBalBranch3MkVBalBranch266(zzz340, zzz341, zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, h)
new_mkVBalBranch3MkVBalBranch281(zzz340, zzz341, Pos(zzz3420), zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, Zero, h) → new_mkVBalBranch3MkVBalBranch248(zzz340, zzz341, zzz3420, zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, h)
new_mkVBalBranch3MkVBalBranch281(zzz340, zzz341, Pos(zzz3420), zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, Succ(zzz670), h) → new_mkVBalBranch3MkVBalBranch248(zzz340, zzz341, zzz3420, zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, h)
new_mkVBalBranch3MkVBalBranch281(zzz340, zzz341, Neg(Succ(Succ(Succ(zzz3420000)))), zzz343, zzz344, zzz510, zzz511, Zero, zzz513, zzz514, zzz31, Succ(Zero), h) → new_mkVBalBranch3MkVBalBranch263(zzz340, zzz341, Succ(Succ(zzz3420000)), zzz343, zzz344, zzz510, zzz511, zzz513, zzz514, zzz31, Succ(zzz3420000), Zero, h)
new_mkVBalBranch3MkVBalBranch281(zzz340, zzz341, Neg(Succ(Succ(Zero))), zzz343, zzz344, zzz510, zzz511, Succ(zzz512000), zzz513, zzz514, zzz31, Succ(Succ(zzz6700)), h) → new_mkVBalBranch3MkVBalBranch280(zzz340, zzz341, Succ(Zero), zzz343, zzz344, zzz510, zzz511, zzz512000, zzz513, zzz514, zzz31, Zero, Succ(Succ(new_primPlusNat2(zzz6700, zzz512000))), h)
new_mkVBalBranch3MkVBalBranch281(zzz340, zzz341, Neg(Succ(Succ(Zero))), zzz343, zzz344, zzz510, zzz511, Succ(zzz512000), zzz513, zzz514, zzz31, Succ(Zero), h) → new_mkVBalBranch3MkVBalBranch280(zzz340, zzz341, Succ(Zero), zzz343, zzz344, zzz510, zzz511, zzz512000, zzz513, zzz514, zzz31, Zero, Succ(zzz512000), h)
new_mkVBalBranch3MkVBalBranch280(zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, zzz1125, zzz1126, zzz1127, zzz1128, zzz1129, Zero, Succ(zzz11310), ff) → new_mkVBalBranch3MkVBalBranch257(zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, zzz1125, zzz1126, zzz1127, zzz1128, zzz1129, ff)
new_mkVBalBranch3MkVBalBranch257(zzz486, zzz487, zzz488, zzz489, zzz490, zzz491, zzz492, zzz493, zzz494, zzz495, zzz496, ea) → new_mkBalBranch(zzz486, zzz487, new_mkVBalBranch4(zzz496, Branch(zzz491, zzz492, Neg(Succ(Succ(zzz493))), zzz494, zzz495), zzz489, ea), zzz490, ty_Ordering, ea)
new_mkVBalBranch3MkVBalBranch263(zzz498, zzz499, zzz500, zzz501, zzz502, zzz503, zzz504, zzz505, zzz506, zzz507, Succ(zzz5080), Zero, ee) → new_mkVBalBranch3MkVBalBranch264(zzz498, zzz499, zzz500, zzz501, zzz502, zzz503, zzz504, zzz505, zzz506, zzz507, ee)
new_mkVBalBranch3MkVBalBranch264(zzz498, zzz499, zzz500, zzz501, zzz502, zzz503, zzz504, zzz505, zzz506, zzz507, ee) → new_mkVBalBranch3MkVBalBranch157(zzz498, zzz499, zzz500, zzz501, zzz502, zzz503, zzz504, zzz505, zzz506, zzz507, new_primMulNat1(zzz500), ee)
new_mkVBalBranch3MkVBalBranch157(zzz498, zzz499, zzz500, zzz501, zzz502, zzz503, zzz504, zzz505, zzz506, zzz507, Succ(zzz8040), ee) → new_mkVBalBranch3MkVBalBranch149(zzz498, zzz499, zzz500, zzz501, zzz502, zzz503, zzz504, Zero, zzz505, zzz506, zzz507, Succ(Zero), Succ(zzz8040), ee)
new_mkVBalBranch3MkVBalBranch157(zzz498, zzz499, zzz500, zzz501, zzz502, zzz503, zzz504, zzz505, zzz506, zzz507, Zero, ee) → new_mkVBalBranch3MkVBalBranch149(zzz498, zzz499, zzz500, zzz501, zzz502, zzz503, zzz504, Zero, zzz505, zzz506, zzz507, Succ(Zero), Zero, ee)
new_mkVBalBranch3MkVBalBranch149(zzz2050, zzz2051, zzz2052, zzz2053, zzz2054, zzz2055, zzz2056, zzz2057, zzz2058, zzz2059, zzz2060, Succ(zzz20610), Zero, ef) → new_mkVBalBranch3MkVBalBranch150(zzz2050, zzz2051, zzz2052, zzz2053, zzz2054, zzz2055, zzz2056, zzz2057, zzz2058, zzz2059, zzz2060, ef)
new_mkVBalBranch3MkVBalBranch150(zzz2050, zzz2051, zzz2052, zzz2053, zzz2054, zzz2055, zzz2056, zzz2057, zzz2058, zzz2059, zzz2060, ef) → new_mkBranch(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))), EQ, zzz2060, Branch(zzz2055, zzz2056, Neg(Succ(zzz2057)), zzz2058, zzz2059), Branch(zzz2050, zzz2051, Neg(Succ(zzz2052)), zzz2053, zzz2054), ty_Ordering, ef)
new_mkVBalBranch3MkVBalBranch149(zzz2050, zzz2051, zzz2052, zzz2053, zzz2054, zzz2055, zzz2056, zzz2057, zzz2058, zzz2059, zzz2060, Succ(zzz20610), Succ(zzz20620), ef) → new_mkVBalBranch3MkVBalBranch149(zzz2050, zzz2051, zzz2052, zzz2053, zzz2054, zzz2055, zzz2056, zzz2057, zzz2058, zzz2059, zzz2060, zzz20610, zzz20620, ef)
new_mkVBalBranch3MkVBalBranch149(zzz2050, zzz2051, zzz2052, zzz2053, zzz2054, zzz2055, zzz2056, zzz2057, zzz2058, zzz2059, zzz2060, Zero, Zero, ef) → new_mkVBalBranch3MkVBalBranch150(zzz2050, zzz2051, zzz2052, zzz2053, zzz2054, zzz2055, zzz2056, zzz2057, zzz2058, zzz2059, zzz2060, ef)
new_mkVBalBranch3MkVBalBranch149(zzz2050, zzz2051, zzz2052, zzz2053, zzz2054, zzz2055, zzz2056, zzz2057, zzz2058, zzz2059, zzz2060, Zero, Succ(zzz20620), ef) → new_mkBalBranch(zzz2055, zzz2056, zzz2058, new_mkVBalBranch4(zzz2060, zzz2059, Branch(zzz2050, zzz2051, Neg(Succ(zzz2052)), zzz2053, zzz2054), ef), ty_Ordering, ef)
new_mkVBalBranch3MkVBalBranch248(zzz340, zzz341, zzz3420, zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, h) → new_mkBalBranch(zzz340, zzz341, new_mkVBalBranch4(zzz31, Branch(zzz510, zzz511, Neg(Succ(zzz51200)), zzz513, zzz514), zzz343, h), zzz344, ty_Ordering, h)
new_mkVBalBranch3MkVBalBranch266(zzz340, zzz341, zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, h) → new_mkBalBranch(zzz340, zzz341, new_mkVBalBranch4(zzz31, Branch(zzz510, zzz511, Neg(Succ(zzz51200)), zzz513, zzz514), zzz343, h), zzz344, ty_Ordering, h)
new_mkVBalBranch3MkVBalBranch280(zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, zzz1125, zzz1126, zzz1127, zzz1128, zzz1129, Succ(zzz11300), Succ(zzz11310), ff) → new_mkVBalBranch3MkVBalBranch280(zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, zzz1125, zzz1126, zzz1127, zzz1128, zzz1129, zzz11300, zzz11310, ff)
new_mkVBalBranch3MkVBalBranch280(zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, zzz1125, zzz1126, zzz1127, zzz1128, zzz1129, Succ(zzz11300), Zero, ff) → new_mkVBalBranch3MkVBalBranch278(zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, zzz1125, zzz1126, zzz1127, zzz1128, zzz1129, ff)
new_mkVBalBranch3MkVBalBranch280(zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, zzz1125, zzz1126, zzz1127, zzz1128, zzz1129, Zero, Zero, ff) → new_mkVBalBranch3MkVBalBranch278(zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, zzz1125, zzz1126, zzz1127, zzz1128, zzz1129, ff)
new_mkVBalBranch3MkVBalBranch278(zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, zzz1125, zzz1126, zzz1127, zzz1128, zzz1129, ff) → new_mkVBalBranch3MkVBalBranch159(zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, zzz1125, zzz1126, zzz1127, zzz1128, zzz1129, new_primMulNat1(zzz1121), ff)
new_mkVBalBranch3MkVBalBranch159(zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, zzz1125, zzz1126, zzz1127, zzz1128, zzz1129, Succ(zzz12130), ff) → new_mkVBalBranch3MkVBalBranch149(zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, zzz1125, Succ(zzz1126), zzz1127, zzz1128, zzz1129, Succ(Succ(zzz1126)), Succ(zzz12130), ff)
new_mkVBalBranch3MkVBalBranch159(zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, zzz1125, zzz1126, zzz1127, zzz1128, zzz1129, Zero, ff) → new_mkVBalBranch3MkVBalBranch149(zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, zzz1125, Succ(zzz1126), zzz1127, zzz1128, zzz1129, Succ(Succ(zzz1126)), Zero, ff)
new_mkVBalBranch3MkVBalBranch263(zzz498, zzz499, zzz500, zzz501, zzz502, zzz503, zzz504, zzz505, zzz506, zzz507, Succ(zzz5080), Succ(zzz5090), ee) → new_mkVBalBranch3MkVBalBranch263(zzz498, zzz499, zzz500, zzz501, zzz502, zzz503, zzz504, zzz505, zzz506, zzz507, zzz5080, zzz5090, ee)
new_mkVBalBranch3MkVBalBranch263(zzz498, zzz499, zzz500, zzz501, zzz502, zzz503, zzz504, zzz505, zzz506, zzz507, Zero, Zero, ee) → new_mkVBalBranch3MkVBalBranch264(zzz498, zzz499, zzz500, zzz501, zzz502, zzz503, zzz504, zzz505, zzz506, zzz507, ee)
new_mkVBalBranch3MkVBalBranch263(zzz498, zzz499, zzz500, zzz501, zzz502, zzz503, zzz504, zzz505, zzz506, zzz507, Zero, Succ(zzz5090), ee) → new_mkBalBranch(zzz498, zzz499, new_mkVBalBranch4(zzz507, Branch(zzz503, zzz504, Neg(Succ(Zero)), zzz505, zzz506), zzz501, ee), zzz502, ty_Ordering, ee)
new_mkVBalBranch3MkVBalBranch249(zzz340, zzz341, zzz342000, zzz343, zzz344, zzz510, zzz511, zzz513, zzz514, zzz31, h) → new_mkVBalBranch3MkVBalBranch250(zzz340, zzz341, zzz342000, zzz343, zzz344, zzz510, zzz511, zzz513, zzz514, zzz31, h)
new_mkVBalBranch3MkVBalBranch250(zzz340, zzz341, zzz342000, zzz343, zzz344, zzz510, zzz511, zzz513, zzz514, zzz31, h) → new_mkVBalBranch3MkVBalBranch157(zzz340, zzz341, Succ(zzz342000), zzz343, zzz344, zzz510, zzz511, zzz513, zzz514, zzz31, new_primMulNat1(Succ(zzz342000)), h)
new_addToFM2(zzz34, zzz31, h) → new_addToFM_C4(zzz34, zzz31, h)
new_addToFM_C4(EmptyFM, zzz31, h) → Branch(EQ, zzz31, Pos(Succ(Zero)), new_emptyFM(h), new_emptyFM(h))
new_addToFM_C4(Branch(GT, zzz341, zzz342, zzz343, zzz344), zzz31, h) → new_mkBalBranch(GT, zzz341, new_addToFM_C4(zzz343, zzz31, h), zzz344, ty_Ordering, h)
new_addToFM_C4(Branch(LT, zzz341, zzz342, zzz343, zzz344), zzz31, h) → new_mkBalBranch(LT, zzz341, zzz343, new_addToFM_C4(zzz344, zzz31, h), ty_Ordering, h)
new_addToFM_C4(Branch(EQ, zzz341, zzz342, zzz343, zzz344), zzz31, h) → Branch(EQ, new_addToFM0(zzz341, zzz31, h), zzz342, zzz343, zzz344)
new_mkVBalBranch3MkVBalBranch133(zzz340, zzz341, zzz34200, zzz343, zzz344, zzz510, zzz511, zzz513, zzz514, zzz31, Succ(zzz1240), h) → new_mkBalBranch(zzz510, zzz511, zzz513, new_mkVBalBranch4(zzz31, zzz514, Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), h), ty_Ordering, h)
new_mkVBalBranch3MkVBalBranch133(zzz340, zzz341, zzz34200, zzz343, zzz344, zzz510, zzz511, zzz513, zzz514, zzz31, Zero, h) → new_mkBranch(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))), EQ, zzz31, Branch(zzz510, zzz511, Neg(Zero), zzz513, zzz514), Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), ty_Ordering, h)
new_mkVBalBranch3MkVBalBranch168(zzz340, zzz341, zzz34200, zzz343, zzz344, zzz510, zzz511, zzz513, zzz514, zzz31, Zero, h) → new_mkBranch(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))), EQ, zzz31, Branch(zzz510, zzz511, Pos(Zero), zzz513, zzz514), Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), ty_Ordering, h)
new_mkVBalBranch3MkVBalBranch168(zzz340, zzz341, zzz34200, zzz343, zzz344, zzz510, zzz511, zzz513, zzz514, zzz31, Succ(zzz1200), h) → new_mkBalBranch(zzz510, zzz511, zzz513, new_mkVBalBranch4(zzz31, zzz514, Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), h), ty_Ordering, h)
new_splitGT28(zzz869, zzz870, zzz871, zzz872, bc) → new_mkVBalBranch3(zzz869, new_splitGT12(zzz871, bc), zzz872, bc)
new_splitGT41(h) → new_emptyFM(h)
new_splitGT210(zzz31, zzz32, zzz33, zzz34, h) → zzz34
new_intersectFM_C2Gts1(zzz869, zzz870, zzz871, zzz872, bc) → new_splitGT28(zzz869, zzz870, zzz871, zzz872, bc)
new_intersectFM_C2Lts(zzz76, zzz77, zzz78, zzz79, bg) → new_splitLT9(zzz76, zzz77, zzz78, zzz79, bg)
new_splitLT9(zzz76, zzz77, zzz78, zzz79, bg) → new_splitLT27(zzz76, zzz77, zzz78, zzz79, bg)
new_splitLT23(zzz76, zzz77, zzz78, zzz79, bg) → new_splitLT15(zzz78, bg)
new_splitLT15(Branch(GT, zzz781, zzz782, zzz783, zzz784), bg) → new_splitLT27(zzz781, zzz782, zzz783, zzz784, bg)
new_splitLT27(zzz76, zzz77, zzz78, zzz79, bg) → new_splitLT23(zzz76, zzz77, zzz78, zzz79, bg)
new_splitLT15(Branch(EQ, zzz781, zzz782, zzz783, zzz784), bg) → new_splitLT26(zzz781, zzz782, zzz783, zzz784, bg)
new_splitLT15(Branch(LT, zzz781, zzz782, zzz783, zzz784), bg) → new_mkVBalBranch2(zzz781, zzz783, new_splitLT15(zzz784, bg), bg)
new_splitLT15(EmptyFM, bg) → new_splitLT41(bg)
new_splitLT41(h) → new_emptyFM(h)
new_mkVBalBranch2(zzz31, Branch(zzz330, zzz331, Neg(Succ(zzz33200)), zzz333, zzz334), Branch(zzz3170, zzz3171, zzz3172, zzz3173, zzz3174), h) → new_mkVBalBranch3MkVBalBranch262(zzz3170, zzz3171, zzz3172, zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, new_primPlusNat2(new_primMulNat0(zzz33200), Succ(zzz33200)), h)
new_mkVBalBranch2(zzz31, EmptyFM, zzz317, h) → new_addToFM1(zzz317, zzz31, h)
new_mkVBalBranch2(zzz31, Branch(zzz330, zzz331, Neg(Zero), zzz333, zzz334), Branch(zzz3170, zzz3171, Pos(Succ(zzz317200)), zzz3173, zzz3174), h) → new_mkBalBranch(zzz3170, zzz3171, new_mkVBalBranch2(zzz31, Branch(zzz330, zzz331, Neg(Zero), zzz333, zzz334), zzz3173, h), zzz3174, ty_Ordering, h)
new_mkVBalBranch2(zzz31, Branch(zzz330, zzz331, zzz332, zzz333, zzz334), EmptyFM, h) → new_addToFM1(Branch(zzz330, zzz331, zzz332, zzz333, zzz334), zzz31, h)
new_mkVBalBranch2(zzz31, Branch(zzz330, zzz331, Neg(Zero), zzz333, zzz334), Branch(zzz3170, zzz3171, Neg(Zero), zzz3173, zzz3174), h) → new_mkBranch(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))), LT, zzz31, Branch(zzz330, zzz331, Neg(Zero), zzz333, zzz334), Branch(zzz3170, zzz3171, Neg(Zero), zzz3173, zzz3174), ty_Ordering, h)
new_mkVBalBranch2(zzz31, Branch(zzz330, zzz331, Pos(Succ(zzz33200)), zzz333, zzz334), Branch(zzz3170, zzz3171, zzz3172, zzz3173, zzz3174), h) → new_mkVBalBranch3MkVBalBranch261(zzz3170, zzz3171, zzz3172, zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, new_primPlusNat2(new_primMulNat0(zzz33200), Succ(zzz33200)), h)
new_mkVBalBranch2(zzz31, Branch(zzz330, zzz331, Neg(Zero), zzz333, zzz334), Branch(zzz3170, zzz3171, Neg(Succ(zzz317200)), zzz3173, zzz3174), h) → new_mkVBalBranch3MkVBalBranch146(zzz3170, zzz3171, zzz317200, zzz3173, zzz3174, zzz330, zzz331, zzz333, zzz334, zzz31, new_primMulNat1(zzz317200), h)
new_mkVBalBranch2(zzz31, Branch(zzz330, zzz331, Pos(Zero), zzz333, zzz334), Branch(zzz3170, zzz3171, Neg(Zero), zzz3173, zzz3174), h) → new_mkBranch(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))), LT, zzz31, Branch(zzz330, zzz331, Pos(Zero), zzz333, zzz334), Branch(zzz3170, zzz3171, Neg(Zero), zzz3173, zzz3174), ty_Ordering, h)
new_mkVBalBranch2(zzz31, Branch(zzz330, zzz331, Neg(Zero), zzz333, zzz334), Branch(zzz3170, zzz3171, Pos(Zero), zzz3173, zzz3174), h) → new_mkBranch(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))), LT, zzz31, Branch(zzz330, zzz331, Neg(Zero), zzz333, zzz334), Branch(zzz3170, zzz3171, Pos(Zero), zzz3173, zzz3174), ty_Ordering, h)
new_mkVBalBranch2(zzz31, Branch(zzz330, zzz331, Pos(Zero), zzz333, zzz334), Branch(zzz3170, zzz3171, Pos(Zero), zzz3173, zzz3174), h) → new_mkBranch(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))), LT, zzz31, Branch(zzz330, zzz331, Pos(Zero), zzz333, zzz334), Branch(zzz3170, zzz3171, Pos(Zero), zzz3173, zzz3174), ty_Ordering, h)
new_mkVBalBranch2(zzz31, Branch(zzz330, zzz331, Pos(Zero), zzz333, zzz334), Branch(zzz3170, zzz3171, Pos(Succ(zzz317200)), zzz3173, zzz3174), h) → new_mkBalBranch(zzz3170, zzz3171, new_mkVBalBranch2(zzz31, Branch(zzz330, zzz331, Pos(Zero), zzz333, zzz334), zzz3173, h), zzz3174, ty_Ordering, h)
new_mkVBalBranch2(zzz31, Branch(zzz330, zzz331, Pos(Zero), zzz333, zzz334), Branch(zzz3170, zzz3171, Neg(Succ(zzz317200)), zzz3173, zzz3174), h) → new_mkVBalBranch3MkVBalBranch145(zzz3170, zzz3171, zzz317200, zzz3173, zzz3174, zzz330, zzz331, zzz333, zzz334, zzz31, new_primMulNat1(zzz317200), h)
new_mkVBalBranch3MkVBalBranch145(zzz3170, zzz3171, zzz317200, zzz3173, zzz3174, zzz330, zzz331, zzz333, zzz334, zzz31, Zero, h) → new_mkBranch(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))), LT, zzz31, Branch(zzz330, zzz331, Pos(Zero), zzz333, zzz334), Branch(zzz3170, zzz3171, Neg(Succ(zzz317200)), zzz3173, zzz3174), ty_Ordering, h)
new_mkVBalBranch3MkVBalBranch145(zzz3170, zzz3171, zzz317200, zzz3173, zzz3174, zzz330, zzz331, zzz333, zzz334, zzz31, Succ(zzz5350), h) → new_mkBalBranch(zzz330, zzz331, zzz333, new_mkVBalBranch2(zzz31, zzz334, Branch(zzz3170, zzz3171, Neg(Succ(zzz317200)), zzz3173, zzz3174), h), ty_Ordering, h)
new_mkVBalBranch3MkVBalBranch146(zzz3170, zzz3171, zzz317200, zzz3173, zzz3174, zzz330, zzz331, zzz333, zzz334, zzz31, Succ(zzz5500), h) → new_mkBalBranch(zzz330, zzz331, zzz333, new_mkVBalBranch2(zzz31, zzz334, Branch(zzz3170, zzz3171, Neg(Succ(zzz317200)), zzz3173, zzz3174), h), ty_Ordering, h)
new_mkVBalBranch3MkVBalBranch146(zzz3170, zzz3171, zzz317200, zzz3173, zzz3174, zzz330, zzz331, zzz333, zzz334, zzz31, Zero, h) → new_mkBranch(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))), LT, zzz31, Branch(zzz330, zzz331, Neg(Zero), zzz333, zzz334), Branch(zzz3170, zzz3171, Neg(Succ(zzz317200)), zzz3173, zzz3174), ty_Ordering, h)
new_mkVBalBranch3MkVBalBranch261(zzz3170, zzz3171, Pos(Succ(zzz317200)), zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, Succ(zzz4170), h) → new_mkVBalBranch3MkVBalBranch275(zzz3170, zzz3171, zzz317200, zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, zzz4170, zzz317200, h)
new_mkVBalBranch3MkVBalBranch261(zzz3170, zzz3171, Pos(Zero), zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, Succ(zzz4170), h) → new_mkVBalBranch3MkVBalBranch279(zzz3170, zzz3171, zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, h)
new_mkVBalBranch3MkVBalBranch261(zzz3170, zzz3171, Pos(Succ(zzz317200)), zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, Zero, h) → new_mkVBalBranch3MkVBalBranch275(zzz3170, zzz3171, zzz317200, zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, Zero, Succ(zzz317200), h)
new_mkVBalBranch3MkVBalBranch261(zzz3170, zzz3171, Pos(Zero), zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, Zero, h) → new_mkVBalBranch3MkVBalBranch279(zzz3170, zzz3171, zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, h)
new_mkVBalBranch3MkVBalBranch261(zzz3170, zzz3171, Neg(Succ(zzz317200)), zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, Zero, h) → new_mkVBalBranch3MkVBalBranch286(zzz3170, zzz3171, Succ(zzz317200), zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, h)
new_mkVBalBranch3MkVBalBranch261(zzz3170, zzz3171, Neg(Zero), zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, Zero, h) → new_mkVBalBranch3MkVBalBranch265(zzz3170, zzz3171, Zero, zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, h)
new_mkVBalBranch3MkVBalBranch261(zzz3170, zzz3171, Neg(zzz31720), zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, Succ(zzz4170), h) → new_mkVBalBranch3MkVBalBranch286(zzz3170, zzz3171, zzz31720, zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, h)
new_mkVBalBranch3MkVBalBranch286(zzz3170, zzz3171, zzz31720, zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, h) → new_mkVBalBranch3MkVBalBranch265(zzz3170, zzz3171, zzz31720, zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, h)
new_mkVBalBranch3MkVBalBranch265(zzz3170, zzz3171, Zero, zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, h) → new_mkBalBranch(zzz330, zzz331, zzz333, new_mkVBalBranch2(zzz31, zzz334, Branch(zzz3170, zzz3171, Neg(Zero), zzz3173, zzz3174), h), ty_Ordering, h)
new_mkVBalBranch3MkVBalBranch265(zzz3170, zzz3171, Succ(zzz317200), zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, h) → new_mkVBalBranch3MkVBalBranch139(zzz3170, zzz3171, zzz317200, zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, new_primPlusNat2(new_primMulNat0(zzz317200), Succ(zzz317200)), h)
new_mkVBalBranch3MkVBalBranch139(zzz3170, zzz3171, zzz317200, zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, Succ(zzz5620), h) → new_mkVBalBranch3MkVBalBranch140(zzz3170, zzz3171, zzz317200, zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, h)
new_mkVBalBranch3MkVBalBranch139(zzz3170, zzz3171, zzz317200, zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, Zero, h) → new_mkVBalBranch3MkVBalBranch140(zzz3170, zzz3171, zzz317200, zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, h)
new_mkVBalBranch3MkVBalBranch140(zzz3170, zzz3171, zzz317200, zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, h) → new_mkBalBranch(zzz330, zzz331, zzz333, new_mkVBalBranch2(zzz31, zzz334, Branch(zzz3170, zzz3171, Neg(Succ(zzz317200)), zzz3173, zzz3174), h), ty_Ordering, h)
new_mkVBalBranch3MkVBalBranch279(zzz3170, zzz3171, zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, h) → new_mkBalBranch(zzz330, zzz331, zzz333, new_mkVBalBranch2(zzz31, zzz334, Branch(zzz3170, zzz3171, Pos(Zero), zzz3173, zzz3174), h), ty_Ordering, h)
new_mkVBalBranch3MkVBalBranch275(zzz958, zzz959, zzz960, zzz961, zzz962, zzz963, zzz964, zzz965, zzz966, zzz967, zzz968, Zero, Succ(zzz9700), fa) → new_mkBalBranch(zzz958, zzz959, new_mkVBalBranch2(zzz968, Branch(zzz963, zzz964, Pos(Succ(zzz965)), zzz966, zzz967), zzz961, fa), zzz962, ty_Ordering, fa)
new_mkVBalBranch3MkVBalBranch275(zzz958, zzz959, zzz960, zzz961, zzz962, zzz963, zzz964, zzz965, zzz966, zzz967, zzz968, Zero, Zero, fa) → new_mkVBalBranch3MkVBalBranch276(zzz958, zzz959, zzz960, zzz961, zzz962, zzz963, zzz964, zzz965, zzz966, zzz967, zzz968, fa)
new_mkVBalBranch3MkVBalBranch275(zzz958, zzz959, zzz960, zzz961, zzz962, zzz963, zzz964, zzz965, zzz966, zzz967, zzz968, Succ(zzz9690), Succ(zzz9700), fa) → new_mkVBalBranch3MkVBalBranch275(zzz958, zzz959, zzz960, zzz961, zzz962, zzz963, zzz964, zzz965, zzz966, zzz967, zzz968, zzz9690, zzz9700, fa)
new_mkVBalBranch3MkVBalBranch275(zzz958, zzz959, zzz960, zzz961, zzz962, zzz963, zzz964, zzz965, zzz966, zzz967, zzz968, Succ(zzz9690), Zero, fa) → new_mkVBalBranch3MkVBalBranch276(zzz958, zzz959, zzz960, zzz961, zzz962, zzz963, zzz964, zzz965, zzz966, zzz967, zzz968, fa)
new_mkVBalBranch3MkVBalBranch276(zzz958, zzz959, zzz960, zzz961, zzz962, zzz963, zzz964, zzz965, zzz966, zzz967, zzz968, fa) → new_mkVBalBranch3MkVBalBranch156(zzz958, zzz959, zzz960, zzz961, zzz962, zzz963, zzz964, zzz965, zzz966, zzz967, zzz968, new_primMulNat1(zzz960), fa)
new_mkVBalBranch3MkVBalBranch156(zzz958, zzz959, zzz960, zzz961, zzz962, zzz963, zzz964, zzz965, zzz966, zzz967, zzz968, Succ(zzz10180), fa) → new_mkVBalBranch3MkVBalBranch152(zzz958, zzz959, zzz960, zzz961, zzz962, zzz963, zzz964, zzz965, zzz966, zzz967, zzz968, Succ(zzz10180), Succ(zzz965), fa)
new_mkVBalBranch3MkVBalBranch156(zzz958, zzz959, zzz960, zzz961, zzz962, zzz963, zzz964, zzz965, zzz966, zzz967, zzz968, Zero, fa) → new_mkVBalBranch3MkVBalBranch152(zzz958, zzz959, zzz960, zzz961, zzz962, zzz963, zzz964, zzz965, zzz966, zzz967, zzz968, Zero, Succ(zzz965), fa)
new_mkVBalBranch3MkVBalBranch152(zzz1337, zzz1338, zzz1339, zzz1340, zzz1341, zzz1342, zzz1343, zzz1344, zzz1345, zzz1346, zzz1347, Zero, Succ(zzz13490), eg) → new_mkBalBranch(zzz1342, zzz1343, zzz1345, new_mkVBalBranch2(zzz1347, zzz1346, Branch(zzz1337, zzz1338, Pos(Succ(zzz1339)), zzz1340, zzz1341), eg), ty_Ordering, eg)
new_mkVBalBranch3MkVBalBranch152(zzz1337, zzz1338, zzz1339, zzz1340, zzz1341, zzz1342, zzz1343, zzz1344, zzz1345, zzz1346, zzz1347, Succ(zzz13480), Succ(zzz13490), eg) → new_mkVBalBranch3MkVBalBranch152(zzz1337, zzz1338, zzz1339, zzz1340, zzz1341, zzz1342, zzz1343, zzz1344, zzz1345, zzz1346, zzz1347, zzz13480, zzz13490, eg)
new_mkVBalBranch3MkVBalBranch152(zzz1337, zzz1338, zzz1339, zzz1340, zzz1341, zzz1342, zzz1343, zzz1344, zzz1345, zzz1346, zzz1347, Succ(zzz13480), Zero, eg) → new_mkVBalBranch3MkVBalBranch151(zzz1337, zzz1338, zzz1339, zzz1340, zzz1341, zzz1342, zzz1343, zzz1344, zzz1345, zzz1346, zzz1347, eg)
new_mkVBalBranch3MkVBalBranch152(zzz1337, zzz1338, zzz1339, zzz1340, zzz1341, zzz1342, zzz1343, zzz1344, zzz1345, zzz1346, zzz1347, Zero, Zero, eg) → new_mkVBalBranch3MkVBalBranch151(zzz1337, zzz1338, zzz1339, zzz1340, zzz1341, zzz1342, zzz1343, zzz1344, zzz1345, zzz1346, zzz1347, eg)
new_mkVBalBranch3MkVBalBranch151(zzz1337, zzz1338, zzz1339, zzz1340, zzz1341, zzz1342, zzz1343, zzz1344, zzz1345, zzz1346, zzz1347, eg) → new_mkBranch(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))), LT, zzz1347, Branch(zzz1342, zzz1343, Pos(Succ(zzz1344)), zzz1345, zzz1346), Branch(zzz1337, zzz1338, Pos(Succ(zzz1339)), zzz1340, zzz1341), ty_Ordering, eg)
new_addToFM1(zzz317, zzz31, h) → new_addToFM_C2(zzz317, zzz31, h)
new_addToFM_C2(EmptyFM, zzz31, h) → Branch(LT, zzz31, Pos(Succ(Zero)), new_emptyFM(h), new_emptyFM(h))
new_addToFM_C2(Branch(GT, zzz3171, zzz3172, zzz3173, zzz3174), zzz31, h) → new_mkBalBranch(GT, zzz3171, new_addToFM_C2(zzz3173, zzz31, h), zzz3174, ty_Ordering, h)
new_addToFM_C2(Branch(EQ, zzz3171, zzz3172, zzz3173, zzz3174), zzz31, h) → new_mkBalBranch(EQ, zzz3171, new_addToFM_C2(zzz3173, zzz31, h), zzz3174, ty_Ordering, h)
new_addToFM_C2(Branch(LT, zzz3171, zzz3172, zzz3173, zzz3174), zzz31, h) → Branch(LT, new_addToFM0(zzz3171, zzz31, h), zzz3172, zzz3173, zzz3174)
new_mkVBalBranch3MkVBalBranch262(zzz3170, zzz3171, Neg(Zero), zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, Zero, h) → new_mkBranch(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))), LT, zzz31, Branch(zzz330, zzz331, Neg(Succ(zzz33200)), zzz333, zzz334), Branch(zzz3170, zzz3171, Neg(Zero), zzz3173, zzz3174), ty_Ordering, h)
new_mkVBalBranch3MkVBalBranch262(zzz3170, zzz3171, Pos(Zero), zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, Zero, h) → new_mkBranch(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))), LT, zzz31, Branch(zzz330, zzz331, Neg(Succ(zzz33200)), zzz333, zzz334), Branch(zzz3170, zzz3171, Pos(Zero), zzz3173, zzz3174), ty_Ordering, h)
new_mkVBalBranch3MkVBalBranch262(zzz3170, zzz3171, Pos(Succ(zzz317200)), zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, Zero, h) → new_mkVBalBranch3MkVBalBranch251(zzz3170, zzz3171, Succ(zzz317200), zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, h)
new_mkVBalBranch3MkVBalBranch262(zzz3170, zzz3171, Pos(zzz31720), zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, Succ(zzz4190), h) → new_mkVBalBranch3MkVBalBranch251(zzz3170, zzz3171, zzz31720, zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, h)
new_mkVBalBranch3MkVBalBranch262(zzz3170, zzz3171, Neg(Succ(zzz317200)), zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, Zero, h) → new_mkVBalBranch3MkVBalBranch246(zzz3170, zzz3171, zzz317200, zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, Succ(zzz317200), Zero, h)
new_mkVBalBranch3MkVBalBranch262(zzz3170, zzz3171, Neg(Zero), zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, Succ(zzz4190), h) → new_mkBalBranch(zzz3170, zzz3171, new_mkVBalBranch2(zzz31, Branch(zzz330, zzz331, Neg(Succ(zzz33200)), zzz333, zzz334), zzz3173, h), zzz3174, ty_Ordering, h)
new_mkVBalBranch3MkVBalBranch262(zzz3170, zzz3171, Neg(Succ(zzz317200)), zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, Succ(zzz4190), h) → new_mkVBalBranch3MkVBalBranch246(zzz3170, zzz3171, zzz317200, zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, zzz317200, zzz4190, h)
new_mkVBalBranch3MkVBalBranch246(zzz972, zzz973, zzz974, zzz975, zzz976, zzz977, zzz978, zzz979, zzz980, zzz981, zzz982, Zero, Zero, cg) → new_mkVBalBranch3MkVBalBranch247(zzz972, zzz973, zzz974, zzz975, zzz976, zzz977, zzz978, zzz979, zzz980, zzz981, zzz982, cg)
new_mkVBalBranch3MkVBalBranch246(zzz972, zzz973, zzz974, zzz975, zzz976, zzz977, zzz978, zzz979, zzz980, zzz981, zzz982, Zero, Succ(zzz9840), cg) → new_mkBalBranch(zzz972, zzz973, new_mkVBalBranch2(zzz982, Branch(zzz977, zzz978, Neg(Succ(zzz979)), zzz980, zzz981), zzz975, cg), zzz976, ty_Ordering, cg)
new_mkVBalBranch3MkVBalBranch246(zzz972, zzz973, zzz974, zzz975, zzz976, zzz977, zzz978, zzz979, zzz980, zzz981, zzz982, Succ(zzz9830), Succ(zzz9840), cg) → new_mkVBalBranch3MkVBalBranch246(zzz972, zzz973, zzz974, zzz975, zzz976, zzz977, zzz978, zzz979, zzz980, zzz981, zzz982, zzz9830, zzz9840, cg)
new_mkVBalBranch3MkVBalBranch246(zzz972, zzz973, zzz974, zzz975, zzz976, zzz977, zzz978, zzz979, zzz980, zzz981, zzz982, Succ(zzz9830), Zero, cg) → new_mkVBalBranch3MkVBalBranch247(zzz972, zzz973, zzz974, zzz975, zzz976, zzz977, zzz978, zzz979, zzz980, zzz981, zzz982, cg)
new_mkVBalBranch3MkVBalBranch247(zzz972, zzz973, zzz974, zzz975, zzz976, zzz977, zzz978, zzz979, zzz980, zzz981, zzz982, cg) → new_mkVBalBranch3MkVBalBranch141(zzz972, zzz973, zzz974, zzz975, zzz976, zzz977, zzz978, zzz979, zzz980, zzz981, zzz982, new_primMulNat1(zzz974), cg)
new_mkVBalBranch3MkVBalBranch141(zzz972, zzz973, zzz974, zzz975, zzz976, zzz977, zzz978, zzz979, zzz980, zzz981, zzz982, Succ(zzz10190), cg) → new_mkVBalBranch3MkVBalBranch134(zzz972, zzz973, zzz974, zzz975, zzz976, zzz977, zzz978, zzz979, zzz980, zzz981, zzz982, Succ(zzz979), Succ(zzz10190), cg)
new_mkVBalBranch3MkVBalBranch141(zzz972, zzz973, zzz974, zzz975, zzz976, zzz977, zzz978, zzz979, zzz980, zzz981, zzz982, Zero, cg) → new_mkVBalBranch3MkVBalBranch134(zzz972, zzz973, zzz974, zzz975, zzz976, zzz977, zzz978, zzz979, zzz980, zzz981, zzz982, Succ(zzz979), Zero, cg)
new_mkVBalBranch3MkVBalBranch134(zzz1851, zzz1852, zzz1853, zzz1854, zzz1855, zzz1856, zzz1857, zzz1858, zzz1859, zzz1860, zzz1861, Succ(zzz18620), Zero, dd) → new_mkVBalBranch3MkVBalBranch135(zzz1851, zzz1852, zzz1853, zzz1854, zzz1855, zzz1856, zzz1857, zzz1858, zzz1859, zzz1860, zzz1861, dd)
new_mkVBalBranch3MkVBalBranch135(zzz1851, zzz1852, zzz1853, zzz1854, zzz1855, zzz1856, zzz1857, zzz1858, zzz1859, zzz1860, zzz1861, dd) → new_mkBranch(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))), LT, zzz1861, Branch(zzz1856, zzz1857, Neg(Succ(zzz1858)), zzz1859, zzz1860), Branch(zzz1851, zzz1852, Neg(Succ(zzz1853)), zzz1854, zzz1855), ty_Ordering, dd)
new_mkVBalBranch3MkVBalBranch134(zzz1851, zzz1852, zzz1853, zzz1854, zzz1855, zzz1856, zzz1857, zzz1858, zzz1859, zzz1860, zzz1861, Succ(zzz18620), Succ(zzz18630), dd) → new_mkVBalBranch3MkVBalBranch134(zzz1851, zzz1852, zzz1853, zzz1854, zzz1855, zzz1856, zzz1857, zzz1858, zzz1859, zzz1860, zzz1861, zzz18620, zzz18630, dd)
new_mkVBalBranch3MkVBalBranch134(zzz1851, zzz1852, zzz1853, zzz1854, zzz1855, zzz1856, zzz1857, zzz1858, zzz1859, zzz1860, zzz1861, Zero, Succ(zzz18630), dd) → new_mkBalBranch(zzz1856, zzz1857, zzz1859, new_mkVBalBranch2(zzz1861, zzz1860, Branch(zzz1851, zzz1852, Neg(Succ(zzz1853)), zzz1854, zzz1855), dd), ty_Ordering, dd)
new_mkVBalBranch3MkVBalBranch134(zzz1851, zzz1852, zzz1853, zzz1854, zzz1855, zzz1856, zzz1857, zzz1858, zzz1859, zzz1860, zzz1861, Zero, Zero, dd) → new_mkVBalBranch3MkVBalBranch135(zzz1851, zzz1852, zzz1853, zzz1854, zzz1855, zzz1856, zzz1857, zzz1858, zzz1859, zzz1860, zzz1861, dd)
new_mkVBalBranch3MkVBalBranch251(zzz3170, zzz3171, zzz31720, zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, h) → new_mkBalBranch(zzz3170, zzz3171, new_mkVBalBranch2(zzz31, Branch(zzz330, zzz331, Neg(Succ(zzz33200)), zzz333, zzz334), zzz3173, h), zzz3174, ty_Ordering, h)
new_splitLT26(zzz31, zzz32, zzz33, zzz34, h) → zzz33
new_intersectFM_C2Gts(zzz76, zzz77, zzz78, zzz79, bg) → new_splitGT9(zzz76, zzz77, zzz78, zzz79, bg)
new_splitGT9(zzz76, zzz77, zzz78, zzz79, bg) → new_splitGT26(zzz76, zzz77, zzz78, zzz79, bg)
new_intersectFM_C2Gts2(zzz883, zzz884, zzz885, zzz886, be) → new_splitGT29(zzz883, zzz884, zzz885, zzz886, be)
new_splitLT7(zzz31, zzz32, zzz33, zzz34, h) → new_splitLT26(zzz31, zzz32, zzz33, zzz34, h)
new_splitLT10(zzz31, zzz32, zzz33, h) → new_mkVBalBranch2(zzz31, zzz33, new_splitLT13(h), h)
new_splitLT13(h) → new_splitLT40(h)
new_splitLT40(h) → new_emptyFM(h)
new_intersectFM_C2Lts1(zzz869, zzz870, zzz871, zzz872, bc) → new_splitLT25(zzz869, zzz870, zzz871, zzz872, bc)
new_splitLT25(zzz869, zzz870, zzz871, zzz872, bc) → new_splitLT12(zzz871, bc)
new_splitLT12(Branch(EQ, zzz8561, zzz8562, zzz8563, zzz8564), ba) → new_splitLT24(zzz8561, zzz8562, zzz8563, zzz8564, ba)
new_splitLT12(Branch(GT, zzz8561, zzz8562, zzz8563, zzz8564), ba) → new_splitLT25(zzz8561, zzz8562, zzz8563, zzz8564, ba)
new_splitLT24(zzz854, zzz855, zzz856, zzz857, ba) → new_splitLT12(zzz856, ba)
new_splitLT12(EmptyFM, ba) → new_splitLT42(ba)
new_splitLT12(Branch(LT, zzz8561, zzz8562, zzz8563, zzz8564), ba) → new_splitLT28(zzz8561, zzz8562, zzz8563, zzz8564, ba)
new_splitLT28(zzz31, zzz32, zzz33, zzz34, h) → zzz33
new_splitLT42(h) → new_emptyFM(h)
new_splitLT11(zzz31, zzz32, zzz33, h) → new_mkVBalBranch4(zzz31, zzz33, new_splitLT13(h), h)
new_splitGT8(zzz31, zzz32, zzz34, h) → new_mkVBalBranch3(zzz31, new_splitGT6(h), zzz34, h)
new_splitGT6(h) → new_splitGT42(h)
new_intersectFM_C2Gts3(zzz2129, cc) → new_splitGT15(zzz2129, cc)
new_splitGT15(Branch(LT, zzz21291, zzz21292, zzz21293, zzz21294), cc) → new_splitGT15(zzz21294, cc)
new_splitGT15(Branch(EQ, zzz21291, zzz21292, zzz21293, zzz21294), cc) → new_splitGT15(zzz21294, cc)
new_splitGT15(EmptyFM, cc) → new_splitGT40(cc)
new_splitGT15(Branch(GT, zzz21291, zzz21292, zzz21293, zzz21294), cc) → zzz21294
new_splitGT40(h) → new_emptyFM(h)
new_splitLT3(zzz31, zzz32, zzz33, zzz34, h) → new_splitLT28(zzz31, zzz32, zzz33, zzz34, h)
new_intersectFM_C2Lts3(zzz2129, cc) → new_splitLT14(zzz2129, cc)
new_splitLT14(Branch(LT, zzz21291, zzz21292, zzz21293, zzz21294), cc) → new_mkVBalBranch2(zzz21291, zzz21293, new_splitLT14(zzz21294, cc), cc)
new_splitLT14(EmptyFM, cc) → new_splitLT40(cc)
new_splitLT14(Branch(EQ, zzz21291, zzz21292, zzz21293, zzz21294), cc) → new_mkVBalBranch4(zzz21291, zzz21293, new_splitLT14(zzz21294, cc), cc)
new_splitLT14(Branch(GT, zzz21291, zzz21292, zzz21293, zzz21294), cc) → zzz21293
new_splitLT6(h) → new_splitLT41(h)
new_intersectFM_C2Lts2(zzz883, zzz884, zzz885, zzz886, be) → new_splitLT15(Branch(LT, zzz883, zzz884, zzz885, zzz886), be)
new_splitGT4(zzz31, zzz32, zzz34, h) → new_mkVBalBranch4(zzz31, new_splitGT13(h), zzz34, h)
new_splitGT13(h) → new_splitGT41(h)
new_splitGT7(zzz31, zzz32, zzz33, zzz34, h) → new_splitGT27(zzz31, zzz32, zzz33, zzz34, h)
new_intersectFM_C2Lts0(zzz854, zzz855, zzz856, zzz857, ba) → new_splitLT24(zzz854, zzz855, zzz856, zzz857, ba)
new_splitGT3(zzz31, zzz32, zzz33, zzz34, h) → new_splitGT210(zzz31, zzz32, zzz33, zzz34, h)
new_splitGT5(zzz31, zzz32, zzz34, h) → new_mkVBalBranch3(zzz31, new_splitGT13(h), zzz34, h)

The set Q consists of the following terms:

new_mkVBalBranch3MkVBalBranch281(x0, x1, Neg(Succ(Succ(Succ(x2)))), x3, x4, x5, x6, Succ(x7), x8, x9, x10, Succ(Succ(x11)), x12)
new_mkBalBranch6MkBalBranch35(x0, x1, x2, x3, Zero, x4, x5)
new_mkVBalBranch2(x0, Branch(x1, x2, Pos(Zero), x3, x4), Branch(x5, x6, Pos(Zero), x7, x8), x9)
new_mkVBalBranch3MkVBalBranch159(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, Zero, x11)
new_addToFM_C2(Branch(LT, x0, x1, x2, x3), x4, x5)
new_primMulNat1(x0)
new_primMinusNat0(Zero, Zero)
new_mkVBalBranch3MkVBalBranch281(x0, x1, Neg(Zero), x2, x3, x4, x5, x6, x7, x8, x9, Succ(x10), x11)
new_mkVBalBranch3MkVBalBranch263(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, Succ(x10), Succ(x11), x12)
new_mkVBalBranch3MkVBalBranch163(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11)
new_primPlusInt(Pos(x0), x1, x2, x3, x4, x5)
new_primMulNat0(x0)
new_mkBalBranch6MkBalBranch116(x0, x1, x2, x3, x4, x5, x6, x7, Succ(x8), x9, x10)
new_mkVBalBranch3(x0, EmptyFM, x1, x2)
new_mkVBalBranch3MkVBalBranch281(x0, x1, Neg(Succ(Succ(x2))), x3, x4, x5, x6, Zero, x7, x8, x9, Zero, x10)
new_mkBalBranch6MkBalBranch411(x0, x1, x2, x3, Pos(Succ(x4)), Pos(x5), x6, x7)
new_mkBalBranch6MkBalBranch1113(x0, x1, x2, x3, x4, x5, x6, x7, Zero, Succ(x8), x9, x10)
new_mkVBalBranch3MkVBalBranch157(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, Succ(x10), x11)
new_mkVBalBranch3MkVBalBranch278(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11)
new_mkVBalBranch3MkVBalBranch281(x0, x1, Neg(Zero), x2, x3, x4, x5, x6, x7, x8, x9, Zero, x10)
new_mkVBalBranch3MkVBalBranch281(x0, x1, Neg(Succ(Succ(x2))), x3, x4, x5, x6, Succ(x7), x8, x9, x10, Zero, x11)
new_mkVBalBranch3MkVBalBranch269(x0, x1, Succ(x2), x3, x4, x5, x6, x7, x8, x9, x10, x11)
new_mkVBalBranch4(x0, Branch(x1, x2, Pos(Zero), x3, x4), Branch(x5, x6, Pos(Succ(x7)), x8, x9), x10)
new_mkVBalBranch3MkVBalBranch247(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11)
new_mkBalBranch6MkBalBranch315(x0, x1, x2, x3, Succ(x4), x5, x6)
new_mkVBalBranch3MkVBalBranch272(x0, x1, Neg(Succ(Zero)), x2, x3, x4, x5, Succ(x6), x7, x8, x9, Zero, x10)
new_mkVBalBranch3(x0, Branch(x1, x2, Neg(Succ(x3)), x4, x5), Branch(x6, x7, x8, x9, x10), x11)
new_addToFM_C3(Branch(EQ, x0, x1, x2, x3), x4, x5)
new_mkVBalBranch3MkVBalBranch158(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11)
new_mkVBalBranch3MkVBalBranch270(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, Succ(x10), Zero, x11)
new_mkVBalBranch3MkVBalBranch159(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, Succ(x11), x12)
new_splitGT4(x0, x1, x2, x3)
new_mkVBalBranch3MkVBalBranch261(x0, x1, Pos(Succ(x2)), x3, x4, x5, x6, x7, x8, x9, x10, Succ(x11), x12)
new_mkVBalBranch3MkVBalBranch137(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, Succ(x11), x12)
new_mkBalBranch6MkBalBranch45(x0, x1, x2, x3, x4, Zero, x5, x6)
new_mkBalBranch6MkBalBranch014(x0, x1, x2, x3, x4, x5, x6, x7, Zero, Zero, x8, x9)
new_mkBalBranch6MkBalBranch111(x0, x1, x2, x3, x4, x5, x6, x7, x8, Zero, x9, x10)
new_mkVBalBranch3(x0, Branch(x1, x2, Neg(Zero), x3, x4), Branch(x5, x6, Neg(Succ(x7)), x8, x9), x10)
new_mkBalBranch6MkBalBranch116(x0, x1, x2, x3, x4, x5, x6, x7, Zero, x8, x9)
new_mkBalBranch6MkBalBranch015(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9)
new_mkBalBranch6MkBalBranch5(x0, x1, x2, x3, Pos(Succ(Succ(Zero))), x4, x5)
new_mkBalBranch6MkBalBranch49(EmptyFM, x0, x1, x2, x3, x4)
new_primMinusNat0(Succ(x0), Zero)
new_mkVBalBranch3MkVBalBranch157(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, Zero, x10)
new_mkBalBranch6MkBalBranch33(x0, Branch(x1, x2, x3, x4, x5), x6, x7, x8, x9)
new_mkVBalBranch3MkVBalBranch266(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10)
new_addToFM_C2(Branch(EQ, x0, x1, x2, x3), x4, x5)
new_mkVBalBranch3MkVBalBranch263(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, Zero, Succ(x10), x11)
new_mkBalBranch6MkBalBranch51(x0, x1, x2, x3, x4, x5)
new_mkVBalBranch3MkVBalBranch287(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10)
new_mkBalBranch6MkBalBranch013(x0, x1, x2, x3, x4, x5, x6, x7, x8, Zero, x9, x10)
new_mkBalBranch6MkBalBranch312(x0, x1, x2, x3, x4, x5, x6, x7)
new_mkVBalBranch3MkVBalBranch267(x0, x1, Pos(Zero), x2, x3, x4, x5, x6, x7, x8, x9, Succ(x10), x11)
new_addToFM2(x0, x1, x2)
new_mkVBalBranch3MkVBalBranch155(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, Zero, x10)
new_splitLT11(x0, x1, x2, x3)
new_mkVBalBranch3MkVBalBranch272(x0, x1, Neg(Succ(Succ(Zero))), x2, x3, x4, x5, Zero, x6, x7, x8, Succ(Succ(x9)), x10)
new_mkVBalBranch3MkVBalBranch281(x0, x1, Neg(Succ(Zero)), x2, x3, x4, x5, Succ(x6), x7, x8, x9, Zero, x10)
new_splitLT6(x0)
new_mkVBalBranch3MkVBalBranch161(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, Zero, x10)
new_mkVBalBranch3MkVBalBranch134(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, Succ(x11), Zero, x12)
new_mkBalBranch6MkBalBranch39(x0, x1, x2, x3, Zero, Zero, x4, x5)
new_splitLT24(x0, x1, x2, x3, x4)
new_mkVBalBranch3MkVBalBranch288(x0, x1, Pos(Zero), x2, x3, x4, x5, x6, x7, x8, x9, Zero, x10)
new_mkBalBranch6MkBalBranch310(x0, x1, x2, x3, Pos(Zero), Neg(x4), x5, x6)
new_mkBalBranch6MkBalBranch310(x0, x1, x2, x3, Neg(Zero), Pos(x4), x5, x6)
new_mkVBalBranch3MkVBalBranch285(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10)
new_mkVBalBranch2(x0, Branch(x1, x2, x3, x4, x5), EmptyFM, x6)
new_mkVBalBranch3MkVBalBranch272(x0, x1, Neg(Succ(Succ(Zero))), x2, x3, x4, x5, Zero, x6, x7, x8, Succ(Zero), x9)
new_mkVBalBranch3MkVBalBranch141(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, Succ(x11), x12)
new_splitLT15(Branch(GT, x0, x1, x2, x3), x4)
new_mkVBalBranch3MkVBalBranch265(x0, x1, Zero, x2, x3, x4, x5, x6, x7, x8, x9, x10)
new_mkVBalBranch3MkVBalBranch267(x0, x1, Pos(Succ(x2)), x3, x4, x5, x6, x7, x8, x9, x10, Zero, x11)
new_mkBalBranch6MkBalBranch017(x0, x1, x2, x3, x4, x5, x6, x7, Pos(Succ(x8)), Pos(x9), x10, x11)
new_mkBalBranch6MkBalBranch412(x0, x1, x2, x3, Zero, Zero, x4, x5)
new_mkVBalBranch3MkVBalBranch288(x0, x1, Pos(Succ(Succ(x2))), x3, x4, x5, x6, Succ(x7), x8, x9, x10, Zero, x11)
new_splitGT41(x0)
new_mkBalBranch6MkBalBranch110(x0, x1, x2, x3, x4, x5, x6, x7, Succ(x8), x9, x10)
new_mkBalBranch6MkBalBranch416(x0, x1, x2, x3, Zero, x4, x5)
new_splitGT15(Branch(GT, x0, x1, x2, x3), x4)
new_mkVBalBranch3MkVBalBranch277(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, Zero, Succ(x10), x11)
new_mkBalBranch6MkBalBranch017(x0, x1, x2, x3, x4, x5, x6, x7, Pos(Zero), Pos(x8), x9, x10)
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_mkBalBranch6MkBalBranch310(x0, x1, x2, x3, Neg(Succ(x4)), Pos(x5), x6, x7)
new_mkBalBranch6MkBalBranch310(x0, x1, x2, x3, Pos(Succ(x4)), Neg(x5), x6, x7)
new_mkVBalBranch2(x0, Branch(x1, x2, Pos(Zero), x3, x4), Branch(x5, x6, Neg(Zero), x7, x8), x9)
new_mkVBalBranch2(x0, Branch(x1, x2, Neg(Zero), x3, x4), Branch(x5, x6, Pos(Zero), x7, x8), x9)
new_mkVBalBranch3MkVBalBranch289(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, Succ(x11), Succ(x12), x13)
new_mkBalBranch6MkBalBranch310(x0, x1, x2, x3, Neg(Succ(x4)), Neg(x5), x6, x7)
new_mkVBalBranch3MkVBalBranch139(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, Succ(x11), x12)
new_splitGT26(x0, x1, x2, x3, x4)
new_mkBalBranch6MkBalBranch1113(x0, x1, x2, x3, x4, x5, x6, x7, Succ(x8), Zero, x9, x10)
new_primPlusNat2(Zero, Zero)
new_mkVBalBranch3MkVBalBranch143(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, Zero, x10)
new_mkVBalBranch3MkVBalBranch277(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, Succ(x10), Zero, x11)
new_splitGT14(Branch(EQ, x0, x1, x2, x3), x4)
new_splitLT10(x0, x1, x2, x3)
new_mkVBalBranch4(x0, Branch(x1, x2, Pos(Succ(x3)), x4, x5), Branch(x6, x7, x8, x9, x10), x11)
new_addToFM_C2(EmptyFM, x0, x1)
new_mkVBalBranch3MkVBalBranch156(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, Zero, x11)
new_mkVBalBranch3MkVBalBranch262(x0, x1, Pos(Succ(x2)), x3, x4, x5, x6, x7, x8, x9, x10, Zero, x11)
new_splitLT12(EmptyFM, x0)
new_mkVBalBranch3MkVBalBranch271(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10)
new_mkVBalBranch4(x0, Branch(x1, x2, x3, x4, x5), EmptyFM, x6)
new_intersectFM_C2Gts1(x0, x1, x2, x3, x4)
new_mkVBalBranch3MkVBalBranch155(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, Succ(x10), x11)
new_mkVBalBranch3MkVBalBranch272(x0, x1, Neg(Succ(Succ(Succ(x2)))), x3, x4, x5, x6, Succ(x7), x8, x9, x10, Succ(Zero), x11)
new_mkBalBranch6MkBalBranch41(x0, x1, x2, x3, x4, x5)
new_mkVBalBranch4(x0, Branch(x1, x2, Neg(Zero), x3, x4), Branch(x5, x6, Neg(Zero), x7, x8), x9)
new_mkVBalBranch3(x0, Branch(x1, x2, Pos(Zero), x3, x4), Branch(x5, x6, Pos(Zero), x7, x8), x9)
new_mkVBalBranch3MkVBalBranch156(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, Succ(x11), x12)
new_mkBalBranch6MkBalBranch018(x0, x1, x2, x3, x4, x5, x6, x7, Succ(x8), x9, x10, x11)
new_mkBalBranch6MkBalBranch1111(x0, x1, x2, x3, x4, x5, x6, x7, Zero, x8, x9, x10)
new_mkVBalBranch3MkVBalBranch270(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, Zero, Succ(x10), x11)
new_primPlusNat2(Zero, Succ(x0))
new_mkBalBranch6MkBalBranch113(x0, x1, x2, x3, x4, x5, x6, x7, Neg(Succ(x8)), Neg(x9), x10, x11)
new_mkVBalBranch3MkVBalBranch272(x0, x1, Neg(Succ(Zero)), x2, x3, x4, x5, Zero, x6, x7, x8, Zero, x9)
new_mkVBalBranch3MkVBalBranch261(x0, x1, Neg(x2), x3, x4, x5, x6, x7, x8, x9, x10, Succ(x11), x12)
new_addToFM1(x0, x1, x2)
new_mkVBalBranch3MkVBalBranch284(x0, x1, Zero, x2, x3, x4, x5, x6, x7, x8, x9, x10)
new_mkVBalBranch3MkVBalBranch136(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11)
new_splitLT15(EmptyFM, x0)
new_mkBalBranch6MkBalBranch013(x0, x1, x2, x3, x4, x5, x6, x7, x8, Succ(x9), x10, x11)
new_mkVBalBranch3MkVBalBranch166(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11)
new_mkVBalBranch3MkVBalBranch144(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, Zero, Zero, x11)
new_splitLT41(x0)
new_mkBalBranch6MkBalBranch5(x0, x1, x2, x3, Neg(Succ(x4)), x5, x6)
new_splitLT4(x0, x1, x2, x3)
new_splitLT14(Branch(GT, x0, x1, x2, x3), x4)
new_mkBalBranch6MkBalBranch010(x0, x1, x2, x3, x4, x5, x6, x7, Zero, x8, x9)
new_primPlusNat3(x0, Zero)
new_mkVBalBranch3MkVBalBranch255(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, Zero, Succ(x11), x12)
new_mkVBalBranch3MkVBalBranch272(x0, x1, Pos(x2), x3, x4, x5, x6, x7, x8, x9, x10, Zero, x11)
new_splitGT25(x0, x1, x2, x3, x4)
new_mkBalBranch6MkBalBranch35(x0, x1, x2, x3, Succ(x4), x5, x6)
new_splitLT12(Branch(LT, x0, x1, x2, x3), x4)
new_intersectFM_C2Gts0(x0, x1, x2, x3, x4)
new_primMulNat(Zero)
new_primPlusNat1(Succ(x0))
new_mkVBalBranch3MkVBalBranch273(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10)
new_mkVBalBranch3MkVBalBranch152(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, Zero, Zero, x11)
new_splitGT15(Branch(EQ, x0, x1, x2, x3), x4)
new_mkVBalBranch3MkVBalBranch262(x0, x1, Pos(x2), x3, x4, x5, x6, x7, x8, x9, x10, Succ(x11), x12)
new_mkBalBranch6MkBalBranch017(x0, x1, x2, x3, x4, x5, x6, x7, Neg(Zero), Pos(x8), x9, x10)
new_primPlusInt2(Pos(x0), x1, x2, x3, x4, x5, x6)
new_mkBalBranch6MkBalBranch017(x0, x1, x2, x3, x4, x5, x6, x7, Pos(Zero), Neg(x8), x9, x10)
new_mkVBalBranch3MkVBalBranch275(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, Succ(x11), Zero, x12)
new_mkVBalBranch3MkVBalBranch255(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, Zero, Zero, x11)
new_addToFM_C2(Branch(GT, x0, x1, x2, x3), x4, x5)
new_splitGT10(x0, x1, x2, x3)
new_mkVBalBranch3MkVBalBranch149(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, Zero, Zero, x11)
new_mkVBalBranch3MkVBalBranch245(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10)
new_mkBalBranch6MkBalBranch39(x0, x1, x2, x3, Zero, Succ(x4), x5, x6)
new_mkVBalBranch3MkVBalBranch289(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, Zero, Zero, x11)
new_mkVBalBranch3MkVBalBranch276(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11)
new_mkVBalBranch3MkVBalBranch275(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, Zero, Zero, x11)
new_mkVBalBranch3MkVBalBranch277(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, Succ(x10), Succ(x11), x12)
new_splitLT7(x0, x1, x2, x3, x4)
new_mkVBalBranch3MkVBalBranch261(x0, x1, Neg(Zero), x2, x3, x4, x5, x6, x7, x8, x9, Zero, x10)
new_splitGT12(Branch(EQ, x0, x1, x2, x3), x4)
new_intersectFM_C2Gts(x0, x1, x2, x3, x4)
new_mkVBalBranch3MkVBalBranch289(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, Zero, Succ(x11), x12)
new_mkVBalBranch3MkVBalBranch281(x0, x1, Neg(Succ(Zero)), x2, x3, x4, x5, x6, x7, x8, x9, Succ(x10), x11)
new_mkBalBranch6MkBalBranch413(x0, x1, x2, x3, Zero, x4, x5)
new_addToFM_C4(Branch(GT, x0, x1, x2, x3), x4, x5)
new_mkBalBranch6MkBalBranch413(x0, x1, x2, x3, Succ(x4), x5, x6)
new_mkVBalBranch3MkVBalBranch281(x0, x1, Neg(Succ(Succ(Succ(x2)))), x3, x4, x5, x6, Succ(x7), x8, x9, x10, Succ(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_mkBalBranch6MkBalBranch34(x0, x1, x2, x3, x4, x5, x6, x7)
new_mkVBalBranch3MkVBalBranch265(x0, x1, Succ(x2), x3, x4, x5, x6, x7, x8, x9, x10, x11)
new_intersectFM_C2Lts3(x0, x1)
new_mkBalBranch6MkBalBranch314(x0, x1, x2, x3, Zero, x4, x5)
new_mkVBalBranch3MkVBalBranch145(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, Succ(x10), x11)
new_splitLT9(x0, x1, x2, x3, x4)
new_mkBalBranch6Size_r(x0, x1, x2, x3, x4, x5)
new_mkBalBranch6MkBalBranch43(x0, x1, x2, x3, x4, x5)
new_mkVBalBranch3MkVBalBranch283(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11)
new_splitGT29(x0, x1, x2, x3, x4)
new_mkBalBranch6MkBalBranch30(x0, x1, x2, x3, Zero, x4, x5)
new_mkVBalBranch3MkVBalBranch146(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, Zero, x10)
new_sizeFM(EmptyFM, x0, x1)
new_mkVBalBranch3MkVBalBranch281(x0, x1, Neg(Succ(Zero)), x2, x3, x4, x5, Zero, x6, x7, x8, Zero, x9)
new_mkVBalBranch3MkVBalBranch281(x0, x1, Neg(Succ(Succ(Succ(x2)))), x3, x4, x5, x6, Zero, x7, x8, x9, Succ(Succ(x10)), x11)
new_mkVBalBranch3MkVBalBranch152(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, Succ(x11), Zero, x12)
new_mkVBalBranch3MkVBalBranch288(x0, x1, Pos(Succ(Succ(x2))), x3, x4, x5, x6, Zero, x7, x8, x9, Succ(Zero), x10)
new_mkVBalBranch3MkVBalBranch249(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10)
new_mkVBalBranch3MkVBalBranch135(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11)
new_mkVBalBranch3MkVBalBranch254(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10)
new_splitLT28(x0, x1, x2, x3, x4)
new_mkBalBranch6MkBalBranch47(x0, x1, x2, x3, Succ(x4), x5, x6, x7)
new_mkBalBranch6MkBalBranch014(x0, x1, x2, x3, x4, x5, x6, x7, Succ(x8), Succ(x9), x10, x11)
new_mkVBalBranch2(x0, Branch(x1, x2, Pos(Zero), x3, x4), Branch(x5, x6, Neg(Succ(x7)), x8, x9), x10)
new_mkVBalBranch2(x0, Branch(x1, x2, Neg(Zero), x3, x4), Branch(x5, x6, Pos(Succ(x7)), x8, x9), x10)
new_addToFM_C4(EmptyFM, x0, x1)
new_mkBalBranch6MkBalBranch313(x0, x1, x2, x3, x4, x5)
new_mkVBalBranch3MkVBalBranch267(x0, x1, Pos(Zero), x2, x3, x4, x5, x6, x7, x8, x9, Zero, x10)
new_mkVBalBranch3MkVBalBranch248(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11)
new_splitGT14(EmptyFM, x0)
new_mkVBalBranch3MkVBalBranch132(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, Succ(x11), Zero, x12)
new_mkVBalBranch3MkVBalBranch144(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, Succ(x11), Succ(x12), x13)
new_mkVBalBranch3MkVBalBranch261(x0, x1, Neg(Succ(x2)), x3, x4, x5, x6, x7, x8, x9, x10, Zero, x11)
new_mkBalBranch6MkBalBranch410(x0, x1, x2, x3, x4, x5, x6)
new_mkVBalBranch2(x0, Branch(x1, x2, Pos(Succ(x3)), x4, x5), Branch(x6, x7, x8, x9, x10), x11)
new_mkBalBranch6MkBalBranch019(x0, x1, x2, x3, x4, x5, x6, x7, Zero, x8, x9)
new_mkVBalBranch3MkVBalBranch280(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, Zero, Succ(x11), x12)
new_mkBalBranch6MkBalBranch014(x0, x1, x2, x3, x4, x5, x6, x7, Succ(x8), Zero, x9, x10)
new_mkVBalBranch3MkVBalBranch272(x0, x1, Neg(Succ(Succ(Zero))), x2, x3, x4, x5, Succ(x6), x7, x8, x9, Succ(Succ(x10)), x11)
new_mkVBalBranch3MkVBalBranch134(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, Zero, Zero, x11)
new_mkVBalBranch3(x0, Branch(x1, x2, Neg(Zero), x3, x4), Branch(x5, x6, Neg(Zero), x7, x8), x9)
new_mkVBalBranch3MkVBalBranch280(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, Succ(x11), Succ(x12), x13)
new_primPlusNat2(Succ(x0), Succ(x1))
new_splitGT12(Branch(GT, x0, x1, x2, x3), x4)
new_mkVBalBranch3MkVBalBranch145(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, Zero, x10)
new_mkVBalBranch3MkVBalBranch272(x0, x1, Neg(Succ(Zero)), x2, x3, x4, x5, x6, x7, x8, x9, Succ(x10), x11)
new_mkVBalBranch3MkVBalBranch288(x0, x1, Pos(Succ(Succ(x2))), x3, x4, x5, x6, Succ(x7), x8, x9, x10, Succ(Succ(x11)), x12)
new_mkVBalBranch3MkVBalBranch262(x0, x1, Neg(Zero), x2, x3, x4, x5, x6, x7, x8, x9, Succ(x10), x11)
new_mkBalBranch6MkBalBranch414(x0, x1, x2, x3, Zero, x4, x5)
new_mkVBalBranch4(x0, Branch(x1, x2, Neg(Zero), x3, x4), Branch(x5, x6, Pos(Zero), x7, x8), x9)
new_mkVBalBranch4(x0, Branch(x1, x2, Pos(Zero), x3, x4), Branch(x5, x6, Neg(Zero), x7, x8), x9)
new_splitGT12(Branch(LT, x0, x1, x2, x3), x4)
new_mkVBalBranch3MkVBalBranch270(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, Zero, Zero, x10)
new_mkVBalBranch3MkVBalBranch288(x0, x1, Pos(Succ(Succ(x2))), x3, x4, x5, x6, Succ(x7), x8, x9, x10, Succ(Zero), x11)
new_splitLT12(Branch(GT, x0, x1, x2, x3), x4)
new_mkVBalBranch3MkVBalBranch282(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11)
new_mkVBalBranch3MkVBalBranch272(x0, x1, Neg(Succ(Succ(Zero))), x2, x3, x4, x5, Succ(x6), x7, x8, x9, Succ(Zero), x10)
new_mkBalBranch6MkBalBranch315(x0, x1, x2, x3, Zero, x4, x5)
new_primPlusInt(Neg(x0), x1, x2, x3, x4, x5)
new_mkVBalBranch3MkVBalBranch272(x0, x1, Pos(x2), x3, x4, x5, x6, x7, x8, x9, x10, Succ(x11), x12)
new_mkVBalBranch3MkVBalBranch149(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, Zero, Succ(x11), x12)
new_mkBalBranch6MkBalBranch019(x0, x1, x2, x3, x4, x5, x6, x7, Succ(x8), x9, x10)
new_mkVBalBranch3MkVBalBranch252(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, Succ(x11), Zero, x12)
new_mkVBalBranch3MkVBalBranch153(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, Zero, x11)
new_mkBalBranch6MkBalBranch32(x0, x1, x2, x3, x4, x5)
new_mkVBalBranch3MkVBalBranch280(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, Zero, Zero, x11)
new_splitGT3(x0, x1, x2, x3, x4)
new_splitLT25(x0, x1, x2, x3, x4)
new_mkBalBranch6MkBalBranch111(x0, x1, x2, x3, x4, x5, x6, x7, x8, Succ(x9), x10, x11)
new_mkVBalBranch3MkVBalBranch164(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, Zero, x10)
new_mkBalBranch6MkBalBranch117(x0, x1, x2, x3, x4, x5, x6, x7, Succ(x8), x9, x10)
new_mkVBalBranch3MkVBalBranch132(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, Zero, Succ(x11), x12)
new_splitGT210(x0, x1, x2, x3, x4)
new_mkBalBranch6MkBalBranch30(x0, x1, x2, x3, Succ(x4), x5, x6)
new_mkVBalBranch3MkVBalBranch165(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11)
new_mkBalBranch6MkBalBranch31(x0, x1, x2, x3, x4, x5)
new_mkVBalBranch3MkVBalBranch133(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, Zero, x10)
new_mkVBalBranch3MkVBalBranch167(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, Succ(x11), x12)
new_mkVBalBranch3MkVBalBranch144(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, Zero, Succ(x11), x12)
new_splitGT8(x0, x1, x2, x3)
new_splitGT9(x0, x1, x2, x3, x4)
new_mkVBalBranch3MkVBalBranch256(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11)
new_intersectFM_C2Gts2(x0, x1, x2, x3, x4)
new_splitGT16(x0)
new_mkVBalBranch3MkVBalBranch260(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10)
new_splitLT42(x0)
new_splitGT15(Branch(LT, x0, x1, x2, x3), x4)
new_splitLT14(EmptyFM, x0)
new_splitLT14(Branch(LT, x0, x1, x2, x3), x4)
new_addToFM_C4(Branch(EQ, x0, x1, x2, x3), x4, x5)
new_mkBalBranch6MkBalBranch1113(x0, x1, x2, x3, x4, x5, x6, x7, Succ(x8), Succ(x9), x10, x11)
new_mkBalBranch6MkBalBranch415(x0, x1, x2, x3, x4, x5, x6, x7)
new_mkBalBranch6MkBalBranch0110(x0, x1, x2, x3, x4, x5, x6, x7, Zero, x8, x9)
new_mkVBalBranch3MkVBalBranch151(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11)
new_mkVBalBranch3MkVBalBranch262(x0, x1, Pos(Zero), x2, x3, x4, x5, x6, x7, x8, x9, Zero, x10)
new_mkVBalBranch3(x0, Branch(x1, x2, Pos(Zero), x3, x4), Branch(x5, x6, Neg(Zero), x7, x8), x9)
new_mkVBalBranch3(x0, Branch(x1, x2, Neg(Zero), x3, x4), Branch(x5, x6, Pos(Zero), x7, x8), x9)
new_splitGT11(x0, x1, x2, x3)
new_mkVBalBranch2(x0, Branch(x1, x2, Neg(Zero), x3, x4), Branch(x5, x6, Neg(Zero), x7, x8), x9)
new_mkVBalBranch3(x0, Branch(x1, x2, x3, x4, x5), EmptyFM, x6)
new_mkVBalBranch3MkVBalBranch263(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, Zero, Zero, x10)
new_mkVBalBranch3(x0, Branch(x1, x2, Pos(Zero), x3, x4), Branch(x5, x6, Pos(Succ(x7)), x8, x9), x10)
new_mkBalBranch6MkBalBranch310(x0, x1, x2, x3, Neg(Zero), Neg(x4), x5, x6)
new_mkVBalBranch3MkVBalBranch147(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, Succ(x11), x12)
new_mkBalBranch6MkBalBranch42(x0, x1, x2, x3, x4, x5, x6, x7)
new_mkBalBranch6MkBalBranch310(x0, x1, x2, x3, Pos(Succ(x4)), Pos(x5), x6, x7)
new_mkVBalBranch3MkVBalBranch275(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, Succ(x11), Succ(x12), x13)
new_splitGT24(x0, x1, x2, x3, x4)
new_mkVBalBranch3MkVBalBranch153(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, Succ(x11), x12)
new_mkVBalBranch3MkVBalBranch288(x0, x1, Pos(Succ(Zero)), x2, x3, x4, x5, Zero, x6, x7, x8, Zero, x9)
new_mkVBalBranch4(x0, Branch(x1, x2, Pos(Zero), x3, x4), Branch(x5, x6, Pos(Zero), x7, x8), x9)
new_mkBalBranch6MkBalBranch1110(x0, x1, x2, x3, x4, x5, x6, x7, Succ(x8), x9, x10)
new_splitGT28(x0, x1, x2, x3, x4)
new_mkBalBranch6MkBalBranch48(x0, x1, x2, x3, Succ(x4), x5, x6)
new_mkVBalBranch3MkVBalBranch275(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, Zero, Succ(x11), x12)
new_mkVBalBranch3MkVBalBranch284(x0, x1, Succ(x2), x3, x4, x5, x6, x7, x8, x9, x10, x11)
new_mkVBalBranch3MkVBalBranch267(x0, x1, Neg(x2), x3, x4, x5, x6, x7, x8, x9, x10, Zero, x11)
new_mkBalBranch6MkBalBranch016(x0, x1, x2, EmptyFM, x3, x4, x5, x6, x7, x8)
new_intersectFM_C2Lts1(x0, x1, x2, x3, x4)
new_mkBalBranch6MkBalBranch416(x0, x1, x2, x3, Succ(x4), x5, x6)
new_mkVBalBranch3MkVBalBranch252(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, Succ(x11), Succ(x12), x13)
new_mkVBalBranch3MkVBalBranch149(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, Succ(x11), Zero, x12)
new_mkVBalBranch3MkVBalBranch146(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, Succ(x10), x11)
new_mkVBalBranch3MkVBalBranch148(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11)
new_mkBalBranch6MkBalBranch113(x0, x1, x2, x3, x4, x5, x6, x7, Pos(Zero), Pos(x8), x9, x10)
new_mkBalBranch6MkBalBranch411(x0, x1, x2, x3, Pos(Zero), Neg(x4), x5, x6)
new_mkBalBranch6MkBalBranch411(x0, x1, x2, x3, Neg(Zero), Pos(x4), x5, x6)
new_mkVBalBranch4(x0, EmptyFM, x1, x2)
new_splitGT13(x0)
new_mkBalBranch6MkBalBranch1115(x0, x1, x2, x3, x4, EmptyFM, x5, x6, x7, x8)
new_splitLT27(x0, x1, x2, x3, x4)
new_mkBalBranch6MkBalBranch5(x0, x1, x2, x3, Pos(Succ(Zero)), x4, x5)
new_primMinusNat0(Zero, Succ(x0))
new_mkBalBranch6MkBalBranch5(x0, x1, x2, x3, Pos(Zero), x4, x5)
new_splitGT12(EmptyFM, x0)
new_mkVBalBranch3MkVBalBranch288(x0, x1, Pos(Succ(Zero)), x2, x3, x4, x5, Succ(x6), x7, x8, x9, Zero, x10)
new_mkBalBranch6MkBalBranch39(x0, x1, x2, x3, Succ(x4), Zero, x5, x6)
new_mkVBalBranch3MkVBalBranch274(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10)
new_mkVBalBranch3MkVBalBranch288(x0, x1, Pos(Succ(Succ(x2))), x3, x4, x5, x6, Zero, x7, x8, x9, Zero, x10)
new_mkBalBranch6MkBalBranch310(x0, x1, x2, x3, Pos(Zero), Pos(x4), x5, x6)
new_mkBalBranch6MkBalBranch411(x0, x1, x2, x3, Neg(Succ(x4)), Neg(x5), x6, x7)
new_mkVBalBranch3MkVBalBranch272(x0, x1, Neg(Succ(Succ(Succ(x2)))), x3, x4, x5, x6, Zero, x7, x8, x9, Succ(Zero), x10)
new_primPlusNat1(Zero)
new_mkVBalBranch3MkVBalBranch263(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, Succ(x10), Zero, x11)
new_mkVBalBranch2(x0, Branch(x1, x2, Pos(Zero), x3, x4), Branch(x5, x6, Pos(Succ(x7)), x8, x9), x10)
new_mkBalBranch6MkBalBranch50(x0, x1, x2, x3, x4, x5)
new_mkBalBranch(x0, x1, x2, x3, x4, x5)
new_mkVBalBranch3MkVBalBranch132(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, Zero, Zero, x11)
new_mkBalBranch6MkBalBranch5(x0, x1, x2, x3, Neg(Zero), x4, x5)
new_mkVBalBranch3MkVBalBranch272(x0, x1, Neg(Zero), x2, x3, x4, x5, x6, x7, x8, x9, Zero, x10)
new_sizeFM(Branch(x0, x1, x2, x3, x4), x5, x6)
new_mkVBalBranch3MkVBalBranch288(x0, x1, Pos(Succ(Zero)), x2, x3, x4, x5, x6, x7, x8, x9, Succ(x10), x11)
new_mkVBalBranch3MkVBalBranch252(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, Zero, Succ(x11), x12)
new_splitLT13(x0)
new_splitGT7(x0, x1, x2, x3, x4)
new_primPlusInt1(x0, Neg(x1))
new_mkBalBranch6MkBalBranch110(x0, x1, x2, x3, x4, x5, x6, x7, Zero, x8, x9)
new_mkBalBranch6MkBalBranch45(x0, x1, x2, x3, x4, Succ(x5), x6, x7)
new_splitLT14(Branch(EQ, x0, x1, x2, x3), x4)
new_mkVBalBranch3MkVBalBranch154(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, Zero, x10)
new_mkVBalBranch3MkVBalBranch264(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10)
new_mkBalBranch6MkBalBranch411(x0, x1, x2, x3, Neg(Zero), Neg(x4), x5, x6)
new_mkBalBranch6MkBalBranch40(x0, x1, x2, x3, x4, x5)
new_mkVBalBranch3MkVBalBranch251(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11)
new_addToFM_C3(Branch(GT, x0, x1, x2, x3), x4, x5)
new_mkBalBranch6MkBalBranch017(x0, x1, x2, x3, x4, x5, x6, x7, Neg(Zero), Neg(x8), x9, x10)
new_mkBalBranch6MkBalBranch112(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9)
new_mkVBalBranch3MkVBalBranch281(x0, x1, Neg(Succ(Succ(Zero))), x2, x3, x4, x5, Succ(x6), x7, x8, x9, Succ(Succ(x10)), x11)
new_mkBalBranch6MkBalBranch411(x0, x1, x2, x3, Neg(Succ(x4)), Pos(x5), x6, x7)
new_mkBalBranch6MkBalBranch411(x0, x1, x2, x3, Pos(Succ(x4)), Neg(x5), x6, x7)
new_mkBalBranch6MkBalBranch012(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9)
new_mkVBalBranch3MkVBalBranch250(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10)
new_mkVBalBranch3MkVBalBranch255(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, Succ(x11), Succ(x12), x13)
new_addToFM0(x0, x1, x2)
new_mkVBalBranch3MkVBalBranch259(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10)
new_mkVBalBranch3MkVBalBranch279(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10)
new_mkVBalBranch3MkVBalBranch281(x0, x1, Neg(Succ(Succ(Succ(x2)))), x3, x4, x5, x6, Zero, x7, x8, x9, Succ(Zero), x10)
new_mkBalBranch6MkBalBranch36(x0, x1, x2, x3, Succ(x4), x5, x6, x7)
new_splitLT23(x0, x1, x2, x3, x4)
new_mkBalBranch6MkBalBranch1111(x0, x1, x2, x3, x4, x5, x6, x7, Succ(x8), x9, x10, x11)
new_mkBalBranch6MkBalBranch0111(x0, x1, x2, x3, x4, x5, x6, x7, Zero, x8, x9)
new_addToFM_C3(EmptyFM, x0, x1)
new_splitGT15(EmptyFM, x0)
new_mkBalBranch6MkBalBranch011(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9)
new_mkVBalBranch3MkVBalBranch143(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, Succ(x10), x11)
new_mkVBalBranch3MkVBalBranch162(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, Zero, Zero, x11)
new_mkVBalBranch3MkVBalBranch134(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, Zero, Succ(x11), x12)
new_mkVBalBranch3MkVBalBranch246(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, Zero, Zero, x11)
new_mkVBalBranch3MkVBalBranch162(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, Succ(x11), Zero, x12)
new_mkVBalBranch3MkVBalBranch289(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, Succ(x11), Zero, x12)
new_mkVBalBranch3MkVBalBranch133(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, Succ(x10), x11)
new_mkVBalBranch3MkVBalBranch141(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, Zero, x11)
new_mkVBalBranch3MkVBalBranch272(x0, x1, Neg(Zero), x2, x3, x4, x5, x6, x7, x8, x9, Succ(x10), x11)
new_primPlusNat2(Succ(x0), Zero)
new_mkBalBranch6MkBalBranch119(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11)
new_mkBalBranch6MkBalBranch38(x0, x1, x2, x3, x4, Succ(x5), x6, x7)
new_mkBalBranch6MkBalBranch33(x0, EmptyFM, x1, x2, x3, x4)
new_splitLT8(x0, x1, x2, x3)
new_mkBalBranch6MkBalBranch46(x0, x1, x2, x3, x4, x5, x6, x7)
new_mkVBalBranch3MkVBalBranch267(x0, x1, Pos(Succ(x2)), x3, x4, x5, x6, x7, x8, x9, x10, Succ(x11), x12)
new_mkVBalBranch3MkVBalBranch152(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, Zero, Succ(x11), x12)
new_mkVBalBranch3MkVBalBranch281(x0, x1, Pos(x2), x3, x4, x5, x6, x7, x8, x9, x10, Zero, x11)
new_mkVBalBranch3MkVBalBranch281(x0, x1, Pos(x2), x3, x4, x5, x6, x7, x8, x9, x10, Succ(x11), x12)
new_mkVBalBranch3MkVBalBranch272(x0, x1, Neg(Succ(Succ(Succ(x2)))), x3, x4, x5, x6, Succ(x7), x8, x9, x10, Succ(Succ(x11)), x12)
new_mkVBalBranch3MkVBalBranch288(x0, x1, Neg(x2), x3, x4, x5, x6, x7, x8, x9, x10, Succ(x11), x12)
new_splitLT40(x0)
new_mkBalBranch6MkBalBranch44(x0, x1, x2, x3, x4, x5, x6, x7)
new_mkVBalBranch3MkVBalBranch138(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11)
new_mkBalBranch6MkBalBranch414(x0, x1, x2, x3, Succ(x4), x5, x6)
new_mkBalBranch6MkBalBranch115(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11)
new_mkVBalBranch3MkVBalBranch253(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11)
new_mkVBalBranch2(x0, Branch(x1, x2, Neg(Zero), x3, x4), Branch(x5, x6, Neg(Succ(x7)), x8, x9), x10)
new_mkBalBranch6MkBalBranch412(x0, x1, x2, x3, Zero, Succ(x4), x5, x6)
new_mkVBalBranch3MkVBalBranch288(x0, x1, Neg(x2), x3, x4, x5, x6, x7, x8, x9, x10, Zero, x11)
new_mkVBalBranch3(x0, Branch(x1, x2, Neg(Zero), x3, x4), Branch(x5, x6, Pos(Succ(x7)), x8, x9), x10)
new_mkVBalBranch3(x0, Branch(x1, x2, Pos(Zero), x3, x4), Branch(x5, x6, Neg(Succ(x7)), x8, x9), x10)
new_mkVBalBranch3MkVBalBranch272(x0, x1, Neg(Succ(Succ(x2))), x3, x4, x5, x6, Succ(x7), x8, x9, x10, Zero, x11)
new_mkVBalBranch3MkVBalBranch286(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11)
new_splitLT12(Branch(EQ, x0, x1, x2, x3), x4)
new_splitLT15(Branch(EQ, x0, x1, x2, x3), x4)
new_mkVBalBranch3MkVBalBranch268(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10)
new_mkVBalBranch3MkVBalBranch270(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, Succ(x10), Succ(x11), x12)
new_mkBalBranch6MkBalBranch314(x0, x1, x2, x3, Succ(x4), x5, x6)
new_mkBalBranch6MkBalBranch49(Branch(x0, x1, x2, x3, x4), x5, x6, x7, x8, x9)
new_mkVBalBranch3MkVBalBranch281(x0, x1, Neg(Succ(Succ(Zero))), x2, x3, x4, x5, Zero, x6, x7, x8, Succ(Zero), x9)
new_mkVBalBranch3MkVBalBranch144(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, Succ(x11), Zero, x12)
new_mkBalBranch6MkBalBranch1113(x0, x1, x2, x3, x4, x5, x6, x7, Zero, Zero, x8, x9)
new_splitLT5(x0, x1, x2, x3)
new_primPlusInt1(x0, Pos(x1))
new_mkBalBranch6MkBalBranch48(x0, x1, x2, x3, Zero, x4, x5)
new_mkVBalBranch3MkVBalBranch149(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, Succ(x11), Succ(x12), x13)
new_mkBalBranch6MkBalBranch412(x0, x1, x2, x3, Succ(x4), Zero, x5, x6)
new_mkBalBranch6MkBalBranch412(x0, x1, x2, x3, Succ(x4), Succ(x5), x6, x7)
new_splitLT15(Branch(LT, x0, x1, x2, x3), x4)
new_mkVBalBranch3MkVBalBranch272(x0, x1, Neg(Succ(Succ(Succ(x2)))), x3, x4, x5, x6, Zero, x7, x8, x9, Succ(Succ(x10)), x11)
new_mkVBalBranch3MkVBalBranch167(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, Zero, x11)
new_mkVBalBranch3MkVBalBranch267(x0, x1, Neg(x2), x3, x4, x5, x6, x7, x8, x9, x10, Succ(x11), x12)
new_mkVBalBranch3MkVBalBranch137(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, Zero, x11)
new_mkBalBranch6MkBalBranch1115(x0, x1, x2, x3, x4, Branch(x5, x6, x7, x8, x9), x10, x11, x12, x13)
new_mkVBalBranch3MkVBalBranch140(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11)
new_mkVBalBranch3MkVBalBranch257(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11)
new_splitGT14(Branch(LT, x0, x1, x2, x3), x4)
new_mkBalBranch6MkBalBranch014(x0, x1, x2, x3, x4, x5, x6, x7, Zero, Succ(x8), x9, x10)
new_mkVBalBranch3MkVBalBranch246(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, Succ(x11), Zero, x12)
new_intersectFM_C2Lts(x0, x1, x2, x3, x4)
new_mkVBalBranch3(x0, Branch(x1, x2, Pos(Succ(x3)), x4, x5), Branch(x6, x7, x8, x9, x10), x11)
new_splitGT14(Branch(GT, x0, x1, x2, x3), x4)
new_mkVBalBranch3MkVBalBranch261(x0, x1, Pos(Zero), x2, x3, x4, x5, x6, x7, x8, x9, Succ(x10), x11)
new_mkVBalBranch3MkVBalBranch131(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, Zero, x11)
new_mkVBalBranch3MkVBalBranch246(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, Zero, Succ(x11), x12)
new_mkBalBranch6MkBalBranch1112(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9)
new_mkVBalBranch3MkVBalBranch261(x0, x1, Pos(Succ(x2)), x3, x4, x5, x6, x7, x8, x9, x10, Zero, x11)
new_mkBalBranch6MkBalBranch113(x0, x1, x2, x3, x4, x5, x6, x7, Pos(Succ(x8)), Pos(x9), x10, x11)
new_mkBalBranch6MkBalBranch018(x0, x1, x2, x3, x4, x5, x6, x7, Zero, x8, x9, x10)
new_mkBalBranch6MkBalBranch5(x0, x1, x2, x3, Pos(Succ(Succ(Succ(x4)))), x5, x6)
new_splitGT40(x0)
new_mkVBalBranch3MkVBalBranch255(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, Succ(x11), Zero, x12)
new_mkVBalBranch3MkVBalBranch262(x0, x1, Neg(Zero), x2, x3, x4, x5, x6, x7, x8, x9, Zero, x10)
new_mkVBalBranch3MkVBalBranch290(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10)
new_addToFM(x0, x1, x2)
new_mkVBalBranch4(x0, Branch(x1, x2, Neg(Zero), x3, x4), Branch(x5, x6, Neg(Succ(x7)), x8, x9), x10)
new_mkVBalBranch3MkVBalBranch288(x0, x1, Pos(Succ(Succ(x2))), x3, x4, x5, x6, Zero, x7, x8, x9, Succ(Succ(x10)), x11)
new_mkVBalBranch3MkVBalBranch164(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, Succ(x10), x11)
new_mkBalBranch6MkBalBranch1114(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9)
new_mkVBalBranch3MkVBalBranch272(x0, x1, Neg(Succ(Succ(x2))), x3, x4, x5, x6, Zero, x7, x8, x9, Zero, x10)
new_mkBalBranch6MkBalBranch113(x0, x1, x2, x3, x4, x5, x6, x7, Neg(Zero), Neg(x8), x9, x10)
new_mkBalBranch6MkBalBranch39(x0, x1, x2, x3, Succ(x4), Succ(x5), x6, x7)
new_mkVBalBranch3MkVBalBranch277(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, Zero, Zero, x10)
new_mkVBalBranch3MkVBalBranch288(x0, x1, Pos(Zero), x2, x3, x4, x5, x6, x7, x8, x9, Succ(x10), x11)
new_mkVBalBranch4(x0, Branch(x1, x2, Neg(Succ(x3)), x4, x5), Branch(x6, x7, x8, x9, x10), x11)
new_mkVBalBranch3MkVBalBranch132(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, Succ(x11), Succ(x12), x13)
new_mkBalBranch6MkBalBranch016(x0, x1, x2, Branch(x3, x4, x5, x6, x7), x8, x9, x10, x11, x12, x13)
new_mkVBalBranch3MkVBalBranch134(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, Succ(x11), Succ(x12), x13)
new_mkVBalBranch3MkVBalBranch154(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, Succ(x10), x11)
new_mkVBalBranch3MkVBalBranch258(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11)
new_intersectFM_C2Lts2(x0, x1, x2, x3, x4)
new_mkVBalBranch2(x0, Branch(x1, x2, Neg(Succ(x3)), x4, x5), Branch(x6, x7, x8, x9, x10), x11)
new_emptyFM(x0)
new_primPlusInt0(x0, Neg(x1))
new_intersectFM_C2Gts3(x0, x1)
new_mkBalBranch6MkBalBranch411(x0, x1, x2, x3, Pos(Zero), Pos(x4), x5, x6)
new_mkVBalBranch3MkVBalBranch281(x0, x1, Neg(Succ(Succ(Zero))), x2, x3, x4, x5, Succ(x6), x7, x8, x9, Succ(Zero), x10)
new_splitGT6(x0)
new_primPlusNat3(x0, Succ(x1))
new_mkVBalBranch3MkVBalBranch168(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, Succ(x10), x11)
new_mkBalBranch6MkBalBranch118(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11)
new_mkVBalBranch3MkVBalBranch280(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, Succ(x11), Zero, x12)
new_mkVBalBranch3MkVBalBranch142(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11)
new_primMulNat(Succ(x0))
new_mkVBalBranch3MkVBalBranch161(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, Succ(x10), x11)
new_mkVBalBranch2(x0, EmptyFM, x1, x2)
new_mkBalBranch6MkBalBranch37(x0, x1, x2, x3, x4, x5, x6, x7)
new_primPlusInt2(Neg(x0), x1, x2, x3, x4, x5, x6)
new_mkVBalBranch3MkVBalBranch162(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, Succ(x11), Succ(x12), x13)
new_mkVBalBranch3MkVBalBranch139(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, Zero, x11)
new_mkVBalBranch3MkVBalBranch281(x0, x1, Neg(Succ(Succ(Zero))), x2, x3, x4, x5, Zero, x6, x7, x8, Succ(Succ(x9)), x10)
new_mkBalBranch6MkBalBranch117(x0, x1, x2, x3, x4, x5, x6, x7, Zero, x8, x9)
new_splitLT3(x0, x1, x2, x3, x4)
new_addToFM_C4(Branch(LT, x0, x1, x2, x3), x4, x5)
new_mkVBalBranch3MkVBalBranch252(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, Zero, Zero, x11)
new_mkVBalBranch3MkVBalBranch246(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, Succ(x11), Succ(x12), x13)
new_mkVBalBranch3MkVBalBranch262(x0, x1, Neg(Succ(x2)), x3, x4, x5, x6, x7, x8, x9, x10, Zero, x11)
new_mkBranch(x0, x1, x2, x3, x4, x5, x6)
new_mkBalBranch6MkBalBranch0111(x0, x1, x2, x3, x4, x5, x6, x7, Succ(x8), x9, x10)
new_mkBalBranch6MkBalBranch38(x0, x1, x2, x3, x4, Zero, x5, x6)
new_primMulNat2(Zero)
new_mkBalBranch6MkBalBranch010(x0, x1, x2, x3, x4, x5, x6, x7, Succ(x8), x9, x10)
new_mkBalBranch6MkBalBranch36(x0, x1, x2, x3, Zero, x4, x5, x6)
new_mkBalBranch6MkBalBranch017(x0, x1, x2, x3, x4, x5, x6, x7, Neg(Succ(x8)), Neg(x9), x10, x11)
new_addToFM_C3(Branch(LT, x0, x1, x2, x3), x4, x5)
new_splitLT26(x0, x1, x2, x3, x4)
new_mkVBalBranch3MkVBalBranch168(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, Zero, x10)
new_mkBalBranch6MkBalBranch0110(x0, x1, x2, x3, x4, x5, x6, x7, Succ(x8), x9, x10)
new_mkBalBranch6MkBalBranch114(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11)
new_mkVBalBranch3MkVBalBranch150(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11)
new_splitGT42(x0)
new_mkBalBranch6MkBalBranch47(x0, x1, x2, x3, Zero, x4, x5, x6)
new_mkVBalBranch3MkVBalBranch261(x0, x1, Pos(Zero), x2, x3, x4, x5, x6, x7, x8, x9, Zero, x10)
new_mkBalBranch6MkBalBranch017(x0, x1, x2, x3, x4, x5, x6, x7, Neg(Succ(x8)), Pos(x9), x10, x11)
new_mkBalBranch6MkBalBranch017(x0, x1, x2, x3, x4, x5, x6, x7, Pos(Succ(x8)), Neg(x9), x10, x11)
new_mkBalBranch6MkBalBranch1110(x0, x1, x2, x3, x4, x5, x6, x7, Zero, x8, x9)
new_mkVBalBranch3MkVBalBranch131(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, Succ(x11), x12)
new_mkVBalBranch4(x0, Branch(x1, x2, Neg(Zero), x3, x4), Branch(x5, x6, Pos(Succ(x7)), x8, x9), x10)
new_mkVBalBranch4(x0, Branch(x1, x2, Pos(Zero), x3, x4), Branch(x5, x6, Neg(Succ(x7)), x8, x9), x10)
new_mkVBalBranch3MkVBalBranch262(x0, x1, Neg(Succ(x2)), x3, x4, x5, x6, x7, x8, x9, x10, Succ(x11), x12)
new_primPlusInt0(x0, Pos(x1))
new_mkVBalBranch3MkVBalBranch162(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, Zero, Succ(x11), x12)
new_mkVBalBranch3MkVBalBranch147(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, Zero, x11)
new_primMulNat2(Succ(x0))
new_intersectFM_C2Lts0(x0, x1, x2, x3, x4)
new_mkVBalBranch3MkVBalBranch269(x0, x1, Zero, x2, x3, x4, x5, x6, x7, x8, x9, x10)
new_splitGT27(x0, x1, x2, x3, x4)
new_splitLT16(x0)
new_mkVBalBranch3MkVBalBranch152(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, Succ(x11), Succ(x12), x13)
new_mkBalBranch6Size_l(x0, x1, x2, x3, x4, x5)
new_mkBalBranch6MkBalBranch311(x0, x1, x2, x3, x4, x5, x6, x7)
new_splitGT5(x0, x1, x2, x3)
new_mkVBalBranch3MkVBalBranch160(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11)
new_primMinusNat0(Succ(x0), Succ(x1))

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_splitLT4(x0, x1, x2, x3)
new_splitGT10(x0, x1, x2, x3)
new_splitGT16(x0)
new_splitGT11(x0, x1, x2, x3)
new_splitLT8(x0, x1, x2, x3)
new_splitLT5(x0, x1, x2, x3)
new_splitLT16(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
                                  ↳ 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_C(Branch(GT, zzz31, zzz32, Branch(GT, zzz331, zzz332, Branch(GT, zzz3331, zzz3332, EmptyFM, zzz3334), zzz334), zzz34), Branch(EQ, zzz41, zzz42, zzz43, zzz44), h) → new_intersectFM_C(new_mkVBalBranch3(zzz31, new_splitGT9(zzz331, zzz332, Branch(GT, zzz3331, zzz3332, EmptyFM, zzz3334), zzz334, h), zzz34, h), zzz44, h)
new_intersectFM_C(Branch(LT, zzz31, zzz32, zzz33, zzz34), Branch(LT, zzz41, zzz42, zzz43, zzz44), h) → new_intersectFM_C(new_splitLT3(zzz31, zzz32, zzz33, zzz34, h), zzz43, h)
new_intersectFM_C2IntersectFM_C16(zzz2208, zzz2209, zzz2210, zzz2211, zzz2212, zzz2213, zzz2214, zzz2215, GT, zzz2217, zzz2218, zzz2219, zzz2220, ca, cb) → new_intersectFM_C2IntersectFM_C18(Branch(LT, zzz2208, zzz2209, zzz2210, zzz2211), zzz2212, zzz2213, zzz2214, zzz2215, zzz2217, zzz2218, zzz2219, zzz2220, ca, cb)
new_intersectFM_C2IntersectFM_C10(zzz869, zzz870, zzz871, zzz872, zzz873, zzz874, zzz875, zzz876, EQ, zzz878, zzz879, EmptyFM, zzz881, bc, bd) → new_intersectFM_C(new_intersectFM_C2Lts1(zzz869, zzz870, zzz871, zzz872, bc), zzz875, bc)
new_intersectFM_C(Branch(GT, zzz31, zzz32, Branch(GT, zzz331, zzz332, Branch(EQ, zzz3331, zzz3332, zzz3333, zzz3334), zzz334), zzz34), Branch(EQ, zzz41, zzz42, zzz43, zzz44), h) → new_intersectFM_C(new_splitGT24(zzz31, zzz32, Branch(GT, zzz331, zzz332, Branch(EQ, zzz3331, zzz3332, zzz3333, zzz3334), zzz334), zzz34, h), zzz44, h)
new_intersectFM_C2IntersectFM_C11(zzz883, zzz884, zzz885, zzz886, zzz887, zzz888, zzz889, zzz890, EQ, zzz892, zzz893, zzz894, zzz895, be, bf) → new_intersectFM_C(new_intersectFM_C2Gts2(zzz883, zzz884, zzz885, zzz886, be), zzz890, be)
new_intersectFM_C2IntersectFM_C14(zzz76, zzz77, zzz78, zzz79, zzz80, zzz81, zzz82, zzz83, zzz871, zzz872, zzz873, zzz874, bg, bh) → new_intersectFM_C(new_intersectFM_C2Gts(zzz76, zzz77, zzz78, zzz79, bg), zzz83, bg)
new_intersectFM_C(Branch(GT, zzz31, zzz32, Branch(GT, zzz331, zzz332, Branch(LT, zzz3331, zzz3332, zzz3333, zzz3334), zzz334), zzz34), Branch(EQ, zzz41, zzz42, zzz43, zzz44), h) → new_intersectFM_C2IntersectFM_C12(zzz31, zzz32, Branch(GT, zzz331, zzz332, Branch(LT, zzz3331, zzz3332, zzz3333, zzz3334), zzz334), zzz34, zzz41, zzz42, zzz43, zzz44, zzz3331, zzz3332, zzz3333, zzz3334, h, h)
new_intersectFM_C2IntersectFM_C17(zzz2223, zzz2224, zzz2225, zzz2226, zzz2227, zzz2228, zzz2229, zzz2230, LT, zzz2232, zzz2233, zzz2234, Branch(zzz22350, zzz22351, zzz22352, zzz22353, zzz22354), ce, cf) → new_intersectFM_C2IntersectFM_C17(zzz2223, zzz2224, zzz2225, zzz2226, zzz2227, zzz2228, zzz2229, zzz2230, zzz22350, zzz22351, zzz22352, zzz22353, zzz22354, ce, cf)
new_intersectFM_C2IntersectFM_C10(zzz869, zzz870, zzz871, zzz872, zzz873, zzz874, zzz875, zzz876, LT, zzz878, zzz879, zzz880, zzz881, bc, bd) → new_intersectFM_C(new_intersectFM_C2Lts1(zzz869, zzz870, zzz871, zzz872, bc), zzz875, bc)
new_intersectFM_C(Branch(EQ, zzz31, zzz32, EmptyFM, zzz34), Branch(LT, zzz41, zzz42, zzz43, zzz44), h) → new_intersectFM_C(new_splitGT4(zzz31, zzz32, zzz34, h), zzz44, h)
new_intersectFM_C2IntersectFM_C114(zzz2223, zzz2224, zzz2225, zzz2226, zzz2227, zzz2228, zzz2229, zzz2230, EmptyFM, ce, cf) → new_intersectFM_C(new_intersectFM_C2Lts3(Branch(EQ, zzz2223, zzz2224, zzz2225, zzz2226), ce), zzz2229, ce)
new_intersectFM_C2IntersectFM_C12(zzz76, zzz77, zzz78, zzz79, zzz80, zzz81, zzz82, zzz83, zzz84, zzz85, zzz86, EmptyFM, bg, bh) → new_intersectFM_C(new_intersectFM_C2Lts(zzz76, zzz77, zzz78, zzz79, bg), zzz82, bg)
new_intersectFM_C2IntersectFM_C112(zzz76, zzz77, zzz78, zzz79, zzz80, zzz81, zzz82, zzz83, Branch(LT, zzz871, zzz872, zzz873, zzz874), bg, bh) → new_intersectFM_C2IntersectFM_C12(zzz76, zzz77, zzz78, zzz79, zzz80, zzz81, zzz82, zzz83, zzz871, zzz872, zzz873, zzz874, bg, bh)
new_intersectFM_C2IntersectFM_C16(zzz2208, zzz2209, zzz2210, zzz2211, zzz2212, zzz2213, zzz2214, zzz2215, LT, zzz2217, zzz2218, zzz2219, EmptyFM, ca, cb) → new_intersectFM_C(new_intersectFM_C2Lts3(Branch(LT, zzz2208, zzz2209, zzz2210, zzz2211), ca), zzz2214, ca)
new_intersectFM_C(Branch(LT, zzz31, zzz32, zzz33, Branch(zzz340, zzz341, zzz342, zzz343, zzz344)), Branch(GT, zzz41, zzz42, zzz43, zzz44), h) → new_intersectFM_C2IntersectFM_C16(zzz31, zzz32, zzz33, Branch(zzz340, zzz341, zzz342, zzz343, zzz344), zzz41, zzz42, zzz43, zzz44, zzz340, zzz341, zzz342, zzz343, zzz344, h, h)
new_intersectFM_C2IntersectFM_C112(zzz76, zzz77, zzz78, zzz79, zzz80, zzz81, zzz82, zzz83, EmptyFM, bg, bh) → new_intersectFM_C(new_intersectFM_C2Gts(zzz76, zzz77, zzz78, zzz79, bg), zzz83, bg)
new_intersectFM_C(Branch(GT, zzz31, zzz32, Branch(GT, zzz331, zzz332, Branch(GT, zzz3331, zzz3332, Branch(EQ, zzz33331, zzz33332, zzz33333, zzz33334), zzz3334), zzz334), zzz34), Branch(EQ, zzz41, zzz42, zzz43, zzz44), h) → new_intersectFM_C(new_intersectFM_C2Gts(zzz31, zzz32, Branch(GT, zzz331, zzz332, Branch(GT, zzz3331, zzz3332, Branch(EQ, zzz33331, zzz33332, zzz33333, zzz33334), zzz3334), zzz334), zzz34, h), zzz44, h)
new_intersectFM_C2IntersectFM_C110(zzz869, zzz870, zzz871, zzz872, zzz873, zzz874, zzz875, zzz876, EmptyFM, bc, bd) → new_intersectFM_C(new_intersectFM_C2Lts1(zzz869, zzz870, zzz871, zzz872, bc), zzz875, bc)
new_intersectFM_C2IntersectFM_C113(zzz2208, zzz2209, zzz2210, zzz2211, zzz2212, zzz2213, zzz2214, zzz2215, Branch(zzz22200, zzz22201, zzz22202, zzz22203, zzz22204), ca, cb) → new_intersectFM_C2IntersectFM_C16(zzz2208, zzz2209, zzz2210, zzz2211, zzz2212, zzz2213, zzz2214, zzz2215, zzz22200, zzz22201, zzz22202, zzz22203, zzz22204, ca, cb)
new_intersectFM_C(Branch(LT, zzz31, zzz32, zzz33, EmptyFM), Branch(GT, zzz41, zzz42, zzz43, zzz44), h) → new_intersectFM_C(new_splitLT10(zzz31, zzz32, zzz33, h), zzz43, h)
new_intersectFM_C2IntersectFM_C16(zzz2208, zzz2209, zzz2210, zzz2211, zzz2212, zzz2213, zzz2214, zzz2215, EQ, zzz2217, zzz2218, zzz2219, zzz2220, ca, cb) → new_intersectFM_C2IntersectFM_C113(zzz2208, zzz2209, zzz2210, zzz2211, zzz2212, zzz2213, zzz2214, zzz2215, zzz2220, ca, cb)
new_intersectFM_C2IntersectFM_C12(zzz76, zzz77, zzz78, zzz79, zzz80, zzz81, zzz82, zzz83, zzz84, zzz85, zzz86, Branch(EQ, zzz871, zzz872, zzz873, zzz874), bg, bh) → new_intersectFM_C(new_intersectFM_C2Gts(zzz76, zzz77, zzz78, zzz79, bg), zzz83, bg)
new_intersectFM_C(Branch(EQ, zzz31, zzz32, zzz33, zzz34), Branch(EQ, zzz41, zzz42, zzz43, zzz44), h) → new_intersectFM_C(new_splitLT7(zzz31, zzz32, zzz33, zzz34, h), zzz43, h)
new_intersectFM_C2IntersectFM_C11(zzz883, zzz884, zzz885, zzz886, zzz887, zzz888, zzz889, zzz890, GT, zzz892, zzz893, EmptyFM, zzz895, be, bf) → new_intersectFM_C(new_intersectFM_C2Lts2(zzz883, zzz884, zzz885, zzz886, be), zzz889, be)
new_intersectFM_C(Branch(GT, zzz31, zzz32, Branch(GT, zzz331, zzz332, Branch(GT, zzz3331, zzz3332, Branch(GT, zzz33331, zzz33332, Branch(EQ, zzz333331, zzz333332, zzz333333, zzz333334), zzz33334), zzz3334), zzz334), zzz34), Branch(EQ, zzz41, zzz42, zzz43, zzz44), h) → new_intersectFM_C2IntersectFM_C14(zzz31, zzz32, Branch(GT, zzz331, zzz332, Branch(GT, zzz3331, zzz3332, Branch(GT, zzz33331, zzz33332, Branch(EQ, zzz333331, zzz333332, zzz333333, zzz333334), zzz33334), zzz3334), zzz334), zzz34, zzz41, zzz42, zzz43, zzz44, zzz333331, zzz333332, zzz333333, zzz333334, h, h)
new_intersectFM_C(Branch(GT, zzz31, zzz32, Branch(GT, zzz331, zzz332, Branch(GT, zzz3331, zzz3332, EmptyFM, zzz3334), zzz334), zzz34), Branch(EQ, zzz41, zzz42, zzz43, zzz44), h) → new_intersectFM_C(new_splitLT9(zzz331, zzz332, Branch(GT, zzz3331, zzz3332, EmptyFM, zzz3334), zzz334, h), zzz43, h)
new_intersectFM_C(Branch(EQ, zzz31, zzz32, zzz33, zzz34), Branch(EQ, zzz41, zzz42, zzz43, zzz44), h) → new_intersectFM_C(new_splitGT7(zzz31, zzz32, zzz33, zzz34, h), zzz44, h)
new_intersectFM_C(Branch(GT, zzz31, zzz32, Branch(LT, zzz331, zzz332, zzz333, zzz334), zzz34), Branch(EQ, zzz41, zzz42, zzz43, zzz44), h) → new_intersectFM_C2IntersectFM_C12(zzz31, zzz32, Branch(LT, zzz331, zzz332, zzz333, zzz334), zzz34, zzz41, zzz42, zzz43, zzz44, zzz331, zzz332, zzz333, zzz334, h, h)
new_intersectFM_C(Branch(GT, zzz31, zzz32, Branch(zzz330, zzz331, zzz332, zzz333, zzz334), zzz34), Branch(LT, zzz41, zzz42, zzz43, zzz44), h) → new_intersectFM_C2IntersectFM_C10(zzz31, zzz32, Branch(zzz330, zzz331, zzz332, zzz333, zzz334), zzz34, zzz41, zzz42, zzz43, zzz44, zzz330, zzz331, zzz332, zzz333, zzz334, h, h)
new_intersectFM_C2IntersectFM_C111(zzz883, zzz884, zzz885, zzz886, zzz887, zzz888, zzz889, zzz890, EmptyFM, be, bf) → new_intersectFM_C(new_intersectFM_C2Lts2(zzz883, zzz884, zzz885, zzz886, be), zzz889, be)
new_intersectFM_C2IntersectFM_C17(zzz2223, zzz2224, zzz2225, zzz2226, zzz2227, zzz2228, zzz2229, zzz2230, LT, zzz2232, zzz2233, zzz2234, EmptyFM, ce, cf) → new_intersectFM_C(new_intersectFM_C2Lts3(Branch(EQ, zzz2223, zzz2224, zzz2225, zzz2226), ce), zzz2229, ce)
new_intersectFM_C2IntersectFM_C19(zzz854, zzz855, zzz856, zzz857, zzz858, zzz859, zzz860, zzz861, EmptyFM, ba, bb) → new_intersectFM_C(new_intersectFM_C2Gts0(zzz854, zzz855, zzz856, zzz857, ba), zzz861, ba)
new_intersectFM_C(Branch(GT, zzz31, zzz32, Branch(GT, zzz331, zzz332, Branch(GT, zzz3331, zzz3332, Branch(EQ, zzz33331, zzz33332, zzz33333, zzz33334), zzz3334), zzz334), zzz34), Branch(EQ, zzz41, zzz42, zzz43, zzz44), h) → new_intersectFM_C(new_intersectFM_C2Lts(zzz31, zzz32, Branch(GT, zzz331, zzz332, Branch(GT, zzz3331, zzz3332, Branch(EQ, zzz33331, zzz33332, zzz33333, zzz33334), zzz3334), zzz334), zzz34, h), zzz43, h)
new_intersectFM_C2IntersectFM_C113(zzz2208, zzz2209, zzz2210, zzz2211, zzz2212, zzz2213, zzz2214, zzz2215, EmptyFM, ca, cb) → new_intersectFM_C(new_intersectFM_C2Lts3(Branch(LT, zzz2208, zzz2209, zzz2210, zzz2211), ca), zzz2214, ca)
new_intersectFM_C(Branch(GT, zzz31, zzz32, Branch(GT, zzz331, zzz332, Branch(GT, zzz3331, zzz3332, Branch(GT, zzz33331, zzz33332, Branch(GT, zzz333331, zzz333332, zzz333333, zzz333334), zzz33334), zzz3334), zzz334), zzz34), Branch(EQ, zzz41, zzz42, zzz43, zzz44), h) → new_intersectFM_C2IntersectFM_C15(zzz31, zzz32, Branch(GT, zzz331, zzz332, Branch(GT, zzz3331, zzz3332, Branch(GT, zzz33331, zzz33332, Branch(GT, zzz333331, zzz333332, zzz333333, zzz333334), zzz33334), zzz3334), zzz334), zzz34, zzz41, zzz42, zzz43, zzz44, zzz333331, zzz333332, zzz333333, zzz333334, h, h)
new_intersectFM_C2IntersectFM_C14(zzz76, zzz77, zzz78, zzz79, zzz80, zzz81, zzz82, zzz83, zzz871, zzz872, zzz873, zzz874, bg, bh) → new_intersectFM_C(new_intersectFM_C2Lts(zzz76, zzz77, zzz78, zzz79, bg), zzz82, bg)
new_intersectFM_C2IntersectFM_C12(zzz76, zzz77, zzz78, zzz79, zzz80, zzz81, zzz82, zzz83, zzz84, zzz85, zzz86, Branch(LT, zzz871, zzz872, zzz873, zzz874), bg, bh) → new_intersectFM_C2IntersectFM_C12(zzz76, zzz77, zzz78, zzz79, zzz80, zzz81, zzz82, zzz83, zzz871, zzz872, zzz873, zzz874, bg, bh)
new_intersectFM_C(Branch(GT, zzz31, zzz32, Branch(GT, zzz331, zzz332, Branch(EQ, zzz3331, zzz3332, zzz3333, zzz3334), zzz334), zzz34), Branch(EQ, zzz41, zzz42, zzz43, zzz44), h) → new_intersectFM_C(new_splitLT23(zzz31, zzz32, Branch(GT, zzz331, zzz332, Branch(EQ, zzz3331, zzz3332, zzz3333, zzz3334), zzz334), zzz34, h), zzz43, h)
new_intersectFM_C(Branch(LT, zzz31, zzz32, zzz33, EmptyFM), Branch(EQ, zzz41, zzz42, zzz43, zzz44), h) → new_intersectFM_C(new_mkVBalBranch2(zzz31, zzz33, new_splitLT6(h), h), zzz43, h)
new_intersectFM_C(Branch(EQ, zzz31, zzz32, zzz33, EmptyFM), Branch(GT, zzz41, zzz42, zzz43, zzz44), h) → new_intersectFM_C(new_splitLT11(zzz31, zzz32, zzz33, h), zzz43, h)
new_intersectFM_C2IntersectFM_C10(zzz869, zzz870, zzz871, zzz872, zzz873, zzz874, zzz875, zzz876, EQ, zzz878, zzz879, Branch(zzz8800, zzz8801, zzz8802, zzz8803, zzz8804), zzz881, bc, bd) → new_intersectFM_C2IntersectFM_C10(zzz869, zzz870, zzz871, zzz872, zzz873, zzz874, zzz875, zzz876, zzz8800, zzz8801, zzz8802, zzz8803, zzz8804, bc, bd)
new_intersectFM_C2IntersectFM_C17(zzz2223, zzz2224, zzz2225, zzz2226, zzz2227, zzz2228, zzz2229, zzz2230, GT, zzz2232, zzz2233, zzz2234, zzz2235, ce, cf) → new_intersectFM_C2IntersectFM_C18(Branch(EQ, zzz2223, zzz2224, zzz2225, zzz2226), zzz2227, zzz2228, zzz2229, zzz2230, zzz2232, zzz2233, zzz2234, zzz2235, ce, cf)
new_intersectFM_C2IntersectFM_C110(zzz869, zzz870, zzz871, zzz872, zzz873, zzz874, zzz875, zzz876, Branch(zzz8800, zzz8801, zzz8802, zzz8803, zzz8804), bc, bd) → new_intersectFM_C2IntersectFM_C10(zzz869, zzz870, zzz871, zzz872, zzz873, zzz874, zzz875, zzz876, zzz8800, zzz8801, zzz8802, zzz8803, zzz8804, bc, bd)
new_intersectFM_C(Branch(GT, zzz31, zzz32, Branch(EQ, zzz331, zzz332, zzz333, zzz334), zzz34), Branch(EQ, zzz41, zzz42, zzz43, zzz44), h) → new_intersectFM_C(new_splitLT7(zzz331, zzz332, zzz333, zzz334, h), zzz43, h)
new_intersectFM_C(Branch(EQ, zzz31, zzz32, Branch(zzz330, zzz331, zzz332, zzz333, zzz334), zzz34), Branch(LT, zzz41, zzz42, zzz43, zzz44), h) → new_intersectFM_C2IntersectFM_C1(zzz31, zzz32, Branch(zzz330, zzz331, zzz332, zzz333, zzz334), zzz34, zzz41, zzz42, zzz43, zzz44, zzz330, zzz331, zzz332, zzz333, zzz334, h, h)
new_intersectFM_C2IntersectFM_C114(zzz2223, zzz2224, zzz2225, zzz2226, zzz2227, zzz2228, zzz2229, zzz2230, Branch(zzz22350, zzz22351, zzz22352, zzz22353, zzz22354), ce, cf) → new_intersectFM_C2IntersectFM_C17(zzz2223, zzz2224, zzz2225, zzz2226, zzz2227, zzz2228, zzz2229, zzz2230, zzz22350, zzz22351, zzz22352, zzz22353, zzz22354, ce, cf)
new_intersectFM_C2IntersectFM_C11(zzz883, zzz884, zzz885, zzz886, zzz887, zzz888, zzz889, zzz890, EQ, zzz892, zzz893, zzz894, zzz895, be, bf) → new_intersectFM_C(new_intersectFM_C2Lts2(zzz883, zzz884, zzz885, zzz886, be), zzz889, be)
new_intersectFM_C2IntersectFM_C18(zzz2129, zzz2130, zzz2131, zzz2132, zzz2133, zzz2134, zzz2135, zzz2136, zzz2137, cc, cd) → new_intersectFM_C(new_intersectFM_C2Gts3(zzz2129, cc), zzz2133, cc)
new_intersectFM_C(Branch(EQ, zzz31, zzz32, zzz33, Branch(zzz340, zzz341, zzz342, zzz343, zzz344)), Branch(GT, zzz41, zzz42, zzz43, zzz44), h) → new_intersectFM_C2IntersectFM_C17(zzz31, zzz32, zzz33, Branch(zzz340, zzz341, zzz342, zzz343, zzz344), zzz41, zzz42, zzz43, zzz44, zzz340, zzz341, zzz342, zzz343, zzz344, h, h)
new_intersectFM_C2IntersectFM_C112(zzz76, zzz77, zzz78, zzz79, zzz80, zzz81, zzz82, zzz83, EmptyFM, bg, bh) → new_intersectFM_C(new_intersectFM_C2Lts(zzz76, zzz77, zzz78, zzz79, bg), zzz82, bg)
new_intersectFM_C2IntersectFM_C10(zzz869, zzz870, zzz871, zzz872, zzz873, zzz874, zzz875, zzz876, LT, zzz878, zzz879, zzz880, zzz881, bc, bd) → new_intersectFM_C(new_intersectFM_C2Gts1(zzz869, zzz870, zzz871, zzz872, bc), zzz876, bc)
new_intersectFM_C2IntersectFM_C10(zzz869, zzz870, zzz871, zzz872, zzz873, zzz874, zzz875, zzz876, GT, zzz878, zzz879, zzz880, zzz881, bc, bd) → new_intersectFM_C2IntersectFM_C110(zzz869, zzz870, zzz871, zzz872, zzz873, zzz874, zzz875, zzz876, zzz880, bc, bd)
new_intersectFM_C2IntersectFM_C110(zzz869, zzz870, zzz871, zzz872, zzz873, zzz874, zzz875, zzz876, EmptyFM, bc, bd) → new_intersectFM_C(new_intersectFM_C2Gts1(zzz869, zzz870, zzz871, zzz872, bc), zzz876, bc)
new_intersectFM_C2IntersectFM_C112(zzz76, zzz77, zzz78, zzz79, zzz80, zzz81, zzz82, zzz83, Branch(GT, zzz871, zzz872, zzz873, zzz874), bg, bh) → new_intersectFM_C2IntersectFM_C112(zzz76, zzz77, zzz78, zzz79, zzz80, zzz81, zzz82, zzz83, zzz873, bg, bh)
new_intersectFM_C2IntersectFM_C11(zzz883, zzz884, zzz885, zzz886, zzz887, zzz888, zzz889, zzz890, GT, zzz892, zzz893, Branch(zzz8940, zzz8941, zzz8942, zzz8943, zzz8944), zzz895, be, bf) → new_intersectFM_C2IntersectFM_C11(zzz883, zzz884, zzz885, zzz886, zzz887, zzz888, zzz889, zzz890, zzz8940, zzz8941, zzz8942, zzz8943, zzz8944, be, bf)
new_intersectFM_C(Branch(GT, zzz31, zzz32, EmptyFM, zzz34), Branch(LT, zzz41, zzz42, zzz43, zzz44), h) → new_intersectFM_C(new_splitGT5(zzz31, zzz32, zzz34, h), zzz44, h)
new_intersectFM_C2IntersectFM_C19(zzz854, zzz855, zzz856, zzz857, zzz858, zzz859, zzz860, zzz861, EmptyFM, ba, bb) → new_intersectFM_C(new_intersectFM_C2Lts0(zzz854, zzz855, zzz856, zzz857, ba), zzz860, ba)
new_intersectFM_C2IntersectFM_C112(zzz76, zzz77, zzz78, zzz79, zzz80, zzz81, zzz82, zzz83, Branch(EQ, zzz871, zzz872, zzz873, zzz874), bg, bh) → new_intersectFM_C(new_intersectFM_C2Lts(zzz76, zzz77, zzz78, zzz79, bg), zzz82, bg)
new_intersectFM_C(Branch(LT, zzz31, zzz32, zzz33, Branch(zzz340, zzz341, zzz342, zzz343, zzz344)), Branch(EQ, zzz41, zzz42, zzz43, zzz44), h) → new_intersectFM_C2IntersectFM_C11(zzz31, zzz32, zzz33, Branch(zzz340, zzz341, zzz342, zzz343, zzz344), zzz41, zzz42, zzz43, zzz44, zzz340, zzz341, zzz342, zzz343, zzz344, h, h)
new_intersectFM_C(Branch(GT, zzz31, zzz32, zzz33, zzz34), Branch(GT, zzz41, zzz42, zzz43, zzz44), h) → new_intersectFM_C2IntersectFM_C18(Branch(GT, zzz31, zzz32, zzz33, zzz34), zzz41, zzz42, zzz43, zzz44, zzz31, zzz32, zzz33, zzz34, h, h)
new_intersectFM_C2IntersectFM_C114(zzz2223, zzz2224, zzz2225, zzz2226, zzz2227, zzz2228, zzz2229, zzz2230, EmptyFM, ce, cf) → new_intersectFM_C(new_intersectFM_C2Gts3(Branch(EQ, zzz2223, zzz2224, zzz2225, zzz2226), ce), zzz2230, ce)
new_intersectFM_C2IntersectFM_C1(zzz854, zzz855, zzz856, zzz857, zzz858, zzz859, zzz860, zzz861, EQ, zzz863, zzz864, Branch(zzz8650, zzz8651, zzz8652, zzz8653, zzz8654), zzz866, ba, bb) → new_intersectFM_C2IntersectFM_C1(zzz854, zzz855, zzz856, zzz857, zzz858, zzz859, zzz860, zzz861, zzz8650, zzz8651, zzz8652, zzz8653, zzz8654, ba, bb)
new_intersectFM_C2IntersectFM_C11(zzz883, zzz884, zzz885, zzz886, zzz887, zzz888, zzz889, zzz890, GT, zzz892, zzz893, EmptyFM, zzz895, be, bf) → new_intersectFM_C(new_intersectFM_C2Gts2(zzz883, zzz884, zzz885, zzz886, be), zzz890, be)
new_intersectFM_C2IntersectFM_C13(zzz76, zzz77, zzz78, zzz79, zzz80, zzz81, zzz82, zzz83, zzz871, zzz872, zzz873, zzz874, bg, bh) → new_intersectFM_C2IntersectFM_C12(zzz76, zzz77, zzz78, zzz79, zzz80, zzz81, zzz82, zzz83, zzz871, zzz872, zzz873, zzz874, bg, bh)
new_intersectFM_C2IntersectFM_C18(zzz2129, zzz2130, zzz2131, zzz2132, zzz2133, zzz2134, zzz2135, zzz2136, zzz2137, cc, cd) → new_intersectFM_C(new_intersectFM_C2Lts3(zzz2129, cc), zzz2132, cc)
new_intersectFM_C2IntersectFM_C12(zzz76, zzz77, zzz78, zzz79, zzz80, zzz81, zzz82, zzz83, zzz84, zzz85, zzz86, EmptyFM, bg, bh) → new_intersectFM_C(new_intersectFM_C2Gts(zzz76, zzz77, zzz78, zzz79, bg), zzz83, bg)
new_intersectFM_C2IntersectFM_C111(zzz883, zzz884, zzz885, zzz886, zzz887, zzz888, zzz889, zzz890, EmptyFM, be, bf) → new_intersectFM_C(new_intersectFM_C2Gts2(zzz883, zzz884, zzz885, zzz886, be), zzz890, be)
new_intersectFM_C2IntersectFM_C112(zzz76, zzz77, zzz78, zzz79, zzz80, zzz81, zzz82, zzz83, Branch(EQ, zzz871, zzz872, zzz873, zzz874), bg, bh) → new_intersectFM_C(new_intersectFM_C2Gts(zzz76, zzz77, zzz78, zzz79, bg), zzz83, bg)
new_intersectFM_C2IntersectFM_C111(zzz883, zzz884, zzz885, zzz886, zzz887, zzz888, zzz889, zzz890, Branch(zzz8940, zzz8941, zzz8942, zzz8943, zzz8944), be, bf) → new_intersectFM_C2IntersectFM_C11(zzz883, zzz884, zzz885, zzz886, zzz887, zzz888, zzz889, zzz890, zzz8940, zzz8941, zzz8942, zzz8943, zzz8944, be, bf)
new_intersectFM_C2IntersectFM_C1(zzz854, zzz855, zzz856, zzz857, zzz858, zzz859, zzz860, zzz861, EQ, zzz863, zzz864, EmptyFM, zzz866, ba, bb) → new_intersectFM_C(new_intersectFM_C2Gts0(zzz854, zzz855, zzz856, zzz857, ba), zzz861, ba)
new_intersectFM_C(Branch(GT, zzz31, zzz32, Branch(GT, zzz331, zzz332, Branch(GT, zzz3331, zzz3332, Branch(GT, zzz33331, zzz33332, EmptyFM, zzz33334), zzz3334), zzz334), zzz34), Branch(EQ, zzz41, zzz42, zzz43, zzz44), h) → new_intersectFM_C(new_intersectFM_C2Lts(zzz31, zzz32, Branch(GT, zzz331, zzz332, Branch(GT, zzz3331, zzz3332, Branch(GT, zzz33331, zzz33332, EmptyFM, zzz33334), zzz3334), zzz334), zzz34, h), zzz43, h)
new_intersectFM_C2IntersectFM_C17(zzz2223, zzz2224, zzz2225, zzz2226, zzz2227, zzz2228, zzz2229, zzz2230, EQ, zzz2232, zzz2233, zzz2234, zzz2235, ce, cf) → new_intersectFM_C2IntersectFM_C114(zzz2223, zzz2224, zzz2225, zzz2226, zzz2227, zzz2228, zzz2229, zzz2230, zzz2235, ce, cf)
new_intersectFM_C2IntersectFM_C11(zzz883, zzz884, zzz885, zzz886, zzz887, zzz888, zzz889, zzz890, LT, zzz892, zzz893, zzz894, zzz895, be, bf) → new_intersectFM_C2IntersectFM_C111(zzz883, zzz884, zzz885, zzz886, zzz887, zzz888, zzz889, zzz890, zzz895, be, bf)
new_intersectFM_C2IntersectFM_C1(zzz854, zzz855, zzz856, zzz857, zzz858, zzz859, zzz860, zzz861, LT, zzz863, zzz864, zzz865, zzz866, ba, bb) → new_intersectFM_C(new_intersectFM_C2Lts0(zzz854, zzz855, zzz856, zzz857, ba), zzz860, ba)
new_intersectFM_C2IntersectFM_C1(zzz854, zzz855, zzz856, zzz857, zzz858, zzz859, zzz860, zzz861, LT, zzz863, zzz864, zzz865, zzz866, ba, bb) → new_intersectFM_C(new_intersectFM_C2Gts0(zzz854, zzz855, zzz856, zzz857, ba), zzz861, ba)
new_intersectFM_C2IntersectFM_C19(zzz854, zzz855, zzz856, zzz857, zzz858, zzz859, zzz860, zzz861, Branch(zzz8650, zzz8651, zzz8652, zzz8653, zzz8654), ba, bb) → new_intersectFM_C2IntersectFM_C1(zzz854, zzz855, zzz856, zzz857, zzz858, zzz859, zzz860, zzz861, zzz8650, zzz8651, zzz8652, zzz8653, zzz8654, ba, bb)
new_intersectFM_C2IntersectFM_C113(zzz2208, zzz2209, zzz2210, zzz2211, zzz2212, zzz2213, zzz2214, zzz2215, EmptyFM, ca, cb) → new_intersectFM_C(new_intersectFM_C2Gts3(Branch(LT, zzz2208, zzz2209, zzz2210, zzz2211), ca), zzz2215, ca)
new_intersectFM_C(Branch(GT, zzz31, zzz32, Branch(GT, zzz331, zzz332, Branch(GT, zzz3331, zzz3332, Branch(GT, zzz33331, zzz33332, EmptyFM, zzz33334), zzz3334), zzz334), zzz34), Branch(EQ, zzz41, zzz42, zzz43, zzz44), h) → new_intersectFM_C(new_intersectFM_C2Gts(zzz31, zzz32, Branch(GT, zzz331, zzz332, Branch(GT, zzz3331, zzz3332, Branch(GT, zzz33331, zzz33332, EmptyFM, zzz33334), zzz3334), zzz334), zzz34, h), zzz44, h)
new_intersectFM_C2IntersectFM_C1(zzz854, zzz855, zzz856, zzz857, zzz858, zzz859, zzz860, zzz861, EQ, zzz863, zzz864, EmptyFM, zzz866, ba, bb) → new_intersectFM_C(new_intersectFM_C2Lts0(zzz854, zzz855, zzz856, zzz857, ba), zzz860, ba)
new_intersectFM_C2IntersectFM_C16(zzz2208, zzz2209, zzz2210, zzz2211, zzz2212, zzz2213, zzz2214, zzz2215, LT, zzz2217, zzz2218, zzz2219, Branch(zzz22200, zzz22201, zzz22202, zzz22203, zzz22204), ca, cb) → new_intersectFM_C2IntersectFM_C16(zzz2208, zzz2209, zzz2210, zzz2211, zzz2212, zzz2213, zzz2214, zzz2215, zzz22200, zzz22201, zzz22202, zzz22203, zzz22204, ca, cb)
new_intersectFM_C(Branch(LT, zzz31, zzz32, zzz33, zzz34), Branch(LT, zzz41, zzz42, zzz43, zzz44), h) → new_intersectFM_C(new_splitGT3(zzz31, zzz32, zzz33, zzz34, h), zzz44, h)
new_intersectFM_C(Branch(GT, zzz31, zzz32, Branch(GT, zzz331, zzz332, EmptyFM, zzz334), zzz34), Branch(EQ, zzz41, zzz42, zzz43, zzz44), h) → new_intersectFM_C(new_mkVBalBranch3(zzz31, new_splitGT8(zzz331, zzz332, zzz334, h), zzz34, h), zzz44, h)
new_intersectFM_C2IntersectFM_C17(zzz2223, zzz2224, zzz2225, zzz2226, zzz2227, zzz2228, zzz2229, zzz2230, LT, zzz2232, zzz2233, zzz2234, EmptyFM, ce, cf) → new_intersectFM_C(new_intersectFM_C2Gts3(Branch(EQ, zzz2223, zzz2224, zzz2225, zzz2226), ce), zzz2230, ce)
new_intersectFM_C2IntersectFM_C12(zzz76, zzz77, zzz78, zzz79, zzz80, zzz81, zzz82, zzz83, zzz84, zzz85, zzz86, Branch(GT, zzz871, zzz872, zzz873, zzz874), bg, bh) → new_intersectFM_C2IntersectFM_C112(zzz76, zzz77, zzz78, zzz79, zzz80, zzz81, zzz82, zzz83, zzz873, bg, bh)
new_intersectFM_C(Branch(GT, zzz31, zzz32, Branch(GT, zzz331, zzz332, Branch(GT, zzz3331, zzz3332, Branch(LT, zzz33331, zzz33332, zzz33333, zzz33334), zzz3334), zzz334), zzz34), Branch(EQ, zzz41, zzz42, zzz43, zzz44), h) → new_intersectFM_C2IntersectFM_C12(zzz31, zzz32, Branch(GT, zzz331, zzz332, Branch(GT, zzz3331, zzz3332, Branch(LT, zzz33331, zzz33332, zzz33333, zzz33334), zzz3334), zzz334), zzz34, zzz41, zzz42, zzz43, zzz44, zzz33331, zzz33332, zzz33333, zzz33334, h, h)
new_intersectFM_C(Branch(GT, zzz31, zzz32, EmptyFM, zzz34), Branch(EQ, zzz41, zzz42, zzz43, zzz44), h) → new_intersectFM_C(new_splitGT8(zzz31, zzz32, zzz34, h), zzz44, h)
new_intersectFM_C2IntersectFM_C15(zzz76, zzz77, zzz78, zzz79, zzz80, zzz81, zzz82, zzz83, zzz871, zzz872, zzz873, zzz874, bg, bh) → new_intersectFM_C2IntersectFM_C112(zzz76, zzz77, zzz78, zzz79, zzz80, zzz81, zzz82, zzz83, zzz873, bg, bh)
new_intersectFM_C(Branch(GT, zzz31, zzz32, Branch(GT, zzz331, zzz332, Branch(GT, zzz3331, zzz3332, Branch(GT, zzz33331, zzz33332, Branch(LT, zzz333331, zzz333332, zzz333333, zzz333334), zzz33334), zzz3334), zzz334), zzz34), Branch(EQ, zzz41, zzz42, zzz43, zzz44), h) → new_intersectFM_C2IntersectFM_C13(zzz31, zzz32, Branch(GT, zzz331, zzz332, Branch(GT, zzz3331, zzz3332, Branch(GT, zzz33331, zzz33332, Branch(LT, zzz333331, zzz333332, zzz333333, zzz333334), zzz33334), zzz3334), zzz334), zzz34, zzz41, zzz42, zzz43, zzz44, zzz333331, zzz333332, zzz333333, zzz333334, h, h)
new_intersectFM_C2IntersectFM_C10(zzz869, zzz870, zzz871, zzz872, zzz873, zzz874, zzz875, zzz876, EQ, zzz878, zzz879, EmptyFM, zzz881, bc, bd) → new_intersectFM_C(new_intersectFM_C2Gts1(zzz869, zzz870, zzz871, zzz872, bc), zzz876, bc)
new_intersectFM_C(Branch(GT, zzz31, zzz32, Branch(EQ, zzz331, zzz332, zzz333, zzz334), zzz34), Branch(EQ, zzz41, zzz42, zzz43, zzz44), h) → new_intersectFM_C(new_mkVBalBranch3(zzz31, new_splitGT7(zzz331, zzz332, zzz333, zzz334, h), zzz34, h), zzz44, h)
new_intersectFM_C2IntersectFM_C16(zzz2208, zzz2209, zzz2210, zzz2211, zzz2212, zzz2213, zzz2214, zzz2215, LT, zzz2217, zzz2218, zzz2219, EmptyFM, ca, cb) → new_intersectFM_C(new_intersectFM_C2Gts3(Branch(LT, zzz2208, zzz2209, zzz2210, zzz2211), ca), zzz2215, ca)
new_intersectFM_C2IntersectFM_C12(zzz76, zzz77, zzz78, zzz79, zzz80, zzz81, zzz82, zzz83, zzz84, zzz85, zzz86, Branch(EQ, zzz871, zzz872, zzz873, zzz874), bg, bh) → new_intersectFM_C(new_intersectFM_C2Lts(zzz76, zzz77, zzz78, zzz79, bg), zzz82, bg)
new_intersectFM_C2IntersectFM_C1(zzz854, zzz855, zzz856, zzz857, zzz858, zzz859, zzz860, zzz861, GT, zzz863, zzz864, zzz865, zzz866, ba, bb) → new_intersectFM_C2IntersectFM_C19(zzz854, zzz855, zzz856, zzz857, zzz858, zzz859, zzz860, zzz861, zzz865, ba, bb)

The TRS R consists of the following rules:

new_splitGT24(zzz76, zzz77, zzz78, zzz79, bg) → new_mkVBalBranch3(zzz76, new_splitGT14(zzz78, bg), zzz79, bg)
new_splitGT14(EmptyFM, be) → new_splitGT42(be)
new_splitGT14(Branch(GT, zzz8861, zzz8862, zzz8863, zzz8864), be) → new_splitGT26(zzz8861, zzz8862, zzz8863, zzz8864, be)
new_splitGT14(Branch(LT, zzz8861, zzz8862, zzz8863, zzz8864), be) → new_splitGT29(zzz8861, zzz8862, zzz8863, zzz8864, be)
new_splitGT29(zzz883, zzz884, zzz885, zzz886, be) → new_splitGT14(zzz886, be)
new_splitGT14(Branch(EQ, zzz8861, zzz8862, zzz8863, zzz8864), be) → new_splitGT27(zzz8861, zzz8862, zzz8863, zzz8864, be)
new_mkVBalBranch3(zzz31, Branch(zzz520, zzz521, Neg(Zero), zzz523, zzz524), Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), h) → new_mkVBalBranch3MkVBalBranch155(zzz340, zzz341, zzz34200, zzz343, zzz344, zzz520, zzz521, zzz523, zzz524, zzz31, new_primMulNat1(zzz34200), h)
new_mkVBalBranch3(zzz31, Branch(zzz520, zzz521, Pos(Zero), zzz523, zzz524), Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), h) → new_mkVBalBranch3MkVBalBranch154(zzz340, zzz341, zzz34200, zzz343, zzz344, zzz520, zzz521, zzz523, zzz524, zzz31, new_primMulNat1(zzz34200), h)
new_mkVBalBranch3(zzz31, Branch(zzz520, zzz521, zzz522, zzz523, zzz524), EmptyFM, h) → new_addToFM(Branch(zzz520, zzz521, zzz522, zzz523, zzz524), zzz31, h)
new_mkVBalBranch3(zzz31, EmptyFM, zzz34, h) → new_addToFM(zzz34, zzz31, h)
new_mkVBalBranch3(zzz31, Branch(zzz520, zzz521, Pos(Zero), zzz523, zzz524), Branch(zzz340, zzz341, Pos(Succ(zzz34200)), zzz343, zzz344), h) → new_mkBalBranch(zzz340, zzz341, new_mkVBalBranch3(zzz31, Branch(zzz520, zzz521, Pos(Zero), zzz523, zzz524), zzz343, h), zzz344, ty_Ordering, h)
new_mkVBalBranch3(zzz31, Branch(zzz520, zzz521, Neg(Zero), zzz523, zzz524), Branch(zzz340, zzz341, Pos(Zero), zzz343, zzz344), h) → new_mkBranch(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))), GT, zzz31, Branch(zzz520, zzz521, Neg(Zero), zzz523, zzz524), Branch(zzz340, zzz341, Pos(Zero), zzz343, zzz344), ty_Ordering, h)
new_mkVBalBranch3(zzz31, Branch(zzz520, zzz521, Pos(Zero), zzz523, zzz524), Branch(zzz340, zzz341, Neg(Zero), zzz343, zzz344), h) → new_mkBranch(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))), GT, zzz31, Branch(zzz520, zzz521, Pos(Zero), zzz523, zzz524), Branch(zzz340, zzz341, Neg(Zero), zzz343, zzz344), ty_Ordering, h)
new_mkVBalBranch3(zzz31, Branch(zzz520, zzz521, Pos(Zero), zzz523, zzz524), Branch(zzz340, zzz341, Pos(Zero), zzz343, zzz344), h) → new_mkBranch(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))), GT, zzz31, Branch(zzz520, zzz521, Pos(Zero), zzz523, zzz524), Branch(zzz340, zzz341, Pos(Zero), zzz343, zzz344), ty_Ordering, h)
new_mkVBalBranch3(zzz31, Branch(zzz520, zzz521, Neg(Succ(zzz52200)), zzz523, zzz524), Branch(zzz340, zzz341, zzz342, zzz343, zzz344), h) → new_mkVBalBranch3MkVBalBranch272(zzz340, zzz341, zzz342, zzz343, zzz344, zzz520, zzz521, zzz52200, zzz523, zzz524, zzz31, new_primMulNat0(zzz52200), h)
new_mkVBalBranch3(zzz31, Branch(zzz520, zzz521, Neg(Zero), zzz523, zzz524), Branch(zzz340, zzz341, Pos(Succ(zzz34200)), zzz343, zzz344), h) → new_mkBalBranch(zzz340, zzz341, new_mkVBalBranch3(zzz31, Branch(zzz520, zzz521, Neg(Zero), zzz523, zzz524), zzz343, h), zzz344, ty_Ordering, h)
new_mkVBalBranch3(zzz31, Branch(zzz520, zzz521, Pos(Succ(zzz52200)), zzz523, zzz524), Branch(zzz340, zzz341, zzz342, zzz343, zzz344), h) → new_mkVBalBranch3MkVBalBranch267(zzz340, zzz341, zzz342, zzz343, zzz344, zzz520, zzz521, zzz52200, zzz523, zzz524, zzz31, new_primMulNat0(zzz52200), h)
new_mkVBalBranch3(zzz31, Branch(zzz520, zzz521, Neg(Zero), zzz523, zzz524), Branch(zzz340, zzz341, Neg(Zero), zzz343, zzz344), h) → new_mkBranch(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))), GT, zzz31, Branch(zzz520, zzz521, Neg(Zero), zzz523, zzz524), Branch(zzz340, zzz341, Neg(Zero), zzz343, zzz344), ty_Ordering, h)
new_mkBranch(zzz2265, zzz2266, zzz2267, zzz2268, zzz2269, ec, ed) → Branch(zzz2266, zzz2267, new_primPlusInt(new_primPlusInt0(Succ(Zero), new_sizeFM(zzz2268, ec, ed)), zzz2268, zzz2269, zzz2266, ec, ed), zzz2268, zzz2269)
new_sizeFM(EmptyFM, fb, fc) → Pos(Zero)
new_sizeFM(Branch(zzz13040, zzz13041, zzz13042, zzz13043, zzz13044), fb, fc) → zzz13042
new_primPlusInt0(zzz1311, Neg(zzz13130)) → new_primMinusNat0(zzz1311, zzz13130)
new_primPlusInt0(zzz1311, Pos(zzz13130)) → Pos(new_primPlusNat2(zzz1311, zzz13130))
new_primPlusInt(Pos(zzz22720), zzz2268, zzz2269, zzz2266, ec, ed) → new_primPlusInt0(zzz22720, new_sizeFM(zzz2269, ec, ed))
new_primPlusInt(Neg(zzz22720), zzz2268, zzz2269, zzz2266, ec, ed) → new_primPlusInt1(zzz22720, new_sizeFM(zzz2269, ec, ed))
new_primPlusInt1(zzz13120, Pos(zzz13150)) → new_primMinusNat0(zzz13150, zzz13120)
new_primPlusInt1(zzz13120, Neg(zzz13150)) → Neg(new_primPlusNat2(zzz13120, zzz13150))
new_primPlusNat2(Succ(zzz900), Succ(zzz9100)) → Succ(Succ(new_primPlusNat2(zzz900, zzz9100)))
new_primPlusNat2(Zero, Succ(zzz9100)) → Succ(zzz9100)
new_primPlusNat2(Succ(zzz900), Zero) → Succ(zzz900)
new_primPlusNat2(Zero, Zero) → Zero
new_primMinusNat0(Succ(zzz100100), Zero) → Pos(Succ(zzz100100))
new_primMinusNat0(Zero, Zero) → Pos(Zero)
new_primMinusNat0(Zero, Succ(zzz542000)) → Neg(Succ(zzz542000))
new_primMinusNat0(Succ(zzz100100), Succ(zzz542000)) → new_primMinusNat0(zzz100100, zzz542000)
new_primMulNat0(zzz6200) → new_primPlusNat3(Succ(new_primPlusNat3(new_primPlusNat1(zzz6200), zzz6200)), Succ(zzz6200))
new_mkVBalBranch3MkVBalBranch267(zzz340, zzz341, Pos(Zero), zzz343, zzz344, zzz520, zzz521, zzz52200, zzz523, zzz524, zzz31, Succ(zzz680), h) → new_mkVBalBranch3MkVBalBranch268(zzz340, zzz341, zzz343, zzz344, zzz520, zzz521, zzz52200, zzz523, zzz524, zzz31, h)
new_mkVBalBranch3MkVBalBranch267(zzz340, zzz341, Neg(zzz3420), zzz343, zzz344, zzz520, zzz521, zzz52200, zzz523, zzz524, zzz31, Zero, h) → new_mkVBalBranch3MkVBalBranch269(zzz340, zzz341, zzz3420, zzz343, zzz344, zzz520, zzz521, zzz52200, zzz523, zzz524, zzz31, h)
new_mkVBalBranch3MkVBalBranch267(zzz340, zzz341, Pos(Zero), zzz343, zzz344, zzz520, zzz521, zzz52200, zzz523, zzz524, zzz31, Zero, h) → new_mkVBalBranch3MkVBalBranch268(zzz340, zzz341, zzz343, zzz344, zzz520, zzz521, zzz52200, zzz523, zzz524, zzz31, h)
new_mkVBalBranch3MkVBalBranch267(zzz340, zzz341, Neg(zzz3420), zzz343, zzz344, zzz520, zzz521, zzz52200, zzz523, zzz524, zzz31, Succ(zzz680), h) → new_mkVBalBranch3MkVBalBranch269(zzz340, zzz341, zzz3420, zzz343, zzz344, zzz520, zzz521, zzz52200, zzz523, zzz524, zzz31, h)
new_mkVBalBranch3MkVBalBranch267(zzz340, zzz341, Pos(Succ(zzz34200)), zzz343, zzz344, zzz520, zzz521, zzz52200, zzz523, zzz524, zzz31, Zero, h) → new_mkVBalBranch3MkVBalBranch252(zzz340, zzz341, zzz34200, zzz343, zzz344, zzz520, zzz521, zzz52200, zzz523, zzz524, zzz31, zzz52200, zzz34200, h)
new_mkVBalBranch3MkVBalBranch267(zzz340, zzz341, Pos(Succ(zzz34200)), zzz343, zzz344, zzz520, zzz521, zzz52200, zzz523, zzz524, zzz31, Succ(zzz680), h) → new_mkVBalBranch3MkVBalBranch252(zzz340, zzz341, zzz34200, zzz343, zzz344, zzz520, zzz521, zzz52200, zzz523, zzz524, zzz31, Succ(new_primPlusNat2(zzz680, zzz52200)), zzz34200, h)
new_mkVBalBranch3MkVBalBranch252(zzz929, zzz930, zzz931, zzz932, zzz933, zzz934, zzz935, zzz936, zzz937, zzz938, zzz939, Succ(zzz9400), Succ(zzz9410), dc) → new_mkVBalBranch3MkVBalBranch252(zzz929, zzz930, zzz931, zzz932, zzz933, zzz934, zzz935, zzz936, zzz937, zzz938, zzz939, zzz9400, zzz9410, dc)
new_mkVBalBranch3MkVBalBranch252(zzz929, zzz930, zzz931, zzz932, zzz933, zzz934, zzz935, zzz936, zzz937, zzz938, zzz939, Succ(zzz9400), Zero, dc) → new_mkVBalBranch3MkVBalBranch253(zzz929, zzz930, zzz931, zzz932, zzz933, zzz934, zzz935, zzz936, zzz937, zzz938, zzz939, dc)
new_mkVBalBranch3MkVBalBranch253(zzz929, zzz930, zzz931, zzz932, zzz933, zzz934, zzz935, zzz936, zzz937, zzz938, zzz939, dc) → new_mkVBalBranch3MkVBalBranch131(zzz929, zzz930, zzz931, zzz932, zzz933, zzz934, zzz935, zzz936, zzz937, zzz938, zzz939, new_primMulNat1(zzz931), dc)
new_primMulNat1(zzz34200) → new_primPlusNat2(new_primMulNat0(zzz34200), Succ(zzz34200))
new_mkVBalBranch3MkVBalBranch131(zzz929, zzz930, zzz931, zzz932, zzz933, zzz934, zzz935, zzz936, zzz937, zzz938, zzz939, Succ(zzz10020), dc) → new_mkVBalBranch3MkVBalBranch132(zzz929, zzz930, zzz931, zzz932, zzz933, zzz934, zzz935, zzz936, zzz937, zzz938, zzz939, Succ(zzz10020), Succ(zzz936), dc)
new_mkVBalBranch3MkVBalBranch131(zzz929, zzz930, zzz931, zzz932, zzz933, zzz934, zzz935, zzz936, zzz937, zzz938, zzz939, Zero, dc) → new_mkVBalBranch3MkVBalBranch132(zzz929, zzz930, zzz931, zzz932, zzz933, zzz934, zzz935, zzz936, zzz937, zzz938, zzz939, Zero, Succ(zzz936), dc)
new_mkVBalBranch3MkVBalBranch132(zzz2033, zzz2034, zzz2035, zzz2036, zzz2037, zzz2038, zzz2039, zzz2040, zzz2041, zzz2042, zzz2043, Zero, Succ(zzz20450), fg) → new_mkBalBranch(zzz2038, zzz2039, zzz2041, new_mkVBalBranch3(zzz2043, zzz2042, Branch(zzz2033, zzz2034, Pos(Succ(zzz2035)), zzz2036, zzz2037), fg), ty_Ordering, fg)
new_mkBalBranch(zzz2930, zzz2931, zzz2127, zzz2934, da, db) → new_mkBalBranch6MkBalBranch5(zzz2934, zzz2127, zzz2930, zzz2931, new_primPlusInt2(new_mkBalBranch6Size_l(zzz2934, zzz2127, zzz2930, zzz2931, db, da), zzz2934, zzz2127, zzz2930, zzz2931, db, da), da, db)
new_mkBalBranch6Size_l(zzz2934, zzz2127, zzz2930, zzz2931, db, da) → new_sizeFM(zzz2127, da, db)
new_primPlusInt2(Pos(zzz21410), zzz2934, zzz2127, zzz2930, zzz2931, db, da) → new_primPlusInt0(zzz21410, new_sizeFM(zzz2934, da, db))
new_primPlusInt2(Neg(zzz21410), zzz2934, zzz2127, zzz2930, zzz2931, db, da) → new_primPlusInt1(zzz21410, new_sizeFM(zzz2934, da, db))
new_mkBalBranch6MkBalBranch5(zzz2934, zzz2127, zzz2930, zzz2931, Neg(Succ(zzz213900)), da, db) → new_mkBalBranch6MkBalBranch51(zzz2934, zzz2127, zzz2930, zzz2931, da, db)
new_mkBalBranch6MkBalBranch5(zzz2934, zzz2127, zzz2930, zzz2931, Pos(Succ(Succ(Zero))), da, db) → new_mkBalBranch6MkBalBranch50(zzz2934, zzz2127, zzz2930, zzz2931, da, db)
new_mkBalBranch6MkBalBranch5(zzz2934, zzz2127, zzz2930, zzz2931, Pos(Succ(Zero)), da, db) → new_mkBalBranch6MkBalBranch51(zzz2934, zzz2127, zzz2930, zzz2931, da, db)
new_mkBalBranch6MkBalBranch5(zzz2934, zzz2127, zzz2930, zzz2931, Neg(Zero), da, db) → new_mkBalBranch6MkBalBranch51(zzz2934, zzz2127, zzz2930, zzz2931, da, db)
new_mkBalBranch6MkBalBranch5(zzz2934, zzz2127, zzz2930, zzz2931, Pos(Succ(Succ(Succ(zzz21390000)))), da, db) → new_mkBalBranch6MkBalBranch50(zzz2934, zzz2127, zzz2930, zzz2931, da, db)
new_mkBalBranch6MkBalBranch5(zzz2934, zzz2127, zzz2930, zzz2931, Pos(Zero), da, db) → new_mkBalBranch6MkBalBranch51(zzz2934, zzz2127, zzz2930, zzz2931, da, db)
new_mkBalBranch6MkBalBranch51(zzz2934, zzz2127, zzz2930, zzz2931, da, db) → new_mkBranch(Zero, zzz2930, zzz2931, zzz2127, zzz2934, da, db)
new_mkBalBranch6MkBalBranch50(zzz2934, zzz2127, zzz2930, zzz2931, da, db) → new_mkBalBranch6MkBalBranch410(zzz2934, zzz2127, zzz2930, zzz2931, new_mkBalBranch6Size_l(zzz2934, zzz2127, zzz2930, zzz2931, db, da), da, db)
new_mkBalBranch6MkBalBranch410(zzz2934, zzz2127, zzz2930, zzz2931, zzz2206, da, db) → new_mkBalBranch6MkBalBranch411(zzz2934, zzz2127, zzz2930, zzz2931, new_mkBalBranch6Size_r(zzz2934, zzz2127, zzz2930, zzz2931, db, da), zzz2206, da, db)
new_mkBalBranch6Size_r(zzz2934, zzz2127, zzz2930, zzz2931, db, da) → new_sizeFM(zzz2934, da, db)
new_mkBalBranch6MkBalBranch411(zzz2934, zzz2127, zzz2930, zzz2931, Neg(Zero), Pos(zzz22060), da, db) → new_mkBalBranch6MkBalBranch416(zzz2934, zzz2127, zzz2930, zzz2931, new_primMulNat(zzz22060), da, db)
new_mkBalBranch6MkBalBranch411(zzz2934, zzz2127, zzz2930, zzz2931, Neg(Zero), Neg(zzz22060), da, db) → new_mkBalBranch6MkBalBranch413(zzz2934, zzz2127, zzz2930, zzz2931, new_primMulNat(zzz22060), da, db)
new_mkBalBranch6MkBalBranch411(zzz2934, zzz2127, zzz2930, zzz2931, Pos(Succ(zzz222100)), Neg(zzz22060), da, db) → new_mkBalBranch6MkBalBranch415(zzz2934, zzz2127, zzz2930, zzz2931, zzz222100, new_primMulNat(zzz22060), da, db)
new_mkBalBranch6MkBalBranch411(zzz2934, zzz2127, zzz2930, zzz2931, Pos(Zero), Pos(zzz22060), da, db) → new_mkBalBranch6MkBalBranch414(zzz2934, zzz2127, zzz2930, zzz2931, new_primMulNat(zzz22060), da, db)
new_mkBalBranch6MkBalBranch411(zzz2934, zzz2127, zzz2930, zzz2931, Pos(Succ(zzz222100)), Pos(zzz22060), da, db) → new_mkBalBranch6MkBalBranch44(zzz2934, zzz2127, zzz2930, zzz2931, zzz222100, new_primMulNat(zzz22060), da, db)
new_mkBalBranch6MkBalBranch411(zzz2934, zzz2127, zzz2930, zzz2931, Neg(Succ(zzz222100)), Neg(zzz22060), da, db) → new_mkBalBranch6MkBalBranch46(zzz2934, zzz2127, zzz2930, zzz2931, zzz222100, new_primMulNat(zzz22060), da, db)
new_mkBalBranch6MkBalBranch411(zzz2934, zzz2127, zzz2930, zzz2931, Pos(Zero), Neg(zzz22060), da, db) → new_mkBalBranch6MkBalBranch48(zzz2934, zzz2127, zzz2930, zzz2931, new_primMulNat(zzz22060), da, db)
new_mkBalBranch6MkBalBranch411(zzz2934, zzz2127, zzz2930, zzz2931, Neg(Succ(zzz222100)), Pos(zzz22060), da, db) → new_mkBalBranch6MkBalBranch42(zzz2934, zzz2127, zzz2930, zzz2931, zzz222100, new_primMulNat(zzz22060), da, db)
new_primMulNat(Zero) → Zero
new_primMulNat(Succ(zzz206300)) → new_primPlusNat2(new_primMulNat0(zzz206300), Succ(zzz206300))
new_mkBalBranch6MkBalBranch42(zzz2934, zzz2127, zzz2930, zzz2931, zzz222100, zzz2240, da, db) → new_mkBalBranch6MkBalBranch43(zzz2934, zzz2127, zzz2930, zzz2931, da, db)
new_mkBalBranch6MkBalBranch43(zzz2934, zzz2127, zzz2930, zzz2931, da, db) → new_mkBalBranch6MkBalBranch41(zzz2934, zzz2127, zzz2930, zzz2931, da, db)
new_mkBalBranch6MkBalBranch41(zzz2934, zzz2127, zzz2930, zzz2931, da, db) → new_mkBalBranch6MkBalBranch310(zzz2934, zzz2127, zzz2930, zzz2931, new_mkBalBranch6Size_l(zzz2934, zzz2127, zzz2930, zzz2931, db, da), new_mkBalBranch6Size_r(zzz2934, zzz2127, zzz2930, zzz2931, db, da), da, db)
new_mkBalBranch6MkBalBranch310(zzz2934, zzz2127, zzz2930, zzz2931, Pos(Zero), Neg(zzz22450), da, db) → new_mkBalBranch6MkBalBranch315(zzz2934, zzz2127, zzz2930, zzz2931, new_primMulNat(zzz22450), da, db)
new_mkBalBranch6MkBalBranch310(zzz2934, zzz2127, zzz2930, zzz2931, Neg(Zero), Pos(zzz22450), da, db) → new_mkBalBranch6MkBalBranch30(zzz2934, zzz2127, zzz2930, zzz2931, new_primMulNat(zzz22450), da, db)
new_mkBalBranch6MkBalBranch310(zzz2934, zzz2127, zzz2930, zzz2931, Neg(Zero), Neg(zzz22450), da, db) → new_mkBalBranch6MkBalBranch314(zzz2934, zzz2127, zzz2930, zzz2931, new_primMulNat(zzz22450), da, db)
new_mkBalBranch6MkBalBranch310(zzz2934, zzz2127, zzz2930, zzz2931, Neg(Succ(zzz224400)), Neg(zzz22450), da, db) → new_mkBalBranch6MkBalBranch37(zzz2934, zzz2127, zzz2930, zzz2931, zzz224400, new_primMulNat(zzz22450), da, db)
new_mkBalBranch6MkBalBranch310(zzz2934, zzz2127, zzz2930, zzz2931, Pos(Succ(zzz224400)), Neg(zzz22450), da, db) → new_mkBalBranch6MkBalBranch312(zzz2934, zzz2127, zzz2930, zzz2931, zzz224400, new_primMulNat(zzz22450), da, db)
new_mkBalBranch6MkBalBranch310(zzz2934, zzz2127, zzz2930, zzz2931, Neg(Succ(zzz224400)), Pos(zzz22450), da, db) → new_mkBalBranch6MkBalBranch34(zzz2934, zzz2127, zzz2930, zzz2931, zzz224400, new_primMulNat(zzz22450), da, db)
new_mkBalBranch6MkBalBranch310(zzz2934, zzz2127, zzz2930, zzz2931, Pos(Zero), Pos(zzz22450), da, db) → new_mkBalBranch6MkBalBranch35(zzz2934, zzz2127, zzz2930, zzz2931, new_primMulNat(zzz22450), da, db)
new_mkBalBranch6MkBalBranch310(zzz2934, zzz2127, zzz2930, zzz2931, Pos(Succ(zzz224400)), Pos(zzz22450), da, db) → new_mkBalBranch6MkBalBranch311(zzz2934, zzz2127, zzz2930, zzz2931, zzz224400, new_primMulNat(zzz22450), da, db)
new_mkBalBranch6MkBalBranch311(zzz2934, zzz2127, zzz2930, zzz2931, zzz224400, zzz2248, da, db) → new_mkBalBranch6MkBalBranch38(zzz2934, zzz2127, zzz2930, zzz2931, zzz224400, zzz2248, da, db)
new_mkBalBranch6MkBalBranch38(zzz2934, zzz2127, zzz2930, zzz2931, zzz224400, Succ(zzz22480), da, db) → new_mkBalBranch6MkBalBranch39(zzz2934, zzz2127, zzz2930, zzz2931, zzz224400, zzz22480, da, db)
new_mkBalBranch6MkBalBranch38(zzz2934, zzz2127, zzz2930, zzz2931, zzz224400, Zero, da, db) → new_mkBalBranch6MkBalBranch33(zzz2934, zzz2127, zzz2930, zzz2931, da, db)
new_mkBalBranch6MkBalBranch33(zzz2934, Branch(zzz21270, zzz21271, zzz21272, zzz21273, zzz21274), zzz2930, zzz2931, da, db) → new_mkBalBranch6MkBalBranch113(zzz2934, zzz21270, zzz21271, zzz21272, zzz21273, zzz21274, zzz2930, zzz2931, new_sizeFM(zzz21274, da, db), new_sizeFM(zzz21273, da, db), da, db)
new_mkBalBranch6MkBalBranch33(zzz2934, EmptyFM, zzz2930, zzz2931, da, db) → error([])
new_mkBalBranch6MkBalBranch113(zzz2934, zzz21270, zzz21271, zzz21272, zzz21273, zzz21274, zzz2930, zzz2931, Pos(Zero), Pos(zzz22630), da, db) → new_mkBalBranch6MkBalBranch116(zzz2934, zzz21270, zzz21271, zzz21272, zzz21273, zzz21274, zzz2930, zzz2931, new_primMulNat2(zzz22630), da, db)
new_mkBalBranch6MkBalBranch113(zzz2934, zzz21270, zzz21271, zzz21272, zzz21273, zzz21274, zzz2930, zzz2931, Neg(Zero), Neg(zzz22630), da, db) → new_mkBalBranch6MkBalBranch110(zzz2934, zzz21270, zzz21271, zzz21272, zzz21273, zzz21274, zzz2930, zzz2931, new_primMulNat2(zzz22630), da, db)
new_mkBalBranch6MkBalBranch113(zzz2934, zzz21270, zzz21271, zzz21272, zzz21273, zzz21274, zzz2930, zzz2931, Neg(Succ(zzz226200)), Pos(zzz22630), da, db) → new_mkBalBranch6MkBalBranch118(zzz2934, zzz21270, zzz21271, zzz21272, zzz21273, zzz21274, zzz2930, zzz2931, zzz226200, new_primMulNat2(zzz22630), da, db)
new_mkBalBranch6MkBalBranch113(zzz2934, zzz21270, zzz21271, zzz21272, zzz21273, zzz21274, zzz2930, zzz2931, Pos(Zero), Neg(zzz22630), da, db) → new_mkBalBranch6MkBalBranch117(zzz2934, zzz21270, zzz21271, zzz21272, zzz21273, zzz21274, zzz2930, zzz2931, new_primMulNat2(zzz22630), da, db)
new_mkBalBranch6MkBalBranch113(zzz2934, zzz21270, zzz21271, zzz21272, zzz21273, zzz21274, zzz2930, zzz2931, Neg(Zero), Pos(zzz22630), da, db) → new_mkBalBranch6MkBalBranch1110(zzz2934, zzz21270, zzz21271, zzz21272, zzz21273, zzz21274, zzz2930, zzz2931, new_primMulNat2(zzz22630), da, db)
new_mkBalBranch6MkBalBranch113(zzz2934, zzz21270, zzz21271, zzz21272, zzz21273, zzz21274, zzz2930, zzz2931, Pos(Succ(zzz226200)), Pos(zzz22630), da, db) → new_mkBalBranch6MkBalBranch114(zzz2934, zzz21270, zzz21271, zzz21272, zzz21273, zzz21274, zzz2930, zzz2931, zzz226200, new_primMulNat2(zzz22630), da, db)
new_mkBalBranch6MkBalBranch113(zzz2934, zzz21270, zzz21271, zzz21272, zzz21273, zzz21274, zzz2930, zzz2931, Pos(Succ(zzz226200)), Neg(zzz22630), da, db) → new_mkBalBranch6MkBalBranch115(zzz2934, zzz21270, zzz21271, zzz21272, zzz21273, zzz21274, zzz2930, zzz2931, zzz226200, new_primMulNat2(zzz22630), da, db)
new_mkBalBranch6MkBalBranch113(zzz2934, zzz21270, zzz21271, zzz21272, zzz21273, zzz21274, zzz2930, zzz2931, Neg(Succ(zzz226200)), Neg(zzz22630), da, db) → new_mkBalBranch6MkBalBranch119(zzz2934, zzz21270, zzz21271, zzz21272, zzz21273, zzz21274, zzz2930, zzz2931, zzz226200, new_primMulNat2(zzz22630), da, db)
new_primMulNat2(Succ(zzz224700)) → new_primPlusNat2(new_primPlusNat2(Zero, Succ(zzz224700)), Succ(zzz224700))
new_primMulNat2(Zero) → Zero
new_mkBalBranch6MkBalBranch119(zzz2934, zzz21270, zzz21271, zzz21272, zzz21273, zzz21274, zzz2930, zzz2931, zzz226200, zzz2276, da, db) → new_mkBalBranch6MkBalBranch1111(zzz2934, zzz21270, zzz21271, zzz21272, zzz21273, zzz21274, zzz2930, zzz2931, zzz2276, zzz226200, da, db)
new_mkBalBranch6MkBalBranch1111(zzz2934, zzz21270, zzz21271, zzz21272, zzz21273, zzz21274, zzz2930, zzz2931, Succ(zzz22760), zzz226200, da, db) → new_mkBalBranch6MkBalBranch1113(zzz2934, zzz21270, zzz21271, zzz21272, zzz21273, zzz21274, zzz2930, zzz2931, zzz22760, zzz226200, da, db)
new_mkBalBranch6MkBalBranch1111(zzz2934, zzz21270, zzz21271, zzz21272, zzz21273, zzz21274, zzz2930, zzz2931, Zero, zzz226200, da, db) → new_mkBalBranch6MkBalBranch1112(zzz2934, zzz21270, zzz21271, zzz21272, zzz21273, zzz21274, zzz2930, zzz2931, da, db)
new_mkBalBranch6MkBalBranch1112(zzz2934, zzz21270, zzz21271, zzz21272, zzz21273, zzz21274, zzz2930, zzz2931, da, db) → new_mkBranch(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))), zzz21270, zzz21271, zzz21273, new_mkBranch(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))), zzz2930, zzz2931, zzz21274, zzz2934, da, db), da, db)
new_mkBalBranch6MkBalBranch1113(zzz2934, zzz21270, zzz21271, zzz21272, zzz21273, zzz21274, zzz2930, zzz2931, Succ(zzz2262000), Succ(zzz227000), da, db) → new_mkBalBranch6MkBalBranch1113(zzz2934, zzz21270, zzz21271, zzz21272, zzz21273, zzz21274, zzz2930, zzz2931, zzz2262000, zzz227000, da, db)
new_mkBalBranch6MkBalBranch1113(zzz2934, zzz21270, zzz21271, zzz21272, zzz21273, zzz21274, zzz2930, zzz2931, Zero, Zero, da, db) → new_mkBalBranch6MkBalBranch112(zzz2934, zzz21270, zzz21271, zzz21272, zzz21273, zzz21274, zzz2930, zzz2931, da, db)
new_mkBalBranch6MkBalBranch1113(zzz2934, zzz21270, zzz21271, zzz21272, zzz21273, zzz21274, zzz2930, zzz2931, Succ(zzz2262000), Zero, da, db) → new_mkBalBranch6MkBalBranch1114(zzz2934, zzz21270, zzz21271, zzz21272, zzz21273, zzz21274, zzz2930, zzz2931, da, db)
new_mkBalBranch6MkBalBranch1113(zzz2934, zzz21270, zzz21271, zzz21272, zzz21273, zzz21274, zzz2930, zzz2931, Zero, Succ(zzz227000), da, db) → new_mkBalBranch6MkBalBranch1112(zzz2934, zzz21270, zzz21271, zzz21272, zzz21273, zzz21274, zzz2930, zzz2931, da, db)
new_mkBalBranch6MkBalBranch1114(zzz2934, zzz21270, zzz21271, zzz21272, zzz21273, zzz21274, zzz2930, zzz2931, da, db) → new_mkBalBranch6MkBalBranch1115(zzz2934, zzz21270, zzz21271, zzz21272, zzz21273, zzz21274, zzz2930, zzz2931, da, db)
new_mkBalBranch6MkBalBranch1115(zzz2934, zzz21270, zzz21271, zzz21272, zzz21273, EmptyFM, zzz2930, zzz2931, da, db) → error([])
new_mkBalBranch6MkBalBranch1115(zzz2934, zzz21270, zzz21271, zzz21272, zzz21273, Branch(zzz212740, zzz212741, zzz212742, zzz212743, zzz212744), zzz2930, zzz2931, da, db) → new_mkBranch(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))), zzz212740, zzz212741, new_mkBranch(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))), zzz21270, zzz21271, zzz21273, zzz212743, da, db), new_mkBranch(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))), zzz2930, zzz2931, zzz212744, zzz2934, da, db), da, db)
new_mkBalBranch6MkBalBranch112(zzz2934, zzz21270, zzz21271, zzz21272, zzz21273, zzz21274, zzz2930, zzz2931, da, db) → new_mkBalBranch6MkBalBranch1115(zzz2934, zzz21270, zzz21271, zzz21272, zzz21273, zzz21274, zzz2930, zzz2931, da, db)
new_mkBalBranch6MkBalBranch115(zzz2934, zzz21270, zzz21271, zzz21272, zzz21273, zzz21274, zzz2930, zzz2931, zzz226200, zzz2271, da, db) → new_mkBalBranch6MkBalBranch1114(zzz2934, zzz21270, zzz21271, zzz21272, zzz21273, zzz21274, zzz2930, zzz2931, da, db)
new_mkBalBranch6MkBalBranch114(zzz2934, zzz21270, zzz21271, zzz21272, zzz21273, zzz21274, zzz2930, zzz2931, zzz226200, zzz2270, da, db) → new_mkBalBranch6MkBalBranch111(zzz2934, zzz21270, zzz21271, zzz21272, zzz21273, zzz21274, zzz2930, zzz2931, zzz226200, zzz2270, da, db)
new_mkBalBranch6MkBalBranch111(zzz2934, zzz21270, zzz21271, zzz21272, zzz21273, zzz21274, zzz2930, zzz2931, zzz226200, Succ(zzz22700), da, db) → new_mkBalBranch6MkBalBranch1113(zzz2934, zzz21270, zzz21271, zzz21272, zzz21273, zzz21274, zzz2930, zzz2931, zzz226200, zzz22700, da, db)
new_mkBalBranch6MkBalBranch111(zzz2934, zzz21270, zzz21271, zzz21272, zzz21273, zzz21274, zzz2930, zzz2931, zzz226200, Zero, da, db) → new_mkBalBranch6MkBalBranch1114(zzz2934, zzz21270, zzz21271, zzz21272, zzz21273, zzz21274, zzz2930, zzz2931, da, db)
new_mkBalBranch6MkBalBranch1110(zzz2934, zzz21270, zzz21271, zzz21272, zzz21273, zzz21274, zzz2930, zzz2931, Zero, da, db) → new_mkBalBranch6MkBalBranch112(zzz2934, zzz21270, zzz21271, zzz21272, zzz21273, zzz21274, zzz2930, zzz2931, da, db)
new_mkBalBranch6MkBalBranch1110(zzz2934, zzz21270, zzz21271, zzz21272, zzz21273, zzz21274, zzz2930, zzz2931, Succ(zzz22770), da, db) → new_mkBalBranch6MkBalBranch1112(zzz2934, zzz21270, zzz21271, zzz21272, zzz21273, zzz21274, zzz2930, zzz2931, da, db)
new_mkBalBranch6MkBalBranch117(zzz2934, zzz21270, zzz21271, zzz21272, zzz21273, zzz21274, zzz2930, zzz2931, Zero, da, db) → new_mkBalBranch6MkBalBranch112(zzz2934, zzz21270, zzz21271, zzz21272, zzz21273, zzz21274, zzz2930, zzz2931, da, db)
new_mkBalBranch6MkBalBranch117(zzz2934, zzz21270, zzz21271, zzz21272, zzz21273, zzz21274, zzz2930, zzz2931, Succ(zzz22740), da, db) → new_mkBalBranch6MkBalBranch1114(zzz2934, zzz21270, zzz21271, zzz21272, zzz21273, zzz21274, zzz2930, zzz2931, da, db)
new_mkBalBranch6MkBalBranch118(zzz2934, zzz21270, zzz21271, zzz21272, zzz21273, zzz21274, zzz2930, zzz2931, zzz226200, zzz2275, da, db) → new_mkBalBranch6MkBalBranch1112(zzz2934, zzz21270, zzz21271, zzz21272, zzz21273, zzz21274, zzz2930, zzz2931, da, db)
new_mkBalBranch6MkBalBranch110(zzz2934, zzz21270, zzz21271, zzz21272, zzz21273, zzz21274, zzz2930, zzz2931, Zero, da, db) → new_mkBalBranch6MkBalBranch112(zzz2934, zzz21270, zzz21271, zzz21272, zzz21273, zzz21274, zzz2930, zzz2931, da, db)
new_mkBalBranch6MkBalBranch110(zzz2934, zzz21270, zzz21271, zzz21272, zzz21273, zzz21274, zzz2930, zzz2931, Succ(zzz22780), da, db) → new_mkBalBranch6MkBalBranch111(zzz2934, zzz21270, zzz21271, zzz21272, zzz21273, zzz21274, zzz2930, zzz2931, zzz22780, Zero, da, db)
new_mkBalBranch6MkBalBranch116(zzz2934, zzz21270, zzz21271, zzz21272, zzz21273, zzz21274, zzz2930, zzz2931, Succ(zzz22730), da, db) → new_mkBalBranch6MkBalBranch1111(zzz2934, zzz21270, zzz21271, zzz21272, zzz21273, zzz21274, zzz2930, zzz2931, Zero, zzz22730, da, db)
new_mkBalBranch6MkBalBranch116(zzz2934, zzz21270, zzz21271, zzz21272, zzz21273, zzz21274, zzz2930, zzz2931, Zero, da, db) → new_mkBalBranch6MkBalBranch112(zzz2934, zzz21270, zzz21271, zzz21272, zzz21273, zzz21274, zzz2930, zzz2931, da, db)
new_mkBalBranch6MkBalBranch39(zzz2934, zzz2127, zzz2930, zzz2931, Succ(zzz2244000), Zero, da, db) → new_mkBalBranch6MkBalBranch33(zzz2934, zzz2127, zzz2930, zzz2931, da, db)
new_mkBalBranch6MkBalBranch39(zzz2934, zzz2127, zzz2930, zzz2931, Succ(zzz2244000), Succ(zzz224800), da, db) → new_mkBalBranch6MkBalBranch39(zzz2934, zzz2127, zzz2930, zzz2931, zzz2244000, zzz224800, da, db)
new_mkBalBranch6MkBalBranch39(zzz2934, zzz2127, zzz2930, zzz2931, Zero, Succ(zzz224800), da, db) → new_mkBalBranch6MkBalBranch31(zzz2934, zzz2127, zzz2930, zzz2931, da, db)
new_mkBalBranch6MkBalBranch39(zzz2934, zzz2127, zzz2930, zzz2931, Zero, Zero, da, db) → new_mkBalBranch6MkBalBranch32(zzz2934, zzz2127, zzz2930, zzz2931, da, db)
new_mkBalBranch6MkBalBranch32(zzz2934, zzz2127, zzz2930, zzz2931, da, db) → new_mkBalBranch6MkBalBranch313(zzz2934, zzz2127, zzz2930, zzz2931, da, db)
new_mkBalBranch6MkBalBranch313(zzz2934, zzz2127, zzz2930, zzz2931, da, db) → new_mkBranch(Succ(Zero), zzz2930, zzz2931, zzz2127, zzz2934, da, db)
new_mkBalBranch6MkBalBranch31(zzz2934, zzz2127, zzz2930, zzz2931, da, db) → new_mkBalBranch6MkBalBranch313(zzz2934, zzz2127, zzz2930, zzz2931, da, db)
new_mkBalBranch6MkBalBranch35(zzz2934, zzz2127, zzz2930, zzz2931, Succ(zzz22500), da, db) → new_mkBalBranch6MkBalBranch36(zzz2934, zzz2127, zzz2930, zzz2931, Zero, zzz22500, da, db)
new_mkBalBranch6MkBalBranch35(zzz2934, zzz2127, zzz2930, zzz2931, Zero, da, db) → new_mkBalBranch6MkBalBranch32(zzz2934, zzz2127, zzz2930, zzz2931, da, db)
new_mkBalBranch6MkBalBranch36(zzz2934, zzz2127, zzz2930, zzz2931, Zero, zzz224400, da, db) → new_mkBalBranch6MkBalBranch31(zzz2934, zzz2127, zzz2930, zzz2931, da, db)
new_mkBalBranch6MkBalBranch34(zzz2934, zzz2127, zzz2930, zzz2931, zzz224400, zzz2252, da, db) → new_mkBalBranch6MkBalBranch31(zzz2934, zzz2127, zzz2930, zzz2931, da, db)
new_mkBalBranch6MkBalBranch312(zzz2934, zzz2127, zzz2930, zzz2931, zzz224400, zzz2249, da, db) → new_mkBalBranch6MkBalBranch33(zzz2934, zzz2127, zzz2930, zzz2931, da, db)
new_mkBalBranch6MkBalBranch37(zzz2934, zzz2127, zzz2930, zzz2931, zzz224400, zzz2253, da, db) → new_mkBalBranch6MkBalBranch36(zzz2934, zzz2127, zzz2930, zzz2931, zzz2253, zzz224400, da, db)
new_mkBalBranch6MkBalBranch36(zzz2934, zzz2127, zzz2930, zzz2931, Succ(zzz22530), zzz224400, da, db) → new_mkBalBranch6MkBalBranch39(zzz2934, zzz2127, zzz2930, zzz2931, zzz22530, zzz224400, da, db)
new_mkBalBranch6MkBalBranch314(zzz2934, zzz2127, zzz2930, zzz2931, Succ(zzz22550), da, db) → new_mkBalBranch6MkBalBranch38(zzz2934, zzz2127, zzz2930, zzz2931, zzz22550, Zero, da, db)
new_mkBalBranch6MkBalBranch314(zzz2934, zzz2127, zzz2930, zzz2931, Zero, da, db) → new_mkBalBranch6MkBalBranch32(zzz2934, zzz2127, zzz2930, zzz2931, da, db)
new_mkBalBranch6MkBalBranch30(zzz2934, zzz2127, zzz2930, zzz2931, Succ(zzz22540), da, db) → new_mkBalBranch6MkBalBranch31(zzz2934, zzz2127, zzz2930, zzz2931, da, db)
new_mkBalBranch6MkBalBranch30(zzz2934, zzz2127, zzz2930, zzz2931, Zero, da, db) → new_mkBalBranch6MkBalBranch32(zzz2934, zzz2127, zzz2930, zzz2931, da, db)
new_mkBalBranch6MkBalBranch315(zzz2934, zzz2127, zzz2930, zzz2931, Zero, da, db) → new_mkBalBranch6MkBalBranch32(zzz2934, zzz2127, zzz2930, zzz2931, da, db)
new_mkBalBranch6MkBalBranch315(zzz2934, zzz2127, zzz2930, zzz2931, Succ(zzz22510), da, db) → new_mkBalBranch6MkBalBranch33(zzz2934, zzz2127, zzz2930, zzz2931, da, db)
new_mkBalBranch6MkBalBranch48(zzz2934, zzz2127, zzz2930, zzz2931, Zero, da, db) → new_mkBalBranch6MkBalBranch40(zzz2934, zzz2127, zzz2930, zzz2931, da, db)
new_mkBalBranch6MkBalBranch48(zzz2934, zzz2127, zzz2930, zzz2931, Succ(zzz22390), da, db) → new_mkBalBranch6MkBalBranch49(zzz2934, zzz2127, zzz2930, zzz2931, da, db)
new_mkBalBranch6MkBalBranch49(Branch(zzz29340, zzz29341, zzz29342, zzz29343, zzz29344), zzz2127, zzz2930, zzz2931, da, db) → new_mkBalBranch6MkBalBranch017(zzz29340, zzz29341, zzz29342, zzz29343, zzz29344, zzz2127, zzz2930, zzz2931, new_sizeFM(zzz29343, da, db), new_sizeFM(zzz29344, da, db), da, db)
new_mkBalBranch6MkBalBranch49(EmptyFM, zzz2127, zzz2930, zzz2931, da, db) → error([])
new_mkBalBranch6MkBalBranch017(zzz29340, zzz29341, zzz29342, zzz29343, zzz29344, zzz2127, zzz2930, zzz2931, Neg(Zero), Pos(zzz22470), da, db) → new_mkBalBranch6MkBalBranch010(zzz29340, zzz29341, zzz29342, zzz29343, zzz29344, zzz2127, zzz2930, zzz2931, new_primMulNat2(zzz22470), da, db)
new_mkBalBranch6MkBalBranch017(zzz29340, zzz29341, zzz29342, zzz29343, zzz29344, zzz2127, zzz2930, zzz2931, Pos(Zero), Neg(zzz22470), da, db) → new_mkBalBranch6MkBalBranch0111(zzz29340, zzz29341, zzz29342, zzz29343, zzz29344, zzz2127, zzz2930, zzz2931, new_primMulNat2(zzz22470), da, db)
new_mkBalBranch6MkBalBranch017(zzz29340, zzz29341, zzz29342, zzz29343, zzz29344, zzz2127, zzz2930, zzz2931, Neg(Succ(zzz224600)), Neg(zzz22470), da, db) → new_mkBalBranch6MkBalBranch018(zzz29340, zzz29341, zzz29342, zzz29343, zzz29344, zzz2127, zzz2930, zzz2931, new_primMulNat2(zzz22470), zzz224600, da, db)
new_mkBalBranch6MkBalBranch017(zzz29340, zzz29341, zzz29342, zzz29343, zzz29344, zzz2127, zzz2930, zzz2931, Neg(Succ(zzz224600)), Pos(zzz22470), da, db) → new_mkBalBranch6MkBalBranch011(zzz29340, zzz29341, zzz29342, zzz29343, zzz29344, zzz2127, zzz2930, zzz2931, da, db)
new_mkBalBranch6MkBalBranch017(zzz29340, zzz29341, zzz29342, zzz29343, zzz29344, zzz2127, zzz2930, zzz2931, Pos(Succ(zzz224600)), Neg(zzz22470), da, db) → new_mkBalBranch6MkBalBranch015(zzz29340, zzz29341, zzz29342, zzz29343, zzz29344, zzz2127, zzz2930, zzz2931, da, db)
new_mkBalBranch6MkBalBranch017(zzz29340, zzz29341, zzz29342, zzz29343, zzz29344, zzz2127, zzz2930, zzz2931, Neg(Zero), Neg(zzz22470), da, db) → new_mkBalBranch6MkBalBranch019(zzz29340, zzz29341, zzz29342, zzz29343, zzz29344, zzz2127, zzz2930, zzz2931, new_primMulNat2(zzz22470), da, db)
new_mkBalBranch6MkBalBranch017(zzz29340, zzz29341, zzz29342, zzz29343, zzz29344, zzz2127, zzz2930, zzz2931, Pos(Zero), Pos(zzz22470), da, db) → new_mkBalBranch6MkBalBranch0110(zzz29340, zzz29341, zzz29342, zzz29343, zzz29344, zzz2127, zzz2930, zzz2931, new_primMulNat2(zzz22470), da, db)
new_mkBalBranch6MkBalBranch017(zzz29340, zzz29341, zzz29342, zzz29343, zzz29344, zzz2127, zzz2930, zzz2931, Pos(Succ(zzz224600)), Pos(zzz22470), da, db) → new_mkBalBranch6MkBalBranch013(zzz29340, zzz29341, zzz29342, zzz29343, zzz29344, zzz2127, zzz2930, zzz2931, zzz224600, new_primMulNat2(zzz22470), da, db)
new_mkBalBranch6MkBalBranch013(zzz29340, zzz29341, zzz29342, zzz29343, zzz29344, zzz2127, zzz2930, zzz2931, zzz224600, Zero, da, db) → new_mkBalBranch6MkBalBranch015(zzz29340, zzz29341, zzz29342, zzz29343, zzz29344, zzz2127, zzz2930, zzz2931, da, db)
new_mkBalBranch6MkBalBranch013(zzz29340, zzz29341, zzz29342, zzz29343, zzz29344, zzz2127, zzz2930, zzz2931, zzz224600, Succ(zzz22600), da, db) → new_mkBalBranch6MkBalBranch014(zzz29340, zzz29341, zzz29342, zzz29343, zzz29344, zzz2127, zzz2930, zzz2931, zzz224600, zzz22600, da, db)
new_mkBalBranch6MkBalBranch014(zzz29340, zzz29341, zzz29342, zzz29343, zzz29344, zzz2127, zzz2930, zzz2931, Zero, Zero, da, db) → new_mkBalBranch6MkBalBranch012(zzz29340, zzz29341, zzz29342, zzz29343, zzz29344, zzz2127, zzz2930, zzz2931, da, db)
new_mkBalBranch6MkBalBranch014(zzz29340, zzz29341, zzz29342, zzz29343, zzz29344, zzz2127, zzz2930, zzz2931, Succ(zzz2246000), Succ(zzz226000), da, db) → new_mkBalBranch6MkBalBranch014(zzz29340, zzz29341, zzz29342, zzz29343, zzz29344, zzz2127, zzz2930, zzz2931, zzz2246000, zzz226000, da, db)
new_mkBalBranch6MkBalBranch014(zzz29340, zzz29341, zzz29342, zzz29343, zzz29344, zzz2127, zzz2930, zzz2931, Succ(zzz2246000), Zero, da, db) → new_mkBalBranch6MkBalBranch015(zzz29340, zzz29341, zzz29342, zzz29343, zzz29344, zzz2127, zzz2930, zzz2931, da, db)
new_mkBalBranch6MkBalBranch014(zzz29340, zzz29341, zzz29342, zzz29343, zzz29344, zzz2127, zzz2930, zzz2931, Zero, Succ(zzz226000), da, db) → new_mkBalBranch6MkBalBranch011(zzz29340, zzz29341, zzz29342, zzz29343, zzz29344, zzz2127, zzz2930, zzz2931, da, db)
new_mkBalBranch6MkBalBranch011(zzz29340, zzz29341, zzz29342, zzz29343, zzz29344, zzz2127, zzz2930, zzz2931, da, db) → new_mkBranch(Succ(Succ(Zero)), zzz29340, zzz29341, new_mkBranch(Succ(Succ(Succ(Zero))), zzz2930, zzz2931, zzz2127, zzz29343, da, db), zzz29344, da, db)
new_mkBalBranch6MkBalBranch015(zzz29340, zzz29341, zzz29342, zzz29343, zzz29344, zzz2127, zzz2930, zzz2931, da, db) → new_mkBalBranch6MkBalBranch016(zzz29340, zzz29341, zzz29342, zzz29343, zzz29344, zzz2127, zzz2930, zzz2931, da, db)
new_mkBalBranch6MkBalBranch016(zzz29340, zzz29341, zzz29342, EmptyFM, zzz29344, zzz2127, zzz2930, zzz2931, da, db) → error([])
new_mkBalBranch6MkBalBranch016(zzz29340, zzz29341, zzz29342, Branch(zzz293430, zzz293431, zzz293432, zzz293433, zzz293434), zzz29344, zzz2127, zzz2930, zzz2931, da, db) → new_mkBranch(Succ(Succ(Succ(Succ(Zero)))), zzz293430, zzz293431, new_mkBranch(Succ(Succ(Succ(Succ(Succ(Zero))))), zzz2930, zzz2931, zzz2127, zzz293433, da, db), new_mkBranch(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))), zzz29340, zzz29341, zzz293434, zzz29344, da, db), da, db)
new_mkBalBranch6MkBalBranch012(zzz29340, zzz29341, zzz29342, zzz29343, zzz29344, zzz2127, zzz2930, zzz2931, da, db) → new_mkBalBranch6MkBalBranch016(zzz29340, zzz29341, zzz29342, zzz29343, zzz29344, zzz2127, zzz2930, zzz2931, da, db)
new_mkBalBranch6MkBalBranch0110(zzz29340, zzz29341, zzz29342, zzz29343, zzz29344, zzz2127, zzz2930, zzz2931, Zero, da, db) → new_mkBalBranch6MkBalBranch012(zzz29340, zzz29341, zzz29342, zzz29343, zzz29344, zzz2127, zzz2930, zzz2931, da, db)
new_mkBalBranch6MkBalBranch0110(zzz29340, zzz29341, zzz29342, zzz29343, zzz29344, zzz2127, zzz2930, zzz2931, Succ(zzz22560), da, db) → new_mkBalBranch6MkBalBranch018(zzz29340, zzz29341, zzz29342, zzz29343, zzz29344, zzz2127, zzz2930, zzz2931, Zero, zzz22560, da, db)
new_mkBalBranch6MkBalBranch018(zzz29340, zzz29341, zzz29342, zzz29343, zzz29344, zzz2127, zzz2930, zzz2931, Zero, zzz224600, da, db) → new_mkBalBranch6MkBalBranch011(zzz29340, zzz29341, zzz29342, zzz29343, zzz29344, zzz2127, zzz2930, zzz2931, da, db)
new_mkBalBranch6MkBalBranch019(zzz29340, zzz29341, zzz29342, zzz29343, zzz29344, zzz2127, zzz2930, zzz2931, Zero, da, db) → new_mkBalBranch6MkBalBranch012(zzz29340, zzz29341, zzz29342, zzz29343, zzz29344, zzz2127, zzz2930, zzz2931, da, db)
new_mkBalBranch6MkBalBranch019(zzz29340, zzz29341, zzz29342, zzz29343, zzz29344, zzz2127, zzz2930, zzz2931, Succ(zzz22590), da, db) → new_mkBalBranch6MkBalBranch013(zzz29340, zzz29341, zzz29342, zzz29343, zzz29344, zzz2127, zzz2930, zzz2931, zzz22590, Zero, da, db)
new_mkBalBranch6MkBalBranch018(zzz29340, zzz29341, zzz29342, zzz29343, zzz29344, zzz2127, zzz2930, zzz2931, Succ(zzz22610), zzz224600, da, db) → new_mkBalBranch6MkBalBranch014(zzz29340, zzz29341, zzz29342, zzz29343, zzz29344, zzz2127, zzz2930, zzz2931, zzz22610, zzz224600, da, db)
new_mkBalBranch6MkBalBranch0111(zzz29340, zzz29341, zzz29342, zzz29343, zzz29344, zzz2127, zzz2930, zzz2931, Succ(zzz22570), da, db) → new_mkBalBranch6MkBalBranch015(zzz29340, zzz29341, zzz29342, zzz29343, zzz29344, zzz2127, zzz2930, zzz2931, da, db)
new_mkBalBranch6MkBalBranch0111(zzz29340, zzz29341, zzz29342, zzz29343, zzz29344, zzz2127, zzz2930, zzz2931, Zero, da, db) → new_mkBalBranch6MkBalBranch012(zzz29340, zzz29341, zzz29342, zzz29343, zzz29344, zzz2127, zzz2930, zzz2931, da, db)
new_mkBalBranch6MkBalBranch010(zzz29340, zzz29341, zzz29342, zzz29343, zzz29344, zzz2127, zzz2930, zzz2931, Zero, da, db) → new_mkBalBranch6MkBalBranch012(zzz29340, zzz29341, zzz29342, zzz29343, zzz29344, zzz2127, zzz2930, zzz2931, da, db)
new_mkBalBranch6MkBalBranch010(zzz29340, zzz29341, zzz29342, zzz29343, zzz29344, zzz2127, zzz2930, zzz2931, Succ(zzz22580), da, db) → new_mkBalBranch6MkBalBranch011(zzz29340, zzz29341, zzz29342, zzz29343, zzz29344, zzz2127, zzz2930, zzz2931, da, db)
new_mkBalBranch6MkBalBranch40(zzz2934, zzz2127, zzz2930, zzz2931, da, db) → new_mkBalBranch6MkBalBranch41(zzz2934, zzz2127, zzz2930, zzz2931, da, db)
new_mkBalBranch6MkBalBranch46(zzz2934, zzz2127, zzz2930, zzz2931, zzz222100, zzz2241, da, db) → new_mkBalBranch6MkBalBranch47(zzz2934, zzz2127, zzz2930, zzz2931, zzz2241, zzz222100, da, db)
new_mkBalBranch6MkBalBranch47(zzz2934, zzz2127, zzz2930, zzz2931, Zero, zzz222100, da, db) → new_mkBalBranch6MkBalBranch43(zzz2934, zzz2127, zzz2930, zzz2931, da, db)
new_mkBalBranch6MkBalBranch47(zzz2934, zzz2127, zzz2930, zzz2931, Succ(zzz22410), zzz222100, da, db) → new_mkBalBranch6MkBalBranch412(zzz2934, zzz2127, zzz2930, zzz2931, zzz22410, zzz222100, da, db)
new_mkBalBranch6MkBalBranch412(zzz2934, zzz2127, zzz2930, zzz2931, Succ(zzz2221000), Zero, da, db) → new_mkBalBranch6MkBalBranch49(zzz2934, zzz2127, zzz2930, zzz2931, da, db)
new_mkBalBranch6MkBalBranch412(zzz2934, zzz2127, zzz2930, zzz2931, Zero, Succ(zzz223600), da, db) → new_mkBalBranch6MkBalBranch43(zzz2934, zzz2127, zzz2930, zzz2931, da, db)
new_mkBalBranch6MkBalBranch412(zzz2934, zzz2127, zzz2930, zzz2931, Zero, Zero, da, db) → new_mkBalBranch6MkBalBranch40(zzz2934, zzz2127, zzz2930, zzz2931, da, db)
new_mkBalBranch6MkBalBranch412(zzz2934, zzz2127, zzz2930, zzz2931, Succ(zzz2221000), Succ(zzz223600), da, db) → new_mkBalBranch6MkBalBranch412(zzz2934, zzz2127, zzz2930, zzz2931, zzz2221000, zzz223600, da, db)
new_mkBalBranch6MkBalBranch44(zzz2934, zzz2127, zzz2930, zzz2931, zzz222100, zzz2236, da, db) → new_mkBalBranch6MkBalBranch45(zzz2934, zzz2127, zzz2930, zzz2931, zzz222100, zzz2236, da, db)
new_mkBalBranch6MkBalBranch45(zzz2934, zzz2127, zzz2930, zzz2931, zzz222100, Succ(zzz22360), da, db) → new_mkBalBranch6MkBalBranch412(zzz2934, zzz2127, zzz2930, zzz2931, zzz222100, zzz22360, da, db)
new_mkBalBranch6MkBalBranch45(zzz2934, zzz2127, zzz2930, zzz2931, zzz222100, Zero, da, db) → new_mkBalBranch6MkBalBranch49(zzz2934, zzz2127, zzz2930, zzz2931, da, db)
new_mkBalBranch6MkBalBranch414(zzz2934, zzz2127, zzz2930, zzz2931, Succ(zzz22380), da, db) → new_mkBalBranch6MkBalBranch47(zzz2934, zzz2127, zzz2930, zzz2931, Zero, zzz22380, da, db)
new_mkBalBranch6MkBalBranch414(zzz2934, zzz2127, zzz2930, zzz2931, Zero, da, db) → new_mkBalBranch6MkBalBranch40(zzz2934, zzz2127, zzz2930, zzz2931, da, db)
new_mkBalBranch6MkBalBranch415(zzz2934, zzz2127, zzz2930, zzz2931, zzz222100, zzz2237, da, db) → new_mkBalBranch6MkBalBranch49(zzz2934, zzz2127, zzz2930, zzz2931, da, db)
new_mkBalBranch6MkBalBranch413(zzz2934, zzz2127, zzz2930, zzz2931, Zero, da, db) → new_mkBalBranch6MkBalBranch40(zzz2934, zzz2127, zzz2930, zzz2931, da, db)
new_mkBalBranch6MkBalBranch413(zzz2934, zzz2127, zzz2930, zzz2931, Succ(zzz22430), da, db) → new_mkBalBranch6MkBalBranch45(zzz2934, zzz2127, zzz2930, zzz2931, zzz22430, Zero, da, db)
new_mkBalBranch6MkBalBranch416(zzz2934, zzz2127, zzz2930, zzz2931, Succ(zzz22420), da, db) → new_mkBalBranch6MkBalBranch43(zzz2934, zzz2127, zzz2930, zzz2931, da, db)
new_mkBalBranch6MkBalBranch416(zzz2934, zzz2127, zzz2930, zzz2931, Zero, da, db) → new_mkBalBranch6MkBalBranch40(zzz2934, zzz2127, zzz2930, zzz2931, da, db)
new_mkVBalBranch3MkVBalBranch132(zzz2033, zzz2034, zzz2035, zzz2036, zzz2037, zzz2038, zzz2039, zzz2040, zzz2041, zzz2042, zzz2043, Succ(zzz20440), Succ(zzz20450), fg) → new_mkVBalBranch3MkVBalBranch132(zzz2033, zzz2034, zzz2035, zzz2036, zzz2037, zzz2038, zzz2039, zzz2040, zzz2041, zzz2042, zzz2043, zzz20440, zzz20450, fg)
new_mkVBalBranch3MkVBalBranch132(zzz2033, zzz2034, zzz2035, zzz2036, zzz2037, zzz2038, zzz2039, zzz2040, zzz2041, zzz2042, zzz2043, Zero, Zero, fg) → new_mkVBalBranch3MkVBalBranch166(zzz2033, zzz2034, zzz2035, zzz2036, zzz2037, zzz2038, zzz2039, zzz2040, zzz2041, zzz2042, zzz2043, fg)
new_mkVBalBranch3MkVBalBranch132(zzz2033, zzz2034, zzz2035, zzz2036, zzz2037, zzz2038, zzz2039, zzz2040, zzz2041, zzz2042, zzz2043, Succ(zzz20440), Zero, fg) → new_mkVBalBranch3MkVBalBranch166(zzz2033, zzz2034, zzz2035, zzz2036, zzz2037, zzz2038, zzz2039, zzz2040, zzz2041, zzz2042, zzz2043, fg)
new_mkVBalBranch3MkVBalBranch166(zzz2033, zzz2034, zzz2035, zzz2036, zzz2037, zzz2038, zzz2039, zzz2040, zzz2041, zzz2042, zzz2043, fg) → new_mkBranch(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))), GT, zzz2043, Branch(zzz2038, zzz2039, Pos(Succ(zzz2040)), zzz2041, zzz2042), Branch(zzz2033, zzz2034, Pos(Succ(zzz2035)), zzz2036, zzz2037), ty_Ordering, fg)
new_mkVBalBranch3MkVBalBranch252(zzz929, zzz930, zzz931, zzz932, zzz933, zzz934, zzz935, zzz936, zzz937, zzz938, zzz939, Zero, Zero, dc) → new_mkVBalBranch3MkVBalBranch253(zzz929, zzz930, zzz931, zzz932, zzz933, zzz934, zzz935, zzz936, zzz937, zzz938, zzz939, dc)
new_mkVBalBranch3MkVBalBranch252(zzz929, zzz930, zzz931, zzz932, zzz933, zzz934, zzz935, zzz936, zzz937, zzz938, zzz939, Zero, Succ(zzz9410), dc) → new_mkBalBranch(zzz929, zzz930, new_mkVBalBranch3(zzz939, Branch(zzz934, zzz935, Pos(Succ(zzz936)), zzz937, zzz938), zzz932, dc), zzz933, ty_Ordering, dc)
new_mkVBalBranch3MkVBalBranch269(zzz340, zzz341, Succ(zzz34200), zzz343, zzz344, zzz520, zzz521, zzz52200, zzz523, zzz524, zzz31, h) → new_mkVBalBranch3MkVBalBranch147(zzz340, zzz341, zzz34200, zzz343, zzz344, zzz520, zzz521, zzz52200, zzz523, zzz524, zzz31, new_primPlusNat2(new_primMulNat0(zzz34200), Succ(zzz34200)), h)
new_mkVBalBranch3MkVBalBranch269(zzz340, zzz341, Zero, zzz343, zzz344, zzz520, zzz521, zzz52200, zzz523, zzz524, zzz31, h) → new_mkBalBranch(zzz520, zzz521, zzz523, new_mkVBalBranch3(zzz31, zzz524, Branch(zzz340, zzz341, Neg(Zero), zzz343, zzz344), h), ty_Ordering, h)
new_mkVBalBranch3MkVBalBranch147(zzz340, zzz341, zzz34200, zzz343, zzz344, zzz520, zzz521, zzz52200, zzz523, zzz524, zzz31, Succ(zzz1430), h) → new_mkVBalBranch3MkVBalBranch148(zzz340, zzz341, zzz34200, zzz343, zzz344, zzz520, zzz521, zzz52200, zzz523, zzz524, zzz31, h)
new_mkVBalBranch3MkVBalBranch147(zzz340, zzz341, zzz34200, zzz343, zzz344, zzz520, zzz521, zzz52200, zzz523, zzz524, zzz31, Zero, h) → new_mkVBalBranch3MkVBalBranch148(zzz340, zzz341, zzz34200, zzz343, zzz344, zzz520, zzz521, zzz52200, zzz523, zzz524, zzz31, h)
new_mkVBalBranch3MkVBalBranch148(zzz340, zzz341, zzz34200, zzz343, zzz344, zzz520, zzz521, zzz52200, zzz523, zzz524, zzz31, h) → new_mkBalBranch(zzz520, zzz521, zzz523, new_mkVBalBranch3(zzz31, zzz524, Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), h), ty_Ordering, h)
new_mkVBalBranch3MkVBalBranch268(zzz340, zzz341, zzz343, zzz344, zzz520, zzz521, zzz52200, zzz523, zzz524, zzz31, h) → new_mkBalBranch(zzz520, zzz521, zzz523, new_mkVBalBranch3(zzz31, zzz524, Branch(zzz340, zzz341, Pos(Zero), zzz343, zzz344), h), ty_Ordering, h)
new_primPlusNat1(Succ(zzz62000)) → Succ(Succ(new_primPlusNat1(zzz62000)))
new_primPlusNat1(Zero) → Zero
new_primPlusNat3(zzz90, Succ(zzz910)) → Succ(Succ(new_primPlusNat2(zzz90, zzz910)))
new_primPlusNat3(zzz90, Zero) → Succ(zzz90)
new_mkVBalBranch3MkVBalBranch272(zzz340, zzz341, Neg(Zero), zzz343, zzz344, zzz520, zzz521, zzz52200, zzz523, zzz524, zzz31, Succ(zzz690), h) → new_mkVBalBranch3MkVBalBranch245(zzz340, zzz341, zzz343, zzz344, zzz520, zzz521, zzz52200, zzz523, zzz524, zzz31, h)
new_mkVBalBranch3MkVBalBranch272(zzz340, zzz341, Neg(Succ(Succ(Zero))), zzz343, zzz344, zzz520, zzz521, Zero, zzz523, zzz524, zzz31, Succ(Zero), h) → new_mkVBalBranch3MkVBalBranch277(zzz340, zzz341, Succ(Zero), zzz343, zzz344, zzz520, zzz521, zzz523, zzz524, zzz31, Zero, Zero, h)
new_mkVBalBranch3MkVBalBranch272(zzz340, zzz341, Neg(Succ(Succ(Succ(zzz3420000)))), zzz343, zzz344, zzz520, zzz521, Zero, zzz523, zzz524, zzz31, Succ(Zero), h) → new_mkVBalBranch3MkVBalBranch277(zzz340, zzz341, Succ(Succ(zzz3420000)), zzz343, zzz344, zzz520, zzz521, zzz523, zzz524, zzz31, Succ(zzz3420000), Zero, h)
new_mkVBalBranch3MkVBalBranch272(zzz340, zzz341, Pos(zzz3420), zzz343, zzz344, zzz520, zzz521, zzz52200, zzz523, zzz524, zzz31, Zero, h) → new_mkVBalBranch3MkVBalBranch258(zzz340, zzz341, zzz3420, zzz343, zzz344, zzz520, zzz521, zzz52200, zzz523, zzz524, zzz31, h)
new_mkVBalBranch3MkVBalBranch272(zzz340, zzz341, Neg(Succ(Succ(Zero))), zzz343, zzz344, zzz520, zzz521, Zero, zzz523, zzz524, zzz31, Succ(Succ(zzz6900)), h) → new_mkVBalBranch3MkVBalBranch277(zzz340, zzz341, Succ(Zero), zzz343, zzz344, zzz520, zzz521, zzz523, zzz524, zzz31, Zero, Succ(zzz6900), h)
new_mkVBalBranch3MkVBalBranch272(zzz340, zzz341, Neg(Succ(Zero)), zzz343, zzz344, zzz520, zzz521, zzz52200, zzz523, zzz524, zzz31, Succ(zzz690), h) → new_mkVBalBranch3MkVBalBranch254(zzz340, zzz341, zzz343, zzz344, zzz520, zzz521, zzz52200, zzz523, zzz524, zzz31, h)
new_mkVBalBranch3MkVBalBranch272(zzz340, zzz341, Neg(Succ(Succ(zzz342000))), zzz343, zzz344, zzz520, zzz521, Succ(zzz522000), zzz523, zzz524, zzz31, Zero, h) → new_mkVBalBranch3MkVBalBranch255(zzz340, zzz341, Succ(zzz342000), zzz343, zzz344, zzz520, zzz521, zzz522000, zzz523, zzz524, zzz31, zzz342000, zzz522000, h)
new_mkVBalBranch3MkVBalBranch272(zzz340, zzz341, Neg(Zero), zzz343, zzz344, zzz520, zzz521, zzz52200, zzz523, zzz524, zzz31, Zero, h) → new_mkVBalBranch3MkVBalBranch245(zzz340, zzz341, zzz343, zzz344, zzz520, zzz521, zzz52200, zzz523, zzz524, zzz31, h)
new_mkVBalBranch3MkVBalBranch272(zzz340, zzz341, Neg(Succ(Succ(Zero))), zzz343, zzz344, zzz520, zzz521, Succ(zzz522000), zzz523, zzz524, zzz31, Succ(Zero), h) → new_mkVBalBranch3MkVBalBranch255(zzz340, zzz341, Succ(Zero), zzz343, zzz344, zzz520, zzz521, zzz522000, zzz523, zzz524, zzz31, Zero, Succ(zzz522000), h)
new_mkVBalBranch3MkVBalBranch272(zzz340, zzz341, Pos(zzz3420), zzz343, zzz344, zzz520, zzz521, zzz52200, zzz523, zzz524, zzz31, Succ(zzz690), h) → new_mkVBalBranch3MkVBalBranch258(zzz340, zzz341, zzz3420, zzz343, zzz344, zzz520, zzz521, zzz52200, zzz523, zzz524, zzz31, h)
new_mkVBalBranch3MkVBalBranch272(zzz340, zzz341, Neg(Succ(Succ(Succ(zzz3420000)))), zzz343, zzz344, zzz520, zzz521, Succ(zzz522000), zzz523, zzz524, zzz31, Succ(Succ(zzz6900)), h) → new_mkVBalBranch3MkVBalBranch255(zzz340, zzz341, Succ(Succ(zzz3420000)), zzz343, zzz344, zzz520, zzz521, zzz522000, zzz523, zzz524, zzz31, Succ(zzz3420000), Succ(Succ(new_primPlusNat2(zzz6900, zzz522000))), h)
new_mkVBalBranch3MkVBalBranch272(zzz340, zzz341, Neg(Succ(Succ(Succ(zzz3420000)))), zzz343, zzz344, zzz520, zzz521, Succ(zzz522000), zzz523, zzz524, zzz31, Succ(Zero), h) → new_mkVBalBranch3MkVBalBranch255(zzz340, zzz341, Succ(Succ(zzz3420000)), zzz343, zzz344, zzz520, zzz521, zzz522000, zzz523, zzz524, zzz31, Succ(zzz3420000), Succ(zzz522000), h)
new_mkVBalBranch3MkVBalBranch272(zzz340, zzz341, Neg(Succ(Succ(Succ(zzz3420000)))), zzz343, zzz344, zzz520, zzz521, Zero, zzz523, zzz524, zzz31, Succ(Succ(zzz6900)), h) → new_mkVBalBranch3MkVBalBranch277(zzz340, zzz341, Succ(Succ(zzz3420000)), zzz343, zzz344, zzz520, zzz521, zzz523, zzz524, zzz31, Succ(zzz3420000), Succ(zzz6900), h)
new_mkVBalBranch3MkVBalBranch272(zzz340, zzz341, Neg(Succ(Zero)), zzz343, zzz344, zzz520, zzz521, Zero, zzz523, zzz524, zzz31, Zero, h) → new_mkVBalBranch3MkVBalBranch273(zzz340, zzz341, Zero, zzz343, zzz344, zzz520, zzz521, zzz523, zzz524, zzz31, h)
new_mkVBalBranch3MkVBalBranch272(zzz340, zzz341, Neg(Succ(Zero)), zzz343, zzz344, zzz520, zzz521, Succ(zzz522000), zzz523, zzz524, zzz31, Zero, h) → new_mkVBalBranch3MkVBalBranch254(zzz340, zzz341, zzz343, zzz344, zzz520, zzz521, Succ(zzz522000), zzz523, zzz524, zzz31, h)
new_mkVBalBranch3MkVBalBranch272(zzz340, zzz341, Neg(Succ(Succ(Zero))), zzz343, zzz344, zzz520, zzz521, Succ(zzz522000), zzz523, zzz524, zzz31, Succ(Succ(zzz6900)), h) → new_mkVBalBranch3MkVBalBranch255(zzz340, zzz341, Succ(Zero), zzz343, zzz344, zzz520, zzz521, zzz522000, zzz523, zzz524, zzz31, Zero, Succ(Succ(new_primPlusNat2(zzz6900, zzz522000))), h)
new_mkVBalBranch3MkVBalBranch272(zzz340, zzz341, Neg(Succ(Succ(zzz342000))), zzz343, zzz344, zzz520, zzz521, Zero, zzz523, zzz524, zzz31, Zero, h) → new_mkVBalBranch3MkVBalBranch259(zzz340, zzz341, zzz342000, zzz343, zzz344, zzz520, zzz521, zzz523, zzz524, zzz31, h)
new_mkVBalBranch3MkVBalBranch259(zzz340, zzz341, zzz342000, zzz343, zzz344, zzz520, zzz521, zzz523, zzz524, zzz31, h) → new_mkVBalBranch3MkVBalBranch260(zzz340, zzz341, zzz342000, zzz343, zzz344, zzz520, zzz521, zzz523, zzz524, zzz31, h)
new_mkVBalBranch3MkVBalBranch260(zzz340, zzz341, zzz342000, zzz343, zzz344, zzz520, zzz521, zzz523, zzz524, zzz31, h) → new_mkVBalBranch3MkVBalBranch143(zzz340, zzz341, Succ(zzz342000), zzz343, zzz344, zzz520, zzz521, zzz523, zzz524, zzz31, new_primMulNat1(Succ(zzz342000)), h)
new_mkVBalBranch3MkVBalBranch143(zzz818, zzz819, zzz820, zzz821, zzz822, zzz823, zzz824, zzz825, zzz826, zzz827, Zero, eb) → new_mkVBalBranch3MkVBalBranch144(zzz818, zzz819, zzz820, zzz821, zzz822, zzz823, zzz824, Zero, zzz825, zzz826, zzz827, Succ(Zero), Zero, eb)
new_mkVBalBranch3MkVBalBranch143(zzz818, zzz819, zzz820, zzz821, zzz822, zzz823, zzz824, zzz825, zzz826, zzz827, Succ(zzz8960), eb) → new_mkVBalBranch3MkVBalBranch144(zzz818, zzz819, zzz820, zzz821, zzz822, zzz823, zzz824, Zero, zzz825, zzz826, zzz827, Succ(Zero), Succ(zzz8960), eb)
new_mkVBalBranch3MkVBalBranch144(zzz1702, zzz1703, zzz1704, zzz1705, zzz1706, zzz1707, zzz1708, zzz1709, zzz1710, zzz1711, zzz1712, Succ(zzz17130), Succ(zzz17140), df) → new_mkVBalBranch3MkVBalBranch144(zzz1702, zzz1703, zzz1704, zzz1705, zzz1706, zzz1707, zzz1708, zzz1709, zzz1710, zzz1711, zzz1712, zzz17130, zzz17140, df)
new_mkVBalBranch3MkVBalBranch144(zzz1702, zzz1703, zzz1704, zzz1705, zzz1706, zzz1707, zzz1708, zzz1709, zzz1710, zzz1711, zzz1712, Zero, Succ(zzz17140), df) → new_mkBalBranch(zzz1707, zzz1708, zzz1710, new_mkVBalBranch3(zzz1712, zzz1711, Branch(zzz1702, zzz1703, Neg(Succ(zzz1704)), zzz1705, zzz1706), df), ty_Ordering, df)
new_mkVBalBranch3MkVBalBranch144(zzz1702, zzz1703, zzz1704, zzz1705, zzz1706, zzz1707, zzz1708, zzz1709, zzz1710, zzz1711, zzz1712, Succ(zzz17130), Zero, df) → new_mkVBalBranch3MkVBalBranch138(zzz1702, zzz1703, zzz1704, zzz1705, zzz1706, zzz1707, zzz1708, zzz1709, zzz1710, zzz1711, zzz1712, df)
new_mkVBalBranch3MkVBalBranch144(zzz1702, zzz1703, zzz1704, zzz1705, zzz1706, zzz1707, zzz1708, zzz1709, zzz1710, zzz1711, zzz1712, Zero, Zero, df) → new_mkVBalBranch3MkVBalBranch138(zzz1702, zzz1703, zzz1704, zzz1705, zzz1706, zzz1707, zzz1708, zzz1709, zzz1710, zzz1711, zzz1712, df)
new_mkVBalBranch3MkVBalBranch138(zzz1702, zzz1703, zzz1704, zzz1705, zzz1706, zzz1707, zzz1708, zzz1709, zzz1710, zzz1711, zzz1712, df) → new_mkBranch(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))), GT, zzz1712, Branch(zzz1707, zzz1708, Neg(Succ(zzz1709)), zzz1710, zzz1711), Branch(zzz1702, zzz1703, Neg(Succ(zzz1704)), zzz1705, zzz1706), ty_Ordering, df)
new_mkVBalBranch3MkVBalBranch255(zzz537, zzz538, zzz539, zzz540, zzz541, zzz542, zzz543, zzz544, zzz545, zzz546, zzz547, Zero, Succ(zzz5490), dg) → new_mkBalBranch(zzz537, zzz538, new_mkVBalBranch3(zzz547, Branch(zzz542, zzz543, Neg(Succ(Succ(zzz544))), zzz545, zzz546), zzz540, dg), zzz541, ty_Ordering, dg)
new_mkVBalBranch3MkVBalBranch254(zzz340, zzz341, zzz343, zzz344, zzz520, zzz521, zzz52200, zzz523, zzz524, zzz31, h) → new_mkBalBranch(zzz340, zzz341, new_mkVBalBranch3(zzz31, Branch(zzz520, zzz521, Neg(Succ(zzz52200)), zzz523, zzz524), zzz343, h), zzz344, ty_Ordering, h)
new_mkVBalBranch3MkVBalBranch273(zzz818, zzz819, zzz820, zzz821, zzz822, zzz823, zzz824, zzz825, zzz826, zzz827, eb) → new_mkVBalBranch3MkVBalBranch274(zzz818, zzz819, zzz820, zzz821, zzz822, zzz823, zzz824, zzz825, zzz826, zzz827, eb)
new_mkVBalBranch3MkVBalBranch274(zzz818, zzz819, zzz820, zzz821, zzz822, zzz823, zzz824, zzz825, zzz826, zzz827, eb) → new_mkVBalBranch3MkVBalBranch143(zzz818, zzz819, zzz820, zzz821, zzz822, zzz823, zzz824, zzz825, zzz826, zzz827, new_primMulNat1(zzz820), eb)
new_mkVBalBranch3MkVBalBranch277(zzz1133, zzz1134, zzz1135, zzz1136, zzz1137, zzz1138, zzz1139, zzz1140, zzz1141, zzz1142, Succ(zzz11430), Succ(zzz11440), fd) → new_mkVBalBranch3MkVBalBranch277(zzz1133, zzz1134, zzz1135, zzz1136, zzz1137, zzz1138, zzz1139, zzz1140, zzz1141, zzz1142, zzz11430, zzz11440, fd)
new_mkVBalBranch3MkVBalBranch277(zzz1133, zzz1134, zzz1135, zzz1136, zzz1137, zzz1138, zzz1139, zzz1140, zzz1141, zzz1142, Zero, Zero, fd) → new_mkVBalBranch3MkVBalBranch273(zzz1133, zzz1134, zzz1135, zzz1136, zzz1137, zzz1138, zzz1139, zzz1140, zzz1141, zzz1142, fd)
new_mkVBalBranch3MkVBalBranch277(zzz1133, zzz1134, zzz1135, zzz1136, zzz1137, zzz1138, zzz1139, zzz1140, zzz1141, zzz1142, Zero, Succ(zzz11440), fd) → new_mkBalBranch(zzz1133, zzz1134, new_mkVBalBranch3(zzz1142, Branch(zzz1138, zzz1139, Neg(Succ(Zero)), zzz1140, zzz1141), zzz1136, fd), zzz1137, ty_Ordering, fd)
new_mkVBalBranch3MkVBalBranch277(zzz1133, zzz1134, zzz1135, zzz1136, zzz1137, zzz1138, zzz1139, zzz1140, zzz1141, zzz1142, Succ(zzz11430), Zero, fd) → new_mkVBalBranch3MkVBalBranch274(zzz1133, zzz1134, zzz1135, zzz1136, zzz1137, zzz1138, zzz1139, zzz1140, zzz1141, zzz1142, fd)
new_mkVBalBranch3MkVBalBranch255(zzz537, zzz538, zzz539, zzz540, zzz541, zzz542, zzz543, zzz544, zzz545, zzz546, zzz547, Succ(zzz5480), Succ(zzz5490), dg) → new_mkVBalBranch3MkVBalBranch255(zzz537, zzz538, zzz539, zzz540, zzz541, zzz542, zzz543, zzz544, zzz545, zzz546, zzz547, zzz5480, zzz5490, dg)
new_mkVBalBranch3MkVBalBranch255(zzz537, zzz538, zzz539, zzz540, zzz541, zzz542, zzz543, zzz544, zzz545, zzz546, zzz547, Succ(zzz5480), Zero, dg) → new_mkVBalBranch3MkVBalBranch256(zzz537, zzz538, zzz539, zzz540, zzz541, zzz542, zzz543, zzz544, zzz545, zzz546, zzz547, dg)
new_mkVBalBranch3MkVBalBranch255(zzz537, zzz538, zzz539, zzz540, zzz541, zzz542, zzz543, zzz544, zzz545, zzz546, zzz547, Zero, Zero, dg) → new_mkVBalBranch3MkVBalBranch256(zzz537, zzz538, zzz539, zzz540, zzz541, zzz542, zzz543, zzz544, zzz545, zzz546, zzz547, dg)
new_mkVBalBranch3MkVBalBranch256(zzz537, zzz538, zzz539, zzz540, zzz541, zzz542, zzz543, zzz544, zzz545, zzz546, zzz547, dg) → new_mkVBalBranch3MkVBalBranch153(zzz537, zzz538, zzz539, zzz540, zzz541, zzz542, zzz543, zzz544, zzz545, zzz546, zzz547, new_primMulNat1(zzz539), dg)
new_mkVBalBranch3MkVBalBranch153(zzz537, zzz538, zzz539, zzz540, zzz541, zzz542, zzz543, zzz544, zzz545, zzz546, zzz547, Zero, dg) → new_mkVBalBranch3MkVBalBranch144(zzz537, zzz538, zzz539, zzz540, zzz541, zzz542, zzz543, Succ(zzz544), zzz545, zzz546, zzz547, Succ(Succ(zzz544)), Zero, dg)
new_mkVBalBranch3MkVBalBranch153(zzz537, zzz538, zzz539, zzz540, zzz541, zzz542, zzz543, zzz544, zzz545, zzz546, zzz547, Succ(zzz6990), dg) → new_mkVBalBranch3MkVBalBranch144(zzz537, zzz538, zzz539, zzz540, zzz541, zzz542, zzz543, Succ(zzz544), zzz545, zzz546, zzz547, Succ(Succ(zzz544)), Succ(zzz6990), dg)
new_mkVBalBranch3MkVBalBranch258(zzz340, zzz341, zzz3420, zzz343, zzz344, zzz520, zzz521, zzz52200, zzz523, zzz524, zzz31, h) → new_mkBalBranch(zzz340, zzz341, new_mkVBalBranch3(zzz31, Branch(zzz520, zzz521, Neg(Succ(zzz52200)), zzz523, zzz524), zzz343, h), zzz344, ty_Ordering, h)
new_mkVBalBranch3MkVBalBranch245(zzz340, zzz341, zzz343, zzz344, zzz520, zzz521, zzz52200, zzz523, zzz524, zzz31, h) → new_mkBalBranch(zzz340, zzz341, new_mkVBalBranch3(zzz31, Branch(zzz520, zzz521, Neg(Succ(zzz52200)), zzz523, zzz524), zzz343, h), zzz344, ty_Ordering, h)
new_addToFM(zzz34, zzz31, h) → new_addToFM_C3(zzz34, zzz31, h)
new_addToFM_C3(Branch(EQ, zzz341, zzz342, zzz343, zzz344), zzz31, h) → new_mkBalBranch(EQ, zzz341, zzz343, new_addToFM_C3(zzz344, zzz31, h), ty_Ordering, h)
new_addToFM_C3(Branch(LT, zzz341, zzz342, zzz343, zzz344), zzz31, h) → new_mkBalBranch(LT, zzz341, zzz343, new_addToFM_C3(zzz344, zzz31, h), ty_Ordering, h)
new_addToFM_C3(EmptyFM, zzz31, h) → Branch(GT, zzz31, Pos(Succ(Zero)), new_emptyFM(h), new_emptyFM(h))
new_addToFM_C3(Branch(GT, zzz341, zzz342, zzz343, zzz344), zzz31, h) → Branch(GT, new_addToFM0(zzz341, zzz31, h), zzz342, zzz343, zzz344)
new_addToFM0(zzz71, zzz13, h) → zzz13
new_emptyFM(h) → EmptyFM
new_mkVBalBranch3MkVBalBranch154(zzz340, zzz341, zzz34200, zzz343, zzz344, zzz520, zzz521, zzz523, zzz524, zzz31, Zero, h) → new_mkBranch(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))), GT, zzz31, Branch(zzz520, zzz521, Pos(Zero), zzz523, zzz524), Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), ty_Ordering, h)
new_mkVBalBranch3MkVBalBranch154(zzz340, zzz341, zzz34200, zzz343, zzz344, zzz520, zzz521, zzz523, zzz524, zzz31, Succ(zzz1250), h) → new_mkBalBranch(zzz520, zzz521, zzz523, new_mkVBalBranch3(zzz31, zzz524, Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), h), ty_Ordering, h)
new_mkVBalBranch3MkVBalBranch155(zzz340, zzz341, zzz34200, zzz343, zzz344, zzz520, zzz521, zzz523, zzz524, zzz31, Succ(zzz1290), h) → new_mkBalBranch(zzz520, zzz521, zzz523, new_mkVBalBranch3(zzz31, zzz524, Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), h), ty_Ordering, h)
new_mkVBalBranch3MkVBalBranch155(zzz340, zzz341, zzz34200, zzz343, zzz344, zzz520, zzz521, zzz523, zzz524, zzz31, Zero, h) → new_mkBranch(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))), GT, zzz31, Branch(zzz520, zzz521, Neg(Zero), zzz523, zzz524), Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), ty_Ordering, h)
new_splitGT27(zzz31, zzz32, zzz33, zzz34, h) → zzz34
new_splitGT26(zzz76, zzz77, zzz78, zzz79, bg) → new_splitGT24(zzz76, zzz77, zzz78, zzz79, bg)
new_splitGT42(h) → new_emptyFM(h)
new_intersectFM_C2Gts0(zzz854, zzz855, zzz856, zzz857, ba) → new_splitGT25(zzz854, zzz855, zzz856, zzz857, ba)
new_splitGT25(zzz854, zzz855, zzz856, zzz857, ba) → new_mkVBalBranch4(zzz854, new_splitGT12(zzz856, ba), zzz857, ba)
new_splitGT12(Branch(LT, zzz8561, zzz8562, zzz8563, zzz8564), ba) → new_splitGT210(zzz8561, zzz8562, zzz8563, zzz8564, ba)
new_splitGT12(Branch(EQ, zzz8561, zzz8562, zzz8563, zzz8564), ba) → new_splitGT25(zzz8561, zzz8562, zzz8563, zzz8564, ba)
new_splitGT12(EmptyFM, ba) → new_splitGT41(ba)
new_splitGT12(Branch(GT, zzz8561, zzz8562, zzz8563, zzz8564), ba) → new_splitGT28(zzz8561, zzz8562, zzz8563, zzz8564, ba)
new_mkVBalBranch4(zzz31, EmptyFM, zzz34, h) → new_addToFM2(zzz34, zzz31, h)
new_mkVBalBranch4(zzz31, Branch(zzz510, zzz511, Pos(Zero), zzz513, zzz514), Branch(zzz340, zzz341, Pos(Zero), zzz343, zzz344), h) → new_mkBranch(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))), EQ, zzz31, Branch(zzz510, zzz511, Pos(Zero), zzz513, zzz514), Branch(zzz340, zzz341, Pos(Zero), zzz343, zzz344), ty_Ordering, h)
new_mkVBalBranch4(zzz31, Branch(zzz510, zzz511, Pos(Zero), zzz513, zzz514), Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), h) → new_mkVBalBranch3MkVBalBranch168(zzz340, zzz341, zzz34200, zzz343, zzz344, zzz510, zzz511, zzz513, zzz514, zzz31, new_primMulNat1(zzz34200), h)
new_mkVBalBranch4(zzz31, Branch(zzz510, zzz511, Neg(Zero), zzz513, zzz514), Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), h) → new_mkVBalBranch3MkVBalBranch133(zzz340, zzz341, zzz34200, zzz343, zzz344, zzz510, zzz511, zzz513, zzz514, zzz31, new_primMulNat1(zzz34200), h)
new_mkVBalBranch4(zzz31, Branch(zzz510, zzz511, Neg(Zero), zzz513, zzz514), Branch(zzz340, zzz341, Neg(Zero), zzz343, zzz344), h) → new_mkBranch(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))), EQ, zzz31, Branch(zzz510, zzz511, Neg(Zero), zzz513, zzz514), Branch(zzz340, zzz341, Neg(Zero), zzz343, zzz344), ty_Ordering, h)
new_mkVBalBranch4(zzz31, Branch(zzz510, zzz511, zzz512, zzz513, zzz514), EmptyFM, h) → new_addToFM2(Branch(zzz510, zzz511, zzz512, zzz513, zzz514), zzz31, h)
new_mkVBalBranch4(zzz31, Branch(zzz510, zzz511, Neg(Succ(zzz51200)), zzz513, zzz514), Branch(zzz340, zzz341, zzz342, zzz343, zzz344), h) → new_mkVBalBranch3MkVBalBranch281(zzz340, zzz341, zzz342, zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, new_primMulNat0(zzz51200), h)
new_mkVBalBranch4(zzz31, Branch(zzz510, zzz511, Pos(Zero), zzz513, zzz514), Branch(zzz340, zzz341, Neg(Zero), zzz343, zzz344), h) → new_mkBranch(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))), EQ, zzz31, Branch(zzz510, zzz511, Pos(Zero), zzz513, zzz514), Branch(zzz340, zzz341, Neg(Zero), zzz343, zzz344), ty_Ordering, h)
new_mkVBalBranch4(zzz31, Branch(zzz510, zzz511, Neg(Zero), zzz513, zzz514), Branch(zzz340, zzz341, Pos(Zero), zzz343, zzz344), h) → new_mkBranch(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))), EQ, zzz31, Branch(zzz510, zzz511, Neg(Zero), zzz513, zzz514), Branch(zzz340, zzz341, Pos(Zero), zzz343, zzz344), ty_Ordering, h)
new_mkVBalBranch4(zzz31, Branch(zzz510, zzz511, Pos(Zero), zzz513, zzz514), Branch(zzz340, zzz341, Pos(Succ(zzz34200)), zzz343, zzz344), h) → new_mkBalBranch(zzz340, zzz341, new_mkVBalBranch4(zzz31, Branch(zzz510, zzz511, Pos(Zero), zzz513, zzz514), zzz343, h), zzz344, ty_Ordering, h)
new_mkVBalBranch4(zzz31, Branch(zzz510, zzz511, Pos(Succ(zzz51200)), zzz513, zzz514), Branch(zzz340, zzz341, zzz342, zzz343, zzz344), h) → new_mkVBalBranch3MkVBalBranch288(zzz340, zzz341, zzz342, zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, new_primMulNat0(zzz51200), h)
new_mkVBalBranch4(zzz31, Branch(zzz510, zzz511, Neg(Zero), zzz513, zzz514), Branch(zzz340, zzz341, Pos(Succ(zzz34200)), zzz343, zzz344), h) → new_mkBalBranch(zzz340, zzz341, new_mkVBalBranch4(zzz31, Branch(zzz510, zzz511, Neg(Zero), zzz513, zzz514), zzz343, h), zzz344, ty_Ordering, h)
new_mkVBalBranch3MkVBalBranch288(zzz340, zzz341, Pos(Succ(Succ(zzz342000))), zzz343, zzz344, zzz510, zzz511, Succ(zzz512000), zzz513, zzz514, zzz31, Zero, h) → new_mkVBalBranch3MkVBalBranch289(zzz340, zzz341, Succ(zzz342000), zzz343, zzz344, zzz510, zzz511, zzz512000, zzz513, zzz514, zzz31, zzz512000, zzz342000, h)
new_mkVBalBranch3MkVBalBranch288(zzz340, zzz341, Neg(zzz3420), zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, Zero, h) → new_mkVBalBranch3MkVBalBranch284(zzz340, zzz341, zzz3420, zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, h)
new_mkVBalBranch3MkVBalBranch288(zzz340, zzz341, Pos(Succ(Zero)), zzz343, zzz344, zzz510, zzz511, Succ(zzz512000), zzz513, zzz514, zzz31, Zero, h) → new_mkVBalBranch3MkVBalBranch283(zzz340, zzz341, Zero, zzz343, zzz344, zzz510, zzz511, zzz512000, zzz513, zzz514, zzz31, h)
new_mkVBalBranch3MkVBalBranch288(zzz340, zzz341, Pos(Succ(Succ(zzz342000))), zzz343, zzz344, zzz510, zzz511, Zero, zzz513, zzz514, zzz31, Zero, h) → new_mkVBalBranch3MkVBalBranch290(zzz340, zzz341, zzz342000, zzz343, zzz344, zzz510, zzz511, zzz513, zzz514, zzz31, h)
new_mkVBalBranch3MkVBalBranch288(zzz340, zzz341, Pos(Succ(Succ(zzz342000))), zzz343, zzz344, zzz510, zzz511, Zero, zzz513, zzz514, zzz31, Succ(Succ(zzz6600)), h) → new_mkVBalBranch3MkVBalBranch270(zzz340, zzz341, Succ(zzz342000), zzz343, zzz344, zzz510, zzz511, zzz513, zzz514, zzz31, Succ(zzz6600), zzz342000, h)
new_mkVBalBranch3MkVBalBranch288(zzz340, zzz341, Neg(zzz3420), zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, Succ(zzz660), h) → new_mkVBalBranch3MkVBalBranch284(zzz340, zzz341, zzz3420, zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, h)
new_mkVBalBranch3MkVBalBranch288(zzz340, zzz341, Pos(Zero), zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, Succ(zzz660), h) → new_mkVBalBranch3MkVBalBranch285(zzz340, zzz341, zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, h)
new_mkVBalBranch3MkVBalBranch288(zzz340, zzz341, Pos(Succ(Succ(zzz342000))), zzz343, zzz344, zzz510, zzz511, Succ(zzz512000), zzz513, zzz514, zzz31, Succ(Zero), h) → new_mkVBalBranch3MkVBalBranch289(zzz340, zzz341, Succ(zzz342000), zzz343, zzz344, zzz510, zzz511, zzz512000, zzz513, zzz514, zzz31, Succ(zzz512000), zzz342000, h)
new_mkVBalBranch3MkVBalBranch288(zzz340, zzz341, Pos(Succ(Succ(zzz342000))), zzz343, zzz344, zzz510, zzz511, Succ(zzz512000), zzz513, zzz514, zzz31, Succ(Succ(zzz6600)), h) → new_mkVBalBranch3MkVBalBranch289(zzz340, zzz341, Succ(zzz342000), zzz343, zzz344, zzz510, zzz511, zzz512000, zzz513, zzz514, zzz31, Succ(Succ(new_primPlusNat2(zzz6600, zzz512000))), zzz342000, h)
new_mkVBalBranch3MkVBalBranch288(zzz340, zzz341, Pos(Zero), zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, Zero, h) → new_mkVBalBranch3MkVBalBranch285(zzz340, zzz341, zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, h)
new_mkVBalBranch3MkVBalBranch288(zzz340, zzz341, Pos(Succ(Succ(zzz342000))), zzz343, zzz344, zzz510, zzz511, Zero, zzz513, zzz514, zzz31, Succ(Zero), h) → new_mkVBalBranch3MkVBalBranch270(zzz340, zzz341, Succ(zzz342000), zzz343, zzz344, zzz510, zzz511, zzz513, zzz514, zzz31, Zero, zzz342000, h)
new_mkVBalBranch3MkVBalBranch288(zzz340, zzz341, Pos(Succ(Zero)), zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, Succ(zzz660), h) → new_mkVBalBranch3MkVBalBranch287(zzz340, zzz341, zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, h)
new_mkVBalBranch3MkVBalBranch288(zzz340, zzz341, Pos(Succ(Zero)), zzz343, zzz344, zzz510, zzz511, Zero, zzz513, zzz514, zzz31, Zero, h) → new_mkVBalBranch3MkVBalBranch287(zzz340, zzz341, zzz343, zzz344, zzz510, zzz511, Zero, zzz513, zzz514, zzz31, h)
new_mkVBalBranch3MkVBalBranch287(zzz340, zzz341, zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, h) → new_mkVBalBranch3MkVBalBranch161(zzz340, zzz341, zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, new_primMulNat1(Zero), h)
new_mkVBalBranch3MkVBalBranch161(zzz340, zzz341, zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, Zero, h) → new_mkVBalBranch3MkVBalBranch162(zzz340, zzz341, Zero, zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, Zero, Succ(zzz51200), h)
new_mkVBalBranch3MkVBalBranch161(zzz340, zzz341, zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, Succ(zzz1480), h) → new_mkVBalBranch3MkVBalBranch162(zzz340, zzz341, Zero, zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, Succ(zzz1480), Succ(zzz51200), h)
new_mkVBalBranch3MkVBalBranch162(zzz1986, zzz1987, zzz1988, zzz1989, zzz1990, zzz1991, zzz1992, zzz1993, zzz1994, zzz1995, zzz1996, Succ(zzz19970), Succ(zzz19980), dh) → new_mkVBalBranch3MkVBalBranch162(zzz1986, zzz1987, zzz1988, zzz1989, zzz1990, zzz1991, zzz1992, zzz1993, zzz1994, zzz1995, zzz1996, zzz19970, zzz19980, dh)
new_mkVBalBranch3MkVBalBranch162(zzz1986, zzz1987, zzz1988, zzz1989, zzz1990, zzz1991, zzz1992, zzz1993, zzz1994, zzz1995, zzz1996, Succ(zzz19970), Zero, dh) → new_mkVBalBranch3MkVBalBranch142(zzz1986, zzz1987, zzz1988, zzz1989, zzz1990, zzz1991, zzz1992, zzz1993, zzz1994, zzz1995, zzz1996, dh)
new_mkVBalBranch3MkVBalBranch162(zzz1986, zzz1987, zzz1988, zzz1989, zzz1990, zzz1991, zzz1992, zzz1993, zzz1994, zzz1995, zzz1996, Zero, Zero, dh) → new_mkVBalBranch3MkVBalBranch142(zzz1986, zzz1987, zzz1988, zzz1989, zzz1990, zzz1991, zzz1992, zzz1993, zzz1994, zzz1995, zzz1996, dh)
new_mkVBalBranch3MkVBalBranch162(zzz1986, zzz1987, zzz1988, zzz1989, zzz1990, zzz1991, zzz1992, zzz1993, zzz1994, zzz1995, zzz1996, Zero, Succ(zzz19980), dh) → new_mkBalBranch(zzz1991, zzz1992, zzz1994, new_mkVBalBranch4(zzz1996, zzz1995, Branch(zzz1986, zzz1987, Pos(Succ(zzz1988)), zzz1989, zzz1990), dh), ty_Ordering, dh)
new_mkVBalBranch3MkVBalBranch142(zzz1986, zzz1987, zzz1988, zzz1989, zzz1990, zzz1991, zzz1992, zzz1993, zzz1994, zzz1995, zzz1996, dh) → new_mkBranch(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))), EQ, zzz1996, Branch(zzz1991, zzz1992, Pos(Succ(zzz1993)), zzz1994, zzz1995), Branch(zzz1986, zzz1987, Pos(Succ(zzz1988)), zzz1989, zzz1990), ty_Ordering, dh)
new_mkVBalBranch3MkVBalBranch270(zzz473, zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, zzz481, zzz482, Zero, Zero, eh) → new_mkVBalBranch3MkVBalBranch271(zzz473, zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, zzz481, zzz482, eh)
new_mkVBalBranch3MkVBalBranch270(zzz473, zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, zzz481, zzz482, Zero, Succ(zzz4840), eh) → new_mkBalBranch(zzz473, zzz474, new_mkVBalBranch4(zzz482, Branch(zzz478, zzz479, Pos(Succ(Zero)), zzz480, zzz481), zzz476, eh), zzz477, ty_Ordering, eh)
new_mkVBalBranch3MkVBalBranch271(zzz473, zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, zzz481, zzz482, eh) → new_mkVBalBranch3MkVBalBranch164(zzz473, zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, zzz481, zzz482, new_primMulNat1(zzz475), eh)
new_mkVBalBranch3MkVBalBranch164(zzz473, zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, zzz481, zzz482, Succ(zzz7390), eh) → new_mkVBalBranch3MkVBalBranch162(zzz473, zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, Zero, zzz480, zzz481, zzz482, Succ(zzz7390), Succ(Zero), eh)
new_mkVBalBranch3MkVBalBranch164(zzz473, zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, zzz481, zzz482, Zero, eh) → new_mkVBalBranch3MkVBalBranch162(zzz473, zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, Zero, zzz480, zzz481, zzz482, Zero, Succ(Zero), eh)
new_mkVBalBranch3MkVBalBranch285(zzz340, zzz341, zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, h) → new_mkBalBranch(zzz510, zzz511, zzz513, new_mkVBalBranch4(zzz31, zzz514, Branch(zzz340, zzz341, Pos(Zero), zzz343, zzz344), h), ty_Ordering, h)
new_mkVBalBranch3MkVBalBranch289(zzz1105, zzz1106, zzz1107, zzz1108, zzz1109, zzz1110, zzz1111, zzz1112, zzz1113, zzz1114, zzz1115, Succ(zzz11160), Succ(zzz11170), fh) → new_mkVBalBranch3MkVBalBranch289(zzz1105, zzz1106, zzz1107, zzz1108, zzz1109, zzz1110, zzz1111, zzz1112, zzz1113, zzz1114, zzz1115, zzz11160, zzz11170, fh)
new_mkVBalBranch3MkVBalBranch289(zzz1105, zzz1106, zzz1107, zzz1108, zzz1109, zzz1110, zzz1111, zzz1112, zzz1113, zzz1114, zzz1115, Succ(zzz11160), Zero, fh) → new_mkVBalBranch3MkVBalBranch283(zzz1105, zzz1106, zzz1107, zzz1108, zzz1109, zzz1110, zzz1111, zzz1112, zzz1113, zzz1114, zzz1115, fh)
new_mkVBalBranch3MkVBalBranch283(zzz461, zzz462, zzz463, zzz464, zzz465, zzz466, zzz467, zzz468, zzz469, zzz470, zzz471, de) → new_mkVBalBranch3MkVBalBranch282(zzz461, zzz462, zzz463, zzz464, zzz465, zzz466, zzz467, zzz468, zzz469, zzz470, zzz471, de)
new_mkVBalBranch3MkVBalBranch282(zzz461, zzz462, zzz463, zzz464, zzz465, zzz466, zzz467, zzz468, zzz469, zzz470, zzz471, de) → new_mkVBalBranch3MkVBalBranch165(zzz461, zzz462, zzz463, zzz464, zzz465, zzz466, zzz467, zzz468, zzz469, zzz470, zzz471, de)
new_mkVBalBranch3MkVBalBranch165(zzz461, zzz462, zzz463, zzz464, zzz465, zzz466, zzz467, zzz468, zzz469, zzz470, zzz471, de) → new_mkVBalBranch3MkVBalBranch163(zzz461, zzz462, zzz463, zzz464, zzz465, zzz466, zzz467, zzz468, zzz469, zzz470, zzz471, de)
new_mkVBalBranch3MkVBalBranch163(zzz461, zzz462, zzz463, zzz464, zzz465, zzz466, zzz467, zzz468, zzz469, zzz470, zzz471, de) → new_mkVBalBranch3MkVBalBranch158(zzz461, zzz462, zzz463, zzz464, zzz465, zzz466, zzz467, zzz468, zzz469, zzz470, zzz471, de)
new_mkVBalBranch3MkVBalBranch158(zzz461, zzz462, zzz463, zzz464, zzz465, zzz466, zzz467, zzz468, zzz469, zzz470, zzz471, de) → new_mkVBalBranch3MkVBalBranch136(zzz461, zzz462, zzz463, zzz464, zzz465, zzz466, zzz467, zzz468, zzz469, zzz470, zzz471, de)
new_mkVBalBranch3MkVBalBranch136(zzz461, zzz462, zzz463, zzz464, zzz465, zzz466, zzz467, zzz468, zzz469, zzz470, zzz471, de) → new_mkVBalBranch3MkVBalBranch137(zzz461, zzz462, zzz463, zzz464, zzz465, zzz466, zzz467, zzz468, zzz469, zzz470, zzz471, new_primMulNat1(zzz463), de)
new_mkVBalBranch3MkVBalBranch137(zzz461, zzz462, zzz463, zzz464, zzz465, zzz466, zzz467, zzz468, zzz469, zzz470, zzz471, Zero, de) → new_mkVBalBranch3MkVBalBranch162(zzz461, zzz462, zzz463, zzz464, zzz465, zzz466, zzz467, Succ(zzz468), zzz469, zzz470, zzz471, Zero, Succ(Succ(zzz468)), de)
new_mkVBalBranch3MkVBalBranch137(zzz461, zzz462, zzz463, zzz464, zzz465, zzz466, zzz467, zzz468, zzz469, zzz470, zzz471, Succ(zzz5800), de) → new_mkVBalBranch3MkVBalBranch162(zzz461, zzz462, zzz463, zzz464, zzz465, zzz466, zzz467, Succ(zzz468), zzz469, zzz470, zzz471, Succ(zzz5800), Succ(Succ(zzz468)), de)
new_mkVBalBranch3MkVBalBranch289(zzz1105, zzz1106, zzz1107, zzz1108, zzz1109, zzz1110, zzz1111, zzz1112, zzz1113, zzz1114, zzz1115, Zero, Succ(zzz11170), fh) → new_mkBalBranch(zzz1105, zzz1106, new_mkVBalBranch4(zzz1115, Branch(zzz1110, zzz1111, Pos(Succ(Succ(zzz1112))), zzz1113, zzz1114), zzz1108, fh), zzz1109, ty_Ordering, fh)
new_mkVBalBranch3MkVBalBranch289(zzz1105, zzz1106, zzz1107, zzz1108, zzz1109, zzz1110, zzz1111, zzz1112, zzz1113, zzz1114, zzz1115, Zero, Zero, fh) → new_mkVBalBranch3MkVBalBranch282(zzz1105, zzz1106, zzz1107, zzz1108, zzz1109, zzz1110, zzz1111, zzz1112, zzz1113, zzz1114, zzz1115, fh)
new_mkVBalBranch3MkVBalBranch284(zzz340, zzz341, Succ(zzz34200), zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, h) → new_mkVBalBranch3MkVBalBranch167(zzz340, zzz341, zzz34200, zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, new_primPlusNat2(new_primMulNat0(zzz34200), Succ(zzz34200)), h)
new_mkVBalBranch3MkVBalBranch284(zzz340, zzz341, Zero, zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, h) → new_mkBalBranch(zzz510, zzz511, zzz513, new_mkVBalBranch4(zzz31, zzz514, Branch(zzz340, zzz341, Neg(Zero), zzz343, zzz344), h), ty_Ordering, h)
new_mkVBalBranch3MkVBalBranch167(zzz340, zzz341, zzz34200, zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, Zero, h) → new_mkVBalBranch3MkVBalBranch160(zzz340, zzz341, zzz34200, zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, h)
new_mkVBalBranch3MkVBalBranch167(zzz340, zzz341, zzz34200, zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, Succ(zzz1410), h) → new_mkVBalBranch3MkVBalBranch160(zzz340, zzz341, zzz34200, zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, h)
new_mkVBalBranch3MkVBalBranch160(zzz340, zzz341, zzz34200, zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, h) → new_mkBalBranch(zzz510, zzz511, zzz513, new_mkVBalBranch4(zzz31, zzz514, Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), h), ty_Ordering, h)
new_mkVBalBranch3MkVBalBranch270(zzz473, zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, zzz481, zzz482, Succ(zzz4830), Succ(zzz4840), eh) → new_mkVBalBranch3MkVBalBranch270(zzz473, zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, zzz481, zzz482, zzz4830, zzz4840, eh)
new_mkVBalBranch3MkVBalBranch270(zzz473, zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, zzz481, zzz482, Succ(zzz4830), Zero, eh) → new_mkVBalBranch3MkVBalBranch271(zzz473, zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, zzz481, zzz482, eh)
new_mkVBalBranch3MkVBalBranch290(zzz340, zzz341, zzz342000, zzz343, zzz344, zzz510, zzz511, zzz513, zzz514, zzz31, h) → new_mkBalBranch(zzz340, zzz341, new_mkVBalBranch4(zzz31, Branch(zzz510, zzz511, Pos(Succ(Zero)), zzz513, zzz514), zzz343, h), zzz344, ty_Ordering, h)
new_mkVBalBranch3MkVBalBranch281(zzz340, zzz341, Neg(Succ(Zero)), zzz343, zzz344, zzz510, zzz511, Zero, zzz513, zzz514, zzz31, Zero, h) → new_mkVBalBranch3MkVBalBranch157(zzz340, zzz341, Zero, zzz343, zzz344, zzz510, zzz511, zzz513, zzz514, zzz31, new_primMulNat1(Zero), h)
new_mkVBalBranch3MkVBalBranch281(zzz340, zzz341, Neg(Succ(Succ(Zero))), zzz343, zzz344, zzz510, zzz511, Zero, zzz513, zzz514, zzz31, Succ(Succ(zzz6700)), h) → new_mkVBalBranch3MkVBalBranch263(zzz340, zzz341, Succ(Zero), zzz343, zzz344, zzz510, zzz511, zzz513, zzz514, zzz31, Zero, Succ(zzz6700), h)
new_mkVBalBranch3MkVBalBranch281(zzz340, zzz341, Neg(Zero), zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, Succ(zzz670), h) → new_mkVBalBranch3MkVBalBranch266(zzz340, zzz341, zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, h)
new_mkVBalBranch3MkVBalBranch281(zzz340, zzz341, Neg(Succ(Succ(zzz342000))), zzz343, zzz344, zzz510, zzz511, Zero, zzz513, zzz514, zzz31, Zero, h) → new_mkVBalBranch3MkVBalBranch249(zzz340, zzz341, zzz342000, zzz343, zzz344, zzz510, zzz511, zzz513, zzz514, zzz31, h)
new_mkVBalBranch3MkVBalBranch281(zzz340, zzz341, Neg(Succ(Succ(Succ(zzz3420000)))), zzz343, zzz344, zzz510, zzz511, Succ(zzz512000), zzz513, zzz514, zzz31, Succ(Zero), h) → new_mkVBalBranch3MkVBalBranch280(zzz340, zzz341, Succ(Succ(zzz3420000)), zzz343, zzz344, zzz510, zzz511, zzz512000, zzz513, zzz514, zzz31, Succ(zzz3420000), Succ(zzz512000), h)
new_mkVBalBranch3MkVBalBranch281(zzz340, zzz341, Neg(Succ(Succ(Zero))), zzz343, zzz344, zzz510, zzz511, Zero, zzz513, zzz514, zzz31, Succ(Zero), h) → new_mkVBalBranch3MkVBalBranch263(zzz340, zzz341, Succ(Zero), zzz343, zzz344, zzz510, zzz511, zzz513, zzz514, zzz31, Zero, Zero, h)
new_mkVBalBranch3MkVBalBranch281(zzz340, zzz341, Neg(Succ(Zero)), zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, Succ(zzz670), h) → new_mkBalBranch(zzz340, zzz341, new_mkVBalBranch4(zzz31, Branch(zzz510, zzz511, Neg(Succ(zzz51200)), zzz513, zzz514), zzz343, h), zzz344, ty_Ordering, h)
new_mkVBalBranch3MkVBalBranch281(zzz340, zzz341, Neg(Succ(Succ(Succ(zzz3420000)))), zzz343, zzz344, zzz510, zzz511, Zero, zzz513, zzz514, zzz31, Succ(Succ(zzz6700)), h) → new_mkVBalBranch3MkVBalBranch263(zzz340, zzz341, Succ(Succ(zzz3420000)), zzz343, zzz344, zzz510, zzz511, zzz513, zzz514, zzz31, Succ(zzz3420000), Succ(zzz6700), h)
new_mkVBalBranch3MkVBalBranch281(zzz340, zzz341, Neg(Succ(Zero)), zzz343, zzz344, zzz510, zzz511, Succ(zzz512000), zzz513, zzz514, zzz31, Zero, h) → new_mkVBalBranch3MkVBalBranch257(zzz340, zzz341, Zero, zzz343, zzz344, zzz510, zzz511, zzz512000, zzz513, zzz514, zzz31, h)
new_mkVBalBranch3MkVBalBranch281(zzz340, zzz341, Neg(Succ(Succ(zzz342000))), zzz343, zzz344, zzz510, zzz511, Succ(zzz512000), zzz513, zzz514, zzz31, Zero, h) → new_mkVBalBranch3MkVBalBranch280(zzz340, zzz341, Succ(zzz342000), zzz343, zzz344, zzz510, zzz511, zzz512000, zzz513, zzz514, zzz31, zzz342000, zzz512000, h)
new_mkVBalBranch3MkVBalBranch281(zzz340, zzz341, Neg(Succ(Succ(Succ(zzz3420000)))), zzz343, zzz344, zzz510, zzz511, Succ(zzz512000), zzz513, zzz514, zzz31, Succ(Succ(zzz6700)), h) → new_mkVBalBranch3MkVBalBranch280(zzz340, zzz341, Succ(Succ(zzz3420000)), zzz343, zzz344, zzz510, zzz511, zzz512000, zzz513, zzz514, zzz31, Succ(zzz3420000), Succ(Succ(new_primPlusNat2(zzz6700, zzz512000))), h)
new_mkVBalBranch3MkVBalBranch281(zzz340, zzz341, Neg(Zero), zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, Zero, h) → new_mkVBalBranch3MkVBalBranch266(zzz340, zzz341, zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, h)
new_mkVBalBranch3MkVBalBranch281(zzz340, zzz341, Pos(zzz3420), zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, Zero, h) → new_mkVBalBranch3MkVBalBranch248(zzz340, zzz341, zzz3420, zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, h)
new_mkVBalBranch3MkVBalBranch281(zzz340, zzz341, Pos(zzz3420), zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, Succ(zzz670), h) → new_mkVBalBranch3MkVBalBranch248(zzz340, zzz341, zzz3420, zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, h)
new_mkVBalBranch3MkVBalBranch281(zzz340, zzz341, Neg(Succ(Succ(Succ(zzz3420000)))), zzz343, zzz344, zzz510, zzz511, Zero, zzz513, zzz514, zzz31, Succ(Zero), h) → new_mkVBalBranch3MkVBalBranch263(zzz340, zzz341, Succ(Succ(zzz3420000)), zzz343, zzz344, zzz510, zzz511, zzz513, zzz514, zzz31, Succ(zzz3420000), Zero, h)
new_mkVBalBranch3MkVBalBranch281(zzz340, zzz341, Neg(Succ(Succ(Zero))), zzz343, zzz344, zzz510, zzz511, Succ(zzz512000), zzz513, zzz514, zzz31, Succ(Succ(zzz6700)), h) → new_mkVBalBranch3MkVBalBranch280(zzz340, zzz341, Succ(Zero), zzz343, zzz344, zzz510, zzz511, zzz512000, zzz513, zzz514, zzz31, Zero, Succ(Succ(new_primPlusNat2(zzz6700, zzz512000))), h)
new_mkVBalBranch3MkVBalBranch281(zzz340, zzz341, Neg(Succ(Succ(Zero))), zzz343, zzz344, zzz510, zzz511, Succ(zzz512000), zzz513, zzz514, zzz31, Succ(Zero), h) → new_mkVBalBranch3MkVBalBranch280(zzz340, zzz341, Succ(Zero), zzz343, zzz344, zzz510, zzz511, zzz512000, zzz513, zzz514, zzz31, Zero, Succ(zzz512000), h)
new_mkVBalBranch3MkVBalBranch280(zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, zzz1125, zzz1126, zzz1127, zzz1128, zzz1129, Zero, Succ(zzz11310), ff) → new_mkVBalBranch3MkVBalBranch257(zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, zzz1125, zzz1126, zzz1127, zzz1128, zzz1129, ff)
new_mkVBalBranch3MkVBalBranch257(zzz486, zzz487, zzz488, zzz489, zzz490, zzz491, zzz492, zzz493, zzz494, zzz495, zzz496, ea) → new_mkBalBranch(zzz486, zzz487, new_mkVBalBranch4(zzz496, Branch(zzz491, zzz492, Neg(Succ(Succ(zzz493))), zzz494, zzz495), zzz489, ea), zzz490, ty_Ordering, ea)
new_mkVBalBranch3MkVBalBranch263(zzz498, zzz499, zzz500, zzz501, zzz502, zzz503, zzz504, zzz505, zzz506, zzz507, Succ(zzz5080), Zero, ee) → new_mkVBalBranch3MkVBalBranch264(zzz498, zzz499, zzz500, zzz501, zzz502, zzz503, zzz504, zzz505, zzz506, zzz507, ee)
new_mkVBalBranch3MkVBalBranch264(zzz498, zzz499, zzz500, zzz501, zzz502, zzz503, zzz504, zzz505, zzz506, zzz507, ee) → new_mkVBalBranch3MkVBalBranch157(zzz498, zzz499, zzz500, zzz501, zzz502, zzz503, zzz504, zzz505, zzz506, zzz507, new_primMulNat1(zzz500), ee)
new_mkVBalBranch3MkVBalBranch157(zzz498, zzz499, zzz500, zzz501, zzz502, zzz503, zzz504, zzz505, zzz506, zzz507, Succ(zzz8040), ee) → new_mkVBalBranch3MkVBalBranch149(zzz498, zzz499, zzz500, zzz501, zzz502, zzz503, zzz504, Zero, zzz505, zzz506, zzz507, Succ(Zero), Succ(zzz8040), ee)
new_mkVBalBranch3MkVBalBranch157(zzz498, zzz499, zzz500, zzz501, zzz502, zzz503, zzz504, zzz505, zzz506, zzz507, Zero, ee) → new_mkVBalBranch3MkVBalBranch149(zzz498, zzz499, zzz500, zzz501, zzz502, zzz503, zzz504, Zero, zzz505, zzz506, zzz507, Succ(Zero), Zero, ee)
new_mkVBalBranch3MkVBalBranch149(zzz2050, zzz2051, zzz2052, zzz2053, zzz2054, zzz2055, zzz2056, zzz2057, zzz2058, zzz2059, zzz2060, Succ(zzz20610), Zero, ef) → new_mkVBalBranch3MkVBalBranch150(zzz2050, zzz2051, zzz2052, zzz2053, zzz2054, zzz2055, zzz2056, zzz2057, zzz2058, zzz2059, zzz2060, ef)
new_mkVBalBranch3MkVBalBranch150(zzz2050, zzz2051, zzz2052, zzz2053, zzz2054, zzz2055, zzz2056, zzz2057, zzz2058, zzz2059, zzz2060, ef) → new_mkBranch(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))), EQ, zzz2060, Branch(zzz2055, zzz2056, Neg(Succ(zzz2057)), zzz2058, zzz2059), Branch(zzz2050, zzz2051, Neg(Succ(zzz2052)), zzz2053, zzz2054), ty_Ordering, ef)
new_mkVBalBranch3MkVBalBranch149(zzz2050, zzz2051, zzz2052, zzz2053, zzz2054, zzz2055, zzz2056, zzz2057, zzz2058, zzz2059, zzz2060, Succ(zzz20610), Succ(zzz20620), ef) → new_mkVBalBranch3MkVBalBranch149(zzz2050, zzz2051, zzz2052, zzz2053, zzz2054, zzz2055, zzz2056, zzz2057, zzz2058, zzz2059, zzz2060, zzz20610, zzz20620, ef)
new_mkVBalBranch3MkVBalBranch149(zzz2050, zzz2051, zzz2052, zzz2053, zzz2054, zzz2055, zzz2056, zzz2057, zzz2058, zzz2059, zzz2060, Zero, Zero, ef) → new_mkVBalBranch3MkVBalBranch150(zzz2050, zzz2051, zzz2052, zzz2053, zzz2054, zzz2055, zzz2056, zzz2057, zzz2058, zzz2059, zzz2060, ef)
new_mkVBalBranch3MkVBalBranch149(zzz2050, zzz2051, zzz2052, zzz2053, zzz2054, zzz2055, zzz2056, zzz2057, zzz2058, zzz2059, zzz2060, Zero, Succ(zzz20620), ef) → new_mkBalBranch(zzz2055, zzz2056, zzz2058, new_mkVBalBranch4(zzz2060, zzz2059, Branch(zzz2050, zzz2051, Neg(Succ(zzz2052)), zzz2053, zzz2054), ef), ty_Ordering, ef)
new_mkVBalBranch3MkVBalBranch248(zzz340, zzz341, zzz3420, zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, h) → new_mkBalBranch(zzz340, zzz341, new_mkVBalBranch4(zzz31, Branch(zzz510, zzz511, Neg(Succ(zzz51200)), zzz513, zzz514), zzz343, h), zzz344, ty_Ordering, h)
new_mkVBalBranch3MkVBalBranch266(zzz340, zzz341, zzz343, zzz344, zzz510, zzz511, zzz51200, zzz513, zzz514, zzz31, h) → new_mkBalBranch(zzz340, zzz341, new_mkVBalBranch4(zzz31, Branch(zzz510, zzz511, Neg(Succ(zzz51200)), zzz513, zzz514), zzz343, h), zzz344, ty_Ordering, h)
new_mkVBalBranch3MkVBalBranch280(zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, zzz1125, zzz1126, zzz1127, zzz1128, zzz1129, Succ(zzz11300), Succ(zzz11310), ff) → new_mkVBalBranch3MkVBalBranch280(zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, zzz1125, zzz1126, zzz1127, zzz1128, zzz1129, zzz11300, zzz11310, ff)
new_mkVBalBranch3MkVBalBranch280(zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, zzz1125, zzz1126, zzz1127, zzz1128, zzz1129, Succ(zzz11300), Zero, ff) → new_mkVBalBranch3MkVBalBranch278(zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, zzz1125, zzz1126, zzz1127, zzz1128, zzz1129, ff)
new_mkVBalBranch3MkVBalBranch280(zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, zzz1125, zzz1126, zzz1127, zzz1128, zzz1129, Zero, Zero, ff) → new_mkVBalBranch3MkVBalBranch278(zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, zzz1125, zzz1126, zzz1127, zzz1128, zzz1129, ff)
new_mkVBalBranch3MkVBalBranch278(zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, zzz1125, zzz1126, zzz1127, zzz1128, zzz1129, ff) → new_mkVBalBranch3MkVBalBranch159(zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, zzz1125, zzz1126, zzz1127, zzz1128, zzz1129, new_primMulNat1(zzz1121), ff)
new_mkVBalBranch3MkVBalBranch159(zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, zzz1125, zzz1126, zzz1127, zzz1128, zzz1129, Succ(zzz12130), ff) → new_mkVBalBranch3MkVBalBranch149(zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, zzz1125, Succ(zzz1126), zzz1127, zzz1128, zzz1129, Succ(Succ(zzz1126)), Succ(zzz12130), ff)
new_mkVBalBranch3MkVBalBranch159(zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, zzz1125, zzz1126, zzz1127, zzz1128, zzz1129, Zero, ff) → new_mkVBalBranch3MkVBalBranch149(zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, zzz1125, Succ(zzz1126), zzz1127, zzz1128, zzz1129, Succ(Succ(zzz1126)), Zero, ff)
new_mkVBalBranch3MkVBalBranch263(zzz498, zzz499, zzz500, zzz501, zzz502, zzz503, zzz504, zzz505, zzz506, zzz507, Succ(zzz5080), Succ(zzz5090), ee) → new_mkVBalBranch3MkVBalBranch263(zzz498, zzz499, zzz500, zzz501, zzz502, zzz503, zzz504, zzz505, zzz506, zzz507, zzz5080, zzz5090, ee)
new_mkVBalBranch3MkVBalBranch263(zzz498, zzz499, zzz500, zzz501, zzz502, zzz503, zzz504, zzz505, zzz506, zzz507, Zero, Zero, ee) → new_mkVBalBranch3MkVBalBranch264(zzz498, zzz499, zzz500, zzz501, zzz502, zzz503, zzz504, zzz505, zzz506, zzz507, ee)
new_mkVBalBranch3MkVBalBranch263(zzz498, zzz499, zzz500, zzz501, zzz502, zzz503, zzz504, zzz505, zzz506, zzz507, Zero, Succ(zzz5090), ee) → new_mkBalBranch(zzz498, zzz499, new_mkVBalBranch4(zzz507, Branch(zzz503, zzz504, Neg(Succ(Zero)), zzz505, zzz506), zzz501, ee), zzz502, ty_Ordering, ee)
new_mkVBalBranch3MkVBalBranch249(zzz340, zzz341, zzz342000, zzz343, zzz344, zzz510, zzz511, zzz513, zzz514, zzz31, h) → new_mkVBalBranch3MkVBalBranch250(zzz340, zzz341, zzz342000, zzz343, zzz344, zzz510, zzz511, zzz513, zzz514, zzz31, h)
new_mkVBalBranch3MkVBalBranch250(zzz340, zzz341, zzz342000, zzz343, zzz344, zzz510, zzz511, zzz513, zzz514, zzz31, h) → new_mkVBalBranch3MkVBalBranch157(zzz340, zzz341, Succ(zzz342000), zzz343, zzz344, zzz510, zzz511, zzz513, zzz514, zzz31, new_primMulNat1(Succ(zzz342000)), h)
new_addToFM2(zzz34, zzz31, h) → new_addToFM_C4(zzz34, zzz31, h)
new_addToFM_C4(EmptyFM, zzz31, h) → Branch(EQ, zzz31, Pos(Succ(Zero)), new_emptyFM(h), new_emptyFM(h))
new_addToFM_C4(Branch(GT, zzz341, zzz342, zzz343, zzz344), zzz31, h) → new_mkBalBranch(GT, zzz341, new_addToFM_C4(zzz343, zzz31, h), zzz344, ty_Ordering, h)
new_addToFM_C4(Branch(LT, zzz341, zzz342, zzz343, zzz344), zzz31, h) → new_mkBalBranch(LT, zzz341, zzz343, new_addToFM_C4(zzz344, zzz31, h), ty_Ordering, h)
new_addToFM_C4(Branch(EQ, zzz341, zzz342, zzz343, zzz344), zzz31, h) → Branch(EQ, new_addToFM0(zzz341, zzz31, h), zzz342, zzz343, zzz344)
new_mkVBalBranch3MkVBalBranch133(zzz340, zzz341, zzz34200, zzz343, zzz344, zzz510, zzz511, zzz513, zzz514, zzz31, Succ(zzz1240), h) → new_mkBalBranch(zzz510, zzz511, zzz513, new_mkVBalBranch4(zzz31, zzz514, Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), h), ty_Ordering, h)
new_mkVBalBranch3MkVBalBranch133(zzz340, zzz341, zzz34200, zzz343, zzz344, zzz510, zzz511, zzz513, zzz514, zzz31, Zero, h) → new_mkBranch(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))), EQ, zzz31, Branch(zzz510, zzz511, Neg(Zero), zzz513, zzz514), Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), ty_Ordering, h)
new_mkVBalBranch3MkVBalBranch168(zzz340, zzz341, zzz34200, zzz343, zzz344, zzz510, zzz511, zzz513, zzz514, zzz31, Zero, h) → new_mkBranch(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))), EQ, zzz31, Branch(zzz510, zzz511, Pos(Zero), zzz513, zzz514), Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), ty_Ordering, h)
new_mkVBalBranch3MkVBalBranch168(zzz340, zzz341, zzz34200, zzz343, zzz344, zzz510, zzz511, zzz513, zzz514, zzz31, Succ(zzz1200), h) → new_mkBalBranch(zzz510, zzz511, zzz513, new_mkVBalBranch4(zzz31, zzz514, Branch(zzz340, zzz341, Neg(Succ(zzz34200)), zzz343, zzz344), h), ty_Ordering, h)
new_splitGT28(zzz869, zzz870, zzz871, zzz872, bc) → new_mkVBalBranch3(zzz869, new_splitGT12(zzz871, bc), zzz872, bc)
new_splitGT41(h) → new_emptyFM(h)
new_splitGT210(zzz31, zzz32, zzz33, zzz34, h) → zzz34
new_intersectFM_C2Gts1(zzz869, zzz870, zzz871, zzz872, bc) → new_splitGT28(zzz869, zzz870, zzz871, zzz872, bc)
new_intersectFM_C2Lts(zzz76, zzz77, zzz78, zzz79, bg) → new_splitLT9(zzz76, zzz77, zzz78, zzz79, bg)
new_splitLT9(zzz76, zzz77, zzz78, zzz79, bg) → new_splitLT27(zzz76, zzz77, zzz78, zzz79, bg)
new_splitLT23(zzz76, zzz77, zzz78, zzz79, bg) → new_splitLT15(zzz78, bg)
new_splitLT15(Branch(GT, zzz781, zzz782, zzz783, zzz784), bg) → new_splitLT27(zzz781, zzz782, zzz783, zzz784, bg)
new_splitLT27(zzz76, zzz77, zzz78, zzz79, bg) → new_splitLT23(zzz76, zzz77, zzz78, zzz79, bg)
new_splitLT15(Branch(EQ, zzz781, zzz782, zzz783, zzz784), bg) → new_splitLT26(zzz781, zzz782, zzz783, zzz784, bg)
new_splitLT15(Branch(LT, zzz781, zzz782, zzz783, zzz784), bg) → new_mkVBalBranch2(zzz781, zzz783, new_splitLT15(zzz784, bg), bg)
new_splitLT15(EmptyFM, bg) → new_splitLT41(bg)
new_splitLT41(h) → new_emptyFM(h)
new_mkVBalBranch2(zzz31, Branch(zzz330, zzz331, Neg(Succ(zzz33200)), zzz333, zzz334), Branch(zzz3170, zzz3171, zzz3172, zzz3173, zzz3174), h) → new_mkVBalBranch3MkVBalBranch262(zzz3170, zzz3171, zzz3172, zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, new_primPlusNat2(new_primMulNat0(zzz33200), Succ(zzz33200)), h)
new_mkVBalBranch2(zzz31, EmptyFM, zzz317, h) → new_addToFM1(zzz317, zzz31, h)
new_mkVBalBranch2(zzz31, Branch(zzz330, zzz331, Neg(Zero), zzz333, zzz334), Branch(zzz3170, zzz3171, Pos(Succ(zzz317200)), zzz3173, zzz3174), h) → new_mkBalBranch(zzz3170, zzz3171, new_mkVBalBranch2(zzz31, Branch(zzz330, zzz331, Neg(Zero), zzz333, zzz334), zzz3173, h), zzz3174, ty_Ordering, h)
new_mkVBalBranch2(zzz31, Branch(zzz330, zzz331, zzz332, zzz333, zzz334), EmptyFM, h) → new_addToFM1(Branch(zzz330, zzz331, zzz332, zzz333, zzz334), zzz31, h)
new_mkVBalBranch2(zzz31, Branch(zzz330, zzz331, Neg(Zero), zzz333, zzz334), Branch(zzz3170, zzz3171, Neg(Zero), zzz3173, zzz3174), h) → new_mkBranch(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))), LT, zzz31, Branch(zzz330, zzz331, Neg(Zero), zzz333, zzz334), Branch(zzz3170, zzz3171, Neg(Zero), zzz3173, zzz3174), ty_Ordering, h)
new_mkVBalBranch2(zzz31, Branch(zzz330, zzz331, Pos(Succ(zzz33200)), zzz333, zzz334), Branch(zzz3170, zzz3171, zzz3172, zzz3173, zzz3174), h) → new_mkVBalBranch3MkVBalBranch261(zzz3170, zzz3171, zzz3172, zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, new_primPlusNat2(new_primMulNat0(zzz33200), Succ(zzz33200)), h)
new_mkVBalBranch2(zzz31, Branch(zzz330, zzz331, Neg(Zero), zzz333, zzz334), Branch(zzz3170, zzz3171, Neg(Succ(zzz317200)), zzz3173, zzz3174), h) → new_mkVBalBranch3MkVBalBranch146(zzz3170, zzz3171, zzz317200, zzz3173, zzz3174, zzz330, zzz331, zzz333, zzz334, zzz31, new_primMulNat1(zzz317200), h)
new_mkVBalBranch2(zzz31, Branch(zzz330, zzz331, Pos(Zero), zzz333, zzz334), Branch(zzz3170, zzz3171, Neg(Zero), zzz3173, zzz3174), h) → new_mkBranch(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))), LT, zzz31, Branch(zzz330, zzz331, Pos(Zero), zzz333, zzz334), Branch(zzz3170, zzz3171, Neg(Zero), zzz3173, zzz3174), ty_Ordering, h)
new_mkVBalBranch2(zzz31, Branch(zzz330, zzz331, Neg(Zero), zzz333, zzz334), Branch(zzz3170, zzz3171, Pos(Zero), zzz3173, zzz3174), h) → new_mkBranch(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))), LT, zzz31, Branch(zzz330, zzz331, Neg(Zero), zzz333, zzz334), Branch(zzz3170, zzz3171, Pos(Zero), zzz3173, zzz3174), ty_Ordering, h)
new_mkVBalBranch2(zzz31, Branch(zzz330, zzz331, Pos(Zero), zzz333, zzz334), Branch(zzz3170, zzz3171, Pos(Zero), zzz3173, zzz3174), h) → new_mkBranch(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))), LT, zzz31, Branch(zzz330, zzz331, Pos(Zero), zzz333, zzz334), Branch(zzz3170, zzz3171, Pos(Zero), zzz3173, zzz3174), ty_Ordering, h)
new_mkVBalBranch2(zzz31, Branch(zzz330, zzz331, Pos(Zero), zzz333, zzz334), Branch(zzz3170, zzz3171, Pos(Succ(zzz317200)), zzz3173, zzz3174), h) → new_mkBalBranch(zzz3170, zzz3171, new_mkVBalBranch2(zzz31, Branch(zzz330, zzz331, Pos(Zero), zzz333, zzz334), zzz3173, h), zzz3174, ty_Ordering, h)
new_mkVBalBranch2(zzz31, Branch(zzz330, zzz331, Pos(Zero), zzz333, zzz334), Branch(zzz3170, zzz3171, Neg(Succ(zzz317200)), zzz3173, zzz3174), h) → new_mkVBalBranch3MkVBalBranch145(zzz3170, zzz3171, zzz317200, zzz3173, zzz3174, zzz330, zzz331, zzz333, zzz334, zzz31, new_primMulNat1(zzz317200), h)
new_mkVBalBranch3MkVBalBranch145(zzz3170, zzz3171, zzz317200, zzz3173, zzz3174, zzz330, zzz331, zzz333, zzz334, zzz31, Zero, h) → new_mkBranch(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))), LT, zzz31, Branch(zzz330, zzz331, Pos(Zero), zzz333, zzz334), Branch(zzz3170, zzz3171, Neg(Succ(zzz317200)), zzz3173, zzz3174), ty_Ordering, h)
new_mkVBalBranch3MkVBalBranch145(zzz3170, zzz3171, zzz317200, zzz3173, zzz3174, zzz330, zzz331, zzz333, zzz334, zzz31, Succ(zzz5350), h) → new_mkBalBranch(zzz330, zzz331, zzz333, new_mkVBalBranch2(zzz31, zzz334, Branch(zzz3170, zzz3171, Neg(Succ(zzz317200)), zzz3173, zzz3174), h), ty_Ordering, h)
new_mkVBalBranch3MkVBalBranch146(zzz3170, zzz3171, zzz317200, zzz3173, zzz3174, zzz330, zzz331, zzz333, zzz334, zzz31, Succ(zzz5500), h) → new_mkBalBranch(zzz330, zzz331, zzz333, new_mkVBalBranch2(zzz31, zzz334, Branch(zzz3170, zzz3171, Neg(Succ(zzz317200)), zzz3173, zzz3174), h), ty_Ordering, h)
new_mkVBalBranch3MkVBalBranch146(zzz3170, zzz3171, zzz317200, zzz3173, zzz3174, zzz330, zzz331, zzz333, zzz334, zzz31, Zero, h) → new_mkBranch(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))), LT, zzz31, Branch(zzz330, zzz331, Neg(Zero), zzz333, zzz334), Branch(zzz3170, zzz3171, Neg(Succ(zzz317200)), zzz3173, zzz3174), ty_Ordering, h)
new_mkVBalBranch3MkVBalBranch261(zzz3170, zzz3171, Pos(Succ(zzz317200)), zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, Succ(zzz4170), h) → new_mkVBalBranch3MkVBalBranch275(zzz3170, zzz3171, zzz317200, zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, zzz4170, zzz317200, h)
new_mkVBalBranch3MkVBalBranch261(zzz3170, zzz3171, Pos(Zero), zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, Succ(zzz4170), h) → new_mkVBalBranch3MkVBalBranch279(zzz3170, zzz3171, zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, h)
new_mkVBalBranch3MkVBalBranch261(zzz3170, zzz3171, Pos(Succ(zzz317200)), zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, Zero, h) → new_mkVBalBranch3MkVBalBranch275(zzz3170, zzz3171, zzz317200, zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, Zero, Succ(zzz317200), h)
new_mkVBalBranch3MkVBalBranch261(zzz3170, zzz3171, Pos(Zero), zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, Zero, h) → new_mkVBalBranch3MkVBalBranch279(zzz3170, zzz3171, zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, h)
new_mkVBalBranch3MkVBalBranch261(zzz3170, zzz3171, Neg(Succ(zzz317200)), zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, Zero, h) → new_mkVBalBranch3MkVBalBranch286(zzz3170, zzz3171, Succ(zzz317200), zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, h)
new_mkVBalBranch3MkVBalBranch261(zzz3170, zzz3171, Neg(Zero), zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, Zero, h) → new_mkVBalBranch3MkVBalBranch265(zzz3170, zzz3171, Zero, zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, h)
new_mkVBalBranch3MkVBalBranch261(zzz3170, zzz3171, Neg(zzz31720), zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, Succ(zzz4170), h) → new_mkVBalBranch3MkVBalBranch286(zzz3170, zzz3171, zzz31720, zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, h)
new_mkVBalBranch3MkVBalBranch286(zzz3170, zzz3171, zzz31720, zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, h) → new_mkVBalBranch3MkVBalBranch265(zzz3170, zzz3171, zzz31720, zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, h)
new_mkVBalBranch3MkVBalBranch265(zzz3170, zzz3171, Zero, zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, h) → new_mkBalBranch(zzz330, zzz331, zzz333, new_mkVBalBranch2(zzz31, zzz334, Branch(zzz3170, zzz3171, Neg(Zero), zzz3173, zzz3174), h), ty_Ordering, h)
new_mkVBalBranch3MkVBalBranch265(zzz3170, zzz3171, Succ(zzz317200), zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, h) → new_mkVBalBranch3MkVBalBranch139(zzz3170, zzz3171, zzz317200, zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, new_primPlusNat2(new_primMulNat0(zzz317200), Succ(zzz317200)), h)
new_mkVBalBranch3MkVBalBranch139(zzz3170, zzz3171, zzz317200, zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, Succ(zzz5620), h) → new_mkVBalBranch3MkVBalBranch140(zzz3170, zzz3171, zzz317200, zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, h)
new_mkVBalBranch3MkVBalBranch139(zzz3170, zzz3171, zzz317200, zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, Zero, h) → new_mkVBalBranch3MkVBalBranch140(zzz3170, zzz3171, zzz317200, zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, h)
new_mkVBalBranch3MkVBalBranch140(zzz3170, zzz3171, zzz317200, zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, h) → new_mkBalBranch(zzz330, zzz331, zzz333, new_mkVBalBranch2(zzz31, zzz334, Branch(zzz3170, zzz3171, Neg(Succ(zzz317200)), zzz3173, zzz3174), h), ty_Ordering, h)
new_mkVBalBranch3MkVBalBranch279(zzz3170, zzz3171, zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, h) → new_mkBalBranch(zzz330, zzz331, zzz333, new_mkVBalBranch2(zzz31, zzz334, Branch(zzz3170, zzz3171, Pos(Zero), zzz3173, zzz3174), h), ty_Ordering, h)
new_mkVBalBranch3MkVBalBranch275(zzz958, zzz959, zzz960, zzz961, zzz962, zzz963, zzz964, zzz965, zzz966, zzz967, zzz968, Zero, Succ(zzz9700), fa) → new_mkBalBranch(zzz958, zzz959, new_mkVBalBranch2(zzz968, Branch(zzz963, zzz964, Pos(Succ(zzz965)), zzz966, zzz967), zzz961, fa), zzz962, ty_Ordering, fa)
new_mkVBalBranch3MkVBalBranch275(zzz958, zzz959, zzz960, zzz961, zzz962, zzz963, zzz964, zzz965, zzz966, zzz967, zzz968, Zero, Zero, fa) → new_mkVBalBranch3MkVBalBranch276(zzz958, zzz959, zzz960, zzz961, zzz962, zzz963, zzz964, zzz965, zzz966, zzz967, zzz968, fa)
new_mkVBalBranch3MkVBalBranch275(zzz958, zzz959, zzz960, zzz961, zzz962, zzz963, zzz964, zzz965, zzz966, zzz967, zzz968, Succ(zzz9690), Succ(zzz9700), fa) → new_mkVBalBranch3MkVBalBranch275(zzz958, zzz959, zzz960, zzz961, zzz962, zzz963, zzz964, zzz965, zzz966, zzz967, zzz968, zzz9690, zzz9700, fa)
new_mkVBalBranch3MkVBalBranch275(zzz958, zzz959, zzz960, zzz961, zzz962, zzz963, zzz964, zzz965, zzz966, zzz967, zzz968, Succ(zzz9690), Zero, fa) → new_mkVBalBranch3MkVBalBranch276(zzz958, zzz959, zzz960, zzz961, zzz962, zzz963, zzz964, zzz965, zzz966, zzz967, zzz968, fa)
new_mkVBalBranch3MkVBalBranch276(zzz958, zzz959, zzz960, zzz961, zzz962, zzz963, zzz964, zzz965, zzz966, zzz967, zzz968, fa) → new_mkVBalBranch3MkVBalBranch156(zzz958, zzz959, zzz960, zzz961, zzz962, zzz963, zzz964, zzz965, zzz966, zzz967, zzz968, new_primMulNat1(zzz960), fa)
new_mkVBalBranch3MkVBalBranch156(zzz958, zzz959, zzz960, zzz961, zzz962, zzz963, zzz964, zzz965, zzz966, zzz967, zzz968, Succ(zzz10180), fa) → new_mkVBalBranch3MkVBalBranch152(zzz958, zzz959, zzz960, zzz961, zzz962, zzz963, zzz964, zzz965, zzz966, zzz967, zzz968, Succ(zzz10180), Succ(zzz965), fa)
new_mkVBalBranch3MkVBalBranch156(zzz958, zzz959, zzz960, zzz961, zzz962, zzz963, zzz964, zzz965, zzz966, zzz967, zzz968, Zero, fa) → new_mkVBalBranch3MkVBalBranch152(zzz958, zzz959, zzz960, zzz961, zzz962, zzz963, zzz964, zzz965, zzz966, zzz967, zzz968, Zero, Succ(zzz965), fa)
new_mkVBalBranch3MkVBalBranch152(zzz1337, zzz1338, zzz1339, zzz1340, zzz1341, zzz1342, zzz1343, zzz1344, zzz1345, zzz1346, zzz1347, Zero, Succ(zzz13490), eg) → new_mkBalBranch(zzz1342, zzz1343, zzz1345, new_mkVBalBranch2(zzz1347, zzz1346, Branch(zzz1337, zzz1338, Pos(Succ(zzz1339)), zzz1340, zzz1341), eg), ty_Ordering, eg)
new_mkVBalBranch3MkVBalBranch152(zzz1337, zzz1338, zzz1339, zzz1340, zzz1341, zzz1342, zzz1343, zzz1344, zzz1345, zzz1346, zzz1347, Succ(zzz13480), Succ(zzz13490), eg) → new_mkVBalBranch3MkVBalBranch152(zzz1337, zzz1338, zzz1339, zzz1340, zzz1341, zzz1342, zzz1343, zzz1344, zzz1345, zzz1346, zzz1347, zzz13480, zzz13490, eg)
new_mkVBalBranch3MkVBalBranch152(zzz1337, zzz1338, zzz1339, zzz1340, zzz1341, zzz1342, zzz1343, zzz1344, zzz1345, zzz1346, zzz1347, Succ(zzz13480), Zero, eg) → new_mkVBalBranch3MkVBalBranch151(zzz1337, zzz1338, zzz1339, zzz1340, zzz1341, zzz1342, zzz1343, zzz1344, zzz1345, zzz1346, zzz1347, eg)
new_mkVBalBranch3MkVBalBranch152(zzz1337, zzz1338, zzz1339, zzz1340, zzz1341, zzz1342, zzz1343, zzz1344, zzz1345, zzz1346, zzz1347, Zero, Zero, eg) → new_mkVBalBranch3MkVBalBranch151(zzz1337, zzz1338, zzz1339, zzz1340, zzz1341, zzz1342, zzz1343, zzz1344, zzz1345, zzz1346, zzz1347, eg)
new_mkVBalBranch3MkVBalBranch151(zzz1337, zzz1338, zzz1339, zzz1340, zzz1341, zzz1342, zzz1343, zzz1344, zzz1345, zzz1346, zzz1347, eg) → new_mkBranch(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))), LT, zzz1347, Branch(zzz1342, zzz1343, Pos(Succ(zzz1344)), zzz1345, zzz1346), Branch(zzz1337, zzz1338, Pos(Succ(zzz1339)), zzz1340, zzz1341), ty_Ordering, eg)
new_addToFM1(zzz317, zzz31, h) → new_addToFM_C2(zzz317, zzz31, h)
new_addToFM_C2(EmptyFM, zzz31, h) → Branch(LT, zzz31, Pos(Succ(Zero)), new_emptyFM(h), new_emptyFM(h))
new_addToFM_C2(Branch(GT, zzz3171, zzz3172, zzz3173, zzz3174), zzz31, h) → new_mkBalBranch(GT, zzz3171, new_addToFM_C2(zzz3173, zzz31, h), zzz3174, ty_Ordering, h)
new_addToFM_C2(Branch(EQ, zzz3171, zzz3172, zzz3173, zzz3174), zzz31, h) → new_mkBalBranch(EQ, zzz3171, new_addToFM_C2(zzz3173, zzz31, h), zzz3174, ty_Ordering, h)
new_addToFM_C2(Branch(LT, zzz3171, zzz3172, zzz3173, zzz3174), zzz31, h) → Branch(LT, new_addToFM0(zzz3171, zzz31, h), zzz3172, zzz3173, zzz3174)
new_mkVBalBranch3MkVBalBranch262(zzz3170, zzz3171, Neg(Zero), zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, Zero, h) → new_mkBranch(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))), LT, zzz31, Branch(zzz330, zzz331, Neg(Succ(zzz33200)), zzz333, zzz334), Branch(zzz3170, zzz3171, Neg(Zero), zzz3173, zzz3174), ty_Ordering, h)
new_mkVBalBranch3MkVBalBranch262(zzz3170, zzz3171, Pos(Zero), zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, Zero, h) → new_mkBranch(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))), LT, zzz31, Branch(zzz330, zzz331, Neg(Succ(zzz33200)), zzz333, zzz334), Branch(zzz3170, zzz3171, Pos(Zero), zzz3173, zzz3174), ty_Ordering, h)
new_mkVBalBranch3MkVBalBranch262(zzz3170, zzz3171, Pos(Succ(zzz317200)), zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, Zero, h) → new_mkVBalBranch3MkVBalBranch251(zzz3170, zzz3171, Succ(zzz317200), zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, h)
new_mkVBalBranch3MkVBalBranch262(zzz3170, zzz3171, Pos(zzz31720), zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, Succ(zzz4190), h) → new_mkVBalBranch3MkVBalBranch251(zzz3170, zzz3171, zzz31720, zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, h)
new_mkVBalBranch3MkVBalBranch262(zzz3170, zzz3171, Neg(Succ(zzz317200)), zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, Zero, h) → new_mkVBalBranch3MkVBalBranch246(zzz3170, zzz3171, zzz317200, zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, Succ(zzz317200), Zero, h)
new_mkVBalBranch3MkVBalBranch262(zzz3170, zzz3171, Neg(Zero), zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, Succ(zzz4190), h) → new_mkBalBranch(zzz3170, zzz3171, new_mkVBalBranch2(zzz31, Branch(zzz330, zzz331, Neg(Succ(zzz33200)), zzz333, zzz334), zzz3173, h), zzz3174, ty_Ordering, h)
new_mkVBalBranch3MkVBalBranch262(zzz3170, zzz3171, Neg(Succ(zzz317200)), zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, Succ(zzz4190), h) → new_mkVBalBranch3MkVBalBranch246(zzz3170, zzz3171, zzz317200, zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, zzz317200, zzz4190, h)
new_mkVBalBranch3MkVBalBranch246(zzz972, zzz973, zzz974, zzz975, zzz976, zzz977, zzz978, zzz979, zzz980, zzz981, zzz982, Zero, Zero, cg) → new_mkVBalBranch3MkVBalBranch247(zzz972, zzz973, zzz974, zzz975, zzz976, zzz977, zzz978, zzz979, zzz980, zzz981, zzz982, cg)
new_mkVBalBranch3MkVBalBranch246(zzz972, zzz973, zzz974, zzz975, zzz976, zzz977, zzz978, zzz979, zzz980, zzz981, zzz982, Zero, Succ(zzz9840), cg) → new_mkBalBranch(zzz972, zzz973, new_mkVBalBranch2(zzz982, Branch(zzz977, zzz978, Neg(Succ(zzz979)), zzz980, zzz981), zzz975, cg), zzz976, ty_Ordering, cg)
new_mkVBalBranch3MkVBalBranch246(zzz972, zzz973, zzz974, zzz975, zzz976, zzz977, zzz978, zzz979, zzz980, zzz981, zzz982, Succ(zzz9830), Succ(zzz9840), cg) → new_mkVBalBranch3MkVBalBranch246(zzz972, zzz973, zzz974, zzz975, zzz976, zzz977, zzz978, zzz979, zzz980, zzz981, zzz982, zzz9830, zzz9840, cg)
new_mkVBalBranch3MkVBalBranch246(zzz972, zzz973, zzz974, zzz975, zzz976, zzz977, zzz978, zzz979, zzz980, zzz981, zzz982, Succ(zzz9830), Zero, cg) → new_mkVBalBranch3MkVBalBranch247(zzz972, zzz973, zzz974, zzz975, zzz976, zzz977, zzz978, zzz979, zzz980, zzz981, zzz982, cg)
new_mkVBalBranch3MkVBalBranch247(zzz972, zzz973, zzz974, zzz975, zzz976, zzz977, zzz978, zzz979, zzz980, zzz981, zzz982, cg) → new_mkVBalBranch3MkVBalBranch141(zzz972, zzz973, zzz974, zzz975, zzz976, zzz977, zzz978, zzz979, zzz980, zzz981, zzz982, new_primMulNat1(zzz974), cg)
new_mkVBalBranch3MkVBalBranch141(zzz972, zzz973, zzz974, zzz975, zzz976, zzz977, zzz978, zzz979, zzz980, zzz981, zzz982, Succ(zzz10190), cg) → new_mkVBalBranch3MkVBalBranch134(zzz972, zzz973, zzz974, zzz975, zzz976, zzz977, zzz978, zzz979, zzz980, zzz981, zzz982, Succ(zzz979), Succ(zzz10190), cg)
new_mkVBalBranch3MkVBalBranch141(zzz972, zzz973, zzz974, zzz975, zzz976, zzz977, zzz978, zzz979, zzz980, zzz981, zzz982, Zero, cg) → new_mkVBalBranch3MkVBalBranch134(zzz972, zzz973, zzz974, zzz975, zzz976, zzz977, zzz978, zzz979, zzz980, zzz981, zzz982, Succ(zzz979), Zero, cg)
new_mkVBalBranch3MkVBalBranch134(zzz1851, zzz1852, zzz1853, zzz1854, zzz1855, zzz1856, zzz1857, zzz1858, zzz1859, zzz1860, zzz1861, Succ(zzz18620), Zero, dd) → new_mkVBalBranch3MkVBalBranch135(zzz1851, zzz1852, zzz1853, zzz1854, zzz1855, zzz1856, zzz1857, zzz1858, zzz1859, zzz1860, zzz1861, dd)
new_mkVBalBranch3MkVBalBranch135(zzz1851, zzz1852, zzz1853, zzz1854, zzz1855, zzz1856, zzz1857, zzz1858, zzz1859, zzz1860, zzz1861, dd) → new_mkBranch(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))), LT, zzz1861, Branch(zzz1856, zzz1857, Neg(Succ(zzz1858)), zzz1859, zzz1860), Branch(zzz1851, zzz1852, Neg(Succ(zzz1853)), zzz1854, zzz1855), ty_Ordering, dd)
new_mkVBalBranch3MkVBalBranch134(zzz1851, zzz1852, zzz1853, zzz1854, zzz1855, zzz1856, zzz1857, zzz1858, zzz1859, zzz1860, zzz1861, Succ(zzz18620), Succ(zzz18630), dd) → new_mkVBalBranch3MkVBalBranch134(zzz1851, zzz1852, zzz1853, zzz1854, zzz1855, zzz1856, zzz1857, zzz1858, zzz1859, zzz1860, zzz1861, zzz18620, zzz18630, dd)
new_mkVBalBranch3MkVBalBranch134(zzz1851, zzz1852, zzz1853, zzz1854, zzz1855, zzz1856, zzz1857, zzz1858, zzz1859, zzz1860, zzz1861, Zero, Succ(zzz18630), dd) → new_mkBalBranch(zzz1856, zzz1857, zzz1859, new_mkVBalBranch2(zzz1861, zzz1860, Branch(zzz1851, zzz1852, Neg(Succ(zzz1853)), zzz1854, zzz1855), dd), ty_Ordering, dd)
new_mkVBalBranch3MkVBalBranch134(zzz1851, zzz1852, zzz1853, zzz1854, zzz1855, zzz1856, zzz1857, zzz1858, zzz1859, zzz1860, zzz1861, Zero, Zero, dd) → new_mkVBalBranch3MkVBalBranch135(zzz1851, zzz1852, zzz1853, zzz1854, zzz1855, zzz1856, zzz1857, zzz1858, zzz1859, zzz1860, zzz1861, dd)
new_mkVBalBranch3MkVBalBranch251(zzz3170, zzz3171, zzz31720, zzz3173, zzz3174, zzz330, zzz331, zzz33200, zzz333, zzz334, zzz31, h) → new_mkBalBranch(zzz3170, zzz3171, new_mkVBalBranch2(zzz31, Branch(zzz330, zzz331, Neg(Succ(zzz33200)), zzz333, zzz334), zzz3173, h), zzz3174, ty_Ordering, h)
new_splitLT26(zzz31, zzz32, zzz33, zzz34, h) → zzz33
new_intersectFM_C2Gts(zzz76, zzz77, zzz78, zzz79, bg) → new_splitGT9(zzz76, zzz77, zzz78, zzz79, bg)
new_splitGT9(zzz76, zzz77, zzz78, zzz79, bg) → new_splitGT26(zzz76, zzz77, zzz78, zzz79, bg)
new_intersectFM_C2Gts2(zzz883, zzz884, zzz885, zzz886, be) → new_splitGT29(zzz883, zzz884, zzz885, zzz886, be)
new_splitLT7(zzz31, zzz32, zzz33, zzz34, h) → new_splitLT26(zzz31, zzz32, zzz33, zzz34, h)
new_splitLT10(zzz31, zzz32, zzz33, h) → new_mkVBalBranch2(zzz31, zzz33, new_splitLT13(h), h)
new_splitLT13(h) → new_splitLT40(h)
new_splitLT40(h) → new_emptyFM(h)
new_intersectFM_C2Lts1(zzz869, zzz870, zzz871, zzz872, bc) → new_splitLT25(zzz869, zzz870, zzz871, zzz872, bc)
new_splitLT25(zzz869, zzz870, zzz871, zzz872, bc) → new_splitLT12(zzz871, bc)
new_splitLT12(Branch(EQ, zzz8561, zzz8562, zzz8563, zzz8564), ba) → new_splitLT24(zzz8561, zzz8562, zzz8563, zzz8564, ba)
new_splitLT12(Branch(GT, zzz8561, zzz8562, zzz8563, zzz8564), ba) → new_splitLT25(zzz8561, zzz8562, zzz8563, zzz8564, ba)
new_splitLT24(zzz854, zzz855, zzz856, zzz857, ba) → new_splitLT12(zzz856, ba)
new_splitLT12(EmptyFM, ba) → new_splitLT42(ba)
new_splitLT12(Branch(LT, zzz8561, zzz8562, zzz8563, zzz8564), ba) → new_splitLT28(zzz8561, zzz8562, zzz8563, zzz8564, ba)
new_splitLT28(zzz31, zzz32, zzz33, zzz34, h) → zzz33
new_splitLT42(h) → new_emptyFM(h)
new_splitLT11(zzz31, zzz32, zzz33, h) → new_mkVBalBranch4(zzz31, zzz33, new_splitLT13(h), h)
new_splitGT8(zzz31, zzz32, zzz34, h) → new_mkVBalBranch3(zzz31, new_splitGT6(h), zzz34, h)
new_splitGT6(h) → new_splitGT42(h)
new_intersectFM_C2Gts3(zzz2129, cc) → new_splitGT15(zzz2129, cc)
new_splitGT15(Branch(LT, zzz21291, zzz21292, zzz21293, zzz21294), cc) → new_splitGT15(zzz21294, cc)
new_splitGT15(Branch(EQ, zzz21291, zzz21292, zzz21293, zzz21294), cc) → new_splitGT15(zzz21294, cc)
new_splitGT15(EmptyFM, cc) → new_splitGT40(cc)
new_splitGT15(Branch(GT, zzz21291, zzz21292, zzz21293, zzz21294), cc) → zzz21294
new_splitGT40(h) → new_emptyFM(h)
new_splitLT3(zzz31, zzz32, zzz33, zzz34, h) → new_splitLT28(zzz31, zzz32, zzz33, zzz34, h)
new_intersectFM_C2Lts3(zzz2129, cc) → new_splitLT14(zzz2129, cc)
new_splitLT14(Branch(LT, zzz21291, zzz21292, zzz21293, zzz21294), cc) → new_mkVBalBranch2(zzz21291, zzz21293, new_splitLT14(zzz21294, cc), cc)
new_splitLT14(EmptyFM, cc) → new_splitLT40(cc)
new_splitLT14(Branch(EQ, zzz21291, zzz21292, zzz21293, zzz21294), cc) → new_mkVBalBranch4(zzz21291, zzz21293, new_splitLT14(zzz21294, cc), cc)
new_splitLT14(Branch(GT, zzz21291, zzz21292, zzz21293, zzz21294), cc) → zzz21293
new_splitLT6(h) → new_splitLT41(h)
new_intersectFM_C2Lts2(zzz883, zzz884, zzz885, zzz886, be) → new_splitLT15(Branch(LT, zzz883, zzz884, zzz885, zzz886), be)
new_splitGT4(zzz31, zzz32, zzz34, h) → new_mkVBalBranch4(zzz31, new_splitGT13(h), zzz34, h)
new_splitGT13(h) → new_splitGT41(h)
new_splitGT7(zzz31, zzz32, zzz33, zzz34, h) → new_splitGT27(zzz31, zzz32, zzz33, zzz34, h)
new_intersectFM_C2Lts0(zzz854, zzz855, zzz856, zzz857, ba) → new_splitLT24(zzz854, zzz855, zzz856, zzz857, ba)
new_splitGT3(zzz31, zzz32, zzz33, zzz34, h) → new_splitGT210(zzz31, zzz32, zzz33, zzz34, h)
new_splitGT5(zzz31, zzz32, zzz34, h) → new_mkVBalBranch3(zzz31, new_splitGT13(h), zzz34, h)

The set Q consists of the following terms:

new_mkVBalBranch3MkVBalBranch281(x0, x1, Neg(Succ(Succ(Succ(x2)))), x3, x4, x5, x6, Succ(x7), x8, x9, x10, Succ(Succ(x11)), x12)
new_mkBalBranch6MkBalBranch35(x0, x1, x2, x3, Zero, x4, x5)
new_mkVBalBranch2(x0, Branch(x1, x2, Pos(Zero), x3, x4), Branch(x5, x6, Pos(Zero), x7, x8), x9)
new_mkVBalBranch3MkVBalBranch159(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, Zero, x11)
new_addToFM_C2(Branch(LT, x0, x1, x2, x3), x4, x5)
new_primMulNat1(x0)
new_primMinusNat0(Zero, Zero)
new_mkVBalBranch3MkVBalBranch281(x0, x1, Neg(Zero), x2, x3, x4, x5, x6, x7, x8, x9, Succ(x10), x11)
new_mkVBalBranch3MkVBalBranch263(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, Succ(x10), Succ(x11), x12)
new_mkVBalBranch3MkVBalBranch163(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11)
new_primPlusInt(Pos(x0), x1, x2, x3, x4, x5)
new_primMulNat0(x0)
new_mkBalBranch6MkBalBranch116(x0, x1, x2, x3, x4, x5, x6, x7, Succ(x8), x9, x10)
new_mkVBalBranch3(x0, EmptyFM, x1, x2)
new_mkVBalBranch3MkVBalBranch281(x0, x1, Neg(Succ(Succ(x2))), x3, x4, x5, x6, Zero, x7, x8, x9, Zero, x10)
new_mkBalBranch6MkBalBranch411(x0, x1, x2, x3, Pos(Succ(x4)), Pos(x5), x6, x7)
new_mkBalBranch6MkBalBranch1113(x0, x1, x2, x3, x4, x5, x6, x7, Zero, Succ(x8), x9, x10)
new_mkVBalBranch3MkVBalBranch157(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, Succ(x10), x11)
new_mkVBalBranch3MkVBalBranch278(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11)
new_mkVBalBranch3MkVBalBranch281(x0, x1, Neg(Zero), x2, x3, x4, x5, x6, x7, x8, x9, Zero, x10)
new_mkVBalBranch3MkVBalBranch281(x0, x1, Neg(Succ(Succ(x2))), x3, x4, x5, x6, Succ(x7), x8, x9, x10, Zero, x11)
new_mkVBalBranch3MkVBalBranch269(x0, x1, Succ(x2), x3, x4, x5, x6, x7, x8, x9, x10, x11)
new_mkVBalBranch4(x0, Branch(x1, x2, Pos(Zero), x3, x4), Branch(x5, x6, Pos(Succ(x7)), x8, x9), x10)
new_mkVBalBranch3MkVBalBranch247(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11)
new_mkBalBranch6MkBalBranch315(x0, x1, x2, x3, Succ(x4), x5, x6)
new_mkVBalBranch3MkVBalBranch272(x0, x1, Neg(Succ(Zero)), x2, x3, x4, x5, Succ(x6), x7, x8, x9, Zero, x10)
new_mkVBalBranch3(x0, Branch(x1, x2, Neg(Succ(x3)), x4, x5), Branch(x6, x7, x8, x9, x10), x11)
new_addToFM_C3(Branch(EQ, x0, x1, x2, x3), x4, x5)
new_mkVBalBranch3MkVBalBranch158(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11)
new_mkVBalBranch3MkVBalBranch270(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, Succ(x10), Zero, x11)
new_mkVBalBranch3MkVBalBranch159(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, Succ(x11), x12)
new_splitGT4(x0, x1, x2, x3)
new_mkVBalBranch3MkVBalBranch261(x0, x1, Pos(Succ(x2)), x3, x4, x5, x6, x7, x8, x9, x10, Succ(x11), x12)
new_mkVBalBranch3MkVBalBranch137(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, Succ(x11), x12)
new_mkBalBranch6MkBalBranch45(x0, x1, x2, x3, x4, Zero, x5, x6)
new_mkBalBranch6MkBalBranch014(x0, x1, x2, x3, x4, x5, x6, x7, Zero, Zero, x8, x9)
new_mkBalBranch6MkBalBranch111(x0, x1, x2, x3, x4, x5, x6, x7, x8, Zero, x9, x10)
new_mkVBalBranch3(x0, Branch(x1, x2, Neg(Zero), x3, x4), Branch(x5, x6, Neg(Succ(x7)), x8, x9), x10)
new_mkBalBranch6MkBalBranch116(x0, x1, x2, x3, x4, x5, x6, x7, Zero, x8, x9)
new_mkBalBranch6MkBalBranch015(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9)
new_mkBalBranch6MkBalBranch5(x0, x1, x2, x3, Pos(Succ(Succ(Zero))), x4, x5)
new_mkBalBranch6MkBalBranch49(EmptyFM, x0, x1, x2, x3, x4)
new_primMinusNat0(Succ(x0), Zero)
new_mkVBalBranch3MkVBalBranch157(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, Zero, x10)
new_mkBalBranch6MkBalBranch33(x0, Branch(x1, x2, x3, x4, x5), x6, x7, x8, x9)
new_mkVBalBranch3MkVBalBranch266(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10)
new_addToFM_C2(Branch(EQ, x0, x1, x2, x3), x4, x5)
new_mkVBalBranch3MkVBalBranch263(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, Zero, Succ(x10), x11)
new_mkBalBranch6MkBalBranch51(x0, x1, x2, x3, x4, x5)
new_mkVBalBranch3MkVBalBranch287(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10)
new_mkBalBranch6MkBalBranch013(x0, x1, x2, x3, x4, x5, x6, x7, x8, Zero, x9, x10)
new_mkBalBranch6MkBalBranch312(x0, x1, x2, x3, x4, x5, x6, x7)
new_mkVBalBranch3MkVBalBranch267(x0, x1, Pos(Zero), x2, x3, x4, x5, x6, x7, x8, x9, Succ(x10), x11)
new_addToFM2(x0, x1, x2)
new_mkVBalBranch3MkVBalBranch155(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, Zero, x10)
new_splitLT11(x0, x1, x2, x3)
new_mkVBalBranch3MkVBalBranch272(x0, x1, Neg(Succ(Succ(Zero))), x2, x3, x4, x5, Zero, x6, x7, x8, Succ(Succ(x9)), x10)
new_mkVBalBranch3MkVBalBranch281(x0, x1, Neg(Succ(Zero)), x2, x3, x4, x5, Succ(x6), x7, x8, x9, Zero, x10)
new_splitLT6(x0)
new_mkVBalBranch3MkVBalBranch161(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, Zero, x10)
new_mkVBalBranch3MkVBalBranch134(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, Succ(x11), Zero, x12)
new_mkBalBranch6MkBalBranch39(x0, x1, x2, x3, Zero, Zero, x4, x5)
new_splitLT24(x0, x1, x2, x3, x4)
new_mkVBalBranch3MkVBalBranch288(x0, x1, Pos(Zero), x2, x3, x4, x5, x6, x7, x8, x9, Zero, x10)
new_mkBalBranch6MkBalBranch310(x0, x1, x2, x3, Pos(Zero), Neg(x4), x5, x6)
new_mkBalBranch6MkBalBranch310(x0, x1, x2, x3, Neg(Zero), Pos(x4), x5, x6)
new_mkVBalBranch3MkVBalBranch285(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10)
new_mkVBalBranch2(x0, Branch(x1, x2, x3, x4, x5), EmptyFM, x6)
new_mkVBalBranch3MkVBalBranch272(x0, x1, Neg(Succ(Succ(Zero))), x2, x3, x4, x5, Zero, x6, x7, x8, Succ(Zero), x9)
new_mkVBalBranch3MkVBalBranch141(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, Succ(x11), x12)
new_splitLT15(Branch(GT, x0, x1, x2, x3), x4)
new_mkVBalBranch3MkVBalBranch265(x0, x1, Zero, x2, x3, x4, x5, x6, x7, x8, x9, x10)
new_mkVBalBranch3MkVBalBranch267(x0, x1, Pos(Succ(x2)), x3, x4, x5, x6, x7, x8, x9, x10, Zero, x11)
new_mkBalBranch6MkBalBranch017(x0, x1, x2, x3, x4, x5, x6, x7, Pos(Succ(x8)), Pos(x9), x10, x11)
new_mkBalBranch6MkBalBranch412(x0, x1, x2, x3, Zero, Zero, x4, x5)
new_mkVBalBranch3MkVBalBranch288(x0, x1, Pos(Succ(Succ(x2))), x3, x4, x5, x6, Succ(x7), x8, x9, x10, Zero, x11)
new_splitGT41(x0)
new_mkBalBranch6MkBalBranch110(x0, x1, x2, x3, x4, x5, x6, x7, Succ(x8), x9, x10)
new_mkBalBranch6MkBalBranch416(x0, x1, x2, x3, Zero, x4, x5)
new_splitGT15(Branch(GT, x0, x1, x2, x3), x4)
new_mkVBalBranch3MkVBalBranch277(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, Zero, Succ(x10), x11)
new_mkBalBranch6MkBalBranch017(x0, x1, x2, x3, x4, x5, x6, x7, Pos(Zero), Pos(x8), x9, x10)
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_mkBalBranch6MkBalBranch310(x0, x1, x2, x3, Neg(Succ(x4)), Pos(x5), x6, x7)
new_mkBalBranch6MkBalBranch310(x0, x1, x2, x3, Pos(Succ(x4)), Neg(x5), x6, x7)
new_mkVBalBranch2(x0, Branch(x1, x2, Pos(Zero), x3, x4), Branch(x5, x6, Neg(Zero), x7, x8), x9)
new_mkVBalBranch2(x0, Branch(x1, x2, Neg(Zero), x3, x4), Branch(x5, x6, Pos(Zero), x7, x8), x9)
new_mkVBalBranch3MkVBalBranch289(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, Succ(x11), Succ(x12), x13)
new_mkBalBranch6MkBalBranch310(x0, x1, x2, x3, Neg(Succ(x4)), Neg(x5), x6, x7)
new_mkVBalBranch3MkVBalBranch139(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, Succ(x11), x12)
new_splitGT26(x0, x1, x2, x3, x4)
new_mkBalBranch6MkBalBranch1113(x0, x1, x2, x3, x4, x5, x6, x7, Succ(x8), Zero, x9, x10)
new_primPlusNat2(Zero, Zero)
new_mkVBalBranch3MkVBalBranch143(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, Zero, x10)
new_mkVBalBranch3MkVBalBranch277(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, Succ(x10), Zero, x11)
new_splitGT14(Branch(EQ, x0, x1, x2, x3), x4)
new_splitLT10(x0, x1, x2, x3)
new_mkVBalBranch4(x0, Branch(x1, x2, Pos(Succ(x3)), x4, x5), Branch(x6, x7, x8, x9, x10), x11)
new_addToFM_C2(EmptyFM, x0, x1)
new_mkVBalBranch3MkVBalBranch156(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, Zero, x11)
new_mkVBalBranch3MkVBalBranch262(x0, x1, Pos(Succ(x2)), x3, x4, x5, x6, x7, x8, x9, x10, Zero, x11)
new_splitLT12(EmptyFM, x0)
new_mkVBalBranch3MkVBalBranch271(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10)
new_mkVBalBranch4(x0, Branch(x1, x2, x3, x4, x5), EmptyFM, x6)
new_intersectFM_C2Gts1(x0, x1, x2, x3, x4)
new_mkVBalBranch3MkVBalBranch155(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, Succ(x10), x11)
new_mkVBalBranch3MkVBalBranch272(x0, x1, Neg(Succ(Succ(Succ(x2)))), x3, x4, x5, x6, Succ(x7), x8, x9, x10, Succ(Zero), x11)
new_mkBalBranch6MkBalBranch41(x0, x1, x2, x3, x4, x5)
new_mkVBalBranch4(x0, Branch(x1, x2, Neg(Zero), x3, x4), Branch(x5, x6, Neg(Zero), x7, x8), x9)
new_mkVBalBranch3(x0, Branch(x1, x2, Pos(Zero), x3, x4), Branch(x5, x6, Pos(Zero), x7, x8), x9)
new_mkVBalBranch3MkVBalBranch156(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, Succ(x11), x12)
new_mkBalBranch6MkBalBranch018(x0, x1, x2, x3, x4, x5, x6, x7, Succ(x8), x9, x10, x11)
new_mkBalBranch6MkBalBranch1111(x0, x1, x2, x3, x4, x5, x6, x7, Zero, x8, x9, x10)
new_mkVBalBranch3MkVBalBranch270(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, Zero, Succ(x10), x11)
new_primPlusNat2(Zero, Succ(x0))
new_mkBalBranch6MkBalBranch113(x0, x1, x2, x3, x4, x5, x6, x7, Neg(Succ(x8)), Neg(x9), x10, x11)
new_mkVBalBranch3MkVBalBranch272(x0, x1, Neg(Succ(Zero)), x2, x3, x4, x5, Zero, x6, x7, x8, Zero, x9)
new_mkVBalBranch3MkVBalBranch261(x0, x1, Neg(x2), x3, x4, x5, x6, x7, x8, x9, x10, Succ(x11), x12)
new_addToFM1(x0, x1, x2)
new_mkVBalBranch3MkVBalBranch284(x0, x1, Zero, x2, x3, x4, x5, x6, x7, x8, x9, x10)
new_mkVBalBranch3MkVBalBranch136(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11)
new_splitLT15(EmptyFM, x0)
new_mkBalBranch6MkBalBranch013(x0, x1, x2, x3, x4, x5, x6, x7, x8, Succ(x9), x10, x11)
new_mkVBalBranch3MkVBalBranch166(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11)
new_mkVBalBranch3MkVBalBranch144(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, Zero, Zero, x11)
new_splitLT41(x0)
new_mkBalBranch6MkBalBranch5(x0, x1, x2, x3, Neg(Succ(x4)), x5, x6)
new_splitLT14(Branch(GT, x0, x1, x2, x3), x4)
new_mkBalBranch6MkBalBranch010(x0, x1, x2, x3, x4, x5, x6, x7, Zero, x8, x9)
new_primPlusNat3(x0, Zero)
new_mkVBalBranch3MkVBalBranch255(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, Zero, Succ(x11), x12)
new_mkVBalBranch3MkVBalBranch272(x0, x1, Pos(x2), x3, x4, x5, x6, x7, x8, x9, x10, Zero, x11)
new_splitGT25(x0, x1, x2, x3, x4)
new_mkBalBranch6MkBalBranch35(x0, x1, x2, x3, Succ(x4), x5, x6)
new_splitLT12(Branch(LT, x0, x1, x2, x3), x4)
new_intersectFM_C2Gts0(x0, x1, x2, x3, x4)
new_primMulNat(Zero)
new_primPlusNat1(Succ(x0))
new_mkVBalBranch3MkVBalBranch273(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10)
new_mkVBalBranch3MkVBalBranch152(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, Zero, Zero, x11)
new_splitGT15(Branch(EQ, x0, x1, x2, x3), x4)
new_mkVBalBranch3MkVBalBranch262(x0, x1, Pos(x2), x3, x4, x5, x6, x7, x8, x9, x10, Succ(x11), x12)
new_mkBalBranch6MkBalBranch017(x0, x1, x2, x3, x4, x5, x6, x7, Neg(Zero), Pos(x8), x9, x10)
new_primPlusInt2(Pos(x0), x1, x2, x3, x4, x5, x6)
new_mkBalBranch6MkBalBranch017(x0, x1, x2, x3, x4, x5, x6, x7, Pos(Zero), Neg(x8), x9, x10)
new_mkVBalBranch3MkVBalBranch275(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, Succ(x11), Zero, x12)
new_mkVBalBranch3MkVBalBranch255(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, Zero, Zero, x11)
new_addToFM_C2(Branch(GT, x0, x1, x2, x3), x4, x5)
new_mkVBalBranch3MkVBalBranch149(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, Zero, Zero, x11)
new_mkVBalBranch3MkVBalBranch245(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10)
new_mkBalBranch6MkBalBranch39(x0, x1, x2, x3, Zero, Succ(x4), x5, x6)
new_mkVBalBranch3MkVBalBranch289(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, Zero, Zero, x11)
new_mkVBalBranch3MkVBalBranch276(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11)
new_mkVBalBranch3MkVBalBranch275(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, Zero, Zero, x11)
new_mkVBalBranch3MkVBalBranch277(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, Succ(x10), Succ(x11), x12)
new_splitLT7(x0, x1, x2, x3, x4)
new_mkVBalBranch3MkVBalBranch261(x0, x1, Neg(Zero), x2, x3, x4, x5, x6, x7, x8, x9, Zero, x10)
new_splitGT12(Branch(EQ, x0, x1, x2, x3), x4)
new_intersectFM_C2Gts(x0, x1, x2, x3, x4)
new_mkVBalBranch3MkVBalBranch289(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, Zero, Succ(x11), x12)
new_mkVBalBranch3MkVBalBranch281(x0, x1, Neg(Succ(Zero)), x2, x3, x4, x5, x6, x7, x8, x9, Succ(x10), x11)
new_mkBalBranch6MkBalBranch413(x0, x1, x2, x3, Zero, x4, x5)
new_addToFM_C4(Branch(GT, x0, x1, x2, x3), x4, x5)
new_mkBalBranch6MkBalBranch413(x0, x1, x2, x3, Succ(x4), x5, x6)
new_mkVBalBranch3MkVBalBranch281(x0, x1, Neg(Succ(Succ(Succ(x2)))), x3, x4, x5, x6, Succ(x7), x8, x9, x10, Succ(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_mkBalBranch6MkBalBranch34(x0, x1, x2, x3, x4, x5, x6, x7)
new_mkVBalBranch3MkVBalBranch265(x0, x1, Succ(x2), x3, x4, x5, x6, x7, x8, x9, x10, x11)
new_intersectFM_C2Lts3(x0, x1)
new_mkBalBranch6MkBalBranch314(x0, x1, x2, x3, Zero, x4, x5)
new_mkVBalBranch3MkVBalBranch145(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, Succ(x10), x11)
new_splitLT9(x0, x1, x2, x3, x4)
new_mkBalBranch6Size_r(x0, x1, x2, x3, x4, x5)
new_mkBalBranch6MkBalBranch43(x0, x1, x2, x3, x4, x5)
new_mkVBalBranch3MkVBalBranch283(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11)
new_splitGT29(x0, x1, x2, x3, x4)
new_mkBalBranch6MkBalBranch30(x0, x1, x2, x3, Zero, x4, x5)
new_mkVBalBranch3MkVBalBranch146(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, Zero, x10)
new_sizeFM(EmptyFM, x0, x1)
new_mkVBalBranch3MkVBalBranch281(x0, x1, Neg(Succ(Zero)), x2, x3, x4, x5, Zero, x6, x7, x8, Zero, x9)
new_mkVBalBranch3MkVBalBranch281(x0, x1, Neg(Succ(Succ(Succ(x2)))), x3, x4, x5, x6, Zero, x7, x8, x9, Succ(Succ(x10)), x11)
new_mkVBalBranch3MkVBalBranch152(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, Succ(x11), Zero, x12)
new_mkVBalBranch3MkVBalBranch288(x0, x1, Pos(Succ(Succ(x2))), x3, x4, x5, x6, Zero, x7, x8, x9, Succ(Zero), x10)
new_mkVBalBranch3MkVBalBranch249(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10)
new_mkVBalBranch3MkVBalBranch135(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11)
new_mkVBalBranch3MkVBalBranch254(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10)
new_splitLT28(x0, x1, x2, x3, x4)
new_mkBalBranch6MkBalBranch47(x0, x1, x2, x3, Succ(x4), x5, x6, x7)
new_mkBalBranch6MkBalBranch014(x0, x1, x2, x3, x4, x5, x6, x7, Succ(x8), Succ(x9), x10, x11)
new_mkVBalBranch2(x0, Branch(x1, x2, Pos(Zero), x3, x4), Branch(x5, x6, Neg(Succ(x7)), x8, x9), x10)
new_mkVBalBranch2(x0, Branch(x1, x2, Neg(Zero), x3, x4), Branch(x5, x6, Pos(Succ(x7)), x8, x9), x10)
new_addToFM_C4(EmptyFM, x0, x1)
new_mkBalBranch6MkBalBranch313(x0, x1, x2, x3, x4, x5)
new_mkVBalBranch3MkVBalBranch267(x0, x1, Pos(Zero), x2, x3, x4, x5, x6, x7, x8, x9, Zero, x10)
new_mkVBalBranch3MkVBalBranch248(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11)
new_splitGT14(EmptyFM, x0)
new_mkVBalBranch3MkVBalBranch132(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, Succ(x11), Zero, x12)
new_mkVBalBranch3MkVBalBranch144(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, Succ(x11), Succ(x12), x13)
new_mkVBalBranch3MkVBalBranch261(x0, x1, Neg(Succ(x2)), x3, x4, x5, x6, x7, x8, x9, x10, Zero, x11)
new_mkBalBranch6MkBalBranch410(x0, x1, x2, x3, x4, x5, x6)
new_mkVBalBranch2(x0, Branch(x1, x2, Pos(Succ(x3)), x4, x5), Branch(x6, x7, x8, x9, x10), x11)
new_mkBalBranch6MkBalBranch019(x0, x1, x2, x3, x4, x5, x6, x7, Zero, x8, x9)
new_mkVBalBranch3MkVBalBranch280(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, Zero, Succ(x11), x12)
new_mkBalBranch6MkBalBranch014(x0, x1, x2, x3, x4, x5, x6, x7, Succ(x8), Zero, x9, x10)
new_mkVBalBranch3MkVBalBranch272(x0, x1, Neg(Succ(Succ(Zero))), x2, x3, x4, x5, Succ(x6), x7, x8, x9, Succ(Succ(x10)), x11)
new_mkVBalBranch3MkVBalBranch134(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, Zero, Zero, x11)
new_mkVBalBranch3(x0, Branch(x1, x2, Neg(Zero), x3, x4), Branch(x5, x6, Neg(Zero), x7, x8), x9)
new_mkVBalBranch3MkVBalBranch280(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, Succ(x11), Succ(x12), x13)
new_primPlusNat2(Succ(x0), Succ(x1))
new_splitGT12(Branch(GT, x0, x1, x2, x3), x4)
new_mkVBalBranch3MkVBalBranch145(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, Zero, x10)
new_mkVBalBranch3MkVBalBranch272(x0, x1, Neg(Succ(Zero)), x2, x3, x4, x5, x6, x7, x8, x9, Succ(x10), x11)
new_mkVBalBranch3MkVBalBranch288(x0, x1, Pos(Succ(Succ(x2))), x3, x4, x5, x6, Succ(x7), x8, x9, x10, Succ(Succ(x11)), x12)
new_mkVBalBranch3MkVBalBranch262(x0, x1, Neg(Zero), x2, x3, x4, x5, x6, x7, x8, x9, Succ(x10), x11)
new_mkBalBranch6MkBalBranch414(x0, x1, x2, x3, Zero, x4, x5)
new_mkVBalBranch4(x0, Branch(x1, x2, Neg(Zero), x3, x4), Branch(x5, x6, Pos(Zero), x7, x8), x9)
new_mkVBalBranch4(x0, Branch(x1, x2, Pos(Zero), x3, x4), Branch(x5, x6, Neg(Zero), x7, x8), x9)
new_splitGT12(Branch(LT, x0, x1, x2, x3), x4)
new_mkVBalBranch3MkVBalBranch270(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, Zero, Zero, x10)
new_mkVBalBranch3MkVBalBranch288(x0, x1, Pos(Succ(Succ(x2))), x3, x4, x5, x6, Succ(x7), x8, x9, x10, Succ(Zero), x11)
new_splitLT12(Branch(GT, x0, x1, x2, x3), x4)
new_mkVBalBranch3MkVBalBranch282(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11)
new_mkVBalBranch3MkVBalBranch272(x0, x1, Neg(Succ(Succ(Zero))), x2, x3, x4, x5, Succ(x6), x7, x8, x9, Succ(Zero), x10)
new_mkBalBranch6MkBalBranch315(x0, x1, x2, x3, Zero, x4, x5)
new_primPlusInt(Neg(x0), x1, x2, x3, x4, x5)
new_mkVBalBranch3MkVBalBranch272(x0, x1, Pos(x2), x3, x4, x5, x6, x7, x8, x9, x10, Succ(x11), x12)
new_mkVBalBranch3MkVBalBranch149(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, Zero, Succ(x11), x12)
new_mkBalBranch6MkBalBranch019(x0, x1, x2, x3, x4, x5, x6, x7, Succ(x8), x9, x10)
new_mkVBalBranch3MkVBalBranch252(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, Succ(x11), Zero, x12)
new_mkVBalBranch3MkVBalBranch153(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, Zero, x11)
new_mkBalBranch6MkBalBranch32(x0, x1, x2, x3, x4, x5)
new_mkVBalBranch3MkVBalBranch280(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, Zero, Zero, x11)
new_splitGT3(x0, x1, x2, x3, x4)
new_splitLT25(x0, x1, x2, x3, x4)
new_mkBalBranch6MkBalBranch111(x0, x1, x2, x3, x4, x5, x6, x7, x8, Succ(x9), x10, x11)
new_mkVBalBranch3MkVBalBranch164(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, Zero, x10)
new_mkBalBranch6MkBalBranch117(x0, x1, x2, x3, x4, x5, x6, x7, Succ(x8), x9, x10)
new_mkVBalBranch3MkVBalBranch132(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, Zero, Succ(x11), x12)
new_splitGT210(x0, x1, x2, x3, x4)
new_mkBalBranch6MkBalBranch30(x0, x1, x2, x3, Succ(x4), x5, x6)
new_mkVBalBranch3MkVBalBranch165(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11)
new_mkBalBranch6MkBalBranch31(x0, x1, x2, x3, x4, x5)
new_mkVBalBranch3MkVBalBranch133(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, Zero, x10)
new_mkVBalBranch3MkVBalBranch167(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, Succ(x11), x12)
new_mkVBalBranch3MkVBalBranch144(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, Zero, Succ(x11), x12)
new_splitGT8(x0, x1, x2, x3)
new_splitGT9(x0, x1, x2, x3, x4)
new_mkVBalBranch3MkVBalBranch256(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11)
new_intersectFM_C2Gts2(x0, x1, x2, x3, x4)
new_mkVBalBranch3MkVBalBranch260(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10)
new_splitLT42(x0)
new_splitGT15(Branch(LT, x0, x1, x2, x3), x4)
new_splitLT14(EmptyFM, x0)
new_splitLT14(Branch(LT, x0, x1, x2, x3), x4)
new_addToFM_C4(Branch(EQ, x0, x1, x2, x3), x4, x5)
new_mkBalBranch6MkBalBranch1113(x0, x1, x2, x3, x4, x5, x6, x7, Succ(x8), Succ(x9), x10, x11)
new_mkBalBranch6MkBalBranch415(x0, x1, x2, x3, x4, x5, x6, x7)
new_mkBalBranch6MkBalBranch0110(x0, x1, x2, x3, x4, x5, x6, x7, Zero, x8, x9)
new_mkVBalBranch3MkVBalBranch151(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11)
new_mkVBalBranch3MkVBalBranch262(x0, x1, Pos(Zero), x2, x3, x4, x5, x6, x7, x8, x9, Zero, x10)
new_mkVBalBranch3(x0, Branch(x1, x2, Pos(Zero), x3, x4), Branch(x5, x6, Neg(Zero), x7, x8), x9)
new_mkVBalBranch3(x0, Branch(x1, x2, Neg(Zero), x3, x4), Branch(x5, x6, Pos(Zero), x7, x8), x9)
new_mkVBalBranch2(x0, Branch(x1, x2, Neg(Zero), x3, x4), Branch(x5, x6, Neg(Zero), x7, x8), x9)
new_mkVBalBranch3(x0, Branch(x1, x2, x3, x4, x5), EmptyFM, x6)
new_mkVBalBranch3MkVBalBranch263(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, Zero, Zero, x10)
new_mkVBalBranch3(x0, Branch(x1, x2, Pos(Zero), x3, x4), Branch(x5, x6, Pos(Succ(x7)), x8, x9), x10)
new_mkBalBranch6MkBalBranch310(x0, x1, x2, x3, Neg(Zero), Neg(x4), x5, x6)
new_mkVBalBranch3MkVBalBranch147(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, Succ(x11), x12)
new_mkBalBranch6MkBalBranch42(x0, x1, x2, x3, x4, x5, x6, x7)
new_mkBalBranch6MkBalBranch310(x0, x1, x2, x3, Pos(Succ(x4)), Pos(x5), x6, x7)
new_mkVBalBranch3MkVBalBranch275(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, Succ(x11), Succ(x12), x13)
new_splitGT24(x0, x1, x2, x3, x4)
new_mkVBalBranch3MkVBalBranch153(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, Succ(x11), x12)
new_mkVBalBranch3MkVBalBranch288(x0, x1, Pos(Succ(Zero)), x2, x3, x4, x5, Zero, x6, x7, x8, Zero, x9)
new_mkVBalBranch4(x0, Branch(x1, x2, Pos(Zero), x3, x4), Branch(x5, x6, Pos(Zero), x7, x8), x9)
new_mkBalBranch6MkBalBranch1110(x0, x1, x2, x3, x4, x5, x6, x7, Succ(x8), x9, x10)
new_splitGT28(x0, x1, x2, x3, x4)
new_mkBalBranch6MkBalBranch48(x0, x1, x2, x3, Succ(x4), x5, x6)
new_mkVBalBranch3MkVBalBranch275(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, Zero, Succ(x11), x12)
new_mkVBalBranch3MkVBalBranch284(x0, x1, Succ(x2), x3, x4, x5, x6, x7, x8, x9, x10, x11)
new_mkVBalBranch3MkVBalBranch267(x0, x1, Neg(x2), x3, x4, x5, x6, x7, x8, x9, x10, Zero, x11)
new_mkBalBranch6MkBalBranch016(x0, x1, x2, EmptyFM, x3, x4, x5, x6, x7, x8)
new_intersectFM_C2Lts1(x0, x1, x2, x3, x4)
new_mkBalBranch6MkBalBranch416(x0, x1, x2, x3, Succ(x4), x5, x6)
new_mkVBalBranch3MkVBalBranch252(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, Succ(x11), Succ(x12), x13)
new_mkVBalBranch3MkVBalBranch149(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, Succ(x11), Zero, x12)
new_mkVBalBranch3MkVBalBranch146(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, Succ(x10), x11)
new_mkVBalBranch3MkVBalBranch148(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11)
new_mkBalBranch6MkBalBranch113(x0, x1, x2, x3, x4, x5, x6, x7, Pos(Zero), Pos(x8), x9, x10)
new_mkBalBranch6MkBalBranch411(x0, x1, x2, x3, Pos(Zero), Neg(x4), x5, x6)
new_mkBalBranch6MkBalBranch411(x0, x1, x2, x3, Neg(Zero), Pos(x4), x5, x6)
new_mkVBalBranch4(x0, EmptyFM, x1, x2)
new_splitGT13(x0)
new_mkBalBranch6MkBalBranch1115(x0, x1, x2, x3, x4, EmptyFM, x5, x6, x7, x8)
new_splitLT27(x0, x1, x2, x3, x4)
new_mkBalBranch6MkBalBranch5(x0, x1, x2, x3, Pos(Succ(Zero)), x4, x5)
new_primMinusNat0(Zero, Succ(x0))
new_mkBalBranch6MkBalBranch5(x0, x1, x2, x3, Pos(Zero), x4, x5)
new_splitGT12(EmptyFM, x0)
new_mkVBalBranch3MkVBalBranch288(x0, x1, Pos(Succ(Zero)), x2, x3, x4, x5, Succ(x6), x7, x8, x9, Zero, x10)
new_mkBalBranch6MkBalBranch39(x0, x1, x2, x3, Succ(x4), Zero, x5, x6)
new_mkVBalBranch3MkVBalBranch274(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10)
new_mkVBalBranch3MkVBalBranch288(x0, x1, Pos(Succ(Succ(x2))), x3, x4, x5, x6, Zero, x7, x8, x9, Zero, x10)
new_mkBalBranch6MkBalBranch310(x0, x1, x2, x3, Pos(Zero), Pos(x4), x5, x6)
new_mkBalBranch6MkBalBranch411(x0, x1, x2, x3, Neg(Succ(x4)), Neg(x5), x6, x7)
new_mkVBalBranch3MkVBalBranch272(x0, x1, Neg(Succ(Succ(Succ(x2)))), x3, x4, x5, x6, Zero, x7, x8, x9, Succ(Zero), x10)
new_primPlusNat1(Zero)
new_mkVBalBranch3MkVBalBranch263(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, Succ(x10), Zero, x11)
new_mkVBalBranch2(x0, Branch(x1, x2, Pos(Zero), x3, x4), Branch(x5, x6, Pos(Succ(x7)), x8, x9), x10)
new_mkBalBranch6MkBalBranch50(x0, x1, x2, x3, x4, x5)
new_mkBalBranch(x0, x1, x2, x3, x4, x5)
new_mkVBalBranch3MkVBalBranch132(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, Zero, Zero, x11)
new_mkBalBranch6MkBalBranch5(x0, x1, x2, x3, Neg(Zero), x4, x5)
new_mkVBalBranch3MkVBalBranch272(x0, x1, Neg(Zero), x2, x3, x4, x5, x6, x7, x8, x9, Zero, x10)
new_sizeFM(Branch(x0, x1, x2, x3, x4), x5, x6)
new_mkVBalBranch3MkVBalBranch288(x0, x1, Pos(Succ(Zero)), x2, x3, x4, x5, x6, x7, x8, x9, Succ(x10), x11)
new_mkVBalBranch3MkVBalBranch252(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, Zero, Succ(x11), x12)
new_splitLT13(x0)
new_splitGT7(x0, x1, x2, x3, x4)
new_primPlusInt1(x0, Neg(x1))
new_mkBalBranch6MkBalBranch110(x0, x1, x2, x3, x4, x5, x6, x7, Zero, x8, x9)
new_mkBalBranch6MkBalBranch45(x0, x1, x2, x3, x4, Succ(x5), x6, x7)
new_splitLT14(Branch(EQ, x0, x1, x2, x3), x4)
new_mkVBalBranch3MkVBalBranch154(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, Zero, x10)
new_mkVBalBranch3MkVBalBranch264(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10)
new_mkBalBranch6MkBalBranch411(x0, x1, x2, x3, Neg(Zero), Neg(x4), x5, x6)
new_mkBalBranch6MkBalBranch40(x0, x1, x2, x3, x4, x5)
new_mkVBalBranch3MkVBalBranch251(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11)
new_addToFM_C3(Branch(GT, x0, x1, x2, x3), x4, x5)
new_mkBalBranch6MkBalBranch017(x0, x1, x2, x3, x4, x5, x6, x7, Neg(Zero), Neg(x8), x9, x10)
new_mkBalBranch6MkBalBranch112(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9)
new_mkVBalBranch3MkVBalBranch281(x0, x1, Neg(Succ(Succ(Zero))), x2, x3, x4, x5, Succ(x6), x7, x8, x9, Succ(Succ(x10)), x11)
new_mkBalBranch6MkBalBranch411(x0, x1, x2, x3, Neg(Succ(x4)), Pos(x5), x6, x7)
new_mkBalBranch6MkBalBranch411(x0, x1, x2, x3, Pos(Succ(x4)), Neg(x5), x6, x7)
new_mkBalBranch6MkBalBranch012(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9)
new_mkVBalBranch3MkVBalBranch250(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10)
new_mkVBalBranch3MkVBalBranch255(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, Succ(x11), Succ(x12), x13)
new_addToFM0(x0, x1, x2)
new_mkVBalBranch3MkVBalBranch259(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10)
new_mkVBalBranch3MkVBalBranch279(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10)
new_mkVBalBranch3MkVBalBranch281(x0, x1, Neg(Succ(Succ(Succ(x2)))), x3, x4, x5, x6, Zero, x7, x8, x9, Succ(Zero), x10)
new_mkBalBranch6MkBalBranch36(x0, x1, x2, x3, Succ(x4), x5, x6, x7)
new_splitLT23(x0, x1, x2, x3, x4)
new_mkBalBranch6MkBalBranch1111(x0, x1, x2, x3, x4, x5, x6, x7, Succ(x8), x9, x10, x11)
new_mkBalBranch6MkBalBranch0111(x0, x1, x2, x3, x4, x5, x6, x7, Zero, x8, x9)
new_addToFM_C3(EmptyFM, x0, x1)
new_splitGT15(EmptyFM, x0)
new_mkBalBranch6MkBalBranch011(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9)
new_mkVBalBranch3MkVBalBranch143(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, Succ(x10), x11)
new_mkVBalBranch3MkVBalBranch162(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, Zero, Zero, x11)
new_mkVBalBranch3MkVBalBranch134(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, Zero, Succ(x11), x12)
new_mkVBalBranch3MkVBalBranch246(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, Zero, Zero, x11)
new_mkVBalBranch3MkVBalBranch162(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, Succ(x11), Zero, x12)
new_mkVBalBranch3MkVBalBranch289(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, Succ(x11), Zero, x12)
new_mkVBalBranch3MkVBalBranch133(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, Succ(x10), x11)
new_mkVBalBranch3MkVBalBranch141(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, Zero, x11)
new_mkVBalBranch3MkVBalBranch272(x0, x1, Neg(Zero), x2, x3, x4, x5, x6, x7, x8, x9, Succ(x10), x11)
new_primPlusNat2(Succ(x0), Zero)
new_mkBalBranch6MkBalBranch119(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11)
new_mkBalBranch6MkBalBranch38(x0, x1, x2, x3, x4, Succ(x5), x6, x7)
new_mkBalBranch6MkBalBranch33(x0, EmptyFM, x1, x2, x3, x4)
new_mkBalBranch6MkBalBranch46(x0, x1, x2, x3, x4, x5, x6, x7)
new_mkVBalBranch3MkVBalBranch267(x0, x1, Pos(Succ(x2)), x3, x4, x5, x6, x7, x8, x9, x10, Succ(x11), x12)
new_mkVBalBranch3MkVBalBranch152(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, Zero, Succ(x11), x12)
new_mkVBalBranch3MkVBalBranch281(x0, x1, Pos(x2), x3, x4, x5, x6, x7, x8, x9, x10, Zero, x11)
new_mkVBalBranch3MkVBalBranch281(x0, x1, Pos(x2), x3, x4, x5, x6, x7, x8, x9, x10, Succ(x11), x12)
new_mkVBalBranch3MkVBalBranch272(x0, x1, Neg(Succ(Succ(Succ(x2)))), x3, x4, x5, x6, Succ(x7), x8, x9, x10, Succ(Succ(x11)), x12)
new_mkVBalBranch3MkVBalBranch288(x0, x1, Neg(x2), x3, x4, x5, x6, x7, x8, x9, x10, Succ(x11), x12)
new_splitLT40(x0)
new_mkBalBranch6MkBalBranch44(x0, x1, x2, x3, x4, x5, x6, x7)
new_mkVBalBranch3MkVBalBranch138(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11)
new_mkBalBranch6MkBalBranch414(x0, x1, x2, x3, Succ(x4), x5, x6)
new_mkBalBranch6MkBalBranch115(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11)
new_mkVBalBranch3MkVBalBranch253(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11)
new_mkVBalBranch2(x0, Branch(x1, x2, Neg(Zero), x3, x4), Branch(x5, x6, Neg(Succ(x7)), x8, x9), x10)
new_mkBalBranch6MkBalBranch412(x0, x1, x2, x3, Zero, Succ(x4), x5, x6)
new_mkVBalBranch3MkVBalBranch288(x0, x1, Neg(x2), x3, x4, x5, x6, x7, x8, x9, x10, Zero, x11)
new_mkVBalBranch3(x0, Branch(x1, x2, Neg(Zero), x3, x4), Branch(x5, x6, Pos(Succ(x7)), x8, x9), x10)
new_mkVBalBranch3(x0, Branch(x1, x2, Pos(Zero), x3, x4), Branch(x5, x6, Neg(Succ(x7)), x8, x9), x10)
new_mkVBalBranch3MkVBalBranch272(x0, x1, Neg(Succ(Succ(x2))), x3, x4, x5, x6, Succ(x7), x8, x9, x10, Zero, x11)
new_mkVBalBranch3MkVBalBranch286(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11)
new_splitLT12(Branch(EQ, x0, x1, x2, x3), x4)
new_splitLT15(Branch(EQ, x0, x1, x2, x3), x4)
new_mkVBalBranch3MkVBalBranch268(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10)
new_mkVBalBranch3MkVBalBranch270(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, Succ(x10), Succ(x11), x12)
new_mkBalBranch6MkBalBranch314(x0, x1, x2, x3, Succ(x4), x5, x6)
new_mkBalBranch6MkBalBranch49(Branch(x0, x1, x2, x3, x4), x5, x6, x7, x8, x9)
new_mkVBalBranch3MkVBalBranch281(x0, x1, Neg(Succ(Succ(Zero))), x2, x3, x4, x5, Zero, x6, x7, x8, Succ(Zero), x9)
new_mkVBalBranch3MkVBalBranch144(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, Succ(x11), Zero, x12)
new_mkBalBranch6MkBalBranch1113(x0, x1, x2, x3, x4, x5, x6, x7, Zero, Zero, x8, x9)
new_primPlusInt1(x0, Pos(x1))
new_mkBalBranch6MkBalBranch48(x0, x1, x2, x3, Zero, x4, x5)
new_mkVBalBranch3MkVBalBranch149(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, Succ(x11), Succ(x12), x13)
new_mkBalBranch6MkBalBranch412(x0, x1, x2, x3, Succ(x4), Zero, x5, x6)
new_mkBalBranch6MkBalBranch412(x0, x1, x2, x3, Succ(x4), Succ(x5), x6, x7)
new_splitLT15(Branch(LT, x0, x1, x2, x3), x4)
new_mkVBalBranch3MkVBalBranch272(x0, x1, Neg(Succ(Succ(Succ(x2)))), x3, x4, x5, x6, Zero, x7, x8, x9, Succ(Succ(x10)), x11)
new_mkVBalBranch3MkVBalBranch167(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, Zero, x11)
new_mkVBalBranch3MkVBalBranch267(x0, x1, Neg(x2), x3, x4, x5, x6, x7, x8, x9, x10, Succ(x11), x12)
new_mkVBalBranch3MkVBalBranch137(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, Zero, x11)
new_mkBalBranch6MkBalBranch1115(x0, x1, x2, x3, x4, Branch(x5, x6, x7, x8, x9), x10, x11, x12, x13)
new_mkVBalBranch3MkVBalBranch140(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11)
new_mkVBalBranch3MkVBalBranch257(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11)
new_splitGT14(Branch(LT, x0, x1, x2, x3), x4)
new_mkBalBranch6MkBalBranch014(x0, x1, x2, x3, x4, x5, x6, x7, Zero, Succ(x8), x9, x10)
new_mkVBalBranch3MkVBalBranch246(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, Succ(x11), Zero, x12)
new_intersectFM_C2Lts(x0, x1, x2, x3, x4)
new_mkVBalBranch3(x0, Branch(x1, x2, Pos(Succ(x3)), x4, x5), Branch(x6, x7, x8, x9, x10), x11)
new_splitGT14(Branch(GT, x0, x1, x2, x3), x4)
new_mkVBalBranch3MkVBalBranch261(x0, x1, Pos(Zero), x2, x3, x4, x5, x6, x7, x8, x9, Succ(x10), x11)
new_mkVBalBranch3MkVBalBranch131(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, Zero, x11)
new_mkVBalBranch3MkVBalBranch246(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, Zero, Succ(x11), x12)
new_mkBalBranch6MkBalBranch1112(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9)
new_mkVBalBranch3MkVBalBranch261(x0, x1, Pos(Succ(x2)), x3, x4, x5, x6, x7, x8, x9, x10, Zero, x11)
new_mkBalBranch6MkBalBranch113(x0, x1, x2, x3, x4, x5, x6, x7, Pos(Succ(x8)), Pos(x9), x10, x11)
new_mkBalBranch6MkBalBranch018(x0, x1, x2, x3, x4, x5, x6, x7, Zero, x8, x9, x10)
new_mkBalBranch6MkBalBranch5(x0, x1, x2, x3, Pos(Succ(Succ(Succ(x4)))), x5, x6)
new_splitGT40(x0)
new_mkVBalBranch3MkVBalBranch255(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, Succ(x11), Zero, x12)
new_mkVBalBranch3MkVBalBranch262(x0, x1, Neg(Zero), x2, x3, x4, x5, x6, x7, x8, x9, Zero, x10)
new_mkVBalBranch3MkVBalBranch290(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10)
new_addToFM(x0, x1, x2)
new_mkVBalBranch4(x0, Branch(x1, x2, Neg(Zero), x3, x4), Branch(x5, x6, Neg(Succ(x7)), x8, x9), x10)
new_mkVBalBranch3MkVBalBranch288(x0, x1, Pos(Succ(Succ(x2))), x3, x4, x5, x6, Zero, x7, x8, x9, Succ(Succ(x10)), x11)
new_mkVBalBranch3MkVBalBranch164(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, Succ(x10), x11)
new_mkBalBranch6MkBalBranch1114(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9)
new_mkVBalBranch3MkVBalBranch272(x0, x1, Neg(Succ(Succ(x2))), x3, x4, x5, x6, Zero, x7, x8, x9, Zero, x10)
new_mkBalBranch6MkBalBranch113(x0, x1, x2, x3, x4, x5, x6, x7, Neg(Zero), Neg(x8), x9, x10)
new_mkBalBranch6MkBalBranch39(x0, x1, x2, x3, Succ(x4), Succ(x5), x6, x7)
new_mkVBalBranch3MkVBalBranch277(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, Zero, Zero, x10)
new_mkVBalBranch3MkVBalBranch288(x0, x1, Pos(Zero), x2, x3, x4, x5, x6, x7, x8, x9, Succ(x10), x11)
new_mkVBalBranch4(x0, Branch(x1, x2, Neg(Succ(x3)), x4, x5), Branch(x6, x7, x8, x9, x10), x11)
new_mkVBalBranch3MkVBalBranch132(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, Succ(x11), Succ(x12), x13)
new_mkBalBranch6MkBalBranch016(x0, x1, x2, Branch(x3, x4, x5, x6, x7), x8, x9, x10, x11, x12, x13)
new_mkVBalBranch3MkVBalBranch134(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, Succ(x11), Succ(x12), x13)
new_mkVBalBranch3MkVBalBranch154(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, Succ(x10), x11)
new_mkVBalBranch3MkVBalBranch258(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11)
new_intersectFM_C2Lts2(x0, x1, x2, x3, x4)
new_mkVBalBranch2(x0, Branch(x1, x2, Neg(Succ(x3)), x4, x5), Branch(x6, x7, x8, x9, x10), x11)
new_emptyFM(x0)
new_primPlusInt0(x0, Neg(x1))
new_intersectFM_C2Gts3(x0, x1)
new_mkBalBranch6MkBalBranch411(x0, x1, x2, x3, Pos(Zero), Pos(x4), x5, x6)
new_mkVBalBranch3MkVBalBranch281(x0, x1, Neg(Succ(Succ(Zero))), x2, x3, x4, x5, Succ(x6), x7, x8, x9, Succ(Zero), x10)
new_splitGT6(x0)
new_primPlusNat3(x0, Succ(x1))
new_mkVBalBranch3MkVBalBranch168(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, Succ(x10), x11)
new_mkBalBranch6MkBalBranch118(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11)
new_mkVBalBranch3MkVBalBranch280(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, Succ(x11), Zero, x12)
new_mkVBalBranch3MkVBalBranch142(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11)
new_primMulNat(Succ(x0))
new_mkVBalBranch3MkVBalBranch161(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, Succ(x10), x11)
new_mkVBalBranch2(x0, EmptyFM, x1, x2)
new_mkBalBranch6MkBalBranch37(x0, x1, x2, x3, x4, x5, x6, x7)
new_primPlusInt2(Neg(x0), x1, x2, x3, x4, x5, x6)
new_mkVBalBranch3MkVBalBranch162(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, Succ(x11), Succ(x12), x13)
new_mkVBalBranch3MkVBalBranch139(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, Zero, x11)
new_mkVBalBranch3MkVBalBranch281(x0, x1, Neg(Succ(Succ(Zero))), x2, x3, x4, x5, Zero, x6, x7, x8, Succ(Succ(x9)), x10)
new_mkBalBranch6MkBalBranch117(x0, x1, x2, x3, x4, x5, x6, x7, Zero, x8, x9)
new_splitLT3(x0, x1, x2, x3, x4)
new_addToFM_C4(Branch(LT, x0, x1, x2, x3), x4, x5)
new_mkVBalBranch3MkVBalBranch252(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, Zero, Zero, x11)
new_mkVBalBranch3MkVBalBranch246(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, Succ(x11), Succ(x12), x13)
new_mkVBalBranch3MkVBalBranch262(x0, x1, Neg(Succ(x2)), x3, x4, x5, x6, x7, x8, x9, x10, Zero, x11)
new_mkBranch(x0, x1, x2, x3, x4, x5, x6)
new_mkBalBranch6MkBalBranch0111(x0, x1, x2, x3, x4, x5, x6, x7, Succ(x8), x9, x10)
new_mkBalBranch6MkBalBranch38(x0, x1, x2, x3, x4, Zero, x5, x6)
new_primMulNat2(Zero)
new_mkBalBranch6MkBalBranch010(x0, x1, x2, x3, x4, x5, x6, x7, Succ(x8), x9, x10)
new_mkBalBranch6MkBalBranch36(x0, x1, x2, x3, Zero, x4, x5, x6)
new_mkBalBranch6MkBalBranch017(x0, x1, x2, x3, x4, x5, x6, x7, Neg(Succ(x8)), Neg(x9), x10, x11)
new_addToFM_C3(Branch(LT, x0, x1, x2, x3), x4, x5)
new_splitLT26(x0, x1, x2, x3, x4)
new_mkVBalBranch3MkVBalBranch168(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, Zero, x10)
new_mkBalBranch6MkBalBranch0110(x0, x1, x2, x3, x4, x5, x6, x7, Succ(x8), x9, x10)
new_mkBalBranch6MkBalBranch114(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11)
new_mkVBalBranch3MkVBalBranch150(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11)
new_splitGT42(x0)
new_mkBalBranch6MkBalBranch47(x0, x1, x2, x3, Zero, x4, x5, x6)
new_mkVBalBranch3MkVBalBranch261(x0, x1, Pos(Zero), x2, x3, x4, x5, x6, x7, x8, x9, Zero, x10)
new_mkBalBranch6MkBalBranch017(x0, x1, x2, x3, x4, x5, x6, x7, Neg(Succ(x8)), Pos(x9), x10, x11)
new_mkBalBranch6MkBalBranch017(x0, x1, x2, x3, x4, x5, x6, x7, Pos(Succ(x8)), Neg(x9), x10, x11)
new_mkBalBranch6MkBalBranch1110(x0, x1, x2, x3, x4, x5, x6, x7, Zero, x8, x9)
new_mkVBalBranch3MkVBalBranch131(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, Succ(x11), x12)
new_mkVBalBranch4(x0, Branch(x1, x2, Neg(Zero), x3, x4), Branch(x5, x6, Pos(Succ(x7)), x8, x9), x10)
new_mkVBalBranch4(x0, Branch(x1, x2, Pos(Zero), x3, x4), Branch(x5, x6, Neg(Succ(x7)), x8, x9), x10)
new_mkVBalBranch3MkVBalBranch262(x0, x1, Neg(Succ(x2)), x3, x4, x5, x6, x7, x8, x9, x10, Succ(x11), x12)
new_primPlusInt0(x0, Pos(x1))
new_mkVBalBranch3MkVBalBranch162(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, Zero, Succ(x11), x12)
new_mkVBalBranch3MkVBalBranch147(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, Zero, x11)
new_primMulNat2(Succ(x0))
new_intersectFM_C2Lts0(x0, x1, x2, x3, x4)
new_mkVBalBranch3MkVBalBranch269(x0, x1, Zero, x2, x3, x4, x5, x6, x7, x8, x9, x10)
new_splitGT27(x0, x1, x2, x3, x4)
new_mkVBalBranch3MkVBalBranch152(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, Succ(x11), Succ(x12), x13)
new_mkBalBranch6Size_l(x0, x1, x2, x3, x4, x5)
new_mkBalBranch6MkBalBranch311(x0, x1, x2, x3, x4, x5, x6, x7)
new_splitGT5(x0, x1, x2, x3)
new_mkVBalBranch3MkVBalBranch160(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11)
new_primMinusNat0(Succ(x0), Succ(x1))

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: